tag:blogger.com,1999:blog-57202058971771990202024-03-12T19:58:16.464-07:00Math Coach on DemandThoughts, ideas, links, connections, etc.Unknownnoreply@blogger.comBlogger13125tag:blogger.com,1999:blog-5720205897177199020.post-38054099893632743112018-08-02T21:20:00.002-07:002018-08-02T21:20:15.251-07:00Number Talks as an Intervention Strategy<div dir="ltr" style="text-align: left;" trbidi="on">
So, I haven't been a Math Coach for a long time hence the date of my last post is 2011! In my absence, I had two wonderful babies and taught Grade 7.<br />
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However, this summer I had the wonderful opportunity to act as a Math Coach during the summer school program at one of the sites in the TDSB. This site had 260+ students in Kindergarten to Grade 7. As a Math Coach, I was there to support students by going into classrooms to co-plan/teach with teachers, model lessons/strategies, and/or work directly with students. It was a challenging task because this type of work requires a relationship. Other than two staff members, all the teachers were strangers to me. And, this was not my regular school so all the students were strangers to me too!<br />
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After our initial planning session, I soon decided that Number Talks was going to be my strategy to intervene and fill in the gaps in our students' learning. Many students were coming into the summer school program with computational fluency. Also, while most students did have gaps in their learning, some did not. I felt this strategy addressed all the learners in the room and built on their strengths. <br />
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So, I went into classrooms with my dot patterns and class lists. Here are some photos of what we did together:<br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWrfGs8b6JtxGsIDXI5frEoVMMRNWDU4VwdbldWBGyLspucW21mQw7BLbgEPkmoq1PztMrQimf1wdnxFq8E3NZXXZu-aGcqyMzoXJbDXVkDJ63RfTDtr0h7iTI5fiNCXhLJ3Rp_UaGatQ/s1600/IMG_20180706_1005127.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1067" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWrfGs8b6JtxGsIDXI5frEoVMMRNWDU4VwdbldWBGyLspucW21mQw7BLbgEPkmoq1PztMrQimf1wdnxFq8E3NZXXZu-aGcqyMzoXJbDXVkDJ63RfTDtr0h7iTI5fiNCXhLJ3Rp_UaGatQ/s640/IMG_20180706_1005127.jpg" width="425" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.800000190734863px;">Grade 5 class<br /></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_yd1RAOF4DlmNz4rCu9CAeL-PdClgWS5tnK99eLPlBwBOHme4syebTQl7uCHr0wYzgRi35frXhXEuLvruFezCLHg1CCkP8kJ_a-LtaRAxYxgMRNgJt3u8miPZWAt4o5Y8T99BTJCbxTA/s1600/IMG_20180706_1156381.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1067" data-original-width="1600" height="425" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_yd1RAOF4DlmNz4rCu9CAeL-PdClgWS5tnK99eLPlBwBOHme4syebTQl7uCHr0wYzgRi35frXhXEuLvruFezCLHg1CCkP8kJ_a-LtaRAxYxgMRNgJt3u8miPZWAt4o5Y8T99BTJCbxTA/s640/IMG_20180706_1156381.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Grade 4/5 Class</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjo7wIg0g1igUxuSQjv3aUBjTkJZKTUxNszupAK7ikROK3UQv353dHCPDUFMpxKZhw3aDzWlSg3_ADwYM1uTBDwvTrk5IkrrDiHpngvgMlzuh-U84xHjHOBr0dqPZ64KFHV0qzbgAPurZw/s1600/IMG_20180710_0955155.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1067" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjo7wIg0g1igUxuSQjv3aUBjTkJZKTUxNszupAK7ikROK3UQv353dHCPDUFMpxKZhw3aDzWlSg3_ADwYM1uTBDwvTrk5IkrrDiHpngvgMlzuh-U84xHjHOBr0dqPZ64KFHV0qzbgAPurZw/s640/IMG_20180710_0955155.jpg" width="425" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Grade 4 Class</td></tr>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDmaEBYZ3vxinEqVJsaMrPh3twL8UgdGjBuHwdKE5dZPNG5osUL2oCyuvcQYltX80qFTX1tpkoKNPbRmSEKEzOhk_HjczY7TLDrUoLd4eVuO7QcBJfT_q6ZA7XYyg0DYPC_1iIMmajIps/s1600/IMG_20180706_0921348.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1067" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDmaEBYZ3vxinEqVJsaMrPh3twL8UgdGjBuHwdKE5dZPNG5osUL2oCyuvcQYltX80qFTX1tpkoKNPbRmSEKEzOhk_HjczY7TLDrUoLd4eVuO7QcBJfT_q6ZA7XYyg0DYPC_1iIMmajIps/s640/IMG_20180706_0921348.jpg" width="425" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.800000190734863px;">Grade 3 Class<br /></td></tr>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGF4xczBE-qwf55VXr6WeOJTJ5PLqME6Xiq1woO4G2JpKUkjukKYH37cOzRkI0NX51AlH-gVsGLobiCdB3sRHgYXaMcO0NQwujdGU1fDWRjBCxfm5MVJcJu16Day-kMcJtnWHrFnqGryE/s1600/IMG_20180710_0906270.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1067" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGF4xczBE-qwf55VXr6WeOJTJ5PLqME6Xiq1woO4G2JpKUkjukKYH37cOzRkI0NX51AlH-gVsGLobiCdB3sRHgYXaMcO0NQwujdGU1fDWRjBCxfm5MVJcJu16Day-kMcJtnWHrFnqGryE/s640/IMG_20180710_0906270.jpg" width="425" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.800000190734863px;">Grade 2/3 Class<br /></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAGaU8-zmFMPwy5Egf0xauLdm6WplTuR55efLCEe0Y5JNStn3WVc0ZZrI6MvWzxvWd2xDJLMO630JaEob3AWErEHZ1D4HzSBRrV-qs4lybNifD6gPemJmfKFN6n_PZV3A8AaaNDcDGS-M/s1600/IMG_20180710_0925435.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1067" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAGaU8-zmFMPwy5Egf0xauLdm6WplTuR55efLCEe0Y5JNStn3WVc0ZZrI6MvWzxvWd2xDJLMO630JaEob3AWErEHZ1D4HzSBRrV-qs4lybNifD6gPemJmfKFN6n_PZV3A8AaaNDcDGS-M/s640/IMG_20180710_0925435.jpg" width="425" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Grade 2 Class</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrtWIQ217H0gihJ15QI_RE0WKYgOMwDjKK7yXbIcLFKIhE3ET6czd9v3PU3ZiR9fSuSajWlK-rg-9cdj_njpc1Tv8bPjRsBZUzokGsFdBRShqhGcRbIhREw3FUYsnTWpQtEuOu4avUvho/s1600/IMG_20180711_0934351.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1067" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrtWIQ217H0gihJ15QI_RE0WKYgOMwDjKK7yXbIcLFKIhE3ET6czd9v3PU3ZiR9fSuSajWlK-rg-9cdj_njpc1Tv8bPjRsBZUzokGsFdBRShqhGcRbIhREw3FUYsnTWpQtEuOu4avUvho/s640/IMG_20180711_0934351.jpg" width="425" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Grade 1/2 Class</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsmwqySwxnqgABP9JHNnmvh2GLqvqZMjSwZmruikU0-cbMVBW8HsPzZdC-LvdnlUkU6XDRDs2_MHiL6UVET1fghLisorGJ1erx6ocMr2zD-ARJPVSx41cNWF8R_dkz_48BluP3ter1qoQ/s1600/IMG_20180710_1032033.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto; text-align: center;"><img border="0" data-original-height="1600" data-original-width="1067" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsmwqySwxnqgABP9JHNnmvh2GLqvqZMjSwZmruikU0-cbMVBW8HsPzZdC-LvdnlUkU6XDRDs2_MHiL6UVET1fghLisorGJ1erx6ocMr2zD-ARJPVSx41cNWF8R_dkz_48BluP3ter1qoQ/s640/IMG_20180710_1032033.jpg" width="425" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Grade 1 Class</td></tr>
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As you can see, a number talk with a simple dot pattern provided really valuable information to the teacher in the room as to what his/her students were able to do and what he/she needed to focus on during the 18 days of summer school (e.g., subitizing, orally explaining reasoning, counting, etc.). The student work also provided the perfect vehicle for me to co-plan with each of these teachers about future lessons.</div>
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I happy to say that I was able to work with many of these classes on many more occasions and saw the growth in students' ability to reason, subitize, and articulate their thinking orally. In my next post, I will share with you how I took these number talks and helped students make the connection between mental math and the traditional division algorithm in the Grade 4 and 5 classrooms. </div>
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Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-5720205897177199020.post-71587037231683271382011-11-10T19:35:00.000-08:002011-11-10T19:35:52.416-08:007 Billion and Counting<div dir="ltr" style="text-align: left;" trbidi="on">If you're getting ready to teach your data management unit, here's a site that contains some pretty amazing data that can spark a lot of discussion in your classroom:<br />
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BBC Newsworld<br />
<a href="http://www.bbc.co.uk/news/world-15391515">http://www.bbc.co.uk/news/world-15391515</a><br />
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There are several pieces of authentic data students can get from the site:<br />
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<span class="Apple-style-span" style="font-family: Arial, Helmet, Freesans, sans-serif; font-size: 13px; line-height: 16px;"><strong style="font-family: Arial, Helmet, Freesans, sans-serif; font-weight: bold; line-height: 16px;"><span class="Apple-style-span" style="color: blue;">1. Students fill in their birth date and find out what their number is. This is represented in graphical form. Here's mine:</span></strong></span><br />
<span class="Apple-style-span" style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-size: 13px; line-height: 16px;"><strong style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-weight: bold; line-height: 16px;"><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzKslPrBdh2gPjnhaL8YrJFPOWIXZzZ9ftdDcnpJWZsRgzHWQSaX8Qoxv_ja8BnrkyyPkb4iFpL739mT8N8aYjDiHvvRo63E-aSgQSa-wclVDd0tJdfj9KT0SMHPUgQmkw68KOiUBwb30/s1600/Screen+shot+2011-11-10+at+10.14.12+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="345" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzKslPrBdh2gPjnhaL8YrJFPOWIXZzZ9ftdDcnpJWZsRgzHWQSaX8Qoxv_ja8BnrkyyPkb4iFpL739mT8N8aYjDiHvvRo63E-aSgQSa-wclVDd0tJdfj9KT0SMHPUgQmkw68KOiUBwb30/s640/Screen+shot+2011-11-10+at+10.14.12+PM.png" width="640" /></a></div><span class="Apple-style-span" style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-size: small;"><span class="Apple-style-span" style="font-size: 13px; line-height: 16px;"><b><br />
</b></span></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helmet, Freesans, sans-serif; font-size: 13px; line-height: 16px;"><strong style="font-family: Arial, Helmet, Freesans, sans-serif; font-weight: bold; line-height: 16px;"><span class="Apple-style-span" style="color: blue;">2. Students indicate the country they're living in to find out the birth/death/immigration rate. </span></strong></span><br />
<span class="Apple-style-span" style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-size: 13px; line-height: 16px;"><strong style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-weight: bold; line-height: 16px;"><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIGL5H632BbstsS3_1sND-mSzKb9XbGlBREOhh3MKZGmYFjFJcMZLryMnjtUslnyxCxIXVur3O-KGC_cgNZB5W3NoNzshzcPS_WA-k7fbpcmRuJUU7UXnPYdzNgRnsFtPGq_xGRbGE2jc/s1600/Screen+shot+2011-11-10+at+10.17.59+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="348" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIGL5H632BbstsS3_1sND-mSzKb9XbGlBREOhh3MKZGmYFjFJcMZLryMnjtUslnyxCxIXVur3O-KGC_cgNZB5W3NoNzshzcPS_WA-k7fbpcmRuJUU7UXnPYdzNgRnsFtPGq_xGRbGE2jc/s640/Screen+shot+2011-11-10+at+10.17.59+PM.png" width="640" /></a></div><span class="Apple-style-span" style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-size: small;"><span class="Apple-style-span" style="font-size: 13px; line-height: 16px;"><b><br />
</b></span></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helmet, Freesans, sans-serif; font-size: 13px; line-height: 16px;"><strong style="font-family: Arial, Helmet, Freesans, sans-serif; font-weight: bold; line-height: 16px;"><span class="Apple-style-span" style="color: blue;">3. Students indicate their gender and find out some related facts about the life expectancy of males and females.</span></strong></span><br />
<span class="Apple-style-span" style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-size: 13px; line-height: 16px;"><strong style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-weight: bold; line-height: 16px;"><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPEZpc9FBD8A6XckGBJn0uITjbcp-Ch30g3QZeuIJ2QB1hy8YOqM6JGENj0cRuKNpfXzYDU8FngLzbwjtEmo-2qhOGmazyAynzR_rTpFWVNsF10Fh8fwL-eA_t8dOTda9RGhR-0ov8PyY/s1600/Screen+shot+2011-11-10+at+10.18.15+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="352" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPEZpc9FBD8A6XckGBJn0uITjbcp-Ch30g3QZeuIJ2QB1hy8YOqM6JGENj0cRuKNpfXzYDU8FngLzbwjtEmo-2qhOGmazyAynzR_rTpFWVNsF10Fh8fwL-eA_t8dOTda9RGhR-0ov8PyY/s640/Screen+shot+2011-11-10+at+10.18.15+PM.png" width="640" /></a></div><span class="Apple-style-span" style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-size: small;"><span class="Apple-style-span" style="font-size: 13px; line-height: 16px;"><b><br />
</b></span></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helmet, Freesans, sans-serif; font-size: 13px; line-height: 16px;"><strong style="font-family: Arial, Helmet, Freesans, sans-serif; font-weight: bold; line-height: 16px;"><span class="Apple-style-span" style="color: blue;">Finally, there's a really great video that illustrates the growth of the world's population:</span></strong></span><br />
<span class="Apple-style-span" style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-size: 13px; line-height: 16px;"><strong style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-weight: bold; line-height: 16px;"><br />
</strong></span><br />
<div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/a1vCIwj1IRc?feature=player_embedded' frameborder='0'></iframe></div><span class="Apple-style-span" style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-size: 13px; line-height: 16px;"><strong style="color: #505050; font-family: Arial, Helmet, Freesans, sans-serif; font-weight: bold; line-height: 16px;"><br />
</strong></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helmet, Freesans, sans-serif; font-size: small;"><span class="Apple-style-span" style="font-size: 13px; line-height: 16px;"><b><span class="Apple-style-span" style="color: blue;">Other than connections to large numbers, ratios, rates etc., how else can you use this site in your math program?</span></b></span></span></div>Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-5720205897177199020.post-22383339159107854402011-10-29T18:34:00.000-07:002011-10-29T18:42:26.547-07:00Rounding to the nearest 10, 100, and 1000<div dir="ltr" style="text-align: left;" trbidi="on">Teaching students how to estimate by rounding whole numbers to the nearest 10, 100, 1000 is a challenge. I certainly experienced this as a Grade 4 teacher. Like many teachers, I tried the 'rules' approach: if the number is 5 or more, round up etc. Unfortunately, this created more confusion and I soon learned that the rules didn't mean anything to my students. They needed to 'construct' the rules themselves.<br />
<div><br />
</div><div>I was more successful teaching this concept when I went back to number lines and skip counting. This visual representation of what rounding 'looks like' allowed my students to develop conceptual understanding first. Procedural understanding came later.</div><div><br />
</div><div>This is a great video I found on Youtube that illustrates how to round using number lines:</div><div><br />
</div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/CMdck80SHnw?feature=player_embedded' frameborder='0'></iframe></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: left;">If you're a Grade 6 teacher, you might still want to review how to round to the nearest 10, before moving on to 100 and 1000.</div><div class="separator" style="clear: both; text-align: left;"><br />
</div><div class="separator" style="clear: both; text-align: left;">Once students understand the 'midpoint', they can move on to larger numbers:</div><div style="text-align: center;"></div><br />
<div style="text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/88E1jyWxQIw?feature=player_embedded' frameborder='0'></iframe></div><br />
Independent practice can then be done in fun and interesting ways:<br />
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<div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/OgwkxUmaQqc?feature=player_embedded' frameborder='0'></iframe></div><br />
</div></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-5720205897177199020.post-70407253149694301932011-06-13T13:32:00.000-07:002011-06-16T11:36:15.548-07:00Math Trails<div dir="ltr" style="text-align: left;" trbidi="on"><span class="Apple-style-span" style="color: #666666; font-family: verdana, sans-serif; font-size: 10px;"></span><br />
<div style="background-color: white; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #444444; line-height: normal; margin-bottom: 20px; margin-left: 0px; margin-right: 0px; margin-top: 5px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span class="Apple-style-span" style="font-family: inherit;"><span class="Apple-style-span" style="font-size: small;">I first heard about Math Trails through a presentation by OISE Professor Ron Lancaster. After hearing his presentation, I was excited to try one with students because I saw it as a way to get students to work collaboratively with each other, become active learners, consolidate their learning, and make connections between what they learned, and the world around them.</span></span></div><div style="background-color: white; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #444444; line-height: normal; margin-bottom: 20px; margin-left: 0px; margin-right: 0px; margin-top: 5px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span class="Apple-style-span" style="font-family: inherit;"><span class="Apple-style-span" style="font-size: small;">Last year, I had the opportunity to bring this excitement to life when I collaborated with Kvitka Holman, Grade Three teacher at Donwood Park JPS. Usually, Trails are done outside the school in great locations such as <a href="http://www.mathforamerica.org/c/document_library/get_file?folderId=40&name=DLFE-213.pdf">the Museum of Modern Art in New York City</a>, <a href="http://www.maa.org/mathland/mathtrek_5_29_00.html">the National Gallery of Canada in Ottawa</a> etc. Since we were working with Grade Three students, this was NOT a possibility. So we created a trail around the schoolyard, where supervision was more manageable!</span></span></div><div style="background-color: white; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #444444; line-height: normal; margin-bottom: 20px; margin-left: 0px; margin-right: 0px; margin-top: 5px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span class="Apple-style-span" style="font-size: small;">Here are some pictures of what we did and the questions students solved at each stop on the Donwood Trail:</span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUWPiiU3L6z9049apEdluU8xdMK60zY6Eh1nem_m5kWJ0DHhEqbmRE2l6cShNjosIMhGuTZXAm5pjODCDAaysGuuhb9zZD85IfSU51LMRMPoLc7j4ntFu8SJ50a32qFqFeW1g2ycdI_dw/s1600/Screen+shot+2011-06-13+at+4.22.14+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="background-color: black;"><img border="0" height="227" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUWPiiU3L6z9049apEdluU8xdMK60zY6Eh1nem_m5kWJ0DHhEqbmRE2l6cShNjosIMhGuTZXAm5pjODCDAaysGuuhb9zZD85IfSU51LMRMPoLc7j4ntFu8SJ50a32qFqFeW1g2ycdI_dw/s400/Screen+shot+2011-06-13+at+4.22.14+PM.png" width="400" /></span></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuj_dGyi5cC8aQ5zh4sGvw16esJWgnql84031QtK_THWo6reb4FA9WrCNF9QeBMOIsHVat41K8Bxa2Sg9WhWOVZymvvspO_lLMx5vuUqht9DZrk9CbKUis20qeTLxnAP-hlxtmQF-Rz1Q/s1600/Screen+shot+2011-06-13+at+4.22.39+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="background-color: black;"><img border="0" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuj_dGyi5cC8aQ5zh4sGvw16esJWgnql84031QtK_THWo6reb4FA9WrCNF9QeBMOIsHVat41K8Bxa2Sg9WhWOVZymvvspO_lLMx5vuUqht9DZrk9CbKUis20qeTLxnAP-hlxtmQF-Rz1Q/s400/Screen+shot+2011-06-13+at+4.22.39+PM.png" width="400" /></span></a></div><span class="Apple-style-span" style="background-color: black;"><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg02pETHjvVyUASCfaHEZBBYwGIXD4heOjqJfMak4gdonIcQm0Bd2hIjMKYGUZTWsztcgMtN8I3Qaut8R99jvC7w027RJyAiRcXGpeBrePlWEZoEA7qrRcrzdmIjMXzZWigkDxus5J0u8o/s1600/Screen+shot+2011-06-13+at+4.24.03+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="background-color: black;"><img border="0" height="247" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg02pETHjvVyUASCfaHEZBBYwGIXD4heOjqJfMak4gdonIcQm0Bd2hIjMKYGUZTWsztcgMtN8I3Qaut8R99jvC7w027RJyAiRcXGpeBrePlWEZoEA7qrRcrzdmIjMXzZWigkDxus5J0u8o/s400/Screen+shot+2011-06-13+at+4.24.03+PM.png" width="400" /></span></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1cICLK0Vt_qQe7rrytLNk6ztifIBLPhfq_aIkyLqZGca6geeUWPlManvlT0OlA7j-cwgr7ARAQefjaUEaZDHEem-Ad-M31w0Du6v5P8DwbYSfVgra5DJd-SYHl71ZfarKQajSYqMRz9M/s1600/Screen+shot+2011-06-13+at+4.24.41+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="background-color: black;"><img border="0" height="231" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1cICLK0Vt_qQe7rrytLNk6ztifIBLPhfq_aIkyLqZGca6geeUWPlManvlT0OlA7j-cwgr7ARAQefjaUEaZDHEem-Ad-M31w0Du6v5P8DwbYSfVgra5DJd-SYHl71ZfarKQajSYqMRz9M/s400/Screen+shot+2011-06-13+at+4.24.41+PM.png" width="400" /></span></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgz50E1V3kvRZVbo07ZMOxcrc-o0cNAYKUMcXyGl76FDT_ITyKqaKRbYlukur6m94fJWKJvp_PUhjC-SeZhnKFCdWaxm5Afe3vNQpy45gd2KOShrN80mCoTWJB_J2mKckefAwUktzd60u0/s1600/Screen+shot+2011-06-13+at+4.25.19+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span class="Apple-style-span" style="background-color: black;"><img border="0" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgz50E1V3kvRZVbo07ZMOxcrc-o0cNAYKUMcXyGl76FDT_ITyKqaKRbYlukur6m94fJWKJvp_PUhjC-SeZhnKFCdWaxm5Afe3vNQpy45gd2KOShrN80mCoTWJB_J2mKckefAwUktzd60u0/s400/Screen+shot+2011-06-13+at+4.25.19+PM.png" width="400" /></span></a></div><b><span class="Apple-style-span" style="background-color: yellow;">Getting Started</span></b><span class="Apple-style-span" style="background-color: yellow;">:</span></div><div style="background-color: white; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #444444; line-height: normal; margin-bottom: 20px; margin-left: 0px; margin-right: 0px; margin-top: 5px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"><span class="Apple-style-span" style="font-size: small;">1. Here's an NCTM article outlining the steps to get you started: </span><a href="http://iweb.tntech.edu/jwendt/3150/docs/mathtrails.pdf">Designing Math Trails for the Elementary School</a></div><div style="background-color: white; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #444444; line-height: normal; margin-bottom: 20px; margin-left: 0px; margin-right: 0px; margin-top: 5px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2. Example of Math Trails for Students: <a href="http://www.brocku.ca/cmt/upload/999608510.63275/">Niagara on the Lake</a><br />
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3. Video of Kay Tolliver, math teacher in New York, showing us how to get our students to create their own trail:<br />
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<div class="separator" style="clear: both; text-align: center;"><object class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://2.gvt0.com/vi/0ZKp_iolito/0.jpg" height="266" width="320"><param name="movie" value="http://www.youtube.com/v/0ZKp_iolito&fs=1&source=uds" /><param name="bgcolor" value="#FFFFFF" /><embed width="320" height="266" src="http://www.youtube.com/v/0ZKp_iolito&fs=1&source=uds" type="application/x-shockwave-flash"></embed></object></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: left;">Let us know how it goes, if you decide to try a trail this year!</div></div></div>Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-5720205897177199020.post-71088256618275883952011-03-21T16:30:00.000-07:002011-03-21T16:30:43.469-07:00Mental Math StringsBy this time of the year, most of you have taught your Number Sense unit. Whether it was addition/subtraction or multiplication/division, your students probably still need more practice with mental computational skills. But it's time to move on. So what do you do?<br />
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<div style="text-align: left;">Mental Math Strings are great way to continue building up your students' number sense skills in a short amount of time. Think bellwork, only more interactive and purposeful!</div><div style="text-align: left;"><br />
</div><div style="text-align: left;">Strings are nothing new. They've been around for a long time. I'm not sure who 'invented' them but Cathy Fosnot's name is used often.<br />
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You all have access to a free resource that explains what strings are, how to make them, and what they look like. <a href="http://eworkshop.on.ca/edu/resources/guides/NSN_vol_2_Addition_Subtraction.pdf">The Guide to Effective Instruction in Mathematics 4-6 </a>is the resource. <br />
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</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKkow38cZIIRCmcSDOvB3vG-2WhRFOe2rhnnhL17Gv3mDULqBfTJn3i7RGLAc1SZSAerPFElZZcMhCEfNBO9GkuKPulos47PzCV2eNAfYZV9TPda8dbeOM0AADMeE0uZwsHCHGcSY3mWA/s1600/guide+to+effective+instruction.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKkow38cZIIRCmcSDOvB3vG-2WhRFOe2rhnnhL17Gv3mDULqBfTJn3i7RGLAc1SZSAerPFElZZcMhCEfNBO9GkuKPulos47PzCV2eNAfYZV9TPda8dbeOM0AADMeE0uZwsHCHGcSY3mWA/s400/guide+to+effective+instruction.jpeg" width="316" /></a></div><br />
</div><div style="text-align: left;">A string is a structured sequence of four to seven related computations that are designed to elicit a particular mental computational strategy. (pg. 29)</div><div style="text-align: left;"><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5S87M_83y-wVOS9qzOIEw44dT-UR9CQMpU8C9vfCyACEjtz1w8ogU1hOf7HJ8esK6h0I62wmSXoxeTFE6KuMylfzGJC8yiCHjcPso70g8YXd5_1KdpV92AAWhmPxbwgg9AbRB1NTXlKg/s1600/mental+math+strategies.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5S87M_83y-wVOS9qzOIEw44dT-UR9CQMpU8C9vfCyACEjtz1w8ogU1hOf7HJ8esK6h0I62wmSXoxeTFE6KuMylfzGJC8yiCHjcPso70g8YXd5_1KdpV92AAWhmPxbwgg9AbRB1NTXlKg/s640/mental+math+strategies.jpeg" width="521" /></a></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: left;">Here are some examples of strings that focuses on a particular addition strategy.</div><div class="separator" style="clear: both; text-align: left;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj30aeY9KOsro5x6Xw0yt3AwvI8bAyNRgngr1iKZEtY2Vbzk9_r-EqO1f03tv2ze1L-ZDFsJnIkXSrdXbEN2nl0MiHb9ft83X8XKABIfbdY-lKz56l3OfrUgsaCfEH1y2FOiyHNbzncbNg/s1600/examples+of+strings.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="550" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj30aeY9KOsro5x6Xw0yt3AwvI8bAyNRgngr1iKZEtY2Vbzk9_r-EqO1f03tv2ze1L-ZDFsJnIkXSrdXbEN2nl0MiHb9ft83X8XKABIfbdY-lKz56l3OfrUgsaCfEH1y2FOiyHNbzncbNg/s640/examples+of+strings.jpeg" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: left;">Each string is carefully constructed. Here's the 'formula'.</div><div class="separator" style="clear: both; text-align: left;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJczacYothl_ckVeiyvo6gm90zYLg_CjidX94Myej75TXMvsnA3CIFdQkrWij8NgScCLGf6_vsEF3Jcl8sCR-RyYjxrmGY_r27WuCLy6UvKNqJi1PMAr7LJFV2M-OKbNedRU08YciMy3A/s1600/how+to+make+your+own+string.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="227" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJczacYothl_ckVeiyvo6gm90zYLg_CjidX94Myej75TXMvsnA3CIFdQkrWij8NgScCLGf6_vsEF3Jcl8sCR-RyYjxrmGY_r27WuCLy6UvKNqJi1PMAr7LJFV2M-OKbNedRU08YciMy3A/s640/how+to+make+your+own+string.jpeg" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: left;">Cathy Fosnot does have pre-created resources, if you're interested in purchasing a resource. You can purchase her resources from <a href="http://www.pearsonschoolcanada.ca/index.cfm?locator=PS1zR5&PMDBSUBCATEGORYID=&PMDBSITEID=2621&PMDBSUBSOLUTIONID=&PMDBSOLUTIONID=25862&PMDBSUBJECTAREAID=&PMDBCATEGORYID=&PMDbProgramID=58102">Pearson</a>.</div><div class="separator" style="clear: both; text-align: left;"><br />
</div><div class="separator" style="clear: both; text-align: left;">The following resources are available for K-6 teachers. The junior grade resources are also appropriate for 7-8 students.</div><div class="separator" style="clear: both; text-align: left;"><br />
</div><div class="separator" style="clear: both; text-align: left;"><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; font-family: verdana, arial, helvetica; font-size: 11px;"><a class="lightview" href="http://www.pearsonschoolcanada.ca/index.cfm?locator=PS1zR5&PMDBSUBCATEGORYID=&PMDBSITEID=2621&PMDBSUBSOLUTIONID=&PMDBSOLUTIONID=25862&PMDBSUBJECTAREAID=&PMDBCATEGORYID=&PMDbProgramID=58102#productDescription_2" style="color: #333333; outline-color: initial; outline-style: none; outline-width: initial; text-decoration: none;" title="">Minilessons for Early Addition and Subtraction (K-1)</a></span></div><div class="separator" style="clear: both; text-align: left;"><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; font-family: verdana, arial, helvetica; font-size: 11px;"><a class="lightview" href="http://www.pearsonschoolcanada.ca/index.cfm?locator=PS1zR5&PMDBSUBCATEGORYID=&PMDBSITEID=2621&PMDBSUBSOLUTIONID=&PMDBSOLUTIONID=25862&PMDBSUBJECTAREAID=&PMDBCATEGORYID=&PMDbProgramID=58102#productDescription_3" style="color: #333333; outline-color: initial; outline-style: none; outline-width: initial; text-decoration: none;" title="">Minilessons for Extending Addition and Subtraction (Gr. 2-3</a>)</span></div><div class="separator" style="clear: both; text-align: left;"><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; font-family: verdana, arial, helvetica; font-size: 11px;"><a class="lightview" href="http://www.pearsonschoolcanada.ca/index.cfm?locator=PS1zR5&PMDBSUBCATEGORYID=&PMDBSITEID=2621&PMDBSUBSOLUTIONID=&PMDBSOLUTIONID=25862&PMDBSUBJECTAREAID=&PMDBCATEGORYID=&PMDbProgramID=58102#productDescription_4" style="color: #333333; outline-color: initial; outline-style: none; outline-width: initial; text-decoration: none;" title="">Minilessons for Early Multiplication and Division (Gr. 3-4)</a></span></div><div class="separator" style="clear: both; text-align: left;"><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; font-family: verdana, arial, helvetica; font-size: 11px;"><a class="lightview" href="http://www.pearsonschoolcanada.ca/index.cfm?locator=PS1zR5&PMDBSUBCATEGORYID=&PMDBSITEID=2621&PMDBSUBSOLUTIONID=&PMDBSOLUTIONID=25862&PMDBSUBJECTAREAID=&PMDBCATEGORYID=&PMDbProgramID=58102#productDescription_5" style="color: #333333; outline-color: initial; outline-style: none; outline-width: initial; text-decoration: none;" title="">Minilessons for Extending Multiplication and Division (Gr. 4-5)</a></span></div><div class="separator" style="clear: both; text-align: left;"><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse; font-family: verdana, arial, helvetica; font-size: 11px;"><a class="lightview" href="http://www.pearsonschoolcanada.ca/index.cfm?locator=PS1zR5&PMDBSUBCATEGORYID=&PMDBSITEID=2621&PMDBSUBSOLUTIONID=&PMDBSOLUTIONID=25862&PMDBSUBJECTAREAID=&PMDBCATEGORYID=&PMDbProgramID=58102#productDescription_6" style="color: #333333; outline-color: initial; outline-style: none; outline-width: initial; text-decoration: none;" title="">Minilessons for Operations with Fractions, Decimals, and Percents (Gr. 5-6)</a></span></div><br />
Stay tuned for a video of Laura Thompson going through a string with her Grade 6 class!</div>Unknownnoreply@blogger.com5tag:blogger.com,1999:blog-5720205897177199020.post-9264245515933562852011-02-02T20:32:00.000-08:002011-02-04T12:20:00.143-08:00Determining a Final GradeIt's that time of year: report cards! So I thought we could start a conversation about the achievement chart and the role it plays in determining the math mark that appears on a student's report card.<br />
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In the past, individual marks on a test is added up and a total is written on top of the paper. Sometimes, a letter is written to correspond to the numeric score. <br />
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In addition to this, a student's final grade might be determined by adding up his/her individual marks on tests/quizzes and the mean is calculated. There are many commercial products that are available to help you do this.<br />
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However, our Ontario Math curriculum document indicates that determining a final grade it is not as simple as this. So we (Grade 1 to 12 teachers ) get the achievement chart to help us.<br />
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The achievement chart is misunderstood by many. We're not always sure when or how to use it. But understanding it will help us assess and evaluate our students in a fair and consistent manner.<br />
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The achievement chart does make it clear that Mathematics is not about how much you know or if you get the right answer. It calls for understanding, thinking, and application skills from our students. <br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLSWc0gTL9Jb80eW0HbTO8DDvnkCuMNnyGcPL7kh1E9Vkry2qolMO1sZcOBeZwuO9AER1x7-EBJ5IKGIAX1WhKM0RitB3BrWwwUWqTZ9cBtApBamkr7Dd7e2LeKN0VrScjGour8ZFWTvw/s1600/categories.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLSWc0gTL9Jb80eW0HbTO8DDvnkCuMNnyGcPL7kh1E9Vkry2qolMO1sZcOBeZwuO9AER1x7-EBJ5IKGIAX1WhKM0RitB3BrWwwUWqTZ9cBtApBamkr7Dd7e2LeKN0VrScjGour8ZFWTvw/s320/categories.jpg" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: left;">"The four categories should be considered as interrelated, reflecting the wholeness and interconnectedness of learning" (page 19).</div><div class="separator" style="clear: both; text-align: left;"><br />
</div><div class="separator" style="clear: both; text-align: left;">So with that in mind, the Ontario Curriculum document goes on to say:</div><div class="separator" style="clear: both; text-align: left;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><span class="Apple-style-span" style="color: purple;">Teachers will ensure that student work is assessed and/or evaluated in a balanced manner with respect to the four categories, and that achievement of particular expectations is considered within the appropriate categories. (page 20)</span></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: left;">Essentially, that mark on the report card must reflect a student's achievement of the four categories, in a body of work.</div><div class="separator" style="clear: both; text-align: left;"><br />
</div><div class="separator" style="clear: both; text-align: left;"><b>Design of Assessments/Evaluations</b></div>One of the ways some teachers in SE2 have been making sure that they account for all four categories in their assessments in through their test designs. Here is an example of a grade three test. Thanks for sharing, Marie!<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNrz7wCiRobfNiMeCfiEeN2TYXbY1v-Va-77j2U6q0sRlZAVM2-b7JUKtXPiFQ5kbNsLfwg4BNm0Cp0UzHnEJd11sQYilFutKP5dr5ppO3OhY9anrQDJuUb85HbZKdufCOZV3CANrj00A/s1600/thinking.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNrz7wCiRobfNiMeCfiEeN2TYXbY1v-Va-77j2U6q0sRlZAVM2-b7JUKtXPiFQ5kbNsLfwg4BNm0Cp0UzHnEJd11sQYilFutKP5dr5ppO3OhY9anrQDJuUb85HbZKdufCOZV3CANrj00A/s640/thinking.JPG" width="480" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifHyvMcMX3iyxKAL_Oa-Qthn3cQdXo5JmWvKPnlHmz_FK0wSFzkplmBkZ4PZlgW_MN_8I0pXp_uz04ZetXkaCiPdRDCrnEtP3RcS2OnyjlYWpSJnWSsH7vntzJSxsxHeaS_i0RPwl-BeA/s1600/communication.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifHyvMcMX3iyxKAL_Oa-Qthn3cQdXo5JmWvKPnlHmz_FK0wSFzkplmBkZ4PZlgW_MN_8I0pXp_uz04ZetXkaCiPdRDCrnEtP3RcS2OnyjlYWpSJnWSsH7vntzJSxsxHeaS_i0RPwl-BeA/s640/communication.JPG" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="separator" style="clear: both; text-align: left;"></div><div class="separator" style="clear: both; margin: 0px; text-align: left;"><b>Communication with Students</b></div><div class="separator" style="clear: both; margin: 0px; text-align: left;">I was recently at demonstration lesson in a Grade 6 class when I noticed this:</div><div class="separator" style="clear: both; margin: 0px; text-align: left;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjz8h8fLvzXDycexCtGfJeyBCXocP6J7YncQ8-rHPkTpABezZ95OX2IfY11egmetRd_hGIa4tEn0ukC6ZCeJw-lYzfRD0ZanbxfXdV-5jayx-Q_XksvnvIomKSVYMOnt3H2X0AzG3sXiiI/s1600/jessica.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjz8h8fLvzXDycexCtGfJeyBCXocP6J7YncQ8-rHPkTpABezZ95OX2IfY11egmetRd_hGIa4tEn0ukC6ZCeJw-lYzfRD0ZanbxfXdV-5jayx-Q_XksvnvIomKSVYMOnt3H2X0AzG3sXiiI/s640/jessica.JPG" width="640" /></a></div><div class="separator" style="clear: both; margin: 0px; text-align: left;"><br />
</div><div>Jessica Nip, the classroom teacher, created this with her students. She refers to it regularly. All her students understand that their final grade on the report card is based on their achievement in all four categories.</div><br />
<b>Communication with Parents</b><br />
Many parents believe mathematics is about the knowledge part. Some may argue that a child who knows their multiplication facts up to 25 x 25 should automatically get an A on the report card. <br />
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Sharing the achievement chart with parents is one way to let them know that you're looking for more than a child's knowledge of concepts when determining their report card mark. Also, you can reference a particular category when discussing a child's strength or offering next steps.<br />
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<i>What are your thoughts and/or experiences with using the achievement chart with students? parents?</i>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-5720205897177199020.post-39979901072681010352010-04-29T19:57:00.000-07:002010-04-29T20:01:47.104-07:00Beyond Numbers, Words, and Pictures<span class="Apple-style-span" style="font-family: 'Lucida Grande'; font-size: small;"><span class="Apple-style-span" style="font-size: 11px;"><br />
</span></span>Communication in math has been a popular topic in SE2 recently. Many conversations have been around the use of <span class="Apple-style-span" style="font-style: italic;"><span class="Apple-style-span" style="font-weight: bold;">pictures, numbers, and words</span></span>. This practice became 'popular' back when EQAO started to ask students to 'Use pictures, numbers, and words to explain your thinking.". It caught on and many classrooms back then (and even today) require students to show their thinking using <span class="Apple-style-span" style="font-style: italic;">all three modes</span>.<br />
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My question is this: <span class="Apple-style-span" style="font-style: italic;">can a student communicate effectively without using pictures, numbers AND words? </span><br />
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This Grade 1/2 class was given this problem (I'm paraphrasing!): Two buses can hold 22 students together. The difference between the two buses is 4. How many kids are on each bus? <br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcwlio3HN9RotvkrNyXJUykPRG9HZimQlOypKdybrs5ms1cBEwCmvIlVfG6-fuU7PPNgmIc0tWe2KwXfQbcCiSB9z8RnTXMNM_DwkHmGXhn882gjm6fRWB1CgCXNItjG8cThUABIDWzko/s1600/sample3.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcwlio3HN9RotvkrNyXJUykPRG9HZimQlOypKdybrs5ms1cBEwCmvIlVfG6-fuU7PPNgmIc0tWe2KwXfQbcCiSB9z8RnTXMNM_DwkHmGXhn882gjm6fRWB1CgCXNItjG8cThUABIDWzko/s320/sample3.JPG" /></a></div><br />
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<div style="text-align: center;"><i>Does this student need to write 'words' to convince you they understand the problem? Those two equations alone speak volumes to me!</i></div><div style="text-align: center;"><br />
</div><div style="text-align: left;">Students in this Grade 3 class were given a problem that involves them solving 7x6.</div><div style="text-align: left;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDJRVvTZkgXLzvqPp7zHuasxeglPuyWIe_ZoWqXL52q5R0Z9xCJ83K5BeirK5Ha7zYKR_NzkMFTqR2QKIqJU6YVyRmZpBjWLrLl1powdLpV4WLI7lhyFcP-93BsTUnX1CqeEPNfZwkKHQ/s1600/DSC06395.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDJRVvTZkgXLzvqPp7zHuasxeglPuyWIe_ZoWqXL52q5R0Z9xCJ83K5BeirK5Ha7zYKR_NzkMFTqR2QKIqJU6YVyRmZpBjWLrLl1powdLpV4WLI7lhyFcP-93BsTUnX1CqeEPNfZwkKHQ/s320/DSC06395.JPG" /></a></div><div style="text-align: left;"><br />
</div><div style="text-align: left;"><div style="text-align: center;"><i>What more does this student need to do to convince you he/she is able to solve 7x6 using a variety of strategies? </i></div><div style="text-align: center;"><br />
</div></div><div style="text-align: left;">Students is this Grade 5/6 class were given the task to design a new logo for a car company that involves rotations.</div><div style="text-align: left;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOnzTJb9PyfqUpFRGbo6k3KgCjePELfilscSo3V8Bks_N7uWUJkS9BkFjeKyXscrJE32nc4fh-Hk1ABdbaGkFOiJURONhdXwXysxF4mfOzCAT8syv6DnYIzamKOUXZRdUHH_WpwbrsnXE/s1600/solution5.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOnzTJb9PyfqUpFRGbo6k3KgCjePELfilscSo3V8Bks_N7uWUJkS9BkFjeKyXscrJE32nc4fh-Hk1ABdbaGkFOiJURONhdXwXysxF4mfOzCAT8syv6DnYIzamKOUXZRdUHH_WpwbrsnXE/s320/solution5.JPG" /></a></div><div style="text-align: left;"><br />
</div><div style="text-align: center;"><br />
</div><div style="text-align: center;"><i>Does this student need a write a long narrative explaining their thinking or are we convinced of their understanding of rotations?</i></div><div style="text-align: center;"><br />
</div><div>I'm not suggesting that students NEVER have to use words to explain their thinking. But requests for numbers, words, and pictures usually results in students writing the same thing, three different ways. They start making things up! </div><div><br />
</div><div>What I am suggesting is to have your students choose which mode (s) (pictures, numbers, words) they want to communicate with. Ultimately, we want students to ask themselves this question when looking at their work:<br />
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<span class="Apple-style-span" style="font-weight: bold;">Is my communication clear and concise enough to convince others that I understand this concept?</span><br />
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If we can get students to do this, then they'll make the decision whether or not they need to use pictures, numbers <span class="Apple-style-span" style="font-weight: bold;">or</span> words.<br />
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<div><div style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">Funny enough, EQAO no longers asks students to explain their thinking using pictures, numbers, and words. Prompts such as 'Justify your answer", "Explain your thinking", and 'Show your work' are now used in all three assessments (Primary, Junior, Grade 9) today. <br />
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Stay tuned for a post explaining the difference between the three!</div></div><div></div></div>Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-5720205897177199020.post-47497817869459174882010-02-02T20:06:00.000-08:002011-01-16T16:34:36.593-08:00Why the Missing 'R' in Rubrics?This is a question that's been circling around SE2 lately that's worth a discussion. There are many teachers who are wondering why rubrics only have levels 1 to 4. Some are starting to add the R criteria to teacher-created rubrics. <br />
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Before we can answer this question, we must agree on what we mean by an R or Below 50. Does it mean 'no evidence", 'zero evidence' or 'not enough evidence'?<br />
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Surprisingly, neither the <em>Fresh AER</em> document nor the <em>Ontario Curriculum for Mathematics</em> addresses this matter. Unfortunately, this lack of clarity has created inconsistencies amongst our schools which has ultimately resulted in our students being unfairly asssessed and/or evaluated.<br />
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<em>Growing Success</em> is a document the Ministry of Education has been promising to release to address the inconsistencies and create a common message among all Ontario educators. Unfortunately, it has not grown out of it's draft stage as yet. Luckily, there's a PDF version available:<br />
<br />
<a href="http://www.ocup.org/resources/documents/EDU_GS_binder_010708_BMv2.pdf">http://www.ocup.org/resources/documents/EDU_GS_binder_010708_BMv2.pdf</a><br />
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This is what it has to say about R or Below 50:<br />
<ul><li><span style="color: yellow;">The student has not demonstrated the required knowledge and skills. Extensive remediation is required.</span> <br />
<br />
<div></div></li>
<li><span style="color: yellow;">“R”/ “Below 50” does not correspond to one of the four achievement levels. </span></li>
<li><span style="color: yellow;">“R”/ “Below 50” is used for reporting purposes to flag the need for remediation and parent involvement.</span> <br />
<br />
<div></div></li>
<li><span style="color: yellow;">“R” signals that additional learning is required before the student will begin to achieve success with this grade’s expectations.</span></li>
</ul>Based on this, you can begin to answer the original question: <span style="color: magenta;">does an R belong on a rubric? Are you sure?</span><br />
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Some other questions to consider, while we're on the topic:<br />
<ul><li>Does your grade team/divison/school share the same criteria for R/Below 50? If so, how did you come to this consistent messaging?</li>
<li>What's the difference between an R/Below 50 on an assessment task and an R/Below 50 on the report card? </li>
<li>Can a student get an R or Below 50 on formative assessments and still receive a B or equivalent on the report card? </li>
</ul>Feel free to respond to one or all of the questions by using the Comments link below. The more we have these 'difficult' conversations, the closer we'll come to understanding this widely misunderstood topic of assessment and evaluation!Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-5720205897177199020.post-32998419387172018562009-11-15T19:15:00.000-08:002009-11-16T06:28:48.826-08:00Math and the Arts<div style="text-align: left;">Integrating Math and the Arts is a fun way to engage the creativity of your students while reinforcing important math concepts. Iain Brodie from St. Andrews PS found the opportunity to bring the Arts into his grade two classroom by participating in The Math Performance Festival last year. The Festival is a celebration of mathematics and is organized by the University of Waterloo. Iain's class created this song after reading <i>Who's the Big Bad Wolf? </i>Their song is sung to the theme of <i>Spider-man. </i>Click on the link below the picture to see their performance.<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="http://www.edu.uwo.ca/mpc/images/mf-235.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img align="right" border="0" height="107" src="http://www.edu.uwo.ca/mpc/images/mf-235.jpg" width="200" /></a><br />
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<a href="http://www.edu.uwo.ca/mathscene/mathfest2009/mathfest235.html" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;">11. Chocolate bar v.2</a><br />
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Their performance was the #2 pick by one judge! Congratulations to everyone involved in this project!<br />
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Entries for <a href="http://www.edu.uwo.ca/mpc/mpf2010/index.html">2010</a> are already coming in! If you're thinking of putting in a performance, there's an<a href="http://www.edu.uwo.ca/mpc/overview.html"> overview</a> of the process on the site. You (and your students) can also view past performances (<a href="http://www.edu.uwo.ca/mpc/performances_2008.html">2008, </a><a href="http://www.edu.uwo.ca/mpc/performances.html">2009) </a><br />
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This festival is not just for primary kids. Check out this entry about angles.<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="http://www.edu.uwo.ca/mpc/images/anglehelicopter.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img align="right" border="0" height="81" src="http://www.edu.uwo.ca/mpc/images/anglehelicopter.jpg" width="200" /></a><br />
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<a href="http://www.edu.uwo.ca/mathscene/mathfest2009/mathfest277.html" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;">21. Angle helicopter </a><br />
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<div style="text-align: left;">There's even a category for <a href="http://publish.edu.uwo.ca/george.gadanidis/imaginethis/uoit/index.html">teachers</a>! Any takers?<br />
</div><br />
Beyond music, your students can also create a <a href="http://www.edu.uwo.ca/mpc/mpf2010/mpf2010-104.html">dance</a> (<em>Perimeter and Area</em>), <a href="http://www.edu.uwo.ca/mathscene/mathfest2009/mathfest267.html">skit</a> (<em>Median of a Triangle</em>) or even <a href="http://www.edu.uwo.ca/mathscene/mathfest2009/mathfest243.html">interview a math concept</a> (<em>Let's meet Circle!</em>). The website has several <a href="http://www.edu.uwo.ca/mpc/resources.html">resources</a> full of ideas to get you started.<br />
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<strong>How do you integrate Math with the Arts?</strong> Share your experience with us by leaving a comment below!Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-5720205897177199020.post-81835412980612634942009-10-19T06:25:00.000-07:002009-10-19T07:33:31.301-07:00EQAO for K-8 TeachersA few weeks ago, I met with several Grade 3 and 6 teachers to unpack the EQAO data from Spring 2009. Each group got an overview of how the questions were constructed, organized, and scored. We then looked at each school's IIR report to identify trends and patterns. While there were certain questions that were problematic for certain schools, the trends were obvious for the entire FOS, board, and province. Our primary and junior division students struggled with the following:<br />
<ul><li>solving multi-step problems</li>
<li>answering multiple choice questions</li>
</ul>This was not a surprise to many. EQAO has made these observations for many years. Classroom teachers make these observations on a regular basis, even in non-testing grades. <br />
Each group spent a lot of time discussing the 'why'. We talked about the need for more multi-step problems in classrooms, beyond the problem solving Fridays or Tuesdays. We also discussed the need for the:<br />
<ul><li>consistent use of concrete materials (manipulatives) </li>
<li>modelling of explicit mathematical language by the classroom teacher (e.g., <em>expression, </em><em>equation, equality)</em></li>
<li>application of the Four Step Problem Solving Model (i.e., understand the problem, make a plan, carry out the plan, reflect on the solution)</li>
<li>modelling of appropriate problem solving strategies (e.g., act it out, make a model, draw a diagram, guess and check, make a table)</li>
</ul>These strategies are appropriate for any K-8 classroom and divisions/schools are strongly encouraged to focus on these for school improvement, rather than a particular strand or concept.<br />
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One of the biggest discussion points in all the groups was around the spotlight placed on Grade 3 and 6 teachers. They're feeling the pressure! EQAO has renamed the assessment to send the clear message that the Primary Division Assessment involves K-3 teachers, and the Junior Division Assessment involves 4-6 teachers. Intermediate teachers are not off the hook either! Your students are coming into your classroom with a wealth of knowledge and understanding that they learned from their K-6 teachers.<br />
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As classroom teachers, we all need to understand where our students came from and where they're going. <br />
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Start by looking at the assessment booklets. You can find them (Primary, Junior, Grade 9) in the SE2 Math Lab conference on TEL.<br />
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Thoughts? Questions? Leave me a comment (it's completely anonymous!).Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-5720205897177199020.post-8720850133009127692009-09-22T09:41:00.000-07:002009-09-24T06:35:32.890-07:00Purposeful Long Range PlanningIt's that time of year when long range plans are due and the questions regarding their format, purpose, and use are coming out. The good news is that long range plans in Mathematics vary from teacher to teacher, school to school etc. There's no one right way to construct your long plans.<br /><br />Having said that, there are two key point to keep in mind when creating your plans. The first one is:<br /><ul><li>all grade level expectations from the Ontario Curriculum must be addressed<br /></li></ul><p>That's right: all expectations must be accounted for in instruction so your long range plans should include expectations that won't be addressed on the report card.<br /></p><p>The details depend on you. Some plans may include: </p><ul><li>overall expectations with clusters of specific expectations</li><li>the big ideas of a particular unit of study or strand\</li><li>time period (keep in mind these will change)</li><li>instructional and assessment strategies</li><li>links to core resources </li></ul><p>Here are some examples:<br /><a href="http://docs.google.com/Doc?docid=0AfYrpITfs0DhZGNnemc2OV8wZDlrdzcyNmM&hl=en">Kindergarten (Ecole Glen Park PS)</a><br /><a href="http://docs.google.com/Doc?docid=0AfYrpITfs0DhZGNnemc2OV8xY2hjZ2JiZ24&hl=en">Grade 1/2 (various authors)</a></p><p><a href="http://spreadsheets.google.com/ccc?key=0AvYrpITfs0DhdFJWTy1UTUxkS0xQSXVpUmlVM3Rwc1E&hl=en">Grades 1 to 6 (Elkhorn PS)<br />Grade 7 with Math Makes Sense (Robin Kirk Armstrong)</a><br /></p><p>The second key point to keep in mind is this:</p><ul><li>long range plans should be flexible and responsive to your students. Their strengths, needs, and interests will dictate the rate at which you teach. </li></ul><p>That means your plans can come out of that folder or dusty spot in your classroom throughout the year. Revisiting plans at the end of the first term is a common practice.</p>Reactions, Questions, or Concerns? Leave a comment below.<br /><p></p>Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-5720205897177199020.post-64123289296182704422009-03-05T11:37:00.000-08:002011-02-02T20:46:01.539-08:00What's the point of math anyway?'To get the right answer, of course!"<br />
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Well, not really but our students seem to think so. Unfortunately, our students have lot of misconceptions about Math. Here are a few:<br />
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- just add/subtract/multiply/divide and you'll get the right answer.<br />
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- the problem is too hard if you can't get the answer right away.<br />
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- some people are just good at Math.<br />
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Algorithms feed into these misconceptions. Just follow these steps and you'll always get the answer. Yeah right! Is it really that easy? Try to follow along in the video:<br />
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dxMtx8lr9e2dS3uw9m_YSxudIQ1lFQq94U7dQuKWzxrb2br-R0Zcq748WmmTTI_UuV1BUbbZBvkTqjAvr2GCQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe><br />
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"We learned this stuff so why can't they?"<br />
"I've told them the steps so many times so why can't they remember it?"<br />
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Students struggle because they're taught to memorize these 'rules' without developing any conceptually understanding of why they're 'borrowing' or 'changing' etc.<br />
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One of the goals of Mathematics is to develop flexible thinkers. Teachers also need to be flexible thinkers. Are you a flexible thinker when it comes to the operations? Try the question in the video:<br />
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342 - 173 = ?<br />
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How many of you did the traditional algorithm? That's one way. Try another strategy.<br />
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Here's an example:<br />
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173+7=180<br />
180+20=200<br />
200+100=300<br />
300+42=342<br />
7+20+100+42= 169<br />
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Too long? Too confusing? How about this:<br />
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342=200+142<br />
200-173= 27<br />
142+27=169<br />
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Still confusing? How about this:<br />
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342=199+143<br />
199-173=26<br />
143+26=169<br />
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These are just a few examples. Your students will come up with the rest.Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-5720205897177199020.post-26348456731909499872009-02-02T19:43:00.000-08:002010-04-29T06:44:56.445-07:00Welcome!Hi guys;<br />
Thanks for visiting! This is my first year as a math coach with TDSB and I get requests for all sort of information on a daily basis. There's only one of me so I decided to create a blog. Teachers can access commonly used resources, get answers to FAQs etc. It' s my hope that teachers will also share their experiences with each other. I most definitely don't know everything and I'm always willing to learn something new so bring on the ideas!Unknownnoreply@blogger.com5