tag:blogger.com,1999:blog-22059633982070457492019-05-01T06:31:37.240-04:00Sine Of The TimesA Math Teacher's JourneyDave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.comBlogger153125SineOfTheTimeshttps://feedburner.google.comtag:blogger.com,1999:blog-2205963398207045749.post-68628201715404370132018-01-24T22:56:00.002-05:002018-01-24T22:56:52.399-05:00MPM1D1 - Day 87 Last Day of ClassesToday was the last day of the semester. We started the period by going over a couple of questions that much of the class struggled with then they were able to work independently or in small groups to go over what they thought they should study.<br /><br />A number of students had clearly used the last couple of days off effectively and had some very specific questions to ask. A number of students had a hard time focusing and didn't use the period effectively. I think coming back after an unexpected two day holiday was part of the problem, but perhaps I need think about making some of the review time more structured.<br /><br />I gave students their marks going into the exam and they had lots of questions about the logistics of the next week or so, this being their first time through the exam process.<br /><br />I'm looking forward to seeing how the class does on the exam.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/vAU8wg95VQ4" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com1http://sine-of-the-times.blogspot.com/2018/01/mpm1d1-day-87-last-day-of-classes.htmltag:blogger.com,1999:blog-2205963398207045749.post-52322926287379574662018-01-23T22:12:00.001-05:002018-01-23T22:12:37.171-05:00MPM1D1 - Day 86 More Cancelled BusesToday was pretty much a carbon copy of yesterday.<br /><br />The buses were cancelled so I sent out an email reminding students that they should be studying for their exams and that they could email me if they had any questions.<br /><br />I did have one student show up for class (a different students from yesterday). He worked away on some review and asked some questions when he was stuck. It was really easy to help him since he chose to work at the whiteboard. It made it easy for me to keep track of where he was as he went along.<br /><br />It will be great to see the class again tomorrow.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/egDVMnbFhnk" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2018/01/mpm1d1-day-86-more-cancelled-buses.htmltag:blogger.com,1999:blog-2205963398207045749.post-8015997645653525252018-01-22T22:26:00.000-05:002018-01-22T22:26:34.296-05:00MPM1D1 - Day 86 Cancelled BusesThe buses were cancelled today due to the potential of freezing rain. I emailed students in the class to let them know that they should use their time wisely today and that they should be studying for their exams. I let them know that they should email me if they had any questions.<br /><br />I did have a couple of students stop in for some extra help. It was great to be able to work one on one with these students. I didn't hear from anyone over email. Although I hope it's because they all know exactly what's going on, I'm very aware that many of them likely didn't check their email.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/s2IDF9GLbvU" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2018/01/mpm1d1-day-86-cancelled-buses.htmltag:blogger.com,1999:blog-2205963398207045749.post-55893428595249936362018-01-19T20:16:00.000-05:002018-01-19T20:16:08.463-05:00MPM1D1 - Day 85 Exam ReviewThe first thing students wanted to do today was to discuss some of the problems that they saw on the EQAO test yesterday and the day before. We walked through a couple of the questions that they struggled with. Then they had a bunch of questions about the exam: what it would look like, how it would be different from the test they had just written, how long would it be, etc.<br /><br />I had shared a list of <a href="https://docs.google.com/document/d/1hHqgA1l5RR0nEoOFPMWSeWetq3rDq9fVzulAE6kkIWM/edit?usp=sharing" target="_blank">topics</a> we've covered this semester and reminded them to use if they needed help figuring out what to study. I let them choose whether to work independently or within a small group. Most choose to work with a partner. Some worked on reviewing old tests, others discussed questions from the EQAO test and still others worked on practice exams found online (most settled on <a href="http://frontenacss.limestone.on.ca/teachers/dcasey/0F7D41DD-00870BC8.136/mpm1d%20Exam%20Review.pdf" target="_blank">this</a> one).<br /><br />With about 20 minutes to go our peer tutor took over and had students reviewing some terminology. She created a crossword puzzle for them with a ton of terms. She did a great job. It was a good way for them to be reminded about some of the terms they may have forgotten about.<br /><br />I reminded students that they should be spending some time studying over the weekend. It's hard to believe that the semester is just about over.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/qDqMg9wUxi8" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2018/01/mpm1d1-day-85-exam-review.htmltag:blogger.com,1999:blog-2205963398207045749.post-47450283713369785792018-01-17T22:28:00.000-05:002018-01-17T22:30:07.875-05:00MPM1D1 - Day 83 & 84 Standardized Test DaysStudents wrote their standardized test today and will do the second part tomorrow. Some were nervous about writing. I told them not to be nervous and to just do their best (I know this is easier said than done). I'm very excited that they get the chance to show me what they've learned over the semester.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/BFHD6OAiCds" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2018/01/mpm1d1-day-83-84-standardized-test-day.htmltag:blogger.com,1999:blog-2205963398207045749.post-77298124887445864362018-01-16T19:46:00.000-05:002018-01-16T19:46:43.458-05:00MPM1D1 - Day 82 Final Day of EQAO PracticeToday is the final day before we write the EQAO test.<br /><br />We started with this warm-up at the boards in groups since a number of students said they were having a tough time with geometry.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-fJXwa-dUnbA/Wl6XL_048jI/AAAAAAAANL8/gbexUiSn_mwBjwoRnqcb0F2962ytB89rQCLcBGAs/s1600/Screen%2BShot%2B2018-01-16%2Bat%2B7.20.30%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="408" data-original-width="646" height="251" src="https://2.bp.blogspot.com/-fJXwa-dUnbA/Wl6XL_048jI/AAAAAAAANL8/gbexUiSn_mwBjwoRnqcb0F2962ytB89rQCLcBGAs/s400/Screen%2BShot%2B2018-01-16%2Bat%2B7.20.30%2BPM.png" width="400" /></a></div><br />There was some discussion about what the sum of the interior angles of different figures should add to. Once that was sorted out most groups proceeded fairly quickly.<br /><br />After the warm-up was done students could work on what they thought they needed to work on. Some worked in pairs, others put their headphones on and worked individually. There was a huge variety in the work that was happening. The vast majority of the class was really productive. I'm looking forward to seeing how they do tomorrow and Thursday.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/3e0VUb1QQ1o" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2018/01/mpm1d1-day-82-final-day-of-eqao-practice.htmltag:blogger.com,1999:blog-2205963398207045749.post-50669631454533341372018-01-15T23:21:00.000-05:002018-01-15T23:21:02.219-05:00MPM1D1 - Day 81 Multiple Choice Practice<div class="separator" style="clear: both; text-align: left;"> <span style="text-align: left;">I was pleasantly surprised today to see that a number of students had attempted some of the practice multiple choice question that I had sent to them on Friday.</span></div><div class="separator" style="clear: both; text-align: left;"><span style="text-align: left;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="text-align: left;">I had them start in groups working at the board on a few multi-step multiple choice questions. Here they are: </span></div><div class="separator" style="clear: both; text-align: left;"> </div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-rjkFu_THJl0/Wlz6EIuaDxI/AAAAAAAANLo/xhEkANF9wMs1YrH8-l77mTw0NpYdlTq6wCLcBGAs/s1600/mc1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="350" data-original-width="504" height="222" src="https://2.bp.blogspot.com/-rjkFu_THJl0/Wlz6EIuaDxI/AAAAAAAANLo/xhEkANF9wMs1YrH8-l77mTw0NpYdlTq6wCLcBGAs/s320/mc1.PNG" width="320" /></a></div><br /><hr /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-lEXFJXpvhyY/Wlz6EH-GSUI/AAAAAAAANLg/dag9jV38Dp4SatC3ZpGvxhLyZPdfIprAwCLcBGAs/s1600/mc2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="521" data-original-width="471" height="320" src="https://4.bp.blogspot.com/-lEXFJXpvhyY/Wlz6EH-GSUI/AAAAAAAANLg/dag9jV38Dp4SatC3ZpGvxhLyZPdfIprAwCLcBGAs/s320/mc2.PNG" width="289" /></a></div><br /><hr /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-b0OYYo_KtZs/Wlz6EPcNJAI/AAAAAAAANLk/6qlnFi7HCxon8GR58BKr4F_fcKmt3s4igCLcBGAs/s1600/mc3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="783" data-original-width="386" height="640" src="https://4.bp.blogspot.com/-b0OYYo_KtZs/Wlz6EPcNJAI/AAAAAAAANLk/6qlnFi7HCxon8GR58BKr4F_fcKmt3s4igCLcBGAs/s640/mc3.PNG" width="313" /></a></div><br /><hr /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-aJMM5oFmIrk/Wlz6Eh21FaI/AAAAAAAANLs/-PNL4oqcSqEZ6FvTJyVbeX3YaMo4jDgogCLcBGAs/s1600/mc4.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="538" data-original-width="486" height="320" src="https://1.bp.blogspot.com/-aJMM5oFmIrk/Wlz6Eh21FaI/AAAAAAAANLs/-PNL4oqcSqEZ6FvTJyVbeX3YaMo4jDgogCLcBGAs/s320/mc4.PNG" width="289" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><hr /><div class="separator" style="clear: both; text-align: left;">The reason for starting with these questions was to get students to realize that just because it's a multiple choice question doesn't mean that it's easy. I wanted them to see that there could still be multiple steps involved.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Once they were finished the warm-up questions they could choose to work on the<a href="https://docs.google.com/document/d/1q0sQzCoovGw8EYWGjqV6SAn4d0ztm_H6LVjPJ1YENB8/edit" target="_blank"> Opens Response</a> questions from the other day or to practice the <a href="http://sine-of-the-times.blogspot.ca/2018/01/mpm1d1-day-80-eqao-multiple-choice.html" target="_blank">multiple choice quizzes</a> in D2L. Most students chose to complete the online quizzes but a few worked on the open response questions. I think my favourite part about this time of year is watching students help each gain a better understanding of the content. There seems to be so much transferring of knowledge. It's exciting to watch.</div><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/jcBPdQTQLPc" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2018/01/mpm1d1-day-81-multiple-choice-practice.htmltag:blogger.com,1999:blog-2205963398207045749.post-11622070897743933682018-01-13T09:07:00.003-05:002018-01-13T09:07:36.799-05:00MPM1D1 - Day 80 EQAO Multiple Choice QuestionsThe buses were cancelled today. The plan had been to work through some of the EQAO practice multiple choice questions. From the bank of released questions over the past few years, I created a question library in D2L. From there I created a quiz that randomly selects questions from each of the strands. Students can do the quiz, see how they did and repeat. Every time they do the quiz they get a different set of questions.<br /><br />I fired off an email to all students first thing in the morning showing how they could access the quiz along with a video showing how to do it. Unfortunately, not many of them took the opportunity to try, but hopefully more will over the weekend.<br /><div style="text-align: left;"><br /></div><div style="text-align: left;"><a href="https://drive.google.com/open?id=135PIRIiPyVbJWqsletQsIkVgV8mrXhii" target="_blank">Here's</a> a link to the file containing the quiz if you'd like to import it into D2L. I'm hoping to add more questions as I have time. Below is a video showing how import the quiz.</div><div style="text-align: center;"><br /></div><div style="text-align: center;"><iframe allow="autoplay; encrypted-media" allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/Zmspm8UvTPk" width="560"></iframe></div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/c1vEhc-gT3k" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2018/01/mpm1d1-day-80-eqao-multiple-choice.htmltag:blogger.com,1999:blog-2205963398207045749.post-18606501408751043862018-01-11T22:39:00.001-05:002018-01-11T22:39:12.539-05:00MPM1D1 - Day 79 Open Response QuestionsOur class writes the provincial assessment (<a href="http://www.eqao.com/en" target="_blank">EQAO</a>) next Wednesday and Thursday. So the next few days will be spent practicing and preparing for the test. I always struggle with how to structure these days. On the one hand I want students to be able to focus on what they think they need work on, but on the other hand some students can't seem to handle the independence. I also want them to be able to work with the person(s) that they feel they work with best. The downside is that there may be a disconnect between someone a student chooses to work with and the person they work best with.<div><br /></div><div>In any case we started today all working on the same open response question (perhaps from last year's test?). It's one that was not that different from one of yesterday's test questions.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-h-O2HB5s2aM/WlgsLhm4TZI/AAAAAAAANK0/bq71_L5e1Ts_Fpx_3pMyMuPpCllUHhDKACLcBGAs/s1600/Screen%2BShot%2B2018-01-11%2Bat%2B10.31.18%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="234" data-original-width="600" height="155" src="https://2.bp.blogspot.com/-h-O2HB5s2aM/WlgsLhm4TZI/AAAAAAAANK0/bq71_L5e1Ts_Fpx_3pMyMuPpCllUHhDKACLcBGAs/s400/Screen%2BShot%2B2018-01-11%2Bat%2B10.31.18%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 gave everyone enough time to finish the question and then we wrote up a complete and well communicated solution so that students had an exemplar of what would was expected for these types of questions.</div><div><br /></div><div>Once we were done I gave them access to <a href="https://docs.google.com/document/d/1q0sQzCoovGw8EYWGjqV6SAn4d0ztm_H6LVjPJ1YENB8/edit?usp=sharing" target="_blank">this</a> document with another twenty four open response type questions. As might be expected, some students worked very effectively, while others could have made better use of their time.</div><div><br /></div><div>More practice tomorrow.</div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/RVIfIotYBto" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2018/01/mpm1d1-day-79-open-response-questions.htmltag:blogger.com,1999:blog-2205963398207045749.post-56406940049523878712018-01-10T22:58:00.001-05:002018-01-10T22:58:29.385-05:00MPM1D1 - Day 78 Cycle 4 TestWe finally had the chance to write our last test. I feel like it would have gone better had we done it before the holidays. I guess we'll see how it goes.<br /><br />A number of students came into class with some good questions about problems they worked on from the review. A couple of students asked questions that made me a little nervous.<br /><br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/qSysKoGeLrs" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2018/01/mpm1d1-day-78-cycle-4-test.htmltag:blogger.com,1999:blog-2205963398207045749.post-77065387559635635752018-01-09T22:13:00.000-05:002018-01-09T22:13:17.708-05:00MPM1D1 - Day 77 Test ReviewI changed my mind about how we were going to review today about thirty minutes before class started. I threw together some questions that would be representative of the questions on tomorrow's test. I had students work in groups on the board on these questions. I decided not to do a warm-up today so they could have lots of time to work on the questions.<br /><br />There were some great discussions and arguments about how to do certain questions. There was also lots of peer teaching/coaching, which was great to see.<br /><br />An entire period to be focused was tough. Some groups started to loose their focus with fifteen minutes to go.<br /><br /><a href="https://drive.google.com/open?id=14Ma0hiI6b_HCWpDzLINEwQvy06KPjTnWeFaWOkmVh9M" target="_blank">Here</a> are the questions they worked on.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/ctNYAJfVoC0" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2018/01/mpm1d1-day-77-test-review.htmltag:blogger.com,1999:blog-2205963398207045749.post-30678215761592532512018-01-08T22:25:00.000-05:002018-01-08T22:25:00.400-05:00MPM1D1 - Day 76 EQAO Practice & ReviewI struggled a little with what to do on the first day back after the holidays. We were supposed to write a test the day before the holidays but the buses were cancelled. Writing the test on the first day back after two weeks off would be a bad idea. I wanted students to review but I figured if I let them study on their own that the period might not be that productive.<br /><br />As much as I wanted to get started right away a number of students had lots of questions. Questions about when our test would be, the details about the<a href="http://www.eqao.com/en/assessments/grade-9-math" target="_blank"> EQAO test</a> as well as questions about the exam. I spent way too long talking about what the next couple of weeks look like and then we got to work.<br /><br />The warm-up, at the boards in groups, was this visual pattern:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-VoRzOABwfMk/WlQyGKDBCeI/AAAAAAAANKg/gsH6QBKx8xUBoVWw-L4AmtzcveaJfF2ZgCLcBGAs/s1600/vp48.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="155" data-original-width="382" height="129" src="https://3.bp.blogspot.com/-VoRzOABwfMk/WlQyGKDBCeI/AAAAAAAANKg/gsH6QBKx8xUBoVWw-L4AmtzcveaJfF2ZgCLcBGAs/s320/vp48.PNG" width="320" /></a></div>I asked them to find an equation for the volume of the n<sup>th</sup> term. Once they had finished that they were to do the same but for the surface area. I was very pleased at how quickly the groups got to work and how well they were able to get a solution and explain it. It seems that they haven't forgotten much over the holidays.<br /><br />After the warm-up they worked on the <a href="http://www.eqao.com/en/assessments/grade-9-math/assessment-docs/g9-academic-question-bklt-2017.pdf" target="_blank">multiple-choice questions </a>from last year's EQAO test (in groups at the board). This provided a good overview of much of the content that will appear on their final test of the year. There were some great discussions. It's nice to see them pull the course content together like this.<br /><br />Most groups only made it about halfway through these questions so we'll finish them up tomorrow.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/hkE-of4celQ" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2018/01/mpm1d1-day-76-eqao-practice-review.htmltag:blogger.com,1999:blog-2205963398207045749.post-3570444027960502182017-12-22T21:53:00.001-05:002017-12-22T21:53:38.497-05:00MPM1D1 - Day 75 Snow DayThe buses were cancelled today and as a result I had very few students show up. I did have one girl email me to see if she could write her test today. She came, got some help with a few things and wrote her test. Good for her.<br /><br />I did have a number of struggling students request some extra work to do over the holidays. I was impressed with their desire to improve. So I sent them some work.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/-tpsK8laOLc" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-75-snow-day.htmltag:blogger.com,1999:blog-2205963398207045749.post-69112346341771499132017-12-21T22:44:00.003-05:002017-12-21T22:44:59.964-05:00MPM1D1 - Day 74 Test ReviewWe started today by looking at these two objects that were printed yesterday.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-hRaKJMIAtjA/Wjx6e6-HVNI/AAAAAAAANIo/9FTjtuSgUUMsfsA5w2HOzdulqDpOe3-RACLcBGAs/s1600/IMG_0523.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="800" data-original-width="1600" height="200" src="https://4.bp.blogspot.com/-hRaKJMIAtjA/Wjx6e6-HVNI/AAAAAAAANIo/9FTjtuSgUUMsfsA5w2HOzdulqDpOe3-RACLcBGAs/s400/IMG_0523.JPG" width="400" /></a></div><br />The goal was to consolidate some of yesterday's work and to reinforce one of yesterday's big ideas. Because of the work my students had done with their pentominoes, they knew that each pentomino was made up of five cubes. The cubes on the small pentominoes were 0.5 cm in all direction and the cubes on the large one were 1 cm in all directions. So, I asked how many times bigger the volume of the larger one was compared to the smaller. I received a couple of answers of 2 (which I expected), an answer of 4 (with the justification that that's what they found yesterday) and an answer of 8. I held the figures up and asked if anyone thought it would only take two of the little ones to fit into the bigger one. Strictly by intuition everyone knew that 2 couldn't be the answer. One student offered up an explanation of doubling in more than one dimension. At this point we jumped into a bit of algebra and looked at an expression for the volume of a cube that was x units long and compared that expression to one for a cube that had a length of 2x.<br /><br />The large figure in the picture is a model of an original that is twice the size, in all dimensions. I asked how many of the little ones would fit in the giant one.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-z-n2Ky2AGgg/Wjx-a8v2x_I/AAAAAAAANI0/0JK5Rgzi3_gDzktm3RKiG-MIkE457HwmwCLcBGAs/s1600/Screen%2BShot%2B2017-12-21%2Bat%2B10.38.58%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="256" data-original-width="532" height="191" src="https://2.bp.blogspot.com/-z-n2Ky2AGgg/Wjx-a8v2x_I/AAAAAAAANI0/0JK5Rgzi3_gDzktm3RKiG-MIkE457HwmwCLcBGAs/s400/Screen%2BShot%2B2017-12-21%2Bat%2B10.38.58%2BPM.png" width="400" /></a></div><br />There was some discussion about 16 vs. 64, but eventually we settled on 64 (supported with some algebra). Once the relationship for volume was squared away we quickly touched on the relationship for surface area.<br /><br />It was a good, fun discussion that I think made a lot of sense because of the manipulatives on hand, that were made by the students.<br /><br />After the warm-up we wrote a mastery test on equations of lines then students continued working on the <a href="https://drive.google.com/open?id=1zR_c7fNg07QagDBzr7zPeB2SvFJcs5EDbmMiGsmFEq8" target="_blank">review</a> for their test tomorrow.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/hZ_EpkadC04" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-74-test-review.htmltag:blogger.com,1999:blog-2205963398207045749.post-36299893939822925292017-12-20T20:26:00.001-05:002017-12-20T20:26:40.212-05:00MPM1D1 - Day 73 Finishing Up 3D PrintingToday we picked up right where we left off yesterday with the <a href="https://docs.google.com/document/d/1dAudQrscL8XCSj36fIn0VgHapryJqCR2ZluM0vaD7Uc/edit" target="_blank">pentomino activity</a>. We fired up the 3D printer and started printing right away. Groups that hadn't finished the calculations from yesterday kept working away. They stumbled a little with the different units but eventually most of the groups figured things out. We printed one figure after another but eventually ran out of time. I'll get the others printed at some point.<br /><br />Once groups were done I gave a review for them to work on to prepare for this week's test. I was hoping to do the test Thursday, but after things didn't go well yesterday I figured they would need an extra day. So, yes we are having a test on the last day before the holidays. It's not ideal, but I figure it's better than doing the test Thursday or after the holidays.<br /><br />Generally, most students worked well today, either on the pentominoes assignment or the review. There was also a fair bit of excitement when a group's pentomino began printing.<br /><br />During the printing process today I remembered that prints were not solid plastic. They are infilled with either a hexagonal pattern or a rectilinear pattern. I'll have to do some research to see what percentage we were infilling. This actually adds another layer to the assignment. The more I think about it, the more I think this activity would make a great culminating activity.<br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/GjJif3UiITY" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-73-finishing-up-3d-printing.htmltag:blogger.com,1999:blog-2205963398207045749.post-1798174875668168142017-12-19T22:35:00.000-05:002017-12-19T23:07:36.022-05:00MPM1D1 - Day 72 Surface Area, Volume & 3D PrintingI had seven students away yesterday so I spent some time at the beginning of the period recapping what we did yesterday. Once the recap was done we moved right into some volume and surface area.<br /><br />My own kids have a pentomino based game called <a href="http://en.gigamic.com/game/katamino" target="_blank">Katamino</a>. It's a fun game that really stretches your spatial reasoning skills.<br /><div style="text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-oQnHtIxp33g/WjnQTdEnzgI/AAAAAAAANIE/kZaD992zxkEjpxYH1ivrXxSopTmntXOQgCLcBGAs/s1600/Screen%2BShot%2B2017-12-19%2Bat%2B9.41.34%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="209" data-original-width="492" height="168" src="https://3.bp.blogspot.com/-oQnHtIxp33g/WjnQTdEnzgI/AAAAAAAANIE/kZaD992zxkEjpxYH1ivrXxSopTmntXOQgCLcBGAs/s400/Screen%2BShot%2B2017-12-19%2Bat%2B9.41.34%2BPM.png" width="400" /></a></div><div style="text-align: left;"><br /></div><div style="text-align: left;">I thought it would be fun to make this game the basis for an assignment. If you don't have the game you could always modify the assignment to work with any pentominoes or even have students build their own figures using linking cubes.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">The gist of the lesson is that students get a pentonmino and calculate its surface area and volume. Then they create a scale diagram of a pentomino that is half the size (in all dimensions) of their original pentomino. They calculate the surface area and volume of their model and make note of the relationship between the original and the half-sized model.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">They were given the length of a spool of filament (in metres), the diameter of the filament (in millimetres) and the cost of the spool and they needed to determine the cost of their pentomino. Once they had done all of that they designed their pentomino in <a href="https://www.tinkercad.com/" target="_blank">TinkerCAD</a>. The designing was pretty simple and didn't take long at all. Once their design was complete they were able to print on the 3D printer.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">This was meant to be a bit of a fun lesson but for whatever reason many students didn't seem to be into it. I had students working in pairs which is not something we normally do. They also weren't working at the board. Some students spent a lot of time fidgeting with the pentomino (I thought fidget spinners were so last year?), others watched as their partner did the work. One group took 30 minutes just to get their measurements, despite repeated calls to get going. I think next time I need to get groups to do their work at the whiteboards and maybe I need to be explicit about how they could split up their work. Maybe groups of three would have been better than pairs. I'll have to rethink the logistics of this one.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">Having said that I had two groups print today. They did a great job and were pretty excited about the result. I had one more group that finished everything except for the printing at lunch. They will print first thing tomorrow. We will finish up tomorrow. I'm looking forward to trying this again to see how it goes.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-zxRcUVyy1sY/Wjnh0BtheBI/AAAAAAAANIU/K_WgPh25bKoD1rOeC3DYrMFMjCU20BJZwCLcBGAs/s1600/IMG_0516.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://4.bp.blogspot.com/-zxRcUVyy1sY/Wjnh0BtheBI/AAAAAAAANIU/K_WgPh25bKoD1rOeC3DYrMFMjCU20BJZwCLcBGAs/s400/IMG_0516.JPG" width="298" /></a></div><br /></div><div style="text-align: left;"><a href="https://drive.google.com/open?id=1dAudQrscL8XCSj36fIn0VgHapryJqCR2ZluM0vaD7Uc" target="_blank">Here's</a> a description of the task. This task could also be used in an MFM2P class. I've also modified the task to fit the MBF3C course. You can find that <a href="https://drive.google.com/open?id=1P55qylEZY5sNtB_6eP_c_gs24_Ifr1MDMad2HgpycaQ" target="_blank">here</a>. <a href="https://youtu.be/_B3DvPTO3ZE" target="_blank">Here</a> is a link to a quick introduction to TinkerCAD.</div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/_Cfv5NDPrTM" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-72-surface-area-volume-3d.htmltag:blogger.com,1999:blog-2205963398207045749.post-13933765503724147532017-12-18T22:15:00.000-05:002017-12-18T22:15:01.958-05:00MPM1D1 - Day 71 Rearranging FormulasWe started today practicing solving equations with fractions as groups at the whiteboards. Here we the warm-up questions.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-94I0YB5E7wI/WjiBx7k8gAI/AAAAAAAANHo/i62q7j-osb8kPpHpExvl9jqBqpdJ6JofACLcBGAs/s1600/equations%2Bwith%2Bfractions.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="422" data-original-width="591" height="227" src="https://1.bp.blogspot.com/-94I0YB5E7wI/WjiBx7k8gAI/AAAAAAAANHo/i62q7j-osb8kPpHpExvl9jqBqpdJ6JofACLcBGAs/s320/equations%2Bwith%2Bfractions.PNG" width="320" /></a></div>There weren't any problems with the first question. There were a couple of problems with the second one and more problems with the third. We spent some time working through the issues. Some groups wanted more questions to practice with so I had them make up their own and go from there.<br /><br />Once everyone seemed comfortable solving these equations we moved on to rearranging formulas. I posted a few on the board and let them get to work. Here are the questions they started with.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-dcS-HRGWaiU/WjiC_FzNTEI/AAAAAAAANH0/vC50DAdzIm4AKHHPqjRnFZxs4VdKC_1_ACLcBGAs/s1600/formulas.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="380" data-original-width="604" height="200" src="https://2.bp.blogspot.com/-dcS-HRGWaiU/WjiC_FzNTEI/AAAAAAAANH0/vC50DAdzIm4AKHHPqjRnFZxs4VdKC_1_ACLcBGAs/s320/formulas.PNG" width="320" /></a></div><br />The most challenging one here seemed to be part c. For groups that struggled I gave them an example where y, m and b were given and asked them to solve for x. They had no trouble doing so, so I asked them to replace the numbers with variables. That seemed to be enough to get them going.<br /><br />Once groups were done I gave them some <a href="https://lkueh.files.wordpress.com/2014/03/lesson-6-rearranging-formulas-worksheet.docx" target="_blank">questions</a> to practice.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/s2XZVifhk3w" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/12/mpm1d1-day-71-rearranging-formulas.htmltag: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.html