tag:blogger.com,1999:blog-54739162054249337812024-03-14T02:17:38.888-04:00M^3 (Making Math Meaningful)Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.comBlogger372125tag:blogger.com,1999:blog-5473916205424933781.post-9451068619685383582019-12-06T12:04:00.000-05:002019-12-06T12:04:05.393-05:00November 27<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Last Wednesday was a heartbreaking day for my family. Willow, our Bernese Mountain Dog, died. She was only four years old and losing her has been harder than any of our previous dogs. She had had emergency surgery on the Sunday and the vet said all went well. But she didn't get better.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We first met her and the other seven balls of fluff from her litter when they were only five weeks old. She came home at eight weeks and met Harmonie who taught her many of the things dogs need to know. She was full of mischief and such a lap dog, despite being 85 lbs. She loved big piles of leaves and snow and canoe rides (swimming is greatly overrated) and most of all her soccer ball (after she got rid of all of its stuffing). After we lost Harmonie a couple of years ago she grabbed all the attention from all of her people. She always hopped up on the couch to wait for me when I put the kettle on to make tea as she knew that it was almost cuddle time. She was a good dog.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Rest in peace, Willow.</span></div>
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Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-60952125658205518532019-09-09T15:57:00.001-04:002019-09-09T15:57:39.830-04:00Keeping the Conversation Going<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">There has been lots of buzz on Twitter around Name Tents (Feedback Forms) and rightfully so. I love using them and wrote about the tweaks I made to Sara Van Der Werf's template last year <a href="http://marybourassa.blogspot.com/2018/02/feedback-forms.html" target="_blank"><b>here</b></a>. This included adding a picture of each student and finding out about their siblings. I have since started asking for pronouns, though I tell the class that this is optional as I do not want anyone to feel uncomfortable with what they share. I learn a lot about my students and they get to know me a little along the way.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">At this time a year ago I felt really strongly that I wanted to keep these conversations going throughout the semester. I needed to work harder at fostering a positive relationship with all of my students so I created "Just Checking In..." sheets. I gave my first one at the end of the second week of school. Here is what it looked like:</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">This gave students an avenue to tell me if things weren't going well or if everything was just fine. It gave me a way to start a new conversation and to connect with all my students.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I continued checking in every few weeks. Here are some samples of questions/prompts.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><span style="color: #073763;">If you haven't jumped on the "Two Nice Things" bandwagon yet, read more from Elissa Miller </span><a href="http://misscalculate.blogspot.com/2015/05/two-nice-things-gift.html" target="_blank"><span style="color: #660000;">here</span></a><span style="color: #073763;">. </span></span></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I never required students to complete these, but they did. And at the end of June last year I had a student write me a thank you card that included "I loved when you asked us how we are doing. No other teacher has done that and it made me feel very good." Sometimes it's the little things we do that have a large impact.</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-87786459049906425642019-06-06T14:16:00.000-04:002019-06-06T14:16:05.602-04:00Add Them Up - Equations of Line<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I wanted to do something a little different with my grade 9 class as they prepare for EQAO and their final exam. My plan was to focus on equations of lines so I made some "Add Them Up" questions. I formed random groups of four students by having them draw playing cards and each group received the same sheet. On it were four different versions of the same question. Each group member worked on one question (they took small whiteboards for this) and when they all finished, the sum of their answers was written in the centre. This makes checking answers easy for me and forces the group to find mistakes if the sum is incorrect. Here is the first one:</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I made five of these, with the level of difficulty increasing each time. Here is the last one:</span><br />
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<span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">I photocopied these on five different colours of paper so that I could easily tell which one each group was working on. I was surprised by the number of mistakes, though many came up when they had to add fractions to get the sum of their answers. Fractions are hard. I purposely made many of the answers fractions so that they would be forced to practice these skills. As it turns out, some were really "ugly" so I have edited them and they are now more reasonable.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I was really impressed with my class - they helped each other and taught each other and worked as teams in the best way. I answered very few questions, although I didn't stop walking around and checking in with the groups the entire class.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><a href="https://drive.google.com/file/d/10MuFKYLln1TeL90_WeJyPYZocvuDJGoS/view?usp=sharing" target="_blank"><span style="color: #660000;"><b>Here</b></span></a><span style="color: #073763;"> are all five.</span></span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-69774459458350555542019-02-28T10:08:00.000-05:002019-02-28T10:08:23.325-05:00Grade 9 Academic - Day 16<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Tomorrow is test day so today we did review stations. But first, I took up a question from homework that many were doing incorrectly. </span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">A number of students had not put the 5<i>x</i> + 7 in brackets so we talked about how that was not optional. The other brackets you see above were added after when a student asked if you could do that.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Then I explained how review stations work. There were brightly coloured sheets around the room with questions from an old test on them. Students would be randomly paired up (using cards) and each pair would pick up an answer sheet. They would work on the big whiteboards, transfer their answer to the answer sheet, and bring that to me to see whether they were correct. If so, they got a sticker, if not they got to try again. If they were incorrect a second time, then I went over the question with them. </span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">They were so keen! There were a lot of errors but no complaining. They just got back to work and figured things out. Lots of perseverance. There were high fives and hugs. Crazy good.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Given that tomorrow is then end of unit 1, this is the end of my blog posts. I'll still post when I do things that I think are worth sharing, but I think it's clear that I don't do that every day! Thanks for reading :)</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-73460066093061134012019-02-27T18:00:00.003-05:002019-02-27T18:00:36.526-05:00Grade 9 Academic - Day 15<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We started with this warm up:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnDmgj7r0SHgjyfyiXcFtwQaosERAREvsrrDELaeQAQa8ZHlMa9AvPAeQ0zBk2May2U45rbHVmWMivvHuGX6gAH235mhSgRTxDury2JOwVHQyr25XYA-LVHmCdsv8lfw1ipFQX7jh-jBA/s1600/27-1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="445" data-original-width="766" height="231" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnDmgj7r0SHgjyfyiXcFtwQaosERAREvsrrDELaeQAQa8ZHlMa9AvPAeQ0zBk2May2U45rbHVmWMivvHuGX6gAH235mhSgRTxDury2JOwVHQyr25XYA-LVHmCdsv8lfw1ipFQX7jh-jBA/s400/27-1.JPG" width="400" /></a></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">This was a challenge for many, but at least as many got the correct answer on the first try. The biggest issue seemed to be that if they did not simplify the fractions before multiplying, the numbers got big fast. And then it was too overwhelming to continue. We spent some more time going over this concept. Hopefully it sticks.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I had noticed some issues with certain homework questions so we tackled those next.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">They continued to work on the practice test while I circulated and gave one-on-one help. I had planned on taking it up with them, but time did not allow. I have posted the solutions and hope that they will check their work tonight. We did work on one question together as many students were struggling to start it.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I found it really interesting that using letters actually made the question more approachable for many students. There were simply too many numbers for them to parse through, but once they replaced the bases with <i>x</i> and <i>y</i>, they were able to complete the question.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I also handed out "I can" statements. These are statements written in fairly friendly language that let students self-assess what they know. I'm sorry that the picture below isn't very clear.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Tomorrow we will do review stations!</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-67054126792748876022019-02-26T09:38:00.001-05:002019-02-26T09:38:18.261-05:00Grade 9 Academic - Day 14<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">The sun is shining, the power is on and we had lots of math to do today. We started with this warm up. The intent was to highlight the power of simplifying before multiplying fractions.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I had made an agenda for the day, mostly to keep myself on track, and still managed to go out of order right from the start (sigh). </span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvp_cUkfM4WWSDAnnibAZvTWQUEG0MdjIFQkNxTh_aN1mfq6KQYqzNjShjRR_PUGtJkFlDAEwkXWUco-_eJUbXpoqnl6ZXUXuCCFMTfaCMFJNPUdk2iB4cP3WjMJTwsKKeiIja6MJifEg/s1600/26-2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="471" data-original-width="598" height="252" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvp_cUkfM4WWSDAnnibAZvTWQUEG0MdjIFQkNxTh_aN1mfq6KQYqzNjShjRR_PUGtJkFlDAEwkXWUco-_eJUbXpoqnl6ZXUXuCCFMTfaCMFJNPUdk2iB4cP3WjMJTwsKKeiIja6MJifEg/s320/26-2.JPG" width="320" /></a></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We jumped into the practice test. I am hoping that seeing the format of a test (3 page booklet) and the types of questions from this past test will help ease some of their anxiety on Friday (test day). I asked them to quietly work on it for 30 minutes. Some skipped questions that they didn't know how to do, while others zipped through it. I did not expect them to complete the test in this time, but wanted to break up the time to allow some conversation and learning to occur. At the end of the 30 minutes, they chose cards to organize themselves into random groups, and went to the big whiteboards to compare answers. There were some really good conversations going on and many misconceptions came to light. Some of the questions could have multiple correct answers so it was great to see them checking each other's work. During this time I circulated and made sure the mathematics was correct and answered questions. </span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I saved the last 10 minutes of class to talk about vocabulary. I had made a handout for them which we took up.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I think we are making progress. They are willing to talk about their mistakes with classmates and ask questions when things are clear. With a couple more days of review work I hope things will go well on Friday.</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-31858495493652855752019-02-25T14:26:00.001-05:002019-02-25T14:26:19.937-05:00Grade 9 Academic - Day 13<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Amid power outages due to ridiculously strong winds, we tried to put the material from this unit all together today. We started with the warm up from Friday's group work:</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">The discussion around this was really interesting and many struggled to correct the work so that the answer was correct.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><span style="color: #073763;">They spent the next ~30 minutes working through this </span><a href="https://drive.google.com/file/d/1EEoXw4VzaIUUZ7dQtEOw_Jo4-gEQATCP/view?usp=sharing" target="_blank"><span style="color: #660000;">handout</span></a><span style="color: #073763;"> individually. I told them the goal was for each of them to figure out what they still need to work on. We spent the rest of the class working through each of the examples. Other than the vocabulary, we finished it all!</span></span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-34994675774464468122019-02-22T10:17:00.001-05:002019-02-22T10:17:35.479-05:00Grade 9 Academic - Day 12<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I turned yesterday's quiz question into today's warm up. They worked in random groups on the whiteboards. I reminded them to introduce themselves as not everyone has worked with everyone else yet. To avoid repetition for those who completed the question on the quiz, I had each group draw the simplified expression for each of their questions.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Here are a couple of samples of their work:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJL081SdY4Uaud_mXMk2pCsHrOnn75D66nxrgneMKdjkz3yQGYWHdwJrFvTPoD5Xtobq9bj9NzQSOWU4LCxWFU7zXKys49D7xVaPjgeSobJJloqJQGisvUa2h0SH97ecrMUK0_RblnvPQ/s1600/22-3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1516" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJL081SdY4Uaud_mXMk2pCsHrOnn75D66nxrgneMKdjkz3yQGYWHdwJrFvTPoD5Xtobq9bj9NzQSOWU4LCxWFU7zXKys49D7xVaPjgeSobJJloqJQGisvUa2h0SH97ecrMUK0_RblnvPQ/s400/22-3.jpg" width="378" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8ltRBUOmFzMLY3oZ9ktwaToVW7T3Sco2a9LpwsAHD0ySHvRH_sN8T8cU8FmYB6GKvmmNDKb5BB1LDOD6Hm5p1wHhKF20Z3ZJKLId5-eQ58itAAxc0JvV0dC-2cJZ5r59EOWHCtwOc1gs/s1600/22-4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1543" data-original-width="1600" height="385" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8ltRBUOmFzMLY3oZ9ktwaToVW7T3Sco2a9LpwsAHD0ySHvRH_sN8T8cU8FmYB6GKvmmNDKb5BB1LDOD6Hm5p1wHhKF20Z3ZJKLId5-eQ58itAAxc0JvV0dC-2cJZ5r59EOWHCtwOc1gs/s400/22-4.jpg" width="400" /></a></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I have saved this one as the warm up for Monday - a little error analysis.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQa3juc5r_yyisDW3w_LS49K0CS3u4ey8tpLznOuehts2F0ZcVJjpWbK4bUVynypmknWdaw2HVuWAMqsQMbddKsY_ioRzjWMCgX0pZkZ1-yF6gQ6hVW63GPmVN1FUlLk0tt2QzFM3DBc0/s1600/22-5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1408" data-original-width="1600" height="281" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQa3juc5r_yyisDW3w_LS49K0CS3u4ey8tpLznOuehts2F0ZcVJjpWbK4bUVynypmknWdaw2HVuWAMqsQMbddKsY_ioRzjWMCgX0pZkZ1-yF6gQ6hVW63GPmVN1FUlLk0tt2QzFM3DBc0/s320/22-5.jpg" width="320" /></a></div>
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<span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">I love hearing their conversations while they work. "Two Nice Things" was overheard at some point, which means that they are listening to the words they choose and realize that they matter.</span><br />
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<span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">I returned their quizzes and circulated for the remainder of the period answering questions as they worked through a handout. Several students are also planning on coming in at lunch for a little extra help. I love that they are starting to get comfortable asking questions and want to improve their understanding.</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-75615666642107931642019-02-21T12:09:00.001-05:002019-02-21T12:09:18.012-05:00Grade 9 Academic - Day 11<span style="font-family: "trebuchet ms" , sans-serif;"><span style="color: #073763;">Today's recall was more work with fractions so I thought it would be fun to do a warm up from </span><a href="http://fractiontalks.com/" target="_blank"><span style="color: #660000;">Fraction Talks</span></a><span style="color: #073763;">. I asked them to show multiple ways of finding the answer.</span></span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">I was pleased that they seemed comfortable working with these fractions and showed flexibility when looking at how to regroup the shaded parts.</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">We worked on multiplying and dividing fractions next. Though I tried to channel my inner Fawn Nguyen, I sucked. Oh my, it did not go well. I did a lousy job when answering questions. My explanations were not good. I need to work on all of this... But this is what we did:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcRvsTRHGWlNNTA_BeZet0de7wuseXXNyx66DWtEivOwvAkd6WmZVJYx3odECdW17i8FtFoIHfYqhQYyz3h84GLE0xSbWt9hxu9T16WgFbor2HpbGQSy3CdukvCb-8FJK0nUYvxe3M4qg/s1600/21-4.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="683" data-original-width="747" height="365" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcRvsTRHGWlNNTA_BeZet0de7wuseXXNyx66DWtEivOwvAkd6WmZVJYx3odECdW17i8FtFoIHfYqhQYyz3h84GLE0xSbWt9hxu9T16WgFbor2HpbGQSy3CdukvCb-8FJK0nUYvxe3M4qg/s400/21-4.JPG" width="400" /></a></div>
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">I know that I have the luxury of being able to just move on. My students already have tools for working with fractions,. Many of those tools are memorized, not understood, and I was trying to work on that. Sigh...</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">We also did a few more examples with distributive property and exponent laws. They groaned when they saw the second one, but did a good job nonetheless.</span><br />
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<span style="color: #073763; font-family: trebuchet ms, sans-serif;">Despite knowing that it wasn't a good idea to give the quiz I had planned with only 15 minutes remaining, I did (why do I not listen to myself sometimes???). Many students continued the quiz into lunch which I appreciated. I think I will start tomorrow with the last question from the quiz, in random groups at the big whiteboards. Here it is: </span><br />
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<span style="color: #073763; font-family: trebuchet ms, sans-serif;">"</span><span style="color: #274e13; font-family: Trebuchet MS, sans-serif;"><i><span style="font-size: 11pt;">Martha
simplified an exponent rule question and ended up with the answer </span><span lang="EN-US" style="font-size: 11pt;">-2x</span><span lang="EN-US" style="font-size: 11pt;">²</span><span lang="EN-US" style="font-size: 11pt;">y</span><span style="font-size: 11pt;">. What could the question have been? Determine 3 possible
questions with this answer that demonstrate each of the exponent rules.</span></i></span><span style="color: #073763; font-family: "trebuchet ms", sans-serif;">"</span><br />
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<span style="color: #073763; font-family: trebuchet ms, sans-serif;">I am hoping to see a lot of creative answers that push their collective skills forward. And I will work on my lack of skills teaching fraction multiplication & division...</span><br />
<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;"><br /></span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-74669490887715389822019-02-20T14:07:00.000-05:002019-02-20T14:07:58.145-05:00Grade 9 Academic - Day 10<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">Today started with another WODB? In my haste to hit publish yesterday (it was a very long day), I didn't talk about how I run WODB in my classroom. I ask for 60 seconds of absolute silence for everyone to think about what they see. This is hard for them. I then have them share their reasons in their table groups before we consolidate as a whole class. Each group gets to share one reason then we get extra reasons once each of the 6 groups has had a turn. In this case the 1/20 was blank until the end. They came up with a couple of ideas and then someone impressed the class by using something they had just seen. Taking the reciprocal (that had come up with 20/25) turned 1/20 into a whole number. Along the way we talked about vocabulary and made connections (i.e. numerator > denominator is the same as improper fraction).</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">After the warm up we returned to yesterday's work. We did one more addition/subtraction of fractions question before reviewing how to turn a mixed fraction into an improper fraction.</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">They, as expected, came out with the trick where you multiply the denominator by the whole part and add the numerator. I used that on the next example and got -13/5. We decided that my answer didn't make sense and talked about how to convert a negative mixed fraction into an improper fraction.</span></div>
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">After our review work with fractions, we finally circled back to exponent laws.</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">I think it's really important to make sure that everyone understands what the outside exponent means in a question like the one below. We wrote the power in expanded form first and used the product of powers law and then used the power of a power law to do the same question in a different way.</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">We did another one two ways. There were a lot of questions that arose along the way. Cubing one-third was a challenge!</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">I circulated and gave out stickers as they worked through the next example. I saw that some students got a coefficient of 686. They explained to me what they had done but I'm still a little lost. I think we cleared up how to do it correctly...</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">The last one combined a lot of skills. </span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">We spent the rest of the class taking up yesterday's quiz. I only give feedback on quizzes (no mark/grade) so I asked them to spend a couple of minutes correcting the first question with the help of their notes/neighbours. It was all about terms - type of polynomial, state the coefficients, state the constant, state the degree of the polynomial). We then corrected it together. The big error that I saw was a number of students who changed every x^2 into 2x. We talked about the difference between the two.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkJtK9fVWFtQ3ExAomPwRAg9t4AFv9ZFPixzfUrGxxrh5otO5NqND-4RUQ5fg2_R-UWJklW3Iue2nTvNOO-_HWiNmWvUUrkLH6zZXQqSZyF4FTjDOLuu5XtEncbH2RXPYB9FQJXTp9eK0/s1600/20-10.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="167" data-original-width="567" height="117" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkJtK9fVWFtQ3ExAomPwRAg9t4AFv9ZFPixzfUrGxxrh5otO5NqND-4RUQ5fg2_R-UWJklW3Iue2nTvNOO-_HWiNmWvUUrkLH6zZXQqSZyF4FTjDOLuu5XtEncbH2RXPYB9FQJXTp9eK0/s400/20-10.JPG" width="400" /></a></div>
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;"><br /></span><span style="color: #073763; font-family: trebuchet ms, sans-serif;">Have I mentioned recently that I really love this class? In a happy, exhausted kind of way.</span><br />
<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;"><br /></span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-89513691512754757102019-02-19T17:36:00.001-05:002019-02-19T17:36:34.229-05:00Grade 9 Academic - Day 9<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Today started with a quiz which I have yet to look at. I wanted to get a sense of where they are with the material we have worked on thus far. I have not had a moment to look it yet.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We finished Friday's work on distributive property. It was pretty interesting to work through - there's still a lot of learning to be done. We went over what like terms were again and how to multiply variables together. I worked on my wait time and on trying to find the good in all their answers while still moving them forward.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPWmYckuiGiTgk7FF9KheCOb0bZyRPfTDDl0kPmppLpelZesmVaz8WFjftvUmLgMYMi5hq6BYOEPe0m-ZZCCixvXvzPV5CG9BfrTUfDk8WQg08hSgHfHfGK6shl_DPHFYVVkuyp8LzG48/s1600/19-2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="612" data-original-width="757" height="322" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPWmYckuiGiTgk7FF9KheCOb0bZyRPfTDDl0kPmppLpelZesmVaz8WFjftvUmLgMYMi5hq6BYOEPe0m-ZZCCixvXvzPV5CG9BfrTUfDk8WQg08hSgHfHfGK6shl_DPHFYVVkuyp8LzG48/s400/19-2.JPG" width="400" /></a></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Today's warm up was their very first Which One Doesn't Belong? We practiced on the logo to ensure that they all knew how this worked - there is at least one reason for each member of the set to not belong.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Then we did today's actual warm up. I loved their answers, but even more, I loved their attitude. They actually clapped when an interesting answer was given. Twice. It was so lovely. And one of my quieter students volunteered to share an answer, which was also a great moment.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Our "Recall" for today was adding and subtracting fractions. Well, we didn't even finish all of that, let alone look at exponents again! Here's what we did:</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I distributed graph paper to those who did not have any. I made them stop talking about common denominators and think about a visual model. There were all kinds of models - circles and rectangles and squares. It was a mess. There were a few really good ones too, and they helped us get to this:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUoRuZd6jG0rujA3foc6iEufmgPIKsTG97EN6EUv-7PmWuTkJazarZJRpGkSE9KY_pE-mHCNVbGNbk3dgCfhMW7OpTo1jD53OJlOqxGk0sCBTLqJuNwtDluSCBsKt8OnEpm_n5qnMnveA/s1600/19-6.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="523" data-original-width="615" height="272" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUoRuZd6jG0rujA3foc6iEufmgPIKsTG97EN6EUv-7PmWuTkJazarZJRpGkSE9KY_pE-mHCNVbGNbk3dgCfhMW7OpTo1jD53OJlOqxGk0sCBTLqJuNwtDluSCBsKt8OnEpm_n5qnMnveA/s320/19-6.JPG" width="320" /></a></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">They shared a number of strategies for finding the lowest common denominator and I shared mine with them.</span></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">And that's when the bell rang. Understanding fractions is huge so I think it's worth spending a little time to ensure that they get the basics. We'll continue with more tomorrow, and maybe we'll even get back to those exponents!</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Along the way today, one of my students said to me "Have you ever talked to a mathematician about infinity?" We finished the joke in unison: "They could go on forever!".</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-15044485623519225722019-02-15T14:38:00.003-05:002019-02-15T14:38:39.945-05:00Grade 9 Academic - Day 8<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Today's warm up was challenging. As I circulated, I did not see the same answer twice. But as they talked and compared work, they fixed errors and did a really good job of this. I told them how happy it made me that not a single person did 15 - 2. We then consolidated together.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Next they worked the remainder of yesterday's questions. They did the first two on whiteboards in random groups.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">It was interesting to see the strategies used and the different answers. Once they had attempted both questions, I had all the groups rotate clockwise and give feedback. I asked them to check for mathematical correctness and communication. They wrote notes on the whiteboard then rotated back to their original solutions to see the feedback. We then consolidated together. What's in green for example 2, below, is what they told me had to be true about all the solutions.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Then we finished off the rest of yesterday's handout. Most students were okay working through this on their own, though we did take it up together.</span><br />
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<span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">We did a little refresher lesson on distributive property. </span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We had enough time left to practice a little bit. We talked about what happens when you multiply <i>x</i> by <i>x</i> and what happens when you multiply <i>x</i> by <i>y</i>.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir0kZu5h4_bXp6DWn2LSdcyYa0PVwivl0_gMTHfModTcxVWn2LGcJbmvo5C2i58U2_-SArYs5R_1BXSAaz4mOBg8ZTcPrQ6mkznIdF9QzIM3jQpgIHu9UFnTu736t3yxF8fzuxBcdJSVc/s1600/15-9.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="274" data-original-width="553" height="197" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir0kZu5h4_bXp6DWn2LSdcyYa0PVwivl0_gMTHfModTcxVWn2LGcJbmvo5C2i58U2_-SArYs5R_1BXSAaz4mOBg8ZTcPrQ6mkznIdF9QzIM3jQpgIHu9UFnTu736t3yxF8fzuxBcdJSVc/s400/15-9.JPG" width="400" /></a></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I had a few more questions that I wanted to do with them, but I think it's far more important that my students understand what we have done and feel confident moving forward than just rushing through the work. We'll pick up where we left off on Tuesday.</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-17116144983576592019-02-14T11:13:00.000-05:002019-02-14T11:13:09.991-05:00Grade 9 Academic - Day 7<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We had a special guest visiting our class today - Ann Arden, who works at the board office, wanted to see my class in action. (She was also supposed to come yesterday but the snow storm changed that plan in a hurry!)</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We started with this warm up:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9nIWjZZoXI68NSPRX5_1RRZkY47Hk0LWMY9Mk5MHQ-_1IqGuQkKYW_vQAm5vDdSTx-ju8E6rbpwzqx8tkALJfEhds5dqlFN5XbJoU2C7egUiICCAI8GYQ_dEt1V6hVgpz_SWGBbbJJBU/s1600/14-1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="429" data-original-width="714" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9nIWjZZoXI68NSPRX5_1RRZkY47Hk0LWMY9Mk5MHQ-_1IqGuQkKYW_vQAm5vDdSTx-ju8E6rbpwzqx8tkALJfEhds5dqlFN5XbJoU2C7egUiICCAI8GYQ_dEt1V6hVgpz_SWGBbbJJBU/s320/14-1.JPG" width="320" /></a></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I went back and forth on whether I wanted them to work through this individually or in groups at the whiteboards. I eventually focused on the fact that if they are working on the big whiteboards in random groups, it's to learn something new. This warm up was applying skills that they have already learned so my goal was to see where they are individually which made my decision clear. They each worked on their small whiteboard. I love how they compare work and try to find errors when their answers don't match. We took it up together once they had all had a chance to correct their work.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><span style="color: #073763;">Next I introduced them to Desmos. I showed them Suzanne von Oy's beautiful </span><a href="https://www.desmos.com/calculator/qf35ikrxe4" target="_blank"><span style="color: #660000;">graph</span></a><span style="color: #073763;"> and I showed them a </span><a href="http://www.mathogram.com/" target="_blank"><span style="color: #660000;">Mathogram</span></a><span style="color: #073763;"> (since it's Valentine's Day) before explaining how to get into today's activity. I also went over the rules of borrowing Chromebooks. The activity focused on like terms. It was created by Andrew Stadel and edited by me - I took off a couple of screens and added one that I really liked from a different activity by Cathy Yenca (thanks Andrew & Cathy!). Here is the </span><a href="https://teacher.desmos.com/activitybuilder/custom/5c6490f18c151558704c195f" target="_blank"><span style="color: #660000;">link</span></a><span style="color: #073763;">. They worked through this activity in pairs and had good conversations along the way. The best was when one student said "Can we do more? This is actually fun!".</span></span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">As I looked through the dashboard I saw a lot of different answers for a couple of screens so I hit Pause and we talked about them. Here is one:</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I also had grabbed some snapshots of the last screen and we talked about the interesting, different approaches that were used.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">They were really good at putting the Chromebooks back in the correct bins and did so pretty quickly. I gave each student a handout for the next part of the class.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We went over vocabulary, some of which we have talked about previously, but needed something a little more formal.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We then returned to adding and subtracting polynomials. Well, we really just combined like terms because that's all we had time for. We will continue with that tomorrow.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I also had them fill in a "Just checking in..." form. I like to give them the opportunity to tell me if things are not going well in my class or at school or in life. </span></div>
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<span style="font-family: Trebuchet MS, sans-serif;"><span style="color: #073763;"><br /></span></span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-71766257749980934872019-02-13T10:20:00.000-05:002019-02-13T10:20:02.371-05:00After the Storm<br />
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<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="color: #073763; font-family: Trebuchet MS, sans-serif;">This morning, as I shoveled the vast
quantities of snow that fell last evening and overnight, I could not help but
think about TMC. I tweeted this out as it seemed like where we are. <o:p></o:p></span></span></div>
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<span lang="EN-US" style="mso-ansi-language: EN-US;"><o:p><span style="color: #073763; font-family: Trebuchet MS, sans-serif;"><br /></span></o:p></span></div>
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<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="color: #073763; font-family: Trebuchet MS, sans-serif;">The storm has passed but there is a
mess left behind. We can see where we’ve come from and there’s a path ahead yet to be forged.<o:p></o:p></span></span></div>
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<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I shoveled the snow, at times light
and easy to move, other times hard and so icy that I was forced to work at it at
an angle, not head on, for an hour and a half. When I came in my phone showed
that I had been active for 7 minutes. This too reminds me of where we are with TMC.
I feel like many have been drawn to the issues of the past week, but cannot see
all the work that has been done to bring us to this point. I want to tell my phone
that no, it wasn’t just 7 minutes. It was over 90 minutes. You can see that my
shirt is soaked through and my cheeks are all rosy. But it feels like I’m
making excuses. It feels like if I want to tell everyone what a profound effect
TMC has had on so many educators, it will be seen as making excuses. I want
everyone to thank those who have helped create and sustain TMC thus far, but do
not want to be seen as going against those who have felt left out. I want to
say that no one on team TMC ever wanted anyone to feel excluded, and that we
are all in different places on our journey towards equity. It hurts me to know
that some are being vilified because hurting more people doesn’t solve the
problem. I am starting to understand white fragility but I think that 7 years
of work making something remarkable and special should not be so easily
dismissed. Team TMC has been fractured and dysfunctional for a while now and we
each need to own our part in that. I should have done more. I am quiet by
nature and tend to be happier helping in the background, but I should have
tried harder and made time. I think we would all do things differently if we could
go back, but we can’t so we must try to move forward. Publicly acknowledging
your failures is hard, especially at a time when emotions are running high and
responses are quick and harsh. I am flawed but I continue to try to be a better
person. To learn from others who know more. To listen and to make meaning of
what is being said so that I can do better the next time.<o:p></o:p></span></span></div>
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<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="color: #073763; font-family: Trebuchet MS, sans-serif;">As I head back out into the snow, I
can see my tracks. I see where I did a good job and where I should have tried
harder. Ahead there is only fresh snow, and new paths waiting to be created.<o:p></o:p></span></span></div>
<br />Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-87402830179955768792019-02-12T10:43:00.000-05:002019-02-12T10:43:15.049-05:00Grade 9 Academic - Day 6<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">The plan for today was to get through exponent laws. Tomorrow will likely be a snow day so I wanted them to have the tools to be able to practice working with exponents and order of operations. We had not worked through the examples planned for yesterday so I photocopied the questions and let them work through them in their table groups instead of a warm up.</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">Lots of misconceptions arose and their understanding of both exponents and the order of operations seems to be improving. I decided on the weekend that order of operations is really the crucial foundation they need to build on. If that is not solid, the rest will fall apart.</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">Next, they worked on this question in groups:</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">The conversations were really interesting to listen to. Many groups took our calculators only to find that they weren't helpful as the question asked the expression to be simplified, not evaluated. I'm not sure how much this shows, but this is our consolidation.</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">I am being very intentional about saying "simplifies to 1" and not "cancels".</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">We broke things up a little to state each exponent law individually.</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">We had a little time left to try putting it all together before summarizing.</span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;"><br /></span><span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">Though it seemed a bit rushed to me, we focused on understanding, not memorizing rules. Hopefully the practice they will get over the next couple of snowy days will serve them well.</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-14544288424856614002019-02-11T15:08:00.000-05:002019-02-11T15:08:00.436-05:00Grade 9 Academic - Day 5<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We started today's class by finishing the examples from Friday.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Then I had them do today's warm up in random groups on the white boards.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I asked them to sit down when they finished, but they wouldn't! They were busy comparing answers and trying to figure out who was right and fixing mistakes and it was fantastic! They did eventually all sit down and we talked about the order of operations.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Then we returned to the warm up which they each completed individually before we took it up together. Some were feeling much more confident this time around.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">In light of the 40 cm of snow heading our way Tuesday night into Wednesday, I skipped today's visual pattern :(</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Instead, we launched into exponents. I try to emphasize that an exponent affects only what is immediately in front of it and try to help them make sense of negative numbers raised to an exponent.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Somewhere along the way I returned their quizzed to be corrected tonight. Their quizzes were actually quite encouraging.</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-8876998802834063122019-02-08T10:01:00.001-05:002019-02-08T10:01:19.343-05:00Grade 9 Academic - Day 4<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">After handing back feedback forms, I asked students to take out, but not hand in their homework (they normally hand it in at the beginning of each class, I check it somewhere along the way and return it before the end of class). I asked whether they knew that the answers were in the back of the book and this was news to many! So together we found the answers and I had them check their answers and place a check mark or x next to each question using a different coloured pen. Then they handed it in to me. This simplifies my job as it became very clear whether they struggled with any of the questions. Sometimes we forget the soft skills so I am trying to be deliberate in imparting them to my students.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Instead of a warm up today, I gave a quiz on integers. I realized last night (it was our school's open house so I was here until 8 pm) that I have no firm evidence that my students are understanding the material we have looked at thus far. I made sure to explain to them that they shouldn't be stressed about it, that it would help me know if we need to spend more time on integers or if we are ready to move on.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">After the quiz we carried on where we left off yesterday - like terms.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">The next question sounds like a Marian Small question so I will give her credit. </span><span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">My students did well with answering it, but we had to work hard to explain what everyone's answers would have in common.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Then we practiced combining like terms and dealing with the many misconceptions that came up along the way.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I loved the multiple ways of writing the solution to this next example.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We skipped today's visual pattern, in part because the teacher next door had borrowed my cards, and in part because I wanted to get everyone feeling a little more comfortable with the distributive property before the weekend. We worked through area models with numbers then added a variable. A big thank you to Sheri Walker for sharing this handout with me. Students who were unsure were encouraged to count the number of <i>x</i> tiles to get the area and then try to make sense of that answer in terms of length and width.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We continued to build up our area models and were careful about including brackets when writing out the length x width expressions.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">A little summary and some more examples (I know this is not very exciting - I would change this to become work on whiteboards next time. Actually I can do some of that next class.)</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We had a few more to do, but it was the end of the period so that's the end of the first week.</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-61227313311008133082019-02-07T17:20:00.002-05:002019-02-07T17:20:59.349-05:00Grade 9 Academic - Day 3<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Today started with a warm up and the small whiteboards.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Again, there were many different answers so we went over a few things. We talked about what the dot means and why it is used and a little about order of operations - that multiplication happens before addition or subtraction. Then we did a little recall on multiplying with integers.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We went back to the warm up and I gave them a minute or two to check their work before we took it up.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I took out my playing cards and they created groups for today's visual pattern. They worked on the whiteboards and are slowly getting better at showing the link between the pattern and the algebraic expression. Here is one sample and the sample solution I showed them.</span><br />
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<span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">Next we moved on to the activity that we didn't have time for yesterday. I had prepared a brown paper bag with algebra tiles for each pair of students.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We went over what each tile represented before they tried this out. It seemed to solidify the concept of zero pairs pretty well.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Next we did a more formal lesson on like terms. Well, we started. We didn't get through everything and I have to remember that rushing through material serves no one. If I try to think positively, I have part of my lesson for tomorrow ready to go!</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We did example 1 as a class - it was a good consolidation of the activity they had just done.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We defined like terms and started on the next example which produced some really good discussion.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">And that's all for today. I know we are doing a lot each day so I need to consider whether I need to make some adjustments to my plan to provide a little more breathing room.</span><br />
<span style="color: #073763; font-family: Trebuchet MS, sans-serif;"><br /></span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-34836247382734888012019-02-06T10:21:00.000-05:002019-02-06T10:21:37.447-05:00Grade 9 Academic - Day 2<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We didn't have class yesterday as the school buses were cancelled, so I'm considering today as day 2.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Before class I handed out small whiteboards and markers and organized bags of algebra tiles (which I won't get to until tomorrow as it turns out).</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We started with this warm up which students did on their small whiteboard:</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><span style="color: #073763;">I circulated and then wrote - 10, -5, -2, -6, -4, -7, IDK on the board. Those were some of the answers I had seen. Clearly we had work to do. The reason I wrote all of those answers was for them to see that many students didn't know how to do this correctly - that if they didn't get it right, it was okay. We would work on it together. We then talked about adding and subtracting integers (I have an old blog post about this </span><a href="http://marybourassa.blogspot.com/2013/10/working-with-integers.html" target="_blank"><span style="color: #660000;">here</span></a><span style="color: #073763;">).</span></span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Then I let them try the warm up question again with much better results.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><span style="color: #073763;">Next up, today's visual pattern (</span><a href="http://www.visualpatterns.org/121-140.html" target="_blank"><span style="color: #660000;">#129</span></a><span style="color: #073763;"> but I removed the colour as I found it too leading). We used cards to create random groups of three and their task was to figure out the rule for the pattern in as many ways as possible.</span></span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I confess that I didn't circulate, listen and engage with my students enough while they were doing this as I was also handing out textbooks. However, I was really pleased with the work they did, the fact that no one went to a table and that they are starting to be able to show their thinking. Here are some samples (some got a little help connecting the representations from me):</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3K42yiajuG-SV35E7sGns8pFvonTBE4ZW6ua72pZAA9nWEMgGxt_kcHCiBgkV5JjxX8jqEfy7pUGICQacm2IP22cEnIziVHanPQuyh2yb4dBx_0VWBZubad9yPzGCIHqyX8oGkdJiAds/s1600/6-3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="687" data-original-width="1600" height="137" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3K42yiajuG-SV35E7sGns8pFvonTBE4ZW6ua72pZAA9nWEMgGxt_kcHCiBgkV5JjxX8jqEfy7pUGICQacm2IP22cEnIziVHanPQuyh2yb4dBx_0VWBZubad9yPzGCIHqyX8oGkdJiAds/s320/6-3.jpg" width="320" /></a></div>
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<span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">I had two possible ways of seeing this pattern ready to go, but added a third to capture some of their thinking - many groups made a constant in the middle of the vertical part. Here are those:</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I love that there are so many different ways of seeing these patterns and am always impressed when my students show me a new way of seeing it.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Next, we talked about algebraic models: using algebra tiles to represent expressions.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">We had just enough time for them to try a couple of examples. Honestly, I was too rushed doing this and should really have let touch the actual tiles to truly understand. I will fix that tomorrow.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><span style="color: #073763;">We wrapped up by returning feedback forms (not sure I talked about those - read about them </span><a href="http://marybourassa.blogspot.com/2018/02/feedback-forms.html" target="_blank"><span style="color: #660000;">here</span></a><span style="color: #073763;">). </span></span><br />
<span style="color: #073763; font-family: Trebuchet MS, sans-serif;"><br /></span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-41774973440563417682019-02-04T14:59:00.001-05:002019-02-04T14:59:31.732-05:00Grade 9 Academic (MPM1D) - Day 1<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I'm dusting off the old blog to help me reflect on my first unit of grade 9 academic math. I last taught this course in 2013 and was not happy with how the first unit went so I am making some changes this time around. My plan is to blog daily so that I have a record of what I did, how things went, and what I would do differently next time.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Unit 1 is all about polynomials. Like terms, distributive property, exponent rules. All mixed in with integers and fractions, which are pretty shaky concepts for many of our students. My plan is to work on integers and fractions as daily warm-ups and through the lessons to slowly bring everyone up to the level they need to be in order to be successful. But I'm getting ahead of myself.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Today we started with a puzzle that I found in our textbook (McGraw-Hill Ryerson). I had students pick cards to form random groups of 3 and they worked at the whiteboards around the room.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmcwhkpmJkfy1bE3xVJsaFSDJpVhADkvmWUk3L7V_xVteed5L2hyEvToeADKi19n1XBsIqijaiGrd0bMN6iIs3xJaGKtLo1pIk1X8kAuhb721ydXxgvsJhw_IzZin2piFrhUmEn-V5Uvo/s1600/1d-1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="791" data-original-width="658" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmcwhkpmJkfy1bE3xVJsaFSDJpVhADkvmWUk3L7V_xVteed5L2hyEvToeADKi19n1XBsIqijaiGrd0bMN6iIs3xJaGKtLo1pIk1X8kAuhb721ydXxgvsJhw_IzZin2piFrhUmEn-V5Uvo/s400/1d-1.JPG" width="332" /></a></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I included a hidden extra clue but none of the groups needed it (yay!). They did really well, in terms of the mathematics but also working in teams. I had an extension ready to go for the groups that finished quickly - I asked them to work on creating their own magic square (still 4 x 4) but using some negative numbers. That was <u>very </u>challenging, so I think I might ask them to create a 3 x 3 one next time around.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><span style="color: #073763;">With about 20 minutes remaining (our classes are 75 minutes long), we started our first visual pattern together. If you are not familiar with visual patterns you should head over to Fawn Nguyen's site by clicking </span><a href="http://visualpatterns.org/" target="_blank"><span style="color: #660000;">here</span></a><span style="color: #073763;">.</span></span><br />
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<span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">We came up with three different ways of seeing the pattern growing. For each one we came up with the rule based on the step number.</span><br />
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<span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">i was pleased with their willingness to work with the pattern and not jump to a table. We will do more tomorrow.</span><br />
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<span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">I also asked them to create DeltaMath.com accounts. They will be able to get extra practice there.</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-31558158466335760472018-11-15T14:58:00.001-05:002018-11-15T14:58:44.106-05:00Similar Triangles Introduction<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Somehow this is the week when I am getting caught up on blog posts. Why this week? Apparently extra chaos in my life helps me need to cross things off my to-do list. Two kids with potential concussions and one feeling like throwing up seems to be the motivation I need to blog. Go figure.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Ages ago, in my grade 10 applied class, I made a new intro to similar triangles. I liked it mostly because it was simple and allowed my students to practice other skills they had recently learned, namely right-angle trig and sum of squares (Pythagorean theorem). It looked something like this - what "What do you notice?" at the bottom.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF7Kz6dwlVfuQNh69oQHdm969f9-2BXak9PRfpHXmgZd37TEZJQaThRA0r8ovF-bC9XSG_uCa_CUBG7hvQiX4colNvTzARbAwWNUyM1RjVaQ6HrhvMGnsQUirmRBeCEPa9EhpAzBWb8Yc/s1600/similar+triangles+1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="871" data-original-width="918" height="378" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF7Kz6dwlVfuQNh69oQHdm969f9-2BXak9PRfpHXmgZd37TEZJQaThRA0r8ovF-bC9XSG_uCa_CUBG7hvQiX4colNvTzARbAwWNUyM1RjVaQ6HrhvMGnsQUirmRBeCEPa9EhpAzBWb8Yc/s400/similar+triangles+1.JPG" width="400" /></a></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">This is what we did with it:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyLk2snjIR3D16ztBFLEsn9gtXuRZZQWmrUIA0Hi_RkW45N5jchw8cY_egx_4KuEIplYJN0ZbJ73Ih0okbSATE0cnzqfPZNe8i_MNWSz_epjnCJEpivP0AmZq-ZTJZ6vw0FvTLmY8PGGw/s1600/similar+triangles+2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="825" data-original-width="993" height="331" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyLk2snjIR3D16ztBFLEsn9gtXuRZZQWmrUIA0Hi_RkW45N5jchw8cY_egx_4KuEIplYJN0ZbJ73Ih0okbSATE0cnzqfPZNe8i_MNWSz_epjnCJEpivP0AmZq-ZTJZ6vw0FvTLmY8PGGw/s400/similar+triangles+2.JPG" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA3GJG_k5xdRfJxpZr_H1y-rDGHNUJV9nWhePSPI3HxMJjji_rjby-FVgSxPYVOYegIrP5Rmv8Z7VAksXTH2YtKaF4rY_UnXgYL0cWfZUhrTq9BAehjMEj7nI1TATWa4XCEAw0MMQaFk4/s1600/similar+triangles+3.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="979" height="195" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA3GJG_k5xdRfJxpZr_H1y-rDGHNUJV9nWhePSPI3HxMJjji_rjby-FVgSxPYVOYegIrP5Rmv8Z7VAksXTH2YtKaF4rY_UnXgYL0cWfZUhrTq9BAehjMEj7nI1TATWa4XCEAw0MMQaFk4/s400/similar+triangles+3.JPG" width="400" /></a></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Nothing fancy, but it worked so I thought I would share. I think this qualifies as #unsexymath.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><span style="color: #073763;">If you would like the file, you can find it </span><a href="https://drive.google.com/file/d/1SHdB3p13qwL_TH3mpeoQNcwradQHWRS5/view?usp=sharing" target="_blank"><span style="color: #660000;">here</span></a><span style="color: #073763;">.</span></span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-15753012525446978962018-11-15T08:10:00.002-05:002018-11-15T08:10:40.929-05:00Marshmallow Challenge<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">I have not blogged for a while and this post is about <strike>six</strike> eleven weeks overdue</span><span style="color: #073763; font-family: "trebuchet ms", sans-serif;">. On the first day of school I do the marshmallow challenge with my grade 12 classes. I do not know who deserves credit for this activity (if someone knows, please pass that along) but it's a great team-building exercise that requires collaboration to be completed in the time allowed.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9vYa-DB68jXfzKPCbHlGRXhDV6dDO8GLdqE5TYi2EB0zd0Op8Uqj5a-N9INIgErXmnqKrwJ-ooni7IA0FQiPAwoTn08VnbD1I2elXHWmZRNjA51cKa94qmdHZZ4kWxvjxt9heMKVDXH4/s1600/blog1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="787" data-original-width="678" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9vYa-DB68jXfzKPCbHlGRXhDV6dDO8GLdqE5TYi2EB0zd0Op8Uqj5a-N9INIgErXmnqKrwJ-ooni7IA0FQiPAwoTn08VnbD1I2elXHWmZRNjA51cKa94qmdHZZ4kWxvjxt9heMKVDXH4/s400/blog1.PNG" width="343" /></a></div>
<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;"><br /></span><span style="color: #073763; font-family: "trebuchet ms" , sans-serif;">I hand out cards to organize students into random groups. They start by introducing themselves to their teammates. I then have the groups brainstorm ideas before the clock starts. And then the fun begins. I love watching them try strategies and listening to their conversations. Inevitably they frantically try to finish before the time runs out only to see their structure tilt over when they place the (surprisingly heavy) marshmallow on top. I measure the towers to determine a winning group, but it's really not about winning. </span><br />
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;"><span style="color: #073763;">What I did differently this year, which is really what I wanted to share, was to ask debrief questions after the activity that mirror the great things I see during the activity. </span></span><span style="color: #073763; font-family: "trebuchet ms", sans-serif;">I wanted them to think about how collaborating can help a group reach a goal. How it is important to listen and to talk and that it is important that everyone in the group is engaged. You</span><span style="color: #073763; font-family: "trebuchet ms", sans-serif;"> can find the questions I asked </span><a href="https://drive.google.com/open?id=1LeDUPjSjUNeTC0UB59ix4GqXrHe9oBy8" style="font-family: "trebuchet ms", sans-serif;" target="_blank"><span style="color: #660000;">here</span></a><span style="color: #073763; font-family: "trebuchet ms", sans-serif;"> - I looked at ones that others have asked to get ideas so thanks to all those who have shared in the past. I want to focus on a small, but important part. I start by having them fill in this table:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5iyA5XWXD5qq4uIdrwuVFZ99R6jXJ5C7Lc9IQeqPR40dObIIXaiNu5CEF_xz5u0vmuovYiXAxEe23BVYXynK4zqQST5UU_Bfa8jVde_vsaBY1kGQfMZ5H8rmndcVNG3h9xUsYv99ROEQ/s1600/debrief+1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="350" data-original-width="1418" height="97" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5iyA5XWXD5qq4uIdrwuVFZ99R6jXJ5C7Lc9IQeqPR40dObIIXaiNu5CEF_xz5u0vmuovYiXAxEe23BVYXynK4zqQST5UU_Bfa8jVde_vsaBY1kGQfMZ5H8rmndcVNG3h9xUsYv99ROEQ/s400/debrief+1.JPG" width="400" /></a></div>
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<span style="color: #073763; font-family: "trebuchet ms" , sans-serif;"><span style="color: #073763;">Firstly, they needed to know the names of their teammates. Secondly, they needed to say something complimentary about each of their teammates who are often people that they have never really interacted with before. And they did. They did such a good job. They all found things that their teammates did well. This was important to me because I believe all my students bring positive things to my class. And that along with learning math, we will learn how to be good, kind citizens.</span></span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-34792459016874510942018-08-14T17:44:00.000-04:002018-08-14T17:44:21.800-04:00OAME 2019<div style="text-align: center;">
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I'm very excited to announce that we are now accepting speaker proposals for the Ontario Association for Mathematics Education's annual conference, taking place in Ottawa on May 16-18, 2019.</span><br />
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<span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">We already have an amazing lineup of featured speakers (check out our </span><a href="https://oame2019.ca/" style="font-family: "Trebuchet MS", sans-serif;" target="_blank"><span style="color: #660000;"><b>website</b></span></a><span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">), but this conference couldn't be as incredible as it is without all the great educators who volunteer to share their ideas and practices.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><span style="color: #073763;">In addition to sessions in English and in French, we will have a focus on </span><a href="http://desmos.com/" target="_blank"><span style="color: #38761d;"><b>Desmos</b></span></a><span style="color: #073763;"> on the Saturday of the conference.</span></span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><span style="color: #073763;">We hope you can join us in the nation's capital for three days of mathematical conversations, connections and cheer.</span></span><br />
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<span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">Get started </span><a href="http://www.oame.on.ca/mcis/index.php" style="font-family: "Trebuchet MS", sans-serif;" target="_blank"><span style="color: #660000;"><b>here</b></span></a><span style="color: #073763; font-family: "Trebuchet MS", sans-serif;">. I hope to see many of you in Ottawa in May!</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-62256708548411083492018-08-10T10:26:00.004-04:002018-08-10T10:26:54.617-04:00Intentionality<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">As the new school year approaches, I am reflecting on the last and what changes to make for this one to be more successful. Specifically, if implementing a "thinking classroom" with VNPS & VRG (ugh - the acronyms and appropriated terms here do not make me happy), I need to find a way of making my intentions more obvious to students whose initial reaction is to push back because this is not how they have learned to do school. The choice of opening day activity is important to me but more so will be the connections students can make when reflecting on the implementation of that activity. I want them to see that the result was made better from working in a group. I want them to understand that they each have a voice and that their contributions are all important. I want them to hear why I made the teacher moves I did and why I likely did not answer their questions directly. I want them to think about what they are learning, but also about how they are learning it. How being uncomfortable is not necessarily a bad thing. How not knowing the right path to take should not make them feel lost. How important it is to be able to listen to others' ideas and how important their own contributions are. And that throughout it all, I have their best interests at heart and will do my utmost to ensure that they all understand the material more deeply than they would through a lecture.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">All of this is difficult for me. My not-as-shy-as-I-used-to-be but still shy and introverted self has a hard time approaching these kinds of conversations. This model of learning is about playing the long game whereas I *need* my students to see the benefits before they actually feel the benefits. I need this for them, but I really need this for me.</span><br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">Now, back to summer :)</span>Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com0tag:blogger.com,1999:blog-5473916205424933781.post-74630259478119802032018-07-25T17:55:00.002-04:002018-07-25T17:55:31.194-04:00Unsolicited Post-TMC Advice<br />
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I have been staring at a blank page for some time trying to
figure out how to frame what I want to say. TMC18 has come and gone, but the
energy that fuels the participants lasts far longer than the four days of the
conference. The ideas that are planted during those four days spark enthusiasm
and give new life to tired souls. I do not want to dampen any of that
enthusiasm but want to throw in just a note of caution.<o:p></o:p></span></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">I have now taught for 24 years and the 24<sup>th</sup> was,
by far, the most difficult. For whatever reason, there was more negativity from
both parents and students this past year to the point that I questioned whether
I wanted to continue teaching. Although a number of teachers had to deal with these
storm clouds, I think I felt it most because I do things differently. I spiral
my curriculum and my homework, I don’t teach from the textbook, I implement the
elements of a thinking classroom. I do these things because I truly believe
that they have a positive impact on my students’ learning. But not following
the pack means that difference gets pointed to as the reason for any issues. And
as much as I wish I could let all the negativity wash off like water off a
duck’s back, I can’t. I take things very personally and felt crushed. I’ve been
trying to let it go and get past it, but it all came flooding back when Julie
Reulbach had everyone tweet out why they are a great teacher. All I could think
is “I’m not” and I sobbed through most of her keynote. I have great friends who
have told me that I am good at what I do, but the seed of doubt that has grown
over the past year is hard to dismiss. <o:p></o:p></span></div>
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<span style="color: #073763; font-family: Trebuchet MS, sans-serif;">So here is my advice. Don’t try to do ALL the things. Choose your #1TMCthing and
dive in but if you are making substantial changes to what is considered the
norm at your school, make sure you have a support system in place first. Knowing that
someone has your back is empowering, just as finding out that no one really does
is heartbreaking. Set yourself up for success and don’t forget that you’ve got
the #MTBoS on your side.<o:p></o:p></span></div>
<br />Mary Bourassahttp://www.blogger.com/profile/12427568524129802618noreply@blogger.com