tag:blogger.com,1999:blog-22059633982070457492017-10-18T14:52:08.180-04:00Sine Of The TimesA Math Teacher's JourneyDave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.comBlogger96125SineOfTheTimeshttps://feedburner.google.comtag:blogger.com,1999:blog-2205963398207045749.post-57944993887554586802017-10-17T23:55:00.001-04:002017-10-18T00:00:02.998-04:00MPM1D1 - Day 29 Interior & Exterior Angles<div class="separator" style="clear: both; text-align: left;">I started by having groups up at the board working on this Would You Rather problem.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://www.wouldyourathermath.com/would-you-rather-10/" target="_blank"><img border="0" data-original-height="480" data-original-width="640" height="300" src="https://4.bp.blogspot.com/-2FFX2-_SQ04/Wea_mnh4JeI/AAAAAAAAMzk/-M1wGnidimEEYHvWBbPS3Xsevcc_VqkyACLcBGAs/s400/untitled-drawing2.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;">This was the first time we've worked at the board in a little while. There were a number of people who were quite off task. Others got to work right away but the group dynamics were not what they should have been. Once they were done the activity I sent them back to their seats and we talked about contributing effectively to a group and how it benefits everyone in the group.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The main event for today was some geometry, specifically interior and exterior angles of polygons. I put the image below up on the board and asked students to work at the whiteboards to see how they would do without any instruction. </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/-mGhS8O98pNk/WebGYyg3AXI/AAAAAAAAMz0/pWg0sZ8WrVgft2DXuUnuL2Is4Xo3e1edQCLcBGAs/s1600/missing%2Bangles.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="715" data-original-width="700" height="640" src="https://3.bp.blogspot.com/-mGhS8O98pNk/WebGYyg3AXI/AAAAAAAAMz0/pWg0sZ8WrVgft2DXuUnuL2Is4Xo3e1edQCLcBGAs/s640/missing%2Bangles.PNG" width="625" /></a></div><div class="separator" style="clear: both; text-align: left;">The group work was much better this time around and all groups were able to answer all of the questions. A few groups needed some reminders about supplementary angles and a couple asked about opposite angles. They were doing great.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I brought them back together as a group and we summarized the different types of triangles, supplementary angles, opposite angles and began exploring the sum of interior angles. Everyone knew that the interior angles in a triangle sum to 180° so we began looking at other polygons. We did this by looking at the number of triangles in each polygon:</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/-VWRjvHXoyrA/WebLRUh_11I/AAAAAAAAM0E/hm6qpdHKavgr9HhJkmjJdgYsAPCRX4y4wCLcBGAs/s1600/polygons.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="145" data-original-width="497" height="116" src="https://3.bp.blogspot.com/-VWRjvHXoyrA/WebLRUh_11I/AAAAAAAAM0E/hm6qpdHKavgr9HhJkmjJdgYsAPCRX4y4wCLcBGAs/s400/polygons.PNG" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: left;">From this they were able to determine the sum of the interior angles. Next I had them fill out the table below to come up with an equation.</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/-0Jd5EeBfPxA/WebLqCVfFII/AAAAAAAAM0M/Dc_QSO-vwpssDgDA13ZeP9Hje7yVPpD8gCLcBGAs/s1600/number%2Bof%2Bsides.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="279" data-original-width="421" height="265" src="https://1.bp.blogspot.com/-0Jd5EeBfPxA/WebLqCVfFII/AAAAAAAAM0M/Dc_QSO-vwpssDgDA13ZeP9Hje7yVPpD8gCLcBGAs/s400/number%2Bof%2Bsides.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;">We've done enough visual patterns that to many this process came easily. They had no trouble finding the rate but had to think a bit about the initial value. I had a couple of different results which was neat. The most common was that the sum of the interior angles = 180n-360 and the other was that the sum of the interior angles = 180(n - 2). It was exciting to see these different results.</div><div class="separator" style="clear: both; text-align: left;"><br /></div>We had just enough time to look at exterior angles. To do so I showed this video: <br /><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/rgCJJhRh0S0?rel=0&start=20&end=88" width="560"></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;"><br /></div><div style="text-align: center;"><br /></div> We had a few minutes left which was enough time for me to handout the <a href="https://drive.google.com/file/d/0B7qPrwcXw6-Ba0ZVcWZIdWZvc2M/view?usp=sharing" target="_blank">work</a> for the day.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/F9mdqCZw5SA" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/10/mpm1d1-day-29-interior-exterior-angles.htmltag:blogger.com,1999:blog-2205963398207045749.post-89574467032275470372017-10-16T22:39:00.000-04:002017-10-16T22:39:48.854-04:00MPM1D1 - Day 28 WODB, Tables of Values & Equations of LinesWe started with this <a href="http://wodb.ca/" target="_blank">Which One Doesn't Belong</a>:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-zeAhtP8JIE8/WeViSfUgThI/AAAAAAAAMzU/SwBZRZO7HC0wam61bVQK9rYhxpyNNiJYwCLcBGAs/s1600/wodbG8.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="522" data-original-width="518" height="400" src="https://3.bp.blogspot.com/-zeAhtP8JIE8/WeViSfUgThI/AAAAAAAAMzU/SwBZRZO7HC0wam61bVQK9rYhxpyNNiJYwCLcBGAs/s400/wodbG8.PNG" width="396" /></a></div><br />I figured that this would be a bit of a challenge. I knew that students would be able to look at the equations and pick some characteristics out (which they did). I also knew that my students see these four equations differently than I do. When I see these equations I picture the graphs. My students can't do that yet. We've done a lot of graphing of equations but most of that graphing was with scenarios that are concrete and have some meaning. These equations are very abstract.<br /><br />In any case, I put this up to see what would happen. Right away one student asked for graph paper. Others then started asking if they had to graph it. I told them that they didn't have to. Many said "Wait! What? I don't know how to graph that." I gave them a bit of time to think this one through. I helped a few students who really wanted to be able to graph. We took it up and had some great discussions. I had some superficial type answers (the first one doesn't have a number added or subtracted). I thought I would be disappointed with these types of answers but I really wasn't because each of them led to some talk (led by other students) about what those parts of the equation are, what that means about the relationship and what it means about the graph. The discussions were fantastic. Some of the students were having a hard time connecting all the pieces but it's a conversation we can revisit throughout the semester.<br /><br />This seemed to be a good time to discuss how we can graph a relationship using a table of values. This was a bit of a leap for some students, which surprised me given the number of visual patterns that we've done and the number of times we've graphed those patterns. I think had I told them that each equation came from a certain pattern, and given the pattern, they would have been fine. We took a step up the ladder of abstraction and talked about how we can create a table of values and plot those point. We did this, together, for the equation in the upper left and then they worked on the one in the bottom right. Did I mention this was just the warm-up? #longestWarmUpEver?<br /><br />With the warm-up behind us we could move onto connecting slopes, y-intercepts and equations of lines. As it turns out we already had some equations, tables and graphs on the board. We talked about how to find the slope and y-intercept from the graph, from the table and finally they told me how to find them from the equation. My favourite comment of the day: "You mean we can just look at the equation and get slope and y-intercept? We don't have to graph it or make a table?" I think there was some incentive to understand y=mx+b.<br /><br />I gave them the first two pages of <a href="https://docs.google.com/document/d/1T3cGeSOCgUksuHuGv6zgXwN6pfM2eWhlh9oXLB-hSh0/edit?usp=sharing" target="_blank">this handout</a> (thanks @<a href="https://mrhoggsclass.wordpress.com/page/2/" target="_blank">MrHoggsClass</a>). Once that was done I handed out some <a href="https://drive.google.com/open?id=0B7qPrwcXw6-BdjFZTkRpaC0zVVU" target="_blank">practice</a> on creating tables of values and equations of lines.<br /><br /><br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/CTDxTOmRmx4" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/10/mpm1d1-day-28-wodb-tables-of-values.htmltag:blogger.com,1999:blog-2205963398207045749.post-63093937997355351252017-10-15T19:24:00.000-04:002017-10-15T19:24:35.732-04:00MPM1D1-Day 27 Desmos Linear ActivitiesThe goal for today was to talk about slope. We started with the <a href="https://teacher.desmos.com/polygraph-lines" target="_blank">Polygraph: Lines</a> activity from Desmos. The idea is that they get paired up with another student in the class. One of them chooses a line from a list, the other asks questions that can be answered with a yes or no to help pick which graph their partner chose. It's basically Guess Who with lines. I wanted to start with this to see if students would use some of the vocabulary we've talked about. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-HduYKFCEAzk/WeEIJIJjxRI/AAAAAAAAMyw/Hk_BXxbWHGATAnPACJzge5dHVE85MtjSwCLcBGAs/s1600/polygraph.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="465" data-original-width="726" height="255" src="https://4.bp.blogspot.com/-HduYKFCEAzk/WeEIJIJjxRI/AAAAAAAAMyw/Hk_BXxbWHGATAnPACJzge5dHVE85MtjSwCLcBGAs/s400/polygraph.PNG" width="400" /></a></div><br />They started right away and got right into it. I saw the use of lots of terminology but not much about what we've talked about. I heard comments about corners rather than quadrants. I heard some reference to the origin. And more than once I saw "Is your line straight?". This one drove me crazy! When I asked "Isn't every line straight?" these students would reply with something along the lines of "Yes, but I mean like this", indicating that they were talking about a vertical or horizontal line. We'll keep plugging away at the terminology.<br /><br /> I let them play a round or two then brought them back together as a class. I asked which types of questions they found helpful. I then reminded them of some terminology (slope (positive and negative), quadrants) then introduced some new terms for some (x and y-intercepts). They played again and their questions were much better. There were a couple of math fights about wrong answers to questions such as "You said it had a negative slope. That slope is positive."<br /><br />Once we'd had a bit of experience with the activity we moved onto <a href="https://teacher.desmos.com/activitybuilder/custom/5755ed8c0d942e9b07b65b98" target="_blank">Polygraph: Lines Part 2</a>. They worked through the activity, hopefully improving their vocabulary and understanding of lines. Some students we motoring through the work, others needed a little encouragaement.<br /><br />The last activity for the day was <a href="https://teacher.desmos.com/activitybuilder/custom/57f3dd9dcf3c849008d81007" target="_blank">Put the Point on the Line</a>, where students have to determine where a third point needs to go in order to be on a line with the other two. The best part about these activities is the teacher dashboard that allows me to see all the work my students have done, even after the fact. I can look the work over and see where the gaps are and then look at providing some assistance in those areas and I have a record that will allow me to see a student's growth over time.<br /><br />There are lots of other Desmos activities involving linear relations<a href="https://teacher.desmos.com/linear" target="_blank"> here</a>.<br /><br />Once they were done the activities we talked about finding the slope between two point on a graph. We've done this before but this was a good reminder. Then we moved into finding the slope without a graph. I gave them <a href="https://drive.google.com/open?id=0B7qPrwcXw6-BaUFlVllZMlpfNnM" target="_blank">this handout</a> to practice with. <br /><br /><br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/ILvM05LSmHk" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/10/mpm1d1-day-27-desmos-linear-activities.htmltag:blogger.com,1999:blog-2205963398207045749.post-22309779186973910052017-10-12T20:56:00.003-04:002017-10-12T20:56:54.464-04:00MPM1D1 - Day 26 Solving One & Two Step Equations I was away today so here's what I hope happened.<br /><br />As a lead-in to solving equations students were to work through some <a href="https://solveme.edc.org/Mobiles.html" target="_blank">Solve Me Mobiles</a> as a class. I left about 10 of them to try. I really like using these because the principles are the same as those used to solve equations but students see them as non-threatening puzzles. I guess part of the reason for this could be that the puzzles are very visual and there can be some trial and error. I guess they're not quite as abstract as an equation with letters as unknowns.<br /><br />After the warm-up students watched a video of me working through some examples of solving one and two step equations. After seeing the examples they had some equations to solve. I imagine that a good number of students were done early. If they finished early I'm hoping that they tried more Solve Me Mobiles on their phones.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/wdlmcmuwoWk" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/10/mpm1d1-day-26-solving-one-two-step.htmltag:blogger.com,1999:blog-2205963398207045749.post-77681370653250464202017-10-11T21:03:00.001-04:002017-10-11T21:03:48.323-04:00MPM1D1 - Day 25 Graphing Stories & Collecting Like TermsAs part of Global Math Week I thought I'd start today with the <a href="https://www.youtube.com/watch?v=vh5-U37UWWU" target="_blank">International Math Salute</a>. I had students stand up, put their arms out from, cross their right arm over their left, put their palms together then untwist.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-O4oweaaAL6Q/Wd6-pDfQNoI/AAAAAAAAMyg/zLSqyZl1CgYowWseK2eWcb-K_np_wSkdQCLcBGAs/s1600/image%2B%25281%2529.jpeg" 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/-O4oweaaAL6Q/Wd6-pDfQNoI/AAAAAAAAMyg/zLSqyZl1CgYowWseK2eWcb-K_np_wSkdQCLcBGAs/s400/image%2B%25281%2529.jpeg" width="400" /></a></div><br />The look on their faces as their hands ended in a twisted mess was priceless. I did it a couple of times. Some students said that they had figured it out but they couldn't seem to reproduce it. There were some great conversations going on.<br /><br />Next, I handed out individual whiteboards so that students could sketch graphs of some <a href="http://graphingstories.com/" target="_blank">Graphing Stories</a>. We did the first two stories. The first one was a bit of a challenge given that students were graphing time vs. time. They struggled with this idea but after the first few seconds of the video they figured out what was going on. I let them create a graph then we reiterated some of the terminology. We talked about continuous vs. discrete data, partial vs. direct variation, interpolation vs. extrapolation, slope. These were all terms that we've seen before but based on last week's test many students still need practice with the terminology. We'll do a few more of these at some point.<br /><div><br /></div><div>The goal for today's lesson was to look at adding and subtracting like terms. We started by watching this video:</div><div><br /></div><div style="text-align: center;"><iframe allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/US95J1g6iY4" width="560"></iframe></div><div style="text-align: center;"><br /></div><div style="text-align: left;">I was kind of surprised at how entertaining they found the video. After watching the video I asked if there would have been an easier way to place the order? Someone suggested that we group all of the similar items together and add them up. What a great idea!</div><div style="text-align: left;"><br /></div><div style="text-align: left;">We talked a little about some terminology: terms, polynomials, monomials, binomials, like terms. We took a note on adding and subtracting like terms then I gave them a handout for some practice. I think the 'you can't add a burger and a Coke together' idea really helped some of them understand the idea of only adding (and subtracting) like terms.</div><div><br /></div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/4PdP5CE1_p8" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/10/mpm1d1-day-25-graphing-stories.htmltag:blogger.com,1999:blog-2205963398207045749.post-24160802386680015912017-10-10T20:49:00.000-04:002017-10-10T20:49:07.734-04:00MPM1D1 Day 24 Water Line & Distance-Time GraphsToday we started our second cycle. For the warm-up we looked at a non-linear pattern for the first time (Visual Pattern #1).<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://www.visualpatterns.org/" target="_blank"><img border="0" data-original-height="146" data-original-width="406" height="143" src="https://4.bp.blogspot.com/-7v3qV_6es40/Wd1hklEZ6aI/AAAAAAAAMxw/pHbQ8W8kE_s4YtMePWQrPubEA0kasrFqACLcBGAs/s400/Screen%2BShot%2B2017-10-10%2Bat%2B8.10.34%2BPM.png" width="400" /></a></div><br />The goal was to find out how many square were in the forty-third step and to come up with a general equation for the number of squares in the nth step. It was interesting to see the approach given that we've done so many linear patterns. Most groups created a table of values and found the pattern. They realized that the values weren't going up by the same amount. They were so accustomed to finding the first difference (though we haven't called it that yet), using that as the multiplier in the equation then finding the initial value. Some groups abandoned the idea of using the differences and instead starting looking at how the pattern actually grows from step to step (using the dimensions of the squares). Most groups that did this had no trouble finding an equation. For those that finished early I asked them to determine a rule for the number of toothpicks in each step. For the groups that didn't look at the dimension of the squares, things started to get difficult. They knew that they needed to add two more to what they added in the previous step but they couldn't figure out a way to do that in an equation. We'll do a few more of the quadratic patterns and I'm sure they will get better at them.<br /><br />Once the warm-up was complete I meant to talk about distance-time graphs with motion sensors but I forgot. Instead I moved right into <a href="https://teacher.desmos.com/waterline" target="_blank">Water Line</a>.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-1z1sJz1shL4/Wd1nq81RazI/AAAAAAAAMyA/1zhj0t-3_mwGHWd1yoyexbMDJkTk_wVnQCLcBGAs/s1600/IMG_0407.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://4.bp.blogspot.com/-1z1sJz1shL4/Wd1nq81RazI/AAAAAAAAMyA/1zhj0t-3_mwGHWd1yoyexbMDJkTk_wVnQCLcBGAs/s400/IMG_0407.JPG" width="400" /></a></div><br />It's a great activity that allows students to graph the height of water in a glass over time. Immediate feedback is built right in as students click the play button to see if their graph matches the real life situation. The activity couldn't have gone any better. Students were working hard and some expressed how much fun they were having. Imagine, having fun in a math class! The best part seemed to be making their own glasses and trying to create a graph for their classmates' glasses.<br /><br />After the Water Line activity we moved onto discussing distance-time graphs. What does it look like when you move towards a sensor, away from it, at a constant rate, speeding up, slowing down, etc. Then they practiced with this <a href="https://drive.google.com/open?id=0B7qPrwcXw6-BX2FFNFZZU2Vnams" target="_blank">handout</a>.<br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/-lqAMoN1st8" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/10/mpm1d1-day-24-water-line-distance-time.htmltag:blogger.com,1999:blog-2205963398207045749.post-86521640259804630392017-10-09T19:57:00.001-04:002017-10-09T19:57:05.791-04:00MPM1D1 - Day 23 Test DayWe wrote our first test on Friday. Many students seemed quite nervous as they started. I get excited on test days. I'm excited for students to show me what they have learned. If you're looking for a sports analogy, test day is like game day. We've spent all this time practicing and improving and I'm looking forward to seeing how much my students have improved.<br /><br />As the test progressed I had questions such as "What does this mean?" and "How do I do this?". I told students to try their best. We had talked before the test about how it was important to write something down for every question. I was happy that for the most part they did. Some students need to work a little on presenting our solutions in a manner that's easy to follow.<br /><br />I think that by the end of the test students had a good idea of what they needed work on before the next test. I'm hopeful that this will provide them with some focus for our upcoming work.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/0Z_ZTcCcthg" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/10/mpm1d1-day-23-test-day.htmltag:blogger.com,1999:blog-2205963398207045749.post-70280845942772183312017-10-05T22:32:00.000-04:002017-10-05T22:32:19.803-04:00MPM1D1 Day 22 ReviewToday was a day for students to work through a <a href="https://drive.google.com/open?id=1suyCyCgyzix7b4Q2EpUR9nxxQMUpSK3EqZmoZ9NrDpI" target="_blank">review package</a> to prepare for their test tomorrow. Before they started I answered a bunch of questions about the test, such as "How long is it?" to which I gave my standard response "11 inches". I could have told them it was 8.5 inches wide but they didn't seem interested.<br /><br />The room was just buzzing the entire period. Everyone was working on different things in different ways. Some students put their headphones on and worked on their own, others worked on problems but checked with a group member if they got stuck and a few worked on questions as a group. Some students started on the first question and worked through the questions in order while others focused on the content they felt least confident about. There were some great discussions and some excellent peer teaching. I'm hoping for good things tomorrow.<br /><br />I offered to run an online tutorial tonight through Adobe Connect. As it turns out I didn't have anybody show up. I wonder if that's because they forgot, didn't need it or had technical difficulties. I was unable to login on my Windows machine but had no issues on my Mac or iPad. I guess I'll find out tomorrow.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/U-u6sgYznmk" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/10/mpm1d1-day-22-review.htmltag:blogger.com,1999:blog-2205963398207045749.post-42332810840960363262017-10-04T23:03:00.001-04:002017-10-04T23:03:55.650-04:00MPM1D1 - Day 21 Mowing the LawnToday's warm-up was an Estimation 180 problem. Students had to estimate what percent of the pie was missing as well as the angle formed by the missing piece.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://www.estimation180.com/day-112.html" target="_blank"><img border="0" data-original-height="768" data-original-width="1024" height="300" src="https://2.bp.blogspot.com/-PZdT1zzhoDk/WdWZ7W4cFaI/AAAAAAAAMsQ/exuifv5jjF8gXAvXO521gbmk55f1N14yACLcBGAs/s400/pi.jpg" width="400" /></a></div><br />There was a lot of good discussion. It was interesting to see most students talking about fractions first (half, a quarter, etc) then converting those fractions to percents mentally. The percent estimates were pretty good, the degrees were not as good.<br /><br />The main event for today was <a href="https://tapintoteenminds.com/3act-math/mowing-the-lawn/" target="_blank">Mowing the Lawn</a>. We've done a lot of group work this semester (which has been great) but as we approach the test I want to ensure that students are able to think, work and communicate on their own. I want them to take on more responsibility for their learning. So I asked them to work through this one on their own at their desks. They got to work right away. There were a number of different approaches being used it was a busy period. There were some great conversations about different approaches. I was hoping they would all finish during the period (and many did) but we were interrupted by a fire drill. Those that finished started working on the review for the test. The rest will (hopefully) finish up for homework.<br /><br />Our test is Friday and I feel that some students aren't going to be ready. I've had very few come to see me for extra help at lunch. In the past I've run some evening online tutorials but they have been mostly with senior students. I thought I'd give it a try with this group and see what the response is like. More details to come.<br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/cHA6rfXlYA8" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/10/mpm1d1-day-21-mowing-lawn.htmltag:blogger.com,1999:blog-2205963398207045749.post-90484769548093298142017-10-03T23:22:00.000-04:002017-10-03T23:22:01.567-04:00MPM1D1 - Day 20 Percents & Footprint Data CollectionWe started with a visual pattern today.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-P8hLcEppdkk/WdRRBFJEtwI/AAAAAAAAMrs/di1QGrcknboMsiYkaaDgL8bnXDTIJzOVQCLcBGAs/s1600/vp11.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="186" data-original-width="577" height="128" src="https://4.bp.blogspot.com/-P8hLcEppdkk/WdRRBFJEtwI/AAAAAAAAMrs/di1QGrcknboMsiYkaaDgL8bnXDTIJzOVQCLcBGAs/s400/vp11.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;">All groups came up with the equation and the number of stars in the 43rd step pretty quickly. I sent them back to their seats and had them write up a solution. I explained that I didn't just want an answer, I wanted an explanation of how they got the solution. I collected their work and had a look at it. Some did an amazing job with their explanations, others could use some work.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">We did a quick note summarizing percents (converting to and from decimals and fraction, finding percentages, etc.) and I asked them to finish up the handout I gave out yesterday for homework (for those that hadn't finished already).</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Next up was collecting data and working on graphs for the <a href="https://drive.google.com/file/d/0B7qPrwcXw6-BMk9UWWtmemJjbEE/view" target="_blank">Footprint Assignment</a>. Most groups were very quick to get their measurements and getting started. For whatever reason some students seem to feel like they don't need to do any work if they're holding a metre stick. Odd.</div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/n4kUjpNjKRo" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/10/mpm1d1-day-20-percents-footprint-data.htmltag:blogger.com,1999:blog-2205963398207045749.post-20408242165731002132017-10-02T21:19:00.000-04:002017-10-02T21:19:35.452-04:00MPM1D1 - Day 19 SunflowersWe started with this problem:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/--E7IZswOmAg/WdLh4AqQAzI/AAAAAAAAMrA/bu_VabUhCns8IB3SDeJUsqwzfvr9V_ooACLcBGAs/s1600/which%2Bis%2Bbigger.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="224" data-original-width="407" height="176" src="https://4.bp.blogspot.com/--E7IZswOmAg/WdLh4AqQAzI/AAAAAAAAMrA/bu_VabUhCns8IB3SDeJUsqwzfvr9V_ooACLcBGAs/s320/which%2Bis%2Bbigger.PNG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"></div>I was surprised to see the approaches that students took for this one. I had expected most to convert the fractions to decimals or percents. One of the groups did that. The rest of the groups created equivalent fractions with common denominators and compared that way. It's nice to see the different approaches.<br /><br />Once the warm-up was complete we looked at some trouble spots from last week's assessment (everyone finally wrote it).<br /><br />We then moved onto the <a href="http://schools.alcdsb.on.ca/teachers/morrism/mfm1p/Lists/Calendar/Attachments/209/Sunflower%20Performance%20Task.pdf" target="_blank">Sunflower Task</a>. A few people weren't really sure where to start and some didn't really want to start. Eventually, everyone got going. The goal here was to make connections between the table, the graph and the descriptions of relationships.<br /><br />For those that finished early I gave out some percent practice. Tomorrow we'll go over percents to ensure that everyone has a good grasp.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/dxsaipDpyXM" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/10/mpm1d1-day-19-sunflowers.htmltag:blogger.com,1999:blog-2205963398207045749.post-14295770447030361492017-09-28T20:10:00.000-04:002017-09-28T20:13:18.465-04:00MPM1D1 - Day 18 Optimizing Area & PerimeterFor a warm-up today I had students, individually, do the following:<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-ZK0uv3qjsbU/Wc2OEV0oaiI/AAAAAAAAMqk/jFrRODtuLFc4TyEwbOLi6nQCvOy1-i2kwCLcBGAs/s1600/Screen%2BShot%2B2017-09-28%2Bat%2B8.03.51%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="61" data-original-width="844" height="28" src="https://3.bp.blogspot.com/-ZK0uv3qjsbU/Wc2OEV0oaiI/AAAAAAAAMqk/jFrRODtuLFc4TyEwbOLi6nQCvOy1-i2kwCLcBGAs/s400/Screen%2BShot%2B2017-09-28%2Bat%2B8.03.51%2BPM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;">Once everyone had a figure I had them share with the rest of their group and discuss their thinking. Then I gave them another one to consider on their own. </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/-BvMQPYH3RBQ/Wc2EBWU-W-I/AAAAAAAAMqE/mWnuXxJEsgYuX7_JYwHwkVv57P9HAwSSgCLcBGAs/s1600/Screen%2BShot%2B2017-09-28%2Bat%2B7.21.09%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="50" data-original-width="772" height="25" src="https://2.bp.blogspot.com/-BvMQPYH3RBQ/Wc2EBWU-W-I/AAAAAAAAMqE/mWnuXxJEsgYuX7_JYwHwkVv57P9HAwSSgCLcBGAs/s400/Screen%2BShot%2B2017-09-28%2Bat%2B7.21.09%2BPM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>This one seemed to be a little more challenging for some. I did see lots of squares and a couple of circles. Students had a good sense that these fit the description but they had a hard time explaining why they thought it worked.<br /><br />As we were finishing up, one of the students said "Next you're going to get us to draw a figure that has the same area and perimeter. Aren't you?". I actually hadn't considered that as an option, but since he brought it up, I thought it would be a great idea. Most students thought it was easy and they drew a square. I asked a few to show some dimensions so we could compare the perimeter and the area. Many of them just wrote down a length and a width at random. We discussed, as a class, the shapes and dimensions they chose. Their answers were mostly squares that were 1x1, 2x2, 3x3 and 4x4. I drew a 1x1 and asked about the area and perimeter. Students quickly began changing their minds. We realized that a 4x4 would work. I asked if there were any others. Some suggested multiples of 4, then did a calculation to see if it would work. One student suggested 40x40 only to realize that the area and perimeter differed by a factor of 10. One girl pointed out that the areas were getting bigger faster than the perimeters so there couldn't be any more squares that had equal areas and perimeters. Wow! This would have been a good time to pull out Desmos and graph the perimeter vs. side length and area vs. side length to compare the graphs. Unfortunately, I didn't.<br /><br />Next, we moved onto using a certain number of toothpicks to create all possible rectangles, using all of the toothpicks (we used pieces of straws rather than toothpicks). I gave each group eight straws and I asked them to keep track of the length, width, perimeter and area of each rectangle.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-wAhzJ-R8mRw/Wc2KQAoHFOI/AAAAAAAAMqY/mJKSIJBscAgEJSTjpjcksYthF1VeLY9ZQCLcBGAs/s1600/IMG_0403.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://2.bp.blogspot.com/-wAhzJ-R8mRw/Wc2KQAoHFOI/AAAAAAAAMqY/mJKSIJBscAgEJSTjpjcksYthF1VeLY9ZQCLcBGAs/s400/IMG_0403.JPG" width="400" /></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://4.bp.blogspot.com/-wnOzwkSKSc4/Wc2KMRu07KI/AAAAAAAAMqU/EkQ0EHokkoUCXthE0qH399K62XDRF1_BgCLcBGAs/s1600/IMG_0402.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://4.bp.blogspot.com/-wnOzwkSKSc4/Wc2KMRu07KI/AAAAAAAAMqU/EkQ0EHokkoUCXthE0qH399K62XDRF1_BgCLcBGAs/s400/IMG_0402.JPG" width="400" /></a></div><br /> They repeated the process with twelve and sixteen straws. Then they were asked to look back at their tables to see what they noticed. They needed a push in the right direction but it didn't take too long before they were able to find what I was hoping for. Hopefully this portion gets easier for them as they do it more.<br /><br />We moved onto minimizing perimeter given a certain area. I gave out linking cubes and asked them to do the same sort of thing using 9, 16 and 25 cubes. The instructions I gave can be found <a href="https://docs.google.com/document/d/1AIl49SEijduD8mdjBU3qXyUnF3B2znhgfvRWf6mheKI/edit?usp=sharing" target="_blank">here</a>.<br /><br />Some groups finished and were ready for the homework a couple of minutes before the bell. Others got far enough that they could finish up at home. <a href="https://docs.google.com/document/d/1TXk3QkFX8jf95c1LoMSjx3P3ZHDacqE7kq1_nWOjsMc/edit?usp=sharing" target="_blank">Here's</a> a link to the homework I gave. I feel like I stole this from someone. If it was you let me know so I can give you credit.<br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/imrvFVf4FfU" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-18-optimizing-area-perimeter.htmltag:blogger.com,1999:blog-2205963398207045749.post-16750448341321701522017-09-27T11:59:00.001-04:002017-09-27T11:59:34.685-04:00MPM1D1 - Day 17 Finishing Up Staircase ActivityWe started with a few proportions questions as a warm-up. I've noticed that many students are able to solve these questions but they lack structure in their presentation and in explaining their solutions.<br />I posted these problems on the board and had groups solving the problems at the boards.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-HUWvBHFFzaU/WcvIWPE-wvI/AAAAAAAAMps/S4mVN4XrS9Mut0KuSZNGdAdvZg0ORx_uwCLcBGAs/s1600/proportions.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="390" data-original-width="1115" height="138" src="https://1.bp.blogspot.com/-HUWvBHFFzaU/WcvIWPE-wvI/AAAAAAAAMps/S4mVN4XrS9Mut0KuSZNGdAdvZg0ORx_uwCLcBGAs/s400/proportions.PNG" width="400" /></a></div><br /><br />I told them to focus on making sure their solution was easy to follow for someone who happened to stop by to read their work. Most students had no trouble doing the work so I had them work on their presentation a bit. We talked as a group about part/part relationships vs. part/whole relationships. We summarized ratios and proportions in their notes and they tried some examples on their own.<br /><br />We revisited <a href="http://sine-of-the-times.blogspot.ca/2017/09/mpm1d1-day-16-introduction-to-slope.html" target="_blank">yesterday's work</a> on Staircase and Steepness. Only two students completed the work I assigned for homework. One was able to find a ratio for the base divided by the height that worked. We talked about how the order that his method gave might seem backwards to what would be intuitive. The other student who found a solution went home and taught himself (with the help of the internet) how to use trigonometry to find and angle in a triangle given two sides. I was blown away.<br /><br />Eventually we settled on the base over the height as a good measure of the steepness. We called it slope. I went back to the suggestion by a student yesterday to put the line on a grid. We looked at how to find the slope then the class worked on practicing solving proportions and calculating slopes.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/8OxR8A4z2L8" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-17-finishing-up-staircase.htmltag:blogger.com,1999:blog-2205963398207045749.post-9129977948197220612017-09-26T21:51:00.000-04:002017-09-26T21:51:11.796-04:00MPM1D1 - Day 16 Introduction to SlopeWe started the day with this Which One Doesn't Belong.<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-5S3WDlCPgIY/Wcr7mh2T0oI/AAAAAAAAMpM/QfWx6bGnVfUXkW_alymH1xmNJvC0c6OhgCLcBGAs/s1600/wodb14.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="522" data-original-width="527" height="395" src="https://3.bp.blogspot.com/-5S3WDlCPgIY/Wcr7mh2T0oI/AAAAAAAAMpM/QfWx6bGnVfUXkW_alymH1xmNJvC0c6OhgCLcBGAs/s400/wodb14.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;">The conversations led to a review of some of the terminology that we've covered (quadrants, origin, axes, etc.). One student chose the lower left because it looked different. I asked what he meant. Eventually, he motioned with his hand indicating that it wasn't as steep. Another student helped him find the word steep. We talked about how the other three looked as though they were the same steepness. This led to some discussion about parallel lines and steepness.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">My goal today was to introduce the idea of slope. I used<a href="https://twitter.com/fawnpnguyen" target="_blank"> Fawn Nguyen's</a> <a href="http://fawnnguyen.com/staircase-steepness/" target="_blank">Staircase and Steepness </a>activity. I've used this activity before (with a grade nine applied class I believe) and I seem to remember it working out alright. Today, that was not the case. Students were able to do the first part just fine. They were even keen to measure things. Most opted for a protractor. Those that didn't weren't sure what to measure. After a while I asked how they could come up with a number for the steepness without using a protractor. I threw up Fawn's image so that we were all using the same terminology.</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/-JOQVoa4VnBQ/Wcr_Xnzb9mI/AAAAAAAAMpY/J9aEgY2dzuQP4TpyscDwq1PRBTNEFhkRACLcBGAs/s1600/stairs.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="250" data-original-width="403" height="198" src="https://1.bp.blogspot.com/-JOQVoa4VnBQ/Wcr_Xnzb9mI/AAAAAAAAMpY/J9aEgY2dzuQP4TpyscDwq1PRBTNEFhkRACLcBGAs/s320/stairs.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">Some students measured the slant. I asked them whether adding a step would change the steepness? The answer was no. Would it change the measure of the slant? They went back to work. Other students wanted to find the base times height. We talked about that being the area and how we could increase or decrease the area by adding or subtracting steps but not change the steepness.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">One student suggested putting the steps on a graph like we did for the warm-up. I was liking where this was headed but when I asked how he would determine which was steeper for those that were close he couldn't come up with anything. He was so close.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Many students were starting to pack it in feeling defeated (I wonder if the heat was getting to them). I stepped in and suggested that they look at a bunch of ratios to see if that would help. I told them to divvy up the ratios and complete a table with the ratios for each staircase. This was their homework.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">At the end of class I handed back the assessment from yesterday. There were no overall marks on the page. I gave each question a level and students were looking at each question to see where they went wrong. I was hoping to go over a couple of troubling spots but ran out of time. Have I mentioned that it would be great if this class were fifteen minutes longer? We'll do it tomorrow.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/m47uBh_qkrw" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-16-introduction-to-slope.htmltag:blogger.com,1999:blog-2205963398207045749.post-38133700274900849792017-09-25T22:59:00.000-04:002017-09-25T22:59:06.081-04:00MPM1D1 - Day 15 Desmos Intro & First AssessmentWe started the class by revisiting <a href="http://sine-of-the-times.blogspot.ca/2017/09/mpm1d1-day-12-hula-hoop-relay.html" target="_blank">Hula Hoop Relay</a>. I had a set of Chromebooks and we made our way to <a href="http://desmos.com/" target="_blank">Desmos</a>. This would be our first use of Desmos. We had a few password hiccups and a couple of network issues but they were fairly easily sorted out.<br /><br />I demonstrated how to create a table, adjust the scale and find the equation of the line of best fit. I used a group's set of data to demonstrate. As it turns out the slope and y-intercept had the same absolute value. What an unfortunate and potentially confusing coincidence. The potential was there to dive into expanding and factoring binomials, but it wouldn't serve the purpose for today's lesson so I let it go. We talked about how we could find how long it would take for 43 people to do the challenge. We discussed how we could use the graph to extrapolate and how we could use the equation. It was a nice link between the graph, the equation and what was really going on. We did it both ways and some students seemed surprised that everything matched up.<br /><br />As a result of our Desmos introduction I felt as though some students would be able to do it on their own while many would need a little more practice. There will be plenty of opportunity for more practice.<br /><br />We put the computers away and did the mid-cycle assessment (using the term mid very loosely). A couple of students seemed really worried about how they were going to do. I told them to do their best as it would give them a sense of what they needed to work on for the test at the end of the cycle. This is our first real assessment and I intend for it to be formative. I'm hoping it will provide students with some feedback on what they need to work on. It will also give me a chance to see if there is any particular topic that we need to revisit.<br /><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/AXZbxx4k0bs" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-15-desmos-intro-first.htmltag:blogger.com,1999:blog-2205963398207045749.post-1198301334439216792017-09-21T00:30:00.001-04:002017-09-21T00:30:57.929-04:00MPM1D1 - Days 13 & 14I'm away for the next couple of days but here's the plan.<br /><br /><b>Day 13</b><br />Have students estimate the<a href="http://www.estimation180.com/day-3.html" target="_blank"> height of Mr. Stadel's son</a>. They will guess a number that is too low, too high and an actual guess. They will see the answer and calculate their percent error.<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://www.estimation180.com/uploads/1/3/8/8/13883834/03_orig.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://www.estimation180.com/uploads/1/3/8/8/13883834/03_orig.jpeg" data-original-height="600" data-original-width="800" height="300" width="400" /></a></div><br />Once they are done the estimation they will move on to <a href="http://mrorr-isageek.com/smartcar-smash/" target="_blank">Smart Car Smash</a>. They will take up the fractions mastery test that we did the day before then do another one. If they finish before the bell they will start reviewing for their first assessment next week.<br /><br /><b>Day 14</b><br />They will warm up with this <a href="http://www.wouldyourathermath.com/would-you-rather-50/" target="_blank">Would You Rather Problem</a>.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://i1.wp.com/www.wouldyourathermath.com/wp-content/uploads/2015/01/daisy-chain-vs-off-12.png?resize=640%2C480" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://i1.wp.com/www.wouldyourathermath.com/wp-content/uploads/2015/01/daisy-chain-vs-off-12.png?resize=640%2C480" data-original-height="480" data-original-width="640" height="300" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">After the warm up they will review for next week's test.</div><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/fxBoxPq1JKc" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-days-13-14.htmltag:blogger.com,1999:blog-2205963398207045749.post-29895375400934341452017-09-20T23:53:00.003-04:002017-09-20T23:53:42.685-04:00MPM1D1 - Day 12 Hula Hoop RelayWe started with a number talk. I asked students find as many ways as possible to figure out 12 times 18 without a calculator. There was lots of good thinking and most students were able to come up with the answer. They seem hung up on the answer rather than the process. I'm more interested in the process. We saw a few different solutions and I showed a couple more. I need to work at getting students to not stop once they get the answer. I don't think anyone tried to find the answer more than one way.<br /><br />It's been such a gorgeous week weather wise that it's been hard to work inside. When I saw this tweet from @MrHoggsClass I figured this would be a great excuse to get outside.<br /><br /><br /><blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en">Hula hoop relay today in <a href="https://twitter.com/hashtag/MPM1D?src=hash">#MPM1D</a>. How long would it take for 28 students? For the whole school? <a href="https://twitter.com/scdsbmath">@scdsbmath</a> <a href="https://t.co/cv1OCWNoIh">pic.twitter.com/cv1OCWNoIh</a></div>— Mr. Hogg (@MrHoggsClass) <a href="https://twitter.com/MrHoggsClass/status/908798507808632842">September 15, 2017</a></blockquote>Today was the day to try it. I had students work in groups of 5. I showed <a href="https://www.youtube.com/watch?v=c6SbN1MK4So" target="_blank">this</a> video and gave them <a href="https://docs.google.com/document/d/18R4wJnW3JFJZmJLirMDcYrDohAoUOQWHkIked-DtWVQ/edit?usp=sharing" target="_blank">this</a> handout and a hula hoop and we headed out to the front of the school. I had forgotten that when you mention to grade nine students that you're heading outside, they tend not to listen after that. As a result three quarters of them were missing either something to write with or the page to write on. I should have mentioned it more than once. Next time.<br /><br />Eventually they collected and recorded how long it took their group to complete the relay and then the determined how long it would take for our class and the school to do the relay. Some of them asked if we were going to try it as a class. They were really excited. We will try it but not until everyone is finished. Once they were done that I wanted them to see how long it would take for 1 person, 2 people...5 people. They were to fill in the table then create a scatter plot.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-dl6b5CiO1ps/WcM2UckZKHI/AAAAAAAAMno/hz5N2ocXhEEr5m991qI0R9deXrVINzjdwCLcBGAs/s1600/IMG_0398.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1196" data-original-width="1600" height="297" src="https://4.bp.blogspot.com/-dl6b5CiO1ps/WcM2UckZKHI/AAAAAAAAMno/hz5N2ocXhEEr5m991qI0R9deXrVINzjdwCLcBGAs/s400/IMG_0398.JPG" width="400" /></a></div><br />I was hoping to head back to the classroom and show them how to get an equation for the line of best fit using Desmos, but we didn't get to it today. A number of students weren't going to finish in class. We'll have a look at it again later.<br /><br />We headed back into the classroom to do a mastery test on fractions before the bell went.<br /><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/ulCeJeRNKYw" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-12-hula-hoop-relay.htmltag:blogger.com,1999:blog-2205963398207045749.post-19926239146513352252017-09-19T21:43:00.001-04:002017-09-19T21:43:25.988-04:00MPM1D1 - Day 11 FractionsWe started with this visual pattern:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-laiatntpRME/WcG6ftYm4PI/AAAAAAAAMnE/bKaL5L4N0fA6L5Xrx48u5N0RlBb_UHchwCLcBGAs/s1600/Screen%2BShot%2B2017-09-19%2Bat%2B8.46.19%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="159" data-original-width="584" height="172" src="https://2.bp.blogspot.com/-laiatntpRME/WcG6ftYm4PI/AAAAAAAAMnE/bKaL5L4N0fA6L5Xrx48u5N0RlBb_UHchwCLcBGAs/s640/Screen%2BShot%2B2017-09-19%2Bat%2B8.46.19%2BPM.png" width="640" /></a></div><br /><br />I asked them to find three rules for the pattern: the number of squares, the perimeter and the area. All groups were very quick to find the rate, most using a table and looking at the first differences even though we haven't talked about them yet. Most groups determined that they needed to multiply the rate by the step number but the answer was off so they adjusted, adding the appropriate amount. I love how much of this they're figuring out on their own.<br /><br />For groups that finished early I asked them how things would change if we said that each square was 2 unit by 2 units. Their first reaction was that they just needed to double their previous answer. I asked them to prove it to me and they soon discovered that the area of the new pattern was actually four times the area of the original. Such great thinking by a great group of students.<br /><br />The other day one of my students asked why the rule for dividing fractions worked. I was so happy to hear this. We didn't have time to get into that day so we had a look today.<br /><br />I started with this visual, then moved into looking at dividing with a common denominator.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-MkeqgUEybZQ/WcG9huV3_6I/AAAAAAAAMnQ/XhyH2EoVmrsY8kAPYwD9QBZV-XQ0X87pQCLcBGAs/s1600/Screen%2BShot%2B2017-09-19%2Bat%2B8.58.22%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="253" data-original-width="1151" height="139" src="https://2.bp.blogspot.com/-MkeqgUEybZQ/WcG9huV3_6I/AAAAAAAAMnQ/XhyH2EoVmrsY8kAPYwD9QBZV-XQ0X87pQCLcBGAs/s640/Screen%2BShot%2B2017-09-19%2Bat%2B8.58.22%2BPM.png" width="640" /></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/-YdpBINK_gFE/WcG9-XIW24I/AAAAAAAAMnU/ukJgRXMPPiMsaLl3q-RnksURVUPxe9fCQCLcBGAs/s1600/Screen%2BShot%2B2017-09-19%2Bat%2B9.01.23%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="545" data-original-width="1143" height="304" src="https://2.bp.blogspot.com/-YdpBINK_gFE/WcG9-XIW24I/AAAAAAAAMnU/ukJgRXMPPiMsaLl3q-RnksURVUPxe9fCQCLcBGAs/s640/Screen%2BShot%2B2017-09-19%2Bat%2B9.01.23%2BPM.png" width="640" /></a></div>Clearly the picture above wasn't going to cut it so we split things up a little differently.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-9qZ0bdrTM_Y/WcG-XZcvr8I/AAAAAAAAMnY/n7h8_LvQ794b-LD5EC9nLm6_X9b0WP0HACLcBGAs/s1600/Screen%2BShot%2B2017-09-19%2Bat%2B9.03.02%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="165" data-original-width="986" height="106" src="https://4.bp.blogspot.com/-9qZ0bdrTM_Y/WcG-XZcvr8I/AAAAAAAAMnY/n7h8_LvQ794b-LD5EC9nLm6_X9b0WP0HACLcBGAs/s640/Screen%2BShot%2B2017-09-19%2Bat%2B9.03.02%2BPM.png" width="640" /></a></div>From here it was easy to see that the green would fit into the red once (the green rectangles would fit over 8 of the red) leaving one rectangle. So we would need 1 out the 8 green ones. The solution then was that the green fit into the red once plus an eighth. I think many students appreciated the visual nature of this approach. However, when I asked them to try it some of them just wanted to use 'the rule'. We talked a little about how you could do this without drawing a picture. You could find a common denominator then divide the numerators by each other and do the same for the denominators. I love this approach.<br /><br />Next we talked about adding and subtracting fractions, again starting visually, then becoming more abstract. We were running out of time so I had to forgo doing a problem today. I gave them the last 8 minutes to practice operations with fractions.<br /><br />One of the students asked today if we were going to be doing any textbook work this year. Since we don't have any books for this course my reply was no. He seemed happy, which seemed odd given that the homework I give is the kind of work you find in a textbook. The boy sitting beside him was the boy that approached me last week saying he wasn't sure what was going on. He said that he really liked all the group work, problem solving and working at the board.<br /><br />It seems that my daily routine in this class, generally, consists of a warm up, a problem and some skill work. I really like the balance but it's tight to fit it all in everyday. It would be perfect if our classes were 20 minutes longer!<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/7jyO4bmuUJw" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-11-fractions.htmltag:blogger.com,1999:blog-2205963398207045749.post-84234271696729746882017-09-18T22:28:00.002-04:002017-09-18T22:29:11.383-04:00MPM1D1 - Day 10 Finishing Up The Giant ToonieThe warm-up for today was this <a href="http://i0.wp.com/www.wouldyourathermath.com/wp-content/uploads/2016/05/Pools-and-Volume.png" target="_blank">Would You Rather</a> problem:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-oY8D3ID7YQE/WcB8TjwRBBI/AAAAAAAAMmQ/F-lFcAofMqkiGbTLHAO9JnIWzJBa-bfogCLcBGAs/s1600/wyrPool.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="482" data-original-width="640" height="301" src="https://1.bp.blogspot.com/-oY8D3ID7YQE/WcB8TjwRBBI/AAAAAAAAMmQ/F-lFcAofMqkiGbTLHAO9JnIWzJBa-bfogCLcBGAs/s400/wyrPool.PNG" width="400" /></a></div><br />I had students work in groups but at their desks rather than the whiteboards since their work from Friday was still up on the board. It was much harder to see what was going on when students were seated compared to what they would do at the board.<br /><br />One student said he'd prefer the 40' pool because it was longer. He seemed happy to stop their so I asked if he could find out how much water in the pools. Some groups converted the feet to yards, others the yards to feet. One student wanted to use the formula for surface area but fortunately his group convinced him that he was calculating the wrong thing. All the groups had some good success with this problem.<br /><br />We then went on to find out how many toonies would fit in the giant toonie. This problem had multiple steps to it and many students struggled with those steps. This reinforced the importance of being organized and methodical. All groups were able to find the volume of the actual coin, after asking for a formula. Determining the volume of the giant coin proved to be a challenge. They had a hard time figuring out that they needed to find the scale factor, then use the scale factor to find the thickness of the giant toonie. There were a few unit conversion errors but all of the groups knew that they needed to divide the volume of the big coin by the volume of the little coin. Of course this assumes that the coin can be packed in (melted down?) without any space for air.<br /><br />This was a fun problem to watch groups struggle through. They really had to think about what the problem was asking and come up with a plan. Some students were quite frustrated by it, but hopefully this process will get easier for them as we do it more often.<br /><br />Once we were done we did a quick not on calculating area and perimeter and I gave them some questions to practice.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/veSRaHfCXkg" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-10-finishing-up-giant-toonie.htmltag:blogger.com,1999:blog-2205963398207045749.post-38291845333144200902017-09-16T22:53:00.000-04:002017-09-16T22:53:12.521-04:00MPM1D1 - Day 9 Fractions and MeasurementI came across this problem last night so I thought I try it in class since we had been discussing fractions.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://pbs.twimg.com/media/DJuBhE1VAAALoNs.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="450" data-original-width="800" height="225" src="https://pbs.twimg.com/media/DJuBhE1VAAALoNs.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;">Some groups were quick to recognize that the fractions on both sides were equivalent, others performed the calculations and didn't really notice anything that was the same. I asked how they could compare the fractions. That was enough to get them to thing about reducing their answers. Some groups chose to scale the smaller numbers up. All the groups seemed to do just fine with the division, which was a bonus.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-ScYf_QDle6Y/Wb3h7w98xUI/AAAAAAAAMlk/8Am8-Mgvpj8pTs48yepDjafF7jJAPVnOgCLcBGAs/s1600/IMG_0382.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://2.bp.blogspot.com/-ScYf_QDle6Y/Wb3h7w98xUI/AAAAAAAAMlk/8Am8-Mgvpj8pTs48yepDjafF7jJAPVnOgCLcBGAs/s400/IMG_0382.JPG" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="" style="clear: both; text-align: left;">We moved on to Jon Orr's <a href="http://mrorr-isageek.com/tag/r2d2/" target="_blank">R2D2</a>. Which didn't take long to solve. It was interesting to see that the half of the class on the west of the room did it one way (divide the width of the bulletin borad by the width of the sticky note to find how many would be needed, do the same for the width then multiply) and the groups on the east of the room all found the area of the board and the area of a sticky and divided them. Perhaps knowledge was moving around the room but not crossing the centre line.</div><div class="" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-YAxcIJJUoDQ/Wb3h8A0CVyI/AAAAAAAAMlo/XvD0NPMJ9HMvD7A5y-3fhfuflC1WCwl8ACLcBGAs/s1600/IMG_0385.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/-YAxcIJJUoDQ/Wb3h8A0CVyI/AAAAAAAAMlo/XvD0NPMJ9HMvD7A5y-3fhfuflC1WCwl8ACLcBGAs/s400/IMG_0385.JPG" width="400" /></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/-r6BXgCOWtaE/Wb3h5i-o5VI/AAAAAAAAMls/_o2hWAn1nxc4c8gdNEBEEymMxN47weO1QCEwYBhgL/s1600/IMG_0386.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/-r6BXgCOWtaE/Wb3h5i-o5VI/AAAAAAAAMls/_o2hWAn1nxc4c8gdNEBEEymMxN47weO1QCEwYBhgL/s400/IMG_0386.JPG" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="" style="clear: both; text-align: left;">Next up we were going to look Kyle Pearce's <a href="https://tapintoteenminds.com/3act-math/big-nickel/" target="_blank">Big Nickel</a>. I showed the video and asked how many of them had been to Sudbury and how many had seen the Big Nickel. I was surprised to see that only two of my students had seen the Nickel. I then asked how many of them had been to Campbellford to see the Giant Toonie. It was about half the class so I decided to proceed with the toonie.</div><div class="separator" style="clear: both; text-align: left;">I showed a picture of the toonie. </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: center;"><a href="https://1.bp.blogspot.com/-RhOccrjS-IM/Wb3b9U1xWRI/AAAAAAAAMlE/-ryvPm_21t4pjQd2IntZRMSw86MQE-hRwCLcBGAs/s1600/304_0488.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1067" height="400" src="https://1.bp.blogspot.com/-RhOccrjS-IM/Wb3b9U1xWRI/AAAAAAAAMlE/-ryvPm_21t4pjQd2IntZRMSw86MQE-hRwCLcBGAs/s400/304_0488.JPG" width="266" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">They asked some questions such as "How big is it?" and as a class we decided to find out how many real toonies would fit inside. I gave them the following information about the giant toonie and we headed to Wikipedia for details about the actual toonie.</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/-6h41FmZmL8o/Wb3cpkMfaUI/AAAAAAAAMlM/6nFaJJZtDxwy8O-UE2VnxkfyuGSVUvjnACLcBGAs/s1600/toonie.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1067" height="400" src="https://2.bp.blogspot.com/-6h41FmZmL8o/Wb3cpkMfaUI/AAAAAAAAMlM/6nFaJJZtDxwy8O-UE2VnxkfyuGSVUvjnACLcBGAs/s400/toonie.jpg" width="266" /></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/-mS8Wtfm377k/Wb3dUaQa6mI/AAAAAAAAMlU/o7MVLz7nQKIZdZHe3Ik4CRxo_HsxBVkLQCLcBGAs/s1600/Screen%2BShot%2B2017-09-16%2Bat%2B10.25.27%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="150" data-original-width="285" height="210" src="https://3.bp.blogspot.com/-mS8Wtfm377k/Wb3dUaQa6mI/AAAAAAAAMlU/o7MVLz7nQKIZdZHe3Ik4CRxo_HsxBVkLQCLcBGAs/s400/Screen%2BShot%2B2017-09-16%2Bat%2B10.25.27%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;">I told them to assume that the giant toonie was built to scale and then set them loose. We haven't talked about measurement so I was keen to see where this would go. One group started by figuring how many toonies would fit across the diameter of the monument, another calculated the circumference of both. One group wanted to work on volume but couldn't remember how to find the volume of a cylinder so we talked about how to find the volume of a prism and I let them sort things out from there. We ran out of time so we'll have to pick up where we left off Monday.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/jPmGMN7JT2Q" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-9-fractions-and-measurement.htmltag:blogger.com,1999:blog-2205963398207045749.post-90915428563038549532017-09-14T20:15:00.002-04:002017-09-14T20:15:57.637-04:00MPM1D1 - Day 8 Fractions and ProportionsWe started with<a href="http://www.openmiddle.com/comparing-fractions/" target="_blank"> this </a><a href="http://www.openmiddle.com/" target="_blank">Open Middle</a> Problem:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-K_gNsxZQD4k/WbsUuSM1hTI/AAAAAAAAMks/AGFC9Ey6xnQSCwRzF3t-ShwK-bLJkzNPQCEwYBhgL/s1600/fractions.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="417" data-original-width="1352" height="98" src="https://2.bp.blogspot.com/-K_gNsxZQD4k/WbsUuSM1hTI/AAAAAAAAMks/AGFC9Ey6xnQSCwRzF3t-ShwK-bLJkzNPQCEwYBhgL/s320/fractions.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>The idea is to fill the squares using only the digits from 1 to 9, at most one time each. This was fairly easy for the class. Somebody asked if they were allowed to have improper fractions. Some groups drew pictures, while others just worked with the numbers.<br /><br />Since the students were so quick to solve the first one we moved onto <a href="http://www.openmiddle.com/comparing-fractions-2/" target="_blank">this</a> one:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-v1rGW5jXeis/WbsXE33v7tI/AAAAAAAAMk0/LhfaV8qVVZ8GdnvMfzGASkwyBWg_ooL3QCLcBGAs/s1600/Screen%2BShot%2B2017-09-14%2Bat%2B7.55.20%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="541" data-original-width="472" height="400" src="https://1.bp.blogspot.com/-v1rGW5jXeis/WbsXE33v7tI/AAAAAAAAMk0/LhfaV8qVVZ8GdnvMfzGASkwyBWg_ooL3QCLcBGAs/s400/Screen%2BShot%2B2017-09-14%2Bat%2B7.55.20%2BPM.png" width="348" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>Some groups started with pictures but realized that it was tough to tell the difference between 4/9 and 5/11 when they were roughly drawn on the board. Most groups eventually came to the conclusion that they needed a good way to compare the fractions. Some discussed common denominators but most decided to convert the fractions to decimals or percents.<br /><br />We then talked about equivalent fractions, mixed numbers and improper fractions. I mentioned that at some point we'd have to go over performing operations with fractions. Lot of them were keen to do it right then, so we did talk about it.<br /><br />Next up was <a href="http://mrorr-isageek.com/fast-clapper/" target="_blank">Fast Clapper</a>. All but two of my students were pretty excited to be clapping and counting. They found unit rates and solved proportions by considering them equivalent fractions. I was hoping to do <a href="http://mrorr-isageek.com/smartcar-smash/" target="_blank">Smart Car Smash</a> but we were running out of time. Instead I handed back the mastery test from yesterday (overall the results were quite good) and then I handed out a page on equivalent fractions, mixed numbers, improper fractions and multiplying and dividing integers. We'll redo the master test tomorrow.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/SBpo2P5HJNI" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-8-fractions-and-proportions.htmltag:blogger.com,1999:blog-2205963398207045749.post-18353731412341232522017-09-13T20:46:00.002-04:002017-09-13T20:48:50.098-04:00MPM1D1 - Day 7 Mastery Test, Variation & SlopeI've never done three Visual Patterns in one week, but they seemed to tie in nicely with what we were doing this week. A couple of days ago we did this one:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://hpedsb.elearningontario.ca/content/enforced/10332043-BL_1718Sem1__MAT_MPM1D1-948705_a_ELO/PastedImage_vbgj5xf2c8mwh2e6058hsjf7dzu0ogi7001343905746.png?_&d2lSessionVal=X5q19LqyRa0m1cb5UUr43jhCi&ou=10332043" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="209" data-original-width="574" height="145" src="https://hpedsb.elearningontario.ca/content/enforced/10332043-BL_1718Sem1__MAT_MPM1D1-948705_a_ELO/PastedImage_vbgj5xf2c8mwh2e6058hsjf7dzu0ogi7001343905746.png?_&d2lSessionVal=X5q19LqyRa0m1cb5UUr43jhCi&ou=10332043" width="400" /></a></div>Then yesterday we did this one:<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/LD3gg0ZU0S_gAglBdtnB_jK2sUsEQIDov1qIEd9W7796fT9zT5eskuibvtkQQo_E3xqvHj9dPIzJ_tk=w1280-h676" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="640" height="250" src="https://1.bp.blogspot.com/LD3gg0ZU0S_gAglBdtnB_jK2sUsEQIDov1qIEd9W7796fT9zT5eskuibvtkQQo_E3xqvHj9dPIzJ_tk=w1280-h676" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;">Today we did this one:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://hpedsb.elearningontario.ca/content/enforced/10332043-BL_1718Sem1__MAT_MPM1D1-948705_a_ELO/VP4%20-Modified%20Direct%20Variation.png?d2lSessionVal=X5q19LqyRa0m1cb5UUr43jhCi&ou=10332043" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="640" height="250" src="https://hpedsb.elearningontario.ca/content/enforced/10332043-BL_1718Sem1__MAT_MPM1D1-948705_a_ELO/VP4%20-Modified%20Direct%20Variation.png?d2lSessionVal=X5q19LqyRa0m1cb5UUr43jhCi&ou=10332043" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;">All groups found the equation and the number of squares in the forty-third step easily. I wanted to show this one because we talking about direct and partial variation. We talked about how many squares the 0th step would have. We discussed what the graphs of the three patterns would look like (number of squares vs. step number) and connected an initial value of 0 to direct variations. We also talked about what was the same in all four tables and all four graphs. Somebody mentioned that the values in all the tables were going up by the same amount. Almost all groups had created a column for the first differences, even though we've never talked about it. Somebody else realized that the graphs would be going up at the same angle. We took a few minutes to get some information about direct and partial variations along with some information about slope into their notes.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I was happy to get through this when I did. Today was picture day and shortly after I finished about half a dozen students had to leave and get their photos taken.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The rest of the class did a mastery test on integers. Our department uses mastery tests to get at key skills in a course. They are short ten mark quizzes that focus on very specific but important skills. The idea is that we write the mastery test in class. The teacher marks them then hands them back (usually the next day) and go over any trouble spots. We rewrite a similar mastery test which get marked again. After the second attempt students can rewrite as many times as they want (outside of class time) until they get a mark that they are happy with. In this way the assessment is formative until the student decides it should be summative.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">We finished up the mastery test and I handed out a set of data and asked them to create a scatter plot. They had to choose which variables were dependent and independent, create a scale, draw a line of best fit and list the characteristics of the graph (discrete/continuous, partial/direct, positive/negative slope).</div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/vAt4d24ZyCE" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-7-mastery-test-variation.htmltag:blogger.com,1999:blog-2205963398207045749.post-42307277977751421672017-09-12T21:04:00.000-04:002017-09-12T21:04:16.202-04:00MPM1D1 - Day 6 More Cup StackingI modified the Visual Pattern we did yesterday slightly to see how quickly my students would be able to spot the differences and come up with a solution. Again I asked them to find the forty-third step and a rule/equation to find the number of squares in any step. Here's what we started with:<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-NAuxl4567r4/WbfjWtlbuKI/AAAAAAAAMj8/YImWaUOzCog11QBZKtFjUoTrO1v1Q-KwACLcBGAs/s1600/6-VP4-modified.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="640" height="250" src="https://1.bp.blogspot.com/-NAuxl4567r4/WbfjWtlbuKI/AAAAAAAAMj8/YImWaUOzCog11QBZKtFjUoTrO1v1Q-KwACLcBGAs/s400/6-VP4-modified.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;">Most groups started by making a table of values. Those that didn't weren't really sure where to start and so I suggested a table. I was happy to see many groups showing the first differences (though we didn't call them that) in their tables.</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/-7nx0-11r7Yw/WbiA75g6Z3I/AAAAAAAAMkM/YAxTC2sY1IMo9HfUsp6E87Xrt1OHVRHOQCLcBGAs/s1600/IMG_0375.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/-7nx0-11r7Yw/WbiA75g6Z3I/AAAAAAAAMkM/YAxTC2sY1IMo9HfUsp6E87Xrt1OHVRHOQCLcBGAs/s400/IMG_0375.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;"> I asked what was the same and what was different compared to yesterday's pattern. It was great hear things like "The constant is different" or "It's going up by the same amount". We talked a little about how these showed up in the equations.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Next we moved onto more cup stacking. The goal for today was to change how we stacked the cups and how that changed the equation and graph. I asked how many cups would be needed (stacked inside one another) to reach R's height. All groups saw that the height of the stack was changing by the lip of the cup for each additional cup. A couple of groups struggled with the initial value. They thought it should be the height of a cup rather than the body of the cup. Every group did manage to come up with an equation but struggled to solve the 2-step equation needed to find the number of cups (not surprising since we have done much equation solving yet).<br /></div><div class="separator" style="clear: both; text-align: left;">Once they were done finding the number of cups needed to get to R's height they went back to their seats and plotted Height vs. Number of Cups. We talked about how the graph was different from the one they made yesterday. This led to a need for some terminology (partial vs. direct variation) so we wrote a note about graphs. The note included dependent vs. independent variables, continuous vs. discrete data, lines of best fit and interpolation vs. extrapolation. I was hoping to get into partial and direct variation and slope but we ran out of time.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I gave some homework on plotting points on the Cartesian Plane and identifying whether variables were dependent or independent.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">At the end of class I had a student come to me and tell me that he was feeling lost. He said he was able to follow what his group members were saying but he wasn't sure he'd be able to come up with the numbers on his own. He told me that he did well in math last year but wasn't feeling very confident. We chatted for a bit and he agreed to come in tomorrow at lunch so we can go over a few things. I'm curious to see if his issue is related to skill or confidence.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/-26_eZa9cQU" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-6-more-cup-stacking.htmltag:blogger.com,1999:blog-2205963398207045749.post-65570318411927468922017-09-11T12:16:00.000-04:002017-09-12T21:41:52.837-04:00MPM1D1 - Day 5 Cup StackingWe did our first visual pattern today. I started with this one:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-RmWamAa6N5Q/WbaPYfCwsdI/AAAAAAAAMjQ/nhdqpAvDySAu-wrTysnzZsf0k5jzP_0AgCLcBGAs/s1600/vp4.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="208" data-original-width="568" height="146" src="https://1.bp.blogspot.com/-RmWamAa6N5Q/WbaPYfCwsdI/AAAAAAAAMjQ/nhdqpAvDySAu-wrTysnzZsf0k5jzP_0AgCLcBGAs/s400/vp4.PNG" width="400" /></a></div><br />I told them that the images represent the first three steps in a pattern then asked if they could find the number of squares in the forty third step. I also asked if they could they find a rule or equation to represent the number of squares in any step (the n<sup>th</sup> step). Normally I ask for an equation and I think that is often intimidating at first. This time I focused on the rule, which we could then be turned into an equation. They worked at the problem in groups at board. They did a great job. We spent a bit of time talking about what makes an equation.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-APbZbkYhiy0/WbawHnorhuI/AAAAAAAAMjk/FBD9ZI1JyioP_Znxoztxq6wbJZWML20iQCLcBGAs/s1600/IMG_0368.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://4.bp.blogspot.com/-APbZbkYhiy0/WbawHnorhuI/AAAAAAAAMjk/FBD9ZI1JyioP_Znxoztxq6wbJZWML20iQCLcBGAs/s400/IMG_0368.JPG" width="400" /></a></div><br /><br />Then we moved on to <a href="http://blog.mrmeyer.com/2008/linear-fun-2-stacking-cups/" target="_blank">Cup Stacking</a>. I held up a styrofoam cup and asked what they noticed and what they wondered. There were some great observations but they were fairly quiet when I asked what they wondered. So I posed the question "How many cups would be needed to make a stack to my height?". This led to a discussion about how the cups were going to be stacked. Normally when I do this activity I tell the class that I want the cups stacked inside of one another. The class really wanted to stack the cups one on top of the other as shown below, so we started there. I figured we could do it both ways and discuss direct vs. partial variations.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-DdxdN-wThwk/Wbav4RU9mxI/AAAAAAAAMjg/j2Fb5E3czjY32WATXwNwpwxkIy9mZ3R5ACEwYBhgL/s1600/IMG_0373.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/-DdxdN-wThwk/Wbav4RU9mxI/AAAAAAAAMjg/j2Fb5E3czjY32WATXwNwpwxkIy9mZ3R5ACEwYBhgL/s400/IMG_0373.JPG" width="298" /></a></div><br />Most groups came up with a solution pretty quickly. Once they finished I asked if they could come up with an equation that related the number of cups to the height of the stack. I had a few blank looks and reminded them of the visual pattern we did at the beginning of the class. That was enough to get them going.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-YZHkpFEHuF4/WbaxfUiSZTI/AAAAAAAAMjs/QaatXlZBV9Uxb_G-zyUdI69E4R0XEGOsgCLcBGAs/s1600/IMG_0370.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://4.bp.blogspot.com/-YZHkpFEHuF4/WbaxfUiSZTI/AAAAAAAAMjs/QaatXlZBV9Uxb_G-zyUdI69E4R0XEGOsgCLcBGAs/s400/IMG_0370.JPG" width="400" /></a></div><br />We had a bit time left so they created graphs showing the height of a stack of cups vs. the number of cups. Tomorrow we'll see how stacking the cups inside one another compares.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/WC6k4WAQEbE" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com0http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-5-cup-stacking.htmltag:blogger.com,1999:blog-2205963398207045749.post-19266023513217146172017-09-09T21:30:00.002-04:002017-09-09T21:33:57.874-04:00MPM1D1 - Day 4 Order of Operations & Pythagorean TheoremWe had an assembly today so it was a shortened period. I had thought that it might be a good day to try a visual pattern but decided against it.<br /><br />Instead we started with our first <a href="http://wodb.ca/" target="_blank">Which One Doesn't Belong</a>. I decided to use the one below only because my students have seen cards a lot this week. They see them every day to determine where they sit and they saw them when we played integer solitaire. I was curious to see if any of them would make a connection back to the game about black being positive and red being negative. It turns out nobody did.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-yhr6HMdRbYc/WbKc9nXq_lI/AAAAAAAAMjA/Ksxc4iWnCgY1XlBoIKr8_7ffE1UFt8QZACLcBGAs/s1600/wodb%2Bcards.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="451" data-original-width="410" height="400" src="https://4.bp.blogspot.com/-yhr6HMdRbYc/WbKc9nXq_lI/AAAAAAAAMjA/Ksxc4iWnCgY1XlBoIKr8_7ffE1UFt8QZACLcBGAs/s400/wodb%2Bcards.PNG" width="362" /></a></div><br />In our discussion yesterday about multiplying and dividing integers, order of operations came up. They all seemed to know the rules so I went over them fairly quickly but we did spend a bit of time talking about exponents. I gave them a few questions to try and then we took them up.<br /><br />We also went over the Pythagorean Theorem. They knew how to find the length of the hypotenuse from yesterday's work so we worked through an example of finding one of the legs. I gave them some order of operations and Pythagorean Theorem questions for homework.<img src="http://feeds.feedburner.com/~r/SineOfTheTimes/~4/2ZZmnJ37OCE" height="1" width="1" alt=""/>Dave Lanovazhttp://www.blogger.com/profile/09010742221812029616noreply@blogger.com2http://sine-of-the-times.blogspot.com/2017/09/mpm1d1-day-4-order-of-operations.html