tag:blogger.com,1999:blog-22059633982070457492017-12-15T20:43:14.848-05:00Sine Of The TimesA Math Teacher's JourneyDave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.comBlogger136125SineOfTheTimeshttps://feedburner.google.comtag:blogger.com,1999:blog-2205963398207045749.post-72364843440423674162017-12-15T20:43:00.000-05:002017-12-15T20:43:14.951-05:00MPM1D1 - Day 70 Equations of Parallel and Perpendicular LinesDuring <a href="http://sine-of-the-times.blogspot.ca/" target="_blank">yesterday</a>'s warm-up, one group was convinced that two of the lines were perpendicular. Based on that comment I thought today's warm-up should be about perpendicular lines.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-ldDWx32X4hs/WjRvLj32I7I/AAAAAAAANFk/HaxGwOHsssc0CjtCsXnprAq5C273HTh-gCLcBGAs/s1600/Screen%2BShot%2B2017-12-15%2Bat%2B7.52.00%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="657" data-original-width="920" height="285" src="https://2.bp.blogspot.com/-ldDWx32X4hs/WjRvLj32I7I/AAAAAAAANFk/HaxGwOHsssc0CjtCsXnprAq5C273HTh-gCLcBGAs/s400/Screen%2BShot%2B2017-12-15%2Bat%2B7.52.00%2BPM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Once groups found equations for the lines I asked what they knew about how the lines intersected. They responded with the point of intersection and I asked if there was anything else. When they told me that the lines were perpendicular I asked how they knew the lines were perpendicular. Some groups could justify their claim immediately, while others need time to formulate their ideas. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">After the warm-up we moved right into finding equations of parallel and perpendicular lines. We had a conversation to remind them about how to find the equation of a line given two points and what it means for lines to be parallel or perpendicular. They worked on these problems at the board:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-QO-rnp0HDuM/WjRzG-94-EI/AAAAAAAANFw/aVH9Aq8gD88yQDFDjBmsd8qmu8ogiyz4gCLcBGAs/s1600/Screen%2BShot%2B2017-12-15%2Bat%2B8.06.25%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="555" data-original-width="1100" height="201" src="https://3.bp.blogspot.com/-QO-rnp0HDuM/WjRzG-94-EI/AAAAAAAANFw/aVH9Aq8gD88yQDFDjBmsd8qmu8ogiyz4gCLcBGAs/s400/Screen%2BShot%2B2017-12-15%2Bat%2B8.06.25%2BPM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">None of the groups had any trouble with the first two questions. A couple of groups struggled with the third and all groups needed some reminders about rearranging equations for the last question. When they were finished they went to work on some practice questions.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/4gJDvWbJH84" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-70-equations-of-parallel-and.htmltag:blogger.com,1999:blog-2205963398207045749.post-10024898290304067272017-12-14T21:15:00.001-05:002017-12-14T21:15:16.805-05:00MPM1D1 - Day 69 Properties of QuadrilateralsThe warm-up for today was to find the equation of the line segments shown below.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://i0.wp.com/dailydesmos.com/wp-content/uploads/2013/08/128b1.png?w=640" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="509" data-original-width="640" height="254" src="https://i0.wp.com/dailydesmos.com/wp-content/uploads/2013/08/128b1.png?w=640" width="320" /></a></div><br />I figured this would be a good opportunity to practice dealing with horizontal lines, as well as others. One group tried using the formula for slope but when I asked if there was an easier way they told me that they could use the graph. Another group was convinced that the two segments on the right were perpendicular. When I asked if they could explain how they knew this was true, they began doubting themselves and then verified that they were in fact wrong by looking at the slopes of each.<br /><br />The goal for today was to investigate properties of quadrilaterals. I found <a href="https://www.geogebra.org/m/yekC7cDh#material/uzDYDAp2" target="_blank">this</a> Geogebra activity. I had originally thought that I would make something up but finding this saved me some time.. Students worked through the activity at their own pace and took notes about what they observed. Some notes were better than others. I had students working individually on their own computers. I'm thinking it may have been better to have them working in pairs.<br /><br />Once most students were done I summarized with this graphic:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-TcIqgIxgDr8/WjMusYCUbFI/AAAAAAAANFU/yuXO_DAIrwQvKW2CtzUBm_OlFoM8xW0twCLcBGAs/s1600/Screen%2BShot%2B2017-12-14%2Bat%2B9.07.56%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="456" data-original-width="552" height="330" src="https://4.bp.blogspot.com/-TcIqgIxgDr8/WjMusYCUbFI/AAAAAAAANFU/yuXO_DAIrwQvKW2CtzUBm_OlFoM8xW0twCLcBGAs/s400/Screen%2BShot%2B2017-12-14%2Bat%2B9.07.56%2BPM.png" width="400" /></a></div><br /><br />Then it was time for some practice. I gave <a href="https://drive.google.com/open?id=1lRDdcSUmli6vlxlrYEB6_bZjWOLwqbj39K1bJdjrXCU" target="_blank">these</a> questions from <a href="https://olga-sediako.wikispaces.com/file/view/Quadrilateral%20Properties.pdf/475921758/Quadrilateral%20Properties.pdf" target="_blank">this</a> page. Some students chose to work in groups at the board, some chose to work in groups at their desks and some chose to work individually. The two strongest students, who hated working with each other earlier in the semester, decided to team up along with a third person because they realized they could get the work done faster if they worked together. They stayed in past the bell and got it done.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/TVVuzQeLzYk" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-69-properties-of.htmltag:blogger.com,1999:blog-2205963398207045749.post-4426604976520183432017-12-14T00:24:00.001-05:002017-12-14T00:24:51.750-05:00MPM1D1 - Day 68 Speedy LinesWe started with a visual pattern today:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://www.visualpatterns.org/uploads/3/8/7/2/38721349/2017-10-21-19-20-32.jpg" target="_blank"><img border="0" data-original-height="158" data-original-width="400" height="157" src="https://3.bp.blogspot.com/B-MGrB2gx_a8zwDaDTmdDJY8irmgkz6NOrCn8QfNyb2eagjphpTfltpxsV-kGwxXCvmQUV7FwQI=s400" width="400" /></a></div><br />It was interesting to see how students counted the number of watermelons in each step. It seemed as though most groups had a couple of different ways of counting which made for some interesting discussions. I think the hardest part here was generating the table of values. Once they had that, groups quickly came up with the equation and the number of watermelons in the forty-third step.<br /><br />We took up the equations mastery test from yesterday and hopefully cleared up some misconceptions.<br /><br />Today's main event was practicing coming up with the equation for a line of best fit. Everyone can draw a line of best fit but when I ask for the equation many students go to their tables to find the slope. When they do this they don't always choose points that are on the line. We need to work on realizing that we want to use points that are on the line to find the equation.<br /><br />Today we timed to see how long it takes to assemble 5,6,7,8,9 and 10 linking cubes. This is an idea that I modified from <a href="https://twitter.com/MaryBourassa" target="_blank">Mary Bourassa's</a> <a href="http://marybourassa.blogspot.ca/2015/03/mfm2p-day-34-speedy-squares.html" target="_blank">Speedy Squares</a>. Rather than making squares we just connected cubes to form a line. Groups worked to collect data. Some groups needed to work on being consistent but got it sorted out pretty quickly. Then they plotted the data and worked to find an equation of the line of best fit. They then practiced using their equation. Here's the <a href="https://drive.google.com/open?id=1rKs5A0kMZmdVcZBlKuSKTtOmtQfWCvTIorVMYrN10-I" target="_blank">handout</a>.<br /><br />With about fifteen minutes to go we tried the mastery test on solving equations again.<br /><br />It occurred to me at the end of the period that I don't take enough pictures of students working or of their work. Something to work on. Sorry about the lack of photos.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/G9KP9ENujTM" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-68-speedy-lines.htmltag:blogger.com,1999:blog-2205963398207045749.post-5233635536471149052017-12-12T20:30:00.000-05:002017-12-12T20:30:15.110-05:00MPM1D1 - Day 67 Solving Systems of EquationsWhen I first came across today's warm-up question I thought it would be great as a measurement problem solving type question with a bit of algebra thrown in for practice. Here is the problem:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-g_VAu7nWbJ4/WjB8AvnwLDI/AAAAAAAANE4/u3wC9-GOg9IA_8tt8lLxD9bwfHD8ues_wCLcBGAs/s1600/Screen%2BShot%2B2017-12-12%2Bat%2B7.58.32%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="212" data-original-width="892" height="95" src="https://1.bp.blogspot.com/-g_VAu7nWbJ4/WjB8AvnwLDI/AAAAAAAANE4/u3wC9-GOg9IA_8tt8lLxD9bwfHD8ues_wCLcBGAs/s400/Screen%2BShot%2B2017-12-12%2Bat%2B7.58.32%2BPM.png" width="400" /></a></div><br />What I did not anticipate was that this was also a great problem for solving systems of equations. A number of groups realized quickly that they needed an expression for the perimeter of each rectangle and then they had to set them equal to each other. One group quickly said "We don't know how to find the length". I asked them to start with what they did know and go from there. This quickly got the group moving forward.<br /><br />I was amazed to see how easy most groups were able to set the equations equal to each other and solve. For whatever reason they were far better at this than they were last week. I'm guessing it has something to do with the context here. They can see the perimeter and know that the perimeters have to be the same (since it says so in the question). I was very impressed with the results today. One group that finished early said something along the line of "You're going to ask us to find the area next, aren't you?". Too be honest I hadn't thought about that, but it seemed like a great extension for those who were done. So I asked them to find an expression for the areas and asked if they could expand their expressions. What a great way to lead them into multiplying binomials. I love using the great ideas that students have.<br /><br />The goal for today was to have students solve systems of equations graphically (the course only gets as far as solving by graphing). I mentioned earlier, we did this about a week ago. The nice thing about spiralling is that you can visit some trouble areas. This was one of those areas and I wanted to extend a bit by looking at systems in different forms.<br /><br />Here are the questions I had them work on:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Sf16N-sizz8/WjCAV0aUdsI/AAAAAAAANFE/dIx7hmxtr1Y7Gij1ZP9fqrSSmJDae3y3QCLcBGAs/s1600/Screen%2BShot%2B2017-12-12%2Bat%2B8.19.54%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="474" data-original-width="732" height="258" src="https://1.bp.blogspot.com/-Sf16N-sizz8/WjCAV0aUdsI/AAAAAAAANFE/dIx7hmxtr1Y7Gij1ZP9fqrSSmJDae3y3QCLcBGAs/s400/Screen%2BShot%2B2017-12-12%2Bat%2B8.19.54%2BPM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">There were so many great questions that came out of this work. I find students always have a hard time with the equations of vertical and horizontal lines so a bit of extra practice here is alway good. Some students struggled with graphing the second equation in part b). They forgot what the slope was if there was no coefficient showing in front of the x. There was lots of good practice graphing equations and finding ways to graph different forms of equations.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">One girl in the class insisted on solving the equations by substitution. This is easy enough for the first five questions, but I'me guessing she'll have a hard time with the last couple.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">With about 15 minutes to go we moved onto a mastery test on solving equations.</div><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/M5x3yV3a8bg" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-67-solving-systems-of.htmltag:blogger.com,1999:blog-2205963398207045749.post-47921779306618105152017-12-11T19:54:00.001-05:002017-12-11T20:02:04.482-05:00MPM1D1 - Day 66 More Equations With FractionsWe started with the following Fraction Talks, where students had to determine which fraction of the picture was red.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-K7I-07m8sTo/Wi8kheecdzI/AAAAAAAANEY/BVS3cZ7GCdQW4ZR_0aIiTxy7dfdMw7eDACLcBGAs/s1600/Screen%2BShot%2B2017-12-11%2Bat%2B7.34.02%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="447" data-original-width="451" height="395" src="https://4.bp.blogspot.com/-K7I-07m8sTo/Wi8kheecdzI/AAAAAAAANEY/BVS3cZ7GCdQW4ZR_0aIiTxy7dfdMw7eDACLcBGAs/s400/Screen%2BShot%2B2017-12-11%2Bat%2B7.34.02%2BPM.png" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-OHGikZ26lSk/Wi8khcwL5DI/AAAAAAAANEc/sXdWf5qEbM0KpZFNTvI-mPOayIBGp7N3QCLcBGAs/s1600/Screen%2BShot%2B2017-12-11%2Bat%2B7.34.28%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="468" data-original-width="475" height="393" src="https://1.bp.blogspot.com/-OHGikZ26lSk/Wi8khcwL5DI/AAAAAAAANEc/sXdWf5qEbM0KpZFNTvI-mPOayIBGp7N3QCLcBGAs/s400/Screen%2BShot%2B2017-12-11%2Bat%2B7.34.28%2BPM.png" width="400" /></a></div><br />It was interesting to hear all the different ways students did these. Their were some good discussions about adding and multiplying fractions, which was a good reminder for some.<br /><br />I then put the following equations with fractions on the board and had students work individually to solve them.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-8ahkfYPpHGk/Wi8l7dMeTBI/AAAAAAAANEk/2h3PJVjIGPodcqT4w0Ob2VfOR2kqVC8tgCLcBGAs/s1600/Screen%2BShot%2B2017-12-11%2Bat%2B7.41.15%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="274" data-original-width="813" height="133" src="https://4.bp.blogspot.com/-8ahkfYPpHGk/Wi8l7dMeTBI/AAAAAAAANEk/2h3PJVjIGPodcqT4w0Ob2VfOR2kqVC8tgCLcBGAs/s400/Screen%2BShot%2B2017-12-11%2Bat%2B7.41.15%2BPM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">A couple of people asked for a refresher on how to solve equations with fractions so we worked through a question as a class, then they began working away. It was slow going for some, but everyone was moving along and getting a little better. Lots of students were those in their groups who were struggling.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Once they were done, students continued the <a href="https://drive.google.com/file/d/1PPDGcdy4vvJL75-h1QFyXbSZT4XMoS8e/view" target="_blank">handout</a> from Friday. It was a good day of individual work.</div><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/iC4u3VNdXAQ" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-66-more-equations-with.htmltag:blogger.com,1999:blog-2205963398207045749.post-61947544822520909622017-12-10T21:31:00.000-05:002017-12-10T21:31:05.931-05:00MPM1D1 - Day 65 Solving Equations With Fractions<div class="separator" style="clear: both; text-align: left;">We started with this Which One Doesn't Belong:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://wodb.ca/images/number17.jpg" target="_blank"><img border="0" data-original-height="684" data-original-width="684" height="320" src="https://2.bp.blogspot.com/-2qfBvTt1VqM/WiymSD5UKsI/AAAAAAAAND0/mNVUIoDqUKAGGs5OuOhfhyISH7NHGRpPgCLcBGAs/s320/number17.jpg" width="320" /></a></div><br />It was great to hear all of the terminology that came out of the discussions.<br /><br />After the warm-up we moved into solving equations with fractions up at the board in groups. I didn't give any instructions. I gave some equations for groups to solve and they did a great job.<br /><br />Here are the questions they worked on:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-HdyLn8W638A/Wi3mJlFOKzI/AAAAAAAANEE/hCxf0UmmTxs7BtZxa1G5cE_Oc3jJn3FSACLcBGAs/s1600/fractions.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="663" data-original-width="983" height="428" src="https://3.bp.blogspot.com/-HdyLn8W638A/Wi3mJlFOKzI/AAAAAAAANEE/hCxf0UmmTxs7BtZxa1G5cE_Oc3jJn3FSACLcBGAs/s640/fractions.PNG" width="640" /></a></div><br />I was amazed at how well the groups worked. They required little to no assistance from me. They were able to apply what they had learned about solving equations without fractions and things worked out great. It was also great to see the stronger students really working with those that struggled to bring them along. I feel that we've really developed a community of learners in the class and I'm really happy about that. One of the groups consisted of two students who pretty much refused to work with each other at the beginning of the semester. Today they worked as though they were good buddies.<br /><br />Once the groups were done I brought the class together and asked what was different about the equations today. Many students said that these equations were more difficult. When I asked why they were more difficult the response was because of the fractions. We then talked about how we could eliminate the fractions by multiplying both sides of the equation by a common denominator. We did a couple so they could see how it was done then they did the first part of <a href="https://drive.google.com/open?id=1PPDGcdy4vvJL75-h1QFyXbSZT4XMoS8e" target="_blank">this handout</a>.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/X-WxmYxfP1M" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-65-solving-equations-with.htmltag:blogger.com,1999:blog-2205963398207045749.post-85827107872939357892017-12-07T19:17:00.001-05:002017-12-07T19:17:52.154-05:00MPM1D1 - Day 64 Test DayWe had our test today. Students worked away diligently and asked for clarification as needed. I'm hoping for some good results. There are a few topics that we'll revisit in the coming weeks to solidify understanding.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/y70rxi-4qAs" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-64-test-day.htmltag:blogger.com,1999:blog-2205963398207045749.post-32377452538636985772017-12-06T21:35:00.003-05:002017-12-06T21:35:35.016-05:00MPM1D1 - Day 63 Another Day of ReviewThe plan for today was to have students write their individual tests. But, based on what I saw yesterday during the group test, many students would not have been prepared to write today. I decided to give the class another day to work on the review questions.<br /><br />At the beginning of class I made the rounds and discovered that very few students had done much of the review at all. I was a little disappointed.<br /><br />Most students used their time wisely today. It was great to see some of the stronger students helping those that were struggling.<br /><br />Here's hoping for good results tomorrow.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/OHr10kCVKf4" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-63-another-day-of-review.htmltag:blogger.com,1999:blog-2205963398207045749.post-66905768264021448622017-12-05T19:27:00.000-05:002017-12-05T19:27:12.716-05:00MPM1D1 - Day 62 Group TestToday was our group test. I let students choose their own groups. I'm not sure whether this was a good idea or not. It seemed that some students weren't really sure who to work with. Others had a good sense but I had said that the group must be three people. This meant that those hoping to be a group of four had to decide who was going to leave. Not doing random groups today made me really appreciate doing random groups.<br /><br />Each group received the test and started working on their whiteboards. I had each group start at a different question. Some groups were very efficient and others really seemed to have a hard time making headway. I went around and did lots of listening and asked if students could clarify their thinking for me.<br /><br />It was pretty obvious that many students had not studied for the test. There were lots of incorrect assumptions being made along with lots of simple errors. I really like the group test because of all the discussion and learning that is taking place. I also like the fact that I have some conversations (which I recorded today) that I can use to supplement (one way or the other) a student's test results. What I don't like about this extra information is that I don't have a clean way to count it.<br /><br />I struggle with how to assess the group test (and maybe it just needs to be formative). I don't want to penalize a student who learned a ton between the group test and the individual test. I also don't want students to feel like they did well on the group test so they don't need to prepare for the individual test. In any case, I do have a record of the conversations along with photos of all the work that I can use to help in making an overall judgement.<br /><br />The plan for tomorrow was to do the individual test but I don't think my students are ready for that yet.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/jFuqQLnBWh8" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-62-group-test.htmltag:blogger.com,1999:blog-2205963398207045749.post-15330613241998496122017-12-04T21:34:00.000-05:002017-12-04T21:34:03.342-05:00MPM1D1 - Day 61 Solving a System of Equations Algebraically <div class="separator" style="clear: both; text-align: left;">We started the class solving some equations. I wanted students to really focus on showing their work and being methodical in their approach.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-E3ABIDwrIak/WiVcp-fwYLI/AAAAAAAANDU/Pvd0OfRqlCk_12z1P9HQXcJWkYS-S3geQCLcBGAs/s1600/equations.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="238" data-original-width="938" height="101" src="https://3.bp.blogspot.com/-E3ABIDwrIak/WiVcp-fwYLI/AAAAAAAANDU/Pvd0OfRqlCk_12z1P9HQXcJWkYS-S3geQCLcBGAs/s400/equations.PNG" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>After the warm-up we looked at solving a system of equations algebraically. We looked at the Knotted Rope work we did last week and discussed the ways we could determine when the ropes would be the same length. Students mentioned that they could graph it or look at the table. I asked how many of them wanted to fill in the table to get up to 60 knots. We decided that in this case a table would take too long and one student suggested we should use an equation. We talked about how if the lengths of the ropes were equal then the equations representing their lengths must also be equal. I helped them setup the equation and let them solve it.<br /><br />For the remainder of the period students could work on their own or in groups on the <a href="https://docs.google.com/document/d/1eE78coLEcfbJd6AhfFS5C7s7wiyu7Xp1bXvMVeEDfA8/edit?usp=sharing" target="_blank">review</a> for the upcoming test.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/1XtaFG_RleQ" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-61-solving-system-of.htmltag:blogger.com,1999:blog-2205963398207045749.post-49049269007008979302017-12-02T20:01:00.002-05:002017-12-02T20:01:54.698-05:00MPM1D1 - Day 60 More Knotted RopesWe started with another Which One Doesn't Belong.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://wodb.ca/images/graph34.JPG" target="_blank"><img border="0" data-original-height="625" data-original-width="624" height="400" src="https://wodb.ca/images/graph34.JPG" width="398" /></a></div><br />The goal here was to connect the different representations of a linear relation. Students did a great job of discussing slope, y-intercepts, x-intercepts, continuous, discrete and the equations for these relations.<br /><br />They then had some time to finish up the <a href="http://sine-of-the-times.blogspot.ca/2017/11/mpm1d1-day-59-knotted-ropes.html" target="_blank">Knotted Ropes</a> work that they started yesterday. The groups were much more focused today. They graphed the relationship between rope length and number of knots for each roe. They generated an equation and made connections between the slope and y-intercept and what they meant in terms of the rope. I asked them to use there equations to find h<span style="font-family: Arial; font-size: 11pt; white-space: pre-wrap;">ow long will each rope be if it had 25 knots? H</span><span style="font-family: Arial; font-size: 11pt; white-space: pre-wrap;">ow many knots are needed to get each rope to a length of 60 cm?</span> Then they plotted their data in Desmos and performed a linear regression to get the equation of the lines best fit. They then checked on the graph to see where the point of intersection was located.<br /><br />I had hoped to look at how to find the point of intersection algebraically but one or two of the groups weren't quite ready for it yet. I'll pick up here on Monday.<br /><br />Some groups finished early so I gave them some more parallel and perpendicular lines <a href="http://what%20effect%20does%20making%20bigger%20%28or%20smaller%29%20knots%20have%20on%20the%20equations/?%20%20What%20effect%20does%20changing%20the%20length%20of%20the%20rope%20have?%20%20%20How%20does%20changing%20the%20length%20of%20one%20rope%20(or%20the%20size%20of%20the%20knot)%20do%20to%20the%20point%20of%20intersection?" target="_blank">practice</a>. We're having a test next week so I also gave out the test <a href="https://drive.google.com/open?id=1eE78coLEcfbJd6AhfFS5C7s7wiyu7Xp1bXvMVeEDfA8" target="_blank">review</a> in case anyone wanted to get started on it over the weekend.<br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/lcDSgwlpTEw" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-60-more-knotted-ropes.htmltag:blogger.com,1999:blog-2205963398207045749.post-39416772240087891302017-11-30T22:46:00.001-05:002017-12-01T07:57:08.814-05:00MPM1D1 - Day 59 Knotted Ropes<div class="separator" style="clear: both; text-align: left;">The warm-up for today was this Which One Doesn't Belong:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://wodb.ca/images/graph7.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="686" data-original-width="687" height="319" src="https://wodb.ca/images/graph7.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">It was a nice tie in to what we have been doing (slopes, intercepts, parallel lines) and I heard some great reasons for each one not belonging.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">After the warm-up we consolidated the work that we did yesterday on parallel and perpendicular lines. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The goal for today was to have students explore the relationship between the number of knots in a rope and its length (inspired by <a href="http://slamdunkmath.blogspot.ca/2015/02/ropes-of-different-thickness-and-equal.html" target="_blank">this post</a>). Each groups received a length of rope and a length of string. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-T2Br4ooJJ7Y/WiFRiUTSwGI/AAAAAAAANCY/eHKbea9eV2EYbH9JBK7dNtOHl-1naI9HwCLcBGAs/s1600/IMG_0490.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="676" data-original-width="905" height="298" src="https://3.bp.blogspot.com/-T2Br4ooJJ7Y/WiFRiUTSwGI/AAAAAAAANCY/eHKbea9eV2EYbH9JBK7dNtOHl-1naI9HwCLcBGAs/s400/IMG_0490.JPG" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-DplHGcv9vSw/WiFRiXIcxPI/AAAAAAAANCU/RslT-xbpMbM459jkTYGSqWJucZHBfY4vgCLcBGAs/s1600/IMG_0493.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="676" data-original-width="505" height="400" src="https://3.bp.blogspot.com/-DplHGcv9vSw/WiFRiXIcxPI/AAAAAAAANCU/RslT-xbpMbM459jkTYGSqWJucZHBfY4vgCLcBGAs/s400/IMG_0493.JPG" width="298" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-WUcP1-1TuQA/WiFRiTmujdI/AAAAAAAANCQ/RpdRF6wl3ysISqE33zNzDEc3VYGVtnImwCLcBGAs/s1600/IMG_0495.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="676" data-original-width="505" height="400" src="https://3.bp.blogspot.com/-WUcP1-1TuQA/WiFRiTmujdI/AAAAAAAANCQ/RpdRF6wl3ysISqE33zNzDEc3VYGVtnImwCLcBGAs/s400/IMG_0495.JPG" width="298" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">They were to create a table, graph and equation to represent both their rope and string, then determine how many knots were needed to make both ropes the same length (same number of knots in each rope). We only had about 30 minutes to complete the activity. I knew that students wouldn't finish but was hopeful. Most groups worked very effectively, but a couple couldn't seem to measure accurately enough. I might need some larger diameter rope that doesn't stretch so much. A number of groups found that their rope was longer after adding a knot to it.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Nobody got past the graphing stage so we'll finish up tomorrow.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"></div><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/W9cidT7Ihzg" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-59-knotted-ropes.htmltag:blogger.com,1999:blog-2205963398207045749.post-37709488529393916172017-11-29T21:30:00.001-05:002017-11-29T21:30:22.756-05:00MPM1D1 - Day 58 Parallel and Perpendicular Lines<div class="separator" style="clear: both; text-align: left;">Today's problem was one that I was reminded of at a recent professional development session (thanks <a class="ProfileHeaderCard-screennameLink u-linkComplex js-nav" href="https://twitter.com/chrisleechss" style="background: rgb(255, 255, 255); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px; font-weight: 700; text-decoration-line: none !important;"><span class="username u-dir" dir="ltr" style="direction: ltr !important; unicode-bidi: embed;"><span style="color: black;">@<span class="u-linkComplex-target" style="font-weight: normal;">chrisleechss</span></span></span><span style="color: #657786;"> </span></a>).</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-G8nS0t4mOH4/Wh8IXuNa-EI/AAAAAAAANBw/V_UR-ne81oYOsQPuwaugh4WdJo2DLhlzACLcBGAs/s1600/slope.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="302" data-original-width="930" height="128" src="https://3.bp.blogspot.com/-G8nS0t4mOH4/Wh8IXuNa-EI/AAAAAAAANBw/V_UR-ne81oYOsQPuwaugh4WdJo2DLhlzACLcBGAs/s400/slope.PNG" width="400" /></a></div><br />This question generated a lot of discussion. Is 1 a big slope? Does it matter if it's negative or positive? There were lots of good conversations as students continued to solidify their understanding of slopes. For groups that finished early I asked how their answers would differ if they were allowed to use the numbers 0-9.<br /><br />The consolidation of this problem led us to talk about horizontal and vertical lines. We talked (again) about the slopes of these lines but we also talked (unexpectedly) about the equations of horizontal and vertical lines.<br /><br />The main lesson for today was investigating parallel and perpendicular lines. I gave <a href="https://drive.google.com/open?id=1-iBbHo7mTCGiPbvSGZlpXBbE6_-vi_f5" target="_blank">this investigation</a>. It was good for students to practice graphing lines but I think I need to rework it for them to get more out of the perpendicular lines portion.<br /><br />We'll consolidate the investigation tomorrow.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/neNebZM-nHs" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-58-parallel-and.htmltag:blogger.com,1999:blog-2205963398207045749.post-84502826738304336432017-11-28T21:58:00.002-05:002017-11-28T21:58:46.607-05:00MPM1D1 - Day 57 X- and Y-InterceptsIt's been a while since we did any work with percentages so today we looked at this Would You Rather problem:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://i0.wp.com/www.wouldyourathermath.com/wp-content/uploads/2016/05/Copies-1.png" target="_blank"><img border="0" data-original-height="720" data-original-width="960" height="240" src="https://4.bp.blogspot.com/-goUb2y5CDMs/Wh4exULL-pI/AAAAAAAANBM/TmU7O_6XXqMG8-wPzugfwobUQM3vink2wCLcBGAs/s320/Copies-1.png" width="320" /></a><span id="goog_1214102162"></span><a href="https://www.blogger.com/"></a><span id="goog_1214102163"></span></div><br />Some groups were quick to choose a price and start working with it. Other found 40% of 15 and 50% of 25 and chose the smaller number :(. I asked what those numbers meant and eventually got them headed in the right direction. When the first group finished I asked if the price of the book made any difference? Was there better deal always a better deal regardless of book price.<br /><br />Once groups finished I asked them to do the following:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-v9-6BHc1rEw/Wh4fr9JgUPI/AAAAAAAANBU/727d_J_AXgUGacwCGEyqsYgWUr1K9CmjACLcBGAs/s1600/Screen%2BShot%2B2017-11-28%2Bat%2B9.46.36%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="120" data-original-width="607" height="78" src="https://4.bp.blogspot.com/-v9-6BHc1rEw/Wh4fr9JgUPI/AAAAAAAANBU/727d_J_AXgUGacwCGEyqsYgWUr1K9CmjACLcBGAs/s400/Screen%2BShot%2B2017-11-28%2Bat%2B9.46.36%2BPM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I talked individually with groups about what they knew about the y-intercept. We arrived at the fact that they x-coordinate was always 0 and off they went. Having never done this before some groups struggled a bit. I brought the class together for a couple of minutes and we talked about what it means to be an x- or y-intercept. They went off and completed the questions above in their groups. When they were done they worked on question 2 from <a href="https://drive.google.com/open?id=1l_Mo2bvjmY5b-bH1d3A0g8w4VwwdtUKc" target="_blank">yesterday's handout</a>. After everyone was done the questions above we consolidated and wrote a quick note. Students then finished up the practice questions.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/dWVNOEDfGw8" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-57-x-and-y-intercepts.htmltag:blogger.com,1999:blog-2205963398207045749.post-34027181995838020332017-11-27T20:27:00.000-05:002017-11-27T20:27:03.921-05:00MPM1D1 - Day 56 Another Kick at Success Criteria & Standard FormLast week students looked at an incorrect (level 2) solution to the problem below.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-8QGO97PrPvo/Why2wQx0qKI/AAAAAAAANAk/zp8NKJtfoREWVj0QMSFY6vV5uT8fY54XwCLcBGAs/s1600/floored%2Bareas.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="180" data-original-width="400" height="180" src="https://2.bp.blogspot.com/-8QGO97PrPvo/Why2wQx0qKI/AAAAAAAANAk/zp8NKJtfoREWVj0QMSFY6vV5uT8fY54XwCLcBGAs/s400/floored%2Bareas.PNG" width="400" /></a></div><br />They did a good job with it, but I wanted to take some time today to model how to solve a problem and to develop some success criteria for problem solving.<br /><br />I gathered students at a whiteboard at the back of the room and we started working on the problem. As we worked through the problem I would periodically stop and ask what we had just done. The peer tutor wrote a list on a different board of all the things we talked about. Here are some of the things we talked about:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-bCWI0dmst7Q/Why4fyFPJuI/AAAAAAAANAw/M02WWaCdYX4Iry9A4NjRNRZuLQpvMeMPgCLcBGAs/s1600/IMG_0489.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1196" height="400" src="https://1.bp.blogspot.com/-bCWI0dmst7Q/Why4fyFPJuI/AAAAAAAANAw/M02WWaCdYX4Iry9A4NjRNRZuLQpvMeMPgCLcBGAs/s400/IMG_0489.JPG" width="298" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Once we were done most students really wanted to get a picture of the list. I guess something about our process spoke to them as being important. We'll come back to the criteria next time I give out a problem.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The plan for today was to look at the equation of a line in standard form. I had groups do the following:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-O6BrqLnIawg/Why6BeZmtCI/AAAAAAAANA8/IKL_fr7mKFU4rLGy4SqY8dwLWtUK6PMzwCLcBGAs/s1600/Screen%2BShot%2B2017-11-27%2Bat%2B8.19.31%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="301" data-original-width="659" height="182" src="https://3.bp.blogspot.com/-O6BrqLnIawg/Why6BeZmtCI/AAAAAAAANA8/IKL_fr7mKFU4rLGy4SqY8dwLWtUK6PMzwCLcBGAs/s400/Screen%2BShot%2B2017-11-27%2Bat%2B8.19.31%2BPM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Some of them struggled a fair bit with part b, but other groups blasted through it quickly. Once they were finished we talked briefly about what standard form is and consolidated how to convert from standard form to slope/y-intercept form (since many groups ended up doing some rearranging when making a table of values).</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">We did an example, then I gave out some <a href="https://drive.google.com/open?id=1l_Mo2bvjmY5b-bH1d3A0g8w4VwwdtUKc" target="_blank">practice questions</a> (question 1).</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/mAcPt_-ab2Y" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-56-another-kick-at-success.htmltag:blogger.com,1999:blog-2205963398207045749.post-47505595385772687992017-11-23T22:07:00.001-05:002017-11-27T20:02:58.763-05:00MPM1D1 - Day 55 Error Finding and Angle TheoremsToday's warm-up was a little different. We started by looking at a problem with a fully worked solution. The solution contained errors (it was a level 2 exemplar) and students had to identify the errors then present a complete (level 4) solution.<br /><br />I gave out a page with <a href="https://docs.google.com/document/d/14SjgJXbMyBcsXSq7PZsnRGNbHnGrIopSovMbGrI3Fq8/edit?usp=sharing" target="_blank">two problems</a> along with the level 2 solutions.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-QNWSNjQQSnw/WheE5p6L6MI/AAAAAAAANAE/GJuSsHTE4JMPg1gm3ZgNpiKv9TRFidChQCLcBGAs/s1600/floored%2Bareas.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="243" data-original-width="540" height="180" src="https://3.bp.blogspot.com/-QNWSNjQQSnw/WheE5p6L6MI/AAAAAAAANAE/GJuSsHTE4JMPg1gm3ZgNpiKv9TRFidChQCLcBGAs/s400/floored%2Bareas.PNG" width="400" /></a></div><br />The first problem served the purpose of practicing some of the algebra skills that we worked on earlier in the week, that need more work.<br /><br />I had students work in groups of three up at the board to figure out what happened in the solution. This was difficult for some students. They just wanted to solve the problem their way, which was different from the solution. Once groups figured out the approach used in the problem they were able to determine where the errors were and correct them. There were some good discussions about how to fix those errors. I think students were able to solidify their understanding of the distributive property and collecting like terms.<br /><br />As a result of this activity my class has now constructed an exemplar for solving these open response type questions. I'm hopeful that next time we solve a problem like this, we will be able to co-construct the success criteria for solving problems like this.<br /><br />All groups completed the first problem, many were working on the second problem and one group finished both.<br /><br />We then moved onto <a href="http://mail.wecdsb.on.ca/~david_petro/WebSketches/Parallel/index.html" target="_blank">this activity</a> (thanks <span style="background-color: white;"><span class="username u-dir" dir="ltr" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: #657786; direction: ltr; font-family: "segoe ui" , "arial" , sans-serif; font-size: 14px; font-weight: 700; outline: 0px; unicode-bidi: embed;"><a class="ProfileHeaderCard-screennameLink u-linkComplex js-nav" href="https://twitter.com/davidpetro314" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: #657786; font-family: "segoe ui", arial, sans-serif; font-size: 14px; font-weight: 700; outline: 0px;">@<span class="u-linkComplex-target" style="font-weight: normal; text-decoration-line: underline !important;">davidpetro314</span></a>)</span><span class="username u-dir" dir="ltr" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; direction: ltr; font-family: "segoe ui" , "arial" , sans-serif; font-size: 14px; font-weight: 700; outline: 0px; unicode-bidi: embed;"> </span><span class="username u-dir" dir="ltr" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; direction: ltr; font-family: "segoe ui" , "arial" , sans-serif; font-size: 14px; outline: 0px; unicode-bidi: embed;">to investigate parallel lines, transversals and angle theorems. This was review for most students and most of them seemed to remember doing it in grade 8. Once they were finished with the activity I had them create their own note for their notebooks to remind them of the theorems. Some of the notes were excellent, others were not, but who am I to say what type of note would be useful for all students. I then gave them some questions to practice.</span></span><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/92dElgQ3WvM" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-55-error-finding-and-angle.htmltag:blogger.com,1999:blog-2205963398207045749.post-24354417671900408342017-11-22T21:43:00.001-05:002017-11-23T21:23:15.466-05:00MPM1D1 - Day 54 Finishing Up Barbie BungeeToday we finished up Barbie Bungee. A couple of groups wanted to collect more data or double check some of their data from yesterday. Students began analyzing the data. They were creating graphs, both by hand on using Desmos. They were extrapolating using their graphs. They were coming up with the equation of their line of best fit. They were performing linear regressions in Desmos and comparing it to their findings. There was a lot more reasoning about the reasonableness of their answers than I expected. Once students had a number of rubber bands they were happy with they began writing their reports.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-t9pAjbgXrLg/WhYy6UpvRcI/AAAAAAAAM_s/hLmgyJLmjHkFpC-z1J1Qhq2cG2Rn6hM8QCLcBGAs/s1600/IMG_0476.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1196" data-original-width="1600" height="298" src="https://1.bp.blogspot.com/-t9pAjbgXrLg/WhYy6UpvRcI/AAAAAAAAM_s/hLmgyJLmjHkFpC-z1J1Qhq2cG2Rn6hM8QCLcBGAs/s400/IMG_0476.JPG" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">With about twenty minutes left we headed to the stairwell to see who could get Barbie the closest to the floor without hitting it. It was so much fun. We had one person at the bottom recording in slow motion. Some students were at the top of the stair watching, while others chose to observe from below. The closest group had Barbie touch the floor with her outstretched hand, but not touch her head. There was some debate about this should count or not. What do you think?</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-_YZ8Z3JRdyc/WhYzQYeX7PI/AAAAAAAAM_w/D8iT1k-nbig74ByYs0LqrvBqphrPi4_qwCLcBGAs/s1600/IMG_0477.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1196" data-original-width="1600" height="298" src="https://1.bp.blogspot.com/-_YZ8Z3JRdyc/WhYzQYeX7PI/AAAAAAAAM_w/D8iT1k-nbig74ByYs0LqrvBqphrPi4_qwCLcBGAs/s400/IMG_0477.JPG" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-rB-JnvMaS2k/WhYzQc9xgMI/AAAAAAAAM_0/yaeIgyJ7WW8SRIYLp5EQisZBGDCFAyGFwCLcBGAs/s1600/IMG_0478.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1196" data-original-width="1600" height="298" src="https://3.bp.blogspot.com/-rB-JnvMaS2k/WhYzQc9xgMI/AAAAAAAAM_0/yaeIgyJ7WW8SRIYLp5EQisZBGDCFAyGFwCLcBGAs/s400/IMG_0478.JPG" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div>I haven't received a copy of the video yet but once I do I will post it.<br /><br />What a great end to a great activity. I can't wait to read the write-ups.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/xFz25AWZngQ" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-54-finishing-up-barbie-bungee.htmltag:blogger.com,1999:blog-2205963398207045749.post-50698034777220757922017-11-21T22:11:00.000-05:002017-11-21T22:11:55.564-05:00MPM1D1 - Day 53 Barbie BungeeWe skipped the traditional warm-up today and got right into Barbie Bungee. Our warm-up was co-constructing the success criteria.<br /><br />As students came into class they received a card (as they always do) that would assign them to a random group. After the bell went I had students gather at a white board at the back of the room. I explained that each group would receive a Barbie and they had to figure out how many rubber bands to tie onto Barbie so that she got as close to the floor without hitting it when she was dropped from the stairwell. I told them that this was an assignment and I wanted them to go to their boards and come up with a list of criteria that they thought should be included in their assignment. I felt like after the time we spent working on the success criteria for the Pumpkin Time-Bomb assignment, students had a good sense of what should be included in an assignment.<br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-yfsG4J5EMgU/WhTnRMyCj3I/AAAAAAAAM_I/hYb4eFGYP3EYg2v4aiPLxjeZLPcWCSVuACLcBGAs/s1600/IMG_8365.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://2.bp.blogspot.com/-yfsG4J5EMgU/WhTnRMyCj3I/AAAAAAAAM_I/hYb4eFGYP3EYg2v4aiPLxjeZLPcWCSVuACLcBGAs/s400/IMG_8365.jpg" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-vo6Sa9Uq8m8/WhTnPu6a8wI/AAAAAAAAM_E/5JbvEH4GNzABvjcgJpVd1UtjbGcBQDfBwCLcBGAs/s1600/IMG_8367.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://1.bp.blogspot.com/-vo6Sa9Uq8m8/WhTnPu6a8wI/AAAAAAAAM_E/5JbvEH4GNzABvjcgJpVd1UtjbGcBQDfBwCLcBGAs/s400/IMG_8367.jpg" width="300" /></a></div><br /><br />I was not disappointed. The results were far better than they were the first time we co-created success criteria. Each group created a good sized list of useful criteria this time around. After about 10 minutes I stopped them and had them group their criteria into categories of their choosing. As it turned out most, if not all groups, created three different categories. The categories were roughly Data (needed/given/measured), Mathematics (graph, table, equation, line of best fit), Report (description of task and process used, showing your work, proper terminology, units etc.).<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-6Aqwu2tshYk/WhTnWZKf8cI/AAAAAAAAM_Q/bQR_UDiEw4oiD_VXVqs2ifz2AKH-SvXqwCLcBGAs/s1600/IMG_8375.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://4.bp.blogspot.com/-6Aqwu2tshYk/WhTnWZKf8cI/AAAAAAAAM_Q/bQR_UDiEw4oiD_VXVqs2ifz2AKH-SvXqwCLcBGAs/s400/IMG_8375.jpg" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">I brought the class together, we talked about the categories and some of the items in their categories. I told them that I would organize all of their ideas and send them a written copy via email.</div><br />I handed out the Barbies and seven rubber bands and let them go. There were lots of ideas floating around that led to some great thinking.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-zOJ0Us1UvDQ/WhTnIGs1kII/AAAAAAAAM_U/xw1ZyUwNczcVinRRh5p8sXi1AT5I_9jJQCEwYBhgL/s1600/IMG_0471.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1196" height="400" src="https://1.bp.blogspot.com/-zOJ0Us1UvDQ/WhTnIGs1kII/AAAAAAAAM_U/xw1ZyUwNczcVinRRh5p8sXi1AT5I_9jJQCEwYBhgL/s400/IMG_0471.JPG" width="298" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-cOQetxJVbWA/WhTnG4TP_lI/AAAAAAAAM_U/bP9WhTKvlt4KdzrqMsfa6s24RL50Xz7RACEwYBhgL/s1600/IMG_0470.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1196" height="400" src="https://2.bp.blogspot.com/-cOQetxJVbWA/WhTnG4TP_lI/AAAAAAAAM_U/bP9WhTKvlt4KdzrqMsfa6s24RL50Xz7RACEwYBhgL/s400/IMG_0470.JPG" width="298" /></a></div><br /><br /><ul><li>We could measure one band and multiply by seven. </li><li>Should we measure them stretched or not?</li><li>Let's measure from the floor up.</li><li>Our measurements weren't very accurate (In one case adding a 10cm band only added 2cm to the distance Barbie fell).</li><li>Let's do three trials at each level and take an average.</li><li>We should each trial, then watch the video to see how far Barbie fell.</li></ul><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-SLQKqDcM5BE/WhTnSxjvrmI/AAAAAAAAM_U/18_9KdF7TZQgba4LYIQgwJiH8CI10KX7wCEwYBhgL/s1600/IMG_0475.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1196" height="400" src="https://1.bp.blogspot.com/-SLQKqDcM5BE/WhTnSxjvrmI/AAAAAAAAM_U/18_9KdF7TZQgba4LYIQgwJiH8CI10KX7wCEwYBhgL/s400/IMG_0475.JPG" width="298" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-XTtkBEkEBhY/WhTnHwdXZMI/AAAAAAAAM_U/G__XsCYRec8YLXdMtIY3pO6_VZKYiK6XQCEwYBhgL/s1600/IMG_0465.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1196" height="400" src="https://3.bp.blogspot.com/-XTtkBEkEBhY/WhTnHwdXZMI/AAAAAAAAM_U/G__XsCYRec8YLXdMtIY3pO6_VZKYiK6XQCEwYBhgL/s400/IMG_0465.JPG" width="298" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>The data collection was time consuming and messy at times but in the end every group came away with a set of data they felt comfortable with. Although it was time consuming I think having students struggle through those difficulties and errors was very worthwhile.<br /><br />Tomorrow they'll start to analyse their data and begin putting together their individual reports, which will be due sometime next week.<br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/vqRq5FF8ATs" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-53-barbie-bungee.htmltag:blogger.com,1999:blog-2205963398207045749.post-4617828537277706052017-11-20T19:45:00.001-05:002017-11-20T19:45:48.856-05:00MPM1D1 - Day 52 More Optimization<div class="separator" style="clear: both; text-align: left;">We started with a quick <a href="http://www.estimation180.com/" target="_blank">Estimation 180</a> to order the glasses from smallest capacity to largest.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://www.estimation180.com/day-59.html" target="_blank"><img border="0" data-original-height="414" data-original-width="552" height="300" src="https://2.bp.blogspot.com/-bfIbnYHbbZE/WhN0UzXkmDI/AAAAAAAAM-o/NYi_38KJs2Yr-OfQe1-PvUXWqbFwg6qjgCLcBGAs/s400/e180-59.jpg" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Then picked up right where we left off on Friday. Friday some groups did a cylinder question and some did not. It was great to have students working in different groups today. It allowed the expertise to flow through the room. They worked on the two problems below.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-hHwpxSXMHsE/WhLb5pkQfNI/AAAAAAAAM-U/EorZ3RzpJw0cMgIT6jNkD7WyNbQM7eGkwCLcBGAs/s1600/cylinder1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="125" data-original-width="1102" height="72" src="https://1.bp.blogspot.com/-hHwpxSXMHsE/WhLb5pkQfNI/AAAAAAAAM-U/EorZ3RzpJw0cMgIT6jNkD7WyNbQM7eGkwCLcBGAs/s640/cylinder1.PNG" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-9IPrtGEAJso/WhLb5aRgWxI/AAAAAAAAM-Q/YUsSZtVAn4YPyTod23Cyh1_PC7Fe1zzpwCLcBGAs/s1600/cylinder2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="116" data-original-width="1074" height="67" src="https://4.bp.blogspot.com/-9IPrtGEAJso/WhLb5aRgWxI/AAAAAAAAM-Q/YUsSZtVAn4YPyTod23Cyh1_PC7Fe1zzpwCLcBGAs/s640/cylinder2.PNG" width="640" /></a></div><br />The groups that didn't have anyone who had seen a similar problem naturally struggled. I spent some time working with them, but I think they would benefit from some more practice. Once students were done they had some time to work on a couple of questions from each of the pages found on this <a href="https://9b6cc754-a-b7a84b9c-s-sites.googlegroups.com/a/hdsb.ca/dfh-mpm1d1/L8%20Surface%20Area%20and%20Volume%20Optimization%20HW.pdf?attachauth=ANoY7crzxvuDx8wVqZwPnkZDU4Tc5nEfGvwy14to5aXnNgiANmEAUtdji8_6oq94CVbSAleQwahb1MdnY8wq33AHk2LVUCmB2rfrE604FDhKIrERNSSUjvtFxxS9ZxPyFOJCOmaFwh5BlAj-XkET8TVuhDjxrTn-yKnwKInU91kTtrVHV6X8ZRj0Wzi9enrd55tcurura_8cGz7qYAq5IAYVy2POGwOO3iFz6W-eAT_DI05878pDsW8DhelDqhukvUdA3qaLgQQA&attredirects=1" target="_blank">document</a>. Sadly, much of the individual work was seemed very unfocused. I'm thinking we'll have to revisit this topic at some point.<br /><br />With about twenty minutes to go in the period I stopped them and we took up the algebra (collecting like terms and distributive property) mastery test that they wrote last week. After taking it up we wrote it again.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/aB4g1WgVZus" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-52-more-optimization.htmltag:blogger.com,1999:blog-2205963398207045749.post-34797892571002104922017-11-17T22:01:00.000-05:002017-11-17T22:01:26.521-05:00MPM1D1 - Day 51 Optimizing Volume and Surface AreaWe started with these problems:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-LVrDRB_YtrQ/Wg-aUKaSLII/AAAAAAAAM9E/8yst57i1il817uQVMAOI2dmYbfBIQFWBgCLcBGAs/s1600/Screen%2BShot%2B2017-11-17%2Bat%2B9.25.28%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="359" data-original-width="904" height="157" src="https://2.bp.blogspot.com/-LVrDRB_YtrQ/Wg-aUKaSLII/AAAAAAAAM9E/8yst57i1il817uQVMAOI2dmYbfBIQFWBgCLcBGAs/s400/Screen%2BShot%2B2017-11-17%2Bat%2B9.25.28%2BPM.png" width="400" /></a></div>I gave the problems orally, one at a time and groups made their way through them. It was great to watch them work. For groups that made mistakes, it was often enough for me to say "Are you sure?" for them to think a bit about what they did and find their mistakes.<br /><br />We then moved onto today's work.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-nvuQcCcAkfE/Wg-b3mF2xkI/AAAAAAAAM9Q/D-rWC698syMTmt96XVDbc5prOX_HUhbcQCLcBGAs/s1600/Screen%2BShot%2B2017-11-17%2Bat%2B9.32.17%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="181" data-original-width="863" height="83" src="https://1.bp.blogspot.com/-nvuQcCcAkfE/Wg-b3mF2xkI/AAAAAAAAM9Q/D-rWC698syMTmt96XVDbc5prOX_HUhbcQCLcBGAs/s400/Screen%2BShot%2B2017-11-17%2Bat%2B9.32.17%2BPM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">This problem was closely related to yesterday's <a href="http://sine-of-the-times.blogspot.ca/2017/11/mpm1d1-day-49-dandy-candies.html" target="_blank">Dandy Candies</a> only this time the side lengths didn't need to be integer values. Most groups easily made the connection to yesterday's work and quickly came up with a solution. One of the groups was really struggling so I spent some time walking them through it. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Then we moved onto these problems:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-YnXxEkwsQOk/Wg-dZPYnWuI/AAAAAAAAM9c/CRYjFJgX57IWjVQNavI5752MzGXvknyEgCLcBGAs/s1600/Screen%2BShot%2B2017-11-17%2Bat%2B9.38.05%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="261" data-original-width="882" height="117" src="https://1.bp.blogspot.com/-YnXxEkwsQOk/Wg-dZPYnWuI/AAAAAAAAM9c/CRYjFJgX57IWjVQNavI5752MzGXvknyEgCLcBGAs/s400/Screen%2BShot%2B2017-11-17%2Bat%2B9.38.05%2BPM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Theses problems seemed to be at just the right level. Students seemed to be in flow for the entire period. When groups would get stuck I'd ask a question or provided a hint and off they'd go. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The last problem I gave dealt with a cylinder rather than a rectangular prism.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-AF8XlOoeb88/Wg-eNMk_uOI/AAAAAAAAM9k/ZoHou_tdDE03AVvzIGLWDQV005cAF53rgCLcBGAs/s1600/Screen%2BShot%2B2017-11-17%2Bat%2B9.41.43%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="123" data-original-width="869" height="56" src="https://2.bp.blogspot.com/-AF8XlOoeb88/Wg-eNMk_uOI/AAAAAAAAM9k/ZoHou_tdDE03AVvzIGLWDQV005cAF53rgCLcBGAs/s400/Screen%2BShot%2B2017-11-17%2Bat%2B9.41.43%2BPM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">A couple of groups didn't get this far today, but those that did made some great headway. A couple of groups struggled with what the cylindrical equivalent to a cube would be. I asked how they would approach the problem if the top and bottom were rectangles rather than squares. That was enough to get them going. One of the groups, on their own, actually drew a cylinder inside a cube. It was a thing of beauty. I wish I'd taken a picture of it.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">We were out of time so I gave a couple of rectangular prism questions to practice for homework. We'll pick up with the cylinders again on Monday and consolidate all of the optimization.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The period flew by today. Students were right into the work. It was challenging but not so much so that they couldn't overcome the challenges. What a great period.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/4wzvMbvp9c0" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-51-optimizing-volume-and.htmltag:blogger.com,1999:blog-2205963398207045749.post-21146562672668269842017-11-16T21:44:00.001-05:002017-11-17T21:15:07.654-05:00MPM1D1 - Day 50 Dandy CandiesWe started by revisiting this type of problem:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-_tdbh_9GcXI/Wg5I2Yps3PI/AAAAAAAAM8o/tgajf2xx9V8ZEqF5Qwa2YtCLIltsKeyOQCLcBGAs/s1600/optimization.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="163" data-original-width="1152" height="55" src="https://1.bp.blogspot.com/-_tdbh_9GcXI/Wg5I2Yps3PI/AAAAAAAAM8o/tgajf2xx9V8ZEqF5Qwa2YtCLIltsKeyOQCLcBGAs/s400/optimization.PNG" width="400" /></a></div><br />I was curious to see how much of this work that we did a while ago they would remember. Some groups had it figured out right away. Others tried making a table which was great to see. They started with a pen that was 25 by 50 then increased (and decreased) the dimensions by 10. Which meant that they missed the optimal solution. We talked about the properties of the rectangle that seemed to give the largest area and what they noticed about it compared to the others. They quickly realized that their rectangle needed to be a square.<br /><br />Before we moved onto the main event for the day we consolidated the work that we did on the distributive property yesterday. I also gave a couple of questions for them to try.<br /><br />The main event for the day was <a href="http://www.101qs.com/3038" target="_blank">Dandy Candies</a>. I asked what they noticed and what they wondered. There were lots of good observations and a few good questions. The most common thing they wondered about was what question I was going to ask them.<br /><br />We had some good discussion about volume and surface area and they had some practice calculating surface areas. Some went immediately for the formula at which point we had a discussion about what surface area actually means. No formulas were needed after that.<br /><br />We finished up the class with a mastery test on collecting like terms, multiplying and dividing monomials and the distributive property.<br /><br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/4Xd-Xgm_-1o" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-49-dandy-candies.htmltag:blogger.com,1999:blog-2205963398207045749.post-8997795490343246092017-11-15T20:04:00.000-05:002017-11-15T20:21:33.659-05:00MPM1D1 - Day 49 Area Models, Exemplars & Success Criteria We started the class with a number talk. I asked students what 5 times 18 was. They thought quietly about it for a bit and when everyone had an answer we started sharing strategies. I told students that if they found an answer early they should try to come up with another way. I love that my students feel so comfortable with this. They work quietly and for the most part are willing to share their strategies. I also love how there are a huge number of ways to get the answer. On a previous number talk I mentioned the 'doubling and halving' strategy. It was neat to see some students using that strategy today. At the end of the talk I even had a student say "You could also double 18, halve 5 and multiply those together", which led so a good discussion about multiplying by half. Lots of great conversations.<br /><br />After the number talk we revisited the distributive property, but this time using an area model. I pulled out the algebra tiles, we looked at an example as a group and then I let them try a few examples. Reactions were mixed. I heard "This is really easy" but also "I hate using these. Do we have to use them?". I think having multiple tools (the area model being one) to use can be very helpful.<br /><br />Once we had practiced with the tiles we revisited our last assignment (Pumpkin Time-Bomb). The results of the assignment were not very good. My favourite was an email with one phrase in the subject and nothing else, followed by another email with another phrase in the subject and one final email with a link to a graph in the subject line. This was one student's assignment. I don't recall multiple emails using only the subject line being a success criterion.<br /><br />I figured I had two options for this assignment: leave it and move on or spend some time getting it right. I opted for the latter and that's what we did today. I provided an exemplar to groups and asked them to identify the parts or characteristics that make it a good assignment. They came up with some ideas and I helped them notice a few others. They now have a good model. My only fear with providing this is that I'm going to get a class set of assignments that look essentially like the one I did. I'm willing to take a chance on this to see what happens. We will have more assignments later so I'm not too worried about a single assignment. They spent the rest of the period reworking their assignments.<br /><br />I'm struggling a bit with wrapping my head around success criteria. I've had some great conversations both online and in-person with a ton of people who have more experience with this than I do. These conversations are helping me sort our some of the details but I think I'm just going to have to try a bunch of things, fail at some and repeat.<br /><br />Some of the questions I had were:<br /><br /><ul><li>What happens when the success criteria is all 'fluff' (neatly written, includes units) and no math?</li><li>Do I give the exemplar before we develop the criteria or after? If I give it before then am I just paying lip service to their contributions (since they have the standard in front of them)?</li></ul><br />Some of the responses I have received are:<br /><br /><ul><li>Provide students with exemplars at different levels and have them assessed by students. -Melanie</li><li>Try giving a Level 2 exemplar and asking what needs to be fixed. -@chrisleechss</li><li>Model the creation of the exemplar with students. -@klaunderville</li></ul><br />That last one is a big one! I think I'd like to try it but I'm worried that in doing so I will suck the thinking out of the task. I suppose I could model for a similar task and then give them the actual assignment, which would have the same or similar success criteria. However I decide to do it I'll think I'll capture some video and try to get some feedback from the video.<br /><br />Thanks to all those helping me along this journey. If you have any other suggestions or comments please feel free to add them below.<br /><br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/yAR1a1OIRBI" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-49-area-models-exemplars.htmltag:blogger.com,1999:blog-2205963398207045749.post-5245612534034353582017-11-14T23:11:00.002-05:002017-11-14T23:11:21.541-05:00MPM1D1 - Day 48 Distributive PropertyWe started with this <a href="http://i2.wp.com/www.wouldyourathermath.com/wp-content/uploads/2017/10/Reeses-WYR.jpg" target="_blank">Would You Rather</a> question since we haven't done any proportional reasoning for a while.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-R8MJDDw4nyU/Wgu8olZOUkI/AAAAAAAAM8E/mvYD7myZEAAZIiVasujKCYJ9kEdj-6gCgCLcBGAs/s1600/Reeses-WYR.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="720" data-original-width="960" height="300" src="https://3.bp.blogspot.com/-R8MJDDw4nyU/Wgu8olZOUkI/AAAAAAAAM8E/mvYD7myZEAAZIiVasujKCYJ9kEdj-6gCgCLcBGAs/s400/Reeses-WYR.jpg" width="400" /></a></div><br />It was interesting (yet frustrating) to watch how groups tackled this one. Some groups decided to figure out how many cups were in each package and use 'cups' as their unit rate. Some groups seemed obsessed with changing all the units to grams. Some groups wrote out some fractions but weren't really sure what they meant or what to do with them. Finally, a couple of groups figured out what they needed to do. It all took much longer than I expected it to. I sense more proportional reasoning in our future.<br /><br />Things seemed to flow smoothly <a href="http://sine-of-the-times.blogspot.ca/2017/11/mpm1d1-day-47-multiplying-and-dividing.html" target="_blank">yesterday</a> so we continued right along with the distributive property. Once again students worked in groups of three at the whiteboards. I gave out <a href="https://docs.google.com/document/d/1XsNxWrHpAsBxVqcJGvd8yBmvH5ApmR31eMjq-ELMx4g/edit?usp=sharing" target="_blank">these</a> problems one at a time. Some groups motored through the questions, while other groups seemed to be a little more dysfunctional. I think I need to do more get to know you type stuff every day. We did some at the start of the semester but I just kind of assumed everyone would be working well with everyone else by this point. I really like Laura Wheeler's <a href="https://twitter.com/wheeler_laura/status/930603719598706688" target="_blank">idea</a> of having students introduce themselves every day and answering one icebreaker type question. It's probably a tough thing to be changing at this point but I'll keep it in mind for next time.<br /><br />Once groups were finished we consolidated and I gave them some questions to practice individually.<br /><br />The best part of the past couple of days was seeing students' confidence grow as they figured things out. That's what makes all of this so worthwhile.<br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/YqwryK6aGiQ" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-48-distributive-property.htmltag:blogger.com,1999:blog-2205963398207045749.post-13315263367031492292017-11-13T22:43:00.000-05:002017-11-13T22:43:51.562-05:00MPM1D1 - Day 47 Multiplying and Dividing PolynomialsWe started with <a href="https://solveme.edc.org/Mobiles.html" target="_blank">Solve Me Mobile</a> #64.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-L8Dt0Z45Xxk/WgpiI7IbBgI/AAAAAAAAM7o/x1UgiW7eB282-MdRJuOaL1Yo0dxWhQZ3gCLcBGAs/s1600/Screen%2BShot%2B2017-11-13%2Bat%2B10.17.59%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="486" data-original-width="459" height="320" src="https://4.bp.blogspot.com/-L8Dt0Z45Xxk/WgpiI7IbBgI/AAAAAAAAM7o/x1UgiW7eB282-MdRJuOaL1Yo0dxWhQZ3gCLcBGAs/s320/Screen%2BShot%2B2017-11-13%2Bat%2B10.17.59%2BPM.png" width="302" /></a></div><br />This is the most challenging mobile that we've done so far. Students were busy working away. I gave them a few minutes to think it through then I asked for solutions. I explained that I wasn't just looking for the answer I wanted to know how they did it. Some students started on the left side, others started on the right and still others started by subtracting two hearts from both sides. We talked about how we could use variables rather than symbols and about how it was important to follow and write down a process.<br /><br />I was hoping to start Barbie Bungee today but some of my students have not handed in the most recent assignment yet and I didn't think it was fair to start another assignment without having returned the last one.<br /><br />Instead we moved onto multiplying and dividing monomials. I tried to model the work today after the example I saw from <a href="http://www.peterliljedahl.com/" target="_blank">Peter Liljedahl</a> last week when he presented to our board about a thinking classroom. I had students work in groups of three at the board through <a href="https://docs.google.com/document/d/1QwIzZANJxjmu482OxpILR3pL-AOHeOahiL1T7Zuy6a4/edit?usp=sharing" target="_blank">these questions</a>. I gave them one question at a time and I gave it to them orally. I had them create a picture or diagram for the first one so that they could see what was happening. Then they noticed an easier way. I talked to every group about their question to ensure that they were comfortable before moving on. Once they were ready they got the next question. A few groups went to help other groups who were struggling. Overall they moved through the questions quite nicely. We wrote a short summary note, where I levelled to the bottom (I didn't think we were quite ready for students to write their mindful notes). It was a great class.<br /><br />We had some time left so we rewrote an earlier mastery test then I gave <a href="https://drive.google.com/open?id=1wNhcGGNELODhgeiSKn7M_Tg2HnZtJ2vo" target="_blank">these questions</a> for them to practice.<br /><br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/cUox88nT7is" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-47-multiplying-and-dividing.htmltag:blogger.com,1999:blog-2205963398207045749.post-75452964722221249712017-11-10T10:14:00.001-05:002017-11-10T10:14:47.832-05:00MPM1D1 - Day 46 Remebrance Day AssemblyWe had our Remebrance Day assembly today so there was no math class.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/wPr00XOg2_g" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/11/mpm1d1-day-46-remebrance-day-assembly.html