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Source: http://authenticinquirymaths.blogspot.com/feeds/posts/default

1. <?xml version='1.0' encoding='UTF-8'?><?xml-stylesheet href="http://www.blogger.com/styles/atom.css" type="text/css"?><feed xmlns='http://www.w3.org/2005/Atom' xmlns:openSearch='http://a9.com/-/spec/opensearchrss/1.0/' xmlns:blogger='http://schemas.google.com/blogger/2008' xmlns:georss='http://www.georss.org/georss' xmlns:gd="http://schemas.google.com/g/2005" xmlns:thr='http://purl.org/syndication/thread/1.0'><id>tag:blogger.com,1999:blog-8256492698354362046</id><updated>2024-04-14T17:25:52.200+10:00</updated><category term="General"/><category term="Inquiry"/><category term="Area"/><category term="Book Reviews"/><category term="Maths in Sport"/><category term="Fractions"/><category term="Measurement"/><category term="Data"/><category term="Assessment"/><category term="Maths in Dance"/><category term="Multiplication"/><category term="Problem Solving Skills"/><category term="2D Shapes"/><category term="Fun"/><category term="Maths in Science"/><category term="Patterns"/><category term="3D Shapes"/><category term="Graphs"/><category term="Probability"/><category term="Laws of Maths"/><category term="Number"/><category term="PYP Exhibition"/><category term="Financial Literacy"/><category term="Mass"/><category term="Time"/><category term="Addition"/><category term="Angles"/><category term="Chance"/><category term="Numberlines"/><category term="Numeration"/><category term="Percentages"/><category term="Perimeter"/><category term="Puzzles"/><category term="Reflection"/><category term="Technology"/><category term="Volume"/><category term="Attitude"/><category term="Length"/><category term="Lines"/><category term="Magic Squares"/><category term="Place Value"/><category term="Square numbers"/><category term="Subtraction"/><title type='text'>Authentic Inquiry Maths</title><subtitle type='html'></subtitle><link rel='http://schemas.google.com/g/2005#feed' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/posts/default'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/'/><link rel='hub' href='http://pubsubhubbub.appspot.com/'/><link rel='next' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default?start-index=26&amp;max-results=25'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><generator version='7.00' uri='http://www.blogger.com'>Blogger</generator><openSearch:totalResults>276</openSearch:totalResults><openSearch:startIndex>1</openSearch:startIndex><openSearch:itemsPerPage>25</openSearch:itemsPerPage><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-2194756824694062116</id><published>2020-02-27T08:18:00.002+11:00</published><updated>2020-02-27T08:18:48.228+11:00</updated><title type='text'>Results from the Maths Attitude Survey</title><content type='html'>&lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;We got all 120 of the Year 4 students to complete the Maths Attitude Survey last week. (My dream is to get the whole of the school to do it, but we crawl before we walk...)&lt;/span&gt;&lt;br /&gt;
2. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
3. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">I thought it would be interesting to look at their results so I got them to complete the survey as a Google Form. 113 out of the 120 completed it.</span><br />
4. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
5. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Here are the results:</span><br />
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8. <div class="separator" style="clear: both; text-align: center;">
9. <a href="https://1.bp.blogspot.com/-6WWHBdJq0IM/Xk0ZiiRlhPI/AAAAAAAAFPI/ovps0cJ43cwgqI2tl-blaIpf3XwMTSlkgCLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-19%2Bat%2B10.17.13%2Bpm.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="524" data-original-width="1248" height="267" src="https://1.bp.blogspot.com/-6WWHBdJq0IM/Xk0ZiiRlhPI/AAAAAAAAFPI/ovps0cJ43cwgqI2tl-blaIpf3XwMTSlkgCLcBGAsYHQ/s640/Screen%2BShot%2B2020-02-19%2Bat%2B10.17.13%2Bpm.png" width="640" /></a></div>
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12. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So we had more girls complete the survey than boys.</span><br />
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16. <a href="https://1.bp.blogspot.com/-d3-lC20CmwY/Xk0ZirWfw5I/AAAAAAAAFPM/aLEazxJ5YjIlAs6cFmKxUF65W8hP67OigCLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-19%2Bat%2B10.17.30%2Bpm.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="588" data-original-width="1248" height="300" src="https://1.bp.blogspot.com/-d3-lC20CmwY/Xk0ZirWfw5I/AAAAAAAAFPM/aLEazxJ5YjIlAs6cFmKxUF65W8hP67OigCLcBGAsYHQ/s640/Screen%2BShot%2B2020-02-19%2Bat%2B10.17.30%2Bpm.png" width="640" /></a></div>
17. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
18. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Interesting - we still some very positive words being chosen to describe maths. "Fun" was right up there but the No. #1 word of choice was "Challenging". We had a talk about that. The kids thought that this was a word that described maths as being something worthy of effort and rewarding when they succeeded with a puzzle or problem.</span><br />
19. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
20. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">"Scary" was rated very low (good!) but 22 students (19.5%) still chose "boring". This may have been a result of having all 120 kids complete the digital survey together - there may have been some contamination of data. Or maybe this is really what they think.</span><br />
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23. <div class="separator" style="clear: both; text-align: center;">
24. <a href="https://1.bp.blogspot.com/-aBp_WGAMieo/Xk0ZiXrUbeI/AAAAAAAAFPE/7CqFn7zcw4UAZyyiy5zvX6HO9NBjYfy_wCLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-19%2Bat%2B10.17.51%2Bpm.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="622" data-original-width="1244" height="320" src="https://1.bp.blogspot.com/-aBp_WGAMieo/Xk0ZiXrUbeI/AAAAAAAAFPE/7CqFn7zcw4UAZyyiy5zvX6HO9NBjYfy_wCLcBGAsYHQ/s640/Screen%2BShot%2B2020-02-19%2Bat%2B10.17.51%2Bpm.png" width="640" /></a></div>
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35. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
36. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
37. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
38. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">What would you choose to do all day? Art or reading or drama. Maybe this says something about our creative clientele. Maths comes in at #7. (UOI is Unit of Inquiry - we are a PYP school. Surprised this ranked so low.)</span><br />
39. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
40. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And so, on to some questions about explicit maths:</span><br />
41. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
42. <br />
43. <div class="separator" style="clear: both; text-align: center;">
44. <a href="https://1.bp.blogspot.com/-70iksUyp67o/Xk0b44IXDSI/AAAAAAAAFPg/NPzoIrzKq0csHvfGd23SZ5GEKnG8i2I2gCLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-19%2Bat%2B10.26.41%2Bpm.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="520" data-original-width="1244" height="266" src="https://1.bp.blogspot.com/-70iksUyp67o/Xk0b44IXDSI/AAAAAAAAFPg/NPzoIrzKq0csHvfGd23SZ5GEKnG8i2I2gCLcBGAsYHQ/s640/Screen%2BShot%2B2020-02-19%2Bat%2B10.26.41%2Bpm.png" width="640" /></a></div>
45. <br />
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48. <br />
49. <br />
50. <br />
51.  <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">- Not too bad at multiplication...</span><br />
52. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
53. <br />
54. <div class="separator" style="clear: both; text-align: center;">
55. <a href="https://1.bp.blogspot.com/-yHvS4Lg-Zb4/Xk0b48JvzpI/AAAAAAAAFPk/y7Z1A_HTCyguwnhVogGXqldQ-EajZK-owCLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-19%2Bat%2B10.26.50%2Bpm.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="520" data-original-width="1244" height="266" src="https://1.bp.blogspot.com/-yHvS4Lg-Zb4/Xk0b48JvzpI/AAAAAAAAFPk/y7Z1A_HTCyguwnhVogGXqldQ-EajZK-owCLcBGAsYHQ/s640/Screen%2BShot%2B2020-02-19%2Bat%2B10.26.50%2Bpm.png" width="640" /></a></div>
56. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
57. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">...Very confident with 2-digit addition...</span><br />
58. <br />
59. <br />
60. <div class="separator" style="clear: both; text-align: center;">
61. <a href="https://1.bp.blogspot.com/-hxfvQ_2LBDw/Xk0b4xkyiMI/AAAAAAAAFPc/V_pVLyII5dwhqKlOpNrdfajGPgXlXo8hgCLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-19%2Bat%2B10.27.01%2Bpm.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="518" data-original-width="1246" height="266" src="https://1.bp.blogspot.com/-hxfvQ_2LBDw/Xk0b4xkyiMI/AAAAAAAAFPc/V_pVLyII5dwhqKlOpNrdfajGPgXlXo8hgCLcBGAsYHQ/s640/Screen%2BShot%2B2020-02-19%2Bat%2B10.27.01%2Bpm.png" width="640" /></a></div>
62. <br />
63. <br />
64. <br />
65. <br />
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68. <br />
69. <br />
70. <br />
71. <br />
72. <br />
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74. <br />
75. <br />
76. <br />
77. <br />
78. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">...Subtraction not too bad...</span><br />
79. <br />
80. <br />
81. <div class="separator" style="clear: both; text-align: center;">
82. <a href="https://1.bp.blogspot.com/-kG6tYsUZDYI/Xk0b5vxGAZI/AAAAAAAAFPo/mtjpt9eKXJItcMGXUrENxML3erEwumDDQCLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-19%2Bat%2B10.27.11%2Bpm.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="518" data-original-width="1246" height="266" src="https://1.bp.blogspot.com/-kG6tYsUZDYI/Xk0b5vxGAZI/AAAAAAAAFPo/mtjpt9eKXJItcMGXUrENxML3erEwumDDQCLcBGAsYHQ/s640/Screen%2BShot%2B2020-02-19%2Bat%2B10.27.11%2Bpm.png" width="640" /></a></div>
83. <br />
84. <br />
85. <br />
86. <br />
87. <br />
88.  <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">...Division is a bit less certain...</span><br />
89. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
90. <br />
91. <div class="separator" style="clear: both; text-align: center;">
92. <a href="https://1.bp.blogspot.com/-MbBa7DpYP6o/Xk0b55eKCKI/AAAAAAAAFPs/RBc-JLSQGrYw1hN_HAfHjCpiSlyJR1JmgCLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-19%2Bat%2B10.27.22%2Bpm.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="520" data-original-width="1246" height="266" src="https://1.bp.blogspot.com/-MbBa7DpYP6o/Xk0b55eKCKI/AAAAAAAAFPs/RBc-JLSQGrYw1hN_HAfHjCpiSlyJR1JmgCLcBGAsYHQ/s640/Screen%2BShot%2B2020-02-19%2Bat%2B10.27.22%2Bpm.png" width="640" /></a></div>
93. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">... Fractions is equally uncertain...</span><br />
94. <br />
95. <br />
96. <div class="separator" style="clear: both; text-align: center;">
97. <a href="https://1.bp.blogspot.com/-FRvzWBPRWwg/Xk0b6NC-xZI/AAAAAAAAFPw/Tq1i0YX-2zMfr4gmpClAjPkpdXQ8GHPBgCLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-19%2Bat%2B10.27.30%2Bpm.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="516" data-original-width="1246" height="264" src="https://1.bp.blogspot.com/-FRvzWBPRWwg/Xk0b6NC-xZI/AAAAAAAAFPw/Tq1i0YX-2zMfr4gmpClAjPkpdXQ8GHPBgCLcBGAsYHQ/s640/Screen%2BShot%2B2020-02-19%2Bat%2B10.27.30%2Bpm.png" width="640" /></a></div>
98.  <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">... Converting fraction to percentages - not good...</span><br />
99. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
100. <br />
101. <div class="separator" style="clear: both; text-align: center;">
102. <a href="https://1.bp.blogspot.com/-WlLqcU6ZIRA/Xk0b6a188SI/AAAAAAAAFP0/EPwLPQOeOzkZY878PvhBKaZOhtWwiTohQCLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-19%2Bat%2B10.27.39%2Bpm.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="522" data-original-width="1244" height="268" src="https://1.bp.blogspot.com/-WlLqcU6ZIRA/Xk0b6a188SI/AAAAAAAAFP0/EPwLPQOeOzkZY878PvhBKaZOhtWwiTohQCLcBGAsYHQ/s640/Screen%2BShot%2B2020-02-19%2Bat%2B10.27.39%2Bpm.png" width="640" /></a></div>
103. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
104. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
105. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
106. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
107. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
108. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
109. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
110. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
111. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
112. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
113. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
114. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">... Measurement - surprisingly not confident. I thought this would be scored higher. Lots of "mostly".</span><br />
115. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
116. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Then we got to Question 10. Rate yourself on the scale (1-10) to show where you would be:</span><br />
117. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
118. <div class="separator" style="clear: both; text-align: center;">
119. <a href="https://1.bp.blogspot.com/-RRz0u0ieU_4/XlbeevJOAuI/AAAAAAAAFQM/K4uN0cIcn0cv_lCATgRh1ffn_agwq53dACLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-27%2Bat%2B8.07.05%2Bam.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="198" data-original-width="1210" height="104" src="https://1.bp.blogspot.com/-RRz0u0ieU_4/XlbeevJOAuI/AAAAAAAAFQM/K4uN0cIcn0cv_lCATgRh1ffn_agwq53dACLcBGAsYHQ/s640/Screen%2BShot%2B2020-02-27%2Bat%2B8.07.05%2Bam.png" width="640" /></a></div>
120. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
121. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
122. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
123. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
124. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
125. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">On the original survey, students had to draw a cross on the line to show where they thought they would be. On the digital version, I was limited by the fact that I could only give them a maximum of 10 boxes to choose from.</span><br />
126. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
127. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">But the results were even more revealing. Here is the data from all of Year 4:</span><br />
128. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
129. <div class="separator" style="clear: both; text-align: center;">
130. <a href="https://1.bp.blogspot.com/-dvq6lBjCDeI/XlbfDHU9PPI/AAAAAAAAFQU/RRshJdAtkokY1wFds6mbvwktV72K4viBACLcBGAsYHQ/s1600/Graph.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="449" data-original-width="750" height="237" src="https://1.bp.blogspot.com/-dvq6lBjCDeI/XlbfDHU9PPI/AAAAAAAAFQU/RRshJdAtkokY1wFds6mbvwktV72K4viBACLcBGAsYHQ/s400/Graph.png" width="400" /></a></div>
131. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
132. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
133. <br />
134. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
135. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><br />
136. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
137. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
138. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
139. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
140. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
141. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
142. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">In terms of numbers, almost 60% of our boys rate themselves 8 or above.</span><br />
143. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
144. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">In contrast, less than 16% of girls rate themselves 8 or above. </span><br />
145. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
146. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And then, 42% of girls rate themselves 5 or less whereas about 14% of boys rates themselves 5 or less. </span><br />
147. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
148. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">This is huge. These kids are only 9 years old, turning 10. How do they get these ideas about themselves? </span><br />
149. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
150. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Much work to be done on mindset.</span><br />
151. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
152. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
153. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
154. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
155. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
156. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
157. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
158. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
159. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
160. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
161. &lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/2194756824694062116/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2020/02/results-from-maths-attitude-survey.html#comment-form' title='2 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/2194756824694062116'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/2194756824694062116'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2020/02/results-from-maths-attitude-survey.html' title='Results from the Maths Attitude Survey'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://1.bp.blogspot.com/-6WWHBdJq0IM/Xk0ZiiRlhPI/AAAAAAAAFPI/ovps0cJ43cwgqI2tl-blaIpf3XwMTSlkgCLcBGAsYHQ/s72-c/Screen%2BShot%2B2020-02-19%2Bat%2B10.17.13%2Bpm.png" height="72" width="72"/><thr:total>2</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-8928794578902171764</id><published>2020-02-13T23:38:00.000+11:00</published><updated>2020-02-13T23:38:09.970+11:00</updated><title type='text'>Exploring Ratios Reveals the Distributive Law</title><content type='html'>&lt;br /&gt;
162. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">We had been doing an investigation into Vitruvian Man this week. You know, the picture that Leonardo drew:</span><br />
163. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
164. <div class="separator" style="clear: both; text-align: center;">
165. <a href="https://1.bp.blogspot.com/-yjiUDMztmIg/XkU8zDz1d3I/AAAAAAAAFOA/sbGTkApKIzU-tBG0wTofnlEnNDa_tDfhgCLcBGAsYHQ/s1600/virtuvian%2Bman.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="262" data-original-width="192" height="400" src="https://1.bp.blogspot.com/-yjiUDMztmIg/XkU8zDz1d3I/AAAAAAAAFOA/sbGTkApKIzU-tBG0wTofnlEnNDa_tDfhgCLcBGAsYHQ/s400/virtuvian%2Bman.jpeg" width="293" /></a></div>
166. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
167. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
168. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">A fascinating picture with a fascinating story. </span><br />
169. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
170. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Anyway, all the scribble around the outside of the picture is actually Leonardo's mathematical calculations based on the ratios of the human body.</span><br />
171. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
172. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Did you know that, in the "ideal" human body:</span><br />
173. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- a palm is four fingers</span><br />
174. <div class="MsoNormal">
175. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- a foot is four palms<o:p></o:p></span></div>
176. <div class="MsoNormal">
177. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- a cubit is six palms<o:p></o:p></span></div>
178. <div class="MsoNormal">
179. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- four cubits is the height of a man<o:p></o:p></span></div>
180. <div class="MsoNormal">
181. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- a pace is four cubits<o:p></o:p></span></div>
182. <div class="MsoNormal">
183. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- a man is 24 palms tall<o:p></o:p></span></div>
184. <div class="MsoNormal">
185. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- the length of the outspread arms is equal to the height of a
186. man.<o:p></o:p></span></div>
187. <div class="MsoNormal">
188. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- from the hairline to the bottom of the chin is one-tenth of
189. the height of a man.<o:p></o:p></span></div>
190. <div class="MsoNormal">
191. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- from below the chin to the top of the head is one-eighth of
192. the height of a man.<o:p></o:p></span></div>
193. <div class="MsoNormal">
194. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- the maximum width of the shoulders is a quarter of the
195. height of a man.<o:p></o:p></span></div>
196. <div class="MsoNormal">
197. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- the distance from the elbow to the tip of the hand is a
198. quarter of the height of a man.<o:p></o:p></span></div>
199. <div class="MsoNormal">
200. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- the distance from the elbow to the armpit is one-eighth of
201. the height of a man.<o:p></o:p></span></div>
202. <div class="MsoNormal">
203. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- the length of the hand is one-tenth of the height of a man.<o:p></o:p></span></div>
204. <div class="MsoNormal">
205. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- the foot is one-seventh of the height of a man.<o:p></o:p></span></div>
206. <div class="MsoNormal">
207. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- from below the foot to below the knee is a quarter of the
208. height of a man.<o:p></o:p></span></div>
209. <div class="MsoNormal">
210. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- the distance from below the chin to the nose is equal to:<o:p></o:p></span></div>
211. <div class="MsoNormal">
212. </div>
213. <ul>
214. <li><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The
215. distance from the nose to the eye brows</span></li>
216. <li><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The
217. distance from the eyebrows to the hairline</span></li>
218. <li><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The length
219. of the ear</span></li>
220. <li><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">One third
221. of the face</span></li>
222. </ul>
223. <div>
224. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
225. <div>
226. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Well, didn't we have a lot of fun exploring all these ratios and proportions!</span></div>
227. <div>
228. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
229. <div class="separator" style="clear: both; text-align: center;">
230. <a href="https://1.bp.blogspot.com/-rRGk9JvVz1E/XkU_C6W_mCI/AAAAAAAAFOM/d-1_FfXhmJYZbCjg5pbymSXajFh5NIplQCLcBGAsYHQ/s1600/Picture%2B1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="479" data-original-width="897" height="212" src="https://1.bp.blogspot.com/-rRGk9JvVz1E/XkU_C6W_mCI/AAAAAAAAFOM/d-1_FfXhmJYZbCjg5pbymSXajFh5NIplQCLcBGAsYHQ/s400/Picture%2B1.png" width="400" /></a></div>
231. <br />
232. <div class="separator" style="clear: both; text-align: center;">
233. <a href="https://1.bp.blogspot.com/-BRvGQG0ms2k/XkU_DNgHisI/AAAAAAAAFOQ/eLo-Fydg7BUGeKmRp6XoAhXyS5Q-Q8owQCLcBGAsYHQ/s1600/Picture%2B2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="693" data-original-width="664" height="400" src="https://1.bp.blogspot.com/-BRvGQG0ms2k/XkU_DNgHisI/AAAAAAAAFOQ/eLo-Fydg7BUGeKmRp6XoAhXyS5Q-Q8owQCLcBGAsYHQ/s400/Picture%2B2.png" width="382" /></a></div>
234. <div>
235. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
236. <br />
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412.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
413.   Name="List Number 5"/>
414.  <w:LsdException Locked="false" Priority="10" QFormat="true" Name="Title"/>
415.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
416.   Name="Closing"/>
417.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
418.   Name="Signature"/>
419.  <w:LsdException Locked="false" Priority="1" SemiHidden="true"
420.   UnhideWhenUsed="true" Name="Default Paragraph Font"/>
421.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
422.   Name="Body Text"/>
423.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
424.   Name="Body Text Indent"/>
425.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
426.   Name="List Continue"/>
427.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
428.   Name="List Continue 2"/>
429.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
430.   Name="List Continue 3"/>
431.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
432.   Name="List Continue 4"/>
433.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
434.   Name="List Continue 5"/>
435.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
436.   Name="Message Header"/>
437.  <w:LsdException Locked="false" Priority="11" QFormat="true" Name="Subtitle"/>
438.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
439.   Name="Salutation"/>
440.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
441.   Name="Date"/>
442.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
443.   Name="Body Text First Indent"/>
444.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
445.   Name="Body Text First Indent 2"/>
446.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
447.   Name="Note Heading"/>
448.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
449.   Name="Body Text 2"/>
450.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
451.   Name="Body Text 3"/>
452.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
453.   Name="Body Text Indent 2"/>
454.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
455.   Name="Body Text Indent 3"/>
456.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
457.   Name="Block Text"/>
458.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
459.   Name="Hyperlink"/>
460.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
461.   Name="FollowedHyperlink"/>
462.  <w:LsdException Locked="false" Priority="22" QFormat="true" Name="Strong"/>
463.  <w:LsdException Locked="false" Priority="20" QFormat="true" Name="Emphasis"/>
464.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
465.   Name="Document Map"/>
466.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
467.   Name="Plain Text"/>
468.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
469.   Name="E-mail Signature"/>
470.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
471.   Name="HTML Top of Form"/>
472.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
473.   Name="HTML Bottom of Form"/>
474.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
475.   Name="Normal (Web)"/>
476.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
477.   Name="HTML Acronym"/>
478.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
479.   Name="HTML Address"/>
480.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
481.   Name="HTML Cite"/>
482.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
483.   Name="HTML Code"/>
484.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
485.   Name="HTML Definition"/>
486.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
487.   Name="HTML Keyboard"/>
488.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
489.   Name="HTML Preformatted"/>
490.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
491.   Name="HTML Sample"/>
492.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
493.   Name="HTML Typewriter"/>
494.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
495.   Name="HTML Variable"/>
496.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
497.   Name="Normal Table"/>
498.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
499.   Name="annotation subject"/>
500.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
501.   Name="No List"/>
502.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
503.   Name="Outline List 1"/>
504.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
505.   Name="Outline List 2"/>
506.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
507.   Name="Outline List 3"/>
508.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
509.   Name="Table Simple 1"/>
510.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
511.   Name="Table Simple 2"/>
512.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
513.   Name="Table Simple 3"/>
514.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
515.   Name="Table Classic 1"/>
516.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
517.   Name="Table Classic 2"/>
518.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
519.   Name="Table Classic 3"/>
520.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
521.   Name="Table Classic 4"/>
522.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
523.   Name="Table Colorful 1"/>
524.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
525.   Name="Table Colorful 2"/>
526.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
527.   Name="Table Colorful 3"/>
528.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
529.   Name="Table Columns 1"/>
530.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
531.   Name="Table Columns 2"/>
532.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
533.   Name="Table Columns 3"/>
534.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
535.   Name="Table Columns 4"/>
536.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
537.   Name="Table Columns 5"/>
538.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
539.   Name="Table Grid 1"/>
540.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
541.   Name="Table Grid 2"/>
542.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
543.   Name="Table Grid 3"/>
544.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
545.   Name="Table Grid 4"/>
546.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
547.   Name="Table Grid 5"/>
548.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
549.   Name="Table Grid 6"/>
550.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
551.   Name="Table Grid 7"/>
552.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
553.   Name="Table Grid 8"/>
554.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
555.   Name="Table List 1"/>
556.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
557.   Name="Table List 2"/>
558.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
559.   Name="Table List 3"/>
560.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
561.   Name="Table List 4"/>
562.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
563.   Name="Table List 5"/>
564.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
565.   Name="Table List 6"/>
566.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
567.   Name="Table List 7"/>
568.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
569.   Name="Table List 8"/>
570.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
571.   Name="Table 3D effects 1"/>
572.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
573.   Name="Table 3D effects 2"/>
574.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
575.   Name="Table 3D effects 3"/>
576.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
577.   Name="Table Contemporary"/>
578.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
579.   Name="Table Elegant"/>
580.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
581.   Name="Table Professional"/>
582.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
583.   Name="Table Subtle 1"/>
584.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
585.   Name="Table Subtle 2"/>
586.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
587.   Name="Table Web 1"/>
588.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
589.   Name="Table Web 2"/>
590.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
591.   Name="Table Web 3"/>
592.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
593.   Name="Balloon Text"/>
594.  <w:LsdException Locked="false" Priority="39" Name="Table Grid"/>
595.  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
596.   Name="Table Theme"/>
597.  <w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/>
598.  <w:LsdException Locked="false" Priority="1" QFormat="true" Name="No Spacing"/>
599.  <w:LsdException Locked="false" Priority="60" Name="Light Shading"/>
600.  <w:LsdException Locked="false" Priority="61" Name="Light List"/>
601.  <w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
602.  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/>
603.  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/>
604.  <w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
605.  <w:LsdException Locked="false" Priority="66" Name="Medium List 2"/>
606.  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
607.  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
608.  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
609.  <w:LsdException Locked="false" Priority="70" Name="Dark List"/>
610.  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
611.  <w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
612.  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
613.  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
614.  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
615.  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
616.  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
617.  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
618.  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
619.  <w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
620.  <w:LsdException Locked="false" Priority="34" QFormat="true"
621.   Name="List Paragraph"/>
622.  <w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
623.  <w:LsdException Locked="false" Priority="30" QFormat="true"
624.   Name="Intense Quote"/>
625.  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
626.  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
627.  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
628.  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
629.  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
630.  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
631.  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
632.  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
633.  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
634.  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
635.  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
636.  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
637.  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
638.  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
639.  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
640.  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
641.  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
642.  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
643.  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
644.  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
645.  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
646.  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
647.  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
648.  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
649.  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
650.  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
651.  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
652.  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
653.  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
654.  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
655.  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
656.  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
657.  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
658.  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
659.  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
660.  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
661.  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
662.  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
663.  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
664.  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
665.  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
666.  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
667.  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
668.  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
669.  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
670.  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
671.  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
672.  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
673.  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
674.  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
675.  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
676.  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
677.  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
678.  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
679.  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
680.  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
681.  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
682.  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
683.  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
684.  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
685.  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
686.  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
687.  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
688.  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
689.  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
690.  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
691.  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
692.  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
693.  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
694.  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
695.  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
696.  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
697.  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
698.  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
699.  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
700.  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
701.  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
702.  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
703.  <w:LsdException Locked="false" Priority="19" QFormat="true"
704.   Name="Subtle Emphasis"/>
705.  <w:LsdException Locked="false" Priority="21" QFormat="true"
706.   Name="Intense Emphasis"/>
707.  <w:LsdException Locked="false" Priority="31" QFormat="true"
708.   Name="Subtle Reference"/>
709.  <w:LsdException Locked="false" Priority="32" QFormat="true"
710.   Name="Intense Reference"/>
711.  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
712.  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
713.   UnhideWhenUsed="true" Name="Bibliography"/>
714.  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
715.   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
716.  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
717.  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
718.  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
719.  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
720.  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
721.  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
722.  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
723.  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
724.  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
725.  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
726.  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
727.  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
728.  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
729.  <w:LsdException Locked="false" Priority="46"
730.   Name="Grid Table 1 Light Accent 1"/>
731.  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
732.  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
733.  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
734.  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
735.  <w:LsdException Locked="false" Priority="51"
736.   Name="Grid Table 6 Colorful Accent 1"/>
737.  <w:LsdException Locked="false" Priority="52"
738.   Name="Grid Table 7 Colorful Accent 1"/>
739.  <w:LsdException Locked="false" Priority="46"
740.   Name="Grid Table 1 Light Accent 2"/>
741.  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
742.  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
743.  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
744.  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
745.  <w:LsdException Locked="false" Priority="51"
746.   Name="Grid Table 6 Colorful Accent 2"/>
747.  <w:LsdException Locked="false" Priority="52"
748.   Name="Grid Table 7 Colorful Accent 2"/>
749.  <w:LsdException Locked="false" Priority="46"
750.   Name="Grid Table 1 Light Accent 3"/>
751.  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
752.  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
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998. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">We got the children to trace their outlines and then start recording measurements and ratios. At the start, they were not too sure what ratios were - by the end they had a better idea.</span><br />
999. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1000. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">So the next day, I took it in another direction. We hadn't played with blocks much this year, so I got some out and asked a few provocative questions:</span><br />
1001. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1002. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- Get one block</span><br />
1003. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- Get two blocks of a different colour</span><br />
1004. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- Get two blocks of the first colour</span><br />
1005. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- Get four blocks of the second colour</span><br />
1006. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1007. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Continue.</span><br />
1008. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1009. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">How much are you increasing by?</span><br />
1010. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1011. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">How many blocks of colour #2 do you need if you start with 6 blocks of colour #1?</span><br />
1012. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1013. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">This was to look at what happens when you use ratios to increase a given value.</span><br />
1014. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1015. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Here is what the kids did:</span><br />
1016. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1017. <div class="separator" style="clear: both; text-align: center;">
1018. <a href="https://1.bp.blogspot.com/-Kp7Ycf0AdHk/XkVAu8DdYhI/AAAAAAAAFOo/LbSIdnrbDKMR7tx4mejMoxpBaMDpocPZwCLcBGAsYHQ/s1600/64D54C69-CA4E-4AD2-B230-8F29A0A80211.heic" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://1.bp.blogspot.com/-Kp7Ycf0AdHk/XkVAu8DdYhI/AAAAAAAAFOo/LbSIdnrbDKMR7tx4mejMoxpBaMDpocPZwCLcBGAsYHQ/s400/64D54C69-CA4E-4AD2-B230-8F29A0A80211.heic" width="300" /></a></div>
1019. <br />
1020. <div class="separator" style="clear: both; text-align: center;">
1021. <a href="https://1.bp.blogspot.com/-LqU5zVGIKYs/XkVAtvyMe2I/AAAAAAAAFOk/QhXEDLUYNiMYcbb_tsjEXBRPhbq1NKOywCLcBGAsYHQ/s1600/BAAC717F-13DF-436C-B3AE-F36B795C7E59.heic" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://1.bp.blogspot.com/-LqU5zVGIKYs/XkVAtvyMe2I/AAAAAAAAFOk/QhXEDLUYNiMYcbb_tsjEXBRPhbq1NKOywCLcBGAsYHQ/s400/BAAC717F-13DF-436C-B3AE-F36B795C7E59.heic" width="300" /></a></div>
1022. <br />
1023. <div class="separator" style="clear: both; text-align: center;">
1024. <a href="https://1.bp.blogspot.com/-locoN41hyhw/XkVAv0M6FFI/AAAAAAAAFOs/2up7V8RDO2QF9ntvp90gxl38zJwgX1JtgCLcBGAsYHQ/s1600/ED2F0F98-E8B8-4D9D-AA8F-1723A07C59B3.heic" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://1.bp.blogspot.com/-locoN41hyhw/XkVAv0M6FFI/AAAAAAAAFOs/2up7V8RDO2QF9ntvp90gxl38zJwgX1JtgCLcBGAsYHQ/s400/ED2F0F98-E8B8-4D9D-AA8F-1723A07C59B3.heic" width="300" /></a></div>
1025. <br />
1026. <div class="separator" style="clear: both; text-align: center;">
1027. <a href="https://1.bp.blogspot.com/-OLv8fUJXNmc/XkVAspZ4OYI/AAAAAAAAFOg/2dTuxUgBMkYB4MI3-K9lgFgJlhyLoc9agCLcBGAsYHQ/s1600/38F09B2A-6DE2-4090-B3F7-4E7BE79F5865.heic" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://1.bp.blogspot.com/-OLv8fUJXNmc/XkVAspZ4OYI/AAAAAAAAFOg/2dTuxUgBMkYB4MI3-K9lgFgJlhyLoc9agCLcBGAsYHQ/s400/38F09B2A-6DE2-4090-B3F7-4E7BE79F5865.heic" width="400" /></a></div>
1028. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1029. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">You can see what is happening here.</span><br />
1030. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1031. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">1 green + 2 yellows = 3 blocks</span><br />
1032. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">2 greens + 4 yellows = 6 blocks</span><br />
1033. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">3 greens + 6 yellows = 9 blocks</span><br />
1034. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1035. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">and so the pattern grows...</span><br />
1036. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1037. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">But if we look at the greens as being our 1x tables (1, 2, 3, 4...) and the yellows as being our 2x tables (2, 4, 6, 8...) then when we add them together we get the 3x tables! (3, 6, 9, 12...)</span><br />
1038. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1039. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">We tried this with 1x and 3x:</span><br />
1040. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1041. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">1 green + 3 yellows = 4 blocks</span><br />
1042. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">2 greens + 6 yellows = 8 blocks</span><br />
1043. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">3 greens + 9 yellows = 12 blocks</span><br />
1044. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1045. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And it worked. (1x tables) + (3x tables) = 4x tables</span><br />
1046. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1047. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">"So what might be another way to work out your 4x tables?" I asked.</span><br />
1048. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1049. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Quick as a flash, one bright young thing said, "2x tables plus 2x tables."</span><br />
1050. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1051. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And he was right.</span><br />
1052. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1053. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The Distributive Law in action.</span><br />
1054. &lt;span style=&quot;font-family: Arial, Helvetica, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/8928794578902171764/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2020/02/exploring-ratios-reveals-distributive.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/8928794578902171764'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/8928794578902171764'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2020/02/exploring-ratios-reveals-distributive.html' title='Exploring Ratios Reveals the Distributive Law'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://1.bp.blogspot.com/-yjiUDMztmIg/XkU8zDz1d3I/AAAAAAAAFOA/sbGTkApKIzU-tBG0wTofnlEnNDa_tDfhgCLcBGAsYHQ/s72-c/virtuvian%2Bman.jpeg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-8008400984874561027</id><published>2020-02-07T08:52:00.000+11:00</published><updated>2020-02-08T23:53:38.918+11:00</updated><title type='text'>Start the Year with an Attitude Survey</title><content type='html'>&lt;br /&gt;
1055. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Here in my part of Australia it is the end of Week 1, Term 1. Being a good teacher, I am always keen to get to know my new class quickly and to find out all about them.</span><br />
1056. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1057. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And this often involves assessment.</span><br />
1058. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1059. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Kind of sad if the first words of greeting are, "Hi kids! Did you have a great holiday? Sit down and do this test."</span><br />
1060. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1061. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Really, doing tests in Week 1 is harsh. But I still want to know about my kids. </span><br />
1062. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1063. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So instead, I give my students an attitudinal survey so they can tell me how they "feel" about maths.</span><br />
1064. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1065. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">I am teaching Year 4 this year. They are some of the kids I taught in Year 2 back in 2018 who did the awesome patterns you may have seen on my blog from back then. So I was hopeful that there would be some pretty strong connection happening with maths. </span><br />
1066. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1067. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">I don't have room to go through the whole 2 pages of the survey (if you want a copy I can email you one) but I want to highlight a few interesting questions and the results from my class.</span><br />
1068. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1069. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><b>Question 1</b></span><br />
1070. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><b><br /></b></span>
1071. <br />
1072. <div class="MsoNormal">
1073. <b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Put a circle around
1074. the words you would use to describe</span></b></div>
1075. <div class="MsoNormal">
1076. <b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">maths:<o:p></o:p></span></b></div>
1077. <div class="MsoNormal">
1078. <b style="mso-bidi-font-weight: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></b></div>
1079. <div class="MsoNormal">
1080. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">boring     cool     exciting     fun     </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">difficult         </span></div>
1081. <div class="MsoNormal">
1082. <span style="line-height: 115%;"><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span></span></span></div>
1083. <div class="MsoNormal">
1084. <span style="line-height: 115%;"><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;">hard        confusing     challenging     </span></span></span><span style="line-height: 115%;"><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;">scary    easy</span></span></span></div>
1085. <div class="MsoNormal">
1086. <span style="line-height: 115%;"><span style="font-size: large;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span></span></span></div>
1087. <div class="MsoNormal">
1088. <br /></div>
1089. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">No - this is not a test to see who knows what a circle is and who can draw one. It is about tuning in to the language that the students use when talking about maths - whether talking out loud or just talking in their heads.</span><br />
1090. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1091. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><b>Results for Question 1</b></span><br />
1092. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><b><br /></b></span>
1093. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Students could circle as many words as they wanted to. This is how the students in 4BF responded:</span><br />
1094. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1095. <br />
1096. <div class="separator" style="clear: both; text-align: center;">
1097. <a href="https://1.bp.blogspot.com/-elcnRb0fdQg/XjyBtvWEKII/AAAAAAAAFNc/PagFELsKC5ojyigV-5L5aJDmFGTkvEFTwCLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-07%2Bat%2B8.13.51%2Bam.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="676" data-original-width="1320" height="323" src="https://1.bp.blogspot.com/-elcnRb0fdQg/XjyBtvWEKII/AAAAAAAAFNc/PagFELsKC5ojyigV-5L5aJDmFGTkvEFTwCLcBGAsYHQ/s640/Screen%2BShot%2B2020-02-07%2Bat%2B8.13.51%2Bam.png" width="640" /></a></div>
1098. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1099. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Interesting.</span><br />
1100. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1101. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">No-one in my class finds maths scary - or maybe they're too scared to admit it.</span><br />
1102. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1103. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The most frequently recorded words were "cool", "fun" and "challenging". This is very positive language. Even "challenging" acknowledges that maths can require effort but that this is seen as a challenge rather than as being simply "difficult".</span><br />
1104. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1105. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The one boy who circled "boring" also circled "hard", "difficult", "challenging" and "confusing". He is not a student that I have taught before. He will be at the top of my list to learn more about and to see where we can make some positive gains.</span><br />
1106. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1107. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">I wonder if the students will still be using the same language at the end of the year?</span><br />
1108. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1109. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Another question that I use asks the students to rate their own ability at maths by putting a cross on a line. It looks like this:</span><br />
1110. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1111. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><b>Question 4</b></span><br />
1112. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1113. <br />
1114. <div class="separator" style="clear: both; text-align: center;">
1115. <a href="https://1.bp.blogspot.com/-Hdho-YlSxW4/XjyEeqjpoMI/AAAAAAAAFNo/SRdG10wLEugntVIxP4y0IjNpQ2-bIwctACLcBGAsYHQ/s1600/IMG_5781.HEIC" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="519" data-original-width="1600" height="128" src="https://1.bp.blogspot.com/-Hdho-YlSxW4/XjyEeqjpoMI/AAAAAAAAFNo/SRdG10wLEugntVIxP4y0IjNpQ2-bIwctACLcBGAsYHQ/s400/IMG_5781.HEIC" width="400" /></a></div>
1116. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1117. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">This example is my "boring" boy from the question above. Definitely need to get involved here.</span><br />
1118. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1119. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The length of the line is 15cm (or 150mm). With this question, I measure the position of the cross in relation to the left hand end of the line and give a score our of 150 (because the line is 150mm long, so 1 point equals 1mm). </span><br />
1120. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1121. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Results were:</span><br />
1122. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1123. <br />
1124. <div class="separator" style="clear: both; text-align: center;">
1125. <a href="https://1.bp.blogspot.com/-wiBMEr-HBS0/XjyFyBCtWII/AAAAAAAAFN0/qCp8YnwWjKsT8z7lTnTqsh5pLcll9ER9ACLcBGAsYHQ/s1600/Screen%2BShot%2B2020-02-07%2Bat%2B8.31.39%2Bam.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="288" data-original-width="666" height="172" src="https://1.bp.blogspot.com/-wiBMEr-HBS0/XjyFyBCtWII/AAAAAAAAFN0/qCp8YnwWjKsT8z7lTnTqsh5pLcll9ER9ACLcBGAsYHQ/s400/Screen%2BShot%2B2020-02-07%2Bat%2B8.31.39%2Bam.png" width="400" /></a></div>
1126. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1127. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So the boys rate themselves pretty highly at maths, even given the "outlier" (above) who scored himself at about 25 out of 150. And the girls have a (significantly) lower opinion of their abilities. Do the boys have an inflated sense of how "good" they are? Are they being realistic? Are the girls too modest? Are they being realistic? Do they doubt themselves?</span><br />
1128. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1129. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">One thing that does stand out - I need to work on attitude. </span><br />
1130. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1131. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">This quick survey gave me a lot of information to think about - probably more than a skills-based number test would have. There were 10 questions in all. Some questions were similar in format to the above, others were short answer and required sentence responses. I can highly recommend that you have a go at doing something similar to start your year. It will tell you a great deal about the students in your care.</span><br />
1132. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1133. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">All 5 of our Year 4 classes did this survey. Hopefully in the next few days I will have data from all the classes that I can share.</span><br />
1134. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1135. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Have fun!</span><br />
1136. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1137. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1138. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1139. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1140. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1141. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1142. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1143. &lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/8008400984874561027/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2020/02/start-year-with-attitude-survey.html#comment-form' title='3 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/8008400984874561027'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/8008400984874561027'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2020/02/start-year-with-attitude-survey.html' title='Start the Year with an Attitude Survey'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://1.bp.blogspot.com/-elcnRb0fdQg/XjyBtvWEKII/AAAAAAAAFNc/PagFELsKC5ojyigV-5L5aJDmFGTkvEFTwCLcBGAsYHQ/s72-c/Screen%2BShot%2B2020-02-07%2Bat%2B8.13.51%2Bam.png" height="72" width="72"/><thr:total>3</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-2168665482733445871</id><published>2019-11-25T21:03:00.003+11:00</published><updated>2019-11-25T21:38:32.601+11:00</updated><title type='text'>miniMaths Book 2</title><content type='html'>&lt;h2&gt;
1144. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></h2>
1145. <h2>
1146. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The Background</span></h2>
1147. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Following our successful application in 2018 for an </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">ACT Government Nature Play grant,</span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"> I submitted an application on behalf of the Canberra Maths Association for another grant in 2019. As we had planned in 2018, we again proposed to:</span><br />
1148. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">- write 10 inquiries/tasks/lessons/resources to be used outside in the natural environment</span><br />
1149. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">- run a series of workshops with preschools to share these resources</span><br />
1150. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">I am very pleased to announce that we were again successful in our application and got the grant. A group of about 10 interested preschool teachers met together one afternoon earlier in the year at Radford College, my school, and brainstormed some ideas. It was a productive time. I went away with pages of notes that I wrote up as the miniMaths Book 2. </span><br />
1151. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The 10 tasks we came up with were:</span><br />
1152. <br />
1153. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">1. Which hand? - an exploration into probability</span><br />
1154. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">2. Hands and feet - measuring with informal units</span><br />
1155. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">3. Symmetrical mandala - building a symmetrical pattern</span><br />
1156. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">4. Leftovers - what to do with remainders when dividing</span><br />
1157. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">5. There and back - giving directions to describe a journey</span><br />
1158. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">6. Pattern dance - using symbols to represent the parts of a dance</span><br />
1159. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">7. Flower count - collecting data about flower colours and representing the data as a "graph"</span><br />
1160. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">8. Shape detective - finding shapes in nature</span><br />
1161. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">9. Treasure sort - sorting objects based on shared and unique features</span><br />
1162. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">10. Fill the pot - how many cups of sand does it take to fill a saucepan?</span><br />
1163. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1164. <br />
1165. <div class="separator" style="clear: both; text-align: center;">
1166. </div>
1167. <div class="separator" style="clear: both; text-align: center;">
1168. <br /></div>
1169. <a href="https://1.bp.blogspot.com/-7Zdgrr7Wdxk/XdumLZJPIcI/AAAAAAAAFNA/nqqz0qKBpFUHWdNgL3cWpuu2sutOyQAiACLcBGAsYHQ/s1600/Mandala.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1533" height="400" src="https://1.bp.blogspot.com/-7Zdgrr7Wdxk/XdumLZJPIcI/AAAAAAAAFNA/nqqz0qKBpFUHWdNgL3cWpuu2sutOyQAiACLcBGAsYHQ/s400/Mandala.jpg" width="381" /></a><br />
1170. <div class="separator" style="clear: both; text-align: center;">
1171. <br /></div>
1172. <div class="separator" style="clear: both; text-align: center;">
1173. <i>A beautiful flower mandala created by the wonderful students </i></div>
1174. <div class="separator" style="clear: both; text-align: center;">
1175. <i>at Orana Steiner School</i></div>
1176. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The 10 tasks make up Book 2 of the miniMaths program. Every preschool and early learning centre in the Australian Capital Territory will receive copies of the book early in 2020.</span><br />
1177. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1178. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1179. <br />
1180. <div class="separator" style="clear: both; text-align: center;">
1181. <a href="https://1.bp.blogspot.com/-ceD9IKH31ec/Xduk-xIhaiI/AAAAAAAAFMs/f-w9O2aA7Q4fEgrI1yvkgt7cMgW52fdegCLcBGAsYHQ/s1600/Book%2B2%2Bcover.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1258" data-original-width="900" height="640" src="https://1.bp.blogspot.com/-ceD9IKH31ec/Xduk-xIhaiI/AAAAAAAAFMs/f-w9O2aA7Q4fEgrI1yvkgt7cMgW52fdegCLcBGAsYHQ/s640/Book%2B2%2Bcover.jpg" width="456" /></a></div>
1182. <div class="separator" style="clear: both; text-align: center;">
1183. <br /></div>
1184. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The 10 tasks have also been uploaded as a website that is available to anyone, not just ACT teachers:</span><br />
1185. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><a href="http://www.minimaths.com.au/">http://www.minimaths.com.au</a> </span><br />
1186. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Over the next week or so, I will post a bit more detail about each of the 10 tasks. Maybe you will find them useful. I would be keen to hear any feedback.</span><br />
1187. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And any Canberra teachers - keep an eye out for the miniMaths workshops rolling out over January and February.</span><br />
1188. &lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;Regards.&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/2168665482733445871/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/11/minimaths-book-2.html#comment-form' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/2168665482733445871'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/2168665482733445871'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/11/minimaths-book-2.html' title='miniMaths Book 2'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://1.bp.blogspot.com/-7Zdgrr7Wdxk/XdumLZJPIcI/AAAAAAAAFNA/nqqz0qKBpFUHWdNgL3cWpuu2sutOyQAiACLcBGAsYHQ/s72-c/Mandala.jpg" height="72" width="72"/><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-1902397513892324591</id><published>2019-07-30T10:48:00.000+10:00</published><updated>2019-07-30T10:48:26.610+10:00</updated><title type='text'>1 10 100 1000 10000 100000 1000000</title><content type='html'>&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;
1189. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Let's have a look at place value with Year 4.</span><br />
1190. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1191. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The Australian Curriculum says:</span><br />
1192. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1193. <div style="text-align: center;">
1194. <span style="font-size: large;"><i><span style="color: #222222; font-family: helvetica, Roboto, "Droid Serif", sans-serif, Raleway, Catamaran, "Hind Guntur";">Recognise, represent and order numbers to at least tens of thousands </span><a class="no-decoration" href="http://www.scootle.edu.au/ec/search?accContentId=ACMNA072" style="box-sizing: inherit; color: #00629b; font-family: helvetica, Roboto, "Droid Serif", sans-serif, Raleway, Catamaran, "Hind Guntur"; text-decoration-line: none;" target="_blank">(ACMNA072)</a></i></span></div>
1195. <div style="text-align: center;">
1196. <span style="font-size: large;"><br /></span></div>
1197. <div style="text-align: left;">
1198. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">So we did.</span></div>
1199. <div style="text-align: left;">
1200. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1201. <div style="text-align: left;">
1202. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">I got some 1mm grid paper and we started off with one tiny square.</span></div>
1203. <div style="text-align: left;">
1204. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1205. <div style="text-align: left;">
1206. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Then we cut out a row of 10.</span></div>
1207. <div style="text-align: left;">
1208. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1209. <div style="text-align: left;">
1210. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Then we cut out a square of 100.</span></div>
1211. <div style="text-align: left;">
1212. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1213. <div style="text-align: left;">
1214. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Then a row of 1000.</span></div>
1215. <div style="text-align: left;">
1216. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1217. <div style="text-align: left;">
1218. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><a href="http://1.bp.blogspot.com/-lLEl7LkYVag/XT-Rs2H8iyI/AAAAAAAAFLg/A999kevrRHo68me2gT921pUI3AS4mb3YQCK4BGAYYCw/s1600/IMG_5960.jpg" imageanchor="1"><img border="0" height="400" src="https://1.bp.blogspot.com/-lLEl7LkYVag/XT-Rs2H8iyI/AAAAAAAAFLg/A999kevrRHo68me2gT921pUI3AS4mb3YQCK4BGAYYCw/s400/IMG_5960.jpg" width="300" /></a></span></div>
1219. <div style="text-align: left;">
1220. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1221. <div style="text-align: left;">
1222. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">It started getting a bit technical here. It seemed like I had hit a developmental barrier - a place that required some additional cognitive effort. I was a bit surprised but we worked our way through. </span></div>
1223. <div style="text-align: left;">
1224. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1225. <div style="text-align: left;">
1226. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Obviously (to me at least) 10 000 was going to be 10 rows of 1000. It didn't appear to be that obvious to the students. Why was there this hesitation? Perhaps this is why the Australian Curriculum identifies this as the target size to go for in Year 4. However, once we started counting by groups of 1000, we soon got the idea of what 10 000 looked like.</span></div>
1227. <div style="text-align: left;">
1228. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1229. <div style="text-align: left;">
1230. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">One of my ambitions with this task was to get a visual experience of what happens when we start multiplying by powers of 10. Also to get the connection with the decimal place value system we use - more of this later.</span></div>
1231. <div style="text-align: left;">
1232. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1233. <div style="text-align: left;">
1234. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Once we had 10 000 sorted, it was a smaller step for mankind to decide what needed to be done to represent </span></div>
1235. <div style="text-align: left;">
1236. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">100 000. It's 10 of the 10 000 squares. </span></div>
1237. <div style="text-align: left;">
1238. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1239. <div style="text-align: left;">
1240. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">At this point, a few students began to see a pattern forming in the way we were representing the numbers:</span></div>
1241. <div style="text-align: left;">
1242. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1243. <div style="text-align: left;">
1244. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">1 = square</span></div>
1245. <div style="text-align: left;">
1246. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">10 = line</span></div>
1247. <div style="text-align: left;">
1248. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">100 = square</span></div>
1249. <div style="text-align: left;">
1250. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">1000 = line</span></div>
1251. <div style="text-align: left;">
1252. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">10 000 = square</span></div>
1253. <div style="text-align: left;">
1254. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">100 000 = line</span></div>
1255. <div style="text-align: left;">
1256. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">1 000 000 = square...</span></div>
1257. <div style="text-align: left;">
1258. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1259. <div style="text-align: left;">
1260. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Well, we haven't quite finished the 1 000 000 square but we are nearly there.</span></div>
1261. <div style="text-align: left;">
1262. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1263. <div class="separator" style="clear: both; text-align: center;">
1264. <a href="http://4.bp.blogspot.com/-de1nzRNOUU0/XT-R6OeqknI/AAAAAAAAFLo/jVOsiP_PNLEfUanS9k7M_ckBlBW3zpdhACK4BGAYYCw/s1600/IMG_5961.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://4.bp.blogspot.com/-de1nzRNOUU0/XT-R6OeqknI/AAAAAAAAFLo/jVOsiP_PNLEfUanS9k7M_ckBlBW3zpdhACK4BGAYYCw/s400/IMG_5961.jpg" width="300" /></a></div>
1265. <div style="text-align: left;">
1266. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1267. <div style="text-align: left;">
1268. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1269. <div style="text-align: left;">
1270. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And the classroom is a bit of a mess - just the time when a member of the executive chooses to walk in...</span></div>
1271. <div style="text-align: left;">
1272. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1273. <div style="text-align: left;">
1274. <a href="http://1.bp.blogspot.com/-A93bH0dfzzY/XT-SOomt2DI/AAAAAAAAFL4/4ptxCUgxDPs59L25i6iH2FfO82WVZdxgwCK4BGAYYCw/s1600/IMG_5957.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="300" src="https://1.bp.blogspot.com/-A93bH0dfzzY/XT-SOomt2DI/AAAAAAAAFL4/4ptxCUgxDPs59L25i6iH2FfO82WVZdxgwCK4BGAYYCw/s400/IMG_5957.jpg" width="400" /></a><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1275. <div style="text-align: left;">
1276. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1277. <div style="text-align: left;">
1278. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1279. <div style="text-align: left;">
1280. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1281. <div style="text-align: left;">
1282. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1283. <div style="text-align: left;">
1284. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1285. <div style="text-align: left;">
1286. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1287. <div style="text-align: left;">
1288. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1289. <div style="text-align: left;">
1290. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1291. <div style="text-align: left;">
1292. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1293. <div style="text-align: left;">
1294. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1295. <div style="text-align: left;">
1296. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1297. <div style="text-align: left;">
1298. <span style="font-family: Arial, Helvetica, sans-serif;"><i>This is the room <b>after</b> we did a bit of a tidy up.</i></span></div>
1299. <div style="text-align: left;">
1300. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1301. <div style="text-align: left;">
1302. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">So now we have models of 1, 10, 100, 1000 etc.</span></div>
1303. <div style="text-align: left;">
1304. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1305. <div style="text-align: left;">
1306. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">A valuable experience.</span></div>
1307. <div style="text-align: left;">
1308. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1309. <div style="text-align: left;">
1310. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">But the other connection I wanted to make was with the decimal place value system. Because with my models, I can now choose any of the samples to be the unit - it doesn't have to be the tiny little square = 1. It could be any of the other models we have made. The very biggest square, that we thought was 1 million when we made it, may in fact become 1 unit, or 1 thousand or 1 anything. </span></div>
1311. <div style="text-align: left;">
1312. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1313. <div style="text-align: left;">
1314. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And if that is the case, then what is the value of the other numbers? And where does that decimal point need to go?</span></div>
1315. <div style="text-align: left;">
1316. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1317. <div style="text-align: left;">
1318. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Time to start playing...</span></div>
1319. <div style="text-align: left;">
1320. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1321. <div style="text-align: left;">
1322. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1323. <div style="text-align: left;">
1324. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1325. </content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/1902397513892324591/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/07/1-10-100-1000-10000-100000-1000000.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/1902397513892324591'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/1902397513892324591'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/07/1-10-100-1000-10000-100000-1000000.html' title='1 10 100 1000 10000 100000 1000000'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://1.bp.blogspot.com/-lLEl7LkYVag/XT-Rs2H8iyI/AAAAAAAAFLg/A999kevrRHo68me2gT921pUI3AS4mb3YQCK4BGAYYCw/s72-c/IMG_5960.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-6112724888869980364</id><published>2019-02-14T22:07:00.001+11:00</published><updated>2019-02-14T22:07:10.284+11:00</updated><title type='text'>miniMATHS - 7. Make a Star</title><content type='html'>&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
1326. <br /></div>
1327. <div class="separator" style="clear: both; text-align: center;">
1328. <a href="https://1.bp.blogspot.com/-UQY6qUZ_-w4/XGVJhl4FFtI/AAAAAAAAFJ4/IgZMhjL8i_c8-GvS8Yjb0I94MOi3Rmv4QCLcBGAs/s1600/page%2B14.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1410" data-original-width="1002" height="640" src="https://1.bp.blogspot.com/-UQY6qUZ_-w4/XGVJhl4FFtI/AAAAAAAAFJ4/IgZMhjL8i_c8-GvS8Yjb0I94MOi3Rmv4QCLcBGAs/s640/page%2B14.jpg" width="454" /></a></div>
1329. <div class="separator" style="clear: both; text-align: center;">
1330. <br /></div>
1331. <div class="separator" style="clear: both; text-align: left;">
1332. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">This is my favourite.</span></div>
1333. <div class="separator" style="clear: both; text-align: left;">
1334. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1335. <div class="separator" style="clear: both; text-align: left;">
1336. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">I know - you're not meant to have favourite children.</span></div>
1337. <div class="separator" style="clear: both; text-align: left;">
1338. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1339. <div class="separator" style="clear: both; text-align: left;">
1340. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">But this one is where it all started. This was my first idea for the miniMaths series of tasks. So I think I had given it more thought and probably used it as the benchmark for what I imagined the other tasks would look like.</span></div>
1341. <div class="separator" style="clear: both; text-align: left;">
1342. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1343. <div class="separator" style="clear: both; text-align: left;">
1344. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And this one has real maths behind it. As you build up your star, you are adding a constant value to your pattern - one rock for each arm of the pattern. It is symmetry. It is an arithmetic sequence. It is pre-algebra. It is the connection between repeated addition and multiplication. And it is fun. It makes a cool looking pattern.</span></div>
1345. <div class="separator" style="clear: both; text-align: left;">
1346. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1347. <div class="separator" style="clear: both; text-align: center;">
1348. <a href="https://3.bp.blogspot.com/-baSoLYg4f-I/XGVJhdFfnrI/AAAAAAAAFJ0/-Io-zXB4Z_gKLstNmwfxjrOiPRpuAMmOACLcBGAs/s1600/page%2B13.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1410" data-original-width="1001" height="640" src="https://3.bp.blogspot.com/-baSoLYg4f-I/XGVJhdFfnrI/AAAAAAAAFJ0/-Io-zXB4Z_gKLstNmwfxjrOiPRpuAMmOACLcBGAs/s640/page%2B13.jpg" width="454" /></a></div>
1349. <div class="separator" style="clear: both; text-align: left;">
1350. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1351. <div class="separator" style="clear: both; text-align: left;">
1352. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">This task is linked to EYLF - Outcome 4, focusing on the disposition of the learner. The task itself is open enough to allow creativity and curiosity. It can be done as a collaborative and cooperative task. It can help students develop confidence and perseverance. </span></div>
1353. <div class="separator" style="clear: both; text-align: left;">
1354. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1355. <div class="separator" style="clear: both; text-align: left;">
1356. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Give it a go - it is a great task.</span></div>
1357. <div class="separator" style="clear: both; text-align: left;">
1358. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1359. <div class="separator" style="clear: both; text-align: left;">
1360. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1361. &lt;br /&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/6112724888869980364/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/02/minimaths-7-make-star.html#comment-form' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/6112724888869980364'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/6112724888869980364'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/02/minimaths-7-make-star.html' title='miniMATHS - 7. Make a Star'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://1.bp.blogspot.com/-UQY6qUZ_-w4/XGVJhl4FFtI/AAAAAAAAFJ4/IgZMhjL8i_c8-GvS8Yjb0I94MOi3Rmv4QCLcBGAs/s72-c/page%2B14.jpg" height="72" width="72"/><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-2594342932576153302</id><published>2019-02-13T22:03:00.003+11:00</published><updated>2019-02-13T22:04:07.031+11:00</updated><title type='text'>miniMATHS - 6. Stacking</title><content type='html'>&lt;br /&gt;
1362. <div class="separator" style="clear: both; text-align: center;">
1363. <a href="https://4.bp.blogspot.com/-XNeb8mc2A4k/XGP0vxdQyoI/AAAAAAAAFJY/4TYTRvubpDMvORj5sHoAbmI9dn95uFM6QCLcBGAs/s1600/page%2B12.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1404" data-original-width="1006" height="640" src="https://4.bp.blogspot.com/-XNeb8mc2A4k/XGP0vxdQyoI/AAAAAAAAFJY/4TYTRvubpDMvORj5sHoAbmI9dn95uFM6QCLcBGAs/s640/page%2B12.jpg" width="458" /></a></div>
1364. <br />
1365. <br />
1366. <br />
1367. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">This is fun. I know - I could spend hours doing it. In fact, I used to get kids to do it when I was on playground duty and I would challenge them to get 5 rocks stacked on top of each other.</span><br />
1368. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1369. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">But where is the maths?</span><br />
1370. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1371. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Well, there are a couple of ideas here that need to be explored.</span><br />
1372. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1373. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">1. Have you ever worked with kids (probably Year 2 or Year 3) who had the idea that when constructing a "sum" (or algorithm - addition or otherwise) you had to start with the big number and then perform the subsequent operation on it? And isn't there an addition strategy for counting on that says you need to start with the big number first? Is this somehow related to stacking up rocks or other items where it is a good idea to put the big one on the bottom of the stack? Please note, I'm just asking the questions here - not providing the simple answers.</span><br />
1374. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1375. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">2. Or could this be a revelation of the mathematical concept of combining different values to create new one?</span><br />
1376. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1377. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">3. Or is it an exercise in balance, similar to an equation where one side has to equal the other?</span><br />
1378. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1379. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">4. Or are we playing the mathematical idea of prediction - what happens if...?</span><br />
1380. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1381. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Perhaps the EYLF will give us some insight:</span><br />
1382. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1383. <br />
1384. <div class="separator" style="clear: both; text-align: center;">
1385. <a href="https://4.bp.blogspot.com/-A08m1CK4h_c/XGP0v6LI8HI/AAAAAAAAFJU/iN_C7xOI-fI4rVieMKLLKMuw2g6uGvWpACLcBGAs/s1600/page%2B11.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1411" data-original-width="1002" height="640" src="https://4.bp.blogspot.com/-A08m1CK4h_c/XGP0v6LI8HI/AAAAAAAAFJU/iN_C7xOI-fI4rVieMKLLKMuw2g6uGvWpACLcBGAs/s640/page%2B11.jpg" width="454" /></a></div>
1386. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1387. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The EYLF certainly talks about "balance" as an important element of growth. This task provides a neat entry point for this conversation.</span><br />
1388. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1389. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">This task will also provide an opportunity for students to develop perseverance - to try to get that stack higher and higher. It will also encourage students to reflect on their unsuccessful strategies and modify and improve on the performance. </span><br />
1390. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1391. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So, just as in the "Shadows" task, this activity may not appear at first glance to be explicitly "mathematical", there is great capacity for students to explore deep mathematical thinking by attempting the stacking task.</span><br />
1392. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1393. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">If you haven't seen it yet, there is a miniMaths website:</span><br />
1394. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1395. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><a href="http://www.minimaths.com.au/">http://www.minimaths.com.au</a></span><br />
1396. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1397. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And for people based in the Canberra region, I am running some workshops in preschools and early learning centres over the next six weeks. Details can be found on the miniMaths website.</span><br />
1398. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1399. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">See you there. </span><br />
1400. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1401. <br />
1402. <div class="separator" style="clear: both; text-align: center;">
1403. <a href="https://4.bp.blogspot.com/-0MSMRApa4rU/XGP5coxYQ9I/AAAAAAAAFJo/KFWD_MtbZx0a2xV7iNQuRb0y--xFr31XACLcBGAs/s1600/Screen%2BShot%2B2019-02-13%2Bat%2B10.02.46%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1044" data-original-width="912" height="640" src="https://4.bp.blogspot.com/-0MSMRApa4rU/XGP5coxYQ9I/AAAAAAAAFJo/KFWD_MtbZx0a2xV7iNQuRb0y--xFr31XACLcBGAs/s640/Screen%2BShot%2B2019-02-13%2Bat%2B10.02.46%2BPM.png" width="558" /></a></div>
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1415. &lt;br /&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/2594342932576153302/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/02/minimaths-6-stacking.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/2594342932576153302'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/2594342932576153302'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/02/minimaths-6-stacking.html' title='miniMATHS - 6. Stacking'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://4.bp.blogspot.com/-XNeb8mc2A4k/XGP0vxdQyoI/AAAAAAAAFJY/4TYTRvubpDMvORj5sHoAbmI9dn95uFM6QCLcBGAs/s72-c/page%2B12.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-3020105068229767238</id><published>2019-02-12T21:38:00.000+11:00</published><updated>2019-02-13T21:39:15.469+11:00</updated><title type='text'>miniMATHS - 5. Shadows</title><content type='html'>&lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;
1416. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Sorry about the delay of a few days there - we went back to school last week and I have been a bit distracted getting the class into shape..</span><br />
1417. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1418. <br />
1419. <div class="separator" style="clear: both; text-align: center;">
1420. <a href="https://2.bp.blogspot.com/-mVAEpFjGINc/XGKeBF9dviI/AAAAAAAAFI4/-snpPxDg3HA8hEVDGUtpK0eGvOJe2dmXgCLcBGAs/s1600/Screen%2BShot%2B2019-02-12%2Bat%2B9.20.01%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1206" data-original-width="900" height="640" src="https://2.bp.blogspot.com/-mVAEpFjGINc/XGKeBF9dviI/AAAAAAAAFI4/-snpPxDg3HA8hEVDGUtpK0eGvOJe2dmXgCLcBGAs/s640/Screen%2BShot%2B2019-02-12%2Bat%2B9.20.01%2BPM.png" width="475" /></a></div>
1421. <br />
1422. <br />
1423. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So here we have possibly the first major deviation in the miniMATHS resource tasks. This task, "Shadows", moves away from activities that have direct mathematical concepts as a focus, such as extending patterns or investigating area, to a place where we are investigating a natural phenomenon, such as shadows, using mathematical skills and knowledge. No longer playing directly with maths - now we are using maths as we play with something bigger.</span><br />
1424. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1425. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Shadows are fascinating. There is so much that we can learn by observing them. They are a great leaping off point for exploring time; they are an explicit example of change; we all have that follows us around - and there are lots of games you can play with them.</span><br />
1426. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1427. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">All of the things that are suggested as activities associated with this task can be investigated using mathematical language. This is a key opportunity to develop our use and understanding of words that describe position, shape, movement and change.</span><br />
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1432. </div>
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1435. <a href="https://4.bp.blogspot.com/-8CPragyHnHY/XGKeHpOpmCI/AAAAAAAAFJA/FQ-uqezGwscEv9EERZbQHgaMQhWo8HlygCLcBGAs/s1600/Screen%2BShot%2B2019-02-12%2Bat%2B9.20.28%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1214" data-original-width="900" height="640" src="https://4.bp.blogspot.com/-8CPragyHnHY/XGKeHpOpmCI/AAAAAAAAFJA/FQ-uqezGwscEv9EERZbQHgaMQhWo8HlygCLcBGAs/s640/Screen%2BShot%2B2019-02-12%2Bat%2B9.20.28%2BPM.png" width="474" /></a></div>
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1437. <br /></div>
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1439. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
1440. <div class="separator" style="clear: both; text-align: left;">
1441. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">This task is a great way to engage directly with the natural environment in an explicitly mathematical way. We can record changes over time using the outlines of shadows drawn on the ground. We can discuss the position of the light source relative to the object casting the shadow and the shadow itself. </span></div>
1442. <div class="separator" style="clear: both; text-align: left;">
1443. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
1444. <div class="separator" style="clear: both; text-align: left;">
1445. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The EYLF talks about knowledge of and respect for the natural environment. This task will give students a greater understanding and appreciation of what happens in the world in which they live, helping them to be connected with it and to learn respect for it.</span></div>
1446. <div class="separator" style="clear: both; text-align: left;">
1447. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
1448. <div class="separator" style="clear: both; text-align: left;">
1449. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Is it "maths by stealth"? Sneaking a bit of maths into a fun exploration of a cool phenomenon? </span></div>
1450. <div class="separator" style="clear: both; text-align: left;">
1451. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
1452. <div class="separator" style="clear: both; text-align: left;">
1453. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Well, I would say no - this is what real maths is: using our skills and knowledge to make sense of the world around us. And hopefully we can start this in early year education with young kids, engaging them as mathematicians to learn more about their world.</span></div>
1454. <div class="separator" style="clear: both; text-align: left;">
1455. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
1456. <div class="separator" style="clear: both; text-align: left;">
1457. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
1458. <div class="separator" style="clear: both; text-align: left;">
1459. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
1460. <div class="separator" style="clear: both; text-align: left;">
1461. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
1462. &lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/3020105068229767238/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/02/minimaths-5-shadows.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/3020105068229767238'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/3020105068229767238'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/02/minimaths-5-shadows.html' title='miniMATHS - 5. Shadows'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://2.bp.blogspot.com/-mVAEpFjGINc/XGKeBF9dviI/AAAAAAAAFI4/-snpPxDg3HA8hEVDGUtpK0eGvOJe2dmXgCLcBGAs/s72-c/Screen%2BShot%2B2019-02-12%2Bat%2B9.20.01%2BPM.png" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-4546795440812681008</id><published>2019-01-25T21:40:00.000+11:00</published><updated>2019-01-25T21:40:59.496+11:00</updated><title type='text'>miniMATHS - 4. One More</title><content type='html'>&lt;br /&gt;
1463. <br />
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1465. <div class="separator" style="clear: both; text-align: center;">
1466. <a href="https://1.bp.blogspot.com/-ZBOTVFp1TU4/XErexG04QRI/AAAAAAAAFIE/RcFzyXFTEtIScXpxm_6wtAU7GqytCwsbQCLcBGAs/s1600/page%2B8.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1402" data-original-width="1006" height="640" src="https://1.bp.blogspot.com/-ZBOTVFp1TU4/XErexG04QRI/AAAAAAAAFIE/RcFzyXFTEtIScXpxm_6wtAU7GqytCwsbQCLcBGAs/s640/page%2B8.jpg" width="458" /></a></div>
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1468. <br /></div>
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1470. <br /></div>
1471. <div class="separator" style="clear: both; text-align: left;">
1472. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Task 4 - One More.</span></div>
1473. <div class="separator" style="clear: both; text-align: left;">
1474. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1475. <div class="separator" style="clear: both; text-align: left;">
1476. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Seems like a very simple task.</span></div>
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1478. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1479. <div class="separator" style="clear: both; text-align: left;">
1480. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">You make a line of objects.</span></div>
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1482. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1483. <div class="separator" style="clear: both; text-align: left;">
1484. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">You partner makes a similar line - then adds one more.</span></div>
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1486. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
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1488. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Seems simple because it is simple. But it is also the beginnings of some very significant mathematics. </span></div>
1489. <div class="separator" style="clear: both; text-align: left;">
1490. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1491. <div class="separator" style="clear: both; text-align: left;">
1492. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- One to one correspondence (I make a line, you make a line) is the starting point for counting and giving a value to a collection of objects.</span></div>
1493. <div class="separator" style="clear: both; text-align: left;">
1494. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- "Adding one more" builds the idea of how numbers grow, how to build a sequence that increase by regular steps, how to think about addition.</span></div>
1495. <div class="separator" style="clear: both; text-align: left;">
1496. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- This is also pre-algebra: <i>x, x+1....</i></span></div>
1497. <div class="separator" style="clear: both; text-align: left;">
1498. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- And we are learning about more than and less than.</span></div>
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1500. <br /></div>
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1502. <br /></div>
1503. <br />
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1505. <a href="https://2.bp.blogspot.com/-tzlc7ZA81KE/XErezHdOhRI/AAAAAAAAFII/RqNfp5jKDnEgblsmIjtMuhPhCytPZJYqQCLcBGAs/s1600/page%2B7.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1413" data-original-width="1003" height="640" src="https://2.bp.blogspot.com/-tzlc7ZA81KE/XErezHdOhRI/AAAAAAAAFII/RqNfp5jKDnEgblsmIjtMuhPhCytPZJYqQCLcBGAs/s640/page%2B7.jpg" width="454" /></a></div>
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1507. <br /></div>
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1509. <br /></div>
1510. <div class="separator" style="clear: both; text-align: left;">
1511. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Similar to Task 2 and 3, this task focuses on EYLF Outcome 2, "Children are connected with and contribute to their world."</span></div>
1512. <div class="separator" style="clear: both; text-align: left;">
1513. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1514. <div class="separator" style="clear: both; text-align: left;">
1515. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">One of the big ideas that is raised in this task is the idea of equality. In a mathematical sense, we are talking about the balance between two values. In a broader sense, we can take this conversation to include equality between people.</span></div>
1516. <div class="separator" style="clear: both; text-align: left;">
1517. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
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1519. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Equal shares is an important lesson in childhood. We can use this maths task to springboard into a discussion of how we should live with each other. From this, we can also develop strategies for dealing with inequality. </span></div>
1520. <div class="separator" style="clear: both; text-align: left;">
1521. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1522. <div class="separator" style="clear: both; text-align: left;">
1523. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Check out the miniMaths website:</span></div>
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1525. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
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1527. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1528. <div class="separator" style="clear: both; text-align: left;">
1529. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><a href="http://www.minimaths.com.au/">http://www.minimaths.com.au</a></span></div>
1530. <div class="separator" style="clear: both; text-align: left;">
1531. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
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1539. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
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1541. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
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1543. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
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1545. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1546. &lt;br /&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/4546795440812681008/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/01/minimaths-4-one-more.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/4546795440812681008'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/4546795440812681008'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/01/minimaths-4-one-more.html' title='miniMATHS - 4. One More'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://1.bp.blogspot.com/-ZBOTVFp1TU4/XErexG04QRI/AAAAAAAAFIE/RcFzyXFTEtIScXpxm_6wtAU7GqytCwsbQCLcBGAs/s72-c/page%2B8.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-435443057198833932</id><published>2019-01-24T21:12:00.001+11:00</published><updated>2019-01-24T21:12:17.138+11:00</updated><title type='text'>miniMATHS - 3. Same Same Different</title><content type='html'>&lt;br /&gt;
1547. <div class="separator" style="clear: both; text-align: center;">
1548. <a href="https://4.bp.blogspot.com/-XWLrXimdq84/XEmLQj3lQJI/AAAAAAAAFHs/SQFHPw3kPzs9YWB-1dtxMpr4IrkFtoqfQCLcBGAs/s1600/page%2B6.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1408" data-original-width="1003" height="640" src="https://4.bp.blogspot.com/-XWLrXimdq84/XEmLQj3lQJI/AAAAAAAAFHs/SQFHPw3kPzs9YWB-1dtxMpr4IrkFtoqfQCLcBGAs/s640/page%2B6.jpg" width="452" /></a></div>
1549. <br />
1550. <br />
1551. <br />
1552. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">This task - Same Same Different - is a fun game that children can play in many different contexts. It asks children to collect a set of three objects, two of which have a common feature that is absent in the third object. It is easy to see the potential for individual variation. And it also encourages children to think and to explain their thinking.</span><br />
1553. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1554. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The suggested variations take the task into new places. "Same Same Same" asks the children to find common features in all three of their objects. "Different Different Different" turns the task upside down, requiring the children to identify differences between each of their objects.</span><br />
1555. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1556. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And how is this task mathematical? Isn't it just a matching game? Well, at it's heart, this task is framing up some elementary concepts of algebra - finding common values, identifying sameness and difference, using logic and reasoning. These concepts are also important in numerical operations such as addition, subtraction, multiplication and division.</span><br />
1557. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1558. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1559. <div class="separator" style="clear: both; text-align: center;">
1560. <a href="https://2.bp.blogspot.com/-o3Xt1SjJc8E/XEmNzkKTX1I/AAAAAAAAFH4/ieq_oYWSKM4F5reBg4ONZ_rXNHjtRchHACLcBGAs/s1600/page%2B5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1416" data-original-width="1017" height="640" src="https://2.bp.blogspot.com/-o3Xt1SjJc8E/XEmNzkKTX1I/AAAAAAAAFH4/ieq_oYWSKM4F5reBg4ONZ_rXNHjtRchHACLcBGAs/s640/page%2B5.jpg" width="457" /></a></div>
1561. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1562. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1563. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1564. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">One aspect of the EYLF Outcome 2 looks at finding similarities and differences between people. Sound familiar? Isn't this the overt purpose of this task, finding same and different? This task can provide an ideal opportunity to promote conversations about diversity and individual differences. </span><br />
1565. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1566. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">In the context of play, children can be encouraged to consider deep concepts and to start thinking about their own place in the world. Their connection with and contribution to the world is significant and should be nurtured through positive learning experiences such as this.</span><br />
1567. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1568. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The miniMaths website can be found here:</span><br />
1569. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1570. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><a href="http://www.minimaths.com.au/">http://www.minimaths.com.au</a> </span><br />
1571. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1572. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1573. <br />
1574. <br />
1575. </content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/435443057198833932/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/01/minimaths-3-same-same-different.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/435443057198833932'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/435443057198833932'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/01/minimaths-3-same-same-different.html' title='miniMATHS - 3. Same Same Different'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://4.bp.blogspot.com/-XWLrXimdq84/XEmLQj3lQJI/AAAAAAAAFHs/SQFHPw3kPzs9YWB-1dtxMpr4IrkFtoqfQCLcBGAs/s72-c/page%2B6.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-7337227292279285181</id><published>2019-01-23T22:06:00.000+11:00</published><updated>2019-01-23T22:06:41.415+11:00</updated><title type='text'>miniMATHS - 2. Big Bigger Biggest</title><content type='html'>&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
1576. </div>
1577. <br />
1578. <div class="separator" style="clear: both; text-align: center;">
1579. <a href="https://3.bp.blogspot.com/-e5BBlqqUld8/XEhDg54sX8I/AAAAAAAAFHU/DsZy1SPn96kxsu2cdQsoM5WwddA3AGQPgCLcBGAs/s1600/page%2B4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1405" data-original-width="1012" height="400" src="https://3.bp.blogspot.com/-e5BBlqqUld8/XEhDg54sX8I/AAAAAAAAFHU/DsZy1SPn96kxsu2cdQsoM5WwddA3AGQPgCLcBGAs/s400/page%2B4.jpg" width="287" /></a></div>
1580. <br />
1581. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1582. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">This is my favourite task. If I was in pre-k, I think I could have spent hours with sticks or rocks, lining them up in order of length. Actually, I probably did when I was.</span><br />
1583. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1584. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The big idea behind this task is prompted by something I heard Nora Newcombe say at a conference last year. (Nora is a significant voice in mathematics education and research and has written heaps)  She said that her research had found that, while a sense of number was not something that babies are born with, they do seem to possess an innate sense of "magnitude" - something being "more than" something else.</span><br />
1585. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1586. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So I was interested to include a task where students can develop this skill, looking at objects and arranging them based on an attribute such as length or area. This task also provides an opportunity to reverse the process, to look at small, smaller and smallest. </span><br />
1587. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1588. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">It is not an accident that this task has used the nominative, comparative and superlative. This gives important links to grammar and language development in an informal context.</span><br />
1589. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1590. <br />
1591. <div class="separator" style="clear: both; text-align: center;">
1592. <a href="https://4.bp.blogspot.com/-l2387CD9abM/XEhHsWxO3yI/AAAAAAAAFHg/1uwuhuS9Jk8khWP3SlC6BQ2Nvii-fsptQCLcBGAs/s1600/page%2B3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1415" data-original-width="1017" height="400" src="https://4.bp.blogspot.com/-l2387CD9abM/XEhHsWxO3yI/AAAAAAAAFHg/1uwuhuS9Jk8khWP3SlC6BQ2Nvii-fsptQCLcBGAs/s400/page%2B3.jpg" width="286" /></a></div>
1593. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">This task is linked to the second outcome from the Early Years Learning Framework:</span><br />
1594. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1595. <br />
1596. <div style="text-align: center;">
1597. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><i>Children are connected with and contribute to their world.</i></span></div>
1598. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">A big idea linked to this outcome is "change" - and this can be explored through the task by developing groups of objects that grow in a certain direction - by length, height, mass, area or in some other way. Children can see how they can add new objects to their sequence to make it grow. </span><br />
1599. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1600. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Once again, if anyone gives this one a go and has any feedback, please let me know. I would love to hear about it.</span><br />
1601. <br />
1602. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And here's the link to the website:</span><br />
1603. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1604. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><a href="http://www.minimaths.com.au/">http://www.minimaths.com.au</a> </span>
1605. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1606. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1607. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1608. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1609. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1610. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1611. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1612. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1613. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1614. </content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/7337227292279285181/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/01/minimaths-2-big-bigger-biggest.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/7337227292279285181'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/7337227292279285181'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/01/minimaths-2-big-bigger-biggest.html' title='miniMATHS - 2. Big Bigger Biggest'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://3.bp.blogspot.com/-e5BBlqqUld8/XEhDg54sX8I/AAAAAAAAFHU/DsZy1SPn96kxsu2cdQsoM5WwddA3AGQPgCLcBGAs/s72-c/page%2B4.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-4066850776397640217</id><published>2019-01-22T21:25:00.000+11:00</published><updated>2019-01-22T21:25:07.242+11:00</updated><title type='text'>miniMATHS - 1. How many leaves?</title><content type='html'>&lt;br /&gt;
1615. <br />
1616. <div class="separator" style="clear: both; text-align: center;">
1617. </div>
1618. <br />
1619. <div class="separator" style="clear: both; text-align: center;">
1620. <a href="https://3.bp.blogspot.com/-051n3IqY9wg/XEbhDy_39fI/AAAAAAAAFG4/YEujZ1un1pI_qVYMYLjYUazMalFMOpSzACLcBGAs/s1600/page%2B2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1414" data-original-width="1021" height="640" src="https://3.bp.blogspot.com/-051n3IqY9wg/XEbhDy_39fI/AAAAAAAAFG4/YEujZ1un1pI_qVYMYLjYUazMalFMOpSzACLcBGAs/s640/page%2B2.jpg" width="459" /></a></div>
1621. <div class="separator" style="clear: both; text-align: center;">
1622. <br /></div>
1623. <div class="separator" style="clear: both; text-align: center;">
1624. <i>from the "miniMATHS - Maths Inqiries in Nature" booklet</i></div>
1625. <div class="separator" style="clear: both; text-align: center;">
1626. <br /></div>
1627. <div class="separator" style="clear: both; text-align: left;">
1628. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The tasks are organised based on the Early Years Learning Framework (EYLF). I linked each task to one of the five outcomes and put them in numerical order.</span></div>
1629. <div class="separator" style="clear: both; text-align: left;">
1630. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1631. <div class="separator" style="clear: both; text-align: left;">
1632. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Outcome 1</b> - Children have a strong sense of identity</span></div>
1633. <div class="separator" style="clear: both; text-align: left;">
1634. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Task 1 </b>- How many leaves?</span></div>
1635. <div class="separator" style="clear: both; text-align: left;">
1636. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1637. <div class="separator" style="clear: both; text-align: left;">
1638. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The task is simple to set up. Draw a square in the dirt. See how many leaves you need to fill it up.</span></div>
1639. <div class="separator" style="clear: both; text-align: left;">
1640. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1641. <div class="separator" style="clear: both; text-align: left;">
1642. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">It is measuring area using informal units.</span></div>
1643. <div class="separator" style="clear: both; text-align: left;">
1644. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1645. <div class="separator" style="clear: both; text-align: left;">
1646. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">But you can take this to interesting places:</span></div>
1647. <div class="separator" style="clear: both; text-align: left;">
1648. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1649. <div class="separator" style="clear: both; text-align: left;">
1650. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- move the leaves around in different arrangements to see if the number you need stays the same</span></div>
1651. <div class="separator" style="clear: both; text-align: left;">
1652. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- try using different types of leaves</span></div>
1653. <div class="separator" style="clear: both; text-align: left;">
1654. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- try using different sized shapes to fill up</span></div>
1655. <div class="separator" style="clear: both; text-align: left;">
1656. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- even try using the children themselves to fill up big spaces</span></div>
1657. <div class="separator" style="clear: both; text-align: left;">
1658. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1659. <div class="separator" style="clear: both; text-align: left;">
1660. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">One of the important ideas we want to experience is that "area is the space inside". And we can measure it.</span></div>
1661. <div class="separator" style="clear: both; text-align: left;">
1662. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1663. <div class="separator" style="clear: both; text-align: center;">
1664. <a href="https://1.bp.blogspot.com/-bMsvCzFb58k/XEbodJx9GPI/AAAAAAAAFHI/3in8VE32bcIi8QqOeR5B3wo1JsFwStfkgCLcBGAs/s1600/page%2B1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1405" data-original-width="1013" height="640" src="https://1.bp.blogspot.com/-bMsvCzFb58k/XEbodJx9GPI/AAAAAAAAFHI/3in8VE32bcIi8QqOeR5B3wo1JsFwStfkgCLcBGAs/s640/page%2B1.jpg" width="460" /></a></div>
1665. <div class="separator" style="clear: both; text-align: center;">
1666. <br /></div>
1667. <div class="separator" style="clear: both; text-align: center;">
1668. <i>from the "miniMATHS - Maths Inqiries in Nature" booklet</i></div>
1669. <div class="separator" style="clear: both; text-align: left;">
1670. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1671. <div class="separator" style="clear: both; text-align: left;">
1672. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">One of the important ideas presented in the EYLF outcome #1 relates to perspective. The "How many leaves?" task provides opportunities for students to explore the area of the square in many different ways and to understand that different people will find different solutions.</span></div>
1673. <div class="separator" style="clear: both; text-align: left;">
1674. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1675. <div class="separator" style="clear: both; text-align: left;">
1676. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">"Comparison" is another important concept that this task highlights, finding the area of a shape and comparing materials and strategies to complete it.</span></div>
1677. <div class="separator" style="clear: both; text-align: left;">
1678. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1679. <div class="separator" style="clear: both; text-align: left;">
1680. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">This task is ideal for small group interaction and is firmly based in the Nature Play pedagogy, using natural materials in a natural setting. Students can play with the idea and modify it to pursue their own questions and interests.</span></div>
1681. <div class="separator" style="clear: both; text-align: left;">
1682. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1683. <div class="separator" style="clear: both; text-align: left;">
1684. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">I would be interested in getting feedback from teachers who try out this task in their own schools. I would be particularly interested in hearing what the students have to say. </span></div>
1685. <div class="separator" style="clear: both; text-align: left;">
1686. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1687. <div class="separator" style="clear: both; text-align: left;">
1688. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Let me know.</span></div>
1689. <div class="separator" style="clear: both; text-align: left;">
1690. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1691. <div class="separator" style="clear: both; text-align: left;">
1692. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Thanks.</span></div>
1693. <div class="separator" style="clear: both; text-align: left;">
1694. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1695. <div class="separator" style="clear: both; text-align: left;">
1696. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Here's the miniMATHS website:</span></div>
1697. <div class="separator" style="clear: both; text-align: left;">
1698. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1699. <div class="separator" style="clear: both; text-align: left;">
1700. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><a href="http://www.minimaths.com.au/">http://www.minimaths.com.au</a> </span></div>
1701. <div class="separator" style="clear: both; text-align: left;">
1702. <br /></div>
1703. <div class="separator" style="clear: both; text-align: left;">
1704. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1705. <div class="separator" style="clear: both; text-align: left;">
1706. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1707. <div class="separator" style="clear: both; text-align: left;">
1708. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1709. <div class="separator" style="clear: both; text-align: left;">
1710. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1711. <div class="separator" style="clear: both; text-align: left;">
1712. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
1713. <br />
1714. &lt;br /&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/4066850776397640217/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/01/minimaths-1-how-many-leaves.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/4066850776397640217'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/4066850776397640217'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/01/minimaths-1-how-many-leaves.html' title='miniMATHS - 1. How many leaves?'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://3.bp.blogspot.com/-051n3IqY9wg/XEbhDy_39fI/AAAAAAAAFG4/YEujZ1un1pI_qVYMYLjYUazMalFMOpSzACLcBGAs/s72-c/page%2B2.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-94691317752180735</id><published>2019-01-21T21:28:00.000+11:00</published><updated>2019-01-21T21:28:04.088+11:00</updated><title type='text'>miniMATHS - Maths in Nature Inquiries</title><content type='html'>&lt;br /&gt;
1715. <h2>
1716. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The Background</span></h2>
1717. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1718. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">In 2018, my good friend Sam Hardwicke told me about the </span><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">ACT Government Nature Play grants and suggested</span><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"> I should have a look at putting something in. I submitted an application on behalf of the Canberra Maths Association. We proposed to:</span><br />
1719. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1720. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- write 10 inquiries/tasks/lessons/resources to be used outside in the natural environment</span><br />
1721. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- run 10 workshops with preschools to share these resources</span><br />
1722. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1723. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">We were successful in our application and got the grant. A group of about 10 interested teachers from all levels of education, from early childhood, primary, secondary and tertiary, got together at the CMA conference in August and put together ideas for the 10 tasks. It was a productive time. I went away with pages of notes that I wrote up as the miniMATHS program.</span><br />
1724. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1725. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The 10 tasks we came up with were:</span><br />
1726. <br />
1727. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">1. How many leaves? - using informal units to measure area</span><br />
1728. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">2. Big, bigger, biggest - ordering by length</span><br />
1729. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">3. Same, same, different - identifying common features</span><br />
1730. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">4. One more - you make a number of objects, I'll make one more than you have</span><br />
1731. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">5. Shadows - moving objects to make new shadows</span><br />
1732. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">6. Stacking - building a pile of objects</span><br />
1733. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">7. Make a star - building a radial pattern</span><br />
1734. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">8. Does it float? - playing with floating and sinking</span><br />
1735. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">9. Rolling - looking at objects that roll</span><br />
1736. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">10. Repeat my pattern - if I make a pattern, can you extend it?</span><br />
1737. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1738. <div class="separator" style="clear: both; text-align: center;">
1739. <a href="https://1.bp.blogspot.com/-g8GAm0Bl42w/XEWeQcXiVyI/AAAAAAAAFGg/DKstV7VlTt4khk5fUMLcwcPB--ZI4h2ngCLcBGAs/s1600/star%2Bpattern.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="113" data-original-width="113" height="400" src="https://1.bp.blogspot.com/-g8GAm0Bl42w/XEWeQcXiVyI/AAAAAAAAFGg/DKstV7VlTt4khk5fUMLcwcPB--ZI4h2ngCLcBGAs/s400/star%2Bpattern.jpg" width="400" /></a></div>
1740. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1741. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1742. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">These 10 tasks were shaped into a book. I wanted some sort of printed product that teachers could physically carry with them into the bush, or at least outside into the playground. So some of the grant went into the printing of a book for every preschool in Canberra.</span><br />
1743. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1744. <div class="separator" style="clear: both; text-align: center;">
1745. <a href="https://4.bp.blogspot.com/-f-5Desfd654/XEWef3WZHuI/AAAAAAAAFGo/N-3aUj10yfgZBIGNNk25pkMhJyrwBdfiACLcBGAs/s1600/LBG%2Bat%2Bsunset%2Bwith%2Bwords.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://4.bp.blogspot.com/-f-5Desfd654/XEWef3WZHuI/AAAAAAAAFGo/N-3aUj10yfgZBIGNNk25pkMhJyrwBdfiACLcBGAs/s400/LBG%2Bat%2Bsunset%2Bwith%2Bwords.jpg" width="400" /></a></div>
1746. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1747. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1748. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The 10 tasks have also been uploaded as a website that is available to anyone, not just ACT teachers:</span><br />
1749. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1750. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><a href="http://www.minimaths.com.au/">http://www.minimaths.com.au</a> </span><br />
1751. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1752. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Over the next week or so, I will post a bit more detail about each of the 10 tasks. Maybe you will find them useful. I would be keen to hear any feedback.</span><br />
1753. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1754. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And any Canberra teachers - keep an eye out for the miniMATHS workshops rolling out over January and February.</span><br />
1755. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1756. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Regards.</span><br />
1757. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1758. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1759. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1760. &lt;span style=&quot;font-family: Arial, Helvetica, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/94691317752180735/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/01/minimaths-maths-in-nature-inquiries.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/94691317752180735'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/94691317752180735'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2019/01/minimaths-maths-in-nature-inquiries.html' title='miniMATHS - Maths in Nature Inquiries'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://1.bp.blogspot.com/-g8GAm0Bl42w/XEWeQcXiVyI/AAAAAAAAFGg/DKstV7VlTt4khk5fUMLcwcPB--ZI4h2ngCLcBGAs/s72-c/star%2Bpattern.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-2063720362773438591</id><published>2018-09-12T21:49:00.000+10:00</published><updated>2018-09-12T21:49:03.962+10:00</updated><title type='text'>Adding 5</title><content type='html'>&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif; font-size: large;&quot;&gt;I was interested in exploring how we might represent the addition operation as a pattern. We had been playing with the addition algorithm and looking at adding numbers up to 4 digits.&lt;/span&gt;&lt;br /&gt;
1761. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1762. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">So I took it way back and asked how we might make a pattern to represent adding 5.</span><br />
1763. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1764. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And here is what happened:</span><br />
1765. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1766. <div class="separator" style="clear: both; text-align: center;">
1767. <a href="https://2.bp.blogspot.com/-3lyNosFenlY/W5jzyLqwwVI/AAAAAAAAFFM/9DKVSuBJUswYrIuoUSXR_tqHqBuxedb5ACLcBGAs/s1600/IMG_4402.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://2.bp.blogspot.com/-3lyNosFenlY/W5jzyLqwwVI/AAAAAAAAFFM/9DKVSuBJUswYrIuoUSXR_tqHqBuxedb5ACLcBGAs/s400/IMG_4402.jpg" width="300" /></a></div>
1768. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1769. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1770. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">I was underwhelmed. Surely we could come up with more than simple lines getting bigger by 5 each time. And was it a coincidence that just about every student had represented adding 5 in exactly the same way?</span><br />
1771. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1772. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">So, I drew a long breath and asked our favourite question:</span><br />
1773. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1774. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">"Can you do it a different way?"</span><br />
1775. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1776. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And thankfully the answer was a resounding, "Yes!"</span><br />
1777. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1778. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Here is what our next attempts looked like:</span><br />
1779. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1780. <div class="separator" style="clear: both; text-align: center;">
1781. <a href="https://4.bp.blogspot.com/-0pyDohbSYjU/W5j0ZuxLYAI/AAAAAAAAFFU/b8GtBKgeSZARzUv5-qXUrYmA1dYWVY66gCLcBGAs/s1600/IMG_4403.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1097" data-original-width="1600" height="273" src="https://4.bp.blogspot.com/-0pyDohbSYjU/W5j0ZuxLYAI/AAAAAAAAFFU/b8GtBKgeSZARzUv5-qXUrYmA1dYWVY66gCLcBGAs/s400/IMG_4403.jpg" width="400" /></a></div>
1782. <br />
1783. <div class="separator" style="clear: both; text-align: center;">
1784. <a href="https://4.bp.blogspot.com/-A4t5PBz9v9E/W5j0pOW4GDI/AAAAAAAAFFo/-yfTp6Y85s0CbZ4D7J7yCItzwZThx-iCwCLcBGAs/s1600/IMG_4408.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://4.bp.blogspot.com/-A4t5PBz9v9E/W5j0pOW4GDI/AAAAAAAAFFo/-yfTp6Y85s0CbZ4D7J7yCItzwZThx-iCwCLcBGAs/s400/IMG_4408.jpg" width="300" /></a></div>
1785. <br />
1786. <div class="separator" style="clear: both; text-align: center;">
1787. <a href="https://3.bp.blogspot.com/-1PhQr66btD8/W5j0ueOUFHI/AAAAAAAAFF0/qo_gqCr0cYcR_9s-3L1VUaNZ4ZAqUZHnQCLcBGAs/s1600/IMG_4410.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://3.bp.blogspot.com/-1PhQr66btD8/W5j0ueOUFHI/AAAAAAAAFF0/qo_gqCr0cYcR_9s-3L1VUaNZ4ZAqUZHnQCLcBGAs/s400/IMG_4410.jpg" width="400" /></a></div>
1788. <br />
1789. <div class="separator" style="clear: both; text-align: center;">
1790. <a href="https://2.bp.blogspot.com/-1s2cG6hzTA0/W5j0vN7cnZI/AAAAAAAAFF4/Ndny_pq4NVwuGplqIj_JyOV3biroAAcFQCLcBGAs/s1600/IMG_4411.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://2.bp.blogspot.com/-1s2cG6hzTA0/W5j0vN7cnZI/AAAAAAAAFF4/Ndny_pq4NVwuGplqIj_JyOV3biroAAcFQCLcBGAs/s400/IMG_4411.jpg" width="400" /></a></div>
1791. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1792. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1793. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Several representations looked at groups of 5 being stacked up on top of each other. An interesting idea - take it into another dimension - but similar to the idea of parallel lines.</span><br />
1794. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1795. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1796. <div class="separator" style="clear: both; text-align: center;">
1797. <a href="https://4.bp.blogspot.com/-Tr-L1tJh3fU/W5j0yc99w7I/AAAAAAAAFGY/vXoS1h-uK4oR9wnTqUr9S93S1K2GnXpjACEwYBhgL/s1600/IMG_4414.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://4.bp.blogspot.com/-Tr-L1tJh3fU/W5j0yc99w7I/AAAAAAAAFGY/vXoS1h-uK4oR9wnTqUr9S93S1K2GnXpjACEwYBhgL/s320/IMG_4414.jpg" width="240" /></a></div>
1798. <br />
1799. <div class="separator" style="clear: both; text-align: center;">
1800. <a href="https://2.bp.blogspot.com/-12tAsESXSV4/W5j0v08wAUI/AAAAAAAAFGQ/57IIp8Kgq-wlF0BuDfbvghrTRaB5yj1EwCEwYBhgL/s1600/IMG_4412.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://2.bp.blogspot.com/-12tAsESXSV4/W5j0v08wAUI/AAAAAAAAFGQ/57IIp8Kgq-wlF0BuDfbvghrTRaB5yj1EwCEwYBhgL/s320/IMG_4412.jpg" width="240" /></a></div>
1801. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1802. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Two different students looked at representing the idea of adding 5 as an array. </span><br />
1803. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1804. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1805. <div class="separator" style="clear: both; text-align: center;">
1806. <a href="https://3.bp.blogspot.com/-TLAXKy5izGg/W5j0j8hjH8I/AAAAAAAAFGY/n76gdtNiRk8BV7Pyvak7vxIZshejJPbxwCEwYBhgL/s1600/IMG_4406.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://3.bp.blogspot.com/-TLAXKy5izGg/W5j0j8hjH8I/AAAAAAAAFGY/n76gdtNiRk8BV7Pyvak7vxIZshejJPbxwCEwYBhgL/s400/IMG_4406.jpg" width="300" /></a></div>
1807. <br />
1808. <div class="separator" style="clear: both; text-align: center;">
1809. <a href="https://2.bp.blogspot.com/-BCVS2-KS0oA/W5j0rToykkI/AAAAAAAAFGM/aIMYMyFLaK0mouiclqK2K-CuBw6fGUasgCEwYBhgL/s1600/IMG_4409.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://2.bp.blogspot.com/-BCVS2-KS0oA/W5j0rToykkI/AAAAAAAAFGM/aIMYMyFLaK0mouiclqK2K-CuBw6fGUasgCEwYBhgL/s400/IMG_4409.jpg" width="300" /></a></div>
1810. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1811. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Then we had 2 who make a circular pattern. </span><br />
1812. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1813. <div class="separator" style="clear: both; text-align: center;">
1814. <a href="https://3.bp.blogspot.com/-oYtxtIGWKyI/W5j0fDXiqOI/AAAAAAAAFGI/eISia4ySCtYIOR3gnKxvm_csA7IV0ryMgCEwYBhgL/s1600/IMG_4405.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://3.bp.blogspot.com/-oYtxtIGWKyI/W5j0fDXiqOI/AAAAAAAAFGI/eISia4ySCtYIOR3gnKxvm_csA7IV0ryMgCEwYBhgL/s400/IMG_4405.jpg" width="300" /></a></div>
1815. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1816. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And also a radial pattern.</span><br />
1817. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1818. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1819. <div class="separator" style="clear: both; text-align: center;">
1820. <a href="https://4.bp.blogspot.com/-Jd3NH8WpcmQ/W5j0xHSLMGI/AAAAAAAAFGU/xO2yGdtx-DQOcZM6jkT8Ycqor9EEXVuSwCEwYBhgL/s1600/IMG_4413.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://4.bp.blogspot.com/-Jd3NH8WpcmQ/W5j0xHSLMGI/AAAAAAAAFGU/xO2yGdtx-DQOcZM6jkT8Ycqor9EEXVuSwCEwYBhgL/s400/IMG_4413.jpg" width="400" /></a></div>
1821. <br />
1822. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Then we had a few interesting ideas. Here, the student has decided to start at 3 (the central group of light blue lids) and then adding groups of 5 at each end. Her pattern went 3, 8, 13, 18...</span><br />
1823. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1824. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1825. <div class="separator" style="clear: both; text-align: center;">
1826. <a href="https://1.bp.blogspot.com/-4hnRyQrX8to/W5j0d_PlnAI/AAAAAAAAFGY/FwvP9IYSfBwxQ89OSsywzhLs1Gi6E92awCEwYBhgL/s1600/IMG_4404.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://1.bp.blogspot.com/-4hnRyQrX8to/W5j0d_PlnAI/AAAAAAAAFGY/FwvP9IYSfBwxQ89OSsywzhLs1Gi6E92awCEwYBhgL/s400/IMG_4404.jpg" width="300" /></a></div>
1827. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1828. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">This was a rather unusual idea. I can see the 5 blue lids. I can see several rows that have 5 yellow lids. But I could also see lots with 6 as well. What was going on?</span><br />
1829. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1830. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">"Well, you can start at any lid, and then count 5 in any direction. And then keep going."</span><br />
1831. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1832. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Well, that certainly took it to places I wasn't expecting.</span><br />
1833. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1834. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And then we had this one:</span><br />
1835. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1836. <div class="separator" style="clear: both; text-align: center;">
1837. <a href="https://2.bp.blogspot.com/-VMPBCDc0kf0/W5j0m-NWAtI/AAAAAAAAFGI/y4VtoidF21YPsDQoeeE86fv0Ysw33bFIACEwYBhgL/s1600/IMG_4407.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://2.bp.blogspot.com/-VMPBCDc0kf0/W5j0m-NWAtI/AAAAAAAAFGI/y4VtoidF21YPsDQoeeE86fv0Ysw33bFIACEwYBhgL/s400/IMG_4407.jpg" width="300" /></a></div>
1838. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1839. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">So, this student decided to reinvent numbers, place value, the counting system - everything.</span><br />
1840. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1841. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Each group of lids represents a number in the counting by 5s pattern (5, 10, 15, 20, 25 etc) but the number of lids is not relevant. Each group has a unique arrangement, demonstrating an understanding that all numbers are unique and represent unique values. </span><br />
1842. <br />
1843. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">So much more interesting than a series of parallel lines.</span><br />
1844. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1845. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Like it. Well done, Year 2.</span><br />
1846. <div>
1847. <br /></div>
1848. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1849. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1850. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1851. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1852. &lt;span style=&quot;font-family: Arial, Helvetica, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/2063720362773438591/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/09/adding-5.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/2063720362773438591'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/2063720362773438591'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/09/adding-5.html' title='Adding 5'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://2.bp.blogspot.com/-3lyNosFenlY/W5jzyLqwwVI/AAAAAAAAFFM/9DKVSuBJUswYrIuoUSXR_tqHqBuxedb5ACLcBGAs/s72-c/IMG_4402.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-6485723054720412193</id><published>2018-09-08T09:56:00.000+10:00</published><updated>2018-09-08T09:56:08.114+10:00</updated><title type='text'>AMSI 2018 Excellence in Teaching Award</title><content type='html'>&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
1853. </div>
1854. <div style="margin-left: 1em; margin-right: 1em;">
1855. </div>
1856. <br />
1857. <br />
1858. <div class="separator" style="clear: both; text-align: center;">
1859. </div>
1860. <div style="margin-left: 1em; margin-right: 1em;">
1861. </div>
1862. <br />
1863. <br />
1864. <br />
1865. <br />
1866. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">I was honoured yesterday by the Australian Mathematical Sciences Institute (AMSI) along with 9 other outstanding Australian teachers and received an "Excellence in Teaching" award. </span><br />
1867. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1868. <br />
1869. <div class="separator" style="clear: both; text-align: center;">
1870. <a href="https://scontent-syd2-1.xx.fbcdn.net/v/t1.0-9/41107276_2513828998635230_454653482629070848_n.jpg?_nc_cat=0&oh=153c252d728271334368c42c857b585f&oe=5BF3AB89" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Image may contain: one or more people" border="0" height="300" src="https://scontent-syd2-1.xx.fbcdn.net/v/t1.0-9/41107276_2513828998635230_454653482629070848_n.jpg?_nc_cat=0&oh=153c252d728271334368c42c857b585f&oe=5BF3AB89" width="400" /></a></div>
1871. <div class="separator" style="clear: both; text-align: center;">
1872. <br /></div>
1873. <div class="separator" style="clear: both; text-align: center;">
1874. <br /></div>
1875. <div class="separator" style="clear: both; text-align: center;">
1876. <a href="https://pbs.twimg.com/media/Dmdx3pdU8AA4vzg.jpg:large" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://pbs.twimg.com/media/Dmdx3pdU8AA4vzg.jpg:large" width="300" /></a></div>
1877. <br />
1878. <div style="text-align: center;">
1879. This is me with BHP Principal, Inclusion and Diversity Fiona Vines.</div>
1880. <div style="text-align: center;">
1881. <br /></div>
1882. <div style="text-align: center;">
1883. <br /></div>
1884. <div style="text-align: left;">
1885. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The Canberra Times, our local newspaper, did a very sympathetic write up about me, though I'm not sure about the "rockstar" bit:</span></div>
1886. <br />
1887. <div style="text-align: center;">
1888. <a href="https://www.canberratimes.com.au/national/act/does-canberra-have-its-own-rockstar-maths-teacher-20180906-p5024y.html" target="_blank"><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Does Canberra have its own rockstar maths teacher?</span></a></div>
1889. <br />
1890. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">I would like to thank everyone who has supported me in my mathematical journey, starting with my inspirational and extremely patient wife, my family, my colleagues, you - the readers of this blog - and ultimately my students who challenge me to think clearly and to be creative every day.</span><br />
1891. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1892. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Regards</span><br />
1893. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1894. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Bruce</span><br />
1895. <br />
1896. &lt;br /&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/6485723054720412193/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/09/amsi-2018-excellence-in-teaching-award.html#comment-form' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/6485723054720412193'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/6485723054720412193'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/09/amsi-2018-excellence-in-teaching-award.html' title='AMSI 2018 Excellence in Teaching Award'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-5571805505500284646</id><published>2018-08-21T22:22:00.002+10:00</published><updated>2018-08-21T22:22:35.652+10:00</updated><title type='text'>Nets of Cubes</title><content type='html'>&lt;span style=&quot;font-family: Arial, Helvetica, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;
1897. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">We are exploring polyhedra in Year 2 this week. Yesterday we had a great time playing with shadows and looking at what could be made from a selection of different objects.</span><br />
1898. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1899. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Today we wondered what a cube would look like if you "unfolded" it - laying out each face flat on the ground.</span><br />
1900. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1901. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The kids, perceptive as ever, thought they knew how to do this. With little prompting, they headed off with paper and rulers to make some nets.</span><br />
1902. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1903. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Once everyone had made a net, I asked them to bring them back to the group and share them. Every student had produced a net that looked like this:</span><br />
1904. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1905. <div class="separator" style="clear: both; text-align: center;">
1906. <a href="https://3.bp.blogspot.com/-FQ4ruMuGI9w/W3v-HedNUnI/AAAAAAAAFDw/pCcwNwepEfUF6bwMnzDkoQdSpHnJAAP5gCLcBGAs/s1600/IMG_4302.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://3.bp.blogspot.com/-FQ4ruMuGI9w/W3v-HedNUnI/AAAAAAAAFDw/pCcwNwepEfUF6bwMnzDkoQdSpHnJAAP5gCLcBGAs/s320/IMG_4302.jpg" width="240" /></a></div>
1907. <br />
1908. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1909. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Every student - except one. His net looked like this:</span><br />
1910. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1911. <div class="separator" style="clear: both; text-align: center;">
1912. <a href="https://1.bp.blogspot.com/-pMhqIIVrktk/W3wDDlAhoNI/AAAAAAAAFE4/pKOyEJAdU2ApAO152O16EqFvkGhP1eD6ACLcBGAs/s1600/IMG_4327.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-pMhqIIVrktk/W3wDDlAhoNI/AAAAAAAAFE4/pKOyEJAdU2ApAO152O16EqFvkGhP1eD6ACLcBGAs/s320/IMG_4327.jpg" width="240" /></a></div>
1913. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1914. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1915. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Time for some provocative teacher action. Was it possible that there would be more than one way to make the net of a cube? Is it really true? Are there more ways out there that we haven't found yet? Could we possibly explore and see what we might find?</span><br />
1916. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1917. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">The kids leapt into it. All except one student, who refused to believe there might be other ways. He was dogmatic - there could only be two ways - the two ways we had already found.</span><br />
1918. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1919. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And then the other students started to produce new ways to unfold the cube. Here are a few examples:</span><br />
1920. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1921. <div class="separator" style="clear: both; text-align: center;">
1922. <a href="https://4.bp.blogspot.com/-UQ-3frzCYWU/W3v_Jn62HNI/AAAAAAAAFD8/5A0xcqw8YrwSuevi8YHczvL4bop-0keYgCLcBGAs/s1600/IMG_4306.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://4.bp.blogspot.com/-UQ-3frzCYWU/W3v_Jn62HNI/AAAAAAAAFD8/5A0xcqw8YrwSuevi8YHczvL4bop-0keYgCLcBGAs/s320/IMG_4306.jpg" width="240" /></a></div>
1923. <br />
1924. <div class="separator" style="clear: both; text-align: center;">
1925. <a href="https://2.bp.blogspot.com/-xuE4YcD_oVo/W3v_LgzMVuI/AAAAAAAAFEA/tB3KrKCfVAkzq9jx1biXySyVgO0n380MQCLcBGAs/s1600/IMG_4314.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://2.bp.blogspot.com/-xuE4YcD_oVo/W3v_LgzMVuI/AAAAAAAAFEA/tB3KrKCfVAkzq9jx1biXySyVgO0n380MQCLcBGAs/s320/IMG_4314.jpg" width="240" /></a></div>
1926. <br />
1927. <div class="separator" style="clear: both; text-align: center;">
1928. <a href="https://2.bp.blogspot.com/-5wI4VslJPYg/W3v_L5onHeI/AAAAAAAAFEE/7dUTzVjiGB4VtUXSl61HuY9Z1cvBxllOwCLcBGAs/s1600/IMG_4315.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://2.bp.blogspot.com/-5wI4VslJPYg/W3v_L5onHeI/AAAAAAAAFEE/7dUTzVjiGB4VtUXSl61HuY9Z1cvBxllOwCLcBGAs/s320/IMG_4315.jpg" width="240" /></a></div>
1929. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1930. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1931. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">It only took ten minutes and we already had about 8 different nets for the cube.</span><br />
1932. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1933. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">And in the process, we also discovered something else really interesting - there are some "nets" made up of 6 squares that wouldn't fold up into a cube. Here are a few of those:</span><br />
1934. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1935. <div class="separator" style="clear: both; text-align: center;">
1936. <a href="https://2.bp.blogspot.com/-njvoWE0JAOk/W3v_yjAA45I/AAAAAAAAFEQ/qPeWB8DmUrAh4HTeM_TD5tb13jWzx7GlwCLcBGAs/s1600/IMG_4303.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://2.bp.blogspot.com/-njvoWE0JAOk/W3v_yjAA45I/AAAAAAAAFEQ/qPeWB8DmUrAh4HTeM_TD5tb13jWzx7GlwCLcBGAs/s320/IMG_4303.jpg" width="240" /></a></div>
1937. <br />
1938. <div class="separator" style="clear: both; text-align: center;">
1939. <a href="https://3.bp.blogspot.com/-RE2YiYaqX4Y/W3v_2Cj6qHI/AAAAAAAAFEU/cob8eyvULaYRGiv0c0z9O8E6LOyjXx-yACLcBGAs/s1600/IMG_4318.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://3.bp.blogspot.com/-RE2YiYaqX4Y/W3v_2Cj6qHI/AAAAAAAAFEU/cob8eyvULaYRGiv0c0z9O8E6LOyjXx-yACLcBGAs/s320/IMG_4318.jpg" width="240" /></a></div>
1940. <br />
1941. <div class="separator" style="clear: both; text-align: center;">
1942. <a href="https://2.bp.blogspot.com/-6U5S-QB2N9Y/W3v_2t0f3LI/AAAAAAAAFEY/YZq-CEAH_RwJCASls1xt9jL8XBwthmumgCLcBGAs/s1600/IMG_4319.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://2.bp.blogspot.com/-6U5S-QB2N9Y/W3v_2t0f3LI/AAAAAAAAFEY/YZq-CEAH_RwJCASls1xt9jL8XBwthmumgCLcBGAs/s320/IMG_4319.jpg" width="240" /></a></div>
1943. <br />
1944. <div class="separator" style="clear: both; text-align: center;">
1945. <a href="https://1.bp.blogspot.com/-xvYvpgOCAZg/W3v_3GYdwJI/AAAAAAAAFEc/TJqp5c5_5jYLBVhikdXavlSHKEJ7Gzs1wCLcBGAs/s1600/IMG_4322.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-xvYvpgOCAZg/W3v_3GYdwJI/AAAAAAAAFEc/TJqp5c5_5jYLBVhikdXavlSHKEJ7Gzs1wCLcBGAs/s320/IMG_4322.jpg" width="240" /></a></div>
1946. <br />
1947. <div class="separator" style="clear: both; text-align: center;">
1948. <a href="https://3.bp.blogspot.com/-WQ9MshOg2SE/W3v_4hoLRDI/AAAAAAAAFEg/7xy1qQJ8PqsQ3H48LLN63bdXhp0QhqGgACLcBGAs/s1600/IMG_4323.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://3.bp.blogspot.com/-WQ9MshOg2SE/W3v_4hoLRDI/AAAAAAAAFEg/7xy1qQJ8PqsQ3H48LLN63bdXhp0QhqGgACLcBGAs/s320/IMG_4323.jpg" width="240" /></a></div>
1949. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1950. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1951. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Interesting learning for Year 2 students. Because by exploring the arrangements that wouldn't work, they were able to come up with some "rules" for their nets:</span><br />
1952. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1953. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">1. It has to have 6 squares</span><br />
1954. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1955. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">2. If it is based around a line of 4, you need one square off the the right of the line and another one of to the left.</span><br />
1956. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1957. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Here is what the classroom floor looked like after 25 minutes of exploring:</span><br />
1958. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1959. <div class="separator" style="clear: both; text-align: center;">
1960. <a href="https://2.bp.blogspot.com/-ZNh6BEF0RAA/W3wD2kega-I/AAAAAAAAFFA/Yyrg_oe5ZeouvHrgCANBB5K9yCdVFmcNACLcBGAs/s1600/IMG_4325.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://2.bp.blogspot.com/-ZNh6BEF0RAA/W3wD2kega-I/AAAAAAAAFFA/Yyrg_oe5ZeouvHrgCANBB5K9yCdVFmcNACLcBGAs/s400/IMG_4325.jpg" width="400" /></a></div>
1961. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1962. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1963. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">We were not convinced that we had found all of them - in fact I knew that we hadn't.</span><br />
1964. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1965. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">So it was music to my ears when one girl asked, "Can we keep doing this at home tonight?"</span><br />
1966. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1967. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Taking action. </span><br />
1968. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1969. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">I wonder what we will see in the morning.</span><br />
1970. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1971. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1972. &lt;span style=&quot;font-family: Arial, Helvetica, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/5571805505500284646/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/08/nets-of-cubes.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/5571805505500284646'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/5571805505500284646'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/08/nets-of-cubes.html' title='Nets of Cubes'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://3.bp.blogspot.com/-FQ4ruMuGI9w/W3v-HedNUnI/AAAAAAAAFDw/pCcwNwepEfUF6bwMnzDkoQdSpHnJAAP5gCLcBGAs/s72-c/IMG_4302.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-2856490341136811923</id><published>2018-08-16T12:39:00.001+10:00</published><updated>2018-08-16T12:39:24.791+10:00</updated><title type='text'>400 000</title><content type='html'>&lt;br /&gt;
1973. <br />
1974. <br />
1975. <br />
1976. <div class="separator" style="clear: both; text-align: center;">
1977. <a href="https://2.bp.blogspot.com/-cdufqR9f57Y/W3TjBtn4WiI/AAAAAAAAFDk/P41fWAVkBlgDvvS6y0QotE2nW9vo73N_QCLcBGAs/s1600/400000.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="720" data-original-width="1280" height="225" src="https://2.bp.blogspot.com/-cdufqR9f57Y/W3TjBtn4WiI/AAAAAAAAFDk/P41fWAVkBlgDvvS6y0QotE2nW9vo73N_QCLcBGAs/s400/400000.jpg" width="400" /></a></div>
1978. <br />
1979. <br />
1980. <br />
1981. <div class="separator" style="clear: both; text-align: center;">
1982. <a href="https://1.bp.blogspot.com/-Fh1AUZ7VGns/W3TiVX350lI/AAAAAAAAFDc/vCFfSdtIE2EbaDjvp0LZSJQcUflNV934ACLcBGAs/s1600/Screen%2BShot%2B2018-08-16%2Bat%2B12.31.58%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="470" data-original-width="1554" height="120" src="https://1.bp.blogspot.com/-Fh1AUZ7VGns/W3TiVX350lI/AAAAAAAAFDc/vCFfSdtIE2EbaDjvp0LZSJQcUflNV934ACLcBGAs/s400/Screen%2BShot%2B2018-08-16%2Bat%2B12.31.58%2BPM.png" width="400" /></a></div>
1983. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1984. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1985. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1986. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Data from the blog - cracked 400 000 views yesterday, thanks to some enthusiastic students at ACU Canberra looking at some of the work my kids had done - thanks people.</span><br />
1987. <br />
1988. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Looking forward to the next 400 000.</span><br />
1989. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1990. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">PS - Something happened about 18th March 2016. That's the big spike. Lots of traffic came from France - not sure why. </span><br />
1991. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">A PYP event? Maths conference? Cyber hacker?</span><br />
1992. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
1993. &lt;span style=&quot;font-family: Arial, Helvetica, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/2856490341136811923/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/08/400-000.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/2856490341136811923'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/2856490341136811923'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/08/400-000.html' title='400 000'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://2.bp.blogspot.com/-cdufqR9f57Y/W3TjBtn4WiI/AAAAAAAAFDk/P41fWAVkBlgDvvS6y0QotE2nW9vo73N_QCLcBGAs/s72-c/400000.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-5364739874118747576</id><published>2018-08-16T12:16:00.000+10:00</published><updated>2018-08-16T12:16:05.387+10:00</updated><title type='text'>Kids - They Never Cease to Amaze</title><content type='html'>&lt;br /&gt;
1994. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">We were making patterns yesterday. I wanted the kids to make a staircase pattern using Cuisenaire rods. I do this each year with my kids - I just like to see how they will interpret "staircase" and how they will use the materials provided.</span><br />
1995. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1996. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">For some unknown reason, I seem to expect my present class to be "less" than my previous classes - less creative, less perceptive, less able. Maybe I glamourise my previous students and forget their falibilities, remembering only their moments of glory.</span><br />
1997. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
1998. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">Recycling old tasks gives me the opportunity to be surprised - even though I have expectations of what the new students will do, they never cease to amaze me with their own, individual responses.</span><br />
1999. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span>
2000. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">So when we sat down to make a staircase pattern, I thought it was not going to be as good as last year. </span><br />
2001. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span>
2002. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">Here is what we did in 2017:</span><br />
2003. <br />
2004. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><a href="https://authenticinquirymaths.blogspot.com/2017/08/build-staircase-pattern.html" target="_blank">Click here</a></span><br />
2005. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span>
2006. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">And here is what my current class came up with. Just as creative. Just as intuitive. Just as good.</span><br />
2007. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span>
2008. <div class="separator" style="clear: both; text-align: center;">
2009. <a href="https://3.bp.blogspot.com/-aR2aZhgY_0Q/W3Tdw4cLFdI/AAAAAAAAFCI/1Qfug7uessYPZ_hKo3go4XDgjvmYGl3nQCLcBGAs/s1600/IMG_4284.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://3.bp.blogspot.com/-aR2aZhgY_0Q/W3Tdw4cLFdI/AAAAAAAAFCI/1Qfug7uessYPZ_hKo3go4XDgjvmYGl3nQCLcBGAs/s400/IMG_4284.jpg" width="300" /></a></div>
2010. <div class="separator" style="clear: both; text-align: center;">
2011. <br /></div>
2012. <br />
2013. <div class="separator" style="clear: both; text-align: center;">
2014. <a href="https://3.bp.blogspot.com/--ujjTnsJ8Ig/W3TdxAl0wnI/AAAAAAAAFCM/WcJgBNjyxAQM9keJxaFzfYnUIn7N-sswwCLcBGAs/s1600/IMG_4285.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://3.bp.blogspot.com/--ujjTnsJ8Ig/W3TdxAl0wnI/AAAAAAAAFCM/WcJgBNjyxAQM9keJxaFzfYnUIn7N-sswwCLcBGAs/s400/IMG_4285.jpg" width="300" /></a></div>
2015. <div class="separator" style="clear: both; text-align: center;">
2016. <br /></div>
2017. <br />
2018. <div class="separator" style="clear: both; text-align: center;">
2019. <a href="https://4.bp.blogspot.com/-vxhBNd1qW2k/W3TdxdnSQ8I/AAAAAAAAFCQ/xXvwLCwqzk0Kvmf7DJw3HZXyJPrGROaHgCLcBGAs/s1600/IMG_4286.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://4.bp.blogspot.com/-vxhBNd1qW2k/W3TdxdnSQ8I/AAAAAAAAFCQ/xXvwLCwqzk0Kvmf7DJw3HZXyJPrGROaHgCLcBGAs/s400/IMG_4286.jpg" width="300" /></a></div>
2020. <div class="separator" style="clear: both; text-align: center;">
2021. <br /></div>
2022. <br />
2023. <div class="separator" style="clear: both; text-align: center;">
2024. <a href="https://2.bp.blogspot.com/-tTkt-YM9DO8/W3TdyALveWI/AAAAAAAAFCU/V-WTks8dXlsM4EzPZDeYu2euNOKm57S-gCLcBGAs/s1600/IMG_4287.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://2.bp.blogspot.com/-tTkt-YM9DO8/W3TdyALveWI/AAAAAAAAFCU/V-WTks8dXlsM4EzPZDeYu2euNOKm57S-gCLcBGAs/s400/IMG_4287.jpg" width="300" /></a></div>
2025. <div class="separator" style="clear: both; text-align: center;">
2026. <br /></div>
2027. <br />
2028. <div class="separator" style="clear: both; text-align: center;">
2029. <a href="https://3.bp.blogspot.com/-AE_S5r7sROo/W3TdyiR1yXI/AAAAAAAAFCY/As8P9OncMNIzk74cI7WIFPupnUZssi4ewCLcBGAs/s1600/IMG_4288.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://3.bp.blogspot.com/-AE_S5r7sROo/W3TdyiR1yXI/AAAAAAAAFCY/As8P9OncMNIzk74cI7WIFPupnUZssi4ewCLcBGAs/s400/IMG_4288.jpg" width="300" /></a></div>
2030. <div class="separator" style="clear: both; text-align: center;">
2031. <br /></div>
2032. <br />
2033. <div class="separator" style="clear: both; text-align: center;">
2034. <a href="https://1.bp.blogspot.com/-JMGSlgptJJ8/W3Tdy7Y8v5I/AAAAAAAAFCc/8Jek-I-luZsuCz0HQY6Apwaan9JUbCsqACLcBGAs/s1600/IMG_4289.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://1.bp.blogspot.com/-JMGSlgptJJ8/W3Tdy7Y8v5I/AAAAAAAAFCc/8Jek-I-luZsuCz0HQY6Apwaan9JUbCsqACLcBGAs/s400/IMG_4289.jpg" width="300" /></a></div>
2035. <div class="separator" style="clear: both; text-align: center;">
2036. <br /></div>
2037. <br />
2038. <div class="separator" style="clear: both; text-align: center;">
2039. <a href="https://2.bp.blogspot.com/-0u_Nz7G-GWM/W3TdzCGn2LI/AAAAAAAAFCg/mfLdr3cTTtc6YKjbZZcgCcnr6_V_whEQQCLcBGAs/s1600/IMG_4290.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://2.bp.blogspot.com/-0u_Nz7G-GWM/W3TdzCGn2LI/AAAAAAAAFCg/mfLdr3cTTtc6YKjbZZcgCcnr6_V_whEQQCLcBGAs/s400/IMG_4290.jpg" width="300" /></a></div>
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2044. <a href="https://3.bp.blogspot.com/-yV1pqcJzazE/W3TdzaqQ4YI/AAAAAAAAFCk/8c66RHk1racMuPIg_SvuqcXlazmPRCWiACLcBGAs/s1600/IMG_4291.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://3.bp.blogspot.com/-yV1pqcJzazE/W3TdzaqQ4YI/AAAAAAAAFCk/8c66RHk1racMuPIg_SvuqcXlazmPRCWiACLcBGAs/s400/IMG_4291.jpg" width="300" /></a></div>
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2046. <br /></div>
2047. <br />
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2049. <a href="https://1.bp.blogspot.com/-UoPH1uUPoGo/W3Tdzp1dACI/AAAAAAAAFCo/VHHADJi4saQ3pMf1f0QPgoyXZ7Uu1yc9wCLcBGAs/s1600/IMG_4292.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://1.bp.blogspot.com/-UoPH1uUPoGo/W3Tdzp1dACI/AAAAAAAAFCo/VHHADJi4saQ3pMf1f0QPgoyXZ7Uu1yc9wCLcBGAs/s400/IMG_4292.jpg" width="300" /></a></div>
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2054. <a href="https://4.bp.blogspot.com/-fLI1CzAlRGE/W3TdzxoFXvI/AAAAAAAAFCs/0ITzR3CLzBchI5cbgPoa62UFgZYVO1tFQCLcBGAs/s1600/IMG_4293.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://4.bp.blogspot.com/-fLI1CzAlRGE/W3TdzxoFXvI/AAAAAAAAFCs/0ITzR3CLzBchI5cbgPoa62UFgZYVO1tFQCLcBGAs/s400/IMG_4293.jpg" width="300" /></a></div>
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2056. <br /></div>
2057. <br />
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2059. <a href="https://3.bp.blogspot.com/-Xd1iKXIPWa4/W3Td0gFXChI/AAAAAAAAFCw/fRgJf3dk4jwEqG9AdfQSj7vQwGTUNdomACLcBGAs/s1600/IMG_4294.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://3.bp.blogspot.com/-Xd1iKXIPWa4/W3Td0gFXChI/AAAAAAAAFCw/fRgJf3dk4jwEqG9AdfQSj7vQwGTUNdomACLcBGAs/s400/IMG_4294.jpg" width="300" /></a></div>
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2064. <a href="https://2.bp.blogspot.com/--Y85m1fIOCw/W3Td0jPnJlI/AAAAAAAAFC0/avgyAG1xVRwhvswUNHzUUJBCFvJK-Pj-ACLcBGAs/s1600/IMG_4295.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://2.bp.blogspot.com/--Y85m1fIOCw/W3Td0jPnJlI/AAAAAAAAFC0/avgyAG1xVRwhvswUNHzUUJBCFvJK-Pj-ACLcBGAs/s400/IMG_4295.jpg" width="300" /></a></div>
2065. <div class="separator" style="clear: both; text-align: center;">
2066. <br /></div>
2067. <br />
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2069. <a href="https://3.bp.blogspot.com/-931bVf1s4j0/W3Td03xAkWI/AAAAAAAAFC4/0ICe6Ksd9vwgi9YeRHB6gLmbk1tLT70IgCLcBGAs/s1600/IMG_4296.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="320" data-original-width="240" height="400" src="https://3.bp.blogspot.com/-931bVf1s4j0/W3Td03xAkWI/AAAAAAAAFC4/0ICe6Ksd9vwgi9YeRHB6gLmbk1tLT70IgCLcBGAs/s400/IMG_4296.jpg" width="300" /></a></div>
2070. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span>
2071. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span>
2072. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span>
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2074. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span>
2075. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">Kids - they never cease to amaze.</span><br />
2076. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span>
2077. <br />
2078. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2079. &lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/5364739874118747576/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/08/kids-they-never-cease-to-amaze.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/5364739874118747576'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/5364739874118747576'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/08/kids-they-never-cease-to-amaze.html' title='Kids - They Never Cease to Amaze'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://3.bp.blogspot.com/-aR2aZhgY_0Q/W3Tdw4cLFdI/AAAAAAAAFCI/1Qfug7uessYPZ_hKo3go4XDgjvmYGl3nQCLcBGAs/s72-c/IMG_4284.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-799140478787564131</id><published>2018-07-27T10:35:00.000+10:00</published><updated>2018-07-27T10:35:59.515+10:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Length"/><category scheme="http://www.blogger.com/atom/ns#" term="Measurement"/><title type='text'>Knoks, Moks and Snocks</title><content type='html'>&lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;We have been looking at measurement of length this week.&lt;/span&gt;&lt;br /&gt;
2080. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2081. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Today when they came into the room, the kids were faced with this challenge:</span><br />
2082. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2083. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><i>"Overnight, there was an international disaster - all millimetres, centimetres and metres had disappeared. No-one could remember how long the units were. We had to make some new units of measurement. What would we do?"</i></span><br />
2084. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><i><br /></i></span>
2085. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">After a few suggestions, like, "Let's use feet and inches." I encouraged the students to use their creativity to make a new system.</span><br />
2086. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2087. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">We were using our interlocking cubes to make patterns so it was natural that these blocks became out units.</span><br />
2088. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2089. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">I wasn't happy to have this unit be called a "block" so the kids decided to call it a "knok". </span><br />
2090. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2091. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Next step was to decide on the other units. Here is what they came up with:</span><br />
2092. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2093. <br />
2094. <div class="separator" style="clear: both; text-align: center;">
2095. <a href="https://2.bp.blogspot.com/-pTP0ZJwUWrg/W1m62BZyWHI/AAAAAAAAFBM/YWE3mjGXrpUEip2eSXskCZe8fef_4OndgCLcBGAs/s1600/IMG_4198.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="715" data-original-width="1600" height="178" src="https://2.bp.blogspot.com/-pTP0ZJwUWrg/W1m62BZyWHI/AAAAAAAAFBM/YWE3mjGXrpUEip2eSXskCZe8fef_4OndgCLcBGAs/s400/IMG_4198.jpg" width="400" /></a></div>
2096. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2097. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2098. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">It looked like this:</span><br />
2099. <div class="separator" style="clear: both; text-align: center;">
2100. <a href="https://1.bp.blogspot.com/-g0csV5KmETo/W1pn9INz6KI/AAAAAAAAFB4/KM-UgtlvAi4yYcjKsXAOav7_ZZ4etw17ACLcBGAs/s1600/IMG_4203%2Bcopy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="157" data-original-width="228" src="https://1.bp.blogspot.com/-g0csV5KmETo/W1pn9INz6KI/AAAAAAAAFB4/KM-UgtlvAi4yYcjKsXAOav7_ZZ4etw17ACLcBGAs/s1600/IMG_4203%2Bcopy.jpg" /></a></div>
2101. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2102. <br />
2103. <div style="text-align: center;">
2104. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">2 peas = 1 knok</span></div>
2105. <div style="text-align: center;">
2106. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2107. <div style="text-align: center;">
2108. <div class="separator" style="clear: both; text-align: center;">
2109. <a href="https://1.bp.blogspot.com/-X-wZerTMj7Q/W1pn8zEyiNI/AAAAAAAAFB0/VHxk5lvNhhIBRlwle-7GPqiy8MYO10GJQCLcBGAs/s1600/IMG_4204%2Bcopy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="193" data-original-width="385" height="160" src="https://1.bp.blogspot.com/-X-wZerTMj7Q/W1pn8zEyiNI/AAAAAAAAFB0/VHxk5lvNhhIBRlwle-7GPqiy8MYO10GJQCLcBGAs/s320/IMG_4204%2Bcopy.jpg" width="320" /></a></div>
2110. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2111. <div style="text-align: center;">
2112. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">8 knoks = 1 mok</span></div>
2113. <div style="text-align: center;">
2114. <br /></div>
2115. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2116. <br />
2117. <div class="separator" style="clear: both; text-align: center;">
2118. <a href="https://3.bp.blogspot.com/-tLQkkhKWglU/W1m7PNSg0BI/AAAAAAAAFBU/s8Mb30ymzSME8l_HflnCxBIPW6uh9g18ACLcBGAs/s1600/IMG_4197.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="199" data-original-width="1600" height="48" src="https://3.bp.blogspot.com/-tLQkkhKWglU/W1m7PNSg0BI/AAAAAAAAFBU/s8Mb30ymzSME8l_HflnCxBIPW6uh9g18ACLcBGAs/s400/IMG_4197.jpg" width="400" /></a></div>
2119. <div style="text-align: center;">
2120. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">6 moks = 1 snock</span></div>
2121. <div style="text-align: center;">
2122. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2123. <div style="text-align: center;">
2124. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2125. <div style="text-align: left;">
2126. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And once we had a measurement system, we needed to measure something.</span></div>
2127. <div style="text-align: left;">
2128. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2129. <div style="text-align: left;">
2130. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">"What shall we measure?" I asked.</span></div>
2131. <div style="text-align: left;">
2132. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2133. <div style="text-align: left;">
2134. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">"YOU!" was the emphatic reply.</span></div>
2135. <div style="text-align: left;">
2136. <br /></div>
2137. <div class="separator" style="clear: both; text-align: center;">
2138. <a href="https://4.bp.blogspot.com/-vyCLvJupqBM/W1m9PEg3BTI/AAAAAAAAFBg/7MoSiVAIyrMjJYYLh_lmVvnOoA0Pd7v2wCLcBGAs/s1600/IMG_4200.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="820" height="320" src="https://4.bp.blogspot.com/-vyCLvJupqBM/W1m9PEg3BTI/AAAAAAAAFBg/7MoSiVAIyrMjJYYLh_lmVvnOoA0Pd7v2wCLcBGAs/s320/IMG_4200.jpg" width="164" /></a></div>
2139. <div class="separator" style="clear: both; text-align: center;">
2140. <br /></div>
2141. <div class="separator" style="clear: both; text-align: center;">
2142. <br /></div>
2143. <div class="separator" style="clear: both; text-align: left;">
2144. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So I became the first of many to be measured with our new measurement system.</span></div>
2145. <br />
2146. <div class="separator" style="clear: both; text-align: center;">
2147. <a href="https://1.bp.blogspot.com/-fSw-rHwMIDs/W1m9PIKeP4I/AAAAAAAAFBk/47bsSXhsMDMNYfGZIVRJqbl3x02KJ5ReACLcBGAs/s1600/IMG_4202.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="289" data-original-width="1600" height="71" src="https://1.bp.blogspot.com/-fSw-rHwMIDs/W1m9PIKeP4I/AAAAAAAAFBk/47bsSXhsMDMNYfGZIVRJqbl3x02KJ5ReACLcBGAs/s400/IMG_4202.jpg" width="400" /></a></div>
2148. <div style="text-align: left;">
2149. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2150. <div style="text-align: left;">
2151. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Turns out I am 2 snocks, a mok, 3 knoks and 2 peas tall. (Astute students of place value will notice that the 2 peas should be converted to another knok to make 4 knoks.)</span></div>
2152. <div style="text-align: left;">
2153. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2154. <div style="text-align: left;">
2155. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">I don't think it will ever become an internationally recognised system of measurement, but it gave us an opportunity to explore the idea of standard units and how to convert between units of different sizes.</span></div>
2156. <div style="text-align: left;">
2157. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2158. <div style="text-align: center;">
2159. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2160. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2161. &lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/799140478787564131/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/07/knoks-moks-and-snocks.html#comment-form' title='2 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/799140478787564131'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/799140478787564131'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/07/knoks-moks-and-snocks.html' title='Knoks, Moks and Snocks'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://2.bp.blogspot.com/-pTP0ZJwUWrg/W1m62BZyWHI/AAAAAAAAFBM/YWE3mjGXrpUEip2eSXskCZe8fef_4OndgCLcBGAs/s72-c/IMG_4198.jpg" height="72" width="72"/><thr:total>2</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-632569685913215944</id><published>2018-02-12T21:55:00.001+11:00</published><updated>2018-02-15T10:20:27.477+11:00</updated><title type='text'>Is a picture a pattern?</title><content type='html'>&lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;So we are back into the swing of things here in Canberra, Australia.&amp;nbsp;&lt;/span&gt;&lt;br /&gt;
2162. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2163. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And I wanted to push on with the spatial reasoning and pattern making. </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Once again, it was going to be pattern making first up each morning.</span><br />
2164. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2165. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Day 1 of making patterns and my new class surprised me. I put out a variety of materials - pattern blocks, Cuisenaire rods and tangram shapes - to see what they would produce.</span><br />
2166. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2167. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And I could not believe how many of them produced pictures - symmetrical undoubtedly - but pictures just the same. So were they making patterns? Is a symmetrical picture a pattern? </span><br />
2168. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2169. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Rocket ships:</span><br />
2170. <br />
2171. <div class="separator" style="clear: both; text-align: center;">
2172. <a href="https://1.bp.blogspot.com/-4g1ihozXHhk/WoFxJYYV71I/AAAAAAAAE_Q/I58DRhraqxM3tjAGYmcqqc3LrfmEYkE-ACLcBGAs/s1600/IMG_3614.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="772" data-original-width="1600" height="192" src="https://1.bp.blogspot.com/-4g1ihozXHhk/WoFxJYYV71I/AAAAAAAAE_Q/I58DRhraqxM3tjAGYmcqqc3LrfmEYkE-ACLcBGAs/s400/IMG_3614.JPG" width="400" /></a></div>
2173. <br />
2174. <div class="separator" style="clear: both; text-align: center;">
2175. <a href="https://3.bp.blogspot.com/-dwH1102umSk/WoFxJSEShSI/AAAAAAAAE_M/y1CerAYqomYco_WxxpuA9RnMMsO414r-wCLcBGAs/s1600/IMG_3616.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1468" data-original-width="610" height="400" src="https://3.bp.blogspot.com/-dwH1102umSk/WoFxJSEShSI/AAAAAAAAE_M/y1CerAYqomYco_WxxpuA9RnMMsO414r-wCLcBGAs/s400/IMG_3616.JPG" width="165" /></a></div>
2176. <div class="separator" style="clear: both; text-align: center;">
2177. <br /></div>
2178. <div class="separator" style="clear: both; text-align: center;">
2179. <br /></div>
2180. <div class="separator" style="clear: both; text-align: left;">
2181. <br /></div>
2182. <div class="separator" style="clear: both; text-align: left;">
2183. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Monsters and funny faces:</span></div>
2184. <div class="separator" style="clear: both; text-align: center;">
2185. <br /></div>
2186. <div class="separator" style="clear: both; text-align: center;">
2187. <a href="https://4.bp.blogspot.com/-XFwibH2OOL8/WoFxJitb65I/AAAAAAAAE_U/zdXWtpHOOmUNujC4IHfbfDS_kJ8ZFvv8ACLcBGAs/s1600/IMG_3610.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="936" data-original-width="1600" height="233" src="https://4.bp.blogspot.com/-XFwibH2OOL8/WoFxJitb65I/AAAAAAAAE_U/zdXWtpHOOmUNujC4IHfbfDS_kJ8ZFvv8ACLcBGAs/s400/IMG_3610.JPG" width="400" /></a></div>
2188. <br />
2189. <div class="separator" style="clear: both; text-align: center;">
2190. <a href="https://3.bp.blogspot.com/-XqCrr-1Qc3M/WoFxKjyp2yI/AAAAAAAAE_Y/eunANfjez0EXXqsSAqrFSwZZd3fKBPFrwCLcBGAs/s1600/IMG_3619.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1115" data-original-width="1600" height="277" src="https://3.bp.blogspot.com/-XqCrr-1Qc3M/WoFxKjyp2yI/AAAAAAAAE_Y/eunANfjez0EXXqsSAqrFSwZZd3fKBPFrwCLcBGAs/s400/IMG_3619.JPG" width="400" /></a></div>
2191. <br />
2192. <div class="separator" style="clear: both; text-align: center;">
2193. <a href="https://2.bp.blogspot.com/-34AX7wt9XSw/WoFxLMgZ5tI/AAAAAAAAE_c/wYKsfTPtipAoC4UvGINDWvssspaq_SWiQCLcBGAs/s1600/IMG_3621.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1161" height="400" src="https://2.bp.blogspot.com/-34AX7wt9XSw/WoFxLMgZ5tI/AAAAAAAAE_c/wYKsfTPtipAoC4UvGINDWvssspaq_SWiQCLcBGAs/s400/IMG_3621.JPG" width="290" /></a></div>
2194. <br />
2195. <div class="separator" style="clear: both; text-align: center;">
2196. <a href="https://3.bp.blogspot.com/-Hvdp5rkPnLA/WoFxLSMt_1I/AAAAAAAAE_g/WufOLqIK1Ucefm8kWPDHpg2A85oVowyIQCLcBGAs/s1600/IMG_3623.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1439" height="400" src="https://3.bp.blogspot.com/-Hvdp5rkPnLA/WoFxLSMt_1I/AAAAAAAAE_g/WufOLqIK1Ucefm8kWPDHpg2A85oVowyIQCLcBGAs/s400/IMG_3623.JPG" width="358" /></a></div>
2197. <div class="separator" style="clear: both; text-align: center;">
2198. <br /></div>
2199. <div class="separator" style="clear: both; text-align: center;">
2200. <br /></div>
2201. <div class="separator" style="clear: both; text-align: left;">
2202. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Puppy dog:</span></div>
2203. <br />
2204. <div class="separator" style="clear: both; text-align: center;">
2205. <a href="https://4.bp.blogspot.com/-bRZTrsdQEqM/WoFxLhvbpiI/AAAAAAAAE_k/7uqUDYKRYaUzSy4p1howgdqtLhtEtqyXwCLcBGAs/s1600/IMG_3624%2B2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1278" height="400" src="https://4.bp.blogspot.com/-bRZTrsdQEqM/WoFxLhvbpiI/AAAAAAAAE_k/7uqUDYKRYaUzSy4p1howgdqtLhtEtqyXwCLcBGAs/s400/IMG_3624%2B2.JPG" width="318" /></a></div>
2206. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2207. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2208. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So - nice pictures. Were they patterns? </span><br />
2209. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2210. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">I'll leave that one with you.</span>
2211. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2212. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2213. &lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/632569685913215944/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/02/is-picture-puzzle.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/632569685913215944'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/632569685913215944'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2018/02/is-picture-puzzle.html' title='Is a picture a pattern?'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://1.bp.blogspot.com/-4g1ihozXHhk/WoFxJYYV71I/AAAAAAAAE_Q/I58DRhraqxM3tjAGYmcqqc3LrfmEYkE-ACLcBGAs/s72-c/IMG_3614.JPG" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-5167128035944016045</id><published>2017-12-14T22:35:00.000+11:00</published><updated>2017-12-14T22:35:00.117+11:00</updated><title type='text'>Closing down for Christmas and Summer Hols</title><content type='html'>&lt;br /&gt;
2214. <br />
2215. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">If you are wondering, I am on schools holidays until the first week in February.</span><br />
2216. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2217. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Lots to look forward to next year:</span><br />
2218. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2219. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- I'm back on Year 2 - yay!</span><br />
2220. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2221. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- I will be doing some part time lecturing at ACU in Canberra</span><br />
2222. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2223. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- I will be doing a lightning presentation at the SERC conference in Canberra </span><br />
2224. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2225. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- I will be involved with presenting Maths300 workshops</span><br />
2226. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2227. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">- I hope to be playing bagpipes at the War Memorial on ANZAC Day</span><br />
2228. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2229. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Let's see what happens.</span><br />
2230. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2231. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Have a great holiday.</span><br />
2232. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2233. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">BF</span><br />
2234. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2235. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2236. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2237. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2238. &lt;span style=&quot;font-family: Arial, Helvetica, sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/5167128035944016045/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2017/12/closing-down-for-christmas-and-summer.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/5167128035944016045'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/5167128035944016045'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2017/12/closing-down-for-christmas-and-summer.html' title='Closing down for Christmas and Summer Hols'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-6918095598299452953</id><published>2017-11-21T16:15:00.001+11:00</published><updated>2017-11-21T16:15:11.079+11:00</updated><title type='text'>A Proportional Reasoning Sequence</title><content type='html'>&lt;br /&gt;
2239. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">This is a sequence that went over several days. I don't think we are finished (yet) but I wanted to get the initial stages written to clarify my thinking. </span><br />
2240. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2241. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">I was interested in looking at proportional reasoning. We had done a fair bit with fractions (halves, quarters etc). It was becoming obvious that we might benefit from some time looking at the relationships between the values of numbers and how we could represent this with size/length/area to make the relationship visual.</span><br />
2242. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2243. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">I have represented this sequence as "phases". They might be lessons. They might be something else.</span><br />
2244. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2245. <br />
2246. <h2>
2247. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;">Phase 1 </span></h2>
2248. <br />
2249. <div class="separator" style="clear: both; text-align: center;">
2250. <a href="https://1.bp.blogspot.com/-NiPFsXfVKY8/WhOPrvaZEaI/AAAAAAAAE8M/ktLgw69lrO8QMdW-fhhtMVyFPfv5nYwjgCLcBGAs/s1600/IMG_3386.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://1.bp.blogspot.com/-NiPFsXfVKY8/WhOPrvaZEaI/AAAAAAAAE8M/ktLgw69lrO8QMdW-fhhtMVyFPfv5nYwjgCLcBGAs/s400/IMG_3386.JPG" width="400" /></a></div>
2251. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2252. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">I had a stack of coloured strips cut up.</span><br />
2253. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2254. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The red strip is noticeably shorter (24cm) than the other colours (yellow, orange and green are all 29.5cm - the length of a piece of A4 paper). This was deliberate. I wanted the students to refer to the value they were certain of (red = 8) and use this as the basis of their reasoning, rather than simply fold each strip to the fraction of the whole. </span><br />
2255. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2256. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">eg if yellow = 4 (which is half of 8) then I might be tempted to just fold it in half without having to refer to the red unit at all.</span><br />
2257. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2258. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">After a time, two strategies emerged;</span><br />
2259. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2260. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><u>Strategy 1:</u></span><br />
2261. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2262. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Some students decided that all the coloured strips needed to start off as the same length. Then they could fold yellow in half so it equalled 4; fold orange into quarters and then cut off one section to leave 3/4 because 6 = 3/4 of 8; then fold green into 8 parts and cut off 3 parts (5 = 5/8 of 8)</span><br />
2263. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2264. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><u>Strategy 2:</u></span><br />
2265. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2266. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Other students folded the red strip into 8 equal parts and used this as a "ruler" to measure where to cut each of the other strips.</span><br />
2267. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2268. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">This was an interesting starting point. 8 was a good number because finding 4 and 6 was relatively easy but finding 5 required a bit more thinking.</span><br />
2269. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2270. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2271. <h2>
2272. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;">Phase 2</span></h2>
2273. <div>
2274. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;"><br /></span></div>
2275. <div class="separator" style="clear: both; text-align: center;">
2276. <a href="https://1.bp.blogspot.com/-NGWytcRwGQk/WhOUG_sLnOI/AAAAAAAAE8Y/Zn8G4KhA2d8VPvPzicJ3Tc0UcBRmsE80gCLcBGAs/s1600/IMG_3391%2Bcopy.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://1.bp.blogspot.com/-NGWytcRwGQk/WhOUG_sLnOI/AAAAAAAAE8Y/Zn8G4KhA2d8VPvPzicJ3Tc0UcBRmsE80gCLcBGAs/s400/IMG_3391%2Bcopy.JPG" width="400" /></a></div>
2277. <div class="separator" style="clear: both; text-align: center;">
2278. <br /></div>
2279. <div class="separator" style="clear: both; text-align: center;">
2280. <br /></div>
2281. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2282. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And here are the strips I had prepared:</span><br />
2283. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2284. <div class="separator" style="clear: both; text-align: center;">
2285. <a href="https://3.bp.blogspot.com/-5Sa6DvR1Ew4/WhOUSLDfaNI/AAAAAAAAE8c/h3T6EaFspvwgixgH80_LImW7DBNoTcIWQCLcBGAs/s1600/IMG_3390%2Bcopy.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://3.bp.blogspot.com/-5Sa6DvR1Ew4/WhOUSLDfaNI/AAAAAAAAE8c/h3T6EaFspvwgixgH80_LImW7DBNoTcIWQCLcBGAs/s400/IMG_3390%2Bcopy.JPG" width="300" /></a></div>
2286. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2287. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Look - he's done it again. Can't this guy cut the strips to even lengths?</span><br />
2288. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2289. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">No - I wanted to play with the kids' heads again. This time the purple strip (=24cm) was given a value of 6. How would you work out how long the other strips should be to show 1-5?</span><br />
2290. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2291. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The kids pretty quickly realised they would have to find a way to divide the purple strip into 6 equal parts. Here is what happened:</span><br />
2292. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2293. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><u>Strategy 1:</u></span><br />
2294. <br />
2295. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Some students decided that a good way to find 6 equal parts was to fold the strip in half, then half again, then half again, making 8 equal parts. They then cut off two of the sections leaving 6 qual parts. This then became the measure showing where to cut the other strips. </span><br />
2296. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2297. <div class="separator" style="clear: both; text-align: center;">
2298. <a href="https://3.bp.blogspot.com/-1gx06evIQ2A/WhOqNRz2xPI/AAAAAAAAE9E/DD3PVLzot0QNW6ob_ZXGFd8-XaiCpxlQQCLcBGAs/s1600/IMG_3398%2Bcopy.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://3.bp.blogspot.com/-1gx06evIQ2A/WhOqNRz2xPI/AAAAAAAAE9E/DD3PVLzot0QNW6ob_ZXGFd8-XaiCpxlQQCLcBGAs/s400/IMG_3398%2Bcopy.JPG" width="400" /></a></div>
2299. <div class="separator" style="clear: both; text-align: center;">
2300. <br /></div>
2301. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2302. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><u>Strategy 2:</u></span><br />
2303. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2304. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Other students folded the purple strip into 3 parts using the z-fold technique. Then they folded this in half to make 6 equal parts.</span><br />
2305. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2306. <div class="separator" style="clear: both; text-align: center;">
2307. <a href="https://4.bp.blogspot.com/--Jvp3udeiU8/WhOg1jPp7ZI/AAAAAAAAE8s/qV0yN1x1a7EkJEWIHrMfhF2ydy-ilIeewCLcBGAs/s1600/IMG_3397%2Bcopy.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://4.bp.blogspot.com/--Jvp3udeiU8/WhOg1jPp7ZI/AAAAAAAAE8s/qV0yN1x1a7EkJEWIHrMfhF2ydy-ilIeewCLcBGAs/s400/IMG_3397%2Bcopy.JPG" width="400" /></a></div>
2308. <br />
2309. <br />
2310. <div class="separator" style="clear: both; text-align: center;">
2311. <a href="https://1.bp.blogspot.com/-R-EO_w123BU/WhOqNQdIa1I/AAAAAAAAE88/2rVGC-wJ7asEb3FuQzJXqC9vTCjf3iNiACLcBGAs/s1600/IMG_3400%2Bcopy.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://1.bp.blogspot.com/-R-EO_w123BU/WhOqNQdIa1I/AAAAAAAAE88/2rVGC-wJ7asEb3FuQzJXqC9vTCjf3iNiACLcBGAs/s400/IMG_3400%2Bcopy.JPG" width="400" /></a></div>
2312. <br />
2313. <br />
2314. <div class="separator" style="clear: both; text-align: center;">
2315. </div>
2316. <div class="separator" style="clear: both; text-align: center;">
2317. <a href="https://2.bp.blogspot.com/-RieyhRKH5uc/WhOqPTzoQmI/AAAAAAAAE9Q/GSwPe1OrGPUFajue1XdYghmeFp_1IwzUQCLcBGAs/s1600/IMG_3404%2Bcopy.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://2.bp.blogspot.com/-RieyhRKH5uc/WhOqPTzoQmI/AAAAAAAAE9Q/GSwPe1OrGPUFajue1XdYghmeFp_1IwzUQCLcBGAs/s400/IMG_3404%2Bcopy.JPG" width="300" /></a></div>
2318. <div class="separator" style="clear: both; text-align: center;">
2319. <br /></div>
2320. <div class="separator" style="clear: both; text-align: center;">
2321. <br /></div>
2322. <div class="separator" style="clear: both; text-align: left;">
2323. <br /></div>
2324. <div class="separator" style="clear: both; text-align: left;">
2325. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><u>Strategy 3</u></span></div>
2326. <div class="separator" style="clear: both; text-align: left;">
2327. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><u><br /></u></span></div>
2328. <div class="separator" style="clear: both; text-align: left;">
2329. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Not the most efficient strategy but totally effective, this student worked out how long a unit was, and then proceeded to cut out individual units in each colour and used these to establish the numbers 1-6.</span></div>
2330. <div class="separator" style="clear: both; text-align: left;">
2331. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
2332. <br />
2333. <div class="separator" style="clear: both; text-align: center;">
2334. <a href="https://1.bp.blogspot.com/-LxZ2nmsrFTk/WhOqQgUcxMI/AAAAAAAAE9Y/HXJq-ZxiDbMnomWqSA79rsTdaAUsYJZHQCLcBGAs/s1600/IMG_3408%2Bcopy.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://1.bp.blogspot.com/-LxZ2nmsrFTk/WhOqQgUcxMI/AAAAAAAAE9Y/HXJq-ZxiDbMnomWqSA79rsTdaAUsYJZHQCLcBGAs/s400/IMG_3408%2Bcopy.JPG" width="300" /></a></div>
2335. <div class="separator" style="clear: both; text-align: center;">
2336. <br /></div>
2337. <div class="separator" style="clear: both; text-align: center;">
2338. <br /></div>
2339. <div class="separator" style="clear: both; text-align: left;">
2340. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><u>What we found out</u></span></div>
2341. <div class="separator" style="clear: both; text-align: left;">
2342. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><u><br /></u></span></div>
2343. <div class="separator" style="clear: both; text-align: left;">
2344. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">When we put these staircases into our 1cm grid books, we quickly found out that there was a number pattern. By counting how many squares high each step of the staircase was we found a counting-on pattern.</span></div>
2345. <div class="separator" style="clear: both; text-align: left;">
2346. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
2347. <div class="separator" style="clear: both; text-align: left;">
2348. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">For students who used Strategy 1 or 3, the purple strip was 18cm long. They had started with 24cm then folded it into 8ths and then cut of 2/8 to make 6 equal parts. So their number pattern was the counting by 3's pattern.</span></div>
2349. <div class="separator" style="clear: both; text-align: left;">
2350. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
2351. <div class="separator" style="clear: both; text-align: center;">
2352. <a href="https://1.bp.blogspot.com/-i93JMrCEbFE/WhOuleZpryI/AAAAAAAAE9o/ry8tYTeI_QYF4sbWZVlV-eYB1T-FVjWnwCLcBGAs/s1600/IMG_3420.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1600" height="320" src="https://1.bp.blogspot.com/-i93JMrCEbFE/WhOuleZpryI/AAAAAAAAE9o/ry8tYTeI_QYF4sbWZVlV-eYB1T-FVjWnwCLcBGAs/s320/IMG_3420.JPG" width="320" /></a></div>
2353. <div class="separator" style="clear: both; text-align: left;">
2354. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
2355. <div class="separator" style="clear: both; text-align: left;">
2356. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
2357. <div class="separator" style="clear: both; text-align: left;">
2358. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">For students who used Strategy 2, the pattern was the counting by 4's pattern, since 6 = 24cm, therefore 1 = 4cm.</span></div>
2359. <div class="separator" style="clear: both; text-align: left;">
2360. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span></div>
2361. <br />
2362. <div class="separator" style="clear: both; text-align: center;">
2363. <a href="https://4.bp.blogspot.com/-Mc4a_lSrnGg/WhOqokz6SNI/AAAAAAAAE9c/1TovLwODsdg4tm-odyN9GB4B-zZDM9zcgCLcBGAs/s1600/IMG_3405%2Bcopy.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://4.bp.blogspot.com/-Mc4a_lSrnGg/WhOqokz6SNI/AAAAAAAAE9c/1TovLwODsdg4tm-odyN9GB4B-zZDM9zcgCLcBGAs/s400/IMG_3405%2Bcopy.JPG" width="300" /></a></div>
2364. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2365. <br />
2366. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Interestingly, no-one had considered using a ruler. They were busy exploring the relationships.</span><br />
2367. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2368. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">We also found out it was important to be accurate. In this picture (below) pink = 1 and blue = 5. But when they are put together, they are longer than the purple, which is meant to equal 6. This student has not fully understood the task. Their purple is folded into 8 sections. Their other units for 1-5 are a random series of increasing lengths. </span><br />
2369. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2370. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">At this point we paused and reflected on what we needed to do.</span><br />
2371. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2372. <div class="separator" style="clear: both; text-align: center;">
2373. <a href="https://4.bp.blogspot.com/-5aXzs3Sswhc/WhOqPL_P9qI/AAAAAAAAE9M/ofuw-Q1aiyoUIJWN5cp2qJFaBbSN-t7WQCLcBGAs/s1600/IMG_3403%2Bcopy.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://4.bp.blogspot.com/-5aXzs3Sswhc/WhOqPL_P9qI/AAAAAAAAE9M/ofuw-Q1aiyoUIJWN5cp2qJFaBbSN-t7WQCLcBGAs/s400/IMG_3403%2Bcopy.JPG" width="400" /></a></div>
2374. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2375. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2376. <h2>
2377. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;">Phase 3</span></h2>
2378. <div>
2379. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2380. <div class="separator" style="clear: both; text-align: center;">
2381. <a href="https://4.bp.blogspot.com/-rv-jqqtnRE4/WhOwJHgDx2I/AAAAAAAAE90/grC04NvwmDw6F9-l9ehVF5WbfDV-goRigCLcBGAs/s1600/IMG_3411%2Bcopy.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://4.bp.blogspot.com/-rv-jqqtnRE4/WhOwJHgDx2I/AAAAAAAAE90/grC04NvwmDw6F9-l9ehVF5WbfDV-goRigCLcBGAs/s400/IMG_3411%2Bcopy.JPG" width="400" /></a></div>
2382. <div>
2383. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2384. <div>
2385. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2386. <div>
2387. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And so we moved to the next proposition. If you are given a unit (such as pink = 4) can you find the numbers less than and more than?</span></div>
2388. <div>
2389. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2390. <div>
2391. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The students had made the Cuisenaire staircase hundreds of times. They quickly noticed that I had conveniently provided strips of paper using all 10 of the Cuisenaire colours.</span></div>
2392. <div>
2393. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2394. <div class="separator" style="clear: both; text-align: center;">
2395. <a href="https://1.bp.blogspot.com/-UWI_lNoqSL4/WhOxm6Yce-I/AAAAAAAAE-I/oqA-MjCUiv83HtaiAfc8oxWF14BErYm9ACLcBGAs/s1600/IMG_3410.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://1.bp.blogspot.com/-UWI_lNoqSL4/WhOxm6Yce-I/AAAAAAAAE-I/oqA-MjCUiv83HtaiAfc8oxWF14BErYm9ACLcBGAs/s400/IMG_3410.JPG" width="400" /></a></div>
2396. <div class="separator" style="clear: both; text-align: center;">
2397. <br /></div>
2398. <div class="separator" style="clear: both; text-align: center;">
2399. <i>This is the scene that greeted the kids when they came into the room.</i></div>
2400. <div>
2401. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2402. <div>
2403. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">They also noticed that the coloured strips were of varying sizes. Once again, I didn't want them to rely on any value other then pink = 4.</span></div>
2404. <div>
2405. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2406. <div class="separator" style="clear: both; text-align: center;">
2407. <a href="https://4.bp.blogspot.com/-UHxlxlFVTgE/WhOzBeOL35I/AAAAAAAAE-k/0BHl_wF7Iv0lKjk60EDiXLUW7SHaxrMhwCLcBGAs/s1600/IMG_3421.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1600" height="400" src="https://4.bp.blogspot.com/-UHxlxlFVTgE/WhOzBeOL35I/AAAAAAAAE-k/0BHl_wF7Iv0lKjk60EDiXLUW7SHaxrMhwCLcBGAs/s400/IMG_3421.JPG" width="400" /></a></div>
2408. <div>
2409. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2410. <div>
2411. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2412. <div>
2413. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">We were now showing that we understood the need to use pink = 4 as our basis for our reasoning about where to cut the other coloured strips.</span></div>
2414. <div>
2415. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2416. <div>
2417. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">There was much folding and cutting - and some even began to use additive strategies to find new numbers. For example, once I had calculated 2 and 3, I could work out 5 by putting them together. This showed me where I should cut the yellow for 5. </span></div>
2418. <div>
2419. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2420. <div class="separator" style="clear: both; text-align: center;">
2421. <a href="https://2.bp.blogspot.com/-jClktvWTsD0/WhOxm5zIAHI/AAAAAAAAE-c/VGFV5QoZ1MwAlDaP57nzzbPS2PqBbZuAACEwYBhgL/s1600/IMG_3412.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://2.bp.blogspot.com/-jClktvWTsD0/WhOxm5zIAHI/AAAAAAAAE-c/VGFV5QoZ1MwAlDaP57nzzbPS2PqBbZuAACEwYBhgL/s400/IMG_3412.JPG" width="300" /></a></div>
2422. <div>
2423. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2424. <div>
2425. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2426. <div>
2427. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Some students used the white (=1) to add onto the end of their latest length to make the next length, showing that the number after <i>n</i> is <i>n</i> +1. </span></div>
2428. <div>
2429. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2430. <div class="separator" style="clear: both; text-align: center;">
2431. <a href="https://1.bp.blogspot.com/-McwMCLSUqKI/WhOxm8I2etI/AAAAAAAAE-c/Uw-P1YneGMkbxHC7bMImI-0dO2mJLLIEgCEwYBhgL/s1600/IMG_3413.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1474" height="400" src="https://1.bp.blogspot.com/-McwMCLSUqKI/WhOxm8I2etI/AAAAAAAAE-c/Uw-P1YneGMkbxHC7bMImI-0dO2mJLLIEgCEwYBhgL/s400/IMG_3413.JPG" width="367" /></a></div>
2432. <div>
2433. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2434. <div>
2435. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2436. <div>
2437. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Some other students developed their own "ruler" once they had found the value of white = 1. They used this standard unit ruler to measure where to cut each strip.</span></div>
2438. <div>
2439. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2440. <div class="separator" style="clear: both; text-align: center;">
2441. <a href="https://4.bp.blogspot.com/-40s8noByQkc/WhOxpDooYZI/AAAAAAAAE-c/4-K6x7mTm4ku84TJvTlqS7D_IJkP77AzwCEwYBhgL/s1600/IMG_3416.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="923" data-original-width="1600" height="230" src="https://4.bp.blogspot.com/-40s8noByQkc/WhOxpDooYZI/AAAAAAAAE-c/4-K6x7mTm4ku84TJvTlqS7D_IJkP77AzwCEwYBhgL/s400/IMG_3416.JPG" width="400" /></a></div>
2442. <div>
2443. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2444. <div>
2445. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2446. <div>
2447. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And our friend from yesterday persisted with the strategy of cutting each colour into individual units and the glueing them into the book.</span></div>
2448. <div>
2449. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2450. <div class="separator" style="clear: both; text-align: center;">
2451. <a href="https://1.bp.blogspot.com/-4NZhlRqf3Cg/WhOxpL7oYrI/AAAAAAAAE-c/r8q-7HY0jKYiGBZY4C9dhKAE3nztwcbkgCEwYBhgL/s1600/IMG_3415.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1446" data-original-width="1600" height="361" src="https://1.bp.blogspot.com/-4NZhlRqf3Cg/WhOxpL7oYrI/AAAAAAAAE-c/r8q-7HY0jKYiGBZY4C9dhKAE3nztwcbkgCEwYBhgL/s400/IMG_3415.JPG" width="400" /></a></div>
2452. <div>
2453. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2454. <div>
2455. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2456. <div>
2457. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">As I observed each of these events unfolding, I stopped the class and we had a moment of reflection to see what we could learn from each strategy. </span></div>
2458. <div>
2459. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2460. <div>
2461. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span></div>
2462. <h2>
2463. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;">Once we were done</span></h2>
2464. <div>
2465. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">After we had produced some nice looking staircases, I brought the class back together for another chat.</span></div>
2466. <div>
2467. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span></div>
2468. <div>
2469. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">We had been thinking that pink = 4 all through this task.</span></div>
2470. <div>
2471. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span></div>
2472. <div>
2473. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">But what if pink = 40?</span></div>
2474. <div>
2475. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span></div>
2476. <div>
2477. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">Or 400?</span></div>
2478. <div>
2479. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span></div>
2480. <div>
2481. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">Or 0.4?</span></div>
2482. <div>
2483. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span></div>
2484. <div>
2485. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">Or 40%</span></div>
2486. <div>
2487. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span></div>
2488. <div>
2489. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">Suddenly it all became clear - the model we had played with for half an hour was just a representation of a relationship based on proportion. </span></div>
2490. <div>
2491. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span></div>
2492. <div>
2493. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">We could use reasoning to work out that...</span></div>
2494. <div>
2495. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span></div>
2496. <div>
2497. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">- if pink = 40 then brown must be 80</span></div>
2498. <div>
2499. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span></div>
2500. <div>
2501. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">- if pink = 400 then red must be 200</span></div>
2502. <div>
2503. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span></div>
2504. <div>
2505. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">- if pink = 0.4 then blue must be 0.9 and orange must be 1.</span></div>
2506. <div>
2507. <span style="font-family: arial, helvetica, sans-serif; font-size: large;"><br /></span></div>
2508. <div>
2509. <span style="font-family: arial, helvetica, sans-serif; font-size: large;">"I think it should be 1.0," said one student. "We are talking decimals here you know."</span></div>
2510. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2511. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2512. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2513. &lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/6918095598299452953/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2017/11/a-proportional-reasoning-sequence.html#comment-form' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/6918095598299452953'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/6918095598299452953'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2017/11/a-proportional-reasoning-sequence.html' title='A Proportional Reasoning Sequence'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://1.bp.blogspot.com/-NiPFsXfVKY8/WhOPrvaZEaI/AAAAAAAAE8M/ktLgw69lrO8QMdW-fhhtMVyFPfv5nYwjgCLcBGAs/s72-c/IMG_3386.JPG" height="72" width="72"/><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-3121095273272500289</id><published>2017-11-16T21:52:00.001+11:00</published><updated>2017-11-16T21:52:36.867+11:00</updated><title type='text'>Show me a quarter</title><content type='html'>&lt;br /&gt;
2514. <br />
2515. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">I asked the kids to show me a quarter.</span><br />
2516. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2517. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Here is what they did.</span><br />
2518. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2519. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">I'm not going to say anything.</span><br />
2520. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2521. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Just I love those kids.</span><br />
2522. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
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2533. <a href="https://3.bp.blogspot.com/-lDYyfr3pzyI/Wg1squ_ZJvI/AAAAAAAAE64/ahBZJR4M_TAqYXg3iVh63qne36tl6VowwCLcBGAs/s1600/IMG_3361.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1033" data-original-width="1600" height="257" src="https://3.bp.blogspot.com/-lDYyfr3pzyI/Wg1squ_ZJvI/AAAAAAAAE64/ahBZJR4M_TAqYXg3iVh63qne36tl6VowwCLcBGAs/s400/IMG_3361.jpg" width="400" /></a></div>
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2538. <a href="https://4.bp.blogspot.com/-E5l6Gs0HRsA/Wg1srA54XtI/AAAAAAAAE68/YRI9ouXYbgsbTU5NW0hKtFVoZHJNRgMBgCLcBGAs/s1600/IMG_3362.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1340" data-original-width="1600" height="333" src="https://4.bp.blogspot.com/-E5l6Gs0HRsA/Wg1srA54XtI/AAAAAAAAE68/YRI9ouXYbgsbTU5NW0hKtFVoZHJNRgMBgCLcBGAs/s400/IMG_3362.jpg" width="400" /></a></div>
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2543. <a href="https://3.bp.blogspot.com/-x519pMApr2I/Wg1sqrRFNtI/AAAAAAAAE60/PeLLIMcWuO43EC49eDjL4nCUVn30rT-fQCLcBGAs/s1600/IMG_3363.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="502" data-original-width="1600" height="125" src="https://3.bp.blogspot.com/-x519pMApr2I/Wg1sqrRFNtI/AAAAAAAAE60/PeLLIMcWuO43EC49eDjL4nCUVn30rT-fQCLcBGAs/s400/IMG_3363.jpg" width="400" /></a></div>
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2548. <a href="https://4.bp.blogspot.com/-gm6Dd8fCnSc/Wg1srsN8YGI/AAAAAAAAE7A/RO8SAgq6ZaICVy6DZ9DIZz8CLX1oc-Q8wCLcBGAs/s1600/IMG_3364.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1162" data-original-width="1600" height="290" src="https://4.bp.blogspot.com/-gm6Dd8fCnSc/Wg1srsN8YGI/AAAAAAAAE7A/RO8SAgq6ZaICVy6DZ9DIZz8CLX1oc-Q8wCLcBGAs/s400/IMG_3364.jpg" width="400" /></a></div>
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2553. <a href="https://1.bp.blogspot.com/-xx9WeW1-GvU/Wg1sr9X_IVI/AAAAAAAAE7E/_GulseEM9gsorIcMsIgNvWBoYTbV8vHxACLcBGAs/s1600/IMG_3365.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1483" data-original-width="1600" height="370" src="https://1.bp.blogspot.com/-xx9WeW1-GvU/Wg1sr9X_IVI/AAAAAAAAE7E/_GulseEM9gsorIcMsIgNvWBoYTbV8vHxACLcBGAs/s400/IMG_3365.jpg" width="400" /></a></div>
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2558. <a href="https://1.bp.blogspot.com/-CjXxbj5YGJY/Wg1ssX6qV5I/AAAAAAAAE7I/3bW1rThz1XEB-5p2pxOlP6jN0GdIaieUACLcBGAs/s1600/IMG_3366.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1197" data-original-width="1600" height="298" src="https://1.bp.blogspot.com/-CjXxbj5YGJY/Wg1ssX6qV5I/AAAAAAAAE7I/3bW1rThz1XEB-5p2pxOlP6jN0GdIaieUACLcBGAs/s400/IMG_3366.jpg" width="400" /></a></div>
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2563. <a href="https://1.bp.blogspot.com/-ih8MyU9DGVg/Wg1sshuCS1I/AAAAAAAAE7M/5HwS2aSvwtszqPNk9VZW3_zENy5aC1bLgCLcBGAs/s1600/IMG_3367.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="804" data-original-width="1600" height="200" src="https://1.bp.blogspot.com/-ih8MyU9DGVg/Wg1sshuCS1I/AAAAAAAAE7M/5HwS2aSvwtszqPNk9VZW3_zENy5aC1bLgCLcBGAs/s400/IMG_3367.jpg" width="400" /></a></div>
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2568. <a href="https://2.bp.blogspot.com/-Ai5e-ke4-8Y/Wg1stA6lRwI/AAAAAAAAE7Q/umiUQbmubxoOMKoQpOz6hCpgWc91HSjmwCLcBGAs/s1600/IMG_3368.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="631" data-original-width="1256" height="200" src="https://2.bp.blogspot.com/-Ai5e-ke4-8Y/Wg1stA6lRwI/AAAAAAAAE7Q/umiUQbmubxoOMKoQpOz6hCpgWc91HSjmwCLcBGAs/s400/IMG_3368.jpg" width="400" /></a></div>
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2573. <a href="https://4.bp.blogspot.com/-epk1OnIuJYc/Wg1stnxS9mI/AAAAAAAAE7U/JjIfKOd-NDoq_jpKvVe14QeP-DvPskUCwCLcBGAs/s1600/IMG_3369.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="897" data-original-width="1600" height="223" src="https://4.bp.blogspot.com/-epk1OnIuJYc/Wg1stnxS9mI/AAAAAAAAE7U/JjIfKOd-NDoq_jpKvVe14QeP-DvPskUCwCLcBGAs/s400/IMG_3369.jpg" width="400" /></a></div>
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2578. <a href="https://3.bp.blogspot.com/-0y7RGRBKM9M/Wg1sucyVMBI/AAAAAAAAE7Y/G3HYSeFgN8c6F-KLZnd-5FnoXMrQNOvyACLcBGAs/s1600/IMG_3372.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="864" data-original-width="1275" height="270" src="https://3.bp.blogspot.com/-0y7RGRBKM9M/Wg1sucyVMBI/AAAAAAAAE7Y/G3HYSeFgN8c6F-KLZnd-5FnoXMrQNOvyACLcBGAs/s400/IMG_3372.jpg" width="400" /></a></div>
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2583. <a href="https://1.bp.blogspot.com/-2sTUJBn6I5I/Wg1suXvLKMI/AAAAAAAAE7c/fJyXK7eLM00Sl8cFxYnMtgjzKox-EQdOACLcBGAs/s1600/IMG_3375.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="935" data-original-width="1417" height="262" src="https://1.bp.blogspot.com/-2sTUJBn6I5I/Wg1suXvLKMI/AAAAAAAAE7c/fJyXK7eLM00Sl8cFxYnMtgjzKox-EQdOACLcBGAs/s400/IMG_3375.jpg" width="400" /></a></div>
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2588. <a href="https://1.bp.blogspot.com/-4uAc0zxZ1UM/Wg1sugeTuWI/AAAAAAAAE7g/c0osJnLuqEYjrMxhuTB182swIaul5orkgCLcBGAs/s1600/IMG_3376%255B2%255D.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="640" height="300" src="https://1.bp.blogspot.com/-4uAc0zxZ1UM/Wg1sugeTuWI/AAAAAAAAE7g/c0osJnLuqEYjrMxhuTB182swIaul5orkgCLcBGAs/s400/IMG_3376%255B2%255D.JPG" width="400" /></a></div>
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2590. <br /></div>
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2594. <a href="https://2.bp.blogspot.com/--_4twPz0Gh0/Wg1svugJaiI/AAAAAAAAE7o/TfMu89Qy3WAsx4JJuNMlkV9Q6-wPw9tHACLcBGAs/s1600/IMG_3378%2Bcopy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="640" height="300" src="https://2.bp.blogspot.com/--_4twPz0Gh0/Wg1svugJaiI/AAAAAAAAE7o/TfMu89Qy3WAsx4JJuNMlkV9Q6-wPw9tHACLcBGAs/s400/IMG_3378%2Bcopy.jpg" width="400" /></a></div>
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2599. <a href="https://4.bp.blogspot.com/-1J4d9W2RiIY/Wg1svi9xDHI/AAAAAAAAE7s/gm4ry6S6NLAJ-jLhxtdQQq05VBaNGSyMgCLcBGAs/s1600/IMG_3379%2Bcopy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="279" data-original-width="274" height="400" src="https://4.bp.blogspot.com/-1J4d9W2RiIY/Wg1svi9xDHI/AAAAAAAAE7s/gm4ry6S6NLAJ-jLhxtdQQq05VBaNGSyMgCLcBGAs/s400/IMG_3379%2Bcopy.jpg" width="392" /></a></div>
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2604. <a href="https://1.bp.blogspot.com/-ziNwosz8BMw/Wg1swlrkEbI/AAAAAAAAE7w/SY_AnMrxXKMvar_oTt3FQ6BfgJy3FaGFgCLcBGAs/s1600/IMG_3380%2Bcopy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="228" data-original-width="597" height="151" src="https://1.bp.blogspot.com/-ziNwosz8BMw/Wg1swlrkEbI/AAAAAAAAE7w/SY_AnMrxXKMvar_oTt3FQ6BfgJy3FaGFgCLcBGAs/s400/IMG_3380%2Bcopy.jpg" width="400" /></a></div>
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2609. <a href="https://2.bp.blogspot.com/-AXGIh9OcFgo/Wg1sxDhyOLI/AAAAAAAAE70/7G-JvhqDr1Qwts-jyPFfUizS0_ebfMSlgCLcBGAs/s1600/IMG_3381%2Bcopy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="640" height="300" src="https://2.bp.blogspot.com/-AXGIh9OcFgo/Wg1sxDhyOLI/AAAAAAAAE70/7G-JvhqDr1Qwts-jyPFfUizS0_ebfMSlgCLcBGAs/s400/IMG_3381%2Bcopy.jpg" width="400" /></a></div>
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2611. <br /></div>
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2614. <a href="https://4.bp.blogspot.com/-DgQJfZM6iQk/Wg1sxCxAujI/AAAAAAAAE74/1Xd-vO-pDdQcDymuNnbehbc3wNXE-LtpACLcBGAs/s1600/IMG_3382%2Bcopy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="226" data-original-width="596" height="151" src="https://4.bp.blogspot.com/-DgQJfZM6iQk/Wg1sxCxAujI/AAAAAAAAE74/1Xd-vO-pDdQcDymuNnbehbc3wNXE-LtpACLcBGAs/s400/IMG_3382%2Bcopy.jpg" width="400" /></a></div>
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2619. <a href="https://1.bp.blogspot.com/-0Zi_oWfaW9M/Wg1sxsImQVI/AAAAAAAAE78/abKT54Wioj0Pdfz1TFWpQZkGONaYo7kKwCLcBGAs/s1600/IMG_3383%2Bcopy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="640" height="300" src="https://1.bp.blogspot.com/-0Zi_oWfaW9M/Wg1sxsImQVI/AAAAAAAAE78/abKT54Wioj0Pdfz1TFWpQZkGONaYo7kKwCLcBGAs/s400/IMG_3383%2Bcopy.jpg" width="400" /></a></div>
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2625. <a href="https://3.bp.blogspot.com/-0tYBYjXKmo4/Wg1svYyx-hI/AAAAAAAAE7k/c5Tr9zdEFiocmWb6EpS2ryETtk-1KfY4gCLcBGAs/s1600/IMG_3377%2Bcopy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="640" data-original-width="480" height="400" src="https://3.bp.blogspot.com/-0tYBYjXKmo4/Wg1svYyx-hI/AAAAAAAAE7k/c5Tr9zdEFiocmWb6EpS2ryETtk-1KfY4gCLcBGAs/s400/IMG_3377%2Bcopy.jpg" width="300" /></a></div>
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2629. </div>
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2631. <i>And yes, the yellow line has 3 squares, </i></div>
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2633. <i>which is a quarter of the total 12 squares used...</i></div>
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2701. </div>
2702. <br />
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2704. </div>
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2719. </div>
2720. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2721. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2722. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2723. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2724. <span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span>
2725. &lt;br /&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/3121095273272500289/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2017/11/show-me-quarter.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/3121095273272500289'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/3121095273272500289'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2017/11/show-me-quarter.html' title='Show me a quarter'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://3.bp.blogspot.com/-lDYyfr3pzyI/Wg1squ_ZJvI/AAAAAAAAE64/ahBZJR4M_TAqYXg3iVh63qne36tl6VowwCLcBGAs/s72-c/IMG_3361.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-6680331021913835523</id><published>2017-11-03T14:40:00.000+11:00</published><updated>2017-11-03T14:44:32.291+11:00</updated><title type='text'>Quarter of a Cross</title><content type='html'>&lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;There is a puzzle out there called &quot;Quarter of a Cross&quot;. Amie Albrecht (@nomad_penguin) at the University of South Australia suggested that my Year 2 kids might like to give it a go. It is a puzzle that has appeal for learners from a range of ages. Amie had seen what we were doing with fractions last week and thought it would be interesting for my kids.&lt;/span&gt;&lt;br /&gt;
2726. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2727. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The puzzle looks like this:</span><br />
2728. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2729. <br />
2730. <div class="separator" style="clear: both; text-align: center;">
2731. <a href="https://4.bp.blogspot.com/-POjQMeE7MGY/WfuwK4mO76I/AAAAAAAAE2I/0N2HNc5VUG05_5BE5IJPyquxHwLjmuaRACLcBGAs/s1600/Screen%2BShot%2B2017-11-03%2Bat%2B10.53.52%2BAM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="874" data-original-width="1224" height="285" src="https://4.bp.blogspot.com/-POjQMeE7MGY/WfuwK4mO76I/AAAAAAAAE2I/0N2HNc5VUG05_5BE5IJPyquxHwLjmuaRACLcBGAs/s400/Screen%2BShot%2B2017-11-03%2Bat%2B10.53.52%2BAM.png" width="400" /></a></div>
2732. <div class="separator" style="clear: both; text-align: center;">
2733. <br /></div>
2734. <div class="separator" style="clear: both; text-align: center;">
2735. <i>from <a href="https://amiealbrecht.com/2016/05/21/quarter-the-cross-and-fraction-talks/">https://amiealbrecht.com/2016/05/21/quarter-the-cross-and-fraction-talks/</a> </i></div>
2736. <div class="separator" style="clear: both; text-align: center;">
2737. <br /></div>
2738. <div class="separator" style="clear: both; text-align: left;">
2739. <br /></div>
2740. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So we gave it a go. </span><br />
2741. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2742. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And here is what happened.</span><br />
2743. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2744. <br />
2745. <div class="separator" style="clear: both; text-align: center;">
2746. <a href="https://4.bp.blogspot.com/-BtiGuQ3ot5A/Wfuw4vtIjLI/AAAAAAAAE2M/GrLC7-uNVocvBDTktNrxik2eixO8qNayACLcBGAs/s1600/IMG_3321%2B2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://4.bp.blogspot.com/-BtiGuQ3ot5A/Wfuw4vtIjLI/AAAAAAAAE2M/GrLC7-uNVocvBDTktNrxik2eixO8qNayACLcBGAs/s400/IMG_3321%2B2.JPG" width="400" /></a></div>
2747. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2748. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">The first 10 minutes were spent coming to terms with the problem - what would a quarter look like? </span><br />
2749. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2750. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Well we found lots of things that it wasn't. We soon realised that the cross could be made of five squares, so colouring in one or two of these was not going to make a quarter.</span><br />
2751. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2752. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Back to the drawing board.</span><br />
2753. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2754. <br />
2755. <div class="separator" style="clear: both; text-align: center;">
2756. <a href="https://3.bp.blogspot.com/-13UQtSd-gt8/Wfuw7YsaAvI/AAAAAAAAE2o/ROnb9Ohuj9MxHYd-sxJpkneXZhjHfFoeQCLcBGAs/s1600/IMG_3328%2B2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://3.bp.blogspot.com/-13UQtSd-gt8/Wfuw7YsaAvI/AAAAAAAAE2o/ROnb9Ohuj9MxHYd-sxJpkneXZhjHfFoeQCLcBGAs/s400/IMG_3328%2B2.JPG" width="400" /></a></div>
2757. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2758. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">This was one of my favourite solutions because it showed me the struggle that was going on. It was like a window into the mind of the student.</span><br />
2759. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2760. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">"So, what if I do this? Hmm, no I don't think so. What about... yes that might work!"</span><br />
2761. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2762. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">It was the process of deciding on a "proof" - how to show I had found a quarter. Along the way, I am going to need to eliminate a few ideas but this is all part of the learning process.</span><br />
2763. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2764. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">While doing this task, I pulled the class back in for a "chat" about 3 times. This helped to clarify the question and also to discuss any important information we had discovered. This was shared with the class to help progress the solutions. We also had a break of a few hours and revisited the task in the afternoon. </span><br />
2765. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2766. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And here are a few of the ideas that emerged:</span><br />
2767. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2768. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;">1. You can use one of the "legs" of the cross and add it to 1/4 piece of the inside square. </span><br />
2769. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2770. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">What the students had seen was that 1/5 + 1/20 = 1/4 although they were not able to articulate this.</span><br />
2771. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2772. <br />
2773. <div class="separator" style="clear: both; text-align: center;">
2774. <a href="https://1.bp.blogspot.com/-Q3Z4vJq1npg/WfvfWifGDSI/AAAAAAAAE3w/WDx6uahkoN4t5RnwNnJLD-dT446f2Hs7wCLcBGAs/s1600/1a.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="837" data-original-width="856" height="312" src="https://1.bp.blogspot.com/-Q3Z4vJq1npg/WfvfWifGDSI/AAAAAAAAE3w/WDx6uahkoN4t5RnwNnJLD-dT446f2Hs7wCLcBGAs/s320/1a.JPG" width="320" /></a></div>
2775. <br />
2776. <div class="separator" style="clear: both; text-align: center;">
2777. <a href="https://2.bp.blogspot.com/-aPKCAEHUZws/WfvfXmAZlZI/AAAAAAAAE38/y1Z3df5NlfA7s69RVT-ELV_Qpos2sodQACLcBGAs/s1600/1e.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="767" data-original-width="859" height="285" src="https://2.bp.blogspot.com/-aPKCAEHUZws/WfvfXmAZlZI/AAAAAAAAE38/y1Z3df5NlfA7s69RVT-ELV_Qpos2sodQACLcBGAs/s320/1e.JPG" width="320" /></a></div>
2778. <br />
2779. <div class="separator" style="clear: both; text-align: center;">
2780. <a href="https://1.bp.blogspot.com/-jQtGjaK3FCA/WfvfY43TXJI/AAAAAAAAE4I/wk3CyyfsnRMVI_xic1g04_sAc1ozbBXnQCLcBGAs/s1600/3b.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="821" data-original-width="890" height="295" src="https://1.bp.blogspot.com/-jQtGjaK3FCA/WfvfY43TXJI/AAAAAAAAE4I/wk3CyyfsnRMVI_xic1g04_sAc1ozbBXnQCLcBGAs/s320/3b.JPG" width="320" /></a></div>
2781. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2782. <br />
2783. <div class="separator" style="clear: both; text-align: center;">
2784. <a href="https://2.bp.blogspot.com/-uCVIToe4L2A/WfvgI2CouMI/AAAAAAAAE4c/gy8VKsAPjQ0JKwDr0aRqT8OCkWJDTNNOgCLcBGAs/s1600/1g.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="793" data-original-width="950" height="267" src="https://2.bp.blogspot.com/-uCVIToe4L2A/WfvgI2CouMI/AAAAAAAAE4c/gy8VKsAPjQ0JKwDr0aRqT8OCkWJDTNNOgCLcBGAs/s320/1g.JPG" width="320" /></a></div>
2785. <br />
2786. <div class="separator" style="clear: both; text-align: center;">
2787. <a href="https://3.bp.blogspot.com/-b8qCcxYh_T8/WfvgIyiVSbI/AAAAAAAAE4Y/FeaFjoQTcjc9RaD3rdrjBOiPQuhEaT86QCLcBGAs/s1600/1h.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="810" data-original-width="892" height="290" src="https://3.bp.blogspot.com/-b8qCcxYh_T8/WfvgIyiVSbI/AAAAAAAAE4Y/FeaFjoQTcjc9RaD3rdrjBOiPQuhEaT86QCLcBGAs/s320/1h.JPG" width="320" /></a></div>
2788. <br />
2789. <div class="separator" style="clear: both; text-align: center;">
2790. </div>
2791. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2792. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;">2. </span><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;">Using a line that passes through the centre of the cross</span><br />
2793. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2794. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">This was a good idea. If you extrapolate from this you will find that this method produces an infinite series of solutions as you rotate around the centre point. We only represented 3 solutions.</span><br />
2795. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2796. <br />
2797. <div class="separator" style="clear: both; text-align: center;">
2798. <a href="https://1.bp.blogspot.com/-n0nyUzmKg4g/Wfvhm9qEYVI/AAAAAAAAE4s/gFRhwgY1so0Nl29vONN2CjZTEPobnuSogCLcBGAs/s1600/5a.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="435" data-original-width="1600" height="107" src="https://1.bp.blogspot.com/-n0nyUzmKg4g/Wfvhm9qEYVI/AAAAAAAAE4s/gFRhwgY1so0Nl29vONN2CjZTEPobnuSogCLcBGAs/s400/5a.JPG" width="400" /></a></div>
2799. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2800. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2801. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;">3. There is a left handed and a right handed house</span><br />
2802. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2803. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Interesting - same idea but reflected.</span><br />
2804. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2805. <br />
2806. <div class="separator" style="clear: both; text-align: center;">
2807. <a href="https://3.bp.blogspot.com/-qSNvd_d_xcA/WfvjFv4LaxI/AAAAAAAAE44/gh07f_WjDTIvN8T4eaprH380ek9OE93PQCLcBGAs/s1600/1b.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="694" data-original-width="1600" height="172" src="https://3.bp.blogspot.com/-qSNvd_d_xcA/WfvjFv4LaxI/AAAAAAAAE44/gh07f_WjDTIvN8T4eaprH380ek9OE93PQCLcBGAs/s400/1b.JPG" width="400" /></a></div>
2808. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2809. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2810. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;">4. Colour makes everything look good</span><br />
2811. <div class="separator" style="clear: both; text-align: center;">
2812. <br /></div>
2813. <div class="separator" style="clear: both; text-align: center;">
2814. <a href="https://4.bp.blogspot.com/-QA17gsDcEvY/WfvjSz7S7DI/AAAAAAAAE48/Txpq8XY-QzUdHzJ_P4CY5JPHchM2Gp9FQCLcBGAs/s1600/colour.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="885" data-original-width="1600" height="220" src="https://4.bp.blogspot.com/-QA17gsDcEvY/WfvjSz7S7DI/AAAAAAAAE48/Txpq8XY-QzUdHzJ_P4CY5JPHchM2Gp9FQCLcBGAs/s400/colour.JPG" width="400" /></a></div>
2815. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-large;"><br /></span>
2816. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2817. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2818. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So Amie - hope you like our pics. I think they look great. The kids had a really good time and it was difficult but we got some good learning out of it.</span><br />
2819. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2820. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Now, I wonder what other shapes we could divide up...</span><br />
2821. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2822. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2823. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2824. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2825. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2826. &lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/6680331021913835523/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2017/11/quarter-of-cross.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/6680331021913835523'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/6680331021913835523'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2017/11/quarter-of-cross.html' title='Quarter of a Cross'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://4.bp.blogspot.com/-POjQMeE7MGY/WfuwK4mO76I/AAAAAAAAE2I/0N2HNc5VUG05_5BE5IJPyquxHwLjmuaRACLcBGAs/s72-c/Screen%2BShot%2B2017-11-03%2Bat%2B10.53.52%2BAM.png" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-8256492698354362046.post-7405154054902502348</id><published>2017-10-26T18:46:00.000+11:00</published><updated>2017-10-26T22:41:37.145+11:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Fractions"/><title type='text'>Lego Fractions</title><content type='html'>&lt;br /&gt;
2827. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">We are continuing our exploration of fractions. I thought it might be interesting to see how we could represent unit fractions (1/2, 1/3, 1/4 etc) using one of our favourite learning tools - Lego!</span><br />
2828. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2829. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So we started off gently. Let's have a look at 1/2...</span><br />
2830. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2831. <br />
2832. <div class="separator" style="clear: both; text-align: center;">
2833. <a href="https://4.bp.blogspot.com/-lug-GDohaPQ/WfEG4MeBQ1I/AAAAAAAAE18/IqdMFNMvvcYq18ltVoSgPq058O2B2AytwCEwYBhgL/s1600/DSCN1810.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://4.bp.blogspot.com/-lug-GDohaPQ/WfEG4MeBQ1I/AAAAAAAAE18/IqdMFNMvvcYq18ltVoSgPq058O2B2AytwCEwYBhgL/s400/DSCN1810.jpg" width="400" /></a></div>
2834. <div class="separator" style="clear: both; text-align: center;">
2835. <br /></div>
2836. <br />
2837. <div class="separator" style="clear: both; text-align: center;">
2838. <a href="https://1.bp.blogspot.com/-OOzLv9x6law/WfEG2uIbQ0I/AAAAAAAAE18/XBvOVAp6H4Q0ywUlu1OdAK9TE52YCXVxwCEwYBhgL/s1600/DSCN1807.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://1.bp.blogspot.com/-OOzLv9x6law/WfEG2uIbQ0I/AAAAAAAAE18/XBvOVAp6H4Q0ywUlu1OdAK9TE52YCXVxwCEwYBhgL/s400/DSCN1807.jpg" width="400" /></a></div>
2839. <br />
2840. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2841. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Then 1/3...</span><br />
2842. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2843. <br />
2844. <div class="separator" style="clear: both; text-align: center;">
2845. <a href="https://2.bp.blogspot.com/-lNZSoTN83mY/WfEG4KY02EI/AAAAAAAAE18/gPvj3rqvdCIYIRgGlNZ4N5fnO063e-AOwCEwYBhgL/s1600/DSCN1811.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://2.bp.blogspot.com/-lNZSoTN83mY/WfEG4KY02EI/AAAAAAAAE18/gPvj3rqvdCIYIRgGlNZ4N5fnO063e-AOwCEwYBhgL/s400/DSCN1811.jpg" width="400" /></a></div>
2846. <div class="separator" style="clear: both; text-align: center;">
2847. <br /></div>
2848. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2849. <br />
2850. <div class="separator" style="clear: both; text-align: center;">
2851. <a href="https://3.bp.blogspot.com/-hSewDAjJHHg/WfEG5rIAU4I/AAAAAAAAE18/D9PaSELj42kvjFUIlYUQCt0epKf00HJmgCEwYBhgL/s1600/DSCN1815.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://3.bp.blogspot.com/-hSewDAjJHHg/WfEG5rIAU4I/AAAAAAAAE18/D9PaSELj42kvjFUIlYUQCt0epKf00HJmgCEwYBhgL/s400/DSCN1815.jpg" width="400" /></a></div>
2852. <div class="separator" style="clear: both; text-align: center;">
2853. <br /></div>
2854. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2855. <br />
2856. <div class="separator" style="clear: both; text-align: center;">
2857. <a href="https://1.bp.blogspot.com/-1FHqRJfLkC4/WfEG-gwCM4I/AAAAAAAAE18/WKvwXsNfEQo0ovmENz6y1EdSYanQQE42ACEwYBhgL/s1600/DSCN1830.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="992" data-original-width="1600" height="247" src="https://1.bp.blogspot.com/-1FHqRJfLkC4/WfEG-gwCM4I/AAAAAAAAE18/WKvwXsNfEQo0ovmENz6y1EdSYanQQE42ACEwYBhgL/s400/DSCN1830.jpg" width="400" /></a></div>
2858. <br />
2859. <br />
2860. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2861. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Yep - that was pretty much what I was expecting.</span><br />
2862. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2863. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">So I asked, "Can you do it another way?"</span><br />
2864. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2865. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Never fails...</span><br />
2866. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2867. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Here is what 1/2 could look like:</span><br />
2868. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2869. <br />
2870. <div class="separator" style="clear: both; text-align: center;">
2871. <a href="https://4.bp.blogspot.com/-mXIruyXnRec/WfEG2oxlFGI/AAAAAAAAE18/BVIZpzHUw9Ax89OFfTNhxWd0kz4j6QIGwCEwYBhgL/s1600/DSCN1808.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://4.bp.blogspot.com/-mXIruyXnRec/WfEG2oxlFGI/AAAAAAAAE18/BVIZpzHUw9Ax89OFfTNhxWd0kz4j6QIGwCEwYBhgL/s400/DSCN1808.jpg" width="400" /></a></div>
2872. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2873. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Or this...</span><br />
2874. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2875. <br />
2876. <div class="separator" style="clear: both; text-align: center;">
2877. <a href="https://3.bp.blogspot.com/-WkXHugmGgyw/WfEG2gwuF2I/AAAAAAAAE18/OnG7GvySx1kcF9n-ggiq26E9dFicmbg3QCEwYBhgL/s1600/DSCN1809.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://3.bp.blogspot.com/-WkXHugmGgyw/WfEG2gwuF2I/AAAAAAAAE18/OnG7GvySx1kcF9n-ggiq26E9dFicmbg3QCEwYBhgL/s400/DSCN1809.jpg" width="400" /></a></div>
2878. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2879. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Or this...</span><br />
2880. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2881. <br />
2882. <div class="separator" style="clear: both; text-align: center;">
2883. <a href="https://2.bp.blogspot.com/-ArS6AlB6HG4/WfEG5U731PI/AAAAAAAAE18/qgbg3z2G3rgnYPfsbEnMd-RgAqFt7H1GACEwYBhgL/s1600/DSCN1814.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://2.bp.blogspot.com/-ArS6AlB6HG4/WfEG5U731PI/AAAAAAAAE18/qgbg3z2G3rgnYPfsbEnMd-RgAqFt7H1GACEwYBhgL/s400/DSCN1814.jpg" width="400" /></a></div>
2884. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2885. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And 1/3:</span><br />
2886. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2887. <br />
2888. <div class="separator" style="clear: both; text-align: center;">
2889. <a href="https://3.bp.blogspot.com/-zTuLNYR-Aq0/WfEG83a0SwI/AAAAAAAAE18/4Tgg83wZPu0lCFYBaIrtAxXRY8rTmUkrACEwYBhgL/s1600/DSCN1826.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1138" data-original-width="1600" height="283" src="https://3.bp.blogspot.com/-zTuLNYR-Aq0/WfEG83a0SwI/AAAAAAAAE18/4Tgg83wZPu0lCFYBaIrtAxXRY8rTmUkrACEwYBhgL/s400/DSCN1826.jpg" width="400" /></a></div>
2890. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2891. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And...</span><br />
2892. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2893. <br />
2894. <div class="separator" style="clear: both; text-align: center;">
2895. <a href="https://4.bp.blogspot.com/-FVaf5_GQYEQ/WfEG_6Z2EzI/AAAAAAAAE18/kGVtIXG3gMghKlMHzqTQFskKlk90BwAcgCEwYBhgL/s1600/DSCN1833.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://4.bp.blogspot.com/-FVaf5_GQYEQ/WfEG_6Z2EzI/AAAAAAAAE18/kGVtIXG3gMghKlMHzqTQFskKlk90BwAcgCEwYBhgL/s400/DSCN1833.jpg" width="400" /></a></div>
2896. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2897. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2898. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">And from that, a student worked out 1/1, 1/2, 1/3, 1/4, 1/5...</span><br />
2899. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2900. <br />
2901. <div class="separator" style="clear: both; text-align: center;">
2902. <a href="https://2.bp.blogspot.com/-kX5vQjlcgjw/WfEG7i3kswI/AAAAAAAAE18/FVqxHi9PDOYJrTd_Hn14iXByF7C25lFhACEwYBhgL/s1600/DSCN1820.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://2.bp.blogspot.com/-kX5vQjlcgjw/WfEG7i3kswI/AAAAAAAAE18/FVqxHi9PDOYJrTd_Hn14iXByF7C25lFhACEwYBhgL/s400/DSCN1820.jpg" width="400" /></a></div>
2903. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2904. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2905. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;">Yes, I know, we went beyond the Australian Curriculum requirements for Year 2 - but how do you stop the kids when they are on a roll and obviously know what they are doing?</span><br />
2906. <br />
2907. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2908. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2909. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2910. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2911. <span style="font-family: "arial" , "helvetica" , sans-serif; font-size: large;"><br /></span>
2912. &lt;span style=&quot;font-family: &amp;quot;arial&amp;quot; , &amp;quot;helvetica&amp;quot; , sans-serif; font-size: large;&quot;&gt;&lt;br /&gt;&lt;/span&gt;</content><link rel='replies' type='application/atom+xml' href='http://authenticinquirymaths.blogspot.com/feeds/7405154054902502348/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://authenticinquirymaths.blogspot.com/2017/10/lego-fractions.html#comment-form' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/7405154054902502348'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/8256492698354362046/posts/default/7405154054902502348'/><link rel='alternate' type='text/html' href='http://authenticinquirymaths.blogspot.com/2017/10/lego-fractions.html' title='Lego Fractions'/><author><name>Bruce Ferrington</name><uri>http://www.blogger.com/profile/07947474361978469990</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='24' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_gYSpktohVsvngprKskYAS0dy7HJ-ubkqPi4Ugpcw-qt-sSmsS7MPoBckCQf87lmRxfXMGmruKHo-wLebimqi_cQ-439ZLT7i9mqWaVauZgppCKkD0RDXwjPAaH7RQ/s220/bf2.jpg'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://4.bp.blogspot.com/-lug-GDohaPQ/WfEG4MeBQ1I/AAAAAAAAE18/IqdMFNMvvcYq18ltVoSgPq058O2B2AytwCEwYBhgL/s72-c/DSCN1810.jpg" height="72" width="72"/><thr:total>1</thr:total></entry></feed>