tag:blogger.com,1999:blog-12742309766837307582023-11-16T07:18:42.211+01:00pinkmathematicsMathematics from 'La Ville Rose' - Exploring all the possible things mathematics can be at the International School of Toulouse.Anonymoushttp://www.blogger.com/profile/05835250335807360943noreply@blogger.comBlogger76125tag:blogger.com,1999:blog-1274230976683730758.post-32753613140228047182016-02-10T22:50:00.002+01:002016-03-17T22:05:17.219+01:00Thought Plants<div dir="ltr" style="text-align: left;" trbidi="on">
In Toulouse, at <a href="http://p-r-e-f-a-c-e.fr/" target="_blank">the Pr</a>é<a href="http://p-r-e-f-a-c-e.fr/" target="_blank">face Gallery</a>, two artists<a href="http://www.martinandyoule.com/" target="_blank"> Charlie Youle and Bevis Martin</a> are exhibiting some beautiful sculptures, "Thought Plants".<br />
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The Préface website says:<br />
<blockquote class="tr_bq">
Thought Plants présente un ensemble de sculptures murales réalisées à partir de dessins de plantes faits par des enfants. Les dessins originels sont en réalité issus d’une méthode de calcul pédagogique et ludique destinée à faciliter l’apprentissage des mathématiques. Ainsi, derrière une représentation de la nature Bevis et Charlie nous donnent à voir la relecture d’un motif oscillant entre la spontanéité enfantine et la rigueur mathématique d’un algorithme.</blockquote>
The pictures that the artists based their work on were factor trees featured on this blog. In fact, that's where they encountered the trees! Mr Gregg was amazed when he first heard from the artists, who he'd not met before, about the project.<br />
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Miss Ash and Mr Gregg went to see the private view to open the exhibition. It was wonderful to see how the 2D shapes created by our students had been lovingly recreated in 3D in pastel shades that gave them a sense of being carved in colourful stone.<br />
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In the basement there was more work based on a mathematical theme:<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiASMw00nqh4o5bWLJ15LfPoqVPyTqZ6Qh2DxpYhKYh1dMWkBsaoFm6NQGP-2VftKZFb3EUo3wrZKFuQIOS8V4YkqbNf9-8tqr2XCZ5BK96WpkNYgW9ylBis7u81ndQnMby8B3h34FSakQ/s1600/2016-02-10+20.35.41.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiASMw00nqh4o5bWLJ15LfPoqVPyTqZ6Qh2DxpYhKYh1dMWkBsaoFm6NQGP-2VftKZFb3EUo3wrZKFuQIOS8V4YkqbNf9-8tqr2XCZ5BK96WpkNYgW9ylBis7u81ndQnMby8B3h34FSakQ/s320/2016-02-10+20.35.41.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Miss Ash talking with Charlie Youle</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRhmPT6nUcKJ29OWG7cz3TLBQ6JTr5yzFk56Nky7XDkJ8cSXAICQB7ctZ31nhG4Qn8G9arblvSaukE2o7yBZpboEv-69lTgsO1NFuVVR3moeoZ4xQ7zdCy_gnhKfbPQO7hLY7xKXWD5F0/s1600/2016-02-10+20.45.16.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRhmPT6nUcKJ29OWG7cz3TLBQ6JTr5yzFk56Nky7XDkJ8cSXAICQB7ctZ31nhG4Qn8G9arblvSaukE2o7yBZpboEv-69lTgsO1NFuVVR3moeoZ4xQ7zdCy_gnhKfbPQO7hLY7xKXWD5F0/s320/2016-02-10+20.45.16.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The artists with Mr Gregg</td></tr>
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<br />
Back in 2013 <a href="http://pinkmathematics.blogspot.fr/2013/02/important-factors.html" target="_blank">we posted about the factor trees that the Year 5s had created</a>.<br />
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<img height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHMeso6oDmCzMlo43Pwq2X4f1WDvUydw_mM_HwLMVZYhj7ru-RMCpuY2GzFfrZ_R7NLSTtlqeVtwcJzyNv2-iN0Fc_iTAsZTpTfaoqnyMqQ4VOJPbtNUmvYgLXmoYqnBQNfD-ToZ_Mrwc/s320/Jessica.bmp" width="225" /></div>
It was surprising and wonderful to see them being given a new life as artworks!<br />
<br />
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UPDATE</div>
<br />
Charlie, Bevis and their daughter came to visit us at IST today - see <a href="http://y4atist.blogspot.fr/2016/03/charlie-bevis-and-sukie-visit.html" target="_blank">the Year 4 blog</a>.</div>
Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com2tag:blogger.com,1999:blog-1274230976683730758.post-55090531114988890452015-10-11T21:59:00.002+02:002015-10-11T21:59:21.523+02:00 La Fête des Maths, Beaumont de LomagneWe were invited to have a stall at the wonderful <a href="http://www.fermat-science.com/agenda-manifestations/la-f%C3%AAte-des-maths/" target="_blank">Fête des Maths</a> at Beaumont de Lomagne this year.<br />
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<a href="http://www.fermat-science.com/agenda-manifestations/la-f%C3%AAte-des-maths/" target="_blank"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2rBEeqz__TwzxuV3DNh-t4MP8qbfTNwMsbxxgxu_zbIIdXWDp4JQltrf-HiRYTdVC9Ph8XA2iogpAbsabFE76-0V0xbxJInKVFg_S3S8QDJpxvFm5S5rYCnN1uyPwPTPkTwmnu7iAgI4/s320/fete+des+maths.jpg" width="226" /></a></div>
As well as having some excellent help from some of our students, it was brilliant to see so many families from school coming to enjoy the day at the birthplace and home of <a href="https://en.wikipedia.org/wiki/Pierre_de_Fermat" target="_blank">Pierre de Fermat.</a><br />
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There were lots of fine stalls there, with all sorts of things to play with: puzzles, games, cooking-related activities, origami; We seven different activities on our stall, and they attracted quite a crowd!<br />
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Here's a slideshow of the event:<br />
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Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com2tag:blogger.com,1999:blog-1274230976683730758.post-72542646332304727552015-05-13T11:23:00.002+02:002019-06-12T10:31:40.959+02:00Seven lessons on scaling in Year 4The idea of scaling is really important in mathematics, and everywhere in the world, so in Year 4 we've spent seven days exploring it in different ways.<br />
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<span style="font-size: x-large;"> <a href="https://www.blogger.com/null" name="one">❶</a> </span>We started off by scaling up shapes drawn on grids. We looked at this:<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSZg6zkZ2jIMs53Oh4_pJgcy4p-5_-f3GnN06uWxqTtVdn1Une0I0R2dQ5INHoIPf0RR-NiTJhj90hbkym2ZDTw414q1gFxLPZWU62q5a_pmQigKyU6bfHNbX8XLjNqABhZiaTYz-8imv4/s1600/scaling+up+notice+wonder.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSZg6zkZ2jIMs53Oh4_pJgcy4p-5_-f3GnN06uWxqTtVdn1Une0I0R2dQ5INHoIPf0RR-NiTJhj90hbkym2ZDTw414q1gFxLPZWU62q5a_pmQigKyU6bfHNbX8XLjNqABhZiaTYz-8imv4/s400/scaling+up+notice+wonder.png" width="286" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8000001907349px;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhESsBy-KzdJ9Gza55aWQHl25YWlf_9wqHHlle6HrTdvD34JXh3o4yCSLlKxaUEkRihJttowjdkodDkovNpHCBZKR38LfUQslEbzxl7D5-KFwtsZc3cd-oJ00BiTYcaqHLV0Ytzw9Kdk7zT/s1600/grid_4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="292" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhESsBy-KzdJ9Gza55aWQHl25YWlf_9wqHHlle6HrTdvD34JXh3o4yCSLlKxaUEkRihJttowjdkodDkovNpHCBZKR38LfUQslEbzxl7D5-KFwtsZc3cd-oJ00BiTYcaqHLV0Ytzw9Kdk7zT/s320/grid_4.png" width="320" /></a></td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPO9p4CI0v9cICuNHMQwNsej9Zzk5vGcboN7uLPnwW_V4IH74Jg2YVyBouAlf2c5pvTcs__-ZjdoGYq4MYoyOaRwuK8xYKNc6ooxOcsbuIGAO4P01LrvUzs1rEa6dZZCG1AKh-6bAkH5Ce/s1600/20150428_094623.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPO9p4CI0v9cICuNHMQwNsej9Zzk5vGcboN7uLPnwW_V4IH74Jg2YVyBouAlf2c5pvTcs__-ZjdoGYq4MYoyOaRwuK8xYKNc6ooxOcsbuIGAO4P01LrvUzs1rEa6dZZCG1AKh-6bAkH5Ce/s1600/20150428_094623.jpg" width="198" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8000001907349px;">This is what Rod drew</td></tr>
</tbody></table>
<div style="text-align: center;">
</div>
<div>
Then we made some scaled up shapes ourselves. And we had <a href="https://picasaweb.google.com/mrsimongregg/Scaling?authuser=0&feat=directlink" target="_blank">lots of them</a> (sometimes it went wrong the first time, an we had to re-do it):<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDJHMk39FcVTL92C9Jk7LX-MMleKL7zQkZ5mEB41Ug0vkEwiA51hgM1darDu__CX1vs6X0wtEMdMI9FEbWmGWaM5dAUaG9JVIFUVnKwYLDieQRRhntmYMp1ohYPKx4JMjJ9YVwLz7Uykg/s1600/Holly.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDJHMk39FcVTL92C9Jk7LX-MMleKL7zQkZ5mEB41Ug0vkEwiA51hgM1darDu__CX1vs6X0wtEMdMI9FEbWmGWaM5dAUaG9JVIFUVnKwYLDieQRRhntmYMp1ohYPKx4JMjJ9YVwLz7Uykg/s1600/Holly.jpg" width="226" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFkIOntxnnnIJSqKvS_SpzJ1Bhm6zRMo5A7V_2Bn0db3egZGmjT7TqVWC96Vyg_qlm6dsai1ds06UrjSwBF_qyupflPp2eqzHfkzVTGFK0zvR132HR0vRjc0Ji32n5qtwiPCaWAuNyvwg/s1600/Aditi+2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFkIOntxnnnIJSqKvS_SpzJ1Bhm6zRMo5A7V_2Bn0db3egZGmjT7TqVWC96Vyg_qlm6dsai1ds06UrjSwBF_qyupflPp2eqzHfkzVTGFK0zvR132HR0vRjc0Ji32n5qtwiPCaWAuNyvwg/s1600/Aditi+2.jpg" width="226" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiabtHhxYZSOPDs5LUaXDdZWYXJXFJtlyL71AOFflLFrSFjU17WIzDEibvusxMJwNKPn2TkiTgc0G8apmqAG4218K177DAuezsWBGW2EJLhAEXOWrcBVP0xDd6bylIRQdala4o512akJAw/s1600/DSC01304.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiabtHhxYZSOPDs5LUaXDdZWYXJXFJtlyL71AOFflLFrSFjU17WIzDEibvusxMJwNKPn2TkiTgc0G8apmqAG4218K177DAuezsWBGW2EJLhAEXOWrcBVP0xDd6bylIRQdala4o512akJAw/s200/DSC01304.JPG" width="200" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3Fyp54FuGI4JAt98W-58I6RshTB1juQGYbdKHQQF7DPw6RQ0qUGQlK6MVTlvwD-hdnoO0VnIsv_YMHayGOBQHBSjtNTMzuy_k1zwgloTpIZTrc6uJGRRm8iJbmAExx1Kkf-PsXRTxuZo/s1600/Alonso.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="96" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3Fyp54FuGI4JAt98W-58I6RshTB1juQGYbdKHQQF7DPw6RQ0qUGQlK6MVTlvwD-hdnoO0VnIsv_YMHayGOBQHBSjtNTMzuy_k1zwgloTpIZTrc6uJGRRm8iJbmAExx1Kkf-PsXRTxuZo/s200/Alonso.jpg" width="200" /></a></div>
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<span style="font-size: x-large;"><a href="https://www.blogger.com/null" name="two">❷</a> </span>The next day we made designs with pattern blocks, with a certain ratio: two triangles to one square. (Thanks to John Golden <a href="https://twitter.com/mathhombre/status/590936890544631808" target="_blank">for this idea.</a>)<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0suFem4oUg9Hn9T0fZt5tlGkZTntEOY4XJQiZgtwR9lEOGobnr8ENPZUgdXWFA3DtTVLwU635ErY7fFUTqfK_En7eDGyXuiKI68NMa_Mj1530sXsWp4jL__BXCJF0iD3oSPhscPrGGZw/s1600/2015-04-29+11.22.24.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0suFem4oUg9Hn9T0fZt5tlGkZTntEOY4XJQiZgtwR9lEOGobnr8ENPZUgdXWFA3DtTVLwU635ErY7fFUTqfK_En7eDGyXuiKI68NMa_Mj1530sXsWp4jL__BXCJF0iD3oSPhscPrGGZw/s1600/2015-04-29+11.22.24.jpg" width="200" /></a></div>
There were streets, cats<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvFGHZ9CvYry7yHp-WpaNuB-dOMXH3UuK-mZkPg_AwR_07M8QdzkBqthQnITcKAJwW0niuBc1PWPUs90h-_nVaSBvSOMtFhSnFlkExIa4jeKl52B7lEHaLiY2jHweSbTqQrpPMQ4pU8Ws/s1600/2015-04-29+10.49.57.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="116" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvFGHZ9CvYry7yHp-WpaNuB-dOMXH3UuK-mZkPg_AwR_07M8QdzkBqthQnITcKAJwW0niuBc1PWPUs90h-_nVaSBvSOMtFhSnFlkExIa4jeKl52B7lEHaLiY2jHweSbTqQrpPMQ4pU8Ws/s1600/2015-04-29+10.49.57.jpg" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsjfC8TYkqFUL27Mi04Wr9kH3ijKKtoFYBgi8HbXIkbvpe1btbrI2QpcWBMJ9bCQaYudjLHdUPSokjDBya-JrXSOqOVCqQMX3b8Itqt_H_7GEOmv8JQ5qMf7e4hHCVHF_w3bZACAKdY10/s1600/2015-04-29+11.29.23.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsjfC8TYkqFUL27Mi04Wr9kH3ijKKtoFYBgi8HbXIkbvpe1btbrI2QpcWBMJ9bCQaYudjLHdUPSokjDBya-JrXSOqOVCqQMX3b8Itqt_H_7GEOmv8JQ5qMf7e4hHCVHF_w3bZACAKdY10/s1600/2015-04-29+11.29.23.jpg" width="200" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKko45YN9Hse5ysndDnWk1Bmkb2-HmZSnzLX6fingTb9REwchkenx3U5lLFivN-gIJC_97YS3iUjiXJZqzQa1AWw0OHEZqyok4Ssu6r0hwKTQ9wwjYG0ynkFxu6qgGWooIENLZ8mHwm8U/s1600/DSC01288.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKko45YN9Hse5ysndDnWk1Bmkb2-HmZSnzLX6fingTb9REwchkenx3U5lLFivN-gIJC_97YS3iUjiXJZqzQa1AWw0OHEZqyok4Ssu6r0hwKTQ9wwjYG0ynkFxu6qgGWooIENLZ8mHwm8U/s320/DSC01288.JPG" width="320" /></a></div>
Here are some of them <a href="https://www.desmos.com/calculator/6furgpqdux" target="_blank">put o</a><a href="https://www.desmos.com/calculator/6furgpqdux" target="_blank">n a graph</a>:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB9IqtqlcMeYXylTr02ILQa1nBqNMu8-D3Z6JYpRPgbc3HugopFO-Db0gKqZe3CqkxLDHIzSa8izm8YM3-jBhoi9IxBLjcLrEz1k7I5bpfgETeo6c21k9kgrFASCY5AhU7X2aV1FWMKVmD/s1600/6furgpqdux.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="334" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB9IqtqlcMeYXylTr02ILQa1nBqNMu8-D3Z6JYpRPgbc3HugopFO-Db0gKqZe3CqkxLDHIzSa8izm8YM3-jBhoi9IxBLjcLrEz1k7I5bpfgETeo6c21k9kgrFASCY5AhU7X2aV1FWMKVmD/s1600/6furgpqdux.png" width="640" /></a></div>
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and two charts made on paper:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg31EWNqMw9XQWM3jRG1uR8pOz9alpGw4J-_K7Lqhh0ycM-13ZUo6JzgsdRe1rvg8qFfBraSmv8bDqfrPL5yoNux7xd9Hdnu-Fovf2W9rVT69x39Kpw0do1YZjZa_5wH39WZnz0Z_Z-9QZX/s1600/1304_001.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="414" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg31EWNqMw9XQWM3jRG1uR8pOz9alpGw4J-_K7Lqhh0ycM-13ZUo6JzgsdRe1rvg8qFfBraSmv8bDqfrPL5yoNux7xd9Hdnu-Fovf2W9rVT69x39Kpw0do1YZjZa_5wH39WZnz0Z_Z-9QZX/s640/1304_001.jpg" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLJbXzgaQo6JnOzPEp4FuZWyxf2_HVap_K9DQyaMMj49Dapyl0UUl_OPaXs2Fsgz0IcVEf8vB-508YozSymRngvyQoqKxKRpxfKuB_B5MLN93F9douXooed8dad4b-u4ifZbOvZGUQOOZr/s1600/1304_003.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLJbXzgaQo6JnOzPEp4FuZWyxf2_HVap_K9DQyaMMj49Dapyl0UUl_OPaXs2Fsgz0IcVEf8vB-508YozSymRngvyQoqKxKRpxfKuB_B5MLN93F9douXooed8dad4b-u4ifZbOvZGUQOOZr/s640/1304_003.jpg" width="640" /></a></div>
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What about a pattern that could carry on forever with the same ratio!<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUJfOGvTOQyqW3oC8uYc2yhmwejJSc3GQYYNeiKnwmEGorZl2A78r7b0R0ox7Da3aIYfBlDNkilWY03eljVi1qH49tZiIeDaxXR3Wdn6yztc7o8hV4llYjNitoVinxhLr85r91-XhP3_c/s1600/can+you+solve+these+3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="186" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUJfOGvTOQyqW3oC8uYc2yhmwejJSc3GQYYNeiKnwmEGorZl2A78r7b0R0ox7Da3aIYfBlDNkilWY03eljVi1qH49tZiIeDaxXR3Wdn6yztc7o8hV4llYjNitoVinxhLr85r91-XhP3_c/s400/can+you+solve+these+3.jpg" width="400" /></a></div>
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<span style="font-size: x-large;"><a href="https://www.blogger.com/null" name="three">❸</a> </span>Next up, we looked at A-sizes of paper. We use A4 most of the time, but the wonderful thing about this shape rectangle is that you can cut it in half and it's just the same shape scaled down. So, that's what we did, starting at A2 paper:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEij2JFjadsLx-3zoTq7qMN6KvWelUlVwzOwnB6zNuHgpbzJHWQDTvtEnX7DtTfsyrZ1LCY7rUxKsEGH3JDFAdDfEYNI4fsytFtGaefCMhoRBqGX5MjayeWGJVxDUyu-t6uSWU_90P0JeuU/s1600/2015-05-04+11.16.36.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEij2JFjadsLx-3zoTq7qMN6KvWelUlVwzOwnB6zNuHgpbzJHWQDTvtEnX7DtTfsyrZ1LCY7rUxKsEGH3JDFAdDfEYNI4fsytFtGaefCMhoRBqGX5MjayeWGJVxDUyu-t6uSWU_90P0JeuU/s320/2015-05-04+11.16.36.jpg" width="238" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA24uqo1AUK2OT7dVt5v75E94iX3SlsRLLD8-8rYOyM_Z5aa94_utVKQIdKCLsnTPjG9fpnF5apw_7OUksHdeXq8-YUWouMY_jj2i9HctOCn1m6MHKSjz8lvnKhk69Zg4y6yEx1AR_UoU/s1600/2015-05-04+11.33.07.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA24uqo1AUK2OT7dVt5v75E94iX3SlsRLLD8-8rYOyM_Z5aa94_utVKQIdKCLsnTPjG9fpnF5apw_7OUksHdeXq8-YUWouMY_jj2i9HctOCn1m6MHKSjz8lvnKhk69Zg4y6yEx1AR_UoU/s320/2015-05-04+11.33.07.jpg" width="238" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOxGsUUtLF8yuG9LTEajhXtcw48Qiqs6EFdzkdRM-IyiprUyqnllWN1aWlOm5Y1vBs5LUqjV82xy8XrDraCRwFJM9PdJ7e-IYieHKdqxCmb_yEMVC6hMwpJPMN4yfxgR46rbmYHfmdoTU/s1600/2015-05-04+11.21.49.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="238" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOxGsUUtLF8yuG9LTEajhXtcw48Qiqs6EFdzkdRM-IyiprUyqnllWN1aWlOm5Y1vBs5LUqjV82xy8XrDraCRwFJM9PdJ7e-IYieHKdqxCmb_yEMVC6hMwpJPMN4yfxgR46rbmYHfmdoTU/s320/2015-05-04+11.21.49.jpg" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3tNUEID66dxJpVM8XFxZL3Fq1wPhNu3gQEQyFTngp9GkQzArCSZWC3Clu-C7CpcyVSzL3KgXHZdp7XNeYm1I8koiwRYXb116tgpfTJaCcx7L2d4jHl1Y3i8UtEjyEFVAInc1xicWWjJI/s1600/2015-05-13+11.10.02.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3tNUEID66dxJpVM8XFxZL3Fq1wPhNu3gQEQyFTngp9GkQzArCSZWC3Clu-C7CpcyVSzL3KgXHZdp7XNeYm1I8koiwRYXb116tgpfTJaCcx7L2d4jHl1Y3i8UtEjyEFVAInc1xicWWjJI/s320/2015-05-13+11.10.02.jpg" width="240" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDoh6oPVS6cn6PP3bmuZJqANQXe5U1nuDrwx6TiWUyOaE3ctpELvqafuMI83U2pj6FKovf8G9mtiOcBCHoLYhc2myYXnrKQrkCMyhjrvCJ4deZjdoC51gGUoGB-3u4px3NcJ1cCzSHnJ8/s1600/2015-05-13+11.10.12.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDoh6oPVS6cn6PP3bmuZJqANQXe5U1nuDrwx6TiWUyOaE3ctpELvqafuMI83U2pj6FKovf8G9mtiOcBCHoLYhc2myYXnrKQrkCMyhjrvCJ4deZjdoC51gGUoGB-3u4px3NcJ1cCzSHnJ8/s320/2015-05-13+11.10.12.jpg" width="320" /></a></div>
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<span style="font-size: x-large;"><a href="https://www.blogger.com/null" name="four">❹</a> </span>In our fourth lesson, we looked at two models of the A380. The real A380 is one hundred times longer than the big model, and five hundred times longer than the small one.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0DFAAuAGmCdRpLp_m6opXXQkEPI48UCAYVw0ZrAK-QWD3oExKtJjkU4VghHpOLByS7pOOxo5HhIyKS6yregVm4DPyZEm_JHJpiJebIgw-1qOnhTawjHGRFfIgdY08KfJziHVliaVcdbnz/s1600/2015-05-06+08.45.54.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0DFAAuAGmCdRpLp_m6opXXQkEPI48UCAYVw0ZrAK-QWD3oExKtJjkU4VghHpOLByS7pOOxo5HhIyKS6yregVm4DPyZEm_JHJpiJebIgw-1qOnhTawjHGRFfIgdY08KfJziHVliaVcdbnz/s200/2015-05-06+08.45.54.jpg" width="200" /></a></div>
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Taking the small one, how long would the runway at Blagnac need to be to be the same scale?</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQA629OOC5wwje-DDAZF-IYCEJAnPinelGHBzt9wDoRhtDOmrn3ZGTT2yselANf6ArQJDj7v7XchzmgfNBYB-0ozw9VHJJi615nVRJZx5AeBdyQUHv3gahxbSJtSUAK1TsFxnsG-ddiTiC/s1600/2015-05-06+08.49.20.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQA629OOC5wwje-DDAZF-IYCEJAnPinelGHBzt9wDoRhtDOmrn3ZGTT2yselANf6ArQJDj7v7XchzmgfNBYB-0ozw9VHJJi615nVRJZx5AeBdyQUHv3gahxbSJtSUAK1TsFxnsG-ddiTiC/s200/2015-05-06+08.49.20.jpg" width="200" /></a></div>
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We looked on Google maps:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDWkq7CurTcwiGqFRwazDXAUC7TmkXP9_7cRynib5l6wcjrEC2_5absl8GWQOdyKKQcoyEMM7MBo1_QNxeUB3KUsk4nU7Nn7bMVonG8jj-9UVcP3TcPxkB3ncKdsdf8p5CfW94VBxpdavs/s1600/blagnac+runway.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="292" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDWkq7CurTcwiGqFRwazDXAUC7TmkXP9_7cRynib5l6wcjrEC2_5absl8GWQOdyKKQcoyEMM7MBo1_QNxeUB3KUsk4nU7Nn7bMVonG8jj-9UVcP3TcPxkB3ncKdsdf8p5CfW94VBxpdavs/s400/blagnac+runway.GIF" width="400" /></a></div>
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So, about 4km. We divided this by 500 together, and got...</div>
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<span style="font-size: x-large;">8 metres!</span></div>
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We made some 8 metre runways (they're a bit too thin, but never mind):</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBbzHOtTbV0COW5VoFwqfcWyJEd0Q7LVelgPm2TqfX-WEkpKVjH_dn8Qt2ffdyhvjTvwy6xwIMupNP7gBtFkKkdZxZSLYnf30HddSANBEmE62HJfeyhmiRfOKd8DvkhdbjrmWL_PG0uL51/s1600/DSC01329.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBbzHOtTbV0COW5VoFwqfcWyJEd0Q7LVelgPm2TqfX-WEkpKVjH_dn8Qt2ffdyhvjTvwy6xwIMupNP7gBtFkKkdZxZSLYnf30HddSANBEmE62HJfeyhmiRfOKd8DvkhdbjrmWL_PG0uL51/s200/DSC01329.JPG" width="200" /></a></div>
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<span style="font-size: x-large;"><a href="https://www.blogger.com/null" name="five">❺</a> </span>Another approach was<a href="https://picasaweb.google.com/mrsimongregg/ScalingUpCuisenaireRods?authuser=0&feat=directlink" target="_blank"> to scale up squares of Cuisenaire rods</a>:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh26E-E-ZIuKVtH3b_hzgflQaUGdJAlBEy2CgeocI9Mv0efM0NA7dQZ9Hpbm5tu08rHyLntR0mB9whaWPwpYe1UmjN607w4g4sph06jV7TFbukHt0diTxABjirEl0GUe71-zQK1GDFWQh8/s1600/2015-05-07+11.26.43.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh26E-E-ZIuKVtH3b_hzgflQaUGdJAlBEy2CgeocI9Mv0efM0NA7dQZ9Hpbm5tu08rHyLntR0mB9whaWPwpYe1UmjN607w4g4sph06jV7TFbukHt0diTxABjirEl0GUe71-zQK1GDFWQh8/s200/2015-05-07+11.26.43.jpg" width="200" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjljja-Z-x-D6J6S3iPco4LBXzRZaBCflpsMnVswVId_lCnoKzvmJ9Tr1kSovD7f_5m30cbjVt8te_YNc5GVwVZD72hOWiTgdCcDEaIm_TXhIiie1Zjay6WRW4pjJPcDhOyhLS846I-Yfw/s1600/2015-05-07+11.39.58.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjljja-Z-x-D6J6S3iPco4LBXzRZaBCflpsMnVswVId_lCnoKzvmJ9Tr1kSovD7f_5m30cbjVt8te_YNc5GVwVZD72hOWiTgdCcDEaIm_TXhIiie1Zjay6WRW4pjJPcDhOyhLS846I-Yfw/s200/2015-05-07+11.39.58.jpg" width="200" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPj1VuWEdN8DvS-1Ytwym-b8ghukC3aqMV8fEar_4cF8I4zsg5fgZlsX6ZidecvdD1QgfKVfr1iTDL-huAzGFkuhbb6w6dE8V0ZzG21ipeNqeb1CagGwwZ3z1t8tpL8CCoZYOJXbKwqTo/s1600/2015-05-07+11.41.38.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPj1VuWEdN8DvS-1Ytwym-b8ghukC3aqMV8fEar_4cF8I4zsg5fgZlsX6ZidecvdD1QgfKVfr1iTDL-huAzGFkuhbb6w6dE8V0ZzG21ipeNqeb1CagGwwZ3z1t8tpL8CCoZYOJXbKwqTo/s200/2015-05-07+11.41.38.jpg" width="200" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUaE-X9CEnpOCdqDhbH5yaraEen0VL_wKOZ_Do5VXbc3Ds0BxDZXD8LPPaJ2bLalBwTsEJIn8WpoKmzb74aSZuAdnAUjUHYPr44AnB9Tkb1K4ovZnaCbmCDkPYDnXQzl4rdaWPec3B-k8/s1600/2015-05-07+11.42.02.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUaE-X9CEnpOCdqDhbH5yaraEen0VL_wKOZ_Do5VXbc3Ds0BxDZXD8LPPaJ2bLalBwTsEJIn8WpoKmzb74aSZuAdnAUjUHYPr44AnB9Tkb1K4ovZnaCbmCDkPYDnXQzl4rdaWPec3B-k8/s200/2015-05-07+11.42.02.jpg" width="200" /></a></div>
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<span style="font-size: x-large;"><a href="https://www.blogger.com/null" name="six">❻</a> </span>Next we <a href="http://y4ist.blogspot.fr/2015/05/scaling-up-recipes.html" target="_blank">made chocolate cornflake cupcakes.</a> But we needed to scale up the recipe to make the right number of cupcakes.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhn5yzzGFG98hfgJ7d-gN7-e-Ez98XlKofeUpGGtWUPjFxWMDcF87xsxlsYhfZKwg7WcAGLw0g2RLZwM2wErCpcsmRwkCa9X5oA6yJG6-E10S2RQ0cyKcshY01sWvHvTXAZbWB7-w8bk4Qq/s1600/20150512_095702.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhn5yzzGFG98hfgJ7d-gN7-e-Ez98XlKofeUpGGtWUPjFxWMDcF87xsxlsYhfZKwg7WcAGLw0g2RLZwM2wErCpcsmRwkCa9X5oA6yJG6-E10S2RQ0cyKcshY01sWvHvTXAZbWB7-w8bk4Qq/s320/20150512_095702.jpg" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcGelDuVUXZRp6N-i7BgFfHRwXgpdOqt2y-Ke5h3CmsSNmNo2SP8D4oJ71RMuktu9Wx0gOYZNaFZ0-gCnnwoQXZT_2z5wUPx2kHFH-XnSDWQ7EMPYsYAltCP12ebICj8bfZLsGNyuwcMFq/s1600/20150512_095710.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcGelDuVUXZRp6N-i7BgFfHRwXgpdOqt2y-Ke5h3CmsSNmNo2SP8D4oJ71RMuktu9Wx0gOYZNaFZ0-gCnnwoQXZT_2z5wUPx2kHFH-XnSDWQ7EMPYsYAltCP12ebICj8bfZLsGNyuwcMFq/s320/20150512_095710.jpg" width="320" /></a></div>
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We also had a go at <a href="http://www.iboard.co.uk/iwb/Recipe-Proportions-Scale-Up-361" target="_blank">scaling up</a> with this website</div>
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<a href="http://www.iboard.co.uk/iwb/Recipe-Proportions-Scale-Up-361" target="_blank"><img border="0" height="215" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYXPFrYuAylAn0fz-p16Z9d5yrZIAodRUU_W4sID3h7La-VDGruQL4gzWgTuPykufgjIbrySR8zkWWe4OIvwLoF8hakLupoStXiimTmjKvNCQY0IgnSk4cTbottBhrBDf4Dfb2TD7yNQB-/s320/scale+up.GIF" width="320" /></a></div>
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and <a href="http://www.iboard.co.uk/iwb/Recipe-Proportions-Scale-Down-362" target="_blank">scaling down</a> with this:</div>
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<a href="http://www.iboard.co.uk/iwb/Recipe-Proportions-Scale-Down-362" target="_blank"><img border="0" height="211" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkvyjYtUZKaayUwpL3s-dx4rjXe8N0G9eDpvIJq6O327QYnmVEnpnUEQWd4F55cfqCrMbuB7uker-SUM34maLVhwRLXWdt_c5YImP5-PIhxrs0fROXS4BwclHnwvtziGhYboWXWxXBtcAz/s320/scaling+down.GIF" width="320" /></a></div>
<span style="font-size: x-large;"><a href="https://www.blogger.com/null" name="seven">❼</a> </span>This one was a bit of a challenge. We looked at a clip from Zoolander:<br />
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<iframe allowfullscreen="" frameborder="0" height="281" mozallowfullscreen="" src="https://player.vimeo.com/video/104682338" webkitallowfullscreen="" width="500"></iframe> <br />
Thanks to <a href="http://robertkaplinsky.com/work/how-much-bigger-should-they-make-zoolanders-school/" target="_blank">Robert Kaplinski for this lesson</a>.<br />
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The real question is how many times would you need to scale this model up to make the real school?<br />
And.... how can you work this out?<br />
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We thought about this in groups, and came up with different ideas. But it was a hard question!<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDyHhmRwm1J2GgivMJVyLX22gsRbbnZ03wi04ezNqjg5EgYOzcfIj6B8a47L2zVmXw8ufl1JILKu8CptXYLqI5Hlxlsg6_DqtqK1gEti6OR-BxYrx3pO9IlRYSilYXQOnIgN2LPfv8dfQ/s1600/2015-05-13+10.20.24.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDyHhmRwm1J2GgivMJVyLX22gsRbbnZ03wi04ezNqjg5EgYOzcfIj6B8a47L2zVmXw8ufl1JILKu8CptXYLqI5Hlxlsg6_DqtqK1gEti6OR-BxYrx3pO9IlRYSilYXQOnIgN2LPfv8dfQ/s320/2015-05-13+10.20.24.jpg" width="240" /></a></div>
Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com3tag:blogger.com,1999:blog-1274230976683730758.post-82603600264216419142015-04-07T12:41:00.002+02:002015-04-09T21:42:36.860+02:00International maths Competition in Toulouse<div dir="ltr" style="text-align: left;" trbidi="on">
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What a great weekend! A Carnival of Mathematics</h2>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip_nWxOewqmcm346p6k8_jn0iIBdjh8VUGhl4yOnXuZqCKv8m0blIL2Pf_-zdr-jWy6hsCAxW2khjR8DRWjVZRPj4i4xvnF3aPE6Y4r0t-rYqz_ZlE3x0CKFLd4M6fjhQ68OjHr_l7HCBm/s1600/_DSCF1320.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip_nWxOewqmcm346p6k8_jn0iIBdjh8VUGhl4yOnXuZqCKv8m0blIL2Pf_-zdr-jWy6hsCAxW2khjR8DRWjVZRPj4i4xvnF3aPE6Y4r0t-rYqz_ZlE3x0CKFLd4M6fjhQ68OjHr_l7HCBm/s1600/_DSCF1320.jpg" height="300" width="400" /></a></div>
During the Weekend of the 27th to 29th March 2015, the International School of Toulouse hosted the the ISMTF Middle school Mathematics competition. This is a annual event for students aged 14 and under (There are others for older students too) Each year it takes place in a different host school and this year it was our turn in Toulouse. We have had some great experiences at other events so it was great to have a turn at hosting!<br />
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Teams arrived at the airport throughout the day on Friday and were met by staff and parents from the school who escorted them to Toulouse where they could drop their bags and take part in a great Scavenger hunt around the city! We wanted our visitors to get the most from their visit!<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsgCqTlZO4jv4ASMzDD1IS8IaZHebWNhoU1FcHpi18uB2GqUsRp3oheK1In1T7E4fIPXu2ZJP7Rt3gU1yWYjB0fzKkQz8UR7hI1lrdQGk9W15IAYkZ1pMvA9NiJM4-ZKLi8yxmVJRhkMoc/s1600/_DSCF1139.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsgCqTlZO4jv4ASMzDD1IS8IaZHebWNhoU1FcHpi18uB2GqUsRp3oheK1In1T7E4fIPXu2ZJP7Rt3gU1yWYjB0fzKkQz8UR7hI1lrdQGk9W15IAYkZ1pMvA9NiJM4-ZKLi8yxmVJRhkMoc/s1600/_DSCF1139.jpg" height="240" width="320" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhb-pVbSlXjiDL3jlMX8MxHKJdhDrRf1eGaWS4ejzlgylXV7Ic7qxeTnu2ZGYwVdu3Y3XaejLMozy8OYjqr7FQbGfeXKsB49vxOPhyLah7MWyXK6_nRi522_ba9XMOQT7rH78KJKLrtpWRm/s1600/_DSCF1103a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhb-pVbSlXjiDL3jlMX8MxHKJdhDrRf1eGaWS4ejzlgylXV7Ic7qxeTnu2ZGYwVdu3Y3XaejLMozy8OYjqr7FQbGfeXKsB49vxOPhyLah7MWyXK6_nRi522_ba9XMOQT7rH78KJKLrtpWRm/s1600/_DSCF1103a.jpg" height="240" width="320" /></a></div>
At around 17h they arrived at school where they did some ice breaking activities and gegan getting to know each other and the school before being paired up with their host families from IST who had generously agreed to look after them during the weekend.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhklqiTosUpj8S6VgWfOl_jhc6ASMh3tXrl0UbmzB_TQN8VOftqQ5XM95xLoQAYymBZuiXDmEQwnX0UTgcQYJ4oAbukgh1-GE461j6SlP0QBRLq8eHwmLD7hfugxcY4IKutspqNrsJdV37H/s1600/_DSCF1304.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhklqiTosUpj8S6VgWfOl_jhc6ASMh3tXrl0UbmzB_TQN8VOftqQ5XM95xLoQAYymBZuiXDmEQwnX0UTgcQYJ4oAbukgh1-GE461j6SlP0QBRLq8eHwmLD7hfugxcY4IKutspqNrsJdV37H/s1600/_DSCF1304.jpg" height="240" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfzL64wr-CL3LjAkfWxF-fIr8JG4IqVxNlXifnEgBEHfebg4HgNh3DkyyDkpbSnr7YrW55ziaTSFM3x5Y08MngE6cJPyjwfVSCujKnrBXN3FwE54fYAEr_mNFLhtjGiDuDHTVsVj6voytj/s1600/_DSCF1305.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfzL64wr-CL3LjAkfWxF-fIr8JG4IqVxNlXifnEgBEHfebg4HgNh3DkyyDkpbSnr7YrW55ziaTSFM3x5Y08MngE6cJPyjwfVSCujKnrBXN3FwE54fYAEr_mNFLhtjGiDuDHTVsVj6voytj/s1600/_DSCF1305.jpg" height="240" width="320" /></a></div>
On Saturday morning, competition began in earnest. Teams of three went through several rounds of competition solving problems with only the aid of pencil and paper. This is a challenging competition and not for the faint hearted. Any correct solutions found are to be celebrated!<br />
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After a well earned lunch, we had the privilege of hearing our visiting author Simon Singh talk about his book Fermat's last theorem with great passion. Obviously this is story of some local significance! All this before taking off to see the new Areoscopia museum and the Final Assembly line of the A380.<br />
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After another night with host families students reconvened on Sunday morning for another contest. this time science, technology and were maths combined. Students had a brief to build a machine with certain capabilities which would then be tested to score points. Maths problems had to be solved to get the parts they needed.<br />
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An awards ceremony took place where 1st prize went to the International School of Lausanne for the Saturday competition and then everyone began their long journey home!<br />
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A great event all round and we are so very grateful to all of the people that helped us make this event such a success!<br />
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Anonymoushttp://www.blogger.com/profile/05835250335807360943noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-31348490761107670382015-03-17T12:28:00.002+01:002015-03-20T21:20:35.921+01:00ISMTF Middle School Competition<div dir="ltr" style="text-align: left;" trbidi="on">
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Information for ISToulouse families</h3>
Some time ago, the International School of Toulouse volunteered to host the ISMTF middle school Mathematics competition in 2015. The International Schools Mathematics Teachers Foundation (ISMTF) has been running competitions for many years and students from the International School of Toulouse have taken part in many of them<br />
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They run three competitions every year,<br />
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1. The middle school competition for 14 year old<br />
2. The junior competition for 16 year olds <br />
3. the senior competition for 18 year olds<br />
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Their continued success depends on schools volunteering to host the events. In recent years, students from the IST have taken part in competitions in Paris, Basel, Vienna, Milan, Luxembourg and Geneva all of which have been fabulous experiences. We hope to have many more and, as such, we are only too glad to take our turn of hosting. The competition takes place between the 27th and 29th of March 2015.<br />
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This year the competition will involve 11 students from IST in years 8 and 9 as part of a total of 117 students and 29 visiting teachers from schools from Europe and beyond. We are delighted to welcome all of the schools some of who are coming from as far a field as India, Dubai, Cairo and Tunisia.<br />
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Huge Organisiation</h3>
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Obviously the event has taken a huge amount of preparation lead by the Mathematics department at the school with terrific support from the whole school community. We are so very grateful for all of the support we have from our colleagues, students and parent and governing body. It has been a wonderful coming together of the whole school to work towards a truly international and hopefully very successful event that shows the value of goodwill within the school community. I expect to spend a good deal of time saying thank you after the event and paying back a considerable debt of support that I will owe.</div>
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What does it involve?</h3>
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<li>This competition will involve 117 students between the ages of 11 and 14 in two competitions. </li>
<li>The International School of Toulouse has also entered teams and will provide substitutes for any absentees from other schools. </li>
<li>Students come from International schools in Europe and beyond. </li>
<li>Students will stay with host families from the International School of Toulouse and Coaches will stay in a hotel in Toulouse. </li>
<li>The first competition on Saturday takes place in teams of three where students will represent the school they come from. </li>
<li>The second competition on Sunday involves students competing in teams of 6 where students will be mixed in teams with students from different schools. </li>
<li>On the Saturday afternoon, there will be an excursion to the Airbus A380 final assembly line and the Aeroscopia aviation museum. </li>
<li>We are delighted to welcome author Simon Singh as a guest speaker on Saturday where he will talk about his book, Fermat's last Theorem, which is a story of great local significance.</li>
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Host Families</h3>
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A significant part of the experience is that the visiting students are hosted by families rom our school community. This was always a tall order given how small a school we are, but with the very able Friends of IST and the very obliging parent community we are delighted to be able to offer this experience to students. This also allows the school community to be more involved with the event. Thank you to all of the families who are able to help us with this. We are very grateful.<br />
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Simon Singh</h3>
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We are particularly pleased to welcome author Simon Singh to the school for that weekend. He is best know to mathematicians as the author of 'Fermat's last Theorem' which tells the wonderful story of this enigmatic mathematical problem that local mathematician Pierre de Fermat brought to the world's attention and was finally proven by mathematician Andrew Wiles nearly 400 years later. Some students at the IST will have the opportunity to listen to Simon Singh Speak about his latest book 'The Simpsons and their mathematical secrets', while he is here.<br />
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Information for participating schools is hosted <a href="http://www.teachmathematics.net/page/17710/ismtf-middle-school-competition" target="_blank">here</a>. </div>
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Anonymoushttp://www.blogger.com/profile/05835250335807360943noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-70190557831511159052015-01-08T20:01:00.001+01:002015-01-08T20:02:21.121+01:00Cuisenaire rod patterns in Year 4<div class="separator" style="clear: both; text-align: center;">
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Last term, in pairs, Year4 had a go at <a href="http://y4ist.blogspot.fr/search/label/cube%20patterns" target="_blank">creating sequences of cubes and understanding them</a>. This week they've been trying a similar thing with Cuisenaire rods. And what a great lot of sequences they've created!<br />
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More challenging perhaps, is <i>understanding </i>the patterns and how they grow - and this means understanding them <b>mathematically</b>.<br />
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Some of the students got straight into the number crunching:<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjBLim3jfXOVPUPhcpkMzbJVfEglgD99MyS5LRBg68lRePvRVSCq7WrgoIcqQBXszZu2DeKQKN9Ap-Ml1w38LCO_0_XO5JtywvLjRS1w2hGEHuhstqLSduPXM8xSrc7TcV14zuo9HMyPLD/s1600/2015-01-07+13.00.51.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjBLim3jfXOVPUPhcpkMzbJVfEglgD99MyS5LRBg68lRePvRVSCq7WrgoIcqQBXszZu2DeKQKN9Ap-Ml1w38LCO_0_XO5JtywvLjRS1w2hGEHuhstqLSduPXM8xSrc7TcV14zuo9HMyPLD/s1600/2015-01-07+13.00.51.jpg" height="213" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">oops! - this one is not quite right!</td></tr>
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Others wanted to draw their sequence first:</div>
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They had to think hard about the patterns:</div>
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Some of the students were willing to talk about their patterns:</div>
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<a href="http://y4ist.blogspot.fr/" target="_blank">Originally posted on the Year 4 blog</a></div>
Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-14760803392365663942014-12-21T13:30:00.002+01:002014-12-21T15:11:08.209+01:00Clock flowers in Year 4<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjChyphenhyphenKcofb_GbyLupgUHef_cmgLMd6FW22_SBIWznzJ14sJ9g22Nu9N_fwIb3ODRW6plhEgapG-xMpqoxNtRO42Cb-dBqLK9s4Pu9uM4ENDwGZnIsE1sSokeKuAevqkFH7LmuNGL4WqMJw/s1600/08.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjChyphenhyphenKcofb_GbyLupgUHef_cmgLMd6FW22_SBIWznzJ14sJ9g22Nu9N_fwIb3ODRW6plhEgapG-xMpqoxNtRO42Cb-dBqLK9s4Pu9uM4ENDwGZnIsE1sSokeKuAevqkFH7LmuNGL4WqMJw/s1600/08.PNG" height="200" width="193" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZ5wHasZPgqKKnuZttGXDzfTEBtGIaEkiV0jQpC3QDiII7efRVveCbC4cMz2iP5AVEBeOKr_66CEFjNHDqPUteWFjrRw59SYgZmJ3NvJ2-RttUiMHKfINIhwMfnspYGCqdKzCiDUIdJC0/s1600/09.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZ5wHasZPgqKKnuZttGXDzfTEBtGIaEkiV0jQpC3QDiII7efRVveCbC4cMz2iP5AVEBeOKr_66CEFjNHDqPUteWFjrRw59SYgZmJ3NvJ2-RttUiMHKfINIhwMfnspYGCqdKzCiDUIdJC0/s1600/09.PNG" height="200" width="186" /></a></div>
In the course of <a href="http://pinkmathematics.blogspot.fr/2014/12/counting-circles-in-year-4.html" target="_blank">our counting circle sessions</a> we looked at clock counting (mod 60 counting).
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We took this <a href="http://y4ist.blogspot.fr/search/label/clock%20flowers" target="_blank">a bit further.</a> using a Scratch project to generate these easily. </div>
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<iframe allowfullscreen="" allowtransparency="true" frameborder="0" height="402" src="http://scratch.mit.edu/projects/embed/39502630/?autostart=false" width="485"></iframe>
It was a great opportunity for mathematical noticing, reasoning and claim-making. For instance<br />
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<img src="http://1.bp.blogspot.com/-tRlPeNtg31U/VDbbpUAHKiI/AAAAAAAAABE/NTPDQ-rUjH4/s45/bl_gallery.png" style="max-width: 36px;" /></div>
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<cite class="user" style="font-style: normal; font-weight: bold;"><a href="http://www.blogger.com/profile/02423096890278914302" rel="nofollow" style="color: #4d469c; text-decoration: none;">Rose</a></cite><span class="icon user" style="font-weight: bold;"></span><span class="datetime secondary-text" style="margin-left: 6px;"><a href="http://y4ist.blogspot.com/2014/12/clock-flowers-on-scratch.html?showComment=1418639620459#c168752533841002905" rel="nofollow" style="color: #4d469c; text-decoration: none;">15 December 2014 at 02:33</a></span></div>
<div class="comment-content" id="bc_0_4MC" style="margin-bottom: 8px; text-align: justify;">
The odd numbers go to every stop</div>
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<img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiNJCYBVWosK21DdX6VC8scsJWP5BEuDAoWGgTnP7Y8LGuxok3nF2sbksV5j9L3-RNWdcUY3XPcRg5ivZi2nSa1Yfso4Lo5IZn35k1h6HKrXqz3b4ecyCLPxgZaliND88pASzIh_B1VF3j/s45/Justus.PNG" style="max-width: 36px;" /></div>
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<div class="comment-header" id="bc_0_3M" kind="m" style="margin: 0px 0px 8px;">
<cite class="user" style="font-style: normal; font-weight: bold;"><a href="http://www.blogger.com/profile/11613143702836484767" rel="nofollow" style="color: #4d469c; text-decoration: none;">Justus</a></cite><span class="icon user" style="font-weight: bold;"></span><span class="datetime secondary-text" style="margin-left: 6px;"><a href="http://y4ist.blogspot.com/2014/12/clock-flowers-on-scratch.html?showComment=1418639908913#c8578246979380228566" rel="nofollow" style="color: #4d469c; text-decoration: none;">15 December 2014 at 02:38</a></span></div>
<div class="comment-content" id="bc_0_3MC" style="margin-bottom: 8px; text-align: justify;">
I do not think so, because 15 is a odd number and it does not meet every stop</div>
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and<br />
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<img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiNJCYBVWosK21DdX6VC8scsJWP5BEuDAoWGgTnP7Y8LGuxok3nF2sbksV5j9L3-RNWdcUY3XPcRg5ivZi2nSa1Yfso4Lo5IZn35k1h6HKrXqz3b4ecyCLPxgZaliND88pASzIh_B1VF3j/s45/Justus.PNG" style="max-width: 36px;" /></div>
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<div class="comment-header" id="bc_0_13M" kind="m" style="margin: 0px 0px 8px;">
<cite class="user" style="font-style: normal; font-weight: bold;"><a href="http://www.blogger.com/profile/11613143702836484767" rel="nofollow" style="color: #4d469c; text-decoration: none;">Justus</a></cite><span class="icon user" style="font-weight: bold;"></span><span class="datetime secondary-text" style="margin-left: 6px;"><a href="http://y4ist.blogspot.com/2014/12/clock-flowers-on-scratch.html?showComment=1418639774531#c7302776969738855799" rel="nofollow" style="color: #4d469c; text-decoration: none;">15 December 2014</a></span></div>
<div class="comment-content" id="bc_0_13MC" style="margin-bottom: 8px; text-align: justify;">
I notice that all of the prime number under 22 meet all of the numbers under 59 on the clock.It looks so cool!</div>
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<img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi94bjfNbbAflNQ4JMuRsHg6j6VV12tXDgq6WkzVQiS3ZMZAjrSR3NoyHrm-WN9ih9yQcsPp5RD3FVMiyvv-oUaoAwTD0EUCOi_0SEwE5CnB73hGz9K8m6hLLiu3E7dlbtLnzAajKomz04/s45/Mr%25252BGregg.png" style="max-width: 36px;" /></div>
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<div class="comment-header" id="bc_0_11M" kind="m" style="margin: 0px 0px 8px;">
<cite class="user blog-author" style="font-style: normal; font-weight: bold;"><a href="http://www.blogger.com/profile/15114830266540886842" rel="nofollow" style="color: #4d469c; text-decoration: none;">Mr Grgg</a></cite><span class="icon user blog-author" style="background-image: url(data:image/png; background-repeat: no-repeat; display: inline-block; font-weight: bold; height: 18px; margin: 0px 0px -4px 6px; width: 18px;"></span><span class="datetime secondary-text" style="margin-left: 6px;"><a href="http://y4ist.blogspot.com/2014/12/clock-flowers-on-scratch.html?showComment=1418643057606#c1472037978252392958" rel="nofollow" style="color: #4d469c; text-decoration: none;">15 December 2014</a></span></div>
<div class="comment-content" id="bc_0_11MC" style="margin-bottom: 8px; text-align: justify;">
What you say is almost true, Justus, but what about 2, 3 and 5?<br />
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What do you think?</div>
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<img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiNJCYBVWosK21DdX6VC8scsJWP5BEuDAoWGgTnP7Y8LGuxok3nF2sbksV5j9L3-RNWdcUY3XPcRg5ivZi2nSa1Yfso4Lo5IZn35k1h6HKrXqz3b4ecyCLPxgZaliND88pASzIh_B1VF3j/s45/Justus.PNG" style="max-width: 36px;" /></div>
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<cite class="user" style="font-style: normal; font-weight: bold;"><a href="http://www.blogger.com/profile/11613143702836484767" rel="nofollow" style="color: #4d469c; text-decoration: none;">Justus</a></cite><span class="icon user" style="font-weight: bold;"></span><span class="datetime secondary-text" style="margin-left: 6px;"><a href="http://y4ist.blogspot.com/2014/12/clock-flowers-on-scratch.html?showComment=1418721632389#c6173488667311540043" rel="nofollow" style="color: #4d469c; text-decoration: none;">16 December 2014</a></span></div>
<div class="comment-content" id="bc_0_12MC" style="margin-bottom: 8px; text-align: justify;">
3 5 7 do not visit all of the numbers because are the factors of 60</div>
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The class also had a go at creating some of the "clock flowers" by hand:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx66g0cNN02WEX9tOWTVPk9AlUkCBFJpcZb6g4TTE3rBdSdXtK2ZlBaRrsTZFXCjOUgQc44NLSfu9HejAwL6VzBLkGon39Uc8sI9-XqMcL6FSv6vBUR9buIs1RnfsBAEnyTtao-Aq4q40/s1600/Rod+3+15+20.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx66g0cNN02WEX9tOWTVPk9AlUkCBFJpcZb6g4TTE3rBdSdXtK2ZlBaRrsTZFXCjOUgQc44NLSfu9HejAwL6VzBLkGon39Uc8sI9-XqMcL6FSv6vBUR9buIs1RnfsBAEnyTtao-Aq4q40/s1600/Rod+3+15+20.bmp" height="320" width="227" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiicbV2Pw_gLFfqzDS-MzbHyfGKXdOdn4OJU8-PAeaZJ5zhIEGjFRdm4K2k0BesGG6X4CU09JJqbTM-bFr9XhtDUjYce99DeCGfrbX_8cdWIK6NMqkGIOyNApcxCMcD629q4v1wb0gbhpo/s1600/Samyak+2+5+30.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiicbV2Pw_gLFfqzDS-MzbHyfGKXdOdn4OJU8-PAeaZJ5zhIEGjFRdm4K2k0BesGG6X4CU09JJqbTM-bFr9XhtDUjYce99DeCGfrbX_8cdWIK6NMqkGIOyNApcxCMcD629q4v1wb0gbhpo/s1600/Samyak+2+5+30.bmp" height="320" width="226" /></a></div>
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and looked at the same thing in terms of division:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOpUZdzwpg0RwB3_MMPVAcY-_Gmxg1-f4YTHgqFMYHjn6_nE03M91OzUBYZQBW353S_UntoLxzowCvpIXzNhr3cnV75HnZ_zc4jFxGzYJDkP7GqQKKPblwNUXk_DWYxYOZcoX02E_AABjv/s1600/0919_012.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOpUZdzwpg0RwB3_MMPVAcY-_Gmxg1-f4YTHgqFMYHjn6_nE03M91OzUBYZQBW353S_UntoLxzowCvpIXzNhr3cnV75HnZ_zc4jFxGzYJDkP7GqQKKPblwNUXk_DWYxYOZcoX02E_AABjv/s1600/0919_012.jpg" height="320" width="226" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEickN7l-DKf7S-Hj0jvJzLdBWxpNdl96TKb-hBCsSEU49yvwc2Ipap82aZI3AMRyjqqIyjOhJG0S9izDd3y5i-D8MDmJJnTfWNYX53AdbOWpIjRqGn3AnQhMZh75Nzbhx980VvD3g6KedO4/s1600/0919_005.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEickN7l-DKf7S-Hj0jvJzLdBWxpNdl96TKb-hBCsSEU49yvwc2Ipap82aZI3AMRyjqqIyjOhJG0S9izDd3y5i-D8MDmJJnTfWNYX53AdbOWpIjRqGn3AnQhMZh75Nzbhx980VvD3g6KedO4/s1600/0919_005.jpg" height="320" width="226" /></a></div>
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There's a lot more mileage in these clock patterns. Who knows where we'll take it next time... maybe string patterns?Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com1tag:blogger.com,1999:blog-1274230976683730758.post-32828471221151167242014-12-11T17:27:00.001+01:002014-12-11T18:33:02.690+01:00Fairground Games<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="background-color: transparent; color: #666666; font-family: 'Trebuchet MS'; font-size: 17px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Year 9 have completed their annual probability project where they design, test and run a ‘fairground’ for visiting year 6 students. It is always great fun and this year was no exception. The exercise is all about experimental probabilities. By designing games carefully, you should be able to predict that more people will lose a game than win it. With theoretical games, you can calculate it. The challenge is to make a game that people want to play, that is possible to win, but that people are mostly likely to lose so the stall holder wins in the end. So it is great to put these games to real test. Year 6 obliged and were very discerning with their money. Some of them went home with more than they came with, but on balance the fairground won - just. This years winners were Nicholas and Kieran whose brave ‘wet sponge throw’ (it was cold outside) won the most money. A direct hit in the face was required to win, but apparently the punters felt a body hit was worth the cost! Great design and aesthetics from the ‘Jungle challenge’ and ‘jungle hoops’ and lots of terrific ideas involving everything from Nerf guns and roulette wheels! A terrific event - well done to all who took part! </span><br />
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Anonymoushttp://www.blogger.com/profile/05835250335807360943noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-92114133851086097412014-12-11T12:32:00.000+01:002015-12-09T11:37:21.474+01:00Counting Circles in Year 4<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEis8tVKiphCTpbiGj_SdDAR5-izzIP7thwGJDCUj0_cDpYd3A-dl0oX0KC07LMI5Mux6k_7DoIx8_mItE-_RTyayMNvq39kbZiF_YbU-QShcpey7RJTSRdH-vwuq6hYF92Zy80YEsgbuD4/s1600/100_0209.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEis8tVKiphCTpbiGj_SdDAR5-izzIP7thwGJDCUj0_cDpYd3A-dl0oX0KC07LMI5Mux6k_7DoIx8_mItE-_RTyayMNvq39kbZiF_YbU-QShcpey7RJTSRdH-vwuq6hYF92Zy80YEsgbuD4/s1600/100_0209.JPG" width="320" /></a></div>
We've been trying out "Counting Circles" in Year 4, and it's starting to get into its stride. Obviously there are lots of ways to count, but we've begun to do it in <a href="http://www.nctm.org/Publications/Mathematics-Teaching-in-Middle-School/Blog/Sadie_s-Circles/" target="_blank">a very particular way (here described by John Golden, based on Sadie Estrella's lessons)</a>. This, for us, involves sitting in a circle, and counting from a chosen number in a certain-sized jump. On the first day we started from zero and jumped up in twos, with the teacher writing down the steps on the whiteboard.<br />
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<tr><td class="tr-caption">Day 1</td></tr>
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Easy enough. Then at a certain point (52 on the first day) we stop and the teacher says:<br />
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"What number would Marie (for example) be who's three people after 52? Think about it and put your hand up when you've come up with an answer." </blockquote>
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Then the good bit comes: the explanation. "Who could share the way they worked out that it was 58?"</div>
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Usually there are a number of explanations, and a number of ways of getting to the answer. Children explain their thinking, and we note it down on the whiteboard.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMkRwW0y0EQXvknEIuGv6a4WwuDf-thPhgD-cunYMrZ3dcl8p1WlTMDiiBc0qaAp2ZHV9RN9pi0mBXw9plugzPXNYnu2wLfYQsy42zAAmjlAYjL6qgeW9WRMx2Mevmpd72EeMETGULGBo/s1600/counting+circle+2.jpeg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="172" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMkRwW0y0EQXvknEIuGv6a4WwuDf-thPhgD-cunYMrZ3dcl8p1WlTMDiiBc0qaAp2ZHV9RN9pi0mBXw9plugzPXNYnu2wLfYQsy42zAAmjlAYjL6qgeW9WRMx2Mevmpd72EeMETGULGBo/s1600/counting+circle+2.jpeg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Day 2</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinxVguU3iedanXpwshP66uBHai4oFpfJsbBNOfby-xQgFWi_M7pak7ihGf-Dygze3l1Dx6NvTvrQWiKwqFRrMO9k4IP6jwXHNbmxY66aAwsD7CnKgwXKtXBMyaZ9vvJ_ZCCydwCN3SSVI/s1600/counting+circle+3.bmp" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="176" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinxVguU3iedanXpwshP66uBHai4oFpfJsbBNOfby-xQgFWi_M7pak7ihGf-Dygze3l1Dx6NvTvrQWiKwqFRrMO9k4IP6jwXHNbmxY66aAwsD7CnKgwXKtXBMyaZ9vvJ_ZCCydwCN3SSVI/s1600/counting+circle+3.bmp" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Day 3</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbz683p4iJEVryZn11a-7roARbX7qOrW1G4LHkoqAyM5hOQMv_Mvqf5hmNd11yKkO2Q2fRj5VRke7QS0ZTzPh8yjW6mmnzyv7KM_wekKlfjiay12LXbC6dwaiJpUU3tbve0sUktgi081Q/s1600/counting+circle+04+add+5.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbz683p4iJEVryZn11a-7roARbX7qOrW1G4LHkoqAyM5hOQMv_Mvqf5hmNd11yKkO2Q2fRj5VRke7QS0ZTzPh8yjW6mmnzyv7KM_wekKlfjiay12LXbC6dwaiJpUU3tbve0sUktgi081Q/s1600/counting+circle+04+add+5.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Day 4</td></tr>
</tbody></table>
<div style="text-align: center;">
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNhuNJ3ZC25ECQPi122RFg_v9DhsOpnAX283HROKDHjbVlzF1SFeK1mEgFmDZc3ug1yfxIe4FDxbZomOp0b6XCJspRFezebDHPvk6FSjmZ_dUDSdO_Fo6wuxgrfkxtmrk1f-cObB5rFzY/s1600/counting+circle+6.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNhuNJ3ZC25ECQPi122RFg_v9DhsOpnAX283HROKDHjbVlzF1SFeK1mEgFmDZc3ug1yfxIe4FDxbZomOp0b6XCJspRFezebDHPvk6FSjmZ_dUDSdO_Fo6wuxgrfkxtmrk1f-cObB5rFzY/s1600/counting+circle+6.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.7272720336914px;">Day 5</td></tr>
</tbody></table>
</div>
We've been doing this for perhaps five or ten minutes at the start of some of our lessons, then we leave it and go onto something else. </div>
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<div>
This last week we've been looking at time on the analogue clock, so it made sense to do a bit of clock counting, following the way the minutes go ("counting in mod 60"):</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjY2NHLKooqak5CEjS-jVoaA16kZcV3eKKdVSjIDGEudM92-V9EvzPXIBSEUGH3vi5XjVH-Xnaa4z_NzegZaS_ODIWYGakW8TyqQIFLPXXwEGCgmLZxLxu7tUpw416ppviZbla26Q5iw8w/s1600/clock.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjY2NHLKooqak5CEjS-jVoaA16kZcV3eKKdVSjIDGEudM92-V9EvzPXIBSEUGH3vi5XjVH-Xnaa4z_NzegZaS_ODIWYGakW8TyqQIFLPXXwEGCgmLZxLxu7tUpw416ppviZbla26Q5iw8w/s1600/clock.jpg" width="198" /></a></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2ETWepA4oyabwFbDrquZYwk7d0uVh52tVkF-Uc4LN1oi8LMmHWNnj-mQp3dDtVYFZKltERTDrbaQSC3D5Jd3TktRPZSPLrwN2VIpNJ76JoLVF-a_Ihpo3vl7PB9XGcBjmHuZiT4jgykw/s1600/counting+circle_1.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="169" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2ETWepA4oyabwFbDrquZYwk7d0uVh52tVkF-Uc4LN1oi8LMmHWNnj-mQp3dDtVYFZKltERTDrbaQSC3D5Jd3TktRPZSPLrwN2VIpNJ76JoLVF-a_Ihpo3vl7PB9XGcBjmHuZiT4jgykw/s1600/counting+circle_1.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Day 9: Clock counting</td></tr>
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<iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/TR-EonOlR_g?rel=0" width="560"></iframe>
<span style="font-size: xx-small;">(Apologies - very shaky video!)</span></div>
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The next day was clock counting with jumps of eight (it took two times round the clock to get back to zero).</div>
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The day after, jumps of eleven:<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg87xaq5TYeuLNJbWSHdVNOB3BbVcRCyKZU44l9fL0Y1kRO_vl3gCsgCwsJBAxBIqMeCukdBo7tuz8ovRJPud4c7-fw1S7m42twRzjM1xkBSZF12ZfnlHDAqjYurTsj_sy160Cj9JdcOs/s1600/counting+circle+8a.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg87xaq5TYeuLNJbWSHdVNOB3BbVcRCyKZU44l9fL0Y1kRO_vl3gCsgCwsJBAxBIqMeCukdBo7tuz8ovRJPud4c7-fw1S7m42twRzjM1xkBSZF12ZfnlHDAqjYurTsj_sy160Cj9JdcOs/s1600/counting+circle+8a.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Day 11</td></tr>
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There were lots of great ways of getting the person three jumps on's number. James was looking at the vertical pattern all the way across. Alya spotted a diagonal pattern. Rod added three to each digit, rembering that the 6 for sixty became zero. And Samyak added 33 and knew that 68 is actually just 8 in clock counting.</div>
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It's early days yet. It's been a good moment for us to share our reasoning and see that we often know more than one good method. We'll keep going with it. We'll try new jumps, and also work on not correcting each other's mistakes, and at listening to each other's explanations really carefully.</div>
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PS. See <a href="http://y4ist.blogspot.fr/2014/12/clock-flowers.html" target="_blank">the Year 4 blog</a> to see how we later continued with the clock counting patterns on paper to create Clock Flowers.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgX31Fk1hrxyYr81yrszIvI7Bnp4zh8ulcGb4Eozpnyp8FqJ8eS6makzTS3S28k-isn3eOQbSmhyphenhyphenGU8fisPDb6-ee5tXR0I0OReFp5soTUTBdc-RRGQlDjjmJ8gmUcHsnzUl_ux_UtIjNo/s1600/15.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="197" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgX31Fk1hrxyYr81yrszIvI7Bnp4zh8ulcGb4Eozpnyp8FqJ8eS6makzTS3S28k-isn3eOQbSmhyphenhyphenGU8fisPDb6-ee5tXR0I0OReFp5soTUTBdc-RRGQlDjjmJ8gmUcHsnzUl_ux_UtIjNo/s1600/15.jpg" width="200" /></a></div>
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Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-69156306362522785822014-12-04T08:17:00.003+01:002014-12-04T21:00:19.952+01:00Seeing through these problems<div dir="ltr" style="text-align: left;" trbidi="on">
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At our school in Toulouse, the classrooms have one wall that is almost entirely glass and big double glass doors on the opposite wall. This makes for a lovely light a spacious room but sometimes leaves us short of wall space! Imagine then my delight and discovering 'Window Markers!' My classroom walls are now becoming adorned with lovely maths problems! Here are a couple of problems that are on the door at the moment....<br />
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<blockquote class="twitter-tweet" lang="en">
Can you solve the problem on the door of P5? <a href="https://twitter.com/hashtag/istlive?src=hash">#istlive</a> <a href="http://t.co/HnHkSMub8J">pic.twitter.com/HnHkSMub8J</a><br />
— Mr Noble (@MathsinP5) <a href="https://twitter.com/MathsinP5/status/534626839311171585">November 18, 2014</a></blockquote>
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<script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script>
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I am sure many have seen this problem before, but Mathematics is never going to run out of things for us to spend more time looking at. I picked this up from a friend's daughter's homework they were asking me about. The problem has a couple of particular fascinations for me based on playing with it myself and putting it on my classroom door.<br />
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1. That there are some quite different ways to approach it<br />
2. That there is significance difference between asking students or a particular unknown length and a more general 'given the diagram, what else can you tell me that is true?' approach<br />
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That last thought has occupied me for a while....<br />
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Here is another one!<br />
<blockquote class="twitter-tweet" lang="en">
<div style="text-align: center;">
Another problem on the door of P5 <a href="https://twitter.com/hashtag/istlive?src=hash">#istlive</a> <a href="http://t.co/W5J9nblp1U">pic.twitter.com/W5J9nblp1U</a></div>
<div style="text-align: center;">
— Mr Noble (@MathsinP5) <a href="https://twitter.com/MathsinP5/status/535019875753033728">November 19, 2014</a></div>
</blockquote>
<script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script>
This took even more thought! and even prompted <a class="g-profile" href="https://plus.google.com/107320552619878305218" target="_blank">+Simon Gregg</a> to write this <a href="http://seekecho.blogspot.fr/2014/03/tangential-trapeziums.html" target="_blank">blog post</a> when he first saw it! <br />
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No solutions here as that would spoil the fun!</div>
Anonymoushttp://www.blogger.com/profile/05835250335807360943noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-43781383175450586442014-12-03T10:44:00.000+01:002014-12-04T20:47:07.860+01:00Estimation challengesChildren in Year 4 have had a piece of homework: devise an estimation challenge for the rest of Year 4. You can see the great challenges by <span style="background-color: yellow;"><a href="http://y4ist.blogspot.fr/search/label/estimation" target="_blank">clicking here</a>.</span> They've also been trying to answer each others' questions.<br />
<br />
This came after we've spent a fair bit of time on Andrew Stadel's great site <a href="http://www.estimation180.com/" target="_blank">estimation180.com</a>, recording our upper and lower limits and estimation on the Google docs for some of the challenges. There's something really engaging about being presented with these mystery quantities, amounts, numbers and measurements, and trying to zero in on a reasonably accurate answer.<br />
<br />
The Year 4 students produced a real variety of challenges: measuring ones like <a href="http://y4ist.blogspot.fr/2014/12/how-many-centimeters-does-milly-mesure.html" target="_blank">how tall is Milly, the world's smallest dog?</a><br />
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<a href="http://y4ist.blogspot.fr/2014/12/how-many-centimeters-does-milly-mesure.html" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggIt4j_oJMtQ3tFBu1vDflKOdKAhPvAYAXf89c8keI43COyT_csSG7ZqzVGaZzlDBa9kcQQi4jbyF0MMfvpVbuu-9THFiVPp6euFhCQszKa6N16Cu7HUsWbWfORFIFMqmBGBGLQVXznuw/s1600/Milly.jpg" height="179" width="320" /></a></div>
Ones involving part of a known quantity, like <a href="http://y4ist.blogspot.fr/2014/12/estimation-how-many-matches.html" target="_blank">how many matches are left in the matchbox?</a><br />
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<span style="margin-left: 1em; margin-right: 1em;"><a href="http://y4ist.blogspot.fr/2014/12/estimation-how-many-matches.html" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQbwTTTINg1osaJe8cGb4CgBXgb8MuGgGbxxJHN9wyAJV1hYb3gKbO2zec1UyQSFFgG_EOFgvf3qKhGtVmbscGAY_VTYje1GQp7Rx5cz9AKOn8ggJ6c_H4Fw6Qwyn6Ykp4yBwnUyOJNto/s1600/IMG_20141203_223031.jpg" height="320" width="180" /></a></span></div>
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And lots of counting challenges, including some where you need to sample part of the picture and then scale it up to account for the whole picture, like <a href="http://y4ist.blogspot.fr/2014/11/hama-bead-estimation.html" target="_blank">Hama bead estimation.</a></div>
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<a href="http://y4ist.blogspot.fr/2014/11/hama-bead-estimation.html" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtomW7YXJ4wwM1eBlzL1ZbK729HNGIokruqj-z76ElddMnGaz6IGVr2hlwTlgtGinZK4w6N8hu1Q9L3RM7pULs5jWhojMvOislIEub0jX-GGOtE0pWYBsQHFSrh-sI-hGwBvl9iIrA1rY/s1600/counting+beads.JPG" height="240" width="320" /></a></div>
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It's really great how families have helped with this, with the maths, and with filming and photographing, and also how everyone has been able to write their post, upload their pictures that give clues and also links or videos that reveal the answer. And of course the estimates in the comments have been great too! If you'd like to have a go, please do. No peeking though!</div>
Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com2tag:blogger.com,1999:blog-1274230976683730758.post-37785258356491766072014-10-07T22:56:00.002+02:002014-10-07T22:59:23.760+02:00Patterns of cubes - the first in the sequence<div class="separator" style="clear: both; text-align: left;">
Looking at patterns and how they grow is something we've done lots before. But this time in Year 4 we took particular time over something different: what exactly the first step should be.</div>
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Look at this pattern here, a pattern of "C" shapes:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiKkN2SQ9ZTJa7LX5ABagRvOtfQK9R0OcspSxpWfBLTbngWjSTIHPPt_dxAGa7VeTMRnFA6a5huLD0xBpnZs7zS9AUDz2erUsJ6Aw-sOseujR9SWH_0VMwzv11CkGqbxxafewVFlPCzyhy/s1600/seq.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiKkN2SQ9ZTJa7LX5ABagRvOtfQK9R0OcspSxpWfBLTbngWjSTIHPPt_dxAGa7VeTMRnFA6a5huLD0xBpnZs7zS9AUDz2erUsJ6Aw-sOseujR9SWH_0VMwzv11CkGqbxxafewVFlPCzyhy/s1600/seq.png" height="640" width="409" /></a></div>
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We had a long discussion about that first single cube. Did it really belong in the sequence? Some thought yes, some no. We didn't really come to a definite conclusion, but the good thing was that we were able to explain our reasoning one way or the other.</div>
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For instance with this pattern of "H"s:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_aRiOuF0Gn4u9jLsuVlKqiJys4QAlH6E2aiq8QlIFb_JB78fPdmI5-pTHwdH4dAi2mi4-we3NbZQR45_8IwwO21id22UESDI8htdQB70A6HPTVtZH8fhaw_AOt7w0RYioA-TvqXgVSoa5/s1600/P1030517+(Small).JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_aRiOuF0Gn4u9jLsuVlKqiJys4QAlH6E2aiq8QlIFb_JB78fPdmI5-pTHwdH4dAi2mi4-we3NbZQR45_8IwwO21id22UESDI8htdQB70A6HPTVtZH8fhaw_AOt7w0RYioA-TvqXgVSoa5/s1600/P1030517+(Small).JPG" height="213" width="320" /></a></div>
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The two girls were more than happy to explain their thinking:</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/0B6CaV3dCEZx0NC1kODkxY2ZBWE0/view?usp=sharing" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOfj-lqxiHgpBnO7de56Zh_00gfCm5QziE5KVnmbjXQ-cXoZocgkZFg4ExDfWd5ilAkW3SR6X7wx2vm8BADpv7lwas5xepqNR6E43_ys_foAhyphenhyphen9D4OUbNcMQCX-xlH10tlB2RKBbfnEyYi/s1600/reason.PNG" height="361" width="640" /></a></span></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><a href="https://drive.google.com/file/d/0B6CaV3dCEZx0NC1kODkxY2ZBWE0/view?usp=sharing" target="_blank">Click on picture to see video</a></td></tr>
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How about these other sequences? Do you think the first one is right? </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTt6gQpLVNwUHcerOluImp7hYVT-ZKNmRhcFQwC8KQMrmkcxQlalsqtyO1LCVsVgcMuCqVPudfADrt8qsJfCWBcjJfA1U02KYPSTwrPR0QYBtB8zX_HwPGv8OA-D-gWtLgVSFcEinQEm7e/s1600/P1030518+(Small).JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTt6gQpLVNwUHcerOluImp7hYVT-ZKNmRhcFQwC8KQMrmkcxQlalsqtyO1LCVsVgcMuCqVPudfADrt8qsJfCWBcjJfA1U02KYPSTwrPR0QYBtB8zX_HwPGv8OA-D-gWtLgVSFcEinQEm7e/s1600/P1030518+(Small).JPG" height="213" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihSbLT0jeRZ9Z4tDVxOLbpC3b1lCZGXaZVF8-Z0mQ8quyjG8i5NG8V3J1z8AfRD_XefEKpWQ7pnITkPHgbTL0lKK8-JH0lWwG2UqjI1kkiPaynLvrZfTUW9DdSXhuDYpnRvSCWpeR6-VBy/s1600/P1030521+(Small).JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihSbLT0jeRZ9Z4tDVxOLbpC3b1lCZGXaZVF8-Z0mQ8quyjG8i5NG8V3J1z8AfRD_XefEKpWQ7pnITkPHgbTL0lKK8-JH0lWwG2UqjI1kkiPaynLvrZfTUW9DdSXhuDYpnRvSCWpeR6-VBy/s1600/P1030521+(Small).JPG" height="134" width="320" /></a></div>
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<a href="http://4.bp.blogspot.com/-IJ59CicwxqU/VCr6VgPVXuI/AAAAAAAAAd0/pOO7oYoJGac/s1600/DSC09358.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://4.bp.blogspot.com/-IJ59CicwxqU/VCr6VgPVXuI/AAAAAAAAAd0/pOO7oYoJGac/s1600/DSC09358.JPG" height="240" width="320" /></a></div>
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<a href="http://3.bp.blogspot.com/-5Doc9vwIv0Y/VCr6WH-P_FI/AAAAAAAAAd4/_zf7-ZJyc8w/s1600/DSC09355.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://3.bp.blogspot.com/-5Doc9vwIv0Y/VCr6WH-P_FI/AAAAAAAAAd4/_zf7-ZJyc8w/s1600/DSC09355.JPG" height="240" width="320" /></a></div>
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<a href="http://2.bp.blogspot.com/-1njYUD2jDBs/VCr5E8_g8II/AAAAAAAAAcI/r4J3JKKiJhY/s1600/DSC09330.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://2.bp.blogspot.com/-1njYUD2jDBs/VCr5E8_g8II/AAAAAAAAAcI/r4J3JKKiJhY/s1600/DSC09330.JPG" height="240" width="320" /></a></div>
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<i>You can see more of this Year 4's mathematics learning on <a href="http://y4ist.blogspot.fr/search/label/Maths" target="_blank">the Y4 blog.</a></i></div>
Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-43727288199934170322014-06-20T11:14:00.000+02:002014-06-20T22:13:14.765+02:00A Square of Cubes in Year 4<div class="separator" style="clear: both;">
It's a curious and wondrous fact that<span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.399999618530273px;"> </span><a href="https://en.wikipedia.org/wiki/Squared_triangular_number" target="_blank">the sum of the first n cubes is the square of the nth triangular number</a>.</div>
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For instance, with n=3, the first three cubes</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuu3ydryyP6X9Ny404Mh-SPdyhQ1tlK8dulBfwHBTf_6b3w8ZUANpim7VLfUsjFI_zchBJg15FwkL5FweFqFjQxyZXTPVPgttjjMSgIs5LSbcCRBh_1F1GRiRdh8zsiuogXuNdNOOcM90/s1600/DSC00324.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuu3ydryyP6X9Ny404Mh-SPdyhQ1tlK8dulBfwHBTf_6b3w8ZUANpim7VLfUsjFI_zchBJg15FwkL5FweFqFjQxyZXTPVPgttjjMSgIs5LSbcCRBh_1F1GRiRdh8zsiuogXuNdNOOcM90/s1600/DSC00324.JPG" height="240" width="320" /></a></div>
- here made in Cuisenaire rods - can be reassembled into a square:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhICPRZ0nQzKhS9A9l7dgJ9Iiz0xPmgdepHEDtNk2cxE7R-XHmddE17c9RQDVgHi6Pv5UiJDFQoxbG8l2j0AAg0T_pVFgoaLr4rqWZG42WJ8tzBiRayhKRC0AX_SQDTd8GBG5SnHGqgtAk/s1600/DSC00333.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhICPRZ0nQzKhS9A9l7dgJ9Iiz0xPmgdepHEDtNk2cxE7R-XHmddE17c9RQDVgHi6Pv5UiJDFQoxbG8l2j0AAg0T_pVFgoaLr4rqWZG42WJ8tzBiRayhKRC0AX_SQDTd8GBG5SnHGqgtAk/s1600/DSC00333.JPG" height="240" width="320" /></a></div>
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The square is six units wide, six being the third triangle number.</div>
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The puzzle then, was to <a href="http://year4atist.blogspot.fr/2014/06/cubes-to-squares-puzzle.html" target="_blank">make the cubes and then make a square from them</a>. The class managed that successfully and it might have finished there, but when the following day they were asked <a href="http://year4atist.blogspot.co.uk/2014/06/patterns-in-cuisenaire-rods.html" target="_blank">to create a growing pattern of their own in Cuisenaire rods</a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXygvcTR_EaPfHww3sglyPsSvVzZjO3xU_HPcmpVpWBt1_nprriOGQP5RxeSa3IhHcqiNK5CfD53G2i-JAbN9tXGsms1ygM3UrYKgwPR9eEsR9-7RC6Bm5fn-4oSFou7HS4EVZl655zN0/s1600/2014-06-11+09.15.34.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXygvcTR_EaPfHww3sglyPsSvVzZjO3xU_HPcmpVpWBt1_nprriOGQP5RxeSa3IhHcqiNK5CfD53G2i-JAbN9tXGsms1ygM3UrYKgwPR9eEsR9-7RC6Bm5fn-4oSFou7HS4EVZl655zN0/s1600/2014-06-11+09.15.34.jpg" height="320" width="238" /></a></div>
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four of the girls chose to <a href="http://year4atist.blogspot.fr/2014/06/cubes-to-squares-big.html" target="_blank">return to the square of cubes and make it bigger</a>:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjn-KJOazSKcwJ0l9KuyCiYbG3ZPTqdnqZRneoYxWJjASQuEuZfoNbr5MqyG9xKN6639o7Y7VWK5Qm5234UgDA51YpgO0RwTfff6YEghPW5J6PfPlhYxRmyv5B4b27cqqPVw0hfiYMmk_U/s1600/2014-06-11+10.14.22.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjn-KJOazSKcwJ0l9KuyCiYbG3ZPTqdnqZRneoYxWJjASQuEuZfoNbr5MqyG9xKN6639o7Y7VWK5Qm5234UgDA51YpgO0RwTfff6YEghPW5J6PfPlhYxRmyv5B4b27cqqPVw0hfiYMmk_U/s1600/2014-06-11+10.14.22.jpg" height="320" width="240" /></a></div>
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and bigger - swallowing up all the Cuisenaire rods in the school, until they had created a monster:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvmaejpWuFKo9rdNUDJgp9swTKCELnXnk4HpDFG2ArPYqKyGafLSbtAyCYuRpeT_xCRrJg4UGlka-lM7_xYx95JyagS8_VGg-1aLy1FYfjJeHbISkpd9itQZ-7xFW1Lbp09Zp6T2m3QoE/s1600/2014-06-11+10.42.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvmaejpWuFKo9rdNUDJgp9swTKCELnXnk4HpDFG2ArPYqKyGafLSbtAyCYuRpeT_xCRrJg4UGlka-lM7_xYx95JyagS8_VGg-1aLy1FYfjJeHbISkpd9itQZ-7xFW1Lbp09Zp6T2m3QoE/s1600/2014-06-11+10.42.jpg" height="382" width="400" /></a></div>
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The next day, while the rest of the class <a href="http://year4atist.blogspot.fr/2014/06/looking-closer-at-our-cuisenaire.html" target="_blank">explained their own patterns</a>, the four girls <a href="http://year4atist.blogspot.fr/2014/06/our-feelings-about-square-from-cubes.html" target="_blank">enthused about their creation</a>.</div>
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It was time to <a href="http://year4atist.blogspot.fr/2014/06/square-numbers-cube-numbers-triangle.html" target="_blank">have a closer look at the patterns of numbers</a> hidden inside this huge square:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihNJZ2S5nOlbG-AnWXLXchyeQA3ElNvFWeEZlxrb_O8DBx3UKcNkPU8jJFbAA94dwc8rA-AVc75niZC9omMJI3IEhXMEN8W_zt2LtKxsmhXWqjaefMR8I6bUb0DXvJVLMl2iT5BAv0VNE/s1600/2014-06-17+13.41.45.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihNJZ2S5nOlbG-AnWXLXchyeQA3ElNvFWeEZlxrb_O8DBx3UKcNkPU8jJFbAA94dwc8rA-AVc75niZC9omMJI3IEhXMEN8W_zt2LtKxsmhXWqjaefMR8I6bUb0DXvJVLMl2iT5BAv0VNE/s1600/2014-06-17+13.41.45.jpg" height="240" width="320" /></a></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhc8d48XCu684oetW11qDlSCT8-2EK0_5DfN85lQb9JUuIJKFQMIiZZ77fJexOWf5opL83P7JXHtvTUvODTRl5dRlQieRxzYYNZf6tzPnEQpVWVwHdJAa14I-RN-ykwIcFYKJnpYpMYJEM/s1600/0440_001.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhc8d48XCu684oetW11qDlSCT8-2EK0_5DfN85lQb9JUuIJKFQMIiZZ77fJexOWf5opL83P7JXHtvTUvODTRl5dRlQieRxzYYNZf6tzPnEQpVWVwHdJAa14I-RN-ykwIcFYKJnpYpMYJEM/s1600/0440_001.jpg" height="226" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGW1S-l8igArL_TT_DcDRn3xdGrUm9CRK2JHqK3TtvL_s3i5VYTGK_vXOqEODiFLfMI-XN6B_BDG26CcMWrD9vxWFNtbvRfYnkrwNjBN_EA7QU3LB2U2divgFSYoTK8TLOD_towmiKKzE/s1600/0440_002.bmp" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGW1S-l8igArL_TT_DcDRn3xdGrUm9CRK2JHqK3TtvL_s3i5VYTGK_vXOqEODiFLfMI-XN6B_BDG26CcMWrD9vxWFNtbvRfYnkrwNjBN_EA7QU3LB2U2divgFSYoTK8TLOD_towmiKKzE/s1600/0440_002.bmp" height="193" width="320" /></a></td></tr>
<tr><td class="tr-caption">square numbers</td></tr>
</tbody></table>
</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH9l1jucEsYpy9orNiLD3l7B5LYKFGkuI9Aav1jEE0xXQObq_OVTS5lWpEyXNdgJhKZY6v9Mdm1CqLbYXcC_AWRKxLim8uSTvsYIBuaxbDKzEXZMdwmpLW8MU2QhJMpPeZZB-EQvAQrJk/s1600/TRIANGLE+NUMBERS.bmp" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH9l1jucEsYpy9orNiLD3l7B5LYKFGkuI9Aav1jEE0xXQObq_OVTS5lWpEyXNdgJhKZY6v9Mdm1CqLbYXcC_AWRKxLim8uSTvsYIBuaxbDKzEXZMdwmpLW8MU2QhJMpPeZZB-EQvAQrJk/s1600/TRIANGLE+NUMBERS.bmp" height="320" width="226" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">triangle numbers</td></tr>
</tbody></table>
And then, to round it all off, a display outside the class:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiamRQE8tTmyqNAT4gDSQVzdjX7HkIDcuAKuWyuXrWvsI5OwapQNYmpALIMM_8KjcRA7O2YF56xa7-BDKQt3C0eDfx5YidaWCNSkWd0SjlyaWtxLoHegYRa7q23ssBHhiWk7TydTahEfPE/s1600/DSC00462.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiamRQE8tTmyqNAT4gDSQVzdjX7HkIDcuAKuWyuXrWvsI5OwapQNYmpALIMM_8KjcRA7O2YF56xa7-BDKQt3C0eDfx5YidaWCNSkWd0SjlyaWtxLoHegYRa7q23ssBHhiWk7TydTahEfPE/s1600/DSC00462.JPG" height="194" width="320" /></a></div>
with the invitation to make the cubes and the squares from the same rods:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWwHb7DhOX9qcFr1ya_B1vE86fASzTE_IorgA8vMyqkGtT6UP_36VR5KtMks2_GBAomdNvh2HPQK2gvhz61OcKf_KAqUYFZITpYLk5QsNezeZobFCgFj0fQ_2CcUD_E-0VlEe9Chlf6bo/s1600/can+you.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWwHb7DhOX9qcFr1ya_B1vE86fASzTE_IorgA8vMyqkGtT6UP_36VR5KtMks2_GBAomdNvh2HPQK2gvhz61OcKf_KAqUYFZITpYLk5QsNezeZobFCgFj0fQ_2CcUD_E-0VlEe9Chlf6bo/s1600/can+you.jpg" height="320" width="291" /></a></div>
We rounded it all off by inviting the Year 2s and Year 3s to find out what it was all about. The four girls <a href="https://docs.google.com/a/intst.eu/file/d/0B6CaV3dCEZx0VDFVSldJRDB2VGs/edit" target="_blank">explained their creation brilliantly!</a><br />
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<a href="https://docs.google.com/a/intst.eu/file/d/0B6CaV3dCEZx0VDFVSldJRDB2VGs/edit" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUqxTgHZkewyMorR3HF8xntCsKvy9R84UUhlhQ35SphxlfcG-cHQOFcSVxITbnF_yFqy7KPFWEmGux-SkNWCT-RsrskxkLihMkGLURLvW9KstGiQ0PrZq6OpQN17CpzJxs8xb9FdDIdOA/s1600/squre+of+cubes+video.PNG" height="388" width="640" /></a></div>
Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-41690736483312506182014-05-28T18:31:00.000+02:002014-05-29T17:43:23.581+02:00Weaving the Three Times Table<div dir="ltr" style="text-align: left;" trbidi="on">
This is something from the archives, from Year 1.<br />
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In our topic on clothes, we'd looked at denim under the microscope. It looked something like this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiybgM9G0Sw-TdZWbaN0A-gHHTZUzfIIVZqEPF_7N3dUt_G5EFnZlxlBQkvatRmgK4CBZ_3-vAXViBi0WEG8urnI2oTobkeJ4Y_hGA-ZazXAwqKk4tlo3v4CNhyNjhILr1gEOrtkRjrTwA/s1600/denim.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiybgM9G0Sw-TdZWbaN0A-gHHTZUzfIIVZqEPF_7N3dUt_G5EFnZlxlBQkvatRmgK4CBZ_3-vAXViBi0WEG8urnI2oTobkeJ4Y_hGA-ZazXAwqKk4tlo3v4CNhyNjhILr1gEOrtkRjrTwA/s1600/denim.jpg" height="240" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6JV2E0KHUIe-a0Q5xxWaM3h7XyxN2PtqiglZ4ESirUwa5gac-VQ6ArmTOHeKky-SnNX7QC8mYYqRXyXVy75ysinn6pVS8k7KNw4q9PEqJNCVvzsnYA0epkSSaM4CUxEBIUyyI-jnVLDg/s1600/a_1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6JV2E0KHUIe-a0Q5xxWaM3h7XyxN2PtqiglZ4ESirUwa5gac-VQ6ArmTOHeKky-SnNX7QC8mYYqRXyXVy75ysinn6pVS8k7KNw4q9PEqJNCVvzsnYA0epkSSaM4CUxEBIUyyI-jnVLDg/s1600/a_1.JPG" height="275" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizlfF7JpWUiX8zWKW2SFsflK-19aRbPmYBBku8dYoGbUaC12kE3LeJJfdJ3QJJgZ8lqvs5vNsT0MV8_2c5_sDfikmJ622m-2ItbFTzfxnQU6hlLRaht0rAni7KLrwPSy-MjgtWfVBt1HM/s1600/a_3.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizlfF7JpWUiX8zWKW2SFsflK-19aRbPmYBBku8dYoGbUaC12kE3LeJJfdJ3QJJgZ8lqvs5vNsT0MV8_2c5_sDfikmJ622m-2ItbFTzfxnQU6hlLRaht0rAni7KLrwPSy-MjgtWfVBt1HM/s1600/a_3.JPG" height="320" width="239" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKwK7yAq4kYHz7NcKvjBSbDTWYA_D8JD2z2b9RsHsJrfbBgzB4WoZp4pVh4I-Fde3ettiMPXz3nUUPhpSRmOC2VRkDvxO3-Q-uaNoLEoQMSJvblYESLob2UglWmfYaN0mb4IuanGAEY-Y/s1600/a_4.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKwK7yAq4kYHz7NcKvjBSbDTWYA_D8JD2z2b9RsHsJrfbBgzB4WoZp4pVh4I-Fde3ettiMPXz3nUUPhpSRmOC2VRkDvxO3-Q-uaNoLEoQMSJvblYESLob2UglWmfYaN0mb4IuanGAEY-Y/s1600/a_4.JPG" height="320" width="240" /></a></div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuzHZtqp3uq2q6TXu7Xaeh7Txa-wXbjt6ch8FXGuVmocp4BWKrgov3Lq1O4XjYrafqPRLAuSvToMu_N3uBQEdgeUSXY7cI1gPlodcUBiOhyA3OnqG189-2APDGvLZgo5c8DmgRD0z0Q4I/s1600/b_1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuzHZtqp3uq2q6TXu7Xaeh7Txa-wXbjt6ch8FXGuVmocp4BWKrgov3Lq1O4XjYrafqPRLAuSvToMu_N3uBQEdgeUSXY7cI1gPlodcUBiOhyA3OnqG189-2APDGvLZgo5c8DmgRD0z0Q4I/s1600/b_1.jpg" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">This is the 'back' of it</td></tr>
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We saw the way the blue threads went over two and under one. We made the pattern on a hundred square by filling the right cells white on <a href="https://www.dropbox.com/s/er173al99kfhuy1/denim.doc" target="_blank">a Word document</a>:</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://www.dropbox.com/s/er173al99kfhuy1/denim.doc" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFOzKc9HQ0-lbVcov1Oe_Ibud-ODF2dNRO4124xCj8eDWptL7dxc7z0ULg3n-137hig8ar8NV75X6HVEVH3E5Z9mXIrbh3wlBIc_b0PzwOFK-noEr9ol6TRqrEad9XB7FVTDO6fQDTnII/s1600/denim+3.GIF" height="283" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Click on image to download Word doc</td></tr>
</tbody></table>
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It looked like this when we'd finished (after correcting some mistakes):</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiOOIXlCO0PmQf_hRkeywdhYWwzSzsDdfO3xrz5AYy9Ce_htPA-xgPkgz8QoOjjSvkA4L1qaE_NTg9AOazwm5jSsi1iXovUQHFAWhrsd6RQ0sgpN6EPm2KjdPtGmrCqGSN0vpvu63U4Qs/s1600/denim+4.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiOOIXlCO0PmQf_hRkeywdhYWwzSzsDdfO3xrz5AYy9Ce_htPA-xgPkgz8QoOjjSvkA4L1qaE_NTg9AOazwm5jSsi1iXovUQHFAWhrsd6RQ0sgpN6EPm2KjdPtGmrCqGSN0vpvu63U4Qs/s1600/denim+4.GIF" height="285" width="400" /></a></div>
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Then we used <a href="https://www.dropbox.com/s/0rku23j9gi89zzc/hundred%20square%20for%20weaving%20denim.doc" target="_blank">another Word document</a>, printed onto A3 cartridge paper and cut with a Stanley knife along the vertical lines:<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://www.dropbox.com/s/0rku23j9gi89zzc/hundred%20square%20for%20weaving%20denim.doc" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjg2x5WZW5JrUC91ntX02045T3GkSz3khyphenhyphenhCw0EZffqqj3KoKXlUumDd85yMhdxEqOqadremdMWYSgNfK79tlgaPzLQJRHMmTrR2i-nxOrLIWH1CCDToxOJDFXA_20aFVPCtOw1XrwWGmU/s1600/weaving+3.GIF" height="285" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Click on image to download Word doc</td></tr>
</tbody></table>
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On this sheet we circled the multiples of three. Now it was just a question of threading blue strips in to make the same pattern, over two numbers not circled and under the circled multiples of three. The class really concentrated and got some great results!<br />
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Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-65726591373009506732014-05-21T15:22:00.003+02:002014-05-21T15:22:48.212+02:00Number Balances in Year 4We've been working with our new number balances in Year 4.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxM9fc8wnTRRT9d8PaDA_oBt7pI-NeOpG75nGpm_Z5S1lIvCVKsf06XUP2oVF9KgKZRFIhtiy4ub1rb2ICWvA_3xC5nJa7GjJDWiS0Ruf6QUKZDCCnw_zofUrT5d_x4EdTQMB2SVJeiFI/s1600/DSC09893.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxM9fc8wnTRRT9d8PaDA_oBt7pI-NeOpG75nGpm_Z5S1lIvCVKsf06XUP2oVF9KgKZRFIhtiy4ub1rb2ICWvA_3xC5nJa7GjJDWiS0Ruf6QUKZDCCnw_zofUrT5d_x4EdTQMB2SVJeiFI/s1600/DSC09893.JPG" height="240" width="320" /></a></div>
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The two sides of the balance have to balance.<br />
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We created lots of balanced numbers. Like this:<br />
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You'll notice there's more than one weight on some numbers!</div>
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We also did the same thing with <a href="http://nrich.maths.org/content/id/4725/balancer.swf" target="_blank">an online version from nrich</a>:<br />
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We made lots of them!<br />
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<embed flashvars="host=picasaweb.google.com&noautoplay=1&hl=en_GB&feat=flashalbum&RGB=0x000000&feed=https%3A%2F%2Fpicasaweb.google.com%2Fdata%2Ffeed%2Fapi%2Fuser%2Fmrsimongregg%2Falbumid%2F6015533604385197313%3Falt%3Drss%26kind%3Dphoto%26hl%3Den_GB" height="400" pluginspage="http://www.macromedia.com/go/getflashplayer" src="https://photos.gstatic.com/media/slideshow.swf" type="application/x-shockwave-flash" width="600"></embed><br />
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And a whole lot more!<br />
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<embed flashvars="host=picasaweb.google.com&noautoplay=1&hl=en_GB&feat=flashalbum&RGB=0x000000&feed=https%3A%2F%2Fpicasaweb.google.com%2Fdata%2Ffeed%2Fapi%2Fuser%2Fmrsimongregg%2Falbumid%2F6015821043086241953%3Falt%3Drss%26kind%3Dphoto%26hl%3Den_GB" height="400" pluginspage="http://www.macromedia.com/go/getflashplayer" src="https://photos.gstatic.com/media/slideshow.swf" type="application/x-shockwave-flash" width="600"></embed>
The challenge, though, is to work out where the weights were the next day!<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNFIvRqdbqjJRXi7Ag07tUYPUZ1zWs7fuYD2h-XmceRG8CkRfXpVvktDqDSdq7gm_a3at7UMzBfdWkw7d579ZZrUkj1u32Nigo-UadjiM1h11OLV9f9FYE4QxoFZdzmzLjaXI4i3zmN5E/s1600/DSC09911.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNFIvRqdbqjJRXi7Ag07tUYPUZ1zWs7fuYD2h-XmceRG8CkRfXpVvktDqDSdq7gm_a3at7UMzBfdWkw7d579ZZrUkj1u32Nigo-UadjiM1h11OLV9f9FYE4QxoFZdzmzLjaXI4i3zmN5E/s1600/DSC09911.JPG" height="240" width="320" /></a></div>
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We're writing them as equations:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitWXAoVqfvzmHXb6YNFw4lV16i8N47wmgNZ0tDOHjzYeRSCS3OmQbIKwTHuxR-xAnFjnxz-p1-68NC4S1IZyM_i66DOQHsBX-J1l3vm6aMBoJvV5cSf3CckU0IFSutrmJHx8DpUyQ2al8/s1600/DSC09931.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitWXAoVqfvzmHXb6YNFw4lV16i8N47wmgNZ0tDOHjzYeRSCS3OmQbIKwTHuxR-xAnFjnxz-p1-68NC4S1IZyM_i66DOQHsBX-J1l3vm6aMBoJvV5cSf3CckU0IFSutrmJHx8DpUyQ2al8/s1600/DSC09931.JPG" height="320" width="240" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilMvQet8aYr2Cp7bGZlgvhQeeRAwtm2SWoLWrU-0CX2sStSmSN0VPmRdqjaHB_IBpo4vG2gFc0E87mgw6EXnCaDlUpMBRGWm0bH1DZPEFrowVwKW_15p-r4mrdOI8XGU0IYoKkgoQJ2n8/s1600/DSC09907.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilMvQet8aYr2Cp7bGZlgvhQeeRAwtm2SWoLWrU-0CX2sStSmSN0VPmRdqjaHB_IBpo4vG2gFc0E87mgw6EXnCaDlUpMBRGWm0bH1DZPEFrowVwKW_15p-r4mrdOI8XGU0IYoKkgoQJ2n8/s1600/DSC09907.JPG" height="240" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7cDM_xAXKqHFfMz2sQcddJN9dJW0PCJGyYJOzI4f_j6Gm_fqhe7qVlJFNC-aJcre-XWqAHHVS2ETdS4Wv_nn_fIPxvwM2usZ5sdsIMEH2HjV8C6iFizx6qp4fEBsX_imqJ_PCbjTlesE/s1600/DSC09933.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7cDM_xAXKqHFfMz2sQcddJN9dJW0PCJGyYJOzI4f_j6Gm_fqhe7qVlJFNC-aJcre-XWqAHHVS2ETdS4Wv_nn_fIPxvwM2usZ5sdsIMEH2HjV8C6iFizx6qp4fEBsX_imqJ_PCbjTlesE/s1600/DSC09933.JPG" height="320" width="240" /></a></div>
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<embed flashvars="host=picasaweb.google.com&noautoplay=1&hl=en_GB&feat=flashalbum&RGB=0x000000&feed=https%3A%2F%2Fpicasaweb.google.com%2Fdata%2Ffeed%2Fapi%2Fuser%2Fmrsimongregg%2Falbumid%2F6015819792738878353%3Falt%3Drss%26kind%3Dphoto%26hl%3Den_GB" height="400" pluginspage="http://www.macromedia.com/go/getflashplayer" src="https://photos.gstatic.com/media/slideshow.swf" type="application/x-shockwave-flash" width="600"></embed>
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We also had a go at <a href="http://www.mathplayground.com/balance_scales.html" target="_blank">this balancing game</a> (which starts out easy then gets a little harder):<br />
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<a href="http://www.mathplayground.com/balance_scales.html" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvbzYGPclRJPpT53Im4M-5lmoIhSjE1VCKp2JT1v32xuIClR-N7q7rRvXTS7ck9cSdHM5jTdyT6kmGRfmCd9-8tnsNL5xm-Xh4me2DPtORPnwkBrhOYNjuKujntvC1MklPQiHt1T1aw28/s1600/balance+scales.GIF" height="225" width="320" /></a></div>
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This one, <a href="http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/weigh/index.htm" target="_blank">Weigh It Up</a>, starts out easy and gets harder too:</div>
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<a href="http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/weigh/index.htm" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgllBA4DUW-Hh6wEOoBPNsBb2nh_TpPD2xCwhx0urR_WavPF9bd-PSQiXBCdIuErEGI2IEQ7htiX4yTk6JE8Q5IUphWwvt0AO813xoC4cQe2fndTpth3Qo3XvGIB7eOoXFWg4NjMCuYcWk/s1600/weigh+it+up.GIF" height="169" width="320" /></a></div>
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<i><a href="http://year4atist.blogspot.fr/2014/05/number-balances.html" target="_blank">Also blogged on the Year 4 blog.</a></i></div>
Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-8786931886434840532014-04-26T09:47:00.001+02:002014-04-26T09:47:28.467+02:00Pie charts and percentages with Smarties<div class="separator" style="clear: both; text-align: left;">
This was a nice easy and fun way to explore percentages and pie charts - plus it was edible! It came from an image on Twitter:</div>
<blockquote class="twitter-tweet" lang="en">
Bar charts to pie charts <a href="https://twitter.com/search?q=%23bcme8&src=hash">#bcme8</a> with myself and mike Ollerton and lots of lovely peeps <a href="http://t.co/aziZj7aBaf">pic.twitter.com/aziZj7aBaf</a><br />
— Helen J Williams (@helenjwc) <a href="https://twitter.com/helenjwc/statuses/456439536466145280">April 16, 2014</a></blockquote>
<script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script>
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What a great way of doing pie charts! No arithmetic involved! Normally there is just a little too much involved in achieving a pie chart. How about we combine that with a circle divided into one hundred - then we simply have to count around that circle for the percentage! The paper was there on <a href="http://www.printablepaper.net/category/polar_graph" style="text-align: center;" target="_blank">printablepaper.net</a>.</div>
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So we handed out the boxes of Smarties. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj59BHHEXXynV-v3PCdatxnpPEcFxqYIwnukYhh05G2hPp5D-bMtFGxzLxeNZiOV6DCYF476am6y3XHmBSqJBo_3fm2hXLWu8DCbxQxSUJWhEdqd1AEs3Szj_uk7plEAVoqAYcPFnck4TA/s1600/DSC09572.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj59BHHEXXynV-v3PCdatxnpPEcFxqYIwnukYhh05G2hPp5D-bMtFGxzLxeNZiOV6DCYF476am6y3XHmBSqJBo_3fm2hXLWu8DCbxQxSUJWhEdqd1AEs3Szj_uk7plEAVoqAYcPFnck4TA/s1600/DSC09572.JPG" height="240" width="320" /></a></div>
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We each had a packet, and sorted them into colours. Then we arranged them in a circle. That was the tricky bit. Sometimes we had to jiggle the circle quite a bit so all the Smarties would fit, and so it was fairly circular. We marked off the different colours on the outside circle divided into a hundred.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2a0jixcOxzvsxqqw-Mzd5fTJuKBLAW0eFpm8ESrrbPojGVRB-3xdFhY7X2M3RAgNECAhbjGBatY-jmaUbwJ4ZNGO5o6yl61QScooKbtjAvqKK0lQ7RXytqFuHVLi33EPflQv6yTMs7UI/s1600/DSC09588.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2a0jixcOxzvsxqqw-Mzd5fTJuKBLAW0eFpm8ESrrbPojGVRB-3xdFhY7X2M3RAgNECAhbjGBatY-jmaUbwJ4ZNGO5o6yl61QScooKbtjAvqKK0lQ7RXytqFuHVLi33EPflQv6yTMs7UI/s1600/DSC09588.JPG" height="320" width="240" /></a></div>
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Then we coloured in the circle with the right colour, and added on some pie cuts:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV50ZakNib37ZG8KJPYVFTucfRc4DlJXQyaCNl7RbSU-m22CMqEwPCRpt_02MmMm1qZPIWHj3NHYfpDRTbsr0bl2XDfEMy8XdXDcHz1R8KMEkm_lqqA8IWpXux8NwEdoP3jhsclUakLFY/s1600/DSC09587.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV50ZakNib37ZG8KJPYVFTucfRc4DlJXQyaCNl7RbSU-m22CMqEwPCRpt_02MmMm1qZPIWHj3NHYfpDRTbsr0bl2XDfEMy8XdXDcHz1R8KMEkm_lqqA8IWpXux8NwEdoP3jhsclUakLFY/s1600/DSC09587.JPG" height="240" width="320" /></a></div>
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Here are more photos:<br />
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<embed flashvars="host=picasaweb.google.com&noautoplay=1&hl=en_GB&feat=flashalbum&RGB=0x000000&feed=https%3A%2F%2Fpicasaweb.google.com%2Fdata%2Ffeed%2Fapi%2Fuser%2Fmrsimongregg%2Falbumid%2F6005874226767096769%3Falt%3Drss%26kind%3Dphoto%26hl%3Den_GB" height="400" pluginspage="http://www.macromedia.com/go/getflashplayer" src="https://photos.gstatic.com/media/slideshow.swf" type="application/x-shockwave-flash" width="600"></embed><br />
And the finished pie charts look like this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFbjwoDWqiseUn_TyuPwdLQzVbmoUpBeCyj9eZN50bVM1ZPEW9ISZQmjePa0eU2WRF1JQFz8LjAg_UYSrvmLKiGnocI_GEMqvHmbxzL-y5J4vHAxUjlrUeyBHkYhMRAEGXT2U3kdr5erk/s1600/0373_013.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFbjwoDWqiseUn_TyuPwdLQzVbmoUpBeCyj9eZN50bVM1ZPEW9ISZQmjePa0eU2WRF1JQFz8LjAg_UYSrvmLKiGnocI_GEMqvHmbxzL-y5J4vHAxUjlrUeyBHkYhMRAEGXT2U3kdr5erk/s1600/0373_013.jpg" height="320" width="227" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKKnsusV0_U_cSQqg4JrwjW3f-LWzLcTbexCFS82-zayOkqlXgn2ycIRLl9AUIm86xH94il179bI96e7uP9C3SA1V8JsJ_bdV3PTvdtxJVxUMb5KqkoGc1BKfLnfpbjnXVKswP0Tc-2f0/s1600/0373_005.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKKnsusV0_U_cSQqg4JrwjW3f-LWzLcTbexCFS82-zayOkqlXgn2ycIRLl9AUIm86xH94il179bI96e7uP9C3SA1V8JsJ_bdV3PTvdtxJVxUMb5KqkoGc1BKfLnfpbjnXVKswP0Tc-2f0/s1600/0373_005.jpg" height="320" width="227" /></a></div>
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<i><a href="http://year4atist.blogspot.fr/2014/04/smarties-percentages.html" target="_blank">Also blogged on the Year 4 blog.</a></i></div>
Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-69980701441192147642014-04-23T21:29:00.003+02:002014-04-24T16:41:22.645+02:00Five RectanglesIn Year 4 we've been looking at a puzzle, taken from <a href="http://wordplay.blogs.nytimes.com/2014/04/14/rectangle/" target="_blank">Gary Antonick's 'Numberplay' in the New York Times</a>:<br />
<blockquote class="tr_bq">
Create a set of five rectangles that have sides of length 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 units.</blockquote>
The really quick and easy way to explore this is with Cuisenaire rods:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifynEvEpe4joe4NsD40Ju11KWfXehyeLH1FpHYIetiBt2ZVPyE-Sc1VU7McLbOFnOTtiQJLGFO3dSdWcFnHDtJs23q7lrz9yc-qMbC7QMKeJB-EwAEcnMLnTcLQqZNyEQNV2A4p-L2mgc/s1600/DSC09521.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifynEvEpe4joe4NsD40Ju11KWfXehyeLH1FpHYIetiBt2ZVPyE-Sc1VU7McLbOFnOTtiQJLGFO3dSdWcFnHDtJs23q7lrz9yc-qMbC7QMKeJB-EwAEcnMLnTcLQqZNyEQNV2A4p-L2mgc/s1600/DSC09521.JPG" height="240" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_AJswnuRI907zLZ-rljtwZOUmHoQ7rZCPXStcs3hzfsUorNUlKLUBhMpXzFFm4ghiPfEQ9-EQwj42jyaz1pVznyBoAQOl6mCcwHg_COaKZ_p1OgRRVrHuKoG-EFqS3xej3X6hxGGfM5w/s1600/DSC09527.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_AJswnuRI907zLZ-rljtwZOUmHoQ7rZCPXStcs3hzfsUorNUlKLUBhMpXzFFm4ghiPfEQ9-EQwj42jyaz1pVznyBoAQOl6mCcwHg_COaKZ_p1OgRRVrHuKoG-EFqS3xej3X6hxGGfM5w/s1600/DSC09527.JPG" height="240" width="320" /></a></div>
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After we'd found five rectangles with those side lengths, we recorded them using the <a href="http://nrich.maths.org/content/id/4348/cuisenaire.swf" target="_blank">Cuisenaire Environment</a>:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG46EMMuyP2-kYBSwrMm7EFheVjJV-2HijmdMHVGj67yII5yCDjRpVi-N6jbTSaCjB2WUyA3ZICEHTK1N_WPsIoq_iN2gRnJS3mqYf7V4bse7gZBHaJRhh7qHTgs1P183ZiLICFw8yPNc/s1600/DSC09530.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG46EMMuyP2-kYBSwrMm7EFheVjJV-2HijmdMHVGj67yII5yCDjRpVi-N6jbTSaCjB2WUyA3ZICEHTK1N_WPsIoq_iN2gRnJS3mqYf7V4bse7gZBHaJRhh7qHTgs1P183ZiLICFw8yPNc/s1600/DSC09530.JPG" height="240" width="320" /></a></div>
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Here are more pictures:<br />
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<embed flashvars="host=picasaweb.google.com&noautoplay=1&hl=en_GB&feat=flashalbum&RGB=0x000000&feed=https%3A%2F%2Fpicasaweb.google.com%2Fdata%2Ffeed%2Fapi%2Fuser%2Fmrsimongregg%2Falbumid%2F6005119221092481185%3Falt%3Drss%26kind%3Dphoto%26hl%3Den_GB" height="400" pluginspage="http://www.macromedia.com/go/getflashplayer" src="https://photos.gstatic.com/media/slideshow.swf" type="application/x-shockwave-flash" width="600"></embed>
Then we started looking at the area the rectangles covered.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-Wco5fZdR-ITGN4XpXvuLP30ziyIDL75GVUdI_kF7N72dzolqP9GOZRHIWYBLaqVqlEw8x1uHTUsWnBZ_1uoO5nOD3aOLiwKsgerq7xXBMMkhVIgQIsG7CTbfJA11E4LdPBuySMhk7BI/s1600/2014-04-23+09.21.11.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-Wco5fZdR-ITGN4XpXvuLP30ziyIDL75GVUdI_kF7N72dzolqP9GOZRHIWYBLaqVqlEw8x1uHTUsWnBZ_1uoO5nOD3aOLiwKsgerq7xXBMMkhVIgQIsG7CTbfJA11E4LdPBuySMhk7BI/s1600/2014-04-23+09.21.11.jpg" height="240" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihd9yqcx70mW9xcbxorgmNKpoOD_I2w7Le8jjTi-ykUf41KwdfBVMpdghqAfBfAuIQI5iuqeKuUL2To2P2hdRuA8EYkbhAWE_KB4n9bmKyhN7IJhdW_xIpx9III3679ldBSuD9t60m8Kw/s1600/2014-04-23+09.23.29.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihd9yqcx70mW9xcbxorgmNKpoOD_I2w7Le8jjTi-ykUf41KwdfBVMpdghqAfBfAuIQI5iuqeKuUL2To2P2hdRuA8EYkbhAWE_KB4n9bmKyhN7IJhdW_xIpx9III3679ldBSuD9t60m8Kw/s1600/2014-04-23+09.23.29.jpg" height="240" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUiER3xCm8RNdySPGx2Awg0ztKul3WUy_qWjLclf24JNIr4zZHARFr4j6vKjRpi-t0sO5pOKgi5Zryq_-hzpuLfD_v82rMBs_PGqxihzA475FiGDvJ36oWSpYDJHN3tI_EWBOB-aF_Rh0/s1600/2014-04-23+09.26.11.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUiER3xCm8RNdySPGx2Awg0ztKul3WUy_qWjLclf24JNIr4zZHARFr4j6vKjRpi-t0sO5pOKgi5Zryq_-hzpuLfD_v82rMBs_PGqxihzA475FiGDvJ36oWSpYDJHN3tI_EWBOB-aF_Rh0/s1600/2014-04-23+09.26.11.jpg" height="320" width="240" /></a></div>
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We got total areas of<br />
<span style="font-size: x-large;">120, 121, 123, 125, 130, 154, 161 and 184.</span><br />
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Next question: what is the <span style="font-size: x-large;">biggest</span> possible area?<br />
<br />
Alicia answered this - use the <b>biggest</b> side lengths on the <b>same</b> rectangles:<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVJCpmGr_qosUAbgbOFN0EKNYx76urz5qkEZ-Nu7dGmLfhHz9JCoVVxuRZn_ZoSKrJlQPxkKdzaexWv-AGPljwCDEnYXu-6OETpPYYg07cyqHXqoO5vFth5hdBL6-0Vp6Q2VANbRedBsw/s1600/biggest.GIF" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVJCpmGr_qosUAbgbOFN0EKNYx76urz5qkEZ-Nu7dGmLfhHz9JCoVVxuRZn_ZoSKrJlQPxkKdzaexWv-AGPljwCDEnYXu-6OETpPYYg07cyqHXqoO5vFth5hdBL6-0Vp6Q2VANbRedBsw/s1600/biggest.GIF" height="252" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;">Area = 190</td></tr>
</tbody></table>
Can you see why this is the maximum?<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyHpjZpw77koZApQZGnRxPSBLPYKkXPNBqnQV2rj11S209rw9DKQPVsf7Y3okdEqRu1sx_Ee_gKTnmvlHl6RHm0rY9nyI_Z6bRufu4sscMMnqwM85gXrCPjB3G5n-Kh9kdVscwi0qme9s/s1600/2014-04-23+09.37.32.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyHpjZpw77koZApQZGnRxPSBLPYKkXPNBqnQV2rj11S209rw9DKQPVsf7Y3okdEqRu1sx_Ee_gKTnmvlHl6RHm0rY9nyI_Z6bRufu4sscMMnqwM85gXrCPjB3G5n-Kh9kdVscwi0qme9s/s1600/2014-04-23+09.37.32.jpg" height="240" width="320" /></a></div>
<br />
And then, what is the <span style="font-size: xx-small;">smallest</span> possible area?<br />
<br />
Mimi answered this one - use <b>biggest and smallest</b> lengths on the same rectangle:<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhya25rDr3EVA-Aw_m8JxyuzKsGKRLATBf0zDgvJlfq7wj_K9t4rYT2bh8J0KKfeNoxJ0V9VJGM4teldRHm0i59MOasC61VAS4TwbVumLq8K3urciGvmS8nMvOBzEaynKg7PWQTVsHDG3s/s1600/smallest.GIF" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhya25rDr3EVA-Aw_m8JxyuzKsGKRLATBf0zDgvJlfq7wj_K9t4rYT2bh8J0KKfeNoxJ0V9VJGM4teldRHm0i59MOasC61VAS4TwbVumLq8K3urciGvmS8nMvOBzEaynKg7PWQTVsHDG3s/s1600/smallest.GIF" height="184" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;">Area = 110</td></tr>
</tbody></table>
Can you see why this is the minimum?<br />
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitiM9Ney9Mj3Mw-D43Qy3vGkdrisnPD53SHeAWeWvjrwyNLVHLf_ULmy3wzR2q3nxjEVeodWvML6P2nVIJrS91Y1hhmRHHbL2dstiajMnFmBPCYT1BY5YWG7VOhpYOQF50xIGPkhkpbQw/s1600/2014-04-23+09.40.13.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitiM9Ney9Mj3Mw-D43Qy3vGkdrisnPD53SHeAWeWvjrwyNLVHLf_ULmy3wzR2q3nxjEVeodWvML6P2nVIJrS91Y1hhmRHHbL2dstiajMnFmBPCYT1BY5YWG7VOhpYOQF50xIGPkhkpbQw/s1600/2014-04-23+09.40.13.jpg" height="240" width="320" /></a></div>
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<br /></div>
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This is a great investigation - manageable, easy to understand, and susceptible to taking off in many directions. We didn't try to see how many possible ways of making the rectangles there are - that was a step too far.</div>
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<br /></div>
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But just seeing some of the ways was worthwhile. It works well because the rods and the numbers 1 to 10 are easy to grasp. And the maths it takes us into is worth it - length, area, 2 X 3 = 3 X 2, multiplication facts, addition of five numbers... And then a bit of more abstract thinking - what would the maximum and minimum be, and why.</div>
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It may be the first time a class has tackled this particular puzzle. We can certainly recommend it to other classes!</div>
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We rounded this investigation off with a small puzzle: </div>
<blockquote class="tr_bq" style="clear: both;">
<span style="font-family: inherit;"><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;">Make these rectangles, and then see if you can make a square by putting them together:</span></em><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;"><o:p><br /></o:p></span></em><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;"><o:p> </o:p></span></em><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;">1x6 4x7 5x8 3x9 2x10</span></em><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;"><o:p><br /></o:p></span></em><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;"><o:p> </o:p></span></em><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;">3x6 4x7 2x8 1x9 5x10</span></em><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;"><o:p> </o:p></span></em><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;"><o:p><br /></o:p></span></em><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;">1x2 4x5 3x8 7x9 6x10</span></em><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;"><o:p><br /></o:p></span></em><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;"><o:p> </o:p></span></em><em><span lang="EN-GB" style="background-color: white; background-position: initial initial; background-repeat: initial initial; color: #333333; font-size: 14pt; line-height: 21.466665267944336px;">1x2 4x6 3x7 8x9 5x10</span></em></span></blockquote>
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<i><a href="http://year4atist.blogspot.fr/2014/04/five-rectangles.html" target="_blank">Also blogged on the Year 4 blog.</a></i></div>
Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com1tag:blogger.com,1999:blog-1274230976683730758.post-49920467726871044562014-03-07T10:35:00.002+01:002014-03-07T10:42:09.912+01:00More maths with Cuisenaire rods in Year 4We've posted some of our work with Cuisenaire rods here already (see for instance our work on <a href="http://pinkmathematics.blogspot.fr/2013/12/patterns-in-squares-in-year-4.html" target="_blank">patterns in squares</a>). Since then, we've used them in lots of other ways. Click on the headings to get more detail on the Year 4 blog.<br />
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<h4>
<a href="http://year4atist.blogspot.fr/2014/01/a-cuisenaire-multiplication-square.html" target="_blank">Cuisenaire multiplication square</a></h4>
This was great fun to make, and the image of it has been a great resource to refer to:<br />
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<h4>
<a href="http://year4atist.blogspot.fr/2014/02/squares-and-square-roots.html" target="_blank">Forgetting about square roots (not)</a></h4>
Not usually in the Year 4 (9 and 10 year old) curriculum, so we said forget about it, but of course this paradoxical injunction worked magic! Topped off with a little work on the differences of squares.<br />
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<h4>
<a href="http://year4atist.blogspot.fr/2014/02/cuisenaire-rod-sums.html" target="_blank">Algebra with Cuisenaire rod sums</a></h4>
This seems to be the ideal way to introduce the idea of using a letter instead of a number. (And thanks to <a href="http://donsteward.blogspot.fr/2013/03/cuisenaire-equations.html" target="_blank">Don Steward for the inspiration</a>.)<br />
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<h4>
<a href="http://year4atist.blogspot.fr/2014/02/rozenn-and-pythagoras.html" target="_blank">Rozenn and Pythagoras</a></h4>
When Rozenn came in with something her dad had shown her - Pythagoras Theorem - the rods were the ideal way of quickly seeing that for the 3-4-5 triangle the theorem was right.<br />
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Of course this is Secondary school work really, but just as in art we look at work by, say, Paul Klee, or in music we listen to adult musicians and composers, why shouldn't we look ahead and marvel a little in maths too?!Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com2tag:blogger.com,1999:blog-1274230976683730758.post-71964771096192571932014-01-26T19:48:00.000+01:002014-03-07T10:54:01.173+01:00Co-ordinates games and quizzes in Year 4In Year 4 we've discovered some islands. (Naturally they all have buried treasure on them somewhere.) We've made careful maps of them. All the maps have coordinates, and we've used those to make a guessing game about where the treasure is buried. We started our work using a letter-number coordinate, and referring to the <i>spaces</i>, the squares, rather than the lines. Then we moved on to a number-number system, this time referring to the <i>lines </i>and where they cross.<br />
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For the treasure hunt game, first of all we secretly decide on and write down the coordinates of the treasure. Our partner then has to guess the coordinates. We say "hot" if the guess is in the squares around the buried treasure - and we mark that with a red cube. We say "warm" if it's int he squares around those, marking this with a yellow cube. And "cold" if it's anywhere else.<br />
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We've also used created some <a href="http://year4atist.blogspot.fr/search/label/coordinates%20quiz" target="_blank">coordinates quizzes using Hot Potatoes</a>. Here's one of them:<br />
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<iframe frameborder="0" height="1300" src="https://dl.dropboxusercontent.com/u/18133867/hot%20potatoes%20quizzes%20about%20islands/Ryan.htm" width="600"></iframe>Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-6444892066258362462014-01-09T15:58:00.003+01:002014-03-07T10:37:27.865+01:00Year 4 dodecagons<div class="separator" style="clear: both; text-align: center;">
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Year 4 used pattern blocks each make a different regular dodecagons (= 12-sided shape). At first they were tricky to make, but some people like Ryan, Alicia and Gustavo really got into the swing of things and made more than one!<br />
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<br />Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-73714432233645293922014-01-08T22:48:00.002+01:002014-03-07T10:37:27.875+01:00Tessellations in Year 4<div dir="ltr" style="text-align: left;" trbidi="on">
In Year 4 we looked carefully at the six pattern block shapes.<br />
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Then we made tessellations (regular patterns that could carry on for ever in all directions) with some of them.<br />
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Here are the tessellations we created:</div>
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<i>This post is also <a href="http://year4atist.blogspot.fr/2014/01/tessellations.html" target="_blank">published on the Year 4 blog</a>.</i></div>
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Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-20429773797017324962013-12-14T20:43:00.000+01:002014-03-07T10:37:27.813+01:00Patterns in squares in Year 4<div dir="ltr" style="text-align: left;" trbidi="on">
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We been having a look at patterns of squares using Cuisenaire rods in Year 4, starting by just making any design featuring as square.<br />
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At first it wasn't as simple as that might sound. We were getting a lot of almost-squares. Look, for instance, at this one, created on the <a href="http://nrich.maths.org/content/id/4348/cuisenaire.swf" target="_blank">Cuisenaire Environment</a> -<br />
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At first it fooled a lot of us! It's got at ten on each side...<br />
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A lot of interesting patterns emerged worth following up.<br />
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It would be interesting to think of mathematical question about these shapes. With the faces for instance, how does the perimeter progress in each of the two kinds of pattern? What area of table is visible in each?<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRyTjZhSZYkaap5giM2y5q2huxUWcsr_J9BHOugY9_Qgw_hWG2Bgx87o3NvPLg196eAv9NmMR1owMyuSehaoxpfnwQJ-Cp2CTFazLRBunP-Fzx-8Bad7ADkhyphenhyphenI0Sa1luJEkdXDODtZy4Y/s1600/2013-12-13+14.09.28.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="218" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRyTjZhSZYkaap5giM2y5q2huxUWcsr_J9BHOugY9_Qgw_hWG2Bgx87o3NvPLg196eAv9NmMR1owMyuSehaoxpfnwQJ-Cp2CTFazLRBunP-Fzx-8Bad7ADkhyphenhyphenI0Sa1luJEkdXDODtZy4Y/s320/2013-12-13+14.09.28.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white; color: #333333; font-family: Arial, sans-serif; font-size: 14px; line-height: 18px; text-align: left; white-space: pre-wrap;">Pascal, Paloma, Parsang and Perry Perimeter</span></td></tr>
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<i>(Also published on <a href="http://year4atist.blogspot.fr/2013/12/patterns-in-squares.html" target="_blank">the Year 4 blog</a>.)</i></div>
Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-27408977944780250532013-11-24T15:42:00.000+01:002014-03-07T10:37:27.819+01:00Lego Maths with Y6<span style="font-family: Trebuchet MS, sans-serif;">Unusually this autumn has seen more than its fair share of wet playtimes. During these sessions, many children have been attracted to the box of Lego bricks. Watching them build and play with the bricks, they instinctively know that if they are building with 8-stud bricks, and they run out, then two 4-stud bricks will do, or a 6-stud and a 2-stud, or four 2-studs. Arrays are everywhere. They are doing maths all the time without realising.</span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span><span style="font-family: Trebuchet MS, sans-serif;">Wanting to take advantage of this enthusiasm, I decided to investigate the numerical properties of the bricks with my Year 6 class to see what they came up with. I asked them to look for numbers and (for today) discouraged building. I encouraged recording anything they found out.</span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span><span style="font-family: Trebuchet MS, sans-serif;">They found out evidence of factors, number bonds, arrays, divisibility, sequencing, square numbers and experienced lots of data handling and discussing the numerical properties of their bricks.</span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span><span style="font-family: Trebuchet MS, sans-serif;">One student found out that 100 was not divisible by 8, whilst another was intent on finding patterns of square numbers using 4-stud bricks (numbers of studs and numbers of bricks).</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><br /></span><span style="font-family: Trebuchet MS, sans-serif;"><br /></span><span style="font-family: Trebuchet MS, sans-serif;">Another group were keenly trying to find the relationship between the number of studs on top of a brick with 2 rows of studs and the holes underneath. </span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoyB7r_WP4Djcc9f2elYMs-PHPcsD7vKjRu0XRdmi1V7eSrmVdWI-atdKpJBaG_gjaue6OsD2NILlx4F4P3hiOof1t2XCX4xJRyuebw2yX-kh-fHt6ZzmiAsKt5uRyviXGofpkHMCvuNo/s1600/1385047105717.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoyB7r_WP4Djcc9f2elYMs-PHPcsD7vKjRu0XRdmi1V7eSrmVdWI-atdKpJBaG_gjaue6OsD2NILlx4F4P3hiOof1t2XCX4xJRyuebw2yX-kh-fHt6ZzmiAsKt5uRyviXGofpkHMCvuNo/s320/1385047105717.jpg" width="180" /></a></span></div>
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<span style="font-family: Trebuchet MS, sans-serif;"><br /></span><span style="font-family: Trebuchet MS, sans-serif;">They could see that the number of holes was one less than one 'line' of studs. Once they organised their results and checked their ideas, it was only a small step for them to realise how to explain using maths vocabulary and then with a bit of help created a formula.</span><br />
<span style="font-family: Trebuchet MS, sans-serif;">This sparked ideas in others who wanted to try and find the 'rule' if the flatter base (rather than a brick) had rows of 4 studs instead of 2. Although we ran out of time, the discussion went into the next lesson as one student was determined to explain to me how to get the answer (correctly!).</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggs02-vKtWQskrHnmKsptAmyh_on7jSTYqjLZ2LkPFN7N1Yw6HUyGUSz3L_1UrO8nwPPsiXngh9R-GSAvQ-DEDkOA2TwmReK_zb6j82O1ozQnUb2V1H8lzp0QPcGlBFBjQQYiIU10MZ4s/s1600/1385049885068.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggs02-vKtWQskrHnmKsptAmyh_on7jSTYqjLZ2LkPFN7N1Yw6HUyGUSz3L_1UrO8nwPPsiXngh9R-GSAvQ-DEDkOA2TwmReK_zb6j82O1ozQnUb2V1H8lzp0QPcGlBFBjQQYiIU10MZ4s/s320/1385049885068.jpg" width="180" /></a></div>
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<span style="font-family: Trebuchet MS, sans-serif;">He came up with the mathematical rule and formula overnight. </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">Can anyone else find it too?</span><br />
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Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-1274230976683730758.post-61380431612769218962013-10-11T20:07:00.000+02:002014-03-07T10:37:27.859+01:00This year's Forest of Factors<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwROq_cTpkB57s0SJXYymHh4e8RAfppgbgxsAx6qn7woD6fkYv-7wu1505jlr-QeFyPEsm9zdRYM0acPqFseEwa8rgmz9Ai04gd_pPDBPiDa4FNq86Bj5h0PTsJxxrzOhbZh_pR2EmVQ4/s1600/IMG_4833.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwROq_cTpkB57s0SJXYymHh4e8RAfppgbgxsAx6qn7woD6fkYv-7wu1505jlr-QeFyPEsm9zdRYM0acPqFseEwa8rgmz9Ai04gd_pPDBPiDa4FNq86Bj5h0PTsJxxrzOhbZh_pR2EmVQ4/s320/IMG_4833.JPG" width="223" /></a></div>
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Following on from last year's post <a href="http://pinkmathematics.blogspot.fr/2013/02/important-factors.html" target="_blank">Important Factors</a>, and after our work finding prime numbers with Cuisenaire rods and <a href="http://pinkmathematics.blogspot.fr/2013/10/finding-prime-numbers-in-year-4.html" target="_blank">in the playground</a>, Year 4 had a go at making prime factor trees this year. Here's our Forest of Factors:<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdkYJNk1qM259OotbNlnPlmgYubwSVyUx5xr-OAIiUFlq-gFfsPErugXxGEVrWT-bTC9hI3Lid840-ZYh2yqo-qlUUxPGHiMaTkD-SBy9-eH6bvsaT-RMSjYULltLlia6MQfvz4r2qao8/s1600/01+to+10.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="340" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdkYJNk1qM259OotbNlnPlmgYubwSVyUx5xr-OAIiUFlq-gFfsPErugXxGEVrWT-bTC9hI3Lid840-ZYh2yqo-qlUUxPGHiMaTkD-SBy9-eH6bvsaT-RMSjYULltLlia6MQfvz4r2qao8/s640/01+to+10.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="http://year4atist.blogspot.fr/search/label/factors" target="_blank">See more on the Year 4 blog</a></td></tr>
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Our trees made a really big Forest of Factors display for the primary corridor. As the Year 2 and Year 3 children are passing it regularly, it was a good idea to explain the display to them. We did it without using the words "factor", "multiple" or "prime" so that it would be easier for them to understand:</div>
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"Hello everyone. This is our Forest of Factors."</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_jHPr2-XrlKBMc50jOyj6L13GV96hDjt28eE1grs6AxCXMz9VQIS47Ljp62KvnUgQSyZUMnB3vTG62O3aGhafvie8NISzGU74-qH6JjW65joLgHsqpkxVZQHGdvLhTtJ-65UQKWxqcNg/s1600/2013-10-11+09.32.01.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_jHPr2-XrlKBMc50jOyj6L13GV96hDjt28eE1grs6AxCXMz9VQIS47Ljp62KvnUgQSyZUMnB3vTG62O3aGhafvie8NISzGU74-qH6JjW65joLgHsqpkxVZQHGdvLhTtJ-65UQKWxqcNg/s320/2013-10-11+09.32.01.jpg" width="180" /></a></div>
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"1, 2, 3, 4.... 40"</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXpVRMziwt9wJA_MQQyjVjK_wuOAhQdB5quMF_90E5_ohVG_09D-OjkLPKx0C9eccZbr19n1GWrsa0M7saSZ1tlQm2Gkew-Be3z-p72MKvUL_-oIqVt_aJ8yV3doZp0hMufMQTfwxloD8/s1600/2013-10-11+09.32.36.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXpVRMziwt9wJA_MQQyjVjK_wuOAhQdB5quMF_90E5_ohVG_09D-OjkLPKx0C9eccZbr19n1GWrsa0M7saSZ1tlQm2Gkew-Be3z-p72MKvUL_-oIqVt_aJ8yV3doZp0hMufMQTfwxloD8/s320/2013-10-11+09.32.36.jpg" width="320" /></a></div>
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"What do you notice about our pictures?"</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfZwuc8mbdm5JqRHtvRaF2_Psly1tayEnydPkRWPzucI-uYYmXw_5OzoTsRwpVSlCZTR-0-Ei7HTjSnw7m9OffYpu0FdaT5_En6p_ygKrDDsPCGePKz1hhjnLQ-6pYqeVacE8MGVc0tco/s1600/2013-10-11+09.33.13.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfZwuc8mbdm5JqRHtvRaF2_Psly1tayEnydPkRWPzucI-uYYmXw_5OzoTsRwpVSlCZTR-0-Ei7HTjSnw7m9OffYpu0FdaT5_En6p_ygKrDDsPCGePKz1hhjnLQ-6pYqeVacE8MGVc0tco/s320/2013-10-11+09.33.13.jpg" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjnUzSODiY9QbEncFYMMCccLVvxH5k3eCd4vprPCpD0eEow7ZNoM_yrcb2eAa4Zzmbc-Z8aPYybxkPhlq22OJdy9iPCBSOwD-zzjvB-eWw-mK-I1-q4u9s-t3QN20KXB9SiYzAkUieCwA/s1600/2013-10-11+09.33.31.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjnUzSODiY9QbEncFYMMCccLVvxH5k3eCd4vprPCpD0eEow7ZNoM_yrcb2eAa4Zzmbc-Z8aPYybxkPhlq22OJdy9iPCBSOwD-zzjvB-eWw-mK-I1-q4u9s-t3QN20KXB9SiYzAkUieCwA/s320/2013-10-11+09.33.31.jpg" width="320" /></a></div>
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"Number 1 is my bird. It's different to all the other numbers. If you times something by 1 it just stays the same number."</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgonpJGc23XCP-c5A0yjylAU2TGKmhdF30UsH8VdyvbS1QJP0GqdF6QakG0TvF181vOteGV3zJihnG8vGnhHFtnLTlhMvwCVeMujQPlVBz4y2qB3rKj1xQGb2Vu7M7hTwjwJ_1QnmarJM4/s1600/2013-10-11+09.33.46.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgonpJGc23XCP-c5A0yjylAU2TGKmhdF30UsH8VdyvbS1QJP0GqdF6QakG0TvF181vOteGV3zJihnG8vGnhHFtnLTlhMvwCVeMujQPlVBz4y2qB3rKj1xQGb2Vu7M7hTwjwJ_1QnmarJM4/s320/2013-10-11+09.33.46.jpg" width="320" /></a></div>
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"So 1 is special, and we don't think about it with our trees and mushrooms. It's just flying up in the sky!"</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOkHg2Nvs8OdNvx_3Tn4zJlsFQIkermGwvcXEU_gAeP01A7-jLim-Du_Kv7CicLUqMN9nzr_QrmuLhC_5Df8m4JC1D1xldJjvtbwyJAYqLfeVHWHQDak6e5p9FyzqEWrfMgjjOxt04Tgo/s1600/2013-10-11+09.33.59.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOkHg2Nvs8OdNvx_3Tn4zJlsFQIkermGwvcXEU_gAeP01A7-jLim-Du_Kv7CicLUqMN9nzr_QrmuLhC_5Df8m4JC1D1xldJjvtbwyJAYqLfeVHWHQDak6e5p9FyzqEWrfMgjjOxt04Tgo/s320/2013-10-11+09.33.59.jpg" width="180" /></a></div>
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"Some of the numbers are simple trees. Look at 38. 38 is 19 times 2, so we've given it two branches that finish with flowers."</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxi_lqIeDFJr9AB37_moZqtPwQWYJkfUV2gDvsOX2V_Y0btxPgF6NxpqOO8WNXFhLY5Fhd2EWF9dx5ddHDhd6LQkxc37J9c6QzJL27lLczfwb816TiL-TIcVTKgPTaW6npYYif3tKzatA/s1600/2013-10-11+09.34.26.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxi_lqIeDFJr9AB37_moZqtPwQWYJkfUV2gDvsOX2V_Y0btxPgF6NxpqOO8WNXFhLY5Fhd2EWF9dx5ddHDhd6LQkxc37J9c6QzJL27lLczfwb816TiL-TIcVTKgPTaW6npYYif3tKzatA/s320/2013-10-11+09.34.26.jpg" width="320" /></a></div>
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"Ten is five times two."</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir-xpsgjeCT-J4O4D20i87-qGaIDTdcs27Kb20o-TFLAa3rcAQQ0ZzXWIDyjUrhN3faFvvj4QgM9gdSxK9VysjfSgFXryOKg6ajiqRbjl9HsK2NABmFhPlcALthciLy45ymc_hoNxcVDE/s1600/2013-10-11+09.34.41.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir-xpsgjeCT-J4O4D20i87-qGaIDTdcs27Kb20o-TFLAa3rcAQQ0ZzXWIDyjUrhN3faFvvj4QgM9gdSxK9VysjfSgFXryOKg6ajiqRbjl9HsK2NABmFhPlcALthciLy45ymc_hoNxcVDE/s320/2013-10-11+09.34.41.jpg" width="180" /></a></div>
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"26 is 13 times 2."</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuMLskIgCwOpN1_GYoMo7HZZCOrBnRS_2CbydGFD4mwibOBIBR3o2pg9j5QbthcWmKRfSgN3PhjHVEV7bv2k-ulAw90FUxy09T1xQlMK5gDsEHaUOY25wmxT1Y9D3UNrZprA0iMLcX0yc/s1600/2013-10-11+09.34.53.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuMLskIgCwOpN1_GYoMo7HZZCOrBnRS_2CbydGFD4mwibOBIBR3o2pg9j5QbthcWmKRfSgN3PhjHVEV7bv2k-ulAw90FUxy09T1xQlMK5gDsEHaUOY25wmxT1Y9D3UNrZprA0iMLcX0yc/s320/2013-10-11+09.34.53.jpg" width="320" /></a></div>
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"These ones had just two branches and two flowers."</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLIfEgxwn5SUZICK30u3gcjgTM3ZhGEBscCTwu956BMA63ITBJOKJ3kV3B8-8qrn1N4G1QfSuLBqTr_skCtcpWfrmNrGd3lLBLzsfD5Fa3DJZKjd1HpzopFuU551Gfc_ZW_iyx6_aUDLo/s1600/2013-10-11+09.35.03.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLIfEgxwn5SUZICK30u3gcjgTM3ZhGEBscCTwu956BMA63ITBJOKJ3kV3B8-8qrn1N4G1QfSuLBqTr_skCtcpWfrmNrGd3lLBLzsfD5Fa3DJZKjd1HpzopFuU551Gfc_ZW_iyx6_aUDLo/s320/2013-10-11+09.35.03.jpg" width="320" /></a></div>
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"But some of the trees have more flowers. Like 12, and 32."</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDvsBCVoJHyqD41XVpFII7bgVVX2sd8uAbJNmabmS2R7M62OoUpOIYYFAOlQ6fwmPXwLnutKGsFYIr6bwPTwSiVu9AsnzYW5tJliEpqO34-rC-2QAvqLNp_W5w_n_NJhR2TeqURVymex4/s1600/2013-10-11+09.35.10.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDvsBCVoJHyqD41XVpFII7bgVVX2sd8uAbJNmabmS2R7M62OoUpOIYYFAOlQ6fwmPXwLnutKGsFYIr6bwPTwSiVu9AsnzYW5tJliEpqO34-rC-2QAvqLNp_W5w_n_NJhR2TeqURVymex4/s320/2013-10-11+09.35.10.jpg" width="320" /></a></div>
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"With the mushrooms there's no two numbers that you can times together to make that number."</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYdocdHj7RlaLq0NT7jOdNxao_EbAAdvIbcucqSAti8qVXZ1nuULs0E-WuafbCU7aZdDfH55tAP6JEFCg8PPAIERyqJ86hoz1C80LWNkBimUnEX8C89xO-WVhfh9UiYH7L9IlZr-m1M6E/s1600/2013-10-11+09.35.36.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYdocdHj7RlaLq0NT7jOdNxao_EbAAdvIbcucqSAti8qVXZ1nuULs0E-WuafbCU7aZdDfH55tAP6JEFCg8PPAIERyqJ86hoz1C80LWNkBimUnEX8C89xO-WVhfh9UiYH7L9IlZr-m1M6E/s320/2013-10-11+09.35.36.jpg" width="320" /></a></div>
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"Can you see a number that is a mushroom?"</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLITzp7M-dLnRNnpn8mfP0LND55OHwKPPrvqdgJheSvunohvziz_HaRIfBKd-6YlmkA_uhUNASnZA-e5jQti8MZIAiqtUAIITKNY-0J6i96WNHBImK3yDkqDlSCaRa8wD12wKTWcVb9xM/s1600/2013-10-11+09.36.20.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLITzp7M-dLnRNnpn8mfP0LND55OHwKPPrvqdgJheSvunohvziz_HaRIfBKd-6YlmkA_uhUNASnZA-e5jQti8MZIAiqtUAIITKNY-0J6i96WNHBImK3yDkqDlSCaRa8wD12wKTWcVb9xM/s320/2013-10-11+09.36.20.jpg" width="320" /></a></div>
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"So that's our Forest of Factors. We hope you understand it a bit better now."</div>
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Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com0tag:blogger.com,1999:blog-1274230976683730758.post-58441910879812949222013-10-02T13:46:00.001+02:002014-03-07T10:37:27.851+01:00Finding prime numbers in Year 4In Year 4 we've been looking at prime numbers this week.<br />
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Some of us have been out in the playground, using the hundred square there:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCv_Zg8hujVsAUUs-l8D9VmdFYEvteCp0f1ktCglDP8ALopJ4SHn6mNIoW_MPZchlNNjCNKAeFm-2LyqX5G0SRQTKXJQBWxVIsZ6ziUwEbTUthZxLhNKLqbvJrAPUpbyjRyts5xRFDTaU/s1600/100_0658.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCv_Zg8hujVsAUUs-l8D9VmdFYEvteCp0f1ktCglDP8ALopJ4SHn6mNIoW_MPZchlNNjCNKAeFm-2LyqX5G0SRQTKXJQBWxVIsZ6ziUwEbTUthZxLhNKLqbvJrAPUpbyjRyts5xRFDTaU/s320/100_0658.JPG" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3lMoE7WTFB_cRGHrXYQnHfTlL5KTQ8srOpLJzI03m-RjuBm0NnMlcqo6802_VWgWRc8Ryvirkh2_ziQZVgx5ilctRqj2Csisv6oPOMR4PHTReVR9qM1uuaIi4yXztDptaIt30VTBSfkY/s1600/100_0674.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3lMoE7WTFB_cRGHrXYQnHfTlL5KTQ8srOpLJzI03m-RjuBm0NnMlcqo6802_VWgWRc8Ryvirkh2_ziQZVgx5ilctRqj2Csisv6oPOMR4PHTReVR9qM1uuaIi4yXztDptaIt30VTBSfkY/s320/100_0674.JPG" width="320" /></a></div>
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Here's a how we did it:<br />
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<iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/sAPjTZiQScE?rel=0" width="420"></iframe>
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Later we had a go in the classroom, using a photo of the hundred square (16 colour bitmap format):<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhW4ASQ7ycg9cwEGZUvLdG4YsBt-NgEQU2fiy2jadNBkjIGBKcUb2ZpLndPlHgqwHTAVSC1HrG-9oRhz31SK6A0whyEJ51um_Mj4_DiYdCutrmajg7fS-1UYJQJEqOoPtRRUmQsM8D9zEc/s1600/2013-10-02+07.21.36.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="173" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhW4ASQ7ycg9cwEGZUvLdG4YsBt-NgEQU2fiy2jadNBkjIGBKcUb2ZpLndPlHgqwHTAVSC1HrG-9oRhz31SK6A0whyEJ51um_Mj4_DiYdCutrmajg7fS-1UYJQJEqOoPtRRUmQsM8D9zEc/s320/2013-10-02+07.21.36.bmp" width="320" /></a></div>
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and, on Paint, filling he numbers in the 5, 3, 7 and 2 times table with colour:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMMU3FYtLnzN5aMjhsto1tifllNlu8jofI0cn6igaqkM2gugR2bJQUdWxhsCbnIzwzz-yPQ1-ol7rT0fgHs87h1B-cKGTc8shGzSK9G9FaCR9-6volhiyu-M2dC6T6bHxcvnQUCajHSkc/s1600/Ryan.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="173" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMMU3FYtLnzN5aMjhsto1tifllNlu8jofI0cn6igaqkM2gugR2bJQUdWxhsCbnIzwzz-yPQ1-ol7rT0fgHs87h1B-cKGTc8shGzSK9G9FaCR9-6volhiyu-M2dC6T6bHxcvnQUCajHSkc/s320/Ryan.bmp" width="320" /></a></div>
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And there we have it: the grey ones (except for 1) are the prime numbers!</div>
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(also blogged on the <a href="http://year4atist.blogspot.com./" target="_blank">Year 4 blog</a>)</div>
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Mr Gregghttp://www.blogger.com/profile/15114830266540886842noreply@blogger.com2