tag:blogger.com,1999:blog-71937900936231305542024-02-18T20:52:02.436-08:00MEDIAN + ICT choicesdon stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.comBlogger60125tag:blogger.com,1999:blog-7193790093623130554.post-35807750435206949452017-03-12T01:38:00.001-08:002017-03-12T01:38:08.158-08:00hundreds tens units<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgotMHB3RkgFyOHPoCPmRypgu2lsGA9lEIBpU53mWjjXUQUcVll22a74QlkXIvrWTa7C6whhgSiSq05AyJhRBaqLggT7lWHik57bYpT-fA7hL9SDcxiMoZ4l8SP-CMSP9MpIivwcUWeSBI/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgotMHB3RkgFyOHPoCPmRypgu2lsGA9lEIBpU53mWjjXUQUcVll22a74QlkXIvrWTa7C6whhgSiSq05AyJhRBaqLggT7lWHik57bYpT-fA7hL9SDcxiMoZ4l8SP-CMSP9MpIivwcUWeSBI/s400/Picture1.png" width="400" /></a></div>
<a href="https://www.mathlearningcenter.org/web-apps/number-pieces/">this</a> groups and ungroups<br />
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place values go up to hundredsdon stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-82625394611194495872014-04-29T13:59:00.003-07:002014-04-29T13:59:39.012-07:00Euclidean constructionsthe website <a href="http://sciencevsmagic.net/geo/">sciencevsmagic.net </a>is a great resource for attempting to construct some shapes using a few simple techniques: circle and line drawing<br />
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40 tasks are set with an indication of how many steps it should take<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLv0UPMlZcwywRNWGvPTkagZQBVOQJEEmhL9mAxEM2yXEAsKWkGtvwyzXt2mUET0bh6wYt1YbiHU4JATLcjZjCdzJR_IUQ4JFd8EF-84f3O2H-iBiBR0W5YoGzF2ypcshUqup86L2n2xU/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLv0UPMlZcwywRNWGvPTkagZQBVOQJEEmhL9mAxEM2yXEAsKWkGtvwyzXt2mUET0bh6wYt1YbiHU4JATLcjZjCdzJR_IUQ4JFd8EF-84f3O2H-iBiBR0W5YoGzF2ypcshUqup86L2n2xU/s1600/Picture1.png" height="245" width="400" /></a></div>
<br />don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-21270745852837526322013-04-16T09:53:00.001-07:002013-04-16T09:53:25.394-07:00interactive protractora helpful interactive <a href="http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html">protractor</a><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBKx4P36ABORb36URhxTIBw8GsmjDywAhiVbp2EfaCfT7rBElPp-DTHhwIxoq0JAuLGjQTDnMnUPKbk4C_fyuUEN8lNqX1O6eZ_86XhgkymHEbWOFw_PZ9R_REoFFEjAtmISR4OQK3mjQ/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="285" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBKx4P36ABORb36URhxTIBw8GsmjDywAhiVbp2EfaCfT7rBElPp-DTHhwIxoq0JAuLGjQTDnMnUPKbk4C_fyuUEN8lNqX1O6eZ_86XhgkymHEbWOFw_PZ9R_REoFFEjAtmISR4OQK3mjQ/s400/Picture1.png" width="400" /></a></div>
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<br />don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-23282177436541228842013-04-09T12:47:00.001-07:002013-04-09T12:47:37.419-07:00more grids <div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw1Urir_6OW_XrfBka1dW9sJdFs4houApO9UdEzdpHe0cqoaAtFxBXCmcnQQyCR-WzPcBfUtoa_Y3vkTwE_Ubbn892SNEr5TkEvrSSbQba286iXEsOP2y_-lNXdQtmLCrQ9G3OF9XvweQ/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="321" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw1Urir_6OW_XrfBka1dW9sJdFs4houApO9UdEzdpHe0cqoaAtFxBXCmcnQQyCR-WzPcBfUtoa_Y3vkTwE_Ubbn892SNEr5TkEvrSSbQba286iXEsOP2y_-lNXdQtmLCrQ9G3OF9XvweQ/s400/Picture1.png" width="400" /></a></div>
various grids and templates<br />
from <a href="http://www.mathsphere.co.uk/resources/MathSphereFreeGraphPaper.htm">MathSphere</a>don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-57531172869190398662013-03-31T00:41:00.000-07:002013-03-31T00:41:09.613-07:00Desmos<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIfdnoGviybT8vTn0_zAfdR12jWEtRGnRc7AyGvUc-TcopF4sIXN7w4jGZaFXQF1Rp-v3bbTBarPh0ZWrvvWa3kYLUcI9IEs32_Ucfwu9xcIpvdupc9WWbiDIa_hz78aMozKK_1-tv708/s1600/cubic-points-of-interest.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="238" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIfdnoGviybT8vTn0_zAfdR12jWEtRGnRc7AyGvUc-TcopF4sIXN7w4jGZaFXQF1Rp-v3bbTBarPh0ZWrvvWa3kYLUcI9IEs32_Ucfwu9xcIpvdupc9WWbiDIa_hz78aMozKK_1-tv708/s400/cubic-points-of-interest.jpg" width="400" /></a></div>
an online graphical calculator<br />
you tube introductions:<br />
<a href="http://www.youtube.com/watch?v=z5GtcOpGl7Y">1</a><br />
<a href="http://www.youtube.com/watch?v=8u8IeMFqq4Y">2</a><br />
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downloadable (for free) at <a href="https://www.desmos.com/">Desmos</a>don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-24997952659816039122013-03-23T10:15:00.003-07:002016-08-17T03:02:40.882-07:00hundred number grid<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKrhZSI3TCxNJcX-LShIR165Ys1lZdQ5hZzQWrMBAhZ7WcMHtaatlG_EJw-F3NEnvOXl-95pT5HSzMBwiCQ_SVvrmCK17lI_oJjAsaf6c3gkJrCDLsEZ4M0F5mbBWeBnoWVxJMb7oO9HU/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKrhZSI3TCxNJcX-LShIR165Ys1lZdQ5hZzQWrMBAhZ7WcMHtaatlG_EJw-F3NEnvOXl-95pT5HSzMBwiCQ_SVvrmCK17lI_oJjAsaf6c3gkJrCDLsEZ4M0F5mbBWeBnoWVxJMb7oO9HU/s400/Picture1.png" width="400" /></a></div>
hundred number grid, 0 to 99 number grid and times tables grid<br />
interactive<br />
from <a href="http://www.primaryinteractive.co.uk/online/numbersquare.swf">G Pitchford</a>don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-28444815441047143972012-09-13T23:40:00.002-07:002017-03-12T01:45:50.690-08:00geoboard<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5GBlexds3GLPcOhWJosJ2TpauZiePSuh4bEsgnXXrqwv4ouloBGEZ4WiT0diM_IJVfid69p0KvfcvOkLzxZw8LGknq87U3kGfsC2_m4zymC0jH6rrRUNqsmpG0a3g-qCufoUCo_654NE/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="285" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5GBlexds3GLPcOhWJosJ2TpauZiePSuh4bEsgnXXrqwv4ouloBGEZ4WiT0diM_IJVfid69p0KvfcvOkLzxZw8LGknq87U3kGfsC2_m4zymC0jH6rrRUNqsmpG0a3g-qCufoUCo_654NE/s400/Picture1.png" width="400" /></a></div>
from <a href="https://www.mathlearningcenter.org/web-apps/geoboard/">mathlearning centre</a>don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-17706858183815076802012-07-29T13:45:00.001-07:002014-05-26T23:19:51.082-07:00compass and ruler constructions<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidBoY9SU4ff_EW4zYXVSLRJkNTnJu37Bnu7hvZXCI0I3SZ5IEqwLftDvjGuSdZrYTLyX_RMv5uA4Ikq-6v8wOTXDKkkCweXTESY71Eh9LcT-uZ83YfZScT2ZCuUrSAiBzQR0M5J7Fqz7w/s1600/Bisection_construction.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidBoY9SU4ff_EW4zYXVSLRJkNTnJu37Bnu7hvZXCI0I3SZ5IEqwLftDvjGuSdZrYTLyX_RMv5uA4Ikq-6v8wOTXDKkkCweXTESY71Eh9LcT-uZ83YfZScT2ZCuUrSAiBzQR0M5J7Fqz7w/s400/Bisection_construction.gif" height="400" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLi1E2mYiSeB7SAzNTXTFoiXP_N6cGarbZHugeqfvLLE1gS5ocaWbEp7GJHIkDrObAPEb722L9ZLMUudwMcqhluBf4HH4SITj0GVgRzPlucvf7nTrnk4JNtK5ohw_-aOMnAs8cab9A6D8/s1600/Perpendicular_bisector.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLi1E2mYiSeB7SAzNTXTFoiXP_N6cGarbZHugeqfvLLE1gS5ocaWbEp7GJHIkDrObAPEb722L9ZLMUudwMcqhluBf4HH4SITj0GVgRzPlucvf7nTrnk4JNtK5ohw_-aOMnAs8cab9A6D8/s640/Perpendicular_bisector.gif" height="640" width="384" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaRaPEVdY6vJ4Nn92AM7cGx8hj8u1D2p2B1pazVoF5UIc3bY3k80CUoKocS8CQETB7Sd78DaMHXJnkQaPTcVL0xF_ydQn_1hUtgu4Psd3X9ttyRh-PGzMQCVgos0FZphnLu-plDqIC7oA/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaRaPEVdY6vJ4Nn92AM7cGx8hj8u1D2p2B1pazVoF5UIc3bY3k80CUoKocS8CQETB7Sd78DaMHXJnkQaPTcVL0xF_ydQn_1hUtgu4Psd3X9ttyRh-PGzMQCVgos0FZphnLu-plDqIC7oA/s320/Picture1.png" height="214" width="320" /></a></div>
not interactive, the <a href="http://www.mathopenref.com/constructions.html">MathOpenRef</a> site has a variety of compass and ruler constructions that are demonstrated (videos)<br />
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these can be made full-screen <br />
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you can click an auto-repeat box so that the steps are shown repeatedly <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQOM4hnoJ-yLrpYa7V-0jnzpFmn_8w5OFLG4KUA_-XMEEERuqz0EAg4peieRTjjrdyOdYGxwjR1vAN6ekJSfiqK7C4gEHbrtPqQaCQxVmsZjspZ55TcA8rvB-USopujgPFs8I0n6ykMg8/s1600/Picture2.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQOM4hnoJ-yLrpYa7V-0jnzpFmn_8w5OFLG4KUA_-XMEEERuqz0EAg4peieRTjjrdyOdYGxwjR1vAN6ekJSfiqK7C4gEHbrtPqQaCQxVmsZjspZ55TcA8rvB-USopujgPFs8I0n6ykMg8/s320/Picture2.png" height="248" width="320" /></a></div>
<br />don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-4453582503244001812012-01-19T05:53:00.000-08:002014-05-26T23:20:50.183-07:00boxplot plotting<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPBa6EZitDjVAw5pmUPLT82LMHSopRR_PeRS_-hOP5Zt1NiJLOXDAcPmUrgpS4lG2LzlgmLsrO2mL4GZoZPSXZfyuDp-SohUHBIwWRCEYuxt2z1AMITNyC7UeaQFWZiOVhhtCY3y5qjpo/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPBa6EZitDjVAw5pmUPLT82LMHSopRR_PeRS_-hOP5Zt1NiJLOXDAcPmUrgpS4lG2LzlgmLsrO2mL4GZoZPSXZfyuDp-SohUHBIwWRCEYuxt2z1AMITNyC7UeaQFWZiOVhhtCY3y5qjpo/s400/Picture1.png" height="347" width="400" /></a></div>
you can change the number of data points (up to 16) and choose whether to have them sorted or not<br />
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from <a href="http://www.brainingcamp.com/resources/math/box-plots/interactive.php">Braining Camp</a><br />
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see the effect of changing a single value incrementally don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-33020797574318034712011-11-26T08:28:00.000-08:002011-11-26T08:28:25.804-08:00connect threethis <a href="http://nrich.maths.org/5911">game</a> from NRich provides good practice in adding and subtracting directed numbers - to get three in a line<br />
play against the computer or a partner<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh05c2aUEhrSjLgel4uibKmXaihEHO-f4LHXKPKUQJXOBX5pFV1UkYhjMRGyiDKVzX31N6AQOA9G_toclJfhH2dBZNDLabX0vJqih5SMUPIzOvf5FE3gNjcyEsqHnKb0j7p0bIZBc-OJ2k/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh05c2aUEhrSjLgel4uibKmXaihEHO-f4LHXKPKUQJXOBX5pFV1UkYhjMRGyiDKVzX31N6AQOA9G_toclJfhH2dBZNDLabX0vJqih5SMUPIzOvf5FE3gNjcyEsqHnKb0j7p0bIZBc-OJ2k/s320/Picture1.png" width="320" /></a></div>don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-15684826044496343302011-10-01T21:37:00.000-07:002011-10-01T21:39:38.198-07:00sampling<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCvAGctc7mGpwjuvVOUcvfHiYowze3GZqEarTuN5Wl6OSYaOBygXjwBXqt83hxH8DaQaJoROb6dDNFZRTS-lKWwUxu_erNxZb74pUSJIEqcRt2B9xDdgOoOeSedovLhvYot1ANfp8qrVA/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="179" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCvAGctc7mGpwjuvVOUcvfHiYowze3GZqEarTuN5Wl6OSYaOBygXjwBXqt83hxH8DaQaJoROb6dDNFZRTS-lKWwUxu_erNxZb74pUSJIEqcRt2B9xDdgOoOeSedovLhvYot1ANfp8qrVA/s320/Picture1.png" width="320" /></a></div>this <a href="http://nrich.maths.org/6016">simulation</a>, involves picking a marble at random from a bag: ten times, with replacement<br />
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this task from NRich is a good way of illustrating (on a good day) that longer runs usually lead to more accurate predictions<br />
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students are asked to predict the colours of the ten marbles in the bagdon stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-59967132314837114912011-07-26T07:53:00.000-07:002012-02-12T03:21:11.513-08:00the eyeballing gameget students to use the <a href="http://woodgears.ca/eyeball/">eyeballing game</a> to estimate the positions of various geometric objects<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-aFKC4_dF39hAOSHcrw2RXXIU9cPc6BPj6LxLqsavo1mI9NQGVdut6h9x0qM9_mz8mNBpHDtfMve2mYAs6P3uwBgy3rUILdB8PSFrpAArIAfbY1OixlOOLQYaZByinOYjPjiBgngG4pQ/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="271" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-aFKC4_dF39hAOSHcrw2RXXIU9cPc6BPj6LxLqsavo1mI9NQGVdut6h9x0qM9_mz8mNBpHDtfMve2mYAs6P3uwBgy3rUILdB8PSFrpAArIAfbY1OixlOOLQYaZByinOYjPjiBgngG4pQ/s400/Picture1.png" width="400" /></a></div>and find their average error (for either one, two or three goes)<br />
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there are various aspects to explore<br />
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e.g.<br />
do people improve on their second/third goes?<br />
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which game are the class best/worst at?<br />
<ul></ul>don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-83449121427206417142011-07-13T13:55:00.000-07:002012-02-12T03:10:57.551-08:00fitting polygons together<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgt-Vph9Et-1BE1DZQj8yrKQ-oukeBUH6fH7m1oGfykGrPojdmY_6749PETxIKrcRknNk4g62Pakr5UEN4ba0XaGsvdODrG1FcPxckMn9TW7ppTVSUqrMfQtQRcJlGyilacuAucMTr_4u4/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="228" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgt-Vph9Et-1BE1DZQj8yrKQ-oukeBUH6fH7m1oGfykGrPojdmY_6749PETxIKrcRknNk4g62Pakr5UEN4ba0XaGsvdODrG1FcPxckMn9TW7ppTVSUqrMfQtQRcJlGyilacuAucMTr_4u4/s400/Picture1.png" width="400" /></a></div>octagon loops, produced using the <a href="http://www.superliminal.com/geometry/tyler/Tyler.htm">Tyler applet</a><br />
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enables polygons to be drawn (and removed) easily<br />
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what is the relationship between the inside and outside perimeter of these octagon loops? <br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVoI4nUXv_8VEizuxpsMpAnyFjzjz9kPhTERQk4axE7ecji55fPH9QoaQNkBymi4jDzDS6wRPPYJHlFaGlj50BVeRxV-FppcjvfXjg6CP7XqyjadCd75D27T6fe52W_ZQDEYAVknk_oSY/s1600/Picture2.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVoI4nUXv_8VEizuxpsMpAnyFjzjz9kPhTERQk4axE7ecji55fPH9QoaQNkBymi4jDzDS6wRPPYJHlFaGlj50BVeRxV-FppcjvfXjg6CP7XqyjadCd75D27T6fe52W_ZQDEYAVknk_oSY/s200/Picture2.png" width="193" /></a></div><br />
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some interesting patterns can be formed<br />
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for example, the semi-regular <a href="http://mathworld.wolfram.com/SemiregularTessellation.html">tesselations</a> could be explored<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3HDkzMrfxUrv7ZAboqySvg9-uj1RBHSk4nazb9VykTLOgApWwQqqTFN46fT3HdipOoWsCsPHqc3g-QV_HJ4E41EQPRD2ZCfrxW1lasFifAfmHm5GjA6UknOwGIN6iTMVEVUUqNvs8Fis/s1600/Picture2.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3HDkzMrfxUrv7ZAboqySvg9-uj1RBHSk4nazb9VykTLOgApWwQqqTFN46fT3HdipOoWsCsPHqc3g-QV_HJ4E41EQPRD2ZCfrxW1lasFifAfmHm5GjA6UknOwGIN6iTMVEVUUqNvs8Fis/s200/Picture2.png" width="200" /></a></div><br />
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The illuminations (NCTM) polygon<a href="http://illuminations.nctm.org/ActivityDetail.aspx?ID=202"> fitter</a> is also good. Using this you can group blocks of polygons.<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEEsOfv95nSK0_LlYTNl884-XE7Ja768ICfDNmlcb6EcNdqAcZFcnsuh5liE5Sr5hfmOtHUMj9KJ8d1AR0aVXJSJICeYahCnVz-7IvGQZrNiA2i8Bn99CqjBPrm1j5XIfGmI7tgWKWggY/s1600/Picture4.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="249" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEEsOfv95nSK0_LlYTNl884-XE7Ja768ICfDNmlcb6EcNdqAcZFcnsuh5liE5Sr5hfmOtHUMj9KJ8d1AR0aVXJSJICeYahCnVz-7IvGQZrNiA2i8Bn99CqjBPrm1j5XIfGmI7tgWKWggY/s320/Picture4.png" width="320" /></a></div><br />
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<div class="separator" style="clear: both; text-align: center;"></div>don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-53747981016679423292011-07-11T16:03:00.000-07:002012-02-12T03:14:48.350-08:00spinnersthere are spinners available with most interactive whiteboards<br />
for those that don't have these available - and with some benefits from other functionality - here are 3 examples of programmes:<br />
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<a href="http://nrich.maths.org/content/id/6033/experimenter.swf">experimenter (NRich 6033)</a><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4bNrgalDl-e8nXUjxn4W4trVOA3A9r4E8o-V8IHgY8OHKaiBWvM7nkcJeEOD7N-msLq5WPZll4h2_yqqimjL-PtwKlPVX6dYSvuelD9Etdm8Xm2fbovD5i84gUIj6w-ZdpF1fqGRMGRw/s1600/Picture3.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="231" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4bNrgalDl-e8nXUjxn4W4trVOA3A9r4E8o-V8IHgY8OHKaiBWvM7nkcJeEOD7N-msLq5WPZll4h2_yqqimjL-PtwKlPVX6dYSvuelD9Etdm8Xm2fbovD5i84gUIj6w-ZdpF1fqGRMGRw/s320/Picture3.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTQVq3PtBrVOKFRhhFef9qQFC0NV2p8QtSSS2MpEBoZPhkyYyiYvKlAsZDnpulvcEq1x8uXBJjG9hTkAvQRrakHFwj0G8SnXC1c6KURPEQUNQvKTliqRqkGH_Nl9lQ_nOkvS4u49eeYpw/s1600/Picture2.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="232" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTQVq3PtBrVOKFRhhFef9qQFC0NV2p8QtSSS2MpEBoZPhkyYyiYvKlAsZDnpulvcEq1x8uXBJjG9hTkAvQRrakHFwj0G8SnXC1c6KURPEQUNQvKTliqRqkGH_Nl9lQ_nOkvS4u49eeYpw/s320/Picture2.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHZ4oMsxKe85Eidk4K3_emrxuyqf4D_6yHX701X5PFGpjbsUSn-NlIDO4ZuXBNH3FJ25KNrnb7Vi5-s-78T1B7kJmpCJtwBn6iLS5_-j7MhwCc_skeRU5NqyRji3OGh4HugvMxalwOlT8/s1600/Picture4.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="151" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHZ4oMsxKe85Eidk4K3_emrxuyqf4D_6yHX701X5PFGpjbsUSn-NlIDO4ZuXBNH3FJ25KNrnb7Vi5-s-78T1B7kJmpCJtwBn6iLS5_-j7MhwCc_skeRU5NqyRji3OGh4HugvMxalwOlT8/s320/Picture4.png" width="320" /></a></div>students could use a pencil and a paper clip to simulate using a spinner<br />
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using ICT you can have spinners with various sets of numbers and then add or subtract these<br />
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runs are single, in hundreds or 50 000s<br />
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one interest might be to compare e.g. experimental outcomes for subtracting numbers on two spinners, one with 5 numbers and the other with 4 and then theoretical probabilities (via a two-way 'outcomes' table)<br />
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<a href="http://www.mathsonline.co.uk/nonmembers/resource/prob/spinners.html">spinning spinners (Actis)</a><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_S7xw9PJOykYMvQKtZ7PlMgXG9SZN9V2FkZBjcL4eMdi6eer8vmqnoYlOJ7pUlKz8kIZmtBLFDeLy89GP07Vy0IRDn6q0Z4a4HilnqXVw4OtMrMi6HNSBf-qugeZ-4iPvpMblpx0l9xs/s1600/1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_S7xw9PJOykYMvQKtZ7PlMgXG9SZN9V2FkZBjcL4eMdi6eer8vmqnoYlOJ7pUlKz8kIZmtBLFDeLy89GP07Vy0IRDn6q0Z4a4HilnqXVw4OtMrMi6HNSBf-qugeZ-4iPvpMblpx0l9xs/s320/1.png" width="320" /></a></div>has a restricted set of options and no speedy trialler<br />
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but the visuals are good and it can be left in the background, building up a bar chart<br />
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there is one difficult to caculate option (the bottom one) which is interesting...<br />
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Interactivate (Shodor) has two spinner programmes available:<br />
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<a href="http://www.shodor.org/interactivate/activities/AdjustableSpinner/">adjustable spinner</a><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYAUHvfrazWZN8vVEBsjhnMr5bbdJRL9FzrbsHNEgqJjbl7qZjg1D9cF6_M74PErvG4gpYIZ2HfAxMccL9SSCcfGBGXUe1Vuk028dszSgldyX3EwddJoa-BMmg3M0LnVaTRi7msDJcnNE/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="175" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYAUHvfrazWZN8vVEBsjhnMr5bbdJRL9FzrbsHNEgqJjbl7qZjg1D9cF6_M74PErvG4gpYIZ2HfAxMccL9SSCcfGBGXUe1Vuk028dszSgldyX3EwddJoa-BMmg3M0LnVaTRi7msDJcnNE/s400/Picture1.png" width="400" /></a></div><br />
this automatically compares an experimental with a theoretical outcome<br />
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and <a href="http://www.shodor.org/interactivate/activities/ExpProbability/">experimental probability</a><br />
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<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOPhn8xXRfgO9IepzvCBHXwJ4rtjF5YY1dULKrwDo6Iryd33IKqXEidfb_f0dw3xtLJZ6NSAvQryLUKnoTYPq5dEClROqKbNMdMOgKuTH-WrnQD80_jrrWSQ1oHWRFJY5vBxUpgUJOkb8/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="196" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOPhn8xXRfgO9IepzvCBHXwJ4rtjF5YY1dULKrwDo6Iryd33IKqXEidfb_f0dw3xtLJZ6NSAvQryLUKnoTYPq5dEClROqKbNMdMOgKuTH-WrnQD80_jrrWSQ1oHWRFJY5vBxUpgUJOkb8/s320/Picture1.png" width="320" /></a></div>which enables dice to be created with different numbers on their faces (only the same on both) as well as different spinnersdon stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-63829002173512074272011-07-11T15:38:00.000-07:002012-02-12T03:45:06.946-08:00boxplots NLVM<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj630wTpCSWKVDsahhFFTI6F0hC6EEf2CcoaXC6yO7T1wnMpp9bltt1z9j77PGKj_kI3f_pY-fbuO9BfrrtODK3ZMsnSY4_OZJnJXeoiUBVCDAoJ0BZ8xbmm_R1DIhV6yZcjTsZ7LQ4pH8/s1600/old_faithful.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="270" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj630wTpCSWKVDsahhFFTI6F0hC6EEf2CcoaXC6yO7T1wnMpp9bltt1z9j77PGKj_kI3f_pY-fbuO9BfrrtODK3ZMsnSY4_OZJnJXeoiUBVCDAoJ0BZ8xbmm_R1DIhV6yZcjTsZ7LQ4pH8/s320/old_faithful.png" width="320" /></a></div>the 'Old Faithful' geyser in Yellowstone Park has data for the intervals between eruptions that are sort of bi-modal<br />
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<a href="http://nlvm.usu.edu/en/nav/frames_asid_200_g_4_t_5.html?open=instructions">boxplots NLVM</a><br />
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enables a comparison to be made between a boxplot and the shape of a bar chart (of grouped data)<br />
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several data sets are provided - the 'Old Faithful' data set having 112 points<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjG5rdLJqSW8NDhQ3pVWoc6DEFjhsZKoKJ8AUjSA80lSCj8-0aq25T28I0MrJf017KMiyZDeoL6gnDiUsXzQQF-ubbyqt0jxFCjAd0VR1Md9aLIl1BvsfJ5NIs9iw-AhtnqQDAsOis2KcQ/s1600/Picture4.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjG5rdLJqSW8NDhQ3pVWoc6DEFjhsZKoKJ8AUjSA80lSCj8-0aq25T28I0MrJf017KMiyZDeoL6gnDiUsXzQQF-ubbyqt0jxFCjAd0VR1Md9aLIl1BvsfJ5NIs9iw-AhtnqQDAsOis2KcQ/s320/Picture4.png" width="320" /></a></div><br />
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the group sizes can be changed with a slider <br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkPKqUmFVUkrlAc6FqnMeFPWjbIQAhVIRtjUCcyIWUvomV45TeJeoNII9xzpSIzHQu1bODvVnPbOkjoObe4EjB8jQA_0PUIrv5ZFYRNFtq1D0RDQg2-fnzvTmpwyHWdBhKYmjjjAZ1g6g/s1600/Picture5.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkPKqUmFVUkrlAc6FqnMeFPWjbIQAhVIRtjUCcyIWUvomV45TeJeoNII9xzpSIzHQu1bODvVnPbOkjoObe4EjB8jQA_0PUIrv5ZFYRNFtq1D0RDQg2-fnzvTmpwyHWdBhKYmjjjAZ1g6g/s320/Picture5.png" width="320" /></a></div><br />
students can decide how many groups to have - to provide an overview of the data shape<br />
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students can enter their own data and compare a boxplot with a bar chart<br />
they can also see how their data looks with easily changed class intervals (by means of a slider)don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-15761713766038144622011-07-11T12:55:00.000-07:002012-02-12T03:42:45.528-08:00capture - recapturean interesting use of ratios is in the 'capture-recapture' method for estimating a population size<br />
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pull out a sample<br />
mark it in some way<br />
put the sample back<br />
pull out another sample and use the fraction/ratio of marked things to estimate the full population size<br />
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suppose 40 butterflies are marked in some way and released in a particular location<br />
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then a further 20 are captured as shown:<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZjZOpUW0Myt3JqhQr8B5OEKufSkzSOrrjHPnXPwtwY6yLJqRv0rGvbUTROPA7qnQWrrj8Bo52tRZJgr-gLeq9PeSZkgFmbKj1hZZbCa5x4gBNwyZM9M6Oh95y2PR_V__ctKOdhmRN1ds/s1600/Picture2.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZjZOpUW0Myt3JqhQr8B5OEKufSkzSOrrjHPnXPwtwY6yLJqRv0rGvbUTROPA7qnQWrrj8Bo52tRZJgr-gLeq9PeSZkgFmbKj1hZZbCa5x4gBNwyZM9M6Oh95y2PR_V__ctKOdhmRN1ds/s400/Picture2.png" width="400" /></a></div><br />
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how many butterflies would you estimate there to be from this information?<br />
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this<a href="http://flightline.highline.edu/jbetzzall/BI100/animations/capture_recapture.html"> program</a> enables repeated capturing <br />
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repeatedly making second captures enables a comparison of different estimates, exploring the variation:<br />
what are the extremes and what is the mean?don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-36366622523659829342011-07-11T12:22:00.000-07:002011-07-14T13:00:39.139-07:00cereal packet problem<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6Ejijcg5gtj5CxbNL-QiNv-KtGTl_zPAyFYQdXW_imbOidJCJRyucEClGEXaomSBFBx6eV0iTLNAvvNYWI5m6a8srT3CiUkvnoGjrzCai_lkKm9-ZCk-nMEwAd-nEb_GTrwXJ8GUlQvI/s1600/CIMG1820.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6Ejijcg5gtj5CxbNL-QiNv-KtGTl_zPAyFYQdXW_imbOidJCJRyucEClGEXaomSBFBx6eV0iTLNAvvNYWI5m6a8srT3CiUkvnoGjrzCai_lkKm9-ZCk-nMEwAd-nEb_GTrwXJ8GUlQvI/s200/CIMG1820.JPG" width="200" /></a></div>suppose a cereal packet manufacturer decides to put one of six Harry Potter figures inside each box:<br />
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Harry , Ron , Hermione , Dumbledore , Voldemort , Malfoy<br />
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how many boxes, on average, would it take to collect all six figures?<br />
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six is chosen because of the ease of simulation with a dice <br />
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</div><div class="separator" style="clear: both; text-align: left;">a <a href="http://mste.illinois.edu/reese/cereal/cereal.php">simulation</a> from Illinois enables various numbers of animal free gits to be (all) collected:</div><div class="separator" style="clear: both; text-align: left;"><br />
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</div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: left;">if you don't mind promoting a commercial product (a breakfast cereal) then there is a good <a href="http://www.mathwire.com/data/CerealApplet.html">simulator</a> that plots a histogram when all are collected - showing how many of each were obtained </div><div class="separator" style="clear: both; text-align: left;"><br />
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</div>don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-51181756860799204522011-07-11T11:13:00.000-07:002012-02-12T03:36:22.706-08:00probability experiments - NRichtwo probability experiments from NRich are based upon Geoff Giles' Dime probability kits and utilise the recording 'graph' paper that he developed<br />
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<a href="http://nrich.maths.org/content/id/4311/MusicalChairs.swf">nrich 4311</a><br />
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'Two's company' win if the two blue balls touch each other<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidf3J5AwDelh-1UeGYoxfR5azf1fcfvgESZt5KBK1n6MBjOcVvlQGN5is2j5VVgww3sZgwknwShR8LG9UKvT3dCGcp6XLkgSW76so0EpiEbmyt71f2GPGenrkf8TSrihyphenhyphenYmrAPuwcAOUA/s1600/7.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="280" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidf3J5AwDelh-1UeGYoxfR5azf1fcfvgESZt5KBK1n6MBjOcVvlQGN5is2j5VVgww3sZgwknwShR8LG9UKvT3dCGcp6XLkgSW76so0EpiEbmyt71f2GPGenrkf8TSrihyphenhyphenYmrAPuwcAOUA/s400/7.png" width="400" /></a></div><br />
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as well as the very helpful recording sheet, simulation results and a value for the experimental probability are given<br />
you can keep accumulating 100s of runs <br />
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<a href="http://nrich.maths.org/content/id/4313/MusicalChairs.swf">nrich 4313</a><br />
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'Cosy corner' win if at least one of the red balls is in any one of the three corner positions <br />
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students could be asked to estimate the probabilities after a short run experiment<br />
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theoretical probabilities for both of these simulation 'experiments' can be worked out but are not too easy to calculate (they are given, so could be quoted: 4/7 = 0.571 for 'two's company' and 57/60 = 0.95 for 'cosy corner')<br />
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NRich have a further probability <a href="http://nrich.maths.org/content/id/4304/MusicalChairs.swf">experiment</a> - equivalent to throwing two coins (4304) -a win is if both 'coins' show the same value. This can be a useful experiment to undertake since some students think there are three outcomes (both heads, both tails and one of each) so, mistakenly, think the probability of two the same is 2/3<br />
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it can also be interesting to explore the length of runs of wins or loses - maybe calculating an average length<br />
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NRich do a good copy of the (Geoff Giles) <a href="http://www.blogger.com/goog_1097678356">recording shee</a>t - which has many benefits, especially in showing how results tend towards a certain value for a long run experiment<br />
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It's probably better to print the NRich student recording sheet (pdf) but here are two (ping) versions, for 50 trials:<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEprNDWBrXEOXenYvyQA6C27EH5EK99sVLzbVjTc-WLDOPzo-jM_yGwY0foTD5j7gFzdfFWh3Bdt9aYIDhBdPK8i-rW-HK80nwoRZNaEmkWR7A26BR5ksP1_OpGzf7CY7s9GgmMar1vPU/s1600/Picture2.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="302" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEprNDWBrXEOXenYvyQA6C27EH5EK99sVLzbVjTc-WLDOPzo-jM_yGwY0foTD5j7gFzdfFWh3Bdt9aYIDhBdPK8i-rW-HK80nwoRZNaEmkWR7A26BR5ksP1_OpGzf7CY7s9GgmMar1vPU/s400/Picture2.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4j25CE2JuVzn-gphBumqpvPJyQtF9O-tnURTHycB7GQqiDJ4JA8WAvnyIMeybeu5TfG_qSdnnctDdbSfrqVckoufGguWr2-sUxe9gKGZycJXx6OkA4hSdTwMpJmLWey7S6o7o6G0yzzg/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="287" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4j25CE2JuVzn-gphBumqpvPJyQtF9O-tnURTHycB7GQqiDJ4JA8WAvnyIMeybeu5TfG_qSdnnctDdbSfrqVckoufGguWr2-sUxe9gKGZycJXx6OkA4hSdTwMpJmLWey7S6o7o6G0yzzg/s400/Picture1.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"></div>don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-69093491795908614482011-07-11T10:56:00.000-07:002012-02-12T03:23:15.471-08:00probability - estarters<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio7_msM04CPlH2RrbezvuujrAuprpXjp8bXl8-wuCaIiWciQ_hd-RiZaNAWWa6PDLq2UepDV1fF_mL4OKQy-wnuMkP8w-QKgmv6lNnAuYArU9rfs0Mm08uZtK10ZYtYuZ0WfyBp0G7eAs/s1600/6.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="250" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio7_msM04CPlH2RrbezvuujrAuprpXjp8bXl8-wuCaIiWciQ_hd-RiZaNAWWa6PDLq2UepDV1fF_mL4OKQy-wnuMkP8w-QKgmv6lNnAuYArU9rfs0Mm08uZtK10ZYtYuZ0WfyBp0G7eAs/s400/6.png" width="400" /></a></div><br />
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Matt Dunbar makes excellent use of Excel on <a href="http://www.estarters.com/downloads.html">'estarters</a>', some of which is freely downloadable<br />
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within 'probability theory' are the above two tasks involving a comparison of three probabilities (as fractions and decimals and positions on a probability scale)don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-43676966499539533652011-07-11T10:42:00.000-07:002012-01-18T04:16:53.921-08:00UK statistics<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdOFcA7aNHboBzZ7SJI8cncdCzArR9gXeMlbp6eKgfOUjUCYI9nNlw_-Nfk3e0vHOIHs4fMHcJhDogB-3O1GjENKncCSd5fnRfsRLlXBAp5UUf0pdX_t8Iif1aOghWvJVHe8wjgtwS8Fo/s1600/8.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdOFcA7aNHboBzZ7SJI8cncdCzArR9gXeMlbp6eKgfOUjUCYI9nNlw_-Nfk3e0vHOIHs4fMHcJhDogB-3O1GjENKncCSd5fnRfsRLlXBAp5UUf0pdX_t8Iif1aOghWvJVHe8wjgtwS8Fo/s400/8.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div style="text-align: left;">a <a href="http://www.neighbourhood.statistics.gov.uk/HTMLDocs/dvc2/EWPyramid.html">population pyramid</a> for the UK enables you to choose a year (using a slider) or look at the variation over time (including projections). The display can be made full screen.<br />
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</div>You can also look in more detail at a particular age group by hovering over it with a mouse.don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-89047167527627781102011-07-11T10:32:00.000-07:002012-02-12T03:35:32.821-08:00histogram (bar chart) tool - Illuminations (NCTM)<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKwPukBmArLkr0Gm0u0CzQf8x1QBFKv877g8eWgm6adSHnmkPzwvENyPvX19myYBQMAcdtSlUlr4KPhkMw8ji5sjKqo3SnvoKo5itolb55-MtOCAHSGAmmTIR-LQScyrCwnIDXonWPxGc/s1600/7.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKwPukBmArLkr0Gm0u0CzQf8x1QBFKv877g8eWgm6adSHnmkPzwvENyPvX19myYBQMAcdtSlUlr4KPhkMw8ji5sjKqo3SnvoKo5itolb55-MtOCAHSGAmmTIR-LQScyrCwnIDXonWPxGc/s400/7.png" width="400" /></a></div><br />
<a href="http://illuminations.nctm.org/ActivityDetail.aspx?ID=78">Illuminations histogram tool</a><br />
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6 data sets given, or you can enter your own data<br />
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it is very helpful to be able to explore the shape of the distribution for various groups sizes (using a lovely slider)<br />
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students can consider the number of bars necessary to provide a view of the overall data shape<br />
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for example, in the 'horsepower' example above, a distribution with a further peak (as well as the modal class) gets smoothed out for fewer 'bins'don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-4994835605294958142011-07-11T10:16:00.000-07:002012-02-12T03:34:42.127-08:00cumulative frequency - Waldomaths<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjV_eDd782OM6PH55ROW9ctTmMwKKWF65kZjmTHTgS67ZN9LVEe_LIn1Qsvl6kBBVaPAGPcx95TiHqAOIlBYLTC4u2oc9U2iwjCww2SCka4Vbrta5a7i_B8Q9jMbUUhyphenhyphenRl4mRz4YwB5qec/s1600/4.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="227" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjV_eDd782OM6PH55ROW9ctTmMwKKWF65kZjmTHTgS67ZN9LVEe_LIn1Qsvl6kBBVaPAGPcx95TiHqAOIlBYLTC4u2oc9U2iwjCww2SCka4Vbrta5a7i_B8Q9jMbUUhyphenhyphenRl4mRz4YwB5qec/s400/4.png" width="400" /></a></div><a href="http://www.waldomaths.com/CFreq3N.jsp">Waldomaths</a><br />
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compare the cumulative frequency graph for various (10) standard and other data shapes<br />
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also compare these with the related boxplot<br />
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frequencies can be varied by dragging the red dots on the vertical axis - to see the effect on the cumulative frequency curve<br />
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questions can be asked about e.g. the frequency distribution from the cumulative frequency data and graph or the cumulative frequency graph from the boxplot (by clicking boxes on or off at the bottom)don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-58430415503626428612011-07-11T10:07:00.000-07:002015-03-04T00:40:03.128-08:00scattergraphs - Waldomaths<div class="separator" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;">
<img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfaaBqYND4SW879KrLEQYHqmio1TlfK7FbUO_-93skw5ojdqa8UDaYttTnZM-uN50XmDzJ9dqU_ia6tH_S4nzVCLIw0lYm4MoIHuY9SL4VbqKXEGqtauqUnwDRM8bUY3xrtfMs2M6N7TE/s400/5.png" height="253" width="400" /></div>
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<a href="http://www.waldomaths.com/Scatter1LB.jsp">waldomaths</a><br />
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useful to compare an estimated line of best fit with a computer calculated one. Plot some points using the mouse then drag a line (at the top of the screen) to where you think the line of best fit is located.<br />
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Then show the computer calculated (accurate) line of best fit.don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-6241031668243143252011-07-11T09:10:00.000-07:002012-02-12T03:34:01.068-08:00averaging<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiz8HEJO0hOQJpAucRfizUEi5mt-yhse6YtSzJPm-LPM92oGE9OyND5IbHWPt0smmKDFGBub73GP_dug4lKpU3fLZDokk3_2RiY_qTigf4twcQCVdnYeZjsfrQDyBJ1Mb8m91_RadljUbQ/s1600/Picture3.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="27" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiz8HEJO0hOQJpAucRfizUEi5mt-yhse6YtSzJPm-LPM92oGE9OyND5IbHWPt0smmKDFGBub73GP_dug4lKpU3fLZDokk3_2RiY_qTigf4twcQCVdnYeZjsfrQDyBJ1Mb8m91_RadljUbQ/s400/Picture3.png" width="400" /></a></div><br />
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what happens if you start with 2 numbers, produce a next number which is the average of these two and then iterate this process?<br />
[sometimes this is know by the (fictitious) name 'Littov's' chain] <br />
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all number pairs reach a limit, which has a neat generalisation <br />
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students might explore this for their own two starting values, working on paper initially<br />
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it is also very easy to set up a formula that can be dragged down on a spreadsheet (using abs for the absolute value)<br />
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what happens for (4, 7)? for (10, 4)? for (2, 8)? plus some other ordered pairs....<br />
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<a href="http://www.mathsonline.co.uk/nonmembers/resource/spread/iterate.html">mathsonline</a> has a version of this task ('the mean series') available to non-members, either as an Excel sheet or online. The Excel sheet contains a graph, showing how the values home in (smooth) to their limit value.don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0tag:blogger.com,1999:blog-7193790093623130554.post-70068495979517580732011-07-11T08:27:00.000-07:002012-02-12T03:33:11.520-08:00Galton's quincunx<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFR_uAjPhfcUsveyANx882diCTEdA1kEp-qgsPDtCFOBImBc7uVEzEHqwwkUsFtHUbzud9epVb5JjJ_BLM6PO15T7_YZ3GHrkfxagJwxrFKlFZ4g6xSwQMt2o5woEErijG8PIM7addROo/s1600/Sir_Francis_Galton_by_Gustav_Graef.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFR_uAjPhfcUsveyANx882diCTEdA1kEp-qgsPDtCFOBImBc7uVEzEHqwwkUsFtHUbzud9epVb5JjJ_BLM6PO15T7_YZ3GHrkfxagJwxrFKlFZ4g6xSwQMt2o5woEErijG8PIM7addROo/s200/Sir_Francis_Galton_by_Gustav_Graef.jpg" width="150" /></a></div><div class="MsoNormal">Sir Francis Galton - born in Sparkbrook, Birmingham (UK) in 1822</div><div class="MsoNormal">was a cousin of Charles Darwin<i> </i></div><div class="MsoNormal"><i><br />
</i></div><div class="MsoNormal">made contributions to many branches of Science<i></i></div><div class="MsoNormal"><i><br />
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</i></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHXqpiiixIb0h_2AU8-gy2Olsc8TYzUcej_Cbh0kwCUZcGCoqXUVhmcBiZC7O0HoF-5CMffvO4wxbfpvjbYDRZBag8NOVMPoC2_WtoRte3qmkAiCEXOfWtb2RgXl-5AK4CICdYFSBU47o/s1600/6.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHXqpiiixIb0h_2AU8-gy2Olsc8TYzUcej_Cbh0kwCUZcGCoqXUVhmcBiZC7O0HoF-5CMffvO4wxbfpvjbYDRZBag8NOVMPoC2_WtoRte3qmkAiCEXOfWtb2RgXl-5AK4CICdYFSBU47o/s200/6.jpg" width="172" /></a></div><div class="MsoNormal">used a 'quincunx' (also called a Galton board or bean machine) to show how a distribution tends to a 'normal' curve</div><div class="MsoNormal"><br />
</div><div class="MsoNormal">(original is in the Science museum, Boston (USA))<i><br />
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<i>The purpose of this work is for students to compare (i) a short run experimental probability with (ii) a longer run and (iii) a theoretical value. Hopefully the longer run value will be more accurate.... The task also involves a systematic consideration of all options and hence the theoretical values (which can lead to Pascal's triangle). </i></div><div class="MsoNormal"><br />
</div><div class="MsoNormal">Resources: students will need two copies (front and back) of the 8 quincunx sheet and a coin. It can be helpful for a pair to work together (one copy of the sheet between them). Later they may need the 16 quincunx sheet, when they sort out the theoretical outcomes.</div><div class="MsoNormal"><br />
</div><div class="MsoNormal">Instructions: throw a coin (or roll a dice and look for odds and evens).</div><div class="MsoNormal">If it is a <b style="mso-bidi-font-weight: normal;">head</b>: go right at a junction.</div><div class="MsoNormal">If it is a <b style="mso-bidi-font-weight: normal;">tail</b>: go left. </div><div class="MsoNormal">This can be usefully demonstrated on a board.</div><div class="MsoNormal"><br />
</div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCYEiurTHRzLMLMJXwXdzfwUAkm9CIP1bnR1fZ36xvGfL33IhQRwJ_cfuSd6cZrU97K9o1yEuOy5R3hI-NnT5Fpe8A3pQBcThhAurYn47B6MTxzh5zVE2YScqaQXSEQfHsRqU69ZPnPIE/s1600/Picture1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCYEiurTHRzLMLMJXwXdzfwUAkm9CIP1bnR1fZ36xvGfL33IhQRwJ_cfuSd6cZrU97K9o1yEuOy5R3hI-NnT5Fpe8A3pQBcThhAurYn47B6MTxzh5zVE2YScqaQXSEQfHsRqU69ZPnPIE/s320/Picture1.png" width="191" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="MsoNormal">Four flips of a coin should result in the ball ending up in one of the five bins. Students are asked to record 16 experiments on their own sheets (front and back).</div><div class="MsoNormal"><br />
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“Why do you think it ends up in the middle bin more than the others?”<br />
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After this it might be helpful to consider the purpose of the lesson :</div><div class="MsoNormal">to compare:</div><div class="MsoNormal"><br />
</div><ul style="margin-top: 0cm;" type="disc"><li class="MsoNormal" style="mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;">A short run: your own experimental probabilities (their 16 trials)</li>
</ul><ul style="margin-top: 0cm;" type="disc"><li class="MsoNormal" style="mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;">A long run: collect and sum the frequencies for each box for each pair of students. Label the bins (1 to 5) and work out the overall experimental probabilities from the class results.</li>
</ul><div class="separator" style="clear: both; text-align: center;"></div><ul style="margin-top: 0cm;" type="disc"><li class="MsoNormal">The theoretical probabilities: using another recording sheet ask students to find and/or draw all the different ways of getting from the top to the bottom: as a path or as combinations of 4 letters e.g. LLRR (following discussion). There are 16 ways altogether so they will need to be systematic. <br />
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</div><div class="MsoNormal">“How can we use symmetry to simplify finding all the options?”</div></li>
</ul><ul style="margin-top: 0cm;" type="disc"></ul><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIpkyQ6ypeZ66rFJScLkyBRnr-k3TPBV0CpE6wy1Ozz5IpgztSN6mPMnjn9ifdC7O8HEDjmUHAIz4_lOWtlAiXuS1udHuN7RBAvDhQr1BPJgf9qFvySc6LY8IdYaaaFn75ctE61aAnOjE/s1600/Picture3.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="239" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIpkyQ6ypeZ66rFJScLkyBRnr-k3TPBV0CpE6wy1Ozz5IpgztSN6mPMnjn9ifdC7O8HEDjmUHAIz4_lOWtlAiXuS1udHuN7RBAvDhQr1BPJgf9qFvySc6LY8IdYaaaFn75ctE61aAnOjE/s320/Picture3.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="MsoNormal">The theoretical results are a row of Pascal’s triangle: 1, 4, 6, 4, 1. These frequencies will be out of 16 and can be compared (e.g. as a decimal) with the ‘long run’ results by changing the fractions into decimals.</div><div class="MsoNormal"><br />
Utilising ICT: see (on a good day) how long-run experiments tend towards a theoretical value. </div><div class="MsoNormal">There are several good versions of Galton’s quincunx on the net:</div><div class="MsoNormal"></div><ul><li><a href="http://www.subtangent.com/maths/ig-quincunx.php">Subtangent.com (Duncan Keith)</a> (is good visually when made full size) as you approach a good number of trials, slow down the drop rate with the speed slider - then click on auto-drop to stop the flow. The frequencies just seem to keep on accumulating if you leave it to run. It can be enlarged (bottom left) for a whiteboard. </li>
</ul><ul><li><a href="http://www.math.psu.edu/dlittle/java/probability/plinko/index.html">David Little (Penn State University)</a> colourful (uses Java) can be made to fill a board and is downloadable - find the bin frequencies using the left and right arrow keys when the experiment has been halted, also displayed as percentages </li>
</ul><ul><li><a href="http://www.mathsisfun.com/data/quincunx.html">maths is fun</a> has a bar chart helpfully displayed alongside a frequency count as well as the pinboard - but is a little small for classroom display for 4 layers. Gave the following frequencies for 1000 goes: 58 , 261 , 358 , 270 , 53.</li>
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<ul></ul><div class="MsoNormal"></div><div class="MsoNormal">“Why do you think experimental results should be more accurate when more trials are involved (a longer run)?”</div><div class="MsoNormal"><br />
</div><div class="MsoNormal">“What is the difference between an experimental (short run and long run) probability and a theoretical value?”</div><div class="MsoNormal"><br />
</div><div class="MsoNormal">Extension: students could consider theoretical values for other layers (5 then 6 etc) leading to Pascal’s triangle.</div>don stewardhttp://www.blogger.com/profile/04868382949680830399noreply@blogger.com0