tag:blogger.com,1999:blog-25239465381930541942017-05-16T20:00:43.615-07:00Opposite of a NegativeLesson plans, reflections, student work, and more.Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.comBlogger256125tag:blogger.com,1999:blog-2523946538193054194.post-79958793188998325682017-05-08T21:29:00.002-07:002017-05-08T21:35:20.658-07:003rd @desmos print and student products<div class="separator" style="clear: both;">Today concluded the first of two days with our local librarian Debbie who brought in her 3D printer today. It is called an Ultimaker 2 Go. She started by showing the objects she had printed off of thingiverse as well as a model of herself using some sort of XBox 3D camera? We also passed around the sample from my previous blog post of my daughter's name plate "Everly."</div><br />Then I hooked up her laptop to the classroom display so she could introduce students to the history of 3D printing to it's many uses from decorating food, creating space parts, prosthetics, hearing aids, and much much more.<br /><br />As students listened, they had a chance to ask questions after 15 minutes. Only 1 student asked a question. They were surprised that it would be free at the library. I think the hour time investment of orientation is not appealing to them.<br /><br />Students were given time to continue working on their graphs. Students who had finished were following the steps in my slides to prep it for printing. In essence, it's changing all the equations to the color black, turning off the grids and axes and turning on the projector mode. Then export as a .png, convert it to .svg, import that file to Tinkercad, add a prism or cylinder as a plate, and turn the name into a hole. One student, Chloe, went through this whole process.<br /><br />Three students prepared their graphs and emailed them to me, and I added them to the <a href="https://padlet.com/mjoyce11/xrx5p03px81g">Padlet wall</a>.<br /><br />While students worked we printed out the name plate for my niece Callan. It came out on gray filament. I was able to pass it out with 15 minutes left in the class. Students thought it would be hot but it had already cooled off. The extruder on the machine though gets up to 200 degrees Celsius, which is almost 400 degrees Fahrenheit. A student pointed out that that's how hot an oven must get, which I agreed. It is kind of like baking something at high heat.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://media.padletcdn.com/v13/image/a_exif,c_limit,dpr_1.0,h_647,w_1154/https%3A%2F%2Fpadletuploads.blob.core.windows.net%2Fprod%2F124902108%2F33bd28b60e328fbb91484ee009e5e0c3%2FIMG_9895.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="239" src="https://media.padletcdn.com/v13/image/a_exif,c_limit,dpr_1.0,h_647,w_1154/https%3A%2F%2Fpadletuploads.blob.core.windows.net%2Fprod%2F124902108%2F33bd28b60e328fbb91484ee009e5e0c3%2FIMG_9895.jpg" width="320" /></a></div><br /><br />Then we started Chloe's printing. One obstacle we faced was her creating a Tinkercad account. Debbie suggested I look into whether there is a teacher account so students can login using that.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://media.padletcdn.com/v13/image/a_exif,c_limit,dpr_1.0,h_647,w_1154/https%3A%2F%2Fpadletuploads.blob.core.windows.net%2Fprod%2F124902108%2F0979d3d3d0fc54f17c87796f849c6651%2FIMG_9896.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="239" src="https://media.padletcdn.com/v13/image/a_exif,c_limit,dpr_1.0,h_647,w_1154/https%3A%2F%2Fpadletuploads.blob.core.windows.net%2Fprod%2F124902108%2F0979d3d3d0fc54f17c87796f849c6651%2FIMG_9896.jpg" width="320" /></a></div>What I like about Chloe's is that she used a cylinder as the name plate background. Debbie shrunk it to cut down on the print time. What I love is that one of my students gets to see how math and their own work results in a real artifact from my math class. What a feeling. I personally remember that feeling from my woodshop and ceramics classes in middle and high school respectively. I do remember making a Factor Book in 8th grade Algebra with a Southpark theme but that's a different kind of artifact!<br /><br />Here are my 5th period students getting a final look at the printer before class let out:<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://lh3.googleusercontent.com/-mCSMomp2V5E/WRFGxptB-rI/AAAAAAAADFA/50pCxnSJsgkUbfKBoLGxriZfUJe_xGufwCHM/s640/blogger-image--1926241832.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-mCSMomp2V5E/WRFGxptB-rI/AAAAAAAADFA/50pCxnSJsgkUbfKBoLGxriZfUJe_xGufwCHM/s640/blogger-image--1926241832.jpg" /></a></div>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com2tag:blogger.com,1999:blog-2523946538193054194.post-11571009706971738212017-05-07T21:46:00.003-07:002017-05-07T21:47:02.180-07:00Number Tic-Tac-Toe by @mburnsmath It all began with a tweet by Marilyn Burns a few days ago...<br /><br /><blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en">Another end-of-year game: Number Tic-Tac-Toe. Directions in picture. I included other Tic-Tac-Toe variations in Math for Smarty Pants. <a href="https://t.co/HDqFK0zST4">pic.twitter.com/HDqFK0zST4</a></div>— Marilyn Burns (@mburnsmath) <a href="https://twitter.com/mburnsmath/status/860231506509258752">May 4, 2017</a></blockquote>I figured I would introduce it to my 7th and 8th grade math support for students who had finished their homework. I left the directions on the board. Students enjoyed it immensely! So much so, that other students who were still working on their homework stopped and joined in. This class can be hard to motivate at times so to see them want a play a math game was great.<br /><br />Students liked that they could beat me at the game sometimes. I was really impressed with some of the strategies they were using. We will definitely return to it.<br /><img border="0" src="https://lh3.googleusercontent.com/-edC8b9mp1-o/WQ_3yail7wI/AAAAAAAADEo/3uAYDIMhj-M7JSEspdOr5PKmZlJXyya0wCHM/s640/blogger-image-920035997.jpg" /><br />In 6th grade math support, we focused solely on the game. I left the directions on the board and had students practice with their table partner. They asked if they could use their partner's numbers to make three in a row, and I said yes. Also, some were caught repeating numbers so they had to restart.<br /><br />I played a student and saw that there was a 9 in the middle. They knew they couldn't but anything less than 6 because than I could put a small number and win. So, they put a 7, pushing the sum over 16. I was very impressed.<br /><br />I then printed out a 16 team elimination bracket by googling for it and randomly put the students names in the columns, making sure their first round game would be against someone different than their practice partner.<br /><img border="0" src="https://lh3.googleusercontent.com/-8VplIybYQ5k/WQ_30XTD2oI/AAAAAAAADEs/P_01WWG8Qd4bHB-_RFBLVPTDKVvOGOPfgCHM/s640/blogger-image--1962299847.jpg" /><br />During the practice I could talk strategy and give suggestions, but once the bracket started I couldn't to be fair to both players. Students got ultra competitive! I mean, these are kids that have been disenchanted by math for a long time and they were loving this game. I couldn't believe the spark it provided for students. On Monday we have a semifinal match to finish to decide who plays against Faby for the championship (to win a confiscated ring pop...!)<br /><br />So, thank you so much Marilyn Burns for inspiring my math support students to have fun with a really cool math game.<br /><br />Here are the rules from the tweet:<br /><a href="https://lh3.googleusercontent.com/-IlQ5l-SxkBM/WQ_3wLgBH2I/AAAAAAAADEk/QgJ0TwuxnhMklIS4_sGUnVbnDuc-vliXACHM/s640/blogger-image-604201987.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-IlQ5l-SxkBM/WQ_3wLgBH2I/AAAAAAAADEk/QgJ0TwuxnhMklIS4_sGUnVbnDuc-vliXACHM/s640/blogger-image-604201987.jpg" /></a><br /><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com1tag:blogger.com,1999:blog-2523946538193054194.post-69735807162319564832017-05-03T10:48:00.001-07:002017-05-03T11:06:27.700-07:00Student rough drafts & my 2nd @Desmos 3D printLast week on Monday and Tuesday 8th graders took the SBAC English test for periods 1 through 4 with our 1st period class. Then we had our regularly scheduled 5th and 6th periods. So, for 5th period I had 2 extra periods. What would I do? A head start on writing their names with linear equations on a properly scaled graph that looks the Desmos default graphing window. <br /><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">As you can see in the top left picture collage, I had students mark off their intervals by 0.5 and label the whole numbers. I then demonstrated how I could write Maria's name using horizontal, vertical, and diagonal lines. I then <a href="https://www.desmos.com/calculator/efeccof8ny">displayed my color coded graph</a> so students could see how I wrote the equations with the domain and range restrictions.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Many students started and were successful with a lot of noticing of vertical lines being x=-2 if the line went through -2 on the x axis. They then realized they would have to limit the range to stop it from going all the way up and down. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Some students realized that they couldn't use y=mx+b for some diagonal lines when if they extended it the y-intercept would be off the page. So, there was a need to introduce y=m(x-h)+k or vertex form of a linear function. I told students it basically meant a line with a slope of m still, but it passed through the point (h,k).</div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-eZ9yEsPm0Tg/WQlL7ZMJroI/AAAAAAAADDo/NYTkjlgqX9QsMzkslSADzXa6SnAl6T21QCHM/s640/blogger-image--1791764924.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-H976c7qQZo0/WQlL29An5tI/AAAAAAAADDg/fU9WSV6M4bULZ3BehTw6I04ct7hiVuLKACHM/s640/blogger-image-672304632.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-H976c7qQZo0/WQlL29An5tI/AAAAAAAADDg/fU9WSV6M4bULZ3BehTw6I04ct7hiVuLKACHM/s640/blogger-image-672304632.jpg" /></a></div><div class="separator" style="clear: both;">Above you can see a student color coding the parts of her name to the equations she wrote. In the top right of the collage, this student finished first... Possibly because her first name had no diagonal lines.</div><img border="0" src="https://lh3.googleusercontent.com/-eZ9yEsPm0Tg/WQlL7ZMJroI/AAAAAAAADDo/NYTkjlgqX9QsMzkslSADzXa6SnAl6T21QCHM/s640/blogger-image--1791764924.jpg" /><br />Students were really open to helping each other answer each others questions about their graph and equations.<br /><img border="0" src="https://lh3.googleusercontent.com/-xYmwfDHf5Pc/WQlL99jj9KI/AAAAAAAADDs/YuNugVg3U80g4cae0lCT4ZiBzRQcsyjwgCHM/s640/blogger-image--946480157.jpg" /><br />As you can see, students who had finished were able to use the Desmos iPhone app to start inputting their equations and see their creations come alive. For students whose parents restricted downloading of apps I instructed them to go to desmos.com in Safari and make sure they logged into their school gmail account to save their work.<br /><br />I thought about how I could scaffold this activity better to reach all of my students on day 2, and I came up with the following Google Slides. I'd love some feedback on these. The lesson plan is to introduce learning goals and success criteria first (which can later be used as a rubric possibly). Also, show students the artifact that they could eventually print out with all their hard work. Then, instead of telling them exactly how to write each equation, I showed a slide with the equation matched to it's line segment on the graph. I asked students to notice. The slide right after that is a summary of the discussion points I anticipate that we would review. Some of the language refers to a YouTube video called Slope Dude Says under my Jokes tab at the top of the page where an increasing line is "puff puff positive," a decreasing line is "niiice negative" and a horizontal line is "zero fun." I showed this to students because they kept forgetting to put the negative sign after correctly identifying the vertical and horizontal growth of a line.<br /><br /><iframe allowfullscreen="true" frameborder="0" height="569" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/1Ih2Gsx8IOiE-13HUsz8Hi2IL0RnPI8pkUC1h-8OQWog/embed?start=false&loop=false&delayms=3000" webkitallowfullscreen="true" width="960"></iframe> <br />Below is an idea I had to help students setup their graph for export. I want them to notice all the options that are on in the default Desmos graphing window after clicking on the wrench icon in the top right of the screen. To prepare the graph to export it as an image, students will notice the grid, axis numbers, gridlines, and x and y axis need to be unchecked. The graph also needs to be in projector mode. I screen shotted these when I was on my iPhone app so they could see it easier.<br /><br />Also, all equations must be the color black, and Desmos shared with me a faster way to do this. You click the gear icon to the right of the plus button in your equations window, and then can click on each color and change it to black.<br /><img border="0" src="https://lh3.googleusercontent.com/-6Lof4nfQeyk/WQlL0iQHWII/AAAAAAAADDc/alKM_dJ7WzklW6F2biTmfvad50mrrUAPgCHM/s640/blogger-image-1411811042.jpg" /><br />The default settings are above. You can also see that I haven't changed the color of the lines yet.<br /><img border="0" src="https://lh3.googleusercontent.com/-iTPrbDfQ1pU/WQlL5OpX3dI/AAAAAAAADDk/Js1ngXTxTvcSQ21pySyFbent4cg76WSkQCHM/s640/blogger-image--126794034.jpg" /><br />The above settings show the correct settings as well as the equations in black.<br /><br />If you look at the slides, I show the example of "Mr. Joyce." When I printed this, it printed as individual letters. My next iteration is below. I spelled out my daughter's name with parabolas, absolute value, linear, and exponential functions. This time though I created a rectangular prism around the name. I then matched the heights of the prism and the letters and then changed the letters to a "hole" in Tinkercad. So, as you can see, the letters made a hole in the prism. I want to compare this to an embossed or raised look where the letters are sticking up above the plate next time and see which looks better.<br /><br />So, we have our 2nd week of 8th grade testing next Monday and Tuesday and I have arranged for the local librarian Debbie to come in with the portable 3D printer, give them an introduction, answer questions, print out a sample so they can watch it work, and then have them finish their graphs and prep them to be exported so they can put it in Tinkercad and make the name plate. Then they can export it as a .STL file and be ready to go. Once again, I learned all of this by reading John Stevens' blog post, which is linked in my first blog post, entitled "<a href="http://joyceh1.blogspot.com/2017/01/my-first-desmos-3d-print.html">My First Desmos 3D print.</a>"<br /><br />I also <a href="https://goo.gl/nOU6Vp">created a Padlet wall</a> so students could post their work for myself and other students to see.<br /><img border="0" src="https://lh3.googleusercontent.com/-wzb7q5WYlGk/WQlL_-GFT-I/AAAAAAAADDw/X3SFK8K2-PgsjCJFPPEk4ZN61EmUeHC2wCHM/s640/blogger-image-801021128.jpg" />Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-80034876242019905962017-03-27T21:33:00.000-07:002017-03-27T21:40:22.932-07:00@fractiontalks using @desmos activity by @ms_hansel Part 1I saw Alison Hansel tweet out a super cool Fraction Talks Desmos activity she used with 4th graders after she posted some student work samples. I figured it would be perfect for my 6th grade math support class.<br /><blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en"><a href="https://twitter.com/FractionTalks">@FractionTalks</a> <a href="https://twitter.com/Desmos">@Desmos</a> I'm an Activity Builder novice & created it by editing the "Sketchy Fractions" activity: <a href="https://t.co/kelmIcQN48">https://t.co/kelmIcQN48</a></div>— Alison Hansel (@ms_hansel) <a href="https://twitter.com/ms_hansel/status/843275157166800896">March 19, 2017</a></blockquote><br />Now in a 53 minute period, I only got through TWO slides. And that's OK. It was a rich discussion. And we will definitely be returning to finish this activity at a later date!<br /><br />I believe the images are from <a href="http://fractiontalks.com/">FractionTalks.com</a> and she did the heavy lifting of selecting thought provoking images. This activity takes advantage of the sketch tool in a perfect situation. When working with these on paper, students can get lost in what they are subdividing shapes into. The beauty here is they can label, draw lines, and erase. Then they can describe their thoughts with words, submit to class, and see small sketches and explanations of their classmates.<br /><br />I also used teacher pacing so students would be thoughtful and not just rush on to the next slide. I then PAUSED (big groan from class), asked for Chromebook screens to be almost closed to an acute angle, anonymize class responses, and review students work. Students were slowing it down by claiming work and shouting out it wasn't theres, so it went slowly as I had to remind students of my expectations.<br /><br />MANY students made the following mistake on the first slide:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-KA4ZD5xtpSE/WNnlr6xt0sI/AAAAAAAADCo/S6ZCk-QBM0o6a4lx9jJPSQzFEUX7YT_zQCLcB/s1600/Screen%2BShot%2B2017-03-27%2Bat%2B9.14.25%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="159" src="https://4.bp.blogspot.com/-KA4ZD5xtpSE/WNnlr6xt0sI/AAAAAAAADCo/S6ZCk-QBM0o6a4lx9jJPSQzFEUX7YT_zQCLcB/s320/Screen%2BShot%2B2017-03-27%2Bat%2B9.14.25%2BPM.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">It is the classic mistake of seeing 4 shapes, and since 1 of the shapes is red, then 1 out of 4 shapes are red, or 1/4 of the shape is red. I asked students who disagreed why they did. Eventually they said that you can't compare them if they are not the same shape.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-00QenZaC0eY/WNnlr_0kZHI/AAAAAAAADCk/fZUT7-K2SDoPULd91iOcw6BaVDpYWtnzgCLcB/s1600/Screen%2BShot%2B2017-03-27%2Bat%2B9.14.50%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="159" src="https://2.bp.blogspot.com/-00QenZaC0eY/WNnlr_0kZHI/AAAAAAAADCk/fZUT7-K2SDoPULd91iOcw6BaVDpYWtnzgCLcB/s320/Screen%2BShot%2B2017-03-27%2Bat%2B9.14.50%2BPM.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Then students saw the couple examples that were correct. They could see that these students had divided the other colors into triangles that were of equal size to the red triangle. My colleague had an interesting thought that some students might have said 1/4 because they were color blind and couldn't see the red and orange. I don't believe many students thought this or else they may have said 2/8 is red.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">As we all know, the correct answer is 1/8. One student actually said 1/7, and I wanted to honor what was right about that. That student had described the part to part ratio, or in other words, there was 1 part red to 7 parts NOT red. This thinking is clearly further along than the 1/4 thinking.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Once we had discussed it in depth, we moved on to the next slide. Students felt much more confident and were much better equipped with strategies to succeed with this image. They immediately started dividing everything into triangles and said it was 3/8. Their explanations got A LOT better too.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-N4ezQ2OlTGw/WNnlrx1zHTI/AAAAAAAADCg/O4NQe-6Gs5UATb-0Y8mfTgjlrbApxZfwACLcB/s1600/Screen%2BShot%2B2017-03-27%2Bat%2B9.16.16%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="173" src="https://3.bp.blogspot.com/-N4ezQ2OlTGw/WNnlrx1zHTI/AAAAAAAADCg/O4NQe-6Gs5UATb-0Y8mfTgjlrbApxZfwACLcB/s320/Screen%2BShot%2B2017-03-27%2Bat%2B9.16.16%2BPM.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">And I love the anecdote about the student below here. He had come up with the answer, and kept disagreeing with all of the people that had put 3/8. I saved his for last to analyze.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-KPMEIdcWGAc/WNnlsWNX1sI/AAAAAAAADCs/OdkNzR3gC_oo7vbfnZJzDQy3ei_Oc9N3QCLcB/s1600/Screen%2BShot%2B2017-03-27%2Bat%2B9.16.22%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="168" src="https://1.bp.blogspot.com/-KPMEIdcWGAc/WNnlsWNX1sI/AAAAAAAADCs/OdkNzR3gC_oo7vbfnZJzDQy3ei_Oc9N3QCLcB/s320/Screen%2BShot%2B2017-03-27%2Bat%2B9.16.22%2BPM.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">So, I wrote 6/16 on the board, and 3/8 next to it. I asked the class, "Who is correct?" One student bravely raised her hand and said, they are both right. 6/16 simplifies to 3/8, because you can divide both numbers by 2. Mind you, students had worked on that skill in recent weeks but this student was able to articulate a context in which there would be a NEED to know how to simplify.</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 activity has a few more sketches, and I believe uses the Card Sort feature to do some flag matching, but as I said, we didn't get more than 2 slides in, but it was a very rich discussion and I'd like to thank Alison for providing the link. I will definitely bust this out with my 7th and 8th grade math support during some free time at some point near the end of the year.</div><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-86393311437040011932017-03-22T20:29:00.000-07:002017-03-22T20:29:02.830-07:00Fishbowl... A @CPMmath Study Team StrategyWith one third of the school year left, I felt it was a good time to try out a study team strategy I had never done before: a Fishbowl. I remember doing it at the Academy of Best Practices at Seattle University and finally decided to use it. I think students needed a strong reminder of what the study team norms were.<div class="separator" style="clear: both;"></div><div><br /></div><div>So, I picked 1 group that seemed to work well together the day before, and a table next to them. I then asked the whole class to get their composition book and pencil and without talking surround the two tables. We were going to silently observe them use their study team roles to start and complete the first 2 problems of the lesson 8.2.2. I selected these because the first problem set is review of exponents from yesterday's lesson where they had to write the multiplying of power numbers in a simpler form. The second problem involved error analysis where the student correctly expanded the powers, but put addition signs between them and multiplied them out instead of writing them in simplified exponent form.</div><div><br /></div><div>I asked students take notes on positive actions and actions the team could improve upon. After they finished, we would debrief right there, of course starting with the positives. Then we talked about what they could improve, and then they returned to their seats and I said now show that you can do it just as good or better!</div><div><br /></div><div>In first period, here were my observations:</div><div><br /></div><div>First off, the facilitator immediately asked, "who wants to read?" I then heard one student claim they read first last time, so they didn't want to read. The person that agreed to read was reading fast and mumbling. They weren't reading clearly. I think it was to draw attention to themselves...? J was saying his work aloud, saying how he was expanding the power number or writing it in factored form. T from the other group was doing the same. J asked V, "Are you on 8-60?" One member didn't write it in simplified exponent form, but went back and fixed it. When we debriefed, students noticed that two of the group members barely said anything. In the other group, I complimented I for responding to a students answer by saying, "OK. Why?" That was a great example of a student prompting another for their reasoning. We also talked about how the recorder reporter should have been looking at everyone's paper to be sure it was written correctly to move on. The next day one student asked if we were doing a fish bowl again. I said, "No. Why?" He said that if he was in the group that's the fish bowl he could get a head start on his work... (He usually works ahead, but has gotten better at it with my reinforcements of not doing so)</div><div><br /></div><div>In second period, a student started reading right away, but skipped the introduction! In the other group, they started reading right away, but the introduction first. Group 6 moved on when they were done, and confirmed with their group that everyone was done. Group 7 moved on to the next problem, without going over the answers to 8-59. I observed some weren't finished, and didn't speak up. Group 6 moved on, but didn't write it in simplified exponent form. In the debrief, we saw how both groups started quickly. One moved on too quickly without making sure the group was ready. Also, group 6 didn't fully read the directions of writing it in a simpler form. This reinforced making sure you understood what the question was asking.</div><div><br /></div><div>In fifth period, both groups started reading quickly. A suggested an idea. A also asked, "Are you done writing that down?" In the other group, M confirmed that they agreed with another group members idea. There also were no arguments about who wanted to read. One higher student didn't have the courage to speak up about disagreeing about the team's idea. C suggested an idea. One student said, "It'd be like..." which I mentioned in the debrief. as a good way to describe how you are going to write it, and to get confirmation from your group. When students shared, they said that A was dominating the discussion and not giving other team members a time to share their ideas, or use wait time. I talked about how as teachers we need to give students wait or think time, and students need to give each other time to think also. We also liked how there was some positive nervous clapping when they got an answer right and all agreed.</div><div><br /></div><div>So, in conclusion, this is a great study team strategy. It's perfect to do when you feel like students aren't working together as well as they can and to remind students what the expectations are, by seeing what you should and shouldn't do.</div><div><br /></div><div>Also, I thought it would put the other groups way behind, but they had heard the discussions before, so it made their start a little more smoother and efficient because they had listened to two different groups.</div>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-373027288318892672017-03-18T18:40:00.004-07:002017-03-18T18:40:56.084-07:00Fraction Talks warmup @FractionTalks @mathletepearce<div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-andvj97SM3U/WGGO45qnY-I/AAAAAAAAC74/5QyOdvUU4-c/s640/blogger-image--1980666498.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;">I can't take credit for the below image. I found it on twitter. It's located here and above under my Fav Problems. The variety of ideas and misconceptions with this problem make it a must-do warm-up in every classroom.</div><div class="separator" style="clear: both;"><img border="0" src="https://lh3.googleusercontent.com/-andvj97SM3U/WGGO45qnY-I/AAAAAAAAC74/5QyOdvUU4-c/s640/blogger-image--1980666498.jpg" /></div><div class="separator" style="clear: both;">As you can see below, I treated it like a number talk. I had students share all their answers, without any reaction or judgment, and asked students to defend their answer.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-andvj97SM3U/WGGO45qnY-I/AAAAAAAAC74/5QyOdvUU4-c/s640/blogger-image--1980666498.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-pSAfj4wflR0/WGGO7LFqVPI/AAAAAAAAC78/60u630g0IG4/s640/blogger-image--1228022737.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-pSAfj4wflR0/WGGO7LFqVPI/AAAAAAAAC78/60u630g0IG4/s640/blogger-image--1228022737.jpg" /></a></div><div class="separator" style="clear: both;">As you can see in the top right, Juliana's idea was that there's 1 hexagon in the middle. But if there are 6 trapezoids on the outside, 2 of those trapezoids can be rearranged to make 1 hexagon. So 6 trapezoids would make 3 hexagons. Therefore she reasoned that 1/4 of the shape was yellow, because if the whole shape is 4 hexagons, only 1 of them is yellow.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Victor said that the yellow hexagon in the middle was 2 trapezoids, or 2 reds. So, if there's 6 reds on the outside, that's 8 total. Therefore, he said 2/8 are yellow.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">I did want to acknowledge the wrong answer of 2/6, because that is the ratio of yellow to red, so there's something correct about that. It's just not the part/whole ratio that we are looking for when we say what fraction of the shape is yellow.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">I also asked students how someone could say 1/7. They said they probably saw 1 yellow shape out of 7 total shapes. Students said you couldn't do this because they are not all the same sized shapes.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">One student said 1/2 of the shape is yellow because a hexagon is half of a trapezoid... a good thought that wasn't extended though to the whole shape.</div><br /><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-andvj97SM3U/WGGO45qnY-I/AAAAAAAAC74/5QyOdvUU4-c/s640/blogger-image--1980666498.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-_3b2l4xH608/WGGO9NGKYYI/AAAAAAAAC8A/V6_D6UhDRls/s640/blogger-image--362183562.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-_3b2l4xH608/WGGO9NGKYYI/AAAAAAAAC8A/V6_D6UhDRls/s640/blogger-image--362183562.jpg" /></a></div><div class="separator" style="clear: both;">I had to take a picture of this one because all day this was the only person who thought of it this way. The student said you can make the whole shape triangles, and a hexagon is 6 y yellow triangles, and there would be 24 triangles total, so 6/24 is yellow.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Every period I mention the way I see it if no one has said it yet, which is noticing the shape is symmetrical, and if you cut it in half you have 1 yellow trapezoid out of 4 total trapezoids, for 1/4.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">More images like this can be found on fractiontalks.com. We have also worked in some of the flag matches from that site which are pretty awesome and cross curricular.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">This blog post was inspired to by a video @mathletepearce made and the conversations on Twitter that followed.</div><div class="separator" style="clear: both;"><br /></div><blockquote class="twitter-video" data-lang="en"><div dir="ltr" lang="en">Fraction Constructs: Part-Part Relationships. This time, Doritos Roulette "Hot" or "Not"? <a href="https://twitter.com/hashtag/MTBoS?src=hash">#MTBoS</a> <a href="https://twitter.com/hashtag/mathchat?src=hash">#mathchat</a> <a href="https://twitter.com/hashtag/edchat?src=hash">#edchat</a> <a href="https://t.co/vVX1eohceV">pic.twitter.com/vVX1eohceV</a></div>— Kyle Pearce (@MathletePearce) <a href="https://twitter.com/MathletePearce/status/812044578677288960">December 22, 2016</a></blockquote><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script><blockquote class="twitter-tweet" data-lang="en"><p lang="en" dir="ltr">Fraction Constructs: Part-Part Relationships. This time, Doritos Roulette "Hot" or "Not"? <a href="https://twitter.com/hashtag/MTBoS?src=hash">#MTBoS</a> <a href="https://twitter.com/hashtag/mathchat?src=hash">#mathchat</a> <a href="https://twitter.com/hashtag/edchat?src=hash">#edchat</a> <a href="https://t.co/vVX1eohceV">pic.twitter.com/vVX1eohceV</a></p>— Kyle Pearce (@MathletePearce) <a href="https://twitter.com/MathletePearce/status/812044578677288960">December 22, 2016</a></blockquote><script async src="//platform.twitter.com/widgets.js" charset="utf-8"></script>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-867370194962933432017-03-18T18:09:00.000-07:002017-03-18T18:09:08.032-07:008.SP.4 IM Task 2 way frequency table student survey samples & rubric<div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-jDJROZxEQtA/WL-iyBfXijI/AAAAAAAADAQ/zcdGker5gzA/s640/blogger-image--1391310195.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-jDJROZxEQtA/WL-iyBfXijI/AAAAAAAADAQ/zcdGker5gzA/s640/blogger-image--1391310195.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-TTn_zFgIUTY/WL-iuLbiP0I/AAAAAAAADAI/2G2MRw3S-a8/s640/blogger-image-1173860708.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-TTn_zFgIUTY/WL-iuLbiP0I/AAAAAAAADAI/2G2MRw3S-a8/s640/blogger-image-1173860708.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-9WU8XtmVgBU/WL-iwEae8NI/AAAAAAAADAM/sZXRiAfIMlU/s640/blogger-image--1029799743.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-9WU8XtmVgBU/WL-iwEae8NI/AAAAAAAADAM/sZXRiAfIMlU/s640/blogger-image--1029799743.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-hjuIFz8Qbe4/WL-i0RtthFI/AAAAAAAADAU/uxawwl-OeiU/s640/blogger-image-1625205245.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-hjuIFz8Qbe4/WL-i0RtthFI/AAAAAAAADAU/uxawwl-OeiU/s640/blogger-image-1625205245.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-VbjNJ62rF7Y/WL-in8xVm-I/AAAAAAAAC_8/hLKgA4e7G1I/s640/blogger-image-1585709283.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-btnQYRaaafU/WL-ip6dHzCI/AAAAAAAADAA/eJHArLVFPEo/s640/blogger-image--786905741.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-btnQYRaaafU/WL-ip6dHzCI/AAAAAAAADAA/eJHArLVFPEo/s640/blogger-image--786905741.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-AsYZYDSKw1g/WL-ir3iZzTI/AAAAAAAADAE/ssNQPKHUjro/s640/blogger-image-1440898731.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-AsYZYDSKw1g/WL-ir3iZzTI/AAAAAAAADAE/ssNQPKHUjro/s640/blogger-image-1440898731.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-mC6HcBs8uVM/WL-jhpyVziI/AAAAAAAADAc/ZkOzu-ezWwc/s640/blogger-image-1727980223.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-mC6HcBs8uVM/WL-jhpyVziI/AAAAAAAADAc/ZkOzu-ezWwc/s640/blogger-image-1727980223.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-5j3QSEzVMDE/WL-jjorgetI/AAAAAAAADAg/O9aEDzajVYM/s640/blogger-image-8236284.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;">I wrote a <a href="http://joyceh1.blogspot.com/2017/01/nctm-blog-post-4-replacing-textbook.html">blog post for NCTM</a> about the lesson used. I also have an idea about how to score the assignment using a rubric and already want to label the columns independent variable and the rows dependent variable so students know why they are totalling the columns for the relative frequencies.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">This post will have my reflection notes, the scoring rubric that I'd love feedback to improve, and some interesting student work samples of varying levels of understanding.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">I have improved the <a href="https://docs.google.com/drawings/d/1LApmesk6DaXKSZzjiQKJBiOJcBNPj7RMsWOSxTQyLXs/edit?usp=sharing">survey assignment template</a> with the following: each question is labeled. The independent and dependent variable are labeled on the table and in the hypothesis example sentence. I also added to the conclusion by adding <span style="font-family: inherit;">"<span style="white-space: pre-wrap;">Therefore if ________________________, you are more likely to ___________________.</span></span></div><span id="docs-internal-guid-d87d4062-e36e-03ef-b1c8-a7a0a557a9b3"><span style="font-family: inherit;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="vertical-align: baseline; white-space: pre-wrap;">My hypothesis was...correct or incorrect? conclusive or inconclusive?"</span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;">I also discussed this lesson with some colleagues from my FAME program and one had a great suggestion! An alternative to calling out students name for yes yes, no no, yes, no, or no yes votes you could ask the class who play a musical instrument? If yes, line up in a column on left side of room. If no in a column on the other side of the room, parallel to the rest of the class in the other line.</span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;"><br /></span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;">Then when you ask the next question, do you play a sport? Those groups separate into different corners of the room. For example yes can step forward, no can step back. You now have the four quadrants of the 2 way table and you can visually see how much bigger the group of students may be that play an instrument and a sport, compared to the students who play an instrument and no sport. I want to try this next time.</span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;"><br /></span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;">To help me make a rubric, I looked at each classes results and separated them into piles: 1 pile if they didn't finish the survey or filling out the two way table (only 2 or 3 students per class), another pile if they got the hypothesis, conclusion, and relative frequency percents. Then a middle pile if they were missing the fractions & percents and/or their conclusion.</span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;"><br /></span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;">My rough rubric was students earned a 4, or A if they had their column totals, fractions, percents, hypothesis stated, questions clear, and a conclusion using the data as evidence. Students got a 3 if they were missing the percents or conclusions. A 2 was earned by not stating their hypothesis and hypothesis. A 1 was given to students who completed the survey and filled out the table, a 0.5 if they attempted, and a 0 if I didn't receive the assignment.</span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;"><br /></span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;">Some students did not complete the fractions or relative percents because they were reading the wrong row or column or didn't understand how to do it in general.</span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;"><br /></span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="white-space: pre-wrap;">Note to self, I need to put that rubric as a small footer to the assignment sheet so students know what I am looking for and could make it easier to grade by marking the grade with comments on the rubric.</span></div><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="vertical-align: baseline; white-space: pre-wrap;"><br /></span></div></span></span><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-5j3QSEzVMDE/WL-jjorgetI/AAAAAAAADAg/O9aEDzajVYM/s640/blogger-image-8236284.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-SVNXPpQG84c/WL-jfcqkp9I/AAAAAAAADAY/04Feva3t6pM/s640/blogger-image--314403824.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-SVNXPpQG84c/WL-jfcqkp9I/AAAAAAAADAY/04Feva3t6pM/s640/blogger-image--314403824.jpg" /></a></div><div class="separator" style="clear: both;">Above is my reflection notes with items I wanted to mention in this blog post.</div><img border="0" src="https://lh3.googleusercontent.com/-5j3QSEzVMDE/WL-jjorgetI/AAAAAAAADAg/O9aEDzajVYM/s640/blogger-image-8236284.jpg" /><br />This student nailed the concept and even had time to decorate it a bit. Her hypothesis was correct, if you watch cartoons you have an 88% chance of watching Spongebob.<br /><img border="0" src="https://lh3.googleusercontent.com/-mC6HcBs8uVM/WL-jhpyVziI/AAAAAAAADAc/ZkOzu-ezWwc/s640/blogger-image-1727980223.jpg" /><br />This student mixed up their conclusion a bit. Great survey idea. His hypothesis was correct. What he meant to say I believe is of the 20 people who are 49ers fans, 17 are also giants fans. I also see that his joint frequencies don't add up properly to his marginal frequencies, so there's some type of miscalculation going on here.<br /><img border="0" src="https://lh3.googleusercontent.com/-AsYZYDSKw1g/WL-ir3iZzTI/AAAAAAAADAE/ssNQPKHUjro/s640/blogger-image-1440898731.jpg" /><br />Good work and conclusion, just missing the percents to support the conclusion.<br /><img border="0" src="https://lh3.googleusercontent.com/-btnQYRaaafU/WL-ip6dHzCI/AAAAAAAADAA/eJHArLVFPEo/s640/blogger-image--786905741.jpg" /><br />This was interesting... The above picture is 2 students who had one of their questions be do you like to read? What's shocking is the results are different. To me, this means either some kids changed their answers as the class progressed, or they answered the question differently based on who was asking them the question. I am not sure.<br /><br /><img border="0" src="https://lh3.googleusercontent.com/-VbjNJ62rF7Y/WL-in8xVm-I/AAAAAAAAC_8/hLKgA4e7G1I/s640/blogger-image-1585709283.jpg" /><br />A socioeconomic question that had no surprises. Stellar work. Actually, just noticed that they made a mistake with the top right joint frequency of 7, which should have been 7/7 for 100%.<br /><img border="0" src="https://lh3.googleusercontent.com/-hjuIFz8Qbe4/WL-i0RtthFI/AAAAAAAADAU/uxawwl-OeiU/s640/blogger-image-1625205245.jpg" /><br />Good work here.<br /><img border="0" src="https://lh3.googleusercontent.com/-9WU8XtmVgBU/WL-iwEae8NI/AAAAAAAADAM/sZXRiAfIMlU/s640/blogger-image--1029799743.jpg" /><br />This was interesting. 31 students were asked if they liked school. 20/31 said they didn't like school. Of those 20, 1 of those kids wanted to be a teacher!! Shocking! I'm very curious who this student is. What was surprising also was that of the 11 kids who liked school, none wanted to be a teacher.<br /><img border="0" src="https://lh3.googleusercontent.com/-TTn_zFgIUTY/WL-iuLbiP0I/AAAAAAAADAI/2G2MRw3S-a8/s640/blogger-image-1173860708.jpg" /><br /><img border="0" src="https://lh3.googleusercontent.com/-jDJROZxEQtA/WL-iyBfXijI/AAAAAAAADAQ/zcdGker5gzA/s640/blogger-image--1391310195.jpg" /><br />This student had a great hypothesis and survey. Just made a mistake when calculating the relative frequencies. They used the total student surveyed as the denominator rather than the total students who were born in the U.S. of 26.Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-84668172353890148862017-02-19T19:10:00.005-08:002017-02-21T21:33:09.755-08:00#clotheslinemath Linear EquationsI am going to teach this lesson on Tuesday to all 3 of my Common Core 8 classes. Any feedback or suggestions prior to that are appreciated. A reflection of how it unfolded to follow. I wanted all the images in one place for my colleagues to use and for anyone else to try. All credit goes to Andrew Stadel and Chris Shores for the lesson, I just added a small extension.<br /><br /><iframe allowfullscreen="true" frameborder="0" height="569" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/1qOk_K8tjQwXmcBSnQve8_PlWmuQ6-ZfVE-zZ4tfqxgE/embed?start=false&loop=false&delayms=3000" webkitallowfullscreen="true" width="960"></iframe> UPDATE: (2/21/17)<br /><br />I noticed students drew the number line cards really big after looking at the google slides. For each period after I made sure students knew they needed room on their paper for 2 clothesline and 2 graphs to be pasted on.<br /><br />I had students think for 3 minutes how the 6 parameter cards could be placed on the lower clothesline. I demonstrated how if a card lined up with a number, they would be equal or equivalent. I also demonstrated how you could clip a card underneath another using the clothespin.<br /><br />I then asked students to place the cards individually with 3 minutes of silent independent work time. Then I timed them for another 3 minutes of taking turns sharing out their ideas to their group, to gain confidence in sharing their idea with the class.<br /><br />With 6 parameter cards, I said that we would need 6 different students put up 6 different cards and give a statement to the class about what they did and why they chose to put it there. I had students vote using their thumbs whether they agreed or disagreed with a person's statement. I asked students put their thumb sideways if they didn't whether the person was right or wrong. In first period students immediately went for the growth of line 2, or m2, was 0.<br /><br />Students seemed to see that the blue line's growth had to be 2, because it was the steepest, and it was increasing from left to right so it had to be a positive number, so they said it couldn't be 1 and picked 2. Some students also reasoned that the red line must have a smaller slope but negative because it was decreasing slowly.<br /><br />One student talked about how the y-intercept of the red line had to be 2, because the blue line was also the same distance from zero being at -2. I asked the students what we call distance from zero, and some remembered that was the absolute value.<br /><br />After students had placed cards m1 to m3 and b1 to b3, I handed out the desmos graph. I asked them to paste it in their notebook and then see if they agreed with how the clothesline was from the last image. Students noticed that they appeared the same, and the y-intercepts were definitely the same.<br /><br />I pointed out when students were drawing slope triangles between lattice points, but am not sure if all students correctly did so as I walked around the room.<br /><br />Students had a bit of trouble with the scale of the graph, with each square being 0.5. This lead them to see that the vertical growth was 1.5, and the horizontal growth was 1. I asked them what the slope triangle was in grid squares, which gave 3/2. Students reasoned that must be between 1 and 2.<br /><br />I did not get to the part of putting m4 under -1, and b4 under 1. If I had more time I would have. My colleague said his class also had trouble substituting the new m values into the equation y=mx+b to try to confirm that the lines would intersect algebraically.<br /><br />It was nice to see that after some students noticed the lines would intersect, that they could prove it graphically. In each class a student hung x and y under the respective coordinates for the intersection point.<br /><br />Some students thought there might need to be 3 sets of x and y coordinates since there were 3 different lines.<br /><br />Overall I loved the activity. It had a sense of mystery. Also, having a graph with grid lines achieved my goal of practicing calculating slope. I am still concerned how many students left the class with a solid handle on it. I liked how I made sure they had some independent think time before sharing with their group because if it's straight to group it tends to be the same people sharing. Students also liked the chance of going up to the board with the whole class watching, while others were nudged towards giving their reasons for agreeing with someone from their seat.Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-21628567892518978122017-02-01T21:36:00.001-08:002017-02-01T21:36:22.858-08:00Hot Seat Study team Strategy (@cpmmath Transformations)This past summer I had the pleasure of applying for and being accepted to CPM's TRC research group in Sacramento. After brainstorming ideas, my group was formed with Aristotle and Erica. The great part was that we all taught 8th grade and were concerned about students doing their homework, specifically the Review and Preview. We decided we would focus on taking breaks from the lessons once in awhile to focus class time on individual practice as well as group work on review preview problems. We are also trying to show students the benefits of mixed spaced practice compared to a bunch of practice problems of the same type. Another concern was if students don't do the homework, they are getting very little individual practice to self-assess. It's also important to make homework worth part of the grade, but not a big part. My colleague and I settled on 15%.<br /><br />Part of the work we did was work on how to check it, and with some collaboration with Erica and some ideas from Dylan Wiliam's Embedded Formative Assessment, students have a quarter sheet of paper to check 5 assignments. I can share this if anyone wants it. Most days students self check. Others they peer check. Once in awhile, a whole group switches their work with another group so they get a different group's opinion of their work. Also, if and when students lose the checking sheet, if they want credit, they have to show it to me personally, and of course I look it over a lot more closely!<br /><br />Participation quizzes have been helpful, as well as pair checks, which I detailed in an <a href="http://www.nctm.org/Publications/Mathematics-Teaching-in-Middle-School/Blog/Cooperative-Learning-Strategies/">NCTM blog post recently</a>. After a recent Skype meeting, Erica reminded me and suggested I use the Hot Seat strategy. The rules are detailed below in the Google slides, as well as the problems students focused on. I had never used this strategy before as I was concerned about the competitive feel, students feeling inferior, and the timing of the activity. I will address those concerns in this post.<br /><br /><iframe allowfullscreen="true" frameborder="0" height="569" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/1FEdk22qWrxM4ptwtjLuGnBCmr2xSpZ3zKxu-I-XH2LA/embed?start=false&loop=false&delayms=3000" webkitallowfullscreen="true" width="960"></iframe><br /><br /><br class="Apple-interchange-newline" />So, as described in the first slide above, 1 student brings their seat to the back of the room, and works individually with no help. To make this quick, I said resource manager (assigned team roles based on the alphabetical order of their first name in their group). If they get it right, they earn their team 2 points. If everyone in their group gets it right with all work shown, the team gets 1 point. I kept track of the points, and students were very honest. It was instant formative assessment.<br /><br />As you can see, we are finishing up Chapter 6 which has closure problems. Instead of saying students, work on these problems. I mixed up the order and focused it on transformations.<br /><br />For the first problem, students only needed 3 minutes to figure out the scale factor. Some asked which is the original and which is the new figure? I told them they could decide. I also said to not use calculators.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-XZaXJgRFSqA/WJLCjQdGawI/AAAAAAAAC-o/imHoRZD_frExiLwgEPrvgKrZzEa5YZ0vwCLcB/s1600/IMG_9257.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto; text-align: center;"><img border="0" height="240" src="https://3.bp.blogspot.com/-XZaXJgRFSqA/WJLCjQdGawI/AAAAAAAAC-o/imHoRZD_frExiLwgEPrvgKrZzEa5YZ0vwCLcB/s320/IMG_9257.JPG" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Students in the back row are on the hot seat.</td></tr></tbody></table>After keeping the score, facilitators were up next. I gave them 7 to 8 minutes for this because they had to start with one transformation, and then finish the steps. I would circulate asking questions and giving advice to students who needed it.<br /><br />I asked students for feedback informally in each class. A student that doodles and doesn't engage with her group much liked that it was more individual based and the timing made her focus more on finishing the problem. A struggling student said she didn't like it because she couldn't get help from her group when on the hot seat. Students were much more quickly to adjust their paper and body to point to their work while verbally explaining a concept.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-Xb9vMMq7aGA/WJLCv1EB6YI/AAAAAAAAC-0/BdEfkyKr9bgPqmhttL3yxpufBDFnNVm0ACLcB/s1600/IMG_9263.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto; text-align: center;"><img border="0" height="240" src="https://2.bp.blogspot.com/-Xb9vMMq7aGA/WJLCv1EB6YI/AAAAAAAAC-0/BdEfkyKr9bgPqmhttL3yxpufBDFnNVm0ACLcB/s320/IMG_9263.JPG" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">From my classroom door, you can see everyone focusing on the problem, book, or glancing at the board for the problem.</td></tr></tbody></table>Also, when creating the graph, the class got dead silent in concentration, and then you could start hearing whispers in the groups when they were comparing how they rotated or reflected a shape if their triangles looked the same.<br /><br />I was also able to implement the 5 practices using my Google Drive app by taking photos of student work to share when going over the answer and awarding the points.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-wL_t-eOo6rg/WJLCdxr7-TI/AAAAAAAAC-g/xWIB4_5F_Qs0x2gPnYcQyHqc0JRh9r3qQCLcB/s1600/IMG_9258.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-wL_t-eOo6rg/WJLCdxr7-TI/AAAAAAAAC-g/xWIB4_5F_Qs0x2gPnYcQyHqc0JRh9r3qQCLcB/s320/IMG_9258.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">For the second problem for list 1, it asks for a 180 degree rotation. A student asked which direction clockwise or counterclockwise? Another student answered, "it doesn't matter it will look the same!"</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-w_SlcAn-Rek/WJLCeUapo2I/AAAAAAAAC-k/cYGVD7OLXe8rmAYr3f-ut4sVLKP1USEcQCLcB/s1600/IMG_9259.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-w_SlcAn-Rek/WJLCeUapo2I/AAAAAAAAC-k/cYGVD7OLXe8rmAYr3f-ut4sVLKP1USEcQCLcB/s320/IMG_9259.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Here you can see that same triangle successfully reflected over the y-axis. Then student volunteers said you could then reflect it over the x axis and then translate it up 1 and over 2.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-HBGVXfK7deM/WJLCr42CK8I/AAAAAAAAC-s/XRs8R9Y-AU8LkA51MfvBn8AUWKSx_4FrgCLcB/s1600/IMG_9261.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-HBGVXfK7deM/WJLCr42CK8I/AAAAAAAAC-s/XRs8R9Y-AU8LkA51MfvBn8AUWKSx_4FrgCLcB/s320/IMG_9261.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">This photo shows the same problem, but also the second one where after graphing a triangle students were asked to reflect it over the y axis. Separately they were asked to translate it, and describe what happened to the coordinates.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-LQ2YuL9T2H8/WJLCuUXtnLI/AAAAAAAAC-w/Xk7K2Q_ojLoouCxECtr9sQnnP-o6Ca8NACLcB/s1600/IMG_9265.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-LQ2YuL9T2H8/WJLCuUXtnLI/AAAAAAAAC-w/Xk7K2Q_ojLoouCxECtr9sQnnP-o6Ca8NACLcB/s320/IMG_9265.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Here is 2nd period's scoreboard.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-yDMMnXINOkQ/WJLC4Pnpx0I/AAAAAAAAC-4/eKWgRBHs0RsOIA9x_jta257FrzAF5TaFQCLcB/s1600/IMG_9266.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-yDMMnXINOkQ/WJLC4Pnpx0I/AAAAAAAAC-4/eKWgRBHs0RsOIA9x_jta257FrzAF5TaFQCLcB/s320/IMG_9266.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Numbered steps that were easy to read.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Yy3WlxPfsyw/WJLC6EXaPhI/AAAAAAAAC-8/ylXLMx-F-jsY6SwR4q5RO0WRDmE9ygOKwCLcB/s1600/IMG_9267.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-Yy3WlxPfsyw/WJLC6EXaPhI/AAAAAAAAC-8/ylXLMx-F-jsY6SwR4q5RO0WRDmE9ygOKwCLcB/s320/IMG_9267.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Here you can see the horizontal, then vertical translation. You can also see the correct reflection over the y-axis. I asked students that made mistakes reflecting, "how far away is the shape from the axis you are trying to reflect it over?" This moved them in the correct direction.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-0c5lUyYHOLo/WJLC6VGq0aI/AAAAAAAAC_A/B91osIoNDSMgwvLDs2r0bDL56gCCQsojwCLcB/s1600/IMG_9268.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-0c5lUyYHOLo/WJLC6VGq0aI/AAAAAAAAC_A/B91osIoNDSMgwvLDs2r0bDL56gCCQsojwCLcB/s320/IMG_9268.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Here you can see how students were able to show expressions for what happens to the coordinates when moving 4 to the right and down 6. They would have to add 4 to the x coordinate, and subtract 6 from the y coordinate.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Also, for reflecting, they had to multiply the x coordinate by -1, and leave the y coordinate alone.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">My colleague and his students really enjoyed the hot seat activity as well. I picked a wednesday to try it since it was a shorter period and I knew they wouldn't be able to finish the 6.2.6 lesson during a short period.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Unfortunately, we only got through 3 rounds, but a LOT of learning happened, and these were dense problems. I had a short warm-up, reviewed 2 homework problems briefly, passed back a test that I went over, and then did the Hot Seat. The resource managers didn't get a chance to be on the hot seat, but I'm definitely going to do this again with a goal of students being on the hot seat more than once.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">At the beginning, I told students that the goal of this activity was to see where you are at individually with their understanding, and to also appreciate the PRIVILEGE of working cooperatively in a group. I am very confident that students will be working much harder together tomorrow when working on a problem solving task about scale factors between models and real life objects.</div><br />Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-74064471533844296032017-01-31T20:12:00.003-08:002017-01-31T20:12:30.641-08:00Similar Figures Academic Vocabulary @von_Oy<div class="separator" style="clear: both;">This post was inspired by Suzanne blogging about the precise language she wants by not naming a method "difference of squares" when it could pigeonhole students into a procedure without knowing really why it works. I can also empathize with teaching students the definition of a function through examples. It can be disheartening when the only answer you get is it passes the vertical line test. I like when students on their assessments would draw the vertical line and the points it passes through, labeling those as the input that has 2 different outputs.</div><blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en">New blog post! Weighing how robust math vocab in the classroom can both help and hurt comprehension. <a href="https://twitter.com/hashtag/mtbos?src=hash">#mtbos</a> <a href="https://t.co/NvukQP3Cjv">https://t.co/NvukQP3Cjv</a></div>— Suzanne von Oy (@von_Oy) <a href="https://twitter.com/von_Oy/status/825364314546642945">January 28, 2017</a></blockquote><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script> <div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">I was concerned about how my students were processing the attributes of similar figures. CPM has a great lesson where there is an original quadrilateral with a bunch of other shapes that are similar except for 2 of them. One is horizontally stretched, while the other is vertically stretched. As students compare the shapes, they can see that the corresponding angles of the non-similar shapes are clearly different measurements. Also, corresponding sides that should be parallel are intersecting. They also should be able to count how many times a corresponding side can fit into another similar shapes corresponding side to figure out the scale factor.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Since I was concerned with students understanding, I gave students a post it note, 5 or 6 minutes, and the following prompt:</div><div class="separator" style="clear: both;"><br /></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: white; color: black; font-family: "arial"; font-size: 24pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">How do you know if two shapes are similar? When does a dilation make the shape bigger? Smaller?</span></div><div class="separator" style="clear: both;"><b id="docs-internal-guid-a5088b32-f7d7-64ad-8fed-46674223a634" style="font-weight: normal;"><br /></b></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: white; color: black; font-family: "arial"; font-size: 24pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A complete answer would mention all of the following words:</span></div><div class="separator" style="clear: both;"><b style="font-weight: normal;"><br /></b></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: white; color: black; font-family: "arial"; font-size: 24pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> size, scale factor, angles, congruent, corresponding, parallel</span></div><div class="separator" style="clear: both;"><br /></div><span style="background-color: white; font-family: "arial"; font-size: 15pt; vertical-align: baseline; white-space: pre-wrap;">Feel free to add a labeled diagram to show your thinking.</span><br /><div class="separator" style="clear: both;"><span style="background-color: white; font-family: "arial"; font-size: 15pt; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div><div class="separator" style="clear: both;">I got a variety of responses. Some students included the words, but not in the correct context.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Surprisingly, many students said that similar figures are congruent. To this I commented, "always?" It was hard for students to use the word corresponding and angles in the correct way. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">We don't take notes that often, but synthesized their thinking. Students realized a similar figure that was enlarged would have a scale factor greater than 1, a shape that shrunk would be a fraction between 0 and 1, and a congruent shape would have a scale factor of 1.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-VP9LYPTR3PQ/WI4sbyg0TbI/AAAAAAAAC-I/vkSvPL8a6qI/s640/blogger-image-977781825.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-VP9LYPTR3PQ/WI4sbyg0TbI/AAAAAAAAC-I/vkSvPL8a6qI/s640/blogger-image-977781825.jpg" /></a></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">This work was after dilating on the coordinate plane, and this was nailing down all the academic language.</div>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com2tag:blogger.com,1999:blog-2523946538193054194.post-29836985090318210502017-01-31T19:56:00.002-08:002017-01-31T19:56:31.161-08:00@cpmmath 6.1.2 Rigid Transformations<div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-AWk1Ucb0NpY/WHmsXDThhSI/AAAAAAAAC80/Nxv2Tfewj14/s640/blogger-image-1041328089.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-AWk1Ucb0NpY/WHmsXDThhSI/AAAAAAAAC80/Nxv2Tfewj14/s640/blogger-image-1041328089.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-gFkm5Gih4L0/WHmsZWNFIDI/AAAAAAAAC84/3aMpQfItQp4/s640/blogger-image--1675577679.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;">If you haven't read my blog post about using Google drive, look for the one titled 5 practices. The great benefit of taking photos of students work throughout the period is you can then sequence how they are presented during the closure. Also, if 2nd period doesn't have an alternative method to a problem, but 1st period did, I can show their work and credit the student from the previous class.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">It also makes it much easier to blog about because they are all stored on my Google drive or still in my camera roll.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">As you can see below, students had to follow a set of instructions and transform a triangle using each of the 3 rigid transformations. A common mistake is translating the bottom right vertex and then drawing it as a different vertex such as the bottom left. Students realize they need to process that it's that corresponding point and draw the rest of the figure or translate the remaining points.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Students can visually reflect, but have a hard time describing what operation they are completing on which coordinate, and which coordinate remains the same.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Finally, I used cut up parchment paper and gave each student a piece to use on their first 2 attempts on their skill assessment and anytime during classwork. The final attempt I'm not sure if I'll allow students to use the wax or patty paper.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-gFkm5Gih4L0/WHmsZWNFIDI/AAAAAAAAC84/3aMpQfItQp4/s640/blogger-image--1675577679.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-_DlKxCcejEU/WHmscXegNbI/AAAAAAAAC88/lloEKhb-Etc/s640/blogger-image--465047327.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-_DlKxCcejEU/WHmscXegNbI/AAAAAAAAC88/lloEKhb-Etc/s640/blogger-image--465047327.jpg" /></a></div><img border="0" src="https://lh3.googleusercontent.com/-gFkm5Gih4L0/WHmsZWNFIDI/AAAAAAAAC84/3aMpQfItQp4/s640/blogger-image--1675577679.jpg" /><br /><img border="0" src="https://lh3.googleusercontent.com/-AWk1Ucb0NpY/WHmsXDThhSI/AAAAAAAAC80/Nxv2Tfewj14/s640/blogger-image-1041328089.jpg" />Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-69442082370207316322017-01-31T19:52:00.001-08:002017-01-31T19:52:08.980-08:00@cpmmath 6.1.1 Transformations Intro: Key Lock Puzzles<div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-aI6n1cKCNKs/WHmsi-6MmXI/AAAAAAAAC9A/4ZwtkHX777w/s640/blogger-image--1051664416.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;">CPM offers a pretty cool interface to informal language about rigid transformations. <a href="http://technology.cpm.org/general/keylock/">It's worth a look</a>. Students worked in partners so that they could switch off. That way they could get feedback from their partner. It made students much more engaged. Then they copied down their solving steps after solving each puzzle.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-aI6n1cKCNKs/WHmsi-6MmXI/AAAAAAAAC9A/4ZwtkHX777w/s640/blogger-image--1051664416.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-cnmgvqBRpME/WHmsnPOKJ2I/AAAAAAAAC9I/K8m6ahn8LV4/s640/blogger-image--2004573290.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-cnmgvqBRpME/WHmsnPOKJ2I/AAAAAAAAC9I/K8m6ahn8LV4/s640/blogger-image--2004573290.jpg" /></a></div><img border="0" src="https://lh3.googleusercontent.com/-aI6n1cKCNKs/WHmsi-6MmXI/AAAAAAAAC9A/4ZwtkHX777w/s640/blogger-image--1051664416.jpg" /><br />Above, a student used 2 reflections for each to solve it quickly. I was impressed.<br /><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-aI6n1cKCNKs/WHmsi-6MmXI/AAAAAAAAC9A/4ZwtkHX777w/s640/blogger-image--1051664416.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-yxdxoQb9Ikk/WHmslPw8bZI/AAAAAAAAC9E/5AHy3EJ4WNg/s640/blogger-image--2124053974.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-yxdxoQb9Ikk/WHmslPw8bZI/AAAAAAAAC9E/5AHy3EJ4WNg/s640/blogger-image--2124053974.jpg" /></a></div><div class="separator" style="clear: both;">Above are the posters I made a few years ago and had a student color and decorate. It helps students see the relationship between the informal language of sliding, turning and flipping to translating, rotating, and reflecting.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">As you can see, we reviewed 3 homework problems from the night before where they practicing solving a system using substitution (CPM calls it Equal Values method), solving for y, and a word problem that could be solved using a system of equations.</div>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-31109360566657417162017-01-31T19:46:00.001-08:002017-01-31T19:46:56.011-08:00y=mx+b Learning Log as Exit TicketI gave students about 8 or 9 minutes to graph the linear equation y=-2x+3 and answer questions in the learning log prompt linked below. I looked at all of them from each of my 3 classes, and calculated how many students successfully graphed a linear equation. Since it was an exit ticket formative assessment, I didn't grade it. I only highlighted directions they didn't follow or mistake points I saw. Then a check mark with successfully graphing and checkmark for ideas I agreed with. The statistics, which I discussed with all my classes, are below:<br /><div><br /></div><div>1*: 24/27 or 89%</div><div>2*: 19/24 or 79%</div><div>5*: 20/32 or 63%</div><div><br /></div><div>I discussed with my classes that they're all made up of different levels of students but I think that the biggest class has the most frequency of off topic conversations. Although it's a high energy level coming back from lunch, I talk to all classes that the time of day shouldn't be an excuse and it's up to every individual to be responsible for their own choices.<br /><div><br /></div><div>After passing it out I had students contribute to a whole class google doc of notes on agreed upon answers to the learning log questions. <a href="https://drive.google.com/open?id=1Q0nq1RAfFCgQyl8oeYTNxOXNdifh8Sz9jziSXZ-dSno">That file is available here</a>. The biggest mistake seemed to be students ignoring the negative sign on the growth, or not having an idea about where the y-intercept was or how to find a second point.<br /><br /><br /></div></div><blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en"><a href="https://twitter.com/martinsean">@martinsean</a> What I see happening is kids aren't looking at this as an x-y relationship. Ask them what y is when x is 0. Same for when x is 1</div>— Bowen Kerins 🔗 (@bowenkerins) <a href="https://twitter.com/bowenkerins/status/809611576768688133">December 16, 2016</a></blockquote><br /><br /><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-21826078671623831242017-01-23T21:10:00.004-08:002017-01-23T21:12:12.395-08:00My first @desmos 3D print<div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/--sGtJrSi7Nk/WIbgLi65WQI/AAAAAAAAC9o/5rgHmlHbI98/s640/blogger-image-1439562243.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/--sGtJrSi7Nk/WIbgLi65WQI/AAAAAAAAC9o/5rgHmlHbI98/s640/blogger-image-1439562243.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><br /></div><br />Our education technology specialist took a job at a local charter school and asked me if I wanted to keep the 3D printer in my classroom. Of course I said yes, and it has been collecting dust in my closet. After seeing this tweet from John Stevens, co-author of the <a href="http://www.twitter.com/classroomchef">Classroom Chef</a>, I was inspired to do some research and try setting it up.<br /><blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en">Back to School: <a href="https://twitter.com/Desmos">@Desmos</a> <br />Keychains and Culture<a href="https://t.co/kSxuMW4edo">https://t.co/kSxuMW4edo</a><a href="https://twitter.com/hashtag/mtbos?src=hash">#mtbos</a> <a href="https://twitter.com/hashtag/3dprinting?src=hash">#3dprinting</a></div>— John Stevens (@Jstevens009) <a href="https://twitter.com/Jstevens009/status/818332181189668865">January 9, 2017</a></blockquote><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script> Mind you, this tweet came after he showed some amazing student work samples. If you follow the link there's a Google doc that is a sample of the student instructions, which I followed.<br /><br />Instead of a keychain, I figured students could create a name plate using linear equations and anything else they cared to figure out. I came up with my sample graph:<br /><blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en">Hey <a href="https://twitter.com/hashtag/mtbos?src=hash">#mtbos</a> <a href="https://twitter.com/mathycathy">@mathycathy</a> Reasonable task for gr 8? Make your name using <a href="https://twitter.com/Desmos">@desmos</a>. Link this ex and let em go? <a href="https://t.co/PgoY4ABVfm">https://t.co/PgoY4ABVfm</a> <a href="https://t.co/UAA88OJGnt">pic.twitter.com/UAA88OJGnt</a></div>— Martin Joyce (@martinsean) <a href="https://twitter.com/martinsean/status/819773836061122573">January 13, 2017</a></blockquote><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script> I exported the file after prepping it (John describes the instructions, but it's basically making all equations black, hiding axes and gridlines, and exporting the file as .png file and then converting that to another format to be edited in Tinkercad.<br /><br />I read all the directions to setup the printer, and started leveling the build plate. To my dismay, I kept running into "Fatal temperature error" and couldn't get past that screen. I need to do some more research to troubleshoot it, and vow to persevere.<br /><br />In the meantime, I shared my troubles with a class, and one student volunteered that the local library had a 3D printer anyone could use.<br /><br />I called them and found out that on Mondays and Thursdays I could make a 2 hour appointment from 4 to 6 to get an introduction to 3D printing and use their Ultimaker 3D printer. I went today and learned a lot.<br /><br />I downloaded my .stl file from my Google Drive and opened it with Cura. After adjusting the letters of my name to be 4 millimeters rather than 4, printing commenced.<br /><br />One drawback, is that the print is not on a rectangular name plate background. But, the library employee told me next time I could try an embossed look where I could take a rectangular prism and make the name be hollow or an indentation in the prism. That seems like it would look cool too!<br /><br /><a href="https://lh3.googleusercontent.com/-s-X9JSgXeWY/WIbgOu61miI/AAAAAAAAC9s/43RNO4bdTDg/s640/blogger-image-2040818937.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-s-X9JSgXeWY/WIbgOu61miI/AAAAAAAAC9s/43RNO4bdTDg/s640/blogger-image-2040818937.jpg" /></a><br />Here is the first layer...<br /><img border="0" src="https://lh3.googleusercontent.com/--sGtJrSi7Nk/WIbgLi65WQI/AAAAAAAAC9o/5rgHmlHbI98/s640/blogger-image-1439562243.jpg" /><br />And after carefully scraping it off the build plate, I had my name. Any ideas on what type of material to mount it to? probably use some nice glue.<br /><br />Next steps:<br /><br /><ol><li>Troubleshoot and fix the school's 3D printer.</li><li>Plan time before the end of the year to have students make a rough draft of their name on graph paper, then recreate in desmos.</li><li>Final product would be an .stl file. If I was super awesome, I'd print them all. That is a possibility. Worst case scenario: students take the file and do what I did and get it printed at the library.</li></ol><div>Any feedback is greatly appreciated. Big thanks to John Stevens for the superb instructions and inspiration.</div>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com2tag:blogger.com,1999:blog-2523946538193054194.post-20605104091046972772017-01-10T10:49:00.001-08:002017-01-10T10:49:54.157-08:00NCTM Blog Post #4: Replacing a Textbook Lesson<blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en">In my final blog post I answer <a href="https://twitter.com/gfletchy">@gfletchy</a> shadowcon call to action and replace a textbook lesson with an <a href="https://twitter.com/IllustrateMath">@IllustrateMath</a> lesson. <a href="https://t.co/7znQhq8BrH">https://t.co/7znQhq8BrH</a></div>— Martin Joyce (@martinsean) <a href="https://twitter.com/martinsean/status/811288017491161089">December 20, 2016</a></blockquote><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com1tag:blogger.com,1999:blog-2523946538193054194.post-23728004661317960362017-01-01T21:48:00.000-08:002017-01-01T21:48:16.639-08:00Border problem (@youcubed @joboaler)<blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en">Can never go wrong with border problem # talk popularized by <a href="https://twitter.com/joboaler">@joboaler</a> different reps lead to vastly different looking expressions <a href="https://twitter.com/hashtag/MTBoS?src=hash">#MTBoS</a> <a href="https://t.co/jDlSsUPUvL">pic.twitter.com/jDlSsUPUvL</a></div>— Martin Joyce (@martinsean) <a href="https://twitter.com/martinsean/status/812121024602914817">December 23, 2016</a></blockquote><div class="separator" style="clear: both;"></div><blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en"><a href="https://twitter.com/martinsean">@martinsean</a> <a href="https://twitter.com/joboaler">@joboaler</a> Love visual math examples like this! <a href="https://twitter.com/hashtag/mathmindset?src=hash">#mathmindset</a></div>— WithMathICan (@WithMathICan) <a href="https://twitter.com/WithMathICan/status/813525947810979840">December 26, 2016</a></blockquote>I also saw a video of <a href="https://www.youtube.com/watch?v=I6BJXKp2Sag">Cathy Humphreys demonstrating this task</a>.<br /><br /><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script><a href="https://lh3.googleusercontent.com/-8IdExHQ63mk/WGGPPPiit6I/AAAAAAAAC8I/91liXXbAusM/s640/blogger-image--138895957.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><div class="separator" style="clear: both;">It all starts with the image below (I found it by googling "Math border problems," make sure you don't forget the plural form and math or you'll get a bunch of articles on immigration policy). This is a picture of a square with a side length of 10. The border has been shaded orange. How many orange squares do you see without counting one by one? </div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-8IdExHQ63mk/WGGPPPiit6I/AAAAAAAAC8I/91liXXbAusM/s640/blogger-image--138895957.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-IwAAFWbehro/WGGPNOVElxI/AAAAAAAAC8E/6CWbCAOhaFI/s640/blogger-image-718376176.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-IwAAFWbehro/WGGPNOVElxI/AAAAAAAAC8E/6CWbCAOhaFI/s640/blogger-image-718376176.jpg" /></a></div><div class="separator" style="clear: both;">And then the magic happens...</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">In the particular class pictured below, students got answers of 37, 36, or no answer at all. I put 40 up their because I think some thought that but were too afraid to share it.</div><div class="separator" style="clear: both;"><br /></div><img border="0" src="https://lh3.googleusercontent.com/-8IdExHQ63mk/WGGPPPiit6I/AAAAAAAAC8I/91liXXbAusM/s640/blogger-image--138895957.jpg" /><br />As you can see, there are 5 distinct methods that students in this cass used. The most common I believe is the one in the bottom left where the multiply 10 by 4 and subtract 4 because the corners were overlapping. I made sure students understood that it was subtracted because each corner was counted twice. This leads to 4x-4.<br /><br />One student worked around that by saying there's a spiral of 9 square lengths around the border. It's hard to draw, but you can see it in the upper left. Therefore they got 9*4, which leads to 4(x-1).<br /><br />Another said there were 10 squares on the top and 10 on the bottom. Therefore the left and right sides had 8 each, so 10*2+8*2. We didn't write that one as an algebraic expression.<br /><br />Karin said she saw the square in each corner for a total of 4 corner squares, and 2 rows of 8 and 2 columns of 8.<br /><br />Finally, Sebastian saw it similar to the visual pattern from yesterday, as a square with a total of 10^2 or 100 squares subtracted by the inside white square which is 8^2 or 64. 100-64 gets you 36. This leads to x^2-(x-2)^2.<br /><br />I think I'm going to revisit this warm-up again, but slightly different as a Contemplate then Calculate instructional routine that I saw David Wees present at a Global Math department webinar. I can't find it right now but I'll post a link once I ask him.Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com1tag:blogger.com,1999:blog-2523946538193054194.post-16218178343102898802016-12-31T15:43:00.002-08:002016-12-31T23:38:40.589-08:00Visual Patterns Warmup (@math8_teacher) (@fawnpnguyen)<div class="separator" style="clear: both;">So for this last week before winter break I switched up the warmups from estimations. Mr. Rodinsky was getting fed up with students coming into class with the correct estimate on their paper with no reasoning written. Some see it as a game and I tried to make the analogy that it is like telling someone the ending to a movie before they see it.</div><div class="separator" style="clear: both; text-align: center;"><br></div><div class="" style="clear: both;">I found this visual pattern prompt on twitter, and it's posted under my Favorite Problems link at the top of this page. Here it is again:</div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-kl1ZqpClt4E/VvX9RWevZ3I/AAAAAAAAB64/jzMed2ws8PA/s640/blogger-image--1807659004.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="243" src="https://1.bp.blogspot.com/-kl1ZqpClt4E/VvX9RWevZ3I/AAAAAAAAB64/jzMed2ws8PA/s320/blogger-image--1807659004.jpg" width="320"></a></div><div class="" style="clear: both; text-align: left;">After reading about <a href="https://fivetwelvethirteen.wordpress.com/2016/12/18/implementing-routines-visual-patterns/">Dylan Kane's ideas about Visual Patterns as an instructional routine</a>, I set the timer for 3 minutes of independent think time where they could copy the patterns down if they wanted. Then 3 minutes to tell their elbow partner what they noticed about the pattern. Then we shared out.</div><div class="" style="clear: both; text-align: left;"><br></div><div class="" style="clear: both; text-align: left;">Also, I purposely meant to introduce this pattern the day before introducing the border problem number talk, which I will discuss in the following blog post.</div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">Many students shared that they saw the grey squares as the figure number, squared. So for figure 2, 2^2 is 4, and for figure 3, 3^2=9 the number of grey squares. Students also used what they knew about linear patterns to see that the number of red squares was growing by 4. Some reasoned that the figure before must be 4 so the rule was y=4x+4. Some students used that for question 3 and set 4x+4 equal to 64 to get 4x=60, and x equals 15 or figure 15 having 64 red tiles. 1st period didn't come up with this, but one eager student told me how he solved it first thing in the morning.</div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">For figure 20 in question 1, students reasoned there were 400 grey squares because 20^2 is 400. They said it would have 84 red tiles, because 4(20)+4 is 84. Students reasoned that you could add those two together to get the total squares or you could take the figure number and add 2 to it, then square it.</div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-J76kVvZCle4/WGcUTHLrSdI/AAAAAAAAC8k/i9r9BVQWOdg/s640/blogger-image-883266857.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-J76kVvZCle4/WGcUTHLrSdI/AAAAAAAAC8k/i9r9BVQWOdg/s640/blogger-image-883266857.jpg"></a></div><div class="separator" style="clear: both;">The highlight was one student saying the rule was x^2+4x+4 also. I assumed and asked him if he had learned something outside of my class about dealing with (x+2)^2? The student replied no. The x^2 is the grey tiles, the 4x is the red growing by 4, and the plus 4 is the red corner squares. My jaw dropped. If you didn't figure out, I assumed the student was going to say the dreaded "FOIL" method (I'm a big fan of area model or generic rectangle first). I was incorrect in my assumption. The student also showed how to see which figure had 121 tiles by undoing the squaring on both sides of the expression to get 11=x+2 and getting x=9 for question 2.</div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">So, for a 10 to 15 minute warm-up, it provided rich discussions and laid some foundation for the border problem the next day.</div>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-68843154455657752442016-12-28T21:40:00.002-08:002016-12-28T22:24:43.743-08:005 Practices for Orchestrating Math Discussions (Google Drive enhancement) @cpmmathI have read excerpts from the book in the title and it has been mentioned at many professional developments I've been to. I have been trying to implement it on a daily basis when we start a new lesson from the textbook. The <a href="http://www.mctm.org/mespa/5Practices.pdf">5 practices are outlined in this PDF file</a>. In summary it is:<br /><br /><br /><ol><li> Anticipating. Select a groupworthy task and anticipate how students will approach it (successes and common mistakes).</li><li>Monitoring. Check in on groups to see what ideas are working and which aren't. I have made this much easier by downloading the Google Drive app to my iPhone, and taking photos directly into a folder for that day's lesson, ready to be displayed on my large display screen later.</li><li>Selecting. Basically, once I take a picture of a piece of student work that is most likely part of the closure discussion. I also take a mental or post it note about certain sticking points that students argued and convinced each other on.</li><li>Sequencing. In this case, the files are usually queued up in the correct order of the folder by the order I took the photos in, but in the case of the lesson below I sequenced the two tables of a system of equations, a graph with the points plotted, and the equations written with substitution (or Equal values method) used to solve the solution to the system algebraically.</li><li>Connecting. This happens by questions I ask during the closure. I asked how does two tables help us solve this problem? Where does it show us the answer? (where the same two coordinates are). Then when looking at the graph: how does the graph show us the solution? (the point of intersection where the two lines meet). How does the solution show up in the algebra? (After solving for x, that's the x coordinate of the solution, and when substituted or checked the y value is the y coordinate of the point of intersection).</li></ol><div class="separator" style="clear: both; text-align: left;">The groupworthy task is a problem called Chubby Bunny. A cat weighs 5 pounds but gains 3 pounds per week. A bunny weighs 19 pounds and gains 1 pound per week. When will they be the same weight at the same time? This lesson 5.2.3 from CPM's Core Connections Course 3 asks students to solve the problem multiple ways showing different representations. Some students went straight to the algebraic method. Some went straight the the graph or table. Students realized to make an accurate graph it would be wise to make a table to see how far up and to the right their graph would go and what intervals to choose.</div><div class="separator" style="clear: both; text-align: left;">1st period:</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/-fuPwN-rm71g/WFcMgNAlVWI/AAAAAAAAC6k/e0mGADdMkbUBgMCmGBh4B9SMeMtc27WZACLcB/s1600/IMG_9051.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-fuPwN-rm71g/WFcMgNAlVWI/AAAAAAAAC6k/e0mGADdMkbUBgMCmGBh4B9SMeMtc27WZACLcB/s320/IMG_9051.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">This student used labeled horizontal tables with the values labeled as years and weight.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-yioz2oNw9_0/WFcMgJp_XTI/AAAAAAAAC6o/Obs3c2cqb2ArAE86IQfhvNLcrrW-X1p0QCLcB/s1600/IMG_9052.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-yioz2oNw9_0/WFcMgJp_XTI/AAAAAAAAC6o/Obs3c2cqb2ArAE86IQfhvNLcrrW-X1p0QCLcB/s320/IMG_9052.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">This student also has their graph completed with the point of intersection's coordinates labeled.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-6q0DbA4-OWU/WFcMgEYuhYI/AAAAAAAAC6g/alMxoHeXXjgAEFc2GWEuV_2hTx5xlmsbACLcB/s1600/IMG_9053.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-6q0DbA4-OWU/WFcMgEYuhYI/AAAAAAAAC6g/alMxoHeXXjgAEFc2GWEuV_2hTx5xlmsbACLcB/s320/IMG_9053.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">As you can see, this student used the Equal Values method. They may not hear this method later, so I've tried to tell students that it can also be called substitution, since whatever y is equal to is being substituted into the other equations y variable. This student forgot to omit the y= part in the first line, but thereafter did.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-arHi5utI1QU/WFcMiLPlUdI/AAAAAAAAC6s/umOPgRyQrLwksopI2XamNR3_w9Mi2x0ngCLcB/s1600/IMG_9054.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-arHi5utI1QU/WFcMiLPlUdI/AAAAAAAAC6s/umOPgRyQrLwksopI2XamNR3_w9Mi2x0ngCLcB/s320/IMG_9054.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">The next problem dealt with two schools, one that was shrinking and the other that was growing. Students had to make the jump to writing a negative sign in front of their growth and strictly using an algebraic method since the values were too large to put in a table and/or graph.</div><div class="separator" style="clear: both; text-align: center;"><br /></div>2nd period:<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-5Fpw6S5u0SE/WFcMiOjYDvI/AAAAAAAAC6w/bFuC4Y1wrlMB2n6WptiDAnZ7nPpo26lPACLcB/s1600/IMG_9055.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-5Fpw6S5u0SE/WFcMiOjYDvI/AAAAAAAAC6w/bFuC4Y1wrlMB2n6WptiDAnZ7nPpo26lPACLcB/s320/IMG_9055.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Neatly labeled vertical tables.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-7R0qX00btcc/WFcMiKiNaBI/AAAAAAAAC60/F2qYe5cWUY4dOnFmpmhfdxuTmBuX75TgwCLcB/s1600/IMG_9056.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-7R0qX00btcc/WFcMiKiNaBI/AAAAAAAAC60/F2qYe5cWUY4dOnFmpmhfdxuTmBuX75TgwCLcB/s320/IMG_9056.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Properly scaled graph with two lines.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-80XNS5GardQ/WFcMjZaqZoI/AAAAAAAAC64/14oG0TWEaE8r5sbvTlEzfV4RgUnLpPE1wCLcB/s1600/IMG_9057.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-80XNS5GardQ/WFcMjZaqZoI/AAAAAAAAC64/14oG0TWEaE8r5sbvTlEzfV4RgUnLpPE1wCLcB/s320/IMG_9057.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Steps clearly shown to solve the system.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-LU2SNie3NOk/WFcMk7YAh4I/AAAAAAAAC68/RY4ga_A2vRkx5V9raLcjJtWM1zJmh4DLwCLcB/s1600/IMG_9058.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-LU2SNie3NOk/WFcMk7YAh4I/AAAAAAAAC68/RY4ga_A2vRkx5V9raLcjJtWM1zJmh4DLwCLcB/s320/IMG_9058.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">The next problem solved: 20 years the two high schools will have the same population.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-109qgwVk1V8/WFcMk13ixgI/AAAAAAAAC7E/OPBRi664UxMNkEYt9zi8n-GUMfKNjzfEwCLcB/s1600/IMG_9059.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-109qgwVk1V8/WFcMk13ixgI/AAAAAAAAC7E/OPBRi664UxMNkEYt9zi8n-GUMfKNjzfEwCLcB/s320/IMG_9059.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Vertical tables.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-jN5LJsnb1oY/WFcMk8uqPSI/AAAAAAAAC7A/rnosdxF_AfMGKNvnvwUhpFoK45_EzbAJgCLcB/s1600/IMG_9060.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-jN5LJsnb1oY/WFcMk8uqPSI/AAAAAAAAC7A/rnosdxF_AfMGKNvnvwUhpFoK45_EzbAJgCLcB/s320/IMG_9060.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Color coded graphs.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-BndyJVw_w6Y/WFcMlr6XaOI/AAAAAAAAC7I/mG_jrBSOo2EzEo4T2k_92R5Nnfj2cHX7ACLcB/s1600/IMG_9061.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-BndyJVw_w6Y/WFcMlr6XaOI/AAAAAAAAC7I/mG_jrBSOo2EzEo4T2k_92R5Nnfj2cHX7ACLcB/s320/IMG_9061.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Part of the lesson is asking students what x=7 represents. (The same weight in 7 years) I then ask how you could see what that weight is. When they are not sure, I ask them how they can be sure that x=7 is correct? (Check your solution, which leads to finding out what y equals in each equation)</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-3RAwaBrDwuI/WFcMmM30_AI/AAAAAAAAC7M/DHn2stawzY0Jr1nWnW0Psd14-0StJy_GQCLcB/s1600/IMG_9062.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-3RAwaBrDwuI/WFcMmM30_AI/AAAAAAAAC7M/DHn2stawzY0Jr1nWnW0Psd14-0StJy_GQCLcB/s320/IMG_9062.JPG" width="240" /></a></div><div><br />The main points of the closure discussion were as follows: How did making tables help you find the answer? Students said it was when the weeks and weight were the same amount at the same time, 7 weeks and 26 pounds. Some students thought the answer might be 20 pounds because the bunny was 20 pounds after 1 week, and the cat was 20 pounds after 5 weeks. Their peers told them that it had to be the same weight after the same amount of weeks also. I prompted students to circle the solution in each table.<br /><br />Then I asked the same question about the graph. Students said it was when their two graphes crossed, and the solution was at the point of intersection (7,26). Once again I asked what each number represented in the coordinates.<br /><br />Finally, students described how they combined two equations into one equation. They then described subtracting x from both sides and so on. Like I said, students needed to be prompted and reminded to check their solution afterwards even though they knew their y value using the prior representations.<br /><br />So, this is how I am running most of my lessons now. Circulating, finding common misconceptions, sequencing the order of taking photos of student sample work, prompting them to explain their work during the closure, or asking a volunteer to explain their work. Students absolutely love getting a photo of their work taken because they know the whole class will eventually see it during the closure (last 10 to 12 minutes)</div>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-69231129427901905242016-12-18T13:41:00.000-08:002016-12-19T20:38:36.659-08:00#clotheslinemath Slope Intercept Trial 1<div class="separator" style="clear: both;">I finally got a chance to try out the Slope Intercept clothesline math activity, introduced by <a href="http://www.clotheslinemath.com/">Chris Shore</a> and recapped via <a href="http://www.estimation180.com/slopeintercept.html">video introduction by Andrew Stadel</a>. I took his advice and showed 0 in the middle with the other 4 benchmark numbers turned around. Students reasoned that to the left we should have -1 then -2, and on the right just 1 and 2. I showed students this image before this.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Some background information: I introduced this activity on a Friday in my Math 7/8 support class, but the 7th graders were in the back working on weekend homework and the 8th graders were done with their assignment due friday so I distributed the purple variable or you could technically call them parameters of each linear equation pictured on the following picture:</div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-fIEkpOpkFas/WFcAC-kybgI/AAAAAAAAC6Q/3fYVea7jRG4AIw99nwoOIkVaCF-lUulIgCLcB/s1600/clotheslineslopeintercept.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://2.bp.blogspot.com/-fIEkpOpkFas/WFcAC-kybgI/AAAAAAAAC6Q/3fYVea7jRG4AIw99nwoOIkVaCF-lUulIgCLcB/s320/clotheslineslopeintercept.jpeg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">These students had previously worked on the mixed up algebraic expressions from Mr. Stadel's page where 2 colors of paper worked well. In this activity, in hindsight, it didn't work as well and I know for next time I would do the following: Make the benchmark numbers purple (-2,-1,0,1,2) and make m3 and b3 blue paper because it's a blue line. Make m2 and b2 on white paper because it would show up as black text and red paper (one student saw it as an orange line, which I said doesn't really matter because we know you're not talking about the black or blue line) for the m1 and b1 cards.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">After seeing that above image, I started by asking what students noticed. Some said they saw parallel lines...(?) and another said all the lines are eventually going to intersect (I honestly did not notice that at first). This brought my attention to an idea. There are blank expression cards and I could easily write x on one and y on each and ask if we have an idea what these might be if Tommy thinks these lines will eventually intersect? (You can make the argument that x is 2 and y is 1 if you can convince others that the lines will intersect at (2,1)... but I suppose students could write and solve a system to see what it would be with the agreed upon values..?</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I passed out m1 and b1 to one table, m2 and b2 to another, and m3 and b3 to a third. I wonder if I should only make an x and y clothesline card if they ask for it, or if I have 8 table groups just give each table one clothesline card to bring up in turns after taking notes on a personal whiteboard of where they see it placed in comparison with the other ones. That's what I will do for the next time.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Students knew that b was the starting point or y intercept of the graph and they knew m would be the growth. Aidan reasoned that since the black line doesn't increase or decrease it's growth must be zero, so he put m2 under 0. By the way, all of these are subscript numbers and the students immediately noticed that also.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Emma reasoned that the blue line was increasing so it must have a positive slope so she put m3 under 2. We didn't discuss why 2 may be a better choice than 1 (future conversation). She also reasoned that the y-intercept was on the negative side of the y axis so it must be -2, so she put b3 under -2.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Students struggled with differentiating or figuring out the b values for the 1st and 2nd lines. They especially struggled with the growth of the first line.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The good news is I will revisit this activity with these same students and the rest of the class in the mainstream class and they should have some valuable contributions to make.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Also, for the next time I pasted the graphic of the graph on a google doc 4 pages in a row, and then printed it and changed it to 4 copies per page so I can photocopy and chop the graphs for students to paste into their notebooks and take notes of the activity.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Students also had the option of attaching a second parameter to a first using a clothespin.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-k2Bk0oHHjSY/WFTG7H54caI/AAAAAAAAC6A/fDMFo0qm7eo/s640/blogger-image-1758316888.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-k2Bk0oHHjSY/WFTG7H54caI/AAAAAAAAC6A/fDMFo0qm7eo/s640/blogger-image-1758316888.jpg" /></a></div><div class="separator" style="clear: both;">Update:</div><div class="separator" style="clear: both;">To extend this lesson I could introduce the screen shot of a desmos graph and ask if they are still correct. I restricted the domain so students could draw on a hard copy or prove they intersection using substitution. Open it up to notice and wonder.</div><blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en"><a href="https://twitter.com/mr_stadel">@mr_stadel</a> <a href="https://twitter.com/MathProjects">@MathProjects</a> <a href="https://twitter.com/Desmos">@Desmos</a> after using whole number benchmarks show this. Is our clothesline still correct?</div>— Martin Joyce (@martinsean) <a href="https://twitter.com/martinsean/status/810966387006898176">December 19, 2016</a></blockquote><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script> <div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-m9woZRHvXEI/WFdS41o1nvI/AAAAAAAAC7c/J8cFLrleAws/s640/blogger-image-2009996812.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-m9woZRHvXEI/WFdS41o1nvI/AAAAAAAAC7c/J8cFLrleAws/s640/blogger-image-2009996812.jpg" /></a></div>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-83269956717094996092016-12-13T21:22:00.003-08:002016-12-13T21:22:50.264-08:00Fractions Busters w Video HookThanks to SVMI PD a few years ago who introduced me to this awesome clip from the movie Little Big League..<br /><div class="separator" style="clear: both; text-align: center;"><iframe width="320" height="266" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/pXtFSE7VlL0/0.jpg" src="https://www.youtube.com/embed/pXtFSE7VlL0?feature=player_embedded" frameborder="0" allowfullscreen></iframe></div>I like it for many reasons. First of all, it has humor. Secondly, it shows how the players weren't afraid to TRY the problem and be wrong, something we want our students to be.<br /><br />This is the infamous paint problem, and I remember Jo Boaler talking about it in her summer math course she offered a few years back. My purpose wasn't for them to figure it out with their own method, or for them to sue the work formula. One person paints a house in 3 hours, then other one in 5 hours. How long would it take for them to paint it together?<br /><br />So first we defined the variable x. What are we trying to find out? The time it takes to paint the house together. I asked them how much of the house would the first person paint in one hour? (1/3) So, that's 1/3x. The second person would paint 1/5 of the house in 1 hour, so 1/5x. Then I asked how much of the house they'd want to paint together? The whole thing, so those added together should equal 1. Then I asked them to solve it (1/3x+1/5x=1) I also asked what are you dividing by when you multiply by 1/3? (3) So this equation can also look like x/3 + x/5 = 1.<br /><br />Some students realized the LCD of 3 and 5 was 15, so they converted both fractions to fifteenths. Some didn't realize they could then add the terms together. Others realized you could, and did. Then they were stuck at 8/15x=1. Some realized you could multiply both sides by 15 to get you 8x=15. Some put the 1 over 1 to make it look like a proportion and then to use cross products. Few students realized they could divide by 8/15 on both sides and multiply both sides by 15/8.<br /><br />A few students in my first 2 classes remembered a method called Fraction Busters to eliminate the fractions in the equation that they were introduced to in 7th grade. Many had forgotten this method. I highlighted this method by using the Google Drive app on my iPhone to take a picture to my Google Drive and view it with the whole class and have that student explain their method.<br /><br />Then students practiced on some of the problems in the section of CC3 section 5.1.2:<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-FGq8U8t326U/WFDVvsYSERI/AAAAAAAAC5U/O-pjveV8-nk-enbC6p566O85kEQzsFtFACLcB/s1600/IMG_9010.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-FGq8U8t326U/WFDVvsYSERI/AAAAAAAAC5U/O-pjveV8-nk-enbC6p566O85kEQzsFtFACLcB/s320/IMG_9010.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">This student did not eliminate the fractions.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-ymhTAmj2kfE/WFDVyQictTI/AAAAAAAAC5k/x1Zq4ukCywA7Ksfz7tnLDihTmZ0WC4NiQCLcB/s1600/proportion.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-ymhTAmj2kfE/WFDVyQictTI/AAAAAAAAC5k/x1Zq4ukCywA7Ksfz7tnLDihTmZ0WC4NiQCLcB/s320/proportion.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">This student saw it as a proportion to solve for x at the end.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-dupIKp0glrk/WFDVvibxtLI/AAAAAAAAC5Q/YouAwyy2SdAHpCHb0WwuTwfZxd9TlKlKwCLcB/s1600/IMG_9022.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-dupIKp0glrk/WFDVvibxtLI/AAAAAAAAC5Q/YouAwyy2SdAHpCHb0WwuTwfZxd9TlKlKwCLcB/s320/IMG_9022.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">This student remembered the fraction busters method without me telling them.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-L73U9DwmG0s/WFDVvSLu16I/AAAAAAAAC5M/qeM2IXLaPpkSYctVPdaIdKuK_vYgVqtJACLcB/s1600/IMG_9024.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-L73U9DwmG0s/WFDVvSLu16I/AAAAAAAAC5M/qeM2IXLaPpkSYctVPdaIdKuK_vYgVqtJACLcB/s320/IMG_9024.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">In this practice problem, students realized all the terms had decimals. So, all terms on both sides were multiplied by 10 to make them whole numbers. The Estimation 180 we did at the beginning was really helpful because they estimated the capacity of a soda can. Most students estimated 8 or 12 ounces. The answer was 12.5, so the percent error ratio was 0.5/12.5. I asked students how to write the fraction without decimals. Some students said multiply by 10 to get 5/125. Others multiplied by 2 to make it 1/25. My colleague expected students to multiply by 8 to make a denominator of 100 but I didn't expect any of my students to do that and none did.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-LJlOnXivvqo/WFDVxiXTsYI/AAAAAAAAC5Y/Adij3d3mwuY2QhPKmPc5VspiUGKkCYAygCLcB/s1600/IMG_9025.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-LJlOnXivvqo/WFDVxiXTsYI/AAAAAAAAC5Y/Adij3d3mwuY2QhPKmPc5VspiUGKkCYAygCLcB/s320/IMG_9025.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Here it wasn't completely necessary, but here all terms could be divided by 10 to make it simpler.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-LWwpX7QL-_Q/WFDVxwTRG2I/AAAAAAAAC5c/rWBQzzZmRf0SwW0XL5Fy6aZpGuCxU8xxQCLcB/s1600/IMG_9026.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-LWwpX7QL-_Q/WFDVxwTRG2I/AAAAAAAAC5c/rWBQzzZmRf0SwW0XL5Fy6aZpGuCxU8xxQCLcB/s320/IMG_9026.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Here was a 2 step equation that they figured out.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-lZDs0K2PCmc/WFDVyPuJt4I/AAAAAAAAC5g/AY_Suzx0ujcv8Y5Wd1Q4BJ0mW7VBtsUsQCLcB/s1600/IMG_9027.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-lZDs0K2PCmc/WFDVyPuJt4I/AAAAAAAAC5g/AY_Suzx0ujcv8Y5Wd1Q4BJ0mW7VBtsUsQCLcB/s320/IMG_9027.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">We had a great conversation in all classes about remembering to multiply all terms by 5. Some students forgot to multiply the 1 by 5 on the left side which was a great discussion.</div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br />Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-40275522431285886272016-12-13T21:01:00.000-08:002016-12-13T21:01:15.263-08:00Order of Ops WODB, 5 Practices with 3 Act<div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-4vhuFDc_oRA/WE2JFyBw3cI/AAAAAAAAC3Y/__Ji5EjGwOQi6mren64cI9gGEiV7y9gigCLcB/s1600/IMG_8990.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;">I had a substitute give all my students the following Which One Doesn't Belong prompt on a quarter sheet of paper to all my students as a warm-up. I saw some of my 8th graders got some wrong, so I assumed my 6th graders struggled as well. So, I passed out some brand new copies of it. They spent a lot of time on it.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">As you can see below, most students' first instinct is to simplify it all from left to right. In the bottom right they really want to subtract 6 to 20 rather than subtract 6 from 38.</div><div class="separator" style="clear: both;"><a href="https://3.bp.blogspot.com/-4vhuFDc_oRA/WE2JFyBw3cI/AAAAAAAAC3Y/__Ji5EjGwOQi6mren64cI9gGEiV7y9gigCLcB/s1600/IMG_8990.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-9NGKBDAvO5s/WE2o22z2gNI/AAAAAAAAC40/dlxkNAHiees/s640/blogger-image-427642078.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-9NGKBDAvO5s/WE2o22z2gNI/AAAAAAAAC40/dlxkNAHiees/s640/blogger-image-427642078.jpg" /></a></div><div class="separator" style="clear: both;">We discussed some of the mistakes. But before doing so, for one of them there were almost 5 different answers. I made the analogy that if people in New York get one answer and people here in California get a different answer, we have to agree on a method so we are not getting different answers for the same problem. This is why mathematicians came up with the order of operations. We also confronted the myth that you add before subtracting because "A" comes before "S" in PEMDAS.</div><img border="0" height="320" src="https://3.bp.blogspot.com/-4vhuFDc_oRA/WE2JFyBw3cI/AAAAAAAAC3Y/__Ji5EjGwOQi6mren64cI9gGEiV7y9gigCLcB/s320/IMG_8990.JPG" width="240" /><br /><br />We then dove into Graham Fletcher's <a href="https://gfletchy.com/gassed/">3-act task "Gassed.</a>" To be honest I did not prepare for alternative incorrect solution methods I did reflect and know that if a student got an answer by adding or multiplying incorrectly I could ask for an estimate or how much 2 gallons of gas would cost, or 3? When I asked them if it seemed reasonable, they thought so. Therefore, I have to have a backup question to that initial one.<br /><br />After watching Act 1 of the video, students wondered how much money was given to the gas station. I told them that I never go inside, I just swipe my card because I want to fill it up all the way.<br /><br />Part of a 3 act is then asking students what they want to know to answer the initial Act 1 question. They came up with asking how many gallons could the car hold and how much does it cost per gallon. I showed them these clues (9.52 gallons and $2.09 respectively).<br /><br />Many students just added the numbers together. Others unsuccessfully got past multiplying one factor by the hundredths place (not understanding the placement of the factor multiplying by the tenths place).<br /><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/-7wMipFQK_I4/WE2JF84qofI/AAAAAAAAC3U/xXz9xCn9QzE1VNouCsmbmlrqrDEJp9anACLcB/s1600/IMG_8991.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-7wMipFQK_I4/WE2JF84qofI/AAAAAAAAC3U/xXz9xCn9QzE1VNouCsmbmlrqrDEJp9anACLcB/s320/IMG_8991.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">This student for some reason thought that the $0.23 shown in Act 1 had something to do with the answer.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-0CbexEQ06iM/WE2JG_uR1TI/AAAAAAAAC3c/mkpe-W00F5EqWjnr6NxcfMWmaheyS5C3QCLcB/s1600/IMG_8993.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-0CbexEQ06iM/WE2JG_uR1TI/AAAAAAAAC3c/mkpe-W00F5EqWjnr6NxcfMWmaheyS5C3QCLcB/s320/IMG_8993.JPG" width="246" /></a></div><div class="separator" style="clear: both; text-align: center;">This is the student that was able to estimate the answer was near $20. As you can see above, they did not place their 3rd row of multiplication correctly lined up below the ones place.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-nSGdgRKlTWM/WE2JF1bii6I/AAAAAAAAC3Q/dHEIM2y8jQMRsf2Nrt2X-SHbTbYPny1vwCLcB/s1600/IMG_8992.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-nSGdgRKlTWM/WE2JF1bii6I/AAAAAAAAC3Q/dHEIM2y8jQMRsf2Nrt2X-SHbTbYPny1vwCLcB/s320/IMG_8992.JPG" width="294" /></a></div><div class="separator" style="clear: both; text-align: center;">Once again, struggling with 3 digit by 3 digit multiplication.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-SECtiG9uS8g/WE2JEsaW_FI/AAAAAAAAC3M/cba6GwXRxpI3sfYGLYd0MswZbatyZYIbgCLcB/s1600/IMG_8989.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-SECtiG9uS8g/WE2JEsaW_FI/AAAAAAAAC3M/cba6GwXRxpI3sfYGLYd0MswZbatyZYIbgCLcB/s320/IMG_8989.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">This student ended up lining it up correctly, as you can see with the zeros with the line through them representing the placeholder zeroes. They made one small calculation error for 9*5+1, coming up with 43 there. This affected the rounding.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-W-njolHfJUA/WE2JG02UA9I/AAAAAAAAC3g/XuvhFqKJH4oRalK1CXNyr15a5XWwEHEVgCLcB/s1600/IMG_8994.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="314" src="https://4.bp.blogspot.com/-W-njolHfJUA/WE2JG02UA9I/AAAAAAAAC3g/XuvhFqKJH4oRalK1CXNyr15a5XWwEHEVgCLcB/s320/IMG_8994.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">This person did not make any calculation error here.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div>The best part of the conversation was when they lined up the decimal in their product with the decimals in the factors. Then they said, 1,989.58?? That is WAYY too much money. So, instead of telling them a rule, I asked them where it made SENSE to place the decimal. Then they quickly said after the 19. Unfortunately, we didn't discuss rounding to the nearest penny because we were looking at a students work that miscalculated it slightly. They did come up that their answer was off by a penny.<br /><br />Students also loved watching the money display increase quickly. This relatively simple problem provided a rich discussion in our 6th grade math support class. Thanks Graham!Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com2tag:blogger.com,1999:blog-2523946538193054194.post-22424321821945276282016-12-11T11:07:00.001-08:002016-12-11T11:07:17.776-08:00Productive Peer Feedback in Gallery Walk (Student samples)<div class="separator" style="clear: both; text-align: left;">As a follow-up to my NCTM blog post (#2) about eliciting productive peer feedback, I used the same Google slides to remind students what type of feedback isn't useful and what type of feedback could move the learning forward. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Students had 2 days to complete their posters, and on a minimum day schedule we had a gallery walk where they looked at all the posters then settled on 1 poster to stay at to look at it in more detail and give feedback.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">In one class one particular group was off task and unproductive so there poster was lacking a lot compared to the rest of the posters. Only 1 person went to their poster to give feedback, and I hung all the posters in my room. I told them that it should be a reminder to them of the experience and motivate them to put forth their best effort the next time they are given a poster project.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">For teachers of CPM, this is Core Connections Course 3 4.1.1 where they are exploring the 4 representations of a quadratic tile pattern.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-qC9v0ch2yQk/WE2JZky6LwI/AAAAAAAAC3o/AJsTwyKRZb8h8jSlzuBZTyU1Twah9qyegCLcB/s1600/IMG_8969.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="316" src="https://4.bp.blogspot.com/-qC9v0ch2yQk/WE2JZky6LwI/AAAAAAAAC3o/AJsTwyKRZb8h8jSlzuBZTyU1Twah9qyegCLcB/s320/IMG_8969.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">What I liked about this is the student made a connection between how they wrote their rule, and how another group wrote their. She also elaborated how they got their rule (by making the pattern a rectangle).</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/--mMK30z-sBs/WE2JcNu0yhI/AAAAAAAAC30/DprveMRcLScZ8z0TbpttKUsuMXFgLjCQgCLcB/s1600/IMG_8973.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/--mMK30z-sBs/WE2JcNu0yhI/AAAAAAAAC30/DprveMRcLScZ8z0TbpttKUsuMXFgLjCQgCLcB/s320/IMG_8973.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Here you can see they complimented how the group showed the growth of the tiles by shading.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-BH2EHs9hdyE/WE2JZrk3cRI/AAAAAAAAC3k/M6shOb39EPIbQR8m7iLNFySUMUTbKwnMwCLcB/s1600/IMG_8974.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-BH2EHs9hdyE/WE2JZrk3cRI/AAAAAAAAC3k/M6shOb39EPIbQR8m7iLNFySUMUTbKwnMwCLcB/s320/IMG_8974.JPG" width="301" /></a></div><div class="separator" style="clear: both; text-align: center;">This student likes drawing a lot, so I decided to show how she got creating with her characters showing positive and constructive feedback.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-8X-4xlfl28Y/WE2Jb-hoBAI/AAAAAAAAC3s/fCJJds5QQ_s_Nat4AFqYYpOsr99Q_qLogCLcB/s1600/IMG_8975.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="309" src="https://1.bp.blogspot.com/-8X-4xlfl28Y/WE2Jb-hoBAI/AAAAAAAAC3s/fCJJds5QQ_s_Nat4AFqYYpOsr99Q_qLogCLcB/s320/IMG_8975.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">This student shared their opinion and also why a graph can be more helpful than a table.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-b6aY7nA_rzs/WE2JcJ7qY0I/AAAAAAAAC3w/62RN8uJMLjwBniVlyx-Uz1nQ7MkT6JZ5wCLcB/s1600/IMG_8976.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="218" src="https://1.bp.blogspot.com/-b6aY7nA_rzs/WE2JcJ7qY0I/AAAAAAAAC3w/62RN8uJMLjwBniVlyx-Uz1nQ7MkT6JZ5wCLcB/s320/IMG_8976.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Here they provided some suggestions on how to make their graph more complete and easier to read.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-mGgqxknSf9s/WE2JdVFXz3I/AAAAAAAAC34/4SkdZ0tz0dcGKQkb9z-RK06xCqlu1kz0ACLcB/s1600/IMG_8977.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="257" src="https://2.bp.blogspot.com/-mGgqxknSf9s/WE2JdVFXz3I/AAAAAAAAC34/4SkdZ0tz0dcGKQkb9z-RK06xCqlu1kz0ACLcB/s320/IMG_8977.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">This student noticed how a table group didn't connect the points on their graph and explained why, since it was a discrete graph and there's no such thing as a decimal figure number (that was on the poster).</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-meuknhxehXE/WE2JdlcOOKI/AAAAAAAAC38/CopdYFmxPcIim9zD5jScPJoniQh6q7ZnQCLcB/s1600/IMG_8979.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="315" src="https://1.bp.blogspot.com/-meuknhxehXE/WE2JdlcOOKI/AAAAAAAAC38/CopdYFmxPcIim9zD5jScPJoniQh6q7ZnQCLcB/s320/IMG_8979.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">One group made their y axis scaled by 1 (labor intensive) and this student commented that it inspired him. Haha.</div><br /><br />Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-85634158566887357252016-12-11T10:45:00.002-08:002016-12-11T10:45:10.890-08:00NCTM Blog Post #3: Cooperative Learning Strategies<blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en">Read our new blog post today on cooperative learning strategies! <a href="https://t.co/A9HhNi9veg">https://t.co/A9HhNi9veg</a> <a href="https://twitter.com/hashtag/MTMSBlog?src=hash">#MTMSBlog</a></div>— NCTM - MTMS (@MTMS_at_NCTM) <a href="https://twitter.com/MTMS_at_NCTM/status/805944898683883524">December 6, 2016</a></blockquote><script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script>Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-67344482638452938172016-12-11T10:02:00.001-08:002016-12-11T10:02:52.586-08:00SF Math Teacher Circle<div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-lxgU4t4Sft8/WE2M7cz-hiI/AAAAAAAAC4k/e38hfcl8xpY/s640/blogger-image-1874411000.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;">The first SF Math Teacher Circle was held yesterday, December 10th, at Proof School. It was nice to see some familiar faces that had attended the Oakland PCMI professional development a few weeks ago. We joked how our spouses were asking if there is a math event every weekend. Nope, but just recently.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Paul Zeitz, who organizes the Proof School, organized the event. It was a rainy day and I took BART to avoid any parking issues, and they were very generous with coffee, pastries, and bagels provided as well as some Chinese food for lunch.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">They started with a pledge to not give answers out to spoil it for the rest of the group. We also were seated randomly with cards.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">We started off with a group activity from the awesome Get it Together book. It was an activity I hadn't done before, which was about a sequence. As you can see below, the clues were: a person had 10 acres of land after the first year of the big drought, in the summer of 1914 she had 410 acres of land, after every fall harvest she bought all the fields that shared a fence, and finally each field was a 10 acre square, that shared a fence with 4 neighbors.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">We worked separately then shared ideas. I used a diagram as you can see below, and kept track of the acres with a table. We had a nice discussion about how she had 410 in the summer, so it was BEFORE she had bought more in the fall. So, at the END of 1914, she had 610 acres. From there I just labeled the years going backwards, seeing that the starting point in 1908 was 0,0 when the drought happened.</div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-lxgU4t4Sft8/WE2M7cz-hiI/AAAAAAAAC4k/e38hfcl8xpY/s640/blogger-image-1874411000.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-LJbrb7Ed6IY/WE2M4xnFJZI/AAAAAAAAC4g/1yvk8JgxDa4/s640/blogger-image-372967541.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-LJbrb7Ed6IY/WE2M4xnFJZI/AAAAAAAAC4g/1yvk8JgxDa4/s640/blogger-image-372967541.jpg" /></a></div><div class="separator" style="clear: both;">Then Avery Pickford presented on some voting topics. I like how he started with a table of values and asked us to notice and wonder. We realized each column had the numbers 1 through 5 in different orders. He then added the labels to the table to see how the columns were different sized groups of people and the rows were the food preferences ranked on a scale of 1 to 5, 1 being their favorite.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">The big question was, how could you satisfy the most people? It was interesting, because different methods produced different winners. John in our group did a golf score method where he multiplied the rank by the number of people in the group, then summed those results for each type of food, and burritos had the lowest score. Another method is taking the average of each score, which ends up not being too fair. There were also some other methods we discussed.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">We then looked at how voters would vote based on what type of candidate there was in a 2 party system and a 3 party system. </div><img border="0" src="https://lh3.googleusercontent.com/-lxgU4t4Sft8/WE2M7cz-hiI/AAAAAAAAC4k/e38hfcl8xpY/s640/blogger-image-1874411000.jpg" /><br />Finally, Paul presented on some math games. It reminded a bunch of us of the 21 flags survivor game from PCMI. Game 2 was Basic Takeaway. Start with 16 pennies and remove 1, 2, 3, or 4 pennies. Our strategy was to go first and take 1, leaving your opponent with a multiple of 5 to choose from. The person who grabs the last penny/pennies is the winner.<br /><br />Game 3 was Don't be Greedy. Basically you start off with pennies, but you can take any amount that is not all the pennies. Your opponent can then take that amount, or less.<br /><br />We also investigated a Cat and Mouse Maze that seemed to be never ending, unless the Mouse got to to the top left corner and was trapped.<br /><br />The last one we talked about was breaking the bar. If you have a 8 by 6 chocolate bar like a Hersheys, whoever makes the last "legal move" or break is the winner. Basically, every time you break a piece, you are left with 1 more piece. So, the game has 48 moves, so I BELIEVE you'd want your opponent to go first on this one.<br /><br />Once it was lunch time, I took off because I had to pick up my 6 month old from my parents who were watching her, but it was a fun day. It reminded me that I've got to prepare some Get it Together card sets for my support classes as well as my 8th grade classes.Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0tag:blogger.com,1999:blog-2523946538193054194.post-67473558487787354012016-11-28T11:33:00.000-08:002016-11-28T11:33:02.892-08:003 Act Tasks in Math Intervention<div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-l6eDxsJ7qtQ/WDZyB7ZpxzI/AAAAAAAAC1s/ZGQgutzVjsE/s640/blogger-image--1516090363.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-wBGsdhX1fyU/WDZ1MV7puuI/AAAAAAAAC10/P3sf8xTxOD4/s640/blogger-image--69927205.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-wBGsdhX1fyU/WDZ1MV7puuI/AAAAAAAAC10/P3sf8xTxOD4/s640/blogger-image--69927205.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-jbi1vK792Ak/WDZ1QGA95jI/AAAAAAAAC18/WKOBd7jxiXA/s640/blogger-image--122288960.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-jbi1vK792Ak/WDZ1QGA95jI/AAAAAAAAC18/WKOBd7jxiXA/s640/blogger-image--122288960.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-xalm4L3lzQk/WDZ1SMq_KgI/AAAAAAAAC2A/A8dM8TLZr7w/s640/blogger-image--1051605808.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div><div class="separator" style="clear: both;">I teach a 7th and 8th grade math intervention class 3rd period with about 13 students. Only 3 of them are in my 5th period mainstream class, the rest have different teachers. This makes it a bit hard to coordinate homework at times, but I have a board with teachers names on it where they write in the assignment.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">For the most part, I use the class as a place where they can support each other on their homework and I can do some reteaching. I also occasionally do an estimation, fraction talk, or number talk.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">On Fridays, most teachers don't assign weekend homework, so that's my free day to do a cool lesson. We have made fraction strips out of construction paper, Desmos activities, puzzles, and sometimes a 3 act task.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">I noticed students were having trouble with dividing fractions so I remembered a great task that <a href="http://www.gfletchy.com/">Graham Fletcher has made called The Apple</a>. It's a 4th grade standard, but definitely appropriate for any non-accelerated middle school class.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">As you can see below, we first tackled the task with a too low, high, and just right estimate. The range was between 8 and 150. I was disappointed no students tried repeated subtraction or addition to get to the answer. I'll have to introduce that next time. Students realized they needed to divide, but couldn't figure out how to. Some students converted 3/8 to a decimal, then realized it didn't make the problem easier for them.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">A side note, I love that this problem as a digital scale that measures in fractions, how perfect! Students had different ideas, and after some productive struggle they pieced together each of their ideas into an answer. Miguel said convert 5 1/4 to 21/4. Another student said you needed to flip the 3/8 and write it as 8/3. Then they multiplied across.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">I showed them the common denominator method, and reminded them of the reason we multiply by the reciprocal when dividing by a fraction by modeling the Super Giant One from 7th grade.</div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-xalm4L3lzQk/WDZ1SMq_KgI/AAAAAAAAC2A/A8dM8TLZr7w/s640/blogger-image--1051605808.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-HP_IEUwoE1w/WDZ1OKsnVUI/AAAAAAAAC14/6rsWFl_P-r8/s640/blogger-image-1486254371.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-HP_IEUwoE1w/WDZ1OKsnVUI/AAAAAAAAC14/6rsWFl_P-r8/s640/blogger-image-1486254371.jpg" /></a></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">I have the playing cards for the game 24. You are given 4 numbers, and have to make 24 using each number once and any operation. We did this one, 7, 7, 4, 1 as a group. We struggled together, and I gave them a hint for what times what is 24. So, they then came up with 7 plus 1 is 8, and 7-4 is 3. Multiply those together and you get 24. After they saw the challenge, they were super motivated when playing in partnerships which of course pleased me.</div><img border="0" src="https://lh3.googleusercontent.com/-xalm4L3lzQk/WDZ1SMq_KgI/AAAAAAAAC2A/A8dM8TLZr7w/s640/blogger-image--1051605808.jpg" /><br />The following fraction talk is under the my favorite problems tab at the top of this blog. The quest is what fraction is yellow, and how do you see it?<br /><img border="0" src="https://lh3.googleusercontent.com/-wBGsdhX1fyU/WDZ1MV7puuI/AAAAAAAAC10/P3sf8xTxOD4/s640/blogger-image--69927205.jpg" /><br />As you can see, students came up with 1/3, 2/3. 1/6, 1 1/6, and 1/4.<br /><br />The biggest misconception I can see with those answers is that the students aren't including the yellow part in their denominator. Also, most were not willing to share why they came up with those answers.<br /><br />Miguel was able to explain that 2 red's make a yellow. So, I drew a diagram of his thinking as he explained it. He kept moving the red blocks up to make yellows. Therefore, he had a total of 4 yellow blocks. so, 1 yellow out of 4 yellow blocks is 1/4. Another student converted the yellow into 2 red, so he had 2 red out of 8 total red. I also showed them that since there's a line of symmetry, just like the one going down the middle of your face, you can see how much yellow there is of half of it, which is 1/4.<br /><img border="0" src="https://lh3.googleusercontent.com/-jbi1vK792Ak/WDZ1QGA95jI/AAAAAAAAC18/WKOBd7jxiXA/s640/blogger-image--122288960.jpg" /><br /><br /><br /><div class="separator" style="clear: both;">On another day, we returned to the same 3 act task web site for Rope Jumper. Kids always get a kick out of this one.</div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-l6eDxsJ7qtQ/WDZyB7ZpxzI/AAAAAAAAC1s/ZGQgutzVjsE/s640/blogger-image--1516090363.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://lh3.googleusercontent.com/-mAPfzl3etAk/WDZx_ywEu4I/AAAAAAAAC1o/uFwcNXSv06E/s640/blogger-image--1184251440.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-mAPfzl3etAk/WDZx_ywEu4I/AAAAAAAAC1o/uFwcNXSv06E/s640/blogger-image--1184251440.jpg" /></a></div><div class="separator" style="clear: both;">Once again we start off with low, high, and estimates before Act 2. I asked them what information they would need to figure out the number of jumps in 30 seconds.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">For the 6th graders, they had trouble with this question, so I asked them what do you think is behind the blacked out part of the video?</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Students reasoned it would be a timer, and a counter of how many jumps.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">It's hard to read the writing below, but the main strategy was repeated addition here at first. Mavae reasoned that if it's 41 jumps in 7 seconds, he added 41 + 41 + 41 and 7 + 7 + 7 to get 123 jumps in 21 seconds. He realized he could add 1 more chunk of 41 jumps in 7 seconds to get 164 jumps in 28 seconds.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">When it came to the extra 2 seconds, students struggled with that part, but said well just add 2 jumps for 2 seconds. This would be a great talking point that I could have used to connect the next method with this method, because the next method was unit rate.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Ayman divided 41 by 7 and got 5 point something. He rounded it to 6 and then multiplied it by 30 seconds. So, he basically found the unit rate, then multiplied.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Also, I missed an opportunity to show how you could have used proportions for the problem, but I usually steer the lesson in the direction that the students take it,</div><img border="0" src="https://lh3.googleusercontent.com/-l6eDxsJ7qtQ/WDZyB7ZpxzI/AAAAAAAAC1s/ZGQgutzVjsE/s640/blogger-image--1516090363.jpg" /><br />We also started Clapper, but didn't have time to finish it, so I'll write that one up later.Mr. Joycehttp://www.blogger.com/profile/00531067557915419994noreply@blogger.com0