tag:blogger.com,1999:blog-1774208020168002942018-02-18T07:47:26.735-05:00Math DyalMath Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.comBlogger64125tag:blogger.com,1999:blog-177420802016800294.post-7232153540874319962018-01-06T09:46:00.002-05:002018-01-06T09:46:32.641-05:00Translating a lineI will never forget one of my students telling me after a district exam, "One of the questions asked me to translate a line - what does that mean, write it in Spanish?" I thought I had done just a great job on the linear functions unit, but I had totally missed connecting the idea of translations for them. I had always waited until quadratic functions to talk about <a href="http://mathdyal.blogspot.com/2017/02/para-bowl-as.html" target="_blank">shifts in the parent function as transformations</a>, but when I looked into the standards I realized I was missing a key part of linear functions<span style="font-family: Times, Times New Roman, serif;">. <span style="background-color: white; color: #222222;">CCSS.MATH.CONTENT.HSF.BF.B.3: Identify the effect on the graph of replacing f(x) with f(x)+ k, … for specific values of k (both positive and negative); find the value of k given the graphs. </span></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-Its-CjC7s0U/WlDcxQG1_1I/AAAAAAAACFs/W1lAeOX1sIgtLpu5DNTuj3lZ-a5fcLayACLcBGAs/s1600/linear%2Bfunctions.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="1200" data-original-width="900" height="320" src="https://3.bp.blogspot.com/-Its-CjC7s0U/WlDcxQG1_1I/AAAAAAAACFs/W1lAeOX1sIgtLpu5DNTuj3lZ-a5fcLayACLcBGAs/s320/linear%2Bfunctions.jpg" width="240" /></a></div><div>So I created some <a href="https://www.teacherspayteachers.com/Product/Linear-Translations-Dominoes-and-Interactive-Notebook-Activity-2688856" target="_blank">doodle notes </a>that compare various graphs to the parent function. Each graph already had y = x graphed, so seeing the transformation is easier. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-Z5J1BR3NHEg/WlDdTklmzvI/AAAAAAAACF0/_FWisE8pfDo7IgWk8ljxRhFQBlvGThvbgCLcBGAs/s1600/linear%2Breflection.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="411" data-original-width="244" height="320" src="https://3.bp.blogspot.com/-Z5J1BR3NHEg/WlDdTklmzvI/AAAAAAAACF0/_FWisE8pfDo7IgWk8ljxRhFQBlvGThvbgCLcBGAs/s320/linear%2Breflection.jpg" width="189" /></a></div><div>The standard specifically addresses translations, but I also wanted students to see that changing the slope is actually a dilation and making it negative is a reflection. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-Xh1KFN9QA8Q/WlDeo9s3htI/AAAAAAAACGE/-64OQNLuxqgceinQdLpP5a9pRPkTrXy3QCLcBGAs/s1600/linear%2Bdominoes%2B1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="932" data-original-width="1200" height="248" src="https://3.bp.blogspot.com/-Xh1KFN9QA8Q/WlDeo9s3htI/AAAAAAAACGE/-64OQNLuxqgceinQdLpP5a9pRPkTrXy3QCLcBGAs/s320/linear%2Bdominoes%2B1.jpg" width="320" /></a></div><div><br /></div><div>After finishing the notes, we completed a<a href="https://www.teacherspayteachers.com/Product/Linear-Translations-Dominoes-and-Interactive-Notebook-Activity-2688856" target="_blank"> dominoes activity</a> to practice translations. I love these dominoes because they have an answer bank to work from. They <span style="font-family: Times, Times New Roman, serif;">start with the line y = x and perform the vertical translations up or down. Students match the graph and then perform the next translation.</span></div><div><span style="font-family: Times, Times New Roman, serif;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-uvFLxPeWQDY/WlDgvv8E06I/AAAAAAAACGY/lhAMOzJfgwMs7bLHLKWFt-H7OFXq3X-sgCLcBGAs/s1600/linear%2Bdominoes%2Bwith%2Bequations.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="362" data-original-width="1600" height="72" src="https://1.bp.blogspot.com/-uvFLxPeWQDY/WlDgvv8E06I/AAAAAAAACGY/lhAMOzJfgwMs7bLHLKWFt-H7OFXq3X-sgCLcBGAs/s320/linear%2Bdominoes%2Bwith%2Bequations.png" width="320" /></a></div><div><span style="font-family: Times, Times New Roman, serif;"><br /></span></div><div><span style="font-family: Times, Times New Roman, serif;">For extra practice I had them write the equation of each line, again reinforcing the idea that the constant is the only thing changing in the equation. </span></div><div><span style="font-family: Times, Times New Roman, serif;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-8v87aynQF5M/WlDf7xURL-I/AAAAAAAACGQ/h0ADkN4TNNspvC6U1AWRqwZXxAjyg4kNgCLcBGAs/s1600/linear%2Binb.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="895" data-original-width="1200" height="238" src="https://4.bp.blogspot.com/-8v87aynQF5M/WlDf7xURL-I/AAAAAAAACGQ/h0ADkN4TNNspvC6U1AWRqwZXxAjyg4kNgCLcBGAs/s320/linear%2Binb.png" width="320" /></a></div><div><span style="font-family: Times, Times New Roman, serif;"><br /></span></div><div><span style="font-family: Times, Times New Roman, serif;">Both sheets made up a two-page spread in our interactive notebooks. </span><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-71LVajewQpg/WlDdvZx0GYI/AAAAAAAACF8/Sp-MkWWgiMQCzgwIP57Yq88Arva93RQDwCLcBGAs/s1600/linear%2Btry%2Bit.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="220" data-original-width="344" height="204" src="https://1.bp.blogspot.com/-71LVajewQpg/WlDdvZx0GYI/AAAAAAAACF8/Sp-MkWWgiMQCzgwIP57Yq88Arva93RQDwCLcBGAs/s320/linear%2Btry%2Bit.png" width="320" /></a></div><div><br /></div><div>I wrapped things up with this "Try It" question too. I know that before this lesson, my students would have had no idea how to even tackle it, but they were so confident in their answers. With any luck, when they see questions about "translating" on the next test, it will no longer think of a foreign language. </div><div><br /></div></div>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-15607769480507357202017-12-13T19:00:00.000-05:002017-12-13T19:31:59.980-05:00The Most Magical Holiday<div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/--hqipaMZP9s/WjCOvOugWKI/AAAAAAAACFI/Y0r5b-A8Jes-xBudzWH1Jd-5bW5HJFTfgCLcBGAs/s1600/math-giveaway-blog-hop%2B%25281%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="492" data-original-width="939" height="167" src="https://3.bp.blogspot.com/--hqipaMZP9s/WjCOvOugWKI/AAAAAAAACFI/Y0r5b-A8Jes-xBudzWH1Jd-5bW5HJFTfgCLcBGAs/s320/math-giveaway-blog-hop%2B%25281%2529.png" width="320" /></a></div><br />Hello! I'm spreading holiday cheer with a few of my math friends. Make sure to keep blog-hopping to find more giveaways!<br /><br /><span style="color: red;"><b>My Favorite Holiday Activity</b></span><br /><div class="separator" style="clear: both; text-align: center;"><span style="color: red;"><b><a href="https://3.bp.blogspot.com/-H_HTIFirsCg/WjCLgSrUU5I/AAAAAAAACE4/fBQucFNqCPYrbImm01fS9rKYv_gU4X-fACLcBGAs/s1600/disney2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://3.bp.blogspot.com/-H_HTIFirsCg/WjCLgSrUU5I/AAAAAAAACE4/fBQucFNqCPYrbImm01fS9rKYv_gU4X-fACLcBGAs/s320/disney2.JPG" width="240" /></a></b></span></div><br /><div class="separator" style="clear: both; text-align: center;"></div>This year my favorite holiday activity was going to Disney World! I just returned from a three-day "Princess Trip" with my two-year old daughter and my mom - and it was the most magical vacation. I loved seeing Main Street all decorated with holly in the streets and the tallest tree plopped right at the end. My daughter was ecstatic when she caught her first glimpse of Cinderella's Castle and when Minnie Mouse held Elsa's hand while she sang, "Let It Go," it may have been the most exciting moment of her life so far. Something about being inside the bubble of Disney World makes all your other stresses and worries melt away and was just the break I needed to make it through the next five days of school (we are all counting at this point- right!?).<br /><br /><span style="color: red;"><b><br /></b></span><span style="color: red;"><b>My Favorite Math Activity</b></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-gzX24SSi6Nc/WjCI4-67NFI/AAAAAAAACEo/vXGqlszBagwFll8Pi27fI4ufoFsOizptQCLcBGAs/s1600/linear%2Binequalities%2Bcoloring.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1091" data-original-width="819" height="320" src="https://4.bp.blogspot.com/-gzX24SSi6Nc/WjCI4-67NFI/AAAAAAAACEo/vXGqlszBagwFll8Pi27fI4ufoFsOizptQCLcBGAs/s320/linear%2Binequalities%2Bcoloring.png" width="240" /></a></div>The favorite of me and my students have to be my <a href="https://www.teacherspayteachers.com/Store/Math-Dyal/Category/Coloring-Activities-249305" target="_blank">coloring activities</a>. I find coloring to be so relaxing and soothing (and those are two words students don't usually associate with math!). In all my coloring activities, students get to pick their own colors., which means they do not all look the same. I also love self-checking activities, so that students don't practice incorrectly, and the coloring activities have an answer bank included, so students know when to ask for help. The opportunity to engage the right-brain is so important in math class, and I love giving the students a chance to show their creativity. Plus, with the holiday break so close, a few minutes coloring could be just the hook you need to get the kids to do their work and stop asking, "Can we just have a free day?"<br /><b><span style="color: red;"><br /></span></b><b><span style="color: red;">My Favorite Teacher Tool </span></b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-mkbRJMr3ld8/WjGrPt7DzyI/AAAAAAAACFc/aQTQ56OZCaonjGLmXfMF3KSMqeFvvBsfACLcBGAs/s1600/IMG_3895.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://3.bp.blogspot.com/-mkbRJMr3ld8/WjGrPt7DzyI/AAAAAAAACFc/aQTQ56OZCaonjGLmXfMF3KSMqeFvvBsfACLcBGAs/s320/IMG_3895.JPG" width="240" /></a></div>My go-to daily teacher must-have is a nice strong cup of coffee. I love walking around helping students with their work as I sip it during 1st period. I usually brew my own at home and love to add some peppermint-flavored creamer this time of year. Only once in 10 years have I spilled any on a students' work and it was this year in her interactive notebook, while I was showing her work under the document camera (oops!). Now every time I ask to put her work on the document camera, she says, "Only if you make sure your mug is all the way closed first" 😁<br /><br /><span style="color: red;"><b>Giveaway</b></span><br />So now it's time for your chance to win a present in a GIVEAWAY! I have a $15 Starbucks gift card that I will send to you via snail mail, and my <a href="https://www.teacherspayteachers.com/Product/Algebra-Coloring-Activities-Bundle-2677615" target="_blank">Algebra Coloring Activities Bundle</a> that you can use to keep your little elves engaged all year!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Algebra-Coloring-Activities-Bundle-2677615" target="_blank"><img border="0" data-original-height="768" data-original-width="768" height="320" src="https://2.bp.blogspot.com/-W25-O0hgGgo/WjCO_ch4EfI/AAAAAAAACFM/AvQdwtcelwQBu0NV1Ek0_w5qIglTC4x_ACLcBGAs/s320/coloring%2Bbundle%2Bcover%2B7.16.17.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><a class="rcptr" data-raflid="3ff6d64d6" data-template="" data-theme="classic" href="http://www.rafflecopter.com/rafl/display/3ff6d64d6/" id="rcwidget_fd6emhuj" rel="nofollow">a Rafflecopter giveaway</a><script src="https://widget-prime.rafflecopter.com/launch.js"></script><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><br /><div class="yiv2193116081gmail-MsoNormal" style="background-color: white; color: #26282a;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><b><span style="color: black;">Now it's time to hop over to </span></b><b><a href="http://smithcurriculumconsulting.com/jennifers-favorite-things-giveaway/" target="_blank">Smith Curriculum and Consulting</a></b><b><span style="color: black;">'s blog to enter another giveaway!</span></b><b><span style="color: black;"> </span></b></span></div><div class="yiv2193116081gmail-MsoNormal" style="background-color: white; color: #26282a;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><b><span style="color: black;">Giveaway ends Monday December 18, 2017 at 8PM EST!</span></b> </span><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://smithcurriculumconsulting.com/jennifers-favorite-things-giveaway/" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="320" src="https://2.bp.blogspot.com/-JC6NyOKDP40/WjCOu_1oiyI/AAAAAAAACFE/czfyagJH4743E1e-biHAV2IL0kjGZuAogCEwYBhgL/s320/favorite-math-things-blog-hop-to-next-blog.png" width="320" /></a></div><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span></div>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com12tag:blogger.com,1999:blog-177420802016800294.post-80789593237787839432017-10-11T16:27:00.002-04:002017-10-11T16:27:36.711-04:00Building Community While Taking Attendance<div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-vVeS-GsaJPE/Wd5-pmR1HuI/AAAAAAAACEA/rYs6_NoPV7QjZ1LdndfcmGjTO5jU-2HbQCLcBGAs/s1600/attendance.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="972" data-original-width="758" height="400" src="https://3.bp.blogspot.com/-vVeS-GsaJPE/Wd5-pmR1HuI/AAAAAAAACEA/rYs6_NoPV7QjZ1LdndfcmGjTO5jU-2HbQCLcBGAs/s400/attendance.png" width="311" /></a></div><br />Is there anything more awkward for the first day of school than calling the role? Standing with a clipboard trying to put together letters into a way that doesn't butcher too badly the name their parents had in mind, all while the other students listen, laugh. Not only is this embarrassing for me, but it robs my students of valuable class time. So I have created a system that works better for me and helps build community in my classroom.<br /><br />I tell students from the first day of school that teamwork is essential in my class. My desks are arranged in groups of three and these people are your first resource for anything from pencils to help with the assignment. So I have them turn to their neighbors and introduce themselves. At minimum, you need to know the names of the two people you are sitting with, but I tell them to learn something else about them too.<br /><br />Then during the work period, I circulate with my clipboard. I pick someone at random in the group and ask, "What are your group members' names?" And the student tells me their names. Then I ask another student the same question, then the last student. At that point, I have heard the students say each name twice, which is plenty for me to mark down the attendance. The kids are also more likely to correct each other (even though I beg them to correct me if I pronounce their name wrong, they are usually hesitant to). The best part is that it builds the classroom culture of relying on each other from the beginning. I have already found that students are way more likely to strike up a conversation about a tricky word problem or ask for help finding a mistake if they know the person's name. It makes me sad when, in December, I ask someone to pass out papers and they tell me they don't know anyone's name. I am going to make a point to rotate the groups too and always emphasize that you need to know the names of your group member ... and rely on them for help. Teamwork!Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-58068063398418117262017-07-19T14:42:00.004-04:002017-07-19T14:42:54.229-04:00Why I made Warm Ups extra creditWarm-Ups were always a struggle for me - I like the idea of having something for the kids to work on immediately, but logistically, I had trouble with motivating kids to do it. Some would take forever to get out a Warm Up journal, some would wait until the answer was on the board and just copy, some would ignore it all together. After nine years of trial and error, I finally found a Warm-Up routine that I like: <div><br /></div><div>I create a Warm Up question that will take about three minutes to answer and project it on the board as students enter (it may be review from earlier in the school year or earlier in the unit). I stand at the door greeting students and hand out scrap paper as they walk in. I LOVE recycling, so I just re-use some of the extra paper that I have laying around - old memos, extra copies, and if I ever run low, I just ask in the copy room and they usually have a stack of paper in the recycle bin. Each student gets 1/4 sheet of paper from me as they enter. I also keep an extra container of it on my back table for students who walk in after the bell. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-XfeVIQHMPyk/WW-l8i8deCI/AAAAAAAACDA/ypVOMG_hw6Un0w4TKOu_1PxGKCGKtiGdgCLcBGAs/s1600/IMG_0318.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://2.bp.blogspot.com/-XfeVIQHMPyk/WW-l8i8deCI/AAAAAAAACDA/ypVOMG_hw6Un0w4TKOu_1PxGKCGKtiGdgCLcBGAs/s320/IMG_0318.JPG" width="240" /></a></div><div>I usually give students about three minutes after the bell rings to complete the problem, and I give a 30 second warning. They must show ALL work to receive credit, but they don't have to copy down word problems. Then I or a student volunteer walk around and pick them up. But here is the kicker that makes students actually WANT to try it - after students get five Warm-Up points for the quarter, the rest are EXTRA CREDIT! Just the idea of bonus points is usually enough to get students to try even a challenging problem, plus it takes the pressure off if they get one wrong or are absent or tardy to class. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-VRkL9hkgOmA/WW-llDRgM0I/AAAAAAAACC8/lYbXdjVBqPUMJ0C3WkX1NVr5cPYk0S8fgCEwYBhgL/s1600/IMG_0561.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://2.bp.blogspot.com/-VRkL9hkgOmA/WW-llDRgM0I/AAAAAAAACC8/lYbXdjVBqPUMJ0C3WkX1NVr5cPYk0S8fgCEwYBhgL/s320/IMG_0561.JPG" width="240" /></a></div><div><div><br /></div><div>I can quickly separate the right answers from the wrong and then I make a check-mark on my roster next to everyone who answered correctly. I usually put in Warm-Up grades twice a quarter (once before progress reports and once before the end of the quarter). Students love seeing a score like 7/3 and the bonus points aren't enough to bring up a quarter of slacking, but do help balance out late work or other missed points.</div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-zvqStroXsRg/WW-nsr75_fI/AAAAAAAACDE/FgCNVhcmcaUFhRI29lYwLQRCambYhGUhACLcBGAs/s1600/warm%2Bup%2Bcheck.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1060" data-original-width="795" height="320" src="https://4.bp.blogspot.com/-zvqStroXsRg/WW-nsr75_fI/AAAAAAAACDE/FgCNVhcmcaUFhRI29lYwLQRCambYhGUhACLcBGAs/s320/warm%2Bup%2Bcheck.jpg" width="240" /></a></div><div><br /></div><div>Depending on the nature of the Warm-Up, I may use it to launch into instruction, put a correct answer under the document camera, have a student work it out on the board, or work it out myself. </div>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-9348366628113457582017-04-01T21:14:00.002-04:002017-04-01T21:16:18.963-04:00Linear InequalitiesI usually teach linear inequalities right after systems of equations, but this year I ended that unit right before Thanksgiving break, then we spent the time between Thanksgiving and Christmas on Radicals and Rational Exponents. Then when we came back in the new year, it was on to polynomials and quadratics. Although I kept meaning to find a few days to fit in linear inequalities, it kept getting lost. Then we had a four day week right after we wrapped up the quadratics unit where it fit perfectly. I actually liked having this topic here for a few reasons: 1. Coming off using the quadratic formula to find irrational solutions, this seemed like a breeze! 2. It was a great refresher of graphing linear functions. I reminded them how we graphed one-variable inequalities on the number line with open and closed circles and then we extended that to dashed and solid lines.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-zoxLmwJ36Ig/WNLIgu_h5iI/AAAAAAAACBI/GD4CptATYsI1N6AshQ_p8TqMfo1aCm7YQCLcB/s1600/FullSizeRender%2B%25281%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="297" src="https://1.bp.blogspot.com/-zoxLmwJ36Ig/WNLIgu_h5iI/AAAAAAAACBI/GD4CptATYsI1N6AshQ_p8TqMfo1aCm7YQCLcB/s400/FullSizeRender%2B%25281%2529.jpg" width="400" /></a></div><br />I developed these fun interactive <a href="https://www.teacherspayteachers.com/Product/Graphing-Linear-Inequalities-Interactive-Notes-2596321" target="_blank">notes </a>for students to practice graphing linear inequalities, writing linear inequalities from a graph and solving word problems involving linear inequalities. Students really liked shading their graphs with colored pencils and markers. We did the first one together, then they graphed the second one on their own and we talked about how to shade together.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-h1D07bqRwLw/WOBOgtnBjLI/AAAAAAAACB8/xFF-pefTAfQma6sX6HF2ALLGUyXnTsF2gCLcB/s1600/test%2Bpoint.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="189" src="https://2.bp.blogspot.com/-h1D07bqRwLw/WOBOgtnBjLI/AAAAAAAACB8/xFF-pefTAfQma6sX6HF2ALLGUyXnTsF2gCLcB/s320/test%2Bpoint.jpg" width="320" /></a></div><br /><br />With both these problems projected on the board, at least one student in each class would point out that > are shaded above the line and < are shaded below. Just like any other shortcut, we talked about the limitations and specifically how this only works if y is on the left side of the equation. Some of my students liked to use this shortcut and some preferred to test a point. I modeled with testing (0,0).<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-2wy6wZRHprY/WOBO59FhxkI/AAAAAAAACCA/bN1iasWKItwrxo7aa_RX91u_eSoYbf79wCLcB/s1600/linear%2Binequalities%2Bword%2Bproblems.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="115" src="https://2.bp.blogspot.com/-2wy6wZRHprY/WOBO59FhxkI/AAAAAAAACCA/bN1iasWKItwrxo7aa_RX91u_eSoYbf79wCLcB/s400/linear%2Binequalities%2Bword%2Bproblems.png" width="400" /></a></div><br />Next we took on the word problem together, rearranging the equation in standard form to graph it in y-intercept form. Then we jumped to the other word problem and students tried it on their own. These word problems helped my students understand the shading in context.<br /><br /><a href="https://1.bp.blogspot.com/-fiTNbDFAmL8/WNLKlo96kQI/AAAAAAAACBM/KAp5VpdhA5sDbKGXGX4enw5_oBUaqghwgCLcB/s1600/IMG_5518%2B%25281%2529.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-fiTNbDFAmL8/WNLKlo96kQI/AAAAAAAACBM/KAp5VpdhA5sDbKGXGX4enw5_oBUaqghwgCLcB/s320/IMG_5518%2B%25281%2529.JPG" width="240" /></a><br />Then I had the students complete the other problems on their own. I projected them onto the board and had students work them out.<br /><br /><a href="https://4.bp.blogspot.com/-LeEa1yqWE2o/WOBO9Ie5leI/AAAAAAAACCE/R6j4ocRvUa8TQuGjg5SBuUrHBiIAeybSgCLcB/s1600/linear%2Binequalities%2Bshade.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://4.bp.blogspot.com/-LeEa1yqWE2o/WOBO9Ie5leI/AAAAAAAACCE/R6j4ocRvUa8TQuGjg5SBuUrHBiIAeybSgCLcB/s200/linear%2Binequalities%2Bshade.png" width="200" /></a><br /><div class="separator" style="clear: both; text-align: center;"></div><br />Students practiced with this<a href="https://www.teacherspayteachers.com/Product/Graph-Linear-Inequalities-Coloring-Activity-2588257" target="_blank"> coloring activity</a>. I love all the variety of my creative students!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-TeYmZmwF_B0/WNLQthi1uGI/AAAAAAAACBc/gjBbIs0VLjIraDP8KJRAOG_esuzkmyqzQCLcB/s1600/creative6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://1.bp.blogspot.com/-TeYmZmwF_B0/WNLQthi1uGI/AAAAAAAACBc/gjBbIs0VLjIraDP8KJRAOG_esuzkmyqzQCLcB/s640/creative6.png" width="308" /></a></div><br />At the end of the class, I passed out this <a href="https://drive.google.com/file/d/0B5-n-lm3N6ehN2xkZEFaaDFBbzQ/view?usp=sharing" target="_blank">exit ticket</a>. {click to download for free!}<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-SctVuC1nu5s/WNLQfz_R8dI/AAAAAAAACBY/s30Fgr_GjD4ABKis2mV-YvOyX_F0i3HSgCLcB/s1600/linear%2Binequalities%2Bexit%2Bticket.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="173" src="https://3.bp.blogspot.com/-SctVuC1nu5s/WNLQfz_R8dI/AAAAAAAACBY/s30Fgr_GjD4ABKis2mV-YvOyX_F0i3HSgCLcB/s320/linear%2Binequalities%2Bexit%2Bticket.png" width="320" /></a></div><br />After class, I quickly sorted them into those who answered it perfectly and those who made a mistake. I used my single-hole-punch to make a hole in the stack that answered perfectly. At the start of the next class, I passed back the ones who answered perfectly with a student who needed help and had them assist the student in finding and correcting their error. This method has worked really well for engaging everyone and getting students instant remediation.<br /><br />Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-26167312582972005482017-03-21T22:32:00.001-04:002017-03-22T14:19:26.901-04:00Giving Kids Time To Be Creative <br /><a href="https://2.bp.blogspot.com/-sMan1XpUoew/WNHcCtp_UEI/AAAAAAAACAE/XRrSLp4G-6gxcE5JO63BmEt0vdxHEqAJQCEw/s1600/creative6.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="400" src="https://2.bp.blogspot.com/-sMan1XpUoew/WNHcCtp_UEI/AAAAAAAACAE/XRrSLp4G-6gxcE5JO63BmEt0vdxHEqAJQCEw/s400/creative6.png" width="191" /></a>To say teenagers today are highly-visual is the understatement of the century - they don't even have telephone conversations without looking at the person and spend the majority of their day sending pictures back and forth to their friends - they need visual references that are aesthetically pleasing to look at it. I used to think that any class time used cutting, gluing, coloring, or decorating would be better spent doing another math problem. Then I let the kids actually start spending a little bit of my coveted 90 minutes just being creative, and the results have been amazing! The kids are more engaged in what they are doing, more excited about their notes and work, and have much better retention, but most importantly they are having FUN! Math class usually brings so much anxiety, that any time students say they enjoy my class, I count it as a win. It's a little sad to me that some students say they do more art in my class and in their actual art classes.<br /><br />My favorite way to ignite their creative side is with these <a href="https://www.teacherspayteachers.com/Store/Math-Dyal/Category/Coloring-Activities-249305" target="_blank">coloring activities</a>. The picture at the top serves as their answer bank, so these are self-checking. Plus the "artist" gets to pick the color for each box - so each one is unique!<br /><br /><br /><br /><br /><br /><a href="https://1.bp.blogspot.com/-dis9b-pXJP8/WNHb7-azJdI/AAAAAAAAB_s/79AxWxTGb0cxCEoNLDwCAAl5AXcYhU9RQCEw/s1600/creative1.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-dis9b-pXJP8/WNHb7-azJdI/AAAAAAAAB_s/79AxWxTGb0cxCEoNLDwCAAl5AXcYhU9RQCEw/s320/creative1.jpg" width="249" /></a>When we completed these <a href="https://www.teacherspayteachers.com/Product/Measures-of-Central-Tendency-Doodle-Notes-Mean-Median-Mode-Range-2476824" target="_blank">doodle notes about Mean, Median, Mode and Range</a>, students colored as they took notes and completed the example problems and then I gave them an extra two minutes to add some extra flair -think of it as adding a Snapchat filter ;). Students loved referring back to these notes in their interactive notebooks.<br /><br /><a href="https://1.bp.blogspot.com/-YANEZ48JY_0/WNHcAkz7T1I/AAAAAAAACAE/WMkY8cLfA54DAj3KQD1zPcEf54EAF0sSQCEw/s1600/creative3.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://1.bp.blogspot.com/-YANEZ48JY_0/WNHcAkz7T1I/AAAAAAAACAE/WMkY8cLfA54DAj3KQD1zPcEf54EAF0sSQCEw/s200/creative3.png" width="161" /></a>And the students had fun with these <a href="https://www.teacherspayteachers.com/Product/Quadratic-Formula-Doodle-Notes-2528837" target="_blank">Quadratic Formula notes</a> from Math Giraffe too.<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><a href="https://4.bp.blogspot.com/-diDrw6wqaCQ/WNHb9CZWE0I/AAAAAAAACAE/GZgCV0RhdDs-3p8ZWPTbXDNee8fwreHmACEw/s1600/creative2.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-diDrw6wqaCQ/WNHb9CZWE0I/AAAAAAAACAE/GZgCV0RhdDs-3p8ZWPTbXDNee8fwreHmACEw/s320/creative2.png" width="232" /></a><br />Sometimes we will start the class off with a Warm-Up <a href="https://www.teacherspayteachers.com/Store/Scaffolded-Math-And-Science/Category/-MATH-PENNANTS-232635" target="_blank">pennant</a> (from Scaffolded Math and Science). I will hand them one of these problems as they walk in and they will solve it and decorate it. It allows me to check their work and do a quick scan of who will need extra help later in the class. Plus it starts things off "low key," and the kids are engaged from the beginning.<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><a href="https://2.bp.blogspot.com/-6CsMS06V8aU/WNHb_2xkRLI/AAAAAAAAB_4/Kq1GjURZu0wHVtU8ztIbyzMrMTsnOg6bgCEw/s1600/creative4.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="240" src="https://2.bp.blogspot.com/-6CsMS06V8aU/WNHb_2xkRLI/AAAAAAAAB_4/Kq1GjURZu0wHVtU8ztIbyzMrMTsnOg6bgCEw/s320/creative4.png" width="320" /></a>Sometimes I use these <a href="https://www.teacherspayteachers.com/Product/Quadratic-Formula-Pennant-2430453" target="_blank">pennants </a>as exit tickets too. Again giving me a check of who's got it and letting the kids leave the room with a sense of pride and accomplishment as they hang their pennant on the line. And did I mention how amazing my room looks with all this art work plastered up on the walls. Any visitor (and I get a lot of them) makes sure to point it out!<br /><br /><br /><br /><br /><br /><br /><br /><a href="https://1.bp.blogspot.com/-bzb3oAxIUP8/V4RNRcgU1SI/AAAAAAAABT8/Mdm4bj3SQ9QmWDk6vSAcQV9PctOP0tW3ACLcB/s1600/IMG_1608.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-bzb3oAxIUP8/V4RNRcgU1SI/AAAAAAAABT8/Mdm4bj3SQ9QmWDk6vSAcQV9PctOP0tW3ACLcB/s400/IMG_1608.JPG" width="300" /></a>When I give a traditional exit ticket, and end up with a few extra minutes, I will sometimes have the students flip it over and write a reflection about the lesson. Sometimes I will have them draw a picture. On this one, I told the students to draw something they thought I would like. Can you tell that I eat a banana every day during this morning class?!<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><a href="https://2.bp.blogspot.com/-iGkYgWvI00Q/WNHeWTgs-GI/AAAAAAAACAg/GsAU5oRvRm0CrhuD44VlvcQzrBUCwUAiACLcB/s1600/creative7.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="239" src="https://2.bp.blogspot.com/-iGkYgWvI00Q/WNHeWTgs-GI/AAAAAAAACAg/GsAU5oRvRm0CrhuD44VlvcQzrBUCwUAiACLcB/s320/creative7.png" width="320" /></a><br />Or I will have the students draw how they feel after the lesson of the day. This really helps me to build relationships with my students because they will sometimes draw things that make great conversation starters.<br /><div class="separator" style="clear: both; text-align: center;"></div><a href="https://4.bp.blogspot.com/-t31teMf6g7A/WNHhF0KGBjI/AAAAAAAACAw/Ac4ZoHU7pO4igdPooGWNc6a77VsWHdKRwCLcB/s1600/creative8.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="254" src="https://4.bp.blogspot.com/-t31teMf6g7A/WNHhF0KGBjI/AAAAAAAACAw/Ac4ZoHU7pO4igdPooGWNc6a77VsWHdKRwCLcB/s320/creative8.png" width="320" /></a><br />Even just having the kids make a quick poster about what they learned or flipping over their worksheet and drawing something to summarize their feelings about the lesson has kept my students engaged and allowed them to use their right brain that is too often ignored in math class. Bring on the creativity! If nothing else, they may just draw something that brightens your day!<br /><div class="separator" style="clear: both; text-align: center;"></div>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-72572956443185595502017-03-04T09:42:00.000-05:002017-03-04T12:44:16.304-05:00Tying Factoring to GraphsThis summer I spent some time re-vamping my lesson about the Zero Product Property and helping students to see the connection between factoring and the zeros of a parabola. This week I finally got to teach the lesson using all my new materials and I couldn't be more excited about how it turned out!<br /><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-dXqNs1UQq70/WLrMHghlXOI/AAAAAAAAB_M/wsSIGJHUVm8hIey5cz4uymupKkca2ytvgCEw/s1600/solve%2Bquadratics%2Bnotes.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="257" src="https://3.bp.blogspot.com/-dXqNs1UQq70/WLrMHghlXOI/AAAAAAAAB_M/wsSIGJHUVm8hIey5cz4uymupKkca2ytvgCEw/s400/solve%2Bquadratics%2Bnotes.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><br />My students had fun learning how to <a href="http://mathdyal.blogspot.com/2017/02/free-factoring-fun.html" target="_blank">factor</a> , which is obviously important when we extend it to graphs of parabolas. This summer I made these fun <a href="https://www.teacherspayteachers.com/Product/Solve-Quadratic-Equations-by-Factoring-Interactive-Notes-2709880" target="_blank">doodle notes </a>that I was so excited to try to introduce the Zero Product Property. We factored the problem and set the factors equal to zero and then I asked them to figure out how it was connected to the graph. They were excited to see a real-world application for factoring.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-s80_6xI4xLw/WLrMGlaPDJI/AAAAAAAAB_I/3VTih2WoGoEY-2_1HPV3kON124pbuqO0gCEw/s1600/solve%2Bquadratics%2Bnotes%2Bp1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://3.bp.blogspot.com/-s80_6xI4xLw/WLrMGlaPDJI/AAAAAAAAB_I/3VTih2WoGoEY-2_1HPV3kON124pbuqO0gCEw/s400/solve%2Bquadratics%2Bnotes%2Bp1.png" width="265" /></a></div><br /><br /><br />After we finished the first two problems, I had the students talk about the connection between the factors and the x-intercepts. Then they didn't have any trouble working backward given a graph to an equation. I started the students off on the Try It problems by asking them what the 5x^2 and 10x have in common - they sometimes forget GCF when they are so used to trinomials. Then I had the students complete the Try It problems on their own. I asked students to work the problem on the board so their peers could check their work.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-BO7jN4HHQJA/WLjPfS90vJI/AAAAAAAAB-c/tV3umS2Zxnk5Xj29hyVd9gysMwNU5V9LwCLcB/s1600/IMG_5344.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-BO7jN4HHQJA/WLjPfS90vJI/AAAAAAAAB-c/tV3umS2Zxnk5Xj29hyVd9gysMwNU5V9LwCLcB/s400/IMG_5344.JPG" width="300" /></a></div> Then the students completed this <a href="https://www.teacherspayteachers.com/Product/Quadratic-Equations-Graph-Match-Dominoes-Interactive-Notebook-Activity-2696312" target="_blank">dominoes activity,</a> where they have to factor the quadratic equation, set the factors equal to zero and match it to a graph. Once they match the graph, the other side of the domino gives them their next problem. I liked the structure of this, and the ease at which students completed it. I love days were everyone feels successful!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-Chset8HUyN0/WLjQxltoisI/AAAAAAAAB-o/uqSznIomrpAPvyQQF5bOzhlEUlozTo-aQCLcB/s1600/IMG_5342.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-Chset8HUyN0/WLjQxltoisI/AAAAAAAAB-o/uqSznIomrpAPvyQQF5bOzhlEUlozTo-aQCLcB/s320/IMG_5342.JPG" width="240" /></a></div><br />As groups finished, I traded them for this <a href="https://www.teacherspayteachers.com/Product/Graph-Quadratics-Coloring-Activity-2709806" target="_blank">coloring activity</a>. Some students chose to work from the graphs to the equations, and some chose to factor and solve the equations from the answer bank.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-d1gZP4T-TFA/WLrMre3XNaI/AAAAAAAAB_Y/8rwM-gra3GM_1VPjqtznGZl6TyMRZt41gCLcB/s1600/solve%2Bquadratics%2Bcoloring%2BUSE.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://2.bp.blogspot.com/-d1gZP4T-TFA/WLrMre3XNaI/AAAAAAAAB_Y/8rwM-gra3GM_1VPjqtznGZl6TyMRZt41gCLcB/s400/solve%2Bquadratics%2Bcoloring%2BUSE.png" width="352" /></a></div><br />My students always love any chance to color. I love seeing them break out their sparkly pens, fancy highlighters, or boxes of colored pencils and add some flair to their work.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-tO-0j5LQtFs/WLrMKO0yEiI/AAAAAAAAB_U/e7hklYDc4lsjEG7JjTjd8NvxNOvj1egAwCEw/s1600/graph%2Bquadratics%2Bcoloring%2Bpersonalities.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://3.bp.blogspot.com/-tO-0j5LQtFs/WLrMKO0yEiI/AAAAAAAAB_U/e7hklYDc4lsjEG7JjTjd8NvxNOvj1egAwCEw/s400/graph%2Bquadratics%2Bcoloring%2Bpersonalities.png" width="300" /></a></div><br />I know I did a MUCH better job teaching this concept this year. I just finished grading their Quadratics Test and nearly all of them aced this matching question. That was NOT the case last year, so I'm glad these activities helped them to practice and understand this concept! You can buy a <a href="https://www.teacherspayteachers.com/Product/Solve-Quadratic-Equations-Mini-Bundle-of-Activities-3044851" target="_blank">mini-bundle</a> of the three activities included in this post in my TpT store.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-1JdjyvIwPRo/WLjUIjZ1WRI/AAAAAAAAB-w/u7-BsTA18AUw8iM5bjMF1aKUBXLlv8O-ACLcB/s1600/quadratic%2Bgraph%2Bmatch%2B1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="201" src="https://3.bp.blogspot.com/-1JdjyvIwPRo/WLjUIjZ1WRI/AAAAAAAAB-w/u7-BsTA18AUw8iM5bjMF1aKUBXLlv8O-ACLcB/s400/quadratic%2Bgraph%2Bmatch%2B1.png" width="400" /></a></div><br /><br /><div class="separator" style="clear: both; text-align: center;"></div><br />Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-69951573610896677162017-02-20T21:12:00.003-05:002017-03-07T06:11:16.101-05:00Para-bowl-as!Why is it that so many students insist on pronouncing parabolas as "para-bowl-as"!? I was really excited to jump right in to discovering how factoring ties to parabolas and their graphs, but my students needed some basic vocabulary and graphing practice first. I jogged their memory of input-output table and graphing with a Warm Up of a linear function, then we jumped right into parabolas.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-1TpK4bHfroI/WKuhHKaddnI/AAAAAAAAB94/HaA99McOGUcGaLhXBLwql7L9sLA-ZZGfACLcB/s1600/graph%2Bquad.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-1TpK4bHfroI/WKuhHKaddnI/AAAAAAAAB94/HaA99McOGUcGaLhXBLwql7L9sLA-ZZGfACLcB/s320/graph%2Bquad.png" width="320" /></a></div><div>This summer, I made these cool <a href="https://www.teacherspayteachers.com/Product/Graph-Quadratic-Equations-Interactive-Notes-2709834" target="_blank">doodle notes</a> about graphing quadratics. {It's always exciting when I get to finally use something that I worked so hard on!} This lesson last year took WAY too long, so I expedited things by giving students an partially filled in input-output table and the parent graph. </div><div><br /></div><div>For each section, I would fill in the first row of each input-output table and then set students loose. I would invite one of my early-finishers to graph the parabola on the board, then I would have the students generalize the rule at their tables. Then I would ask them similar questions like : where would the vertex of x^2 +100 be? What about x^2 - 25? Which graph would be wider y = 10x^2 or y =1/4x^2? My students got it - I really liked how they could compare to the parent graph for each one.</div><div><br /></div><div>I loved watching students make connections as they created their graphs. and how they discovered how changing part of the equation changed the parabola. They also quickly noticed that the output values repeat once they find the vertex.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-cs5HVBLXogA/WKuf6zKkLDI/AAAAAAAAB9s/a4hUVCVIhekvom4zXqqaIGtLHlUPzIpQwCLcB/s1600/IMG_5325.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-cs5HVBLXogA/WKuf6zKkLDI/AAAAAAAAB9s/a4hUVCVIhekvom4zXqqaIGtLHlUPzIpQwCLcB/s320/IMG_5325.JPG" width="320" /></a></div><div><br /></div><div>Then to practice even more, I used this Graphing Quadratics Station <a href="https://www.teacherspayteachers.com/Product/Graphing-Quadratic-Equations-Stations-Activity-643415" target="_blank">Activity </a>from All Things Algebra to continue graphing parabola. I did not have them move around to stations though. We did Graph A together, so that I could review all that fun vocabulary we just learned and remind them about domain and range. The students were in pairs, so they played rock-paper-scissors to see who had to pick up their first card from the back table. I printed the answer key and stapled it to the back of the card. I made sure to emphasize that students who were caught copying would NOT get any points. But I actually loved having the students have the answer key so they could self-check as they went. I heard great questions from my students, like "How did they get this answer?" Or "I see my mistake." I caught only a handful of students copying out of all 140 of my Algebra students, so I was really impressed. Plus my students felt confident in their graphing skills when they could check-in as they went without constantly calling me over to verify their work. When they finished a card, they would do another round of Rock-Paper-Scissors and then head to the back table to swap out the card. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-loat_O_FQiA/WKuf_ikjefI/AAAAAAAAB9w/3HOyXDDpbxEOeeQSB8B_o6V6YcOkY7RLQCLcB/s1600/IMG_5326.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://3.bp.blogspot.com/-loat_O_FQiA/WKuf_ikjefI/AAAAAAAAB9w/3HOyXDDpbxEOeeQSB8B_o6V6YcOkY7RLQCLcB/s320/IMG_5326.JPG" width="320" /></a></div><div><br /></div><div>About 5 minutes before the end of class, I had students draw a large star next to an empty graph spot and complete an exit ticket problem. After class, I sorted them into students who got everything in the problem correct and students that missed part of it. During the next class, I had those with perfect papers help their peers make corrections. I love this quick <a href="http://mathdyal.blogspot.com/2017/02/best-pd-ever.html" target="_blank">remediation </a>and empowering my students to teach others.<br /><div class="separator" style="clear: both; text-align: center;"></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-9ZXSzpvB6nc/WKuhHHpZ9EI/AAAAAAAAB98/VhAe3ELlmOwJWe9OLhUK_7YyuutjrYcYgCEw/s1600/graph%2Bet.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-9ZXSzpvB6nc/WKuhHHpZ9EI/AAAAAAAAB98/VhAe3ELlmOwJWe9OLhUK_7YyuutjrYcYgCEw/s320/graph%2Bet.png" width="320" /></a></div><div>Next up, we learned how to use the x-intercepts to match equations to their graphs and applies those factoring skills. Check out that lesson <a href="http://mathdyal.blogspot.com/2017/03/tying-factoring-to-graphs.html" target="_blank">here</a>.</div>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com1tag:blogger.com,1999:blog-177420802016800294.post-21136900712506744382017-02-11T21:56:00.002-05:002017-02-15T20:49:59.482-05:00Best PD EVER!<div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-2TbLQjU53j8/WKUFQCJOjOI/AAAAAAAAB9Q/GzT8B0qzMO0kewzTJjgr2tx0NUDmvcHrwCLcB/s1600/best%2Bpd%2Bever.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-2TbLQjU53j8/WKUFQCJOjOI/AAAAAAAAB9Q/GzT8B0qzMO0kewzTJjgr2tx0NUDmvcHrwCLcB/s320/best%2Bpd%2Bever.jpg" width="320" /></a></div><br />This week I had a unique opportunity to observe a superstar teacher in my district. She teaches at a nearby high school, but her school has had amazing results in getting kids to pass the Algebra 1 End of Course Exam (FSA), and she has been leading the pack. I've heard great things about her class so when my AP asked if I wanted to spend the morning there, I jumped at the chance! In nine years of teaching I have been to countless hours of professional development, but this was definitely the most helpful and relevant. I love that I am part of a community of educators who love watching students succeed so much they are willing to take their time to share their best practices, and lifelong learners willing to constantly refine their craft until they find what works best for the students.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-GyEikfAm9kA/WJ_Mp3M7w7I/AAAAAAAAB8w/vHK9Pq0ICxAiWhIb4GgsfG21zylCkjp1QCLcB/s1600/shs%2B1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://4.bp.blogspot.com/-GyEikfAm9kA/WJ_Mp3M7w7I/AAAAAAAAB8w/vHK9Pq0ICxAiWhIb4GgsfG21zylCkjp1QCLcB/s320/shs%2B1.jpg" width="320" /></a></div><br />It was such a reflective experience to watch someone else teach. She did an amazing job providing real-time remediation to her students via peer tutoring and also spiraling review throughout her warm ups and exit tickets. In the prior class, students completed this exit ticket and then she used it to create groupings for the next class.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-RczJTtGkVnE/WJ_NQFGhM-I/AAAAAAAAB80/4jNfcPhKj6YD5wV0Y_dY0KFirEJpkoj1QCLcB/s1600/shs2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="209" src="https://1.bp.blogspot.com/-RczJTtGkVnE/WJ_NQFGhM-I/AAAAAAAAB80/4jNfcPhKj6YD5wV0Y_dY0KFirEJpkoj1QCLcB/s320/shs2.png" width="320" /></a></div><br />I do a lot of group learning and always encourage students to ask their peers for help, but she had a very intentional method of doing this that I am definitely going to use. She had a quick meeting with her peer tutors and each of the three students was assigned two students to help. The two students in each group who were receiving tutoring reworked exit ticket problems on the window (I never thought to use dry-erase markers there!) and then wrote out how to solve it and the steps in words for solving. They they repeated the process with another problem. This helps address misconceptions before they get out of hand. While these students were doing the tutoring cycle, the rest of the class started on the classwork assignment, and she floated around answering questions. As the tutoring groups finished, they started in on the classwork assignment. I think I sometimes get worried about what it will look like when everyone isn't working on the same thing, but visiting this class showed me that once the students are trained with your expectations, the process can unfold pretty seamlessly.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-no2M1Kkv-oM/WJ_N61tv0FI/AAAAAAAAB88/Hvhl9TiyV9ERncXW90P3ityfMScLxbhjACLcB/s1600/et%2B1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://3.bp.blogspot.com/-no2M1Kkv-oM/WJ_N61tv0FI/AAAAAAAAB88/Hvhl9TiyV9ERncXW90P3ityfMScLxbhjACLcB/s320/et%2B1.jpg" width="320" /></a></div><br />The next day, I tried it in my classroom. I had students complete a graphing quadratics problem as an exit ticket and then quickly sorted them into students who got it 100% correct and students who missed part of it. I had a few students who messed up completely, and they were the ones I targeted. During the next class, I passed the papers back and the students with stars circulated and helped their peers as the others reworked the problem. I have a ways to go before it unfolds as perfectly as what I saw, but I loved how my students received feedback and had an opportunity for revision. I also loved how empowered the students with stars felt and the great explanations I heard them give their peers.Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com4tag:blogger.com,1999:blog-177420802016800294.post-91576617900110321492017-02-08T16:00:00.000-05:002017-02-08T20:03:22.418-05:00Similar TrianglesWhen I taught 7th grade five years ago, it seems like every problem could be solved with a proportion. We spent a lot of time talking about matching up units and ratios when solving a proportion, then we would come to similar triangles and the students wouldn't know what to do, so they would set up their proportion all willy-nilly. So I developed this system for teaching similar figures and I have used it ever since, including just last week when I reviewed similar triangles with my Geometry class.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-GV3ehkQaRDQ/WJu_qNe9f3I/AAAAAAAAB8Y/EsJgmrH4JSwBasDU60-MQgLg_txHysUsACLcB/s1600/similar%2Bfigures%2Bpin.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="https://4.bp.blogspot.com/-GV3ehkQaRDQ/WJu_qNe9f3I/AAAAAAAAB8Y/EsJgmrH4JSwBasDU60-MQgLg_txHysUsACLcB/s320/similar%2Bfigures%2Bpin.png" width="320" /></a></div><br />I have students match up the corresponding sides with shapes. In the picture below XY corresponds with MN, so we drew a cloud around those side length. ZX corresponds to NP, so we drew a box around those side lengths. Then when we set up our proportion, we make sure that the corresponding sides are neighbors and the side lengths in the same triangle are neighbors - either one on top of the other or next to each other. I make sure they know that "neighbors" does not include diagonally.<br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-bHdYAJ_adx0/WJaKMtQRteI/AAAAAAAAB7c/tnS39LIN0IcaolArCivzDfCSza0__6MzQCLcB/s1600/IMG_0660.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="213" src="https://4.bp.blogspot.com/-bHdYAJ_adx0/WJaKMtQRteI/AAAAAAAAB7c/tnS39LIN0IcaolArCivzDfCSza0__6MzQCLcB/s320/IMG_0660.JPG" width="320" /></a></div><div class="" style="clear: both; text-align: left;">Matching the side lengths up like this really helps the students to visualize the proportion. If we have markers handy, we use those too, but I know when they take their assessments, they will not have markers or highlighters so drawing the shapes around the numbers will always work.</div><div class="" style="clear: both; text-align: left;">Since I know similar triangles is so heavily covered in middle school, I covered it pretty quickly with my Honors Geometry class. They did great setting up the proportions after we talked about how to place the numbers. </div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-73cw8ShRwuY/WJaKT3aluPI/AAAAAAAAB7k/EDSpr7aWD4gb8TM5NDWfVgbzfjmSI5yfQCLcB/s1600/IMG_5227.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-73cw8ShRwuY/WJaKT3aluPI/AAAAAAAAB7k/EDSpr7aWD4gb8TM5NDWfVgbzfjmSI5yfQCLcB/s320/IMG_5227.JPG" width="240" /></a></div>We did some problems with algebraic expressions for side lengths and some problems with multiple variables.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-p570_hsYyZY/WJaKXXahRtI/AAAAAAAAB7o/bzYo_Iuok9kWeGYZIw_HUjF26Wp9O4qKwCLcB/s1600/IMG_5234.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-p570_hsYyZY/WJaKXXahRtI/AAAAAAAAB7o/bzYo_Iuok9kWeGYZIw_HUjF26Wp9O4qKwCLcB/s320/IMG_5234.JPG" width="240" /></a></div> And the standard shadow and mirror problems as well as some nested similar triangles.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-lnDRbm2tJZ4/WJaKXg1lHuI/AAAAAAAAB7s/iJLqAqIooGsCdlwiSijpUW-1nev5j5HFgCLcB/s1600/IMG_5235.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-lnDRbm2tJZ4/WJaKXg1lHuI/AAAAAAAAB7s/iJLqAqIooGsCdlwiSijpUW-1nev5j5HFgCLcB/s320/IMG_5235.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">I LOVE these doodle notes from Math Giraffe. They were a perfect way to introduce the Triangle Similarity Shortcuts, which are really easy for my students since we spent so much time on congruent triangles. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-8ssdFQYDqK8/WJaKrCH0UnI/AAAAAAAAB70/M0boa24QGYM1f88cgb8plcI4uVuTc7FyQCLcB/s1600/IMG_5202.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-8ssdFQYDqK8/WJaKrCH0UnI/AAAAAAAAB70/M0boa24QGYM1f88cgb8plcI4uVuTc7FyQCLcB/s320/IMG_5202.JPG" width="320" /></a></div><br />On Day 3, we took some notes about proportions in triangles and then practiced all types of similar triangles problems with some book work.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-QTyFI6w2YNQ/WJaKgg8JFyI/AAAAAAAAB7w/OxH_iWbsh_Ul4u9HVmzF8oCNnoIK7kNRQCLcB/s1600/IMG_5236.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-QTyFI6w2YNQ/WJaKgg8JFyI/AAAAAAAAB7w/OxH_iWbsh_Ul4u9HVmzF8oCNnoIK7kNRQCLcB/s320/IMG_5236.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: left;">Then I tried something new for this mini-unit. I gave them a partner quiz. I told them they had to agree on an answer. I heard some AWESOME discussions while students were doing this. They were really working together well because they had a quiz grade riding on it. They did so well - I may have to try another partner quiz, plus it cut my grading in half ;) </div><br /><br />Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-81573670770182918482017-02-04T14:55:00.002-05:002017-02-04T14:55:32.229-05:00Free Factoring Fun<div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-oCZYLp44yro/WJYwwb5_GdI/AAAAAAAAB60/0YerhOBsiw0MaphutAc1CdFcDNXVWYUGACLcB/s1600/factor%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-oCZYLp44yro/WJYwwb5_GdI/AAAAAAAAB60/0YerhOBsiw0MaphutAc1CdFcDNXVWYUGACLcB/s320/factor%2Bpin.jpg" width="320" /></a></div><br /><br />I remember the first time someone showed me a Diamond Problem - a cool math puzzle that transformed factoring from something scary into something fun. I showed my students an example and had them create the algorithm. Before they knew it, they were slaying factoring problems.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-HHlGX0R_3cU/WJUxh3vO8WI/AAAAAAAAB50/5SbfYFVmb80Tcj2-x71N7uozd83SkX89gCLcB/s1600/IMG_5196.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-HHlGX0R_3cU/WJUxh3vO8WI/AAAAAAAAB50/5SbfYFVmb80Tcj2-x71N7uozd83SkX89gCLcB/s320/IMG_5196.JPG" width="240" /></a></div><br />Then we would review for the EOC, the students would see a factoring problem and get excited because they could answer it with a diamond problem. But I would hear the same question over and over, "Where do the numbers go in the diamond?" It was interesting because they knew they wanted factors that multiply to the constant and add to the middle term, but they were so hung up properly arranging them in the diamond that they got stuck.<br /><br />As the factoring unit approaches this year, I thought back to my beloved diamond problem and how my students were confused about something that didn't matter, and I made the difficult decision to nix the diamond.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-pqkMxtWJIag/WI1bjXOhnYI/AAAAAAAAB3k/igNe3gfa-LU-nAZaa1uxGzKi0X0v-5B2gCLcB/s1600/factor%2Bgame.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-pqkMxtWJIag/WI1bjXOhnYI/AAAAAAAAB3k/igNe3gfa-LU-nAZaa1uxGzKi0X0v-5B2gCLcB/s1600/factor%2Bgame.jpg" /></a></div>I found this great {free} PowerPoint <a href="https://www.teacherspayteachers.com/Product/Lets-Factor-Powerpoint-introduction-to-factoring-2452432">game </a>from <a href="http://scaffoldedmath.blogspot.com/2016/12/introducing-quadratic-factoring-with.html" target="_blank">Scaffolded Math and Science</a>. It got the students thinking about numbers just like the diamond problems did. They loved the game format, and I even offered some candy to the first correct answer just to up the engagement even more.<br /><br /><div class="separator" style="clear: both; text-align: center;"></div>Then I showed them a problem with two binomials in factored and simplified form and asked them to think about how the numbers were connected. I had them put their thumb up when they saw the connection and it was amazing how fast the wheels started turning.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-El66G-q_j7k/WJU1C96LWiI/AAAAAAAAB6Q/cNK2E8pCqqg4XMVg216JlWypUVTrDXKPACLcB/s1600/factor%2Bexamples%2B2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="247" src="https://2.bp.blogspot.com/-El66G-q_j7k/WJU1C96LWiI/AAAAAAAAB6Q/cNK2E8pCqqg4XMVg216JlWypUVTrDXKPACLcB/s320/factor%2Bexamples%2B2.png" width="320" /></a></div>Here is how I had them organize the information and it worked out just as easily as a diamond problem. They knew what the product and sum of the numbers needed to be without any confusion.<br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-SwnN7Y7Rxz0/WJYw2OiRxwI/AAAAAAAAB64/NinHmPhFIao14LuKBLmi94vIXh0UgrQTACEw/s1600/factor%2Bset%2Bup.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="191" src="https://4.bp.blogspot.com/-SwnN7Y7Rxz0/WJYw2OiRxwI/AAAAAAAAB64/NinHmPhFIao14LuKBLmi94vIXh0UgrQTACEw/s320/factor%2Bset%2Bup.png" width="320" /></a></div><br />We filled out this <a href="https://drive.google.com/file/d/0B5-n-lm3N6ehWDV3RGZ1ODBwSDg/view?usp=sharing" target="_blank">table</a>, and I love helped them to see the connection between factoring and distributing.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-kbrioY9QBu8/WJYw2VpldcI/AAAAAAAAB68/6Tc3UoFFsCEUY5jfjnjeMEloU34Lb4K0ACLcB/s1600/factor%2Btable.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="202" src="https://3.bp.blogspot.com/-kbrioY9QBu8/WJYw2VpldcI/AAAAAAAAB68/6Tc3UoFFsCEUY5jfjnjeMEloU34Lb4K0ACLcB/s320/factor%2Btable.png" width="320" /></a></div>I love this {free}<a href="http://www.hoppeninjamath.com/teacherblog/wp-content/uploads/2013/02/Factor-Easy-Trinomials-Search-and-Shade.pdf"> Search and Shade activity </a>to practice. The heart is super timely if you are Factoring right now, but they can celebrate their love for factoring anytime ;)<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-l4sOapnREXg/WI1cQXA2_3I/AAAAAAAAB3w/eSwceZMK9KUH3yTw7906Db1kwgC26i5nwCLcB/s1600/factor%2Bheart.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-l4sOapnREXg/WI1cQXA2_3I/AAAAAAAAB3w/eSwceZMK9KUH3yTw7906Db1kwgC26i5nwCLcB/s320/factor%2Bheart.png" width="292" /></a></div>Now we know the real fun comes when you change the leading coefficient. Stay tuned to see how it goes ...Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-68782117851825221022017-01-30T15:00:00.000-05:002017-06-27T11:35:44.441-04:00GCF Candy TaxHave you read Math = Love's <a href="http://mathequalslove.blogspot.com/2015/01/weird-analogies-halloween-candy-tax.html">Candy Tax analogy for GC</a>F? I love it - I've used it every year since I read that blog post and this year, I made some cute <a href="https://drive.google.com/file/d/0B5-n-lm3N6ehdTA5SFg3OWZycnM/view?usp=sharing" target="_blank">notes </a>to go with it.<br />Here is the gist of Sarah's Candy Tax Analogy, in my own words: When I take my kids trick-or-treating, I impose a candy tax on them for all the work I have to do as a parent. Because I'm fair, I take evenly from both my kids, but because I'm greedy, I take as much as I can. We do the first example and the kids are furious about this candy tax, because you take all of Susie's M&Ms. I tell them, "That's her lesson to trick-or-treat harder next Halloween." Most of the students easily see that you cannot take any Milky Way or Pay Day since they don't both have them (not a shared term).<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-azYFgnvIZN0/WI1hctuFChI/AAAAAAAAB4M/AnWsVA-t5sM8SR9vQjfZZH7Do7tROkwRwCLcB/s1600/gcf%2Bfree%2Bdoodle%2Bnotes%2Bpin.jpg.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-azYFgnvIZN0/WI1hctuFChI/AAAAAAAAB4M/AnWsVA-t5sM8SR9vQjfZZH7Do7tROkwRwCLcB/s320/gcf%2Bfree%2Bdoodle%2Bnotes%2Bpin.jpg.png" width="245" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>These <a href="https://drive.google.com/file/d/0B5-n-lm3N6ehdTA5SFg3OWZycnM/view?usp=sharing" target="_blank">doodle notes </a>also seemed to help hook the idea in their brain, which is so handy when I refer back to GCF as Candy Tax as we continue factoring with the idea of "What do these terms have in common?" The kids also love have places to add pops of color and engage their right brain.<br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><br /><br />We practiced finding the GCF with this fun <a href="https://www.teacherspayteachers.com/Product/Greatest-Common-Factor-of-Algebraic-Expressions-Maze-1702915">maze</a> from Amazing Mathematics. I love a maze for the first time they practice something like this because it's much less intimidating for students to decide among possible GCFs than to write one on their own.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-fsuh3Uo8dMc/WI1hoFUx9JI/AAAAAAAAB4Q/lG7FR1E3HWwNZ78qE0SHVYk4DjaSRcMrgCLcB/s1600/IMG_5063.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-fsuh3Uo8dMc/WI1hoFUx9JI/AAAAAAAAB4Q/lG7FR1E3HWwNZ78qE0SHVYk4DjaSRcMrgCLcB/s320/IMG_5063.JPG" width="240" /></a></div>Then we filled out this table for practicing the connection between factoring and distributing. I'm not sure where I found this one, but it's great for connecting the idea of factor as the undoing of distribution.<br /><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-9Cl_NV3bBL0/WI6aw0VNA6I/AAAAAAAAB4o/pHFYP3j9bJ4rek-13dd0nyFlgoNN2bzmQCLcB/s1600/IMG_5195.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://3.bp.blogspot.com/-9Cl_NV3bBL0/WI6aw0VNA6I/AAAAAAAAB4o/pHFYP3j9bJ4rek-13dd0nyFlgoNN2bzmQCLcB/s320/IMG_5195.JPG" width="320" /></a></div><br />For students who needed more scaffolding, we broke it down like this. And it was a great chance to refer back to those <a href="http://mathdyal.blogspot.com/2016/12/radical-radicals.html">Laws of Exponents Notes</a>.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-cktnYgT144s/WI6c1or_4NI/AAAAAAAAB44/dpGXbMSznck8-WGBsqaA_fvuFhgHvk4lwCLcB/s1600/gcf%2Bexample.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="143" src="https://2.bp.blogspot.com/-cktnYgT144s/WI6c1or_4NI/AAAAAAAAB44/dpGXbMSznck8-WGBsqaA_fvuFhgHvk4lwCLcB/s320/gcf%2Bexample.png" width="320" /></a></div>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-30939143530978655312017-01-28T18:37:00.001-05:002017-02-03T20:41:37.808-05:00The Day I Stopped Bringing Papers Home to Grade<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-89TViv7ec7I/WI0rQZS2FeI/AAAAAAAAB3Q/rUfTLDxN0gEXe-BawQbSliX266fNGSAlwCLcB/s1600/stopped%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-89TViv7ec7I/WI0rQZS2FeI/AAAAAAAAB3Q/rUfTLDxN0gEXe-BawQbSliX266fNGSAlwCLcB/s320/stopped%2Bpin.jpg" width="246" /></a></div><br />One of my least favorite teacher tasks is grading papers. I try to get all my school work done at school (I have a one-year old and four-year old, so not much school work gets accomplished at home). Since I gave a short Polynomials Quiz to round out the week, I decided to bring the quizzes home to grade. Of course they sat in my school bag all weekend without ever being touched - I totally forgot they were even there. Monday morning, I'm unpacking my bag and I pull out an empty water bottle.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-PyAoPmfB61g/WI0nLbBJMtI/AAAAAAAAB2k/7NAQuXuKhc4BNlxYPHVAVMHa0TNCiIk-QCEw/s1600/IMG_5149.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-PyAoPmfB61g/WI0nLbBJMtI/AAAAAAAAB2k/7NAQuXuKhc4BNlxYPHVAVMHa0TNCiIk-QCEw/s320/IMG_5149.JPG" width="240" /></a></div><br /><br />It's 7 am on a Monday morning, so my brain is not firing at 100% and I'm trying to remember if I put an empty water bottle in my bag. The bag didn't even feel wet. That's because I had 140 quizzes in my bag to soak it up!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-rzMEFVIK6g0/WI0ojepXsRI/AAAAAAAAB2w/WCRBJZ49vPAblhREparuyr_fbpwRb3DTACLcB/s1600/IMG_5139.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-rzMEFVIK6g0/WI0ojepXsRI/AAAAAAAAB2w/WCRBJZ49vPAblhREparuyr_fbpwRb3DTACLcB/s320/IMG_5139.JPG" width="240" /></a></div><br /><br />I wanted to throw the whole soggy mess right into the trash can, but instead I put it down and went about teaching my first two classes. Luckily I had "pl-unch" on that Monday {planning and lunch together ;)} so with a two-hour break, I decided to lay the quizzes out to dry. They covered almost every surface in my room.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-WHB532eGNz4/WI0pXUq91GI/AAAAAAAAB3A/tFWbeJpkNLQORiQ_FrO6YZXsbwWUqWO3ACLcB/s1600/IMG_5145.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://2.bp.blogspot.com/-WHB532eGNz4/WI0pXUq91GI/AAAAAAAAB3A/tFWbeJpkNLQORiQ_FrO6YZXsbwWUqWO3ACLcB/s320/IMG_5145.JPG" width="320" /></a></div><br /><br /><div class="separator" style="clear: both; text-align: center;"></div>I decided to open the window to speed up the process and the wind caught it and blew it right off the hinge. So I also got to make an embarrassing phone call to the front office and basically tell them I am an idiot.<br /><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-e4tC3juxR9o/WI0o6ExG2KI/AAAAAAAAB3E/vdy4yjDe8R407QSn_ISZ2q2ONYzeTlmzACEw/s1600/window.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-e4tC3juxR9o/WI0o6ExG2KI/AAAAAAAAB3E/vdy4yjDe8R407QSn_ISZ2q2ONYzeTlmzACEw/s320/window.jpg" width="320" /></a></div><br />Then I walked around with my marker and started grading. Almost every paper had a least one dry corner where I could write the score and look how cool the papers look when you write on them wet. One student asked if I graded them with watercolor paints and another asked if I was so upset with the quiz grades that I threw them in the lake. #thingsteenagerssay.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-ldm_8z4AIq8/WI0o9YZnmeI/AAAAAAAAB24/0quQeS4gKQwuhUmb362e-uqIFx8Cr473QCLcB/s1600/water%2Bcolor.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="204" src="https://1.bp.blogspot.com/-ldm_8z4AIq8/WI0o9YZnmeI/AAAAAAAAB24/0quQeS4gKQwuhUmb362e-uqIFx8Cr473QCLcB/s320/water%2Bcolor.png" width="320" /></a></div>Someone with a badge that said, "glazer" later showed up to fix my window, and give me a mini-lecture about not opening windows during wind advisories, which I totally deserved after he had to stand on a ladder next to my open second story window and screw a hinge back together.<br /><div class="separator" style="clear: both; text-align: center;"></div><br /><br /><b>Morale of the story - Stop bring papers home to grade!! :)</b><br /><br /><br /><br />Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com4tag:blogger.com,1999:blog-177420802016800294.post-36872119646276674952017-01-09T16:16:00.000-05:002017-01-09T16:18:07.919-05:00Low-Tech Student Response System<div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/--oV1Z2vVT_Y/WHP2aMvS_YI/AAAAAAAAB0k/j169Zkf5nf4dQKsz_CdnxTEVu3tTFUHMwCEw/s1600/IMG_5021.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/--oV1Z2vVT_Y/WHP2aMvS_YI/AAAAAAAAB0k/j169Zkf5nf4dQKsz_CdnxTEVu3tTFUHMwCEw/s320/IMG_5021.JPG" width="240" /></a></div><div><br /></div>For the past two years, I've had clickers. I adore them. I could ask a multiple-choice question during instruction and receive instant feedback about what my students thought. I could even print fancy graphs to impress my administrators with my use of data-driven instruction. Then along came our district's mandatory update to Windows 10, which does not play nice with my amazing clickers. And I've been pouting even since. Each time I open a PowerPoint from last year, I see these beautiful multiple-choice questions and I angrily delete them or re-write them.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-bpCVxia6Mo0/WHP4WR5wzvI/AAAAAAAAB1Q/hrd_PLG9Glw318222NwM06f5L49jddMKgCLcB/s1600/classify%2Bpolynomials%2Bex%2B1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-bpCVxia6Mo0/WHP4WR5wzvI/AAAAAAAAB1Q/hrd_PLG9Glw318222NwM06f5L49jddMKgCLcB/s320/classify%2Bpolynomials%2Bex%2B1.jpg" width="320" /></a></div><div><br /></div><div>This week, I was introducing Polynomials, and I had great multiple-choice questions already formatted and ready to go. I decided to leave them in and just have students raise their hand for the correct answer. Lame, I know. </div><div><br /></div><div>We did these <a href="https://www.teacherspayteachers.com/Product/Polynomials-Interactive-Notes-2547140" target="_blank">fun {free} notes</a> to introduce the vocabulary and then it was time to practice with multiple choice, and I had a stroke of genius. I went to my supply cabinet and took out a stack of index card. I told students to write the letter A large with a marker. Then, turn it 90 degrees and write B (yes, upsidedown!). Then flip it and do the same with C and D. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-3gGVH1_ddaY/WHP5PIk4vFI/AAAAAAAAB1U/kQNoI4Xbm-0hvWW1syQpo2QShU5cAmBBACEw/s1600/IMG_5016.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://3.bp.blogspot.com/-3gGVH1_ddaY/WHP5PIk4vFI/AAAAAAAAB1U/kQNoI4Xbm-0hvWW1syQpo2QShU5cAmBBACEw/s320/IMG_5016.JPG" width="320" /></a></div><div><br /></div><div><br /></div><div>I posed the question, and they then held up their answer choice so that I could see it. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-6ealTHaWJLI/WHP2dJsEprI/AAAAAAAAB1M/bf0vYbKgFEYUlm8z6AloG-s5UOEZJCFuQCEw/s1600/IMG_5019.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-6ealTHaWJLI/WHP2dJsEprI/AAAAAAAAB1M/bf0vYbKgFEYUlm8z6AloG-s5UOEZJCFuQCEw/s320/IMG_5019.JPG" width="240" /></a></div><div><br /></div><div><br /></div><div>I was able to quickly assess what students thought (just like my clickers used to allow me to do) and collect data that helps me drive instruction. I can't print out fancy-pants graph (one point clickers). BUT unlike the clickers, were I could only see a break-down of which students responded with each answer after the lesson, the index cards allow me a quick visual of who needs extra help (one point cards). Plus they actually WORK! (100 points cards) - and they will work with all future Windows updates as well ;) </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-1XMtui6xDX4/WHP2ek3xI9I/AAAAAAAAB1M/xkpYRe0nU0wEx-KGlyYppyUP1DMQvGlkQCEw/s1600/IMG_5023.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://4.bp.blogspot.com/-1XMtui6xDX4/WHP2ek3xI9I/AAAAAAAAB1M/xkpYRe0nU0wEx-KGlyYppyUP1DMQvGlkQCEw/s320/IMG_5023.JPG" width="320" /></a></div><div><br /></div><div>At the end of 1st period, I collected the cards and reused them throughout the day. The students had much more fun with this than just raising their hand, and I saw less guessing/cheating/looking around. Another win for active engagement!</div><div><br /></div><div><a href="https://drive.google.com/file/d/0B5-n-lm3N6ehM1hqUDBBZnhlakE/view?usp=sharing" target="_blank">Here </a>are the questions I used about classifying polynomials if you want to try them out. </div>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com2tag:blogger.com,1999:blog-177420802016800294.post-57401267372580391962016-12-16T20:48:00.003-05:002017-01-28T21:11:06.822-05:00Radical RadicalsI finished up my unit on Systems of Equations before the Thanksgiving break and was left with a two-week window before the district said I had to give a Mid-Year Exam. The pacing guide had us starting polynomials and quadratics, but that was not a unit I wanted to break up over the Christmas break, so I decided to spend these two weeks on Radicals. In the past two years, I have crammed in Radicals right before we start reviewing for the EOC, so I liked having the unit at this time instead because I didn't feel so rushed. Coming off Systems of Equations, this was also a chance for students to catch their breath with an easier concept -- before we head into quadratics and really blow their minds ;)<br /><div><br /></div><div>We started with a quick review of the Laws of Exponents and this free <a href="http://mathdyal.blogspot.com/2016/04/radicals.html" target="_blank">foldable</a>. I added some notes for students to fill in summarizing the rule for each step before I sent it to the copier. </div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Q6YCd9RAbKQ/WFSYI-tpc9I/AAAAAAAABzg/AtiqtN0H8O02d9qRSHhHLh57xE6SQIc3gCEw/s1600/laws%2Bof%2Bexp%2Bfoldable.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-Q6YCd9RAbKQ/WFSYI-tpc9I/AAAAAAAABzg/AtiqtN0H8O02d9qRSHhHLh57xE6SQIc3gCEw/s320/laws%2Bof%2Bexp%2Bfoldable.jpg" width="240" /></a></div>I showed them how to expand each problem and then asked them to come up with the rule, which helps them to visualize what's going on, and gives them a strategy to go back to when they forget the rule.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-8Wp20P96br0/WFSYKV9cgaI/AAAAAAAABzs/rgoQNGvTrxwgf4Z-Lv2rnTcQilMQCRrZgCEw/s1600/exp%2Bfold.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-8Wp20P96br0/WFSYKV9cgaI/AAAAAAAABzs/rgoQNGvTrxwgf4Z-Lv2rnTcQilMQCRrZgCEw/s320/exp%2Bfold.png" width="320" /></a></div><br /></div><div>Negative and Zero exponents always throw students for a loop, so they needed their own sheet of notes. I loved this <a href="http://scaffoldedmath.blogspot.com/search?q=negative+exponents" target="_blank">post</a> from Scaffolded Math and Science about Negative Exponents. We did these three problems and then I asked students to find the rule. We continued the pattern to see that what happens when you have negative exponents. </div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-sYyRqss3uLg/WFSYJF3h5MI/AAAAAAAABzk/lGaIrPqDn508GMkB46SkXQv3jGd9MJuMACEw/s1600/neg%2Bpattern.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="167" src="https://4.bp.blogspot.com/-sYyRqss3uLg/WFSYJF3h5MI/AAAAAAAABzk/lGaIrPqDn508GMkB46SkXQv3jGd9MJuMACEw/s320/neg%2Bpattern.jpg" width="320" /></a></div><br /></div><div><br /></div><div>Again, the students summarized the rule and had a pretty good understanding. So I put them to the test with this <a href="https://www.teacherspayteachers.com/Product/Laws-of-Exponents-With-Negative-Exponents-Puzzle-1642450" target="_blank">puzzle</a>. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-p0LMYLJdunE/WFBkaMO2WYI/AAAAAAAABxw/qnMlZ7sg0Kkt7-CAFT2hoaHlaahzORG3gCLcB/s1600/IMG_4429.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://4.bp.blogspot.com/-p0LMYLJdunE/WFBkaMO2WYI/AAAAAAAABxw/qnMlZ7sg0Kkt7-CAFT2hoaHlaahzORG3gCLcB/s320/IMG_4429.JPG" width="320" /></a></div><div>I love listening to students talk about these problems and watching their understanding grow. </div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-2DhzaZChbc0/WFSYIduVD6I/AAAAAAAABzc/U95riPyle2Qu1TYrsKo2RAGIfkAf867HwCEw/s1600/insects.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="188" src="https://3.bp.blogspot.com/-2DhzaZChbc0/WFSYIduVD6I/AAAAAAAABzc/U95riPyle2Qu1TYrsKo2RAGIfkAf867HwCEw/s320/insects.jpg" width="320" /></a></div><br /></div><div>We finished up with a word problem about exponential growth. I love how this problem has students interpret what the negative exponents mean in the context of this word problem - I was proud that students in each class came to the conclusion that negative exponents would indicate time before the experiment started. It also helps them solidify the idea that a zero exponent doesn't equal zero, because it represents the starting point. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-XC03KFmy4-E/WFSYNn3RaBI/AAAAAAAAB0A/VI2oYpL64TsmGAjM5kKSjPGV8_cm5Rt5QCEw/s1600/radicals%2Bnotes.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-XC03KFmy4-E/WFSYNn3RaBI/AAAAAAAAB0A/VI2oYpL64TsmGAjM5kKSjPGV8_cm5Rt5QCEw/s320/radicals%2Bnotes.png" width="240" /></a></div><br /></div><div>Day 2, it was time for radicals! Like<a href="http://mathdyal.blogspot.com/2016/04/radicals.html" target="_blank"> last year</a>, I was determined not to teach a trick. I showed them both how to simplify with prime numbers and perfect squares. I write out a lot of steps, and often students find ways to simplify and shorten once they understand what they are doing. I also made a point of explaining every step. "The square root of 2 squared is 2, so I can simplify it as a whole number outside the radical. But the square root of 5 is an irrational number, so I leave that inside the radical." By repeating this step (what seemed like a million times), I didn't have students trying to bring the number with its exponent outside the radical. I did, however, still have some students tricked by this check all that apply.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-gJq5wVbhYVE/WFSYMuhAW3I/AAAAAAAABz4/Q_WutODXOy0ZCgODIKzNsJV-zas5lXcCwCEw/s1600/radical%2Bcata.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-gJq5wVbhYVE/WFSYMuhAW3I/AAAAAAAABz4/Q_WutODXOy0ZCgODIKzNsJV-zas5lXcCwCEw/s320/radical%2Bcata.png" width="282" /></a></div>That last problem always leads to a debate, but I had far less students thinking it was correct that in years past. We practiced simplifying radicals with this <a href="https://www.teacherspayteachers.com/Product/Simplify-Radical-Expressions-Coloring-Activity-mathdollardeals-2581842" target="_blank">coloring activity</a>. I love that the answer bank allows students to self-check as they go. There is nothing worse than practicing a skill incorrectly, so I like when they have to stop and find their mistake when their answer doesn't match one of the choices. Plus the coloring provides a nice brain break!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-BHrCl1XAx78/WFBm9igtjnI/AAAAAAAABx8/Wb9oKR92MokWJoXGzuvaXcDcz6fYpTp-QCLcB/s1600/IMG_4511.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-BHrCl1XAx78/WFBm9igtjnI/AAAAAAAABx8/Wb9oKR92MokWJoXGzuvaXcDcz6fYpTp-QCLcB/s320/IMG_4511.JPG" width="240" /></a></div><div><br /></div><div>For Day 3, I put a problem up on the board with variables inside the radical and asked students to decide what to do. I've been focusing a lot on hooking everything to their prior knowledge. Someone suggested expanding x^3, and then students could see variables were really no different than dealing with factors. I love these Check All That Apply question types for this topic.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-BHc4_pLsNBs/WFSYKToTaHI/AAAAAAAABzo/2Ze6wLESCFYLm9qn6of66l7Qo4BLB1R2gCEw/s1600/check%2Ball%2Bthat%2Bapply%2Bnotes.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://4.bp.blogspot.com/-BHc4_pLsNBs/WFSYKToTaHI/AAAAAAAABzo/2Ze6wLESCFYLm9qn6of66l7Qo4BLB1R2gCEw/s320/check%2Ball%2Bthat%2Bapply%2Bnotes.png" width="320" /></a></div><br />After a few examples, they practiced with a <a href="https://www.teacherspayteachers.com/Product/Simplify-Radicals-with-Variables-Puzzle-2496970" target="_blank">puzzle</a>. <span style="background-color: white; font-size: 14.85px;"><span style="font-family: "times" , "times new roman" , serif;">Students had to be careful to "attend to precision" because several of the problems and answer choices were similar. This forced students to really focus on their exponents and see the difference between having x^3 inside a radical and x^4. It also meant that students didn't have to keep re-creating a factor tree for each problem. I heard great discussions about what happens when the radical has a coefficient in front of it too.</span></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-q2mdDL98g7E/WFCnXuTwPhI/AAAAAAAAByM/EWxnPKzpM3kniiAPmynlAgfY1pYlz5Q8wCLcB/s1600/radicals%2Bpuzzle.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="213" src="https://1.bp.blogspot.com/-q2mdDL98g7E/WFCnXuTwPhI/AAAAAAAAByM/EWxnPKzpM3kniiAPmynlAgfY1pYlz5Q8wCLcB/s320/radicals%2Bpuzzle.jpg" width="320" /></a></div><div><span style="background-color: white; font-size: 14.85px;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></span></div><div><span style="background-color: white; font-size: 14.85px;"><span style="font-family: "times" , "times new roman" , serif;">Next we moved on to Operations on Radicals - adding, subtracting and multiplying them, which I introduced with these fun <a href="https://www.teacherspayteachers.com/Product/Operations-on-Radical-Expressions-Interactive-Notes-2918631" target="_blank">{FREE} Interactive Notes</a>. Students practice applying the operations on radicals to find the area and perimeter of shapes - and the shapes are super fun to color! </span></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-PEP_UKk8fzg/WFCnvQ9LOFI/AAAAAAAAByQ/EMlF3kUOZ2ETD2ksgYEYdKa48sLnSwdggCLcB/s1600/operations%2Bon%2Bradicals%2Bpin.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-PEP_UKk8fzg/WFCnvQ9LOFI/AAAAAAAAByQ/EMlF3kUOZ2ETD2ksgYEYdKa48sLnSwdggCLcB/s320/operations%2Bon%2Bradicals%2Bpin.png" width="277" /></a></div><div><span style="background-color: white; font-size: 14.85px;"><span style="font-family: "times" , "times new roman" , serif;"><span style="font-size: 14.85px;">We also did some regular practice problems on the neighboring page. </span></span></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-2Cz9brgvpHU/WFSYMvsTRxI/AAAAAAAABz8/wOfQJq8CYek3oZfe6LxY5mapJxjLmP-0gCEw/s1600/operations%2Bon%2Bradicals%2Bnotes.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-2Cz9brgvpHU/WFSYMvsTRxI/AAAAAAAABz8/wOfQJq8CYek3oZfe6LxY5mapJxjLmP-0gCEw/s320/operations%2Bon%2Bradicals%2Bnotes.png" width="240" /></a></div><span style="background-color: white; font-size: 14.85px;"><span style="font-family: "times" , "times new roman" , serif;"><span style="font-size: 14.85px;"><br /></span></span></span></div><div><span style="font-family: "times" , "times new roman" , serif;"><span style="background-color: white; font-size: 14.85px;">Students practiced with a Versatiles activity and then completed an exit ticket/ mini quiz. <a href="https://drive.google.com/file/d/0B5-n-lm3N6ehTjEyUDE1aXd5YnM/view?usp=sharing">Here </a>is a link to the exit tickets if you want to use them.</span></span></div><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-VGnTIsWaKiw/WFCxaHzogFI/AAAAAAAABzI/yfKaNxFSJn8UPHZwqtpl-mKOKT5l37KnwCLcB/s1600/exit%2Bticket%2B1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="223" src="https://2.bp.blogspot.com/-VGnTIsWaKiw/WFCxaHzogFI/AAAAAAAABzI/yfKaNxFSJn8UPHZwqtpl-mKOKT5l37KnwCLcB/s320/exit%2Bticket%2B1.png" width="320" /></a></div><div><span style="font-family: "times" , "times new roman" , serif;"><span style="background-color: white; font-size: 14.85px;"><br /></span></span></div><div><span style="font-family: "times" , "times new roman" , serif;"><span style="background-color: white; font-size: 14.85px;">That left us with one day left for review/wrap up. I love having an extra catch-up day like this at the end of the unit. The exit ticket provided me with some great data for who needed remediation (students who had been absent for a few days were super confused) and who was ready for some enrichment. I reminded students that so far we had been dealing with square roots, which have an index of 2, and then I presented a problem with an index of 3 and asked students how they thought it would be different. Then I did one with an index of 4 - they knew right away what to do. </span></span></div><div><span style="font-family: "times" , "times new roman" , serif;"><span style="background-color: white; font-size: 14.85px;"><br /></span></span></div><div><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-nd9RACkYknM/WFSZQ0fXgiI/AAAAAAAAB0Q/XWTjXD8zloYnbIlmYxeGYwQSE4FSkyqgACLcB/s1600/IMG_4645.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://3.bp.blogspot.com/-nd9RACkYknM/WFSZQ0fXgiI/AAAAAAAAB0Q/XWTjXD8zloYnbIlmYxeGYwQSE4FSkyqgACLcB/s320/IMG_4645.JPG" width="320" /></a></div><br /></div><div><span style="font-family: "times" , "times new roman" , serif;"><span style="background-color: white; font-size: 14.85px;">Next students completed a variety of assignments - those who needed help completed this maze. I love how they receive instant feedback by finding their answer in one of the arrows. This <a href="https://www.teacherspayteachers.com/Product/Simplifying-Radicals-Maze-1676543" target="_blank">maze </a>was perfect for those students still struggling with the overall concept or students who had missed a couple classes over the two -week period. </span></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-McEPr9iCEes/WFCsJvTS0aI/AAAAAAAABy0/KlE6F-2JFjwcsEmMidmRrOOVPCuAQ64swCLcB/s1600/radicals%2Bmaze.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="168" src="https://1.bp.blogspot.com/-McEPr9iCEes/WFCsJvTS0aI/AAAAAAAABy0/KlE6F-2JFjwcsEmMidmRrOOVPCuAQ64swCLcB/s320/radicals%2Bmaze.jpg" width="320" /></a></div><div><span style="font-family: "times" , "times new roman" , serif;"><span style="background-color: white; font-size: 14.85px;"><br /></span></span></div><div><span style="font-family: "times" , "times new roman" , serif;"><span style="background-color: white; font-size: 14.85px;"><br /></span></span></div><div class="separator" style="clear: both; text-align: center;"></div><div><span style="font-family: "times" , "times new roman" , serif;"><span style="background-color: white; font-size: 14.85px;">Some students wrapped up the Simplify Radicals Coloring Activity from earlier in the week. Those who were up for a challenge took on the <a href="https://www.teacherspayteachers.com/Product/Operations-on-Radical-Expressions-Coloring-Activity-2918598" target="_blank">Operations on Radicals Coloring Activity</a>. Again with the answer bank, this time in the flower petals. </span></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-II_nus9X-RY/WFSYKwnraZI/AAAAAAAABzw/9Hr03U0rz-AvG4VLQONwH8aE51w5_e7-wCEw/s1600/op%2Bon%2Brad%2Bcoloring1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://4.bp.blogspot.com/-II_nus9X-RY/WFSYKwnraZI/AAAAAAAABzw/9Hr03U0rz-AvG4VLQONwH8aE51w5_e7-wCEw/s320/op%2Bon%2Brad%2Bcoloring1.png" width="320" /></a></div><br /><br />Students with extra time answered some <a href="https://www.teacherspayteachers.com/Product/Simplifying-Radicals-with-variables-Pennant-2556298" target="_blank">pennant </a>problems - these are my go-to when I have a few minutes left at the end of class that needs to be filled. Plus students love decorating them and seeing their work on display on the walls and halls.<br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-PGz6pCXz1TI/WFCsP_GRkpI/AAAAAAAABy4/GNtzXRB3HYAwPgy1XGLrwmfkI1pCha8wQCLcB/s1600/IMG_4522.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://2.bp.blogspot.com/-PGz6pCXz1TI/WFCsP_GRkpI/AAAAAAAABy4/GNtzXRB3HYAwPgy1XGLrwmfkI1pCha8wQCLcB/s320/IMG_4522.JPG" width="320" /></a></div><br /><br />I also gave students the option to retake the Exit Ticket/ Mini Assessment if they were unhappy with their grade or thought they could do better. I love giving students the opportunity to challenge themselves to get a better score, and to see improvement. Sometimes just one class period makes all the difference in their understanding - like this student who went from a 50% to a 100% :) Totally RADICAL!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-ISMDuujA8ZU/WFCr44rAp3I/AAAAAAAAByw/N2tn9H8_5cQFmbk0mHFPlpwrLHYmtozGwCLcB/s1600/exit%2Bticket%2Bcompare.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-ISMDuujA8ZU/WFCr44rAp3I/AAAAAAAAByw/N2tn9H8_5cQFmbk0mHFPlpwrLHYmtozGwCLcB/s320/exit%2Bticket%2Bcompare.png" width="218" /></a></div><br /><div><span style="background-color: white; font-size: 14.85px;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></span></div>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com1tag:blogger.com,1999:blog-177420802016800294.post-28860482361890767472016-12-06T20:39:00.000-05:002016-12-06T20:40:00.804-05:00When old toys get new life in the classroomA few weekends ago was our neighborhood garage sale. I am always on the lookout for fun stuff for my classroom, and I picked up this fun thing called a <a href="https://www.amazon.com/Perplexus-BL100-Original/dp/B00CNNPNQI/ref=sr_1_5?s=toys-and-games&ie=UTF8&qid=1481074660&sr=1-5&keywords=perplexus" target="_blank">Perplexus </a>for 50 cents. I wasn't exactly sure how it worked but it looked intriguing and like it involved some problem solving skills, and for 50 cents, I couldn't pass it up.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-Urt3A-kTUTc/WEdnMjzwWwI/AAAAAAAABxg/b2g0yBffPb4aiT2-lOlZ3E3TXw5XJWlLgCLcB/s1600/IMG_4247.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://4.bp.blogspot.com/-Urt3A-kTUTc/WEdnMjzwWwI/AAAAAAAABxg/b2g0yBffPb4aiT2-lOlZ3E3TXw5XJWlLgCLcB/s400/IMG_4247.JPG" width="300" /></a></div><br />I wasn't exactly sure what to do with it, so I just set it out in my student supply area the pencil sharpener and cup of pencils and didn't think anything of it. A student in my 1st period who sits up front immediately noticed and asked, "Can I try that if I finish my work early?" I told him, "Of course," and as soon as he finished he grabbed the Perplexus. A few students saw him doing it and leaned over to watch. Now students will come in during passing period instead of roaming the halls to play with it. It's a 3-D maze that you have to guide the ball through and definitely requires thinking ahead and problem solving because the track flips and turns and there are lots of obstacles on the way to the bucket in the center.<br /><br />This thing has become such a hit with my students, and to think just a few weeks it was collecting dust in someone's closet. I started to look around my own house at some toys that have fallen out of favor to see if they could be given new life in a different setting. I asked my son's preschool teacher if she wanted this puzzle and lacing beads for her classroom and she was very excited to have them. My son isn't interested in them at home, but he might be at school, and, like me, his teacher will enjoy having something new and fun to entertain her kiddos.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-8PR6HvMmFes/WB97N1H-ryI/AAAAAAAABus/4N0wZDP2JtwU-35jml9yA8gw5S0i0lqdQCEw/s1600/IMG_4242.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://4.bp.blogspot.com/-8PR6HvMmFes/WB97N1H-ryI/AAAAAAAABus/4N0wZDP2JtwU-35jml9yA8gw5S0i0lqdQCEw/s200/IMG_4242.JPG" width="150" /></a><a href="https://4.bp.blogspot.com/-w-GCO_XMUPg/WB97Oxm7CjI/AAAAAAAABuw/PEwmUqlKapMSQTPC5ZPfA0ZQaufYCfTgwCEw/s1600/IMG_4243.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://4.bp.blogspot.com/-w-GCO_XMUPg/WB97Oxm7CjI/AAAAAAAABuw/PEwmUqlKapMSQTPC5ZPfA0ZQaufYCfTgwCEw/s200/IMG_4243.JPG" width="150" /></a></div><br /><br />Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-7371808251197682092016-11-26T16:02:00.002-05:002016-11-26T16:02:26.944-05:00<a href="https://4.bp.blogspot.com/-3tgeaqEe30Q/WDn4PRhDCKI/AAAAAAAABxI/4XNEVZStWQsd9lJnObV0cUfntu9sUr6EgCLcB/s1600/tpt%2Bgift%2Bcard.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-3tgeaqEe30Q/WDn4PRhDCKI/AAAAAAAABxI/4XNEVZStWQsd9lJnObV0cUfntu9sUr6EgCLcB/s320/tpt%2Bgift%2Bcard.png" width="276" /></a><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif; font-size: x-large;"><br /></span><br /><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif; font-size: x-large;">Make sure to enter to win $10 gift card to Teachers Pay Teachers!</span><br /><a class="rcptr" data-raflid="3ff6d64d5" data-template="" data-theme="classic" href="http://www.rafflecopter.com/rafl/display/3ff6d64d5/" id="rcwidget_blthliy4" rel="nofollow">a Rafflecopter giveaway</a><script src="https://widget-prime.rafflecopter.com/launch.js"></script> Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-16183830269897426302016-11-12T21:22:00.003-05:002016-11-12T21:22:58.915-05:00Reflection: How do you think you did on this test? Why?<div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-LZpGkOs7sh4/WCfOSQmRNpI/AAAAAAAABw4/7rF0QH-YEC8IZ_Ahfmb6QzdkPjGfIHe2ACLcB/s1600/student%2Breflection%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-LZpGkOs7sh4/WCfOSQmRNpI/AAAAAAAABw4/7rF0QH-YEC8IZ_Ahfmb6QzdkPjGfIHe2ACLcB/s320/student%2Breflection%2Bpin.jpg" width="320" /></a></div><br />I hate grading tests! I've tried to trick myself into having fun doing it by buying cool pens to grade with, sitting in a comfy chair, eating a snack. I even tell myself the lie that, "I could go home and grade them on my couch," and then the tests make a round-trip from home to school without ever leaving my school bag. There is ONE thing I do love about grading tests though, and it's the last question I put on every test and quiz.<br /><h4 style="text-align: center;"><span style="font-family: Trebuchet MS, sans-serif;">"Reflection: How do you think you did on this assessment? Why?"</span></h4><div><span style="font-family: Times, Times New Roman, serif;">Here are some reasons why I love this question:</span></div><div><span style="font-family: Times, Times New Roman, serif;">1. Metacognition - thinking about thinking. Students have to reflect on what they learned and how the learned it and decide how that translated to the assessment. This student knew which questions she struggled with (both content and question type)</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-nqMElKGLv5s/WCfJWxMTeYI/AAAAAAAABwI/kMZxRW6eIl8_r7RPHgKNRmQ32lTEnnE2gCLcB/s1600/Picture3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="194" src="https://3.bp.blogspot.com/-nqMElKGLv5s/WCfJWxMTeYI/AAAAAAAABwI/kMZxRW6eIl8_r7RPHgKNRmQ32lTEnnE2gCLcB/s320/Picture3.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div><span style="font-family: Times, Times New Roman, serif;">2. Ownership in student learning - I'm a firm believer that students should be the one driving most of the work in my classroom. If they didn't learn what they needed to in order to be successful, I want to know why they think that happened. </span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-7NMlIKQPLjQ/WCfJXUbE1jI/AAAAAAAABwY/r2jDAN7I_A09tS8eZej7L6FIt6sOjubngCLcB/s1600/Picture6.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="96" src="https://2.bp.blogspot.com/-7NMlIKQPLjQ/WCfJXUbE1jI/AAAAAAAABwY/r2jDAN7I_A09tS8eZej7L6FIt6sOjubngCLcB/s320/Picture6.jpg" width="320" /></a></div><div><span style="font-family: Times, Times New Roman, serif;">Also if they feel they successfully mastered a skill, I want to know why they think that happened as well.</span></div><div><span style="font-family: Times, Times New Roman, serif;"><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-mU-W4fbSzI0/WCfJXVQBRXI/AAAAAAAABwQ/dufMY6ECctEpw1O0qvIYc57oeQpQzEGlwCLcB/s1600/Picture5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="102" src="https://1.bp.blogspot.com/-mU-W4fbSzI0/WCfJXVQBRXI/AAAAAAAABwQ/dufMY6ECctEpw1O0qvIYc57oeQpQzEGlwCLcB/s320/Picture5.jpg" width="320" /></a></div><div><span style="font-family: Times, Times New Roman, serif;"><br /></span></div><div><span style="font-family: Times, Times New Roman, serif;">3. Accountability - I love when students tell me what they could do differently to improve the outcome. This student says, "I should have spent more time studying the study guide. No doubt this is the grade I deserve."</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-KhtdZAMACEA/WCfJXdSOl3I/AAAAAAAABwc/Ag8qNZtwe54_UO96VTy4NiYFyKH1brXdACLcB/s1600/Picture1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="182" src="https://2.bp.blogspot.com/-KhtdZAMACEA/WCfJXdSOl3I/AAAAAAAABwc/Ag8qNZtwe54_UO96VTy4NiYFyKH1brXdACLcB/s320/Picture1.png" width="320" /></a></div><br />4. Insight - Sometimes students are willing to write things that they wouldn't say out loud. Language arts teachers already know this, but math teachers don't have as many opportunities for them to open up with writing. This open-ended question lets them express anything, like this student who was just having a bad day.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-dJra7O19-Vk/WCfJYJ6qNnI/AAAAAAAABwg/v-Qp7KEiJbArOVAaSo986QR-KfFAw3TFQCLcB/s1600/Picture8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="278" src="https://3.bp.blogspot.com/-dJra7O19-Vk/WCfJYJ6qNnI/AAAAAAAABwg/v-Qp7KEiJbArOVAaSo986QR-KfFAw3TFQCLcB/s320/Picture8.png" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"></div>5. Easy points - As long as they answer it, they will get it right. No hunting for errors or partial credit, this is a point everyone can get. I always remind them that they do get credit as long as they answer the question and tell them, "Don't miss that one, it's the easiest question on the test." </span><span style="font-family: Times, Times New Roman, serif;"><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-EePVRjPI11o/WCfJW2cU9CI/AAAAAAAABwE/dCyopz7hO9YDOCNOO3TnCiCBc0PljqlvACLcB/s1600/Picture2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="149" src="https://3.bp.blogspot.com/-EePVRjPI11o/WCfJW2cU9CI/AAAAAAAABwE/dCyopz7hO9YDOCNOO3TnCiCBc0PljqlvACLcB/s320/Picture2.jpg" width="320" /></a></div> 6. Teenagers are funny - I already know this by spending all day with them, but sometimes they will write some hilarious things.</span><span style="font-family: Times, Times New Roman, serif;"><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-3EpSnCreaVE/WCfJXcamoXI/AAAAAAAABwU/MoDmornsIaQnyf1JJEMGJi5Un-koOR3rgCLcB/s1600/Picture7.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="116" src="https://4.bp.blogspot.com/-3EpSnCreaVE/WCfJXcamoXI/AAAAAAAABwU/MoDmornsIaQnyf1JJEMGJi5Un-koOR3rgCLcB/s320/Picture7.jpg" width="320" /></a></div></span></div><div class="separator" style="clear: both; text-align: center;"></div><div>I hope you will give a question like this a try sometime on a test or quiz, you may just be surprised at what your students have to say.</div><div><span style="font-family: Times, Times New Roman, serif;"><br /><br /><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"></div></span></div>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-39754919778370812292016-10-27T21:12:00.000-04:002016-10-27T21:12:07.451-04:00Old Math GuyLast week we gave the PSAT to all the 10th and 11th graders at our school. The seniors had a special assembly and freshmen reported to their homeroom class. The homerooms are assigned by building alphabetically, so the students in our homeroom are usually not in any of our classes. I happened to have a sophomore homeroom this year, so I spent the morning proctoring the PSAT. [I swear three minutes sometimes seems like an eternity when you waiting for the session to end.] Needless to say, it was a long day. So testing ate up the first four hours of the day, then I saw my Geometry class and then one of my five algebra classes for only an hour (classes are usually 90 minutes). By the end of that day, everyone was fried - my students had either spent the morning testing or sitting in their homeroom bored. But I do not ever give free days, so I knew I wanted to do something that will help them with the linear functions unit we were working on, but a standard lesson was not going to hold their attention today.<br /><br />My friend, Amanda, at <a href="https://www.teacherspayteachers.com/Store/Free-To-Discover" target="_blank">Free to Discover</a>, has an awesome set of products called, "Old Math Guy," that I have been wanting to try out, and this was the perfect opportunity. I decided on <a href="https://www.teacherspayteachers.com/Product/Slope-Intercept-Form-Card-Game-1910285" target="_blank">Matching Linear Graphs to Equations in Slope Intercept Form</a>. I asked the kids if anyone knew how to play "Old Maid," and a few said they did. I had a few kids tag-team explaining the rules of "Old Maid." Then one of my students said, "Did you bring in cards for us to play Old Maid?" I nodded. Then he said, "Wait, these are going to have math problems on them, aren't they?" I said, "Of course they are!" The rules are the same as Old Maid - they look for matches and lay them down and they draw from their neighbors hand until all the cards are out and someone ends up with the Old Math Guy.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-FLHSUtVVi8Q/WBKiN8l9VqI/AAAAAAAABt8/zztNqALLZD4Cqajd6IRxB2OCpb0Gmm6rwCLcB/s1600/IMG_3922.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-FLHSUtVVi8Q/WBKiN8l9VqI/AAAAAAAABt8/zztNqALLZD4Cqajd6IRxB2OCpb0Gmm6rwCLcB/s320/IMG_3922.JPG" width="240" /></a></div>My students had a lot of fun with this activity, and I overheard some great conversations about what made a "match." The students would watch each other like hawks to make sure their equations really matched their graphs (attend to precision!). Some students had good poker faces with Old Math Guy and some didn't. They all had fun, and it was a great brain break for the end of a long, off-schedule day.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-5iCbdP6YCJQ/WBKiUJB2rSI/AAAAAAAABuE/ofJolhY7EXM65KX9PwHB6szIQft4HyRXwCLcB/s1600/IMG_3925.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-5iCbdP6YCJQ/WBKiUJB2rSI/AAAAAAAABuE/ofJolhY7EXM65KX9PwHB6szIQft4HyRXwCLcB/s320/IMG_3925.JPG" width="240" /></a></div>I think this is a great engaging activity that I cannot wait to use again! With the holidays coming up, we need a lot of tricks up our sleeve, and this one kept their attention and allowed for great practice in a unique way.<br /><br />Amanda even has a freebie in her store to try out with your kiddos: <a href="https://www.teacherspayteachers.com/Product/Translating-Algebraic-Expressions-Card-Game-2786939" target="_blank">Old Math Guy Translating Algebraic Expressions </a><br /><br /><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"></div>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-18705928427030479952016-10-22T14:17:00.002-04:002016-10-22T14:17:21.907-04:00Math-y Door Decor<div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-t1Iaa-LiNOM/WAuskQBa69I/AAAAAAAABtg/pghsWmCcj0A8GzkLrEl--KkK_sQP3uR0ACLcB/s1600/mathy%2Bdoor%2Bdecor%2Bpin.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://2.bp.blogspot.com/-t1Iaa-LiNOM/WAuskQBa69I/AAAAAAAABtg/pghsWmCcj0A8GzkLrEl--KkK_sQP3uR0ACLcB/s400/mathy%2Bdoor%2Bdecor%2Bpin.png" width="302" /></a></div><div style="text-align: center;"><br /></div>Last week is annual "Jacksonville Goes to College Week," so our guidance counselors challenged us to a door decorating contest. I typically write those off as, "Ain't nobody got time for that," but I had such luck with my <a href="http://mathdyal.blogspot.com/2016/07/christmas-in-july.html" target="_blank">Christmas Door Decorations</a> that I wanted to give it a try. Just like when I did my Christmas door, I also did not want to lose any instruction time. <a href="https://www.teacherspayteachers.com/Store/Scaffolded-Math-And-Science" target="_blank">Scaffolded Math and Science</a> had the perfect solution for me - a <a href="https://www.teacherspayteachers.com/Product/Slope-Tree-2804300" target="_blank">Slope Tree</a>, which fit right into our Linear Functions unit.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-YFnoU77YZOg/WAuqARtguTI/AAAAAAAABs4/tUdiSfbQO986feNwNM-xoFEkElBm2HDhACLcB/s1600/slope%2Btree%2Bsms.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-YFnoU77YZOg/WAuqARtguTI/AAAAAAAABs4/tUdiSfbQO986feNwNM-xoFEkElBm2HDhACLcB/s320/slope%2Btree%2Bsms.jpg" width="320" /></a></div><br />I gave each student a leaf and they found the slope between two points and then decorated it. It was a nice exit ticket for our class on slope. We put them all together to make a tree.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-DzCDXlftEIA/WAuqI5jmYtI/AAAAAAAABs8/NQqpE7Nc7k8AHtzQPt2Z3dt3yAv0QMOOgCLcB/s1600/IMG_3820.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://2.bp.blogspot.com/-DzCDXlftEIA/WAuqI5jmYtI/AAAAAAAABs8/NQqpE7Nc7k8AHtzQPt2Z3dt3yAv0QMOOgCLcB/s320/IMG_3820.JPG" width="320" /></a></div><br />The idea for my "pun-ny" sign actually came a student who said, "If this is an exit ticket, can we 'leaf' when we finish it." I took that and said, "We are ready for college when we 'leaf' ACHS." Then one of my students added some color to it when she finished a test early.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-0I9uyGmcZqk/WAurKyis_HI/AAAAAAAABtM/bVwpL56zIHoG8Rj6rh0cpTmURSW6YcHFQCLcB/s1600/slope%2Btree%2Bsign.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="239" src="https://3.bp.blogspot.com/-0I9uyGmcZqk/WAurKyis_HI/AAAAAAAABtM/bVwpL56zIHoG8Rj6rh0cpTmURSW6YcHFQCLcB/s320/slope%2Btree%2Bsign.jpg" width="320" /></a></div><br />I think it turned out great - a perfect fall decoration! And best of all - no instructional time was lost in the making of this awesome math-y door decor!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-wKHoG_Hi7Tk/WAuqSHflXKI/AAAAAAAABtE/Q_9KqwopsScDidR75P7qGagUSipJ2zpPgCEw/s1600/IMG_3838.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-wKHoG_Hi7Tk/WAuqSHflXKI/AAAAAAAABtE/Q_9KqwopsScDidR75P7qGagUSipJ2zpPgCEw/s320/IMG_3838.JPG" width="240" /></a></div>P.S. If you are looking for those awesome Welcome sign letters, they are from Math=Love <a href="http://mathequalslove.blogspot.com/2016/07/free-printable-math-y-welcome-banner.html?m=1" target="_blank">here </a>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-58043579201940575722016-10-09T15:14:00.000-04:002016-10-09T15:14:09.283-04:00Hurricane Matthew: From Inside the Cone of Uncertainty<div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-kEwbnAWUW98/V_qWvGqEmaI/AAAAAAAABrs/8LqWuC-lTO49vAjPtCj-B0giPhSEPjNqACLcB/s1600/hurricane%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-kEwbnAWUW98/V_qWvGqEmaI/AAAAAAAABrs/8LqWuC-lTO49vAjPtCj-B0giPhSEPjNqACLcB/s320/hurricane%2Bpin.jpg" width="320" /></a></div>I grew up in the Midwest and left 10 years ago, trading the brutal winters for year-round sunshine. Although we have had a few near-hurricanes and tropical storms in my time as a Floridian, nothing has hit close to home like Hurricane Matthew. I live in Jacksonville, Florida about five miles from the coast, where we can afford a house but can also have our toes in the sand in 10 minutes flat, with my husband (also a teacher and a native Floridian) and our two children, 4 and 1.<br /><br />On Monday, my husband texted me this picture and we talked vaguely about what would happen if the hurricane actually came near us in Jacksonville, but we didn't make any real plans.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-1EwCuvYQ09k/V_qG-TOV7-I/AAAAAAAABqI/JmtbeLVFprgyDwInJL3mtCci-0BMMCT-wCLcB/s1600/matthew%2Bmonday.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="179" src="https://4.bp.blogspot.com/-1EwCuvYQ09k/V_qG-TOV7-I/AAAAAAAABqI/JmtbeLVFprgyDwInJL3mtCci-0BMMCT-wCLcB/s320/matthew%2Bmonday.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;">On Tuesday, the clouds over my school looked a little ominous in the morning. The storm path hadn't changed much, so I stopped at the grocery store after school to stock up on water, snacks, and batteries and I filled my gas tank with a short wait.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Ce1UbRiDvMY/V_qIOpVBpjI/AAAAAAAABqU/idWwxORGx8wsLHgUHcs3nfsz1lQT_rU_wCLcB/s1600/IMG_3699.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-Ce1UbRiDvMY/V_qIOpVBpjI/AAAAAAAABqU/idWwxORGx8wsLHgUHcs3nfsz1lQT_rU_wCLcB/s320/IMG_3699.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">By Wednesday, the mood around campus was that of uncertainly - Matthew had already torn through Haiti and Cuba and its strength was undeniable. The forecast path brought it closer to home. The students minds were filled with "What ifs" and I must have been asked if school would be canceled at least 50 times. Imagine teaching the day before a holiday break and multiply it by 10, that's how distracted these students' minds were, and mine was too. I was filled with uncertainty of what the weather would bring for me and my family and what decisions I should be making. I had a quiz scheduled (the end of the 1st quarter is nearing next week), but everyone was so preoccupied that I decided to make it open notes. I tried to make my lesson on slope as low-key as possible, we watched the <a href="https://www.youtube.com/watch?v=avS6C6_kvXM" target="_blank">Adventures of Slope Dude</a>, took some notes and practiced with a Versatiles activity. I found that the kids needed the distraction as much as I did as the rain outside beat against the windows.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-CHRIMWxMc1g/V_qK2fCB3cI/AAAAAAAABqw/TlVhPCSxbeAtOzn6cO3u0S4aPkFUyqnuACLcB/s1600/slope%2Bdude.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="270" src="https://3.bp.blogspot.com/-CHRIMWxMc1g/V_qK2fCB3cI/AAAAAAAABqw/TlVhPCSxbeAtOzn6cO3u0S4aPkFUyqnuACLcB/s320/slope%2Bdude.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">By the end of the last period of the day, the principal announced that school was canceled for Thursday and Friday and everyone, teachers included, needed to be off campus by 2:30. Leaving was so nerve-racking, not knowing what I would come back to. I unplugged everything, took a few pictures of my possessions, and headed out.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-IZnOJLaK9B8/V_qLbSeRg4I/AAAAAAAABq0/MJLo7MNA61MoMAjK9pQz4Xdoy9f0PdIUACLcB/s1600/IMG_3725.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-IZnOJLaK9B8/V_qLbSeRg4I/AAAAAAAABq0/MJLo7MNA61MoMAjK9pQz4Xdoy9f0PdIUACLcB/s320/IMG_3725.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">The few times I get to leave school at 2:30, I usually zip home and have free reign over all the stores. Today traffic was already building on the highways, and the line at the gas station stretched out onto the road with at least 10 cars waiting in each direction. I was happy to have already taken care of these stops earlier. When I got home, the news now projected this path:</div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-Yk4ZuvSNzaA/V_qMnb_GxvI/AAAAAAAABrE/-EBqHPK1UjAbckFRhZn-vNVyqIHdyRnnwCLcB/s1600/matt%2Btrack%2Bthurs.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://2.bp.blogspot.com/-Yk4ZuvSNzaA/V_qMnb_GxvI/AAAAAAAABrE/-EBqHPK1UjAbckFRhZn-vNVyqIHdyRnnwCLcB/s320/matt%2Btrack%2Bthurs.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">Being a math teacher, I like making decisions based on odds and probability of events occurring, but it seemed like every time I looked at the news, the odds were changing. The meteorologists were giving the hurricane a 15 percent chance of making landfall in Jacksonville as a Category 4 storm. As I tried to go to bed that night - I began to truly understand the term "<b>Cone of Uncertainty</b>." Did it make sense for our family to leave town? Where would we go - we have family near Orlando and Tampa, but would the weather be just as bad there? And what would traffic be like as we went there and returned home after the storm? What if the storm did significant damage to our house and no one was there to protect it because we had left? What is the storm did significant damage to our house and we were there with our two babies? What would it be like to have two small children without power in our house? Would I be able to remain calm if a true category 4 hurricane came through? </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I decided to pack a bag with clothes for everyone for five days, snacks and water, and all my hard drives of family photos, and sleep on the decision. I woke to find this on my phone: </div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-w_5JN62pCQw/V_qMLDqPI8I/AAAAAAAABrA/aXOEyCYHvUwWW7MdiCyFsGM2HnKy7Sj6QCLcB/s1600/IMG_3729.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-w_5JN62pCQw/V_qMLDqPI8I/AAAAAAAABrA/aXOEyCYHvUwWW7MdiCyFsGM2HnKy7Sj6QCLcB/s320/IMG_3729.PNG" width="180" /></a></div><div class="separator" style="clear: both; text-align: left;">The uncertainty was too much, and I knew staying and waiting would make me a nervous wreck for the next few days, which I knew would have a 100% chance of negatively impacting my parenting skills. My husband decided to stay back and board up the house and deal with any damages or issues, and I buckled the kids in their car seats and hit the road for Grandma's house. My mother-in-law lives just south of Orlando and their weather forecast called for 35 mph winds and rain, which sounded much better than the 100 mph winds that could be possible in Jacksonville. I decided that the worst-case scenario of evacuating would be a traffic jam, and the worse-case scenario of staying was being huddled into the bathroom with my two little ones as a tree crashed through our roof. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-wWdeAjD7VuI/V_qWJtyibgI/AAAAAAAABro/hjYxZ0mCbYgFG3X_ozDWbfUcnLmMO4IOACLcB/s1600/FullSizeRender.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="209" src="https://4.bp.blogspot.com/-wWdeAjD7VuI/V_qWJtyibgI/AAAAAAAABro/hjYxZ0mCbYgFG3X_ozDWbfUcnLmMO4IOACLcB/s320/FullSizeRender.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">My husband weathered the storm at home without ever losing power. The wind was fierce and the rain was relentless, but our house escaped unscathed, except for some downed tree branches and mud puddles in our backyard. Many of my friends and neighbors were not so lucky.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Today my husband asked me, "If you had this to do over again, would you do it the same?" Again comes that "Cone of Uncertainty," did I make the right decision? Did I over-react by leaving? Was it overkill to board up our windows? As a math teacher, my brain is trained to be analytical, but Mother Nature cannot be tied down with logic and reason. I do know that as this storm shifted countless times with different trajectories, I was happy to be watching from a safe distance away. </div><div class="separator" style="clear: both; text-align: left;"><br /></div>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-79182239200410496042016-10-04T20:55:00.001-04:002016-10-04T21:03:14.510-04:00How a hole puncher saved the day: Proving Lines Parallel Proof Activity<div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-3m2f4g_12vU/V_RRTVS7ZxI/AAAAAAAABpg/79toSRtR7QwdkCRIKkWHULyrQyFG82okQCLcB/s1600/parallel%2Blines%2Bproof%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-3m2f4g_12vU/V_RRTVS7ZxI/AAAAAAAABpg/79toSRtR7QwdkCRIKkWHULyrQyFG82okQCLcB/s320/parallel%2Blines%2Bproof%2Bpin.jpg" width="320" /></a></div>Even in the 7th week of school, Geometry proofs still strike fear into my little freshmen. For today's lesson on proving lines parallel, I knew I wanted them to do proofs. I found this great cut and paste <a href="https://www.teacherspayteachers.com/Product/Proving-Lines-Parallel-Proof-Activity-2767926" target="_blank">activity</a> from Amazing Mathematics. I chose to print the version that has the statements filled in and students only have to come up with the reasons for each step. By the time we get to triangle congruence, they will be writing both sides, but I was OK with giving them the outline today.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-6183feE3Uww/V_RMi9YQbMI/AAAAAAAABo4/PbBvgadlkf4bM1YLz2vKezcrB8AvpGs-QCLcB/s1600/IMG_3715.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://4.bp.blogspot.com/-6183feE3Uww/V_RMi9YQbMI/AAAAAAAABo4/PbBvgadlkf4bM1YLz2vKezcrB8AvpGs-QCLcB/s320/IMG_3715.JPG" width="320" /></a></div>We reviewed all the theorems and converses and theorems and did a few examples together in their interactive notebooks, and then I set them lose on the proofs. I have my students grouped in threes, which is plenty of brain power to figure out these proofs. I gave each group a strip of paper and had them write the numbers 1-6 on it. Each group started with a proof (I only used 1-4 in the first round because they get increasingly more difficult). They worked together to correctly place the reasons in the proof. When the group agreed, they called me over for a check.<br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-yaNEqdTkaNg/V_RNfeCUbsI/AAAAAAAABpA/PauBsyZLUPk7mnTHLPsd3429opJcs5Z5ACLcB/s1600/IMG_3717.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://4.bp.blogspot.com/-yaNEqdTkaNg/V_RNfeCUbsI/AAAAAAAABpA/PauBsyZLUPk7mnTHLPsd3429opJcs5Z5ACLcB/s320/IMG_3717.JPG" width="320" /></a></div><br />If it was right, I took my blue marker and scribbled off the number of the proof they finished. Then I saw a student look the other blue markers in my supply box with a gleam in his eye. And I realized with this system, there is no way I would be able to keep them from cheating. I changed the scribble to my initials, and then I had a better idea... I dug into the depths of my desk drawer and I got out my single hole puncher and punched a hole over the number when they completed it. The students LOVED it! It's amazing how something so simple totally changes the game. Then they wanted to use the hole puncher - and they would fight over whose turn it was to make the punch. The click of the puncher and the creation of the hole was as satisfying as correctly completing the proof. After I (or they) punched the number, they scrambled up the pieces and took it to the middle table and exchanged it for another proof. They kept doing this until they finished all six proofs.<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-w_P72MD-V8U/V_RMivNFntI/AAAAAAAABow/o-HYjneZpQk80-YEDjf5Zk95Cti0XmotACLcB/s1600/IMG_3705.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-w_P72MD-V8U/V_RMivNFntI/AAAAAAAABow/o-HYjneZpQk80-YEDjf5Zk95Cti0XmotACLcB/s320/IMG_3705.JPG" width="240" /></a></div><br /><br /><br /><a href="https://3.bp.blogspot.com/-PI_7XXB7n10/V_RMi1JHYkI/AAAAAAAABo0/zj5MW6bqZRI3HSKcPuuG-HMS7bXo2MC1gCLcB/s1600/IMG_3704.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-PI_7XXB7n10/V_RMi1JHYkI/AAAAAAAABo0/zj5MW6bqZRI3HSKcPuuG-HMS7bXo2MC1gCLcB/s320/IMG_3704.JPG" width="240" /></a>Typically telling students they would be completing six Geometry proofs to prove lines parallel would be met with moans and groans, but my students were very engaged and motivated to finish the problems. I definitely see my hole puncher making future appearances in class!<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />Next they are going to try out this <a href="https://www.teacherspayteachers.com/Product/Proving-Lines-Parallel-Geometry-Proofs-Crossword-Puzzle-2616399" target="_blank">Proving Lines Parallel Crossword Puzzle</a>. The outline of the proof is still there, but they have to come up with some missing statements and reasons. They still get the self-checking benefit of the crossword puzzle though.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-CPh52-7gj2w/V_RQJeFStfI/AAAAAAAABpY/STirFYQFANAjuaK3c2FSGNuXYZG3dB1IQCLcB/s1600/IMG_0188.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="213" src="https://4.bp.blogspot.com/-CPh52-7gj2w/V_RQJeFStfI/AAAAAAAABpY/STirFYQFANAjuaK3c2FSGNuXYZG3dB1IQCLcB/s320/IMG_0188.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /><br />Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com2tag:blogger.com,1999:blog-177420802016800294.post-21142133054223408752016-10-01T21:44:00.000-04:002016-10-01T22:12:12.675-04:00Connecting Inequalities to Domain and RangeThere are some concepts that I know I do a great job of explaining and others that I struggle with. At the end of the school year, I made a list of things I want to do better, and a few topics from the functions unit were on there: domain and range, using the term f(x), understanding linear translations, and focusing on parent functions. As we finished up the unit on Inequalities, I knew that I wanted to start the functions unit with domain and range so that I can refer to domain and range throughout the entire unit. As I was preparing my notes, I had a "A-Ha" moment that I could present it as a compound inequality. I loved the lesson I found on <a href="http://mathdyal.blogspot.com/2016/09/inequalities-ideas.html" target="_blank">compound inequalities</a> and my students had a good understanding of writing and graphing them.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-lHm1fv_te9U/V_Bln_iEcOI/AAAAAAAABn0/neeoCdZJkEgTKksbhdXDY90I7YbO-t6yQCLcB/s1600/domain%2Band%2Brange%2Btop.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="192" src="https://1.bp.blogspot.com/-lHm1fv_te9U/V_Bln_iEcOI/AAAAAAAABn0/neeoCdZJkEgTKksbhdXDY90I7YbO-t6yQCLcB/s320/domain%2Band%2Brange%2Btop.png" width="320" /></a></div><br />First we talked about the vocabulary for domain and range. I told them I remember that range is for y because both the g in range and y are descender, which means they dip below the writing line. I told them to pick two colored markers and color-code the words domain and range everywhere they saw them on the page. (I also made a point to tell them to pick two colors that will look different on salmon colored paper, after a student picked red and pink and couldn't tell the difference.)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-mdPcd9uXSuI/V_BloJtvPwI/AAAAAAAABn4/2hspr1JAZsQi_WU7dapKCctQdLc3v3-dACEw/s1600/domain%2Band%2Brange%2Bbottom.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="244" src="https://3.bp.blogspot.com/-mdPcd9uXSuI/V_BloJtvPwI/AAAAAAAABn4/2hspr1JAZsQi_WU7dapKCctQdLc3v3-dACEw/s320/domain%2Band%2Brange%2Bbottom.png" width="320" /></a></div><br />The first two examples are pretty straight forward. It's when we get to the graph that things get fun. I tried the method of making the smallest possible box around the function, but several students got confused, so I changed it to finding the farthest left and right point and drawing a line to the x-axis. I then shaded the x-axis between these two values and asked, "Who can write an inequality that describes this?" I told them because this was tricky, I was offering a "Dum-Dum" to anyone will to take a risk and try it. I don't break out the candy often - it's week 7 and this was the first candy-sighting in my room, but I knew this concept was difficult. Students were fighting over trying the inequality for y.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-Pb-_j_ypEzA/V_BmFZSEaGI/AAAAAAAABoU/TZiGNpB9JtMw3rZtzZBCbrQklrYDhnzdgCLcB/s1600/IMG_3577.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://3.bp.blogspot.com/-Pb-_j_ypEzA/V_BmFZSEaGI/AAAAAAAABoU/TZiGNpB9JtMw3rZtzZBCbrQklrYDhnzdgCLcB/s320/IMG_3577.JPG" width="320" /></a></div><br />Then I presented these three problems and asked students to talk about how they were similar and different. They pointed out that the first graph has only points, the next has endpoints, and the last has arrows, meaning it continues forever. I did the domain for the first problem and had students come up to do the range and domain and range for the middle function. For the last one, we shaded the whole x-axis and I reminded them about problems where every number is a solution and connected that idea to the domain of all real numbers. Then I asked for the maximum, which students identified at 4, so I shaded the whole y-axis below 4. Students easily saw that as y<u><</u>4. Yay!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-v674knxnu-g/V_Blxf1oiMI/AAAAAAAABoE/i5r4nWXGebYYd5HXkGeKEALgOGC1uYL2QCEw/s1600/IMG_3584.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-v674knxnu-g/V_Blxf1oiMI/AAAAAAAABoE/i5r4nWXGebYYd5HXkGeKEALgOGC1uYL2QCEw/s320/IMG_3584.JPG" width="240" /></a></div><br />Next it was time for some scaffolded practice. I LOVE this <a href="https://www.teacherspayteachers.com/Product/Domain-and-Range-Matching-Activity-INEQUALITIES-VERSION-2166947" target="_blank">sorting activity</a>. I kept the cards together (they print 4 per page) and cut apart the slips for domain and range. I find that sometimes less moving pieces helps students to focus. I loved the variety of these 20 problems and the great conversations I overheard. Students struggled most with the circles and the line, but these led to more great discussions and opportunities for me to relate them to problems they have seen. By week 7, my students are learning that I will not give them the answer, but I will ask them questions to help them come to the answer on their own [Give a man a fish, and he eats for a day. Teach a man to fish, and he will eat for a lifetime.]<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-1_zHeQOmop8/V_Bl2UBK_qI/AAAAAAAABoQ/QUxoCS3qrmQUlc2gG_J32zTY3DIqF2k-ACEw/s1600/IMG_3585.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://4.bp.blogspot.com/-1_zHeQOmop8/V_Bl2UBK_qI/AAAAAAAABoQ/QUxoCS3qrmQUlc2gG_J32zTY3DIqF2k-ACEw/s320/IMG_3585.JPG" width="320" /></a></div><br />As they finished, I gave them <a href="https://www.teacherspayteachers.com/Product/Domain-and-Range-Pennant-2279423" target="_blank">pennant problems</a> to practice on their own. On Wednesday, we followed an early release schedule, so each student did one problem. My students on Thursday did three each. Following the gradual release, this was a great way to end because students had to come up with the domain and range on their own. And they could! They learned so much, we ran out of room on the yarn! On to more functions fun next week!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-HuzW77mChyw/V_Blx8_-KxI/AAAAAAAABoM/-AKf1nzNsXEmuNPAvk9_Vs0HLPZI8AoJgCEw/s1600/IMG_3606.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-HuzW77mChyw/V_Blx8_-KxI/AAAAAAAABoM/-AKf1nzNsXEmuNPAvk9_Vs0HLPZI8AoJgCEw/s320/IMG_3606.JPG" width="240" /></a></div><br />Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0tag:blogger.com,1999:blog-177420802016800294.post-17095783628704641842016-09-27T21:00:00.000-04:002016-09-27T21:00:05.630-04:00Inequalities Ideas<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-E69H8NKOUV4/V-sTu0F0O0I/AAAAAAAABm4/O3zAYLjYq9Y_1mm2E8vpLnnDH3dk7r0-QCLcB/s1600/IMG_3569.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-E69H8NKOUV4/V-sTu0F0O0I/AAAAAAAABm4/O3zAYLjYq9Y_1mm2E8vpLnnDH3dk7r0-QCLcB/s320/IMG_3569.JPG" width="240" /></a></div><a href="https://4.bp.blogspot.com/-IwtZb2B36zA/V-sTv5N6a1I/AAAAAAAABnE/YiagShjuW9IFrIoZo6YpWsGSN2POROQNQCLcB/s1600/IMG_3570.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-IwtZb2B36zA/V-sTv5N6a1I/AAAAAAAABnE/YiagShjuW9IFrIoZo6YpWsGSN2POROQNQCLcB/s320/IMG_3570.JPG" width="240" /></a>My students had such a good handle on equations that Inequalities was pretty much a breeze. I started with the discussion of the prefix in- , which most of my students could tell me meant not, and how these problems would not have an equals sign. I talked about how they would have a whole solution set instead.<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><br /></div>We started with this <a href="https://www.teacherspayteachers.com/Product/Write-and-Graph-Inequalities-Foldable-2414227" target="_blank">foldable</a>, a freebie in my TPT store! It was easily the most referenced notes in this unit. I loved watching the students flip back and look at it as we worked through the unit. We did a few notes about how to write a inequality from a number line and vice versa. Several students pointed out the trick about the inequality being an arrow showing where to shade, and I asked then if there was a difference between x>1 and 1>x, since both arrows points the same way. I told them that instead of memorizing a trick, they should think about which direction would make the inequality true or test a number to figure out how to shade. Nix the Tricks, boys and girls, and make math make sense! Every since time I graphed an inequality (and it was a lot over five sections of Algebra for four class periods), I talked through how to figure out which direction to shade an never once did I mention this trick, so hopefully they forgot it ;)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-y6Zx7jeF3W0/V-sTuwsCi1I/AAAAAAAABnA/x678mjXxyLoCJIy9mZ1s2Hsj35HoautQgCEw/s1600/IMG_3567.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-y6Zx7jeF3W0/V-sTuwsCi1I/AAAAAAAABnA/x678mjXxyLoCJIy9mZ1s2Hsj35HoautQgCEw/s320/IMG_3567.JPG" width="240" /></a></div><br />Day 2 we started off with some simple inequalities word problems - I love starting with word problems, and I have found that this year my students are not so afraid of them because we have been tackling word problems since day one. We also have fun using highlighters to pick out key words from the problems. I then introduced the key difference between inequalities and equations - if you divide by a negative, you flip the inequality symbol. We talked about why and then did some examples in "To Flip or Not To Flip." I liked these examples because my students often overgeneralize and just assume that if the problem involves a negative number, they flip the sign. These examples helped them to see when to flip and when not to flip.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-HbLvg0tZfgo/V-sTfFituoI/AAAAAAAABmU/Cj4vR7uzZxYUiELCFBVE6L7322RPNU-9QCEw/s1600/IMG_3488.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-HbLvg0tZfgo/V-sTfFituoI/AAAAAAAABmU/Cj4vR7uzZxYUiELCFBVE6L7322RPNU-9QCEw/s320/IMG_3488.JPG" width="320" /></a></div><br /><br />For classwork, we did this <a href="https://www.teacherspayteachers.com/Product/Two-Step-Inequalities-on-a-Number-Line-Matching-Cards-1913282" target="_blank">matching activity</a> by Amazing Mathematics that I loved! You start with a word problem and then match it to the inequality (I saw a lot of students using their foldables for this), then solve it, then graph it.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-yBKhuH3D4gA/V-sTmRT137I/AAAAAAAABm0/V_Fb1NN_tSMYJHgRUGnO-NyGu09Aw3FHQCEw/s1600/IMG_3490.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-yBKhuH3D4gA/V-sTmRT137I/AAAAAAAABm0/V_Fb1NN_tSMYJHgRUGnO-NyGu09Aw3FHQCEw/s320/IMG_3490.JPG" width="240" /></a></div><br />The students were a little overwhelmed at first, but they worked together to conquer. I told them everyone doesn't have to work out every problem, but you all have to agree on the work. This lead to some great discussions when someone had an answer that a group member wanted. This was a great activity with awesome discussions, teamwork and inequalities practice.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-7ITbHrC5Mv4/V-sTv9zMAEI/AAAAAAAABnI/P5lH4ssOzvktVnaSzPKMwCaOd1t5FJ-VgCEw/s1600/IMG_3571.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-7ITbHrC5Mv4/V-sTv9zMAEI/AAAAAAAABnI/P5lH4ssOzvktVnaSzPKMwCaOd1t5FJ-VgCEw/s320/IMG_3571.JPG" width="240" /></a></div><br />The next day we took on some Multi-Step Inequalities, including special solutions. Students practiced with this <a href="https://www.teacherspayteachers.com/Product/Multi-Step-Inequalities-Puzzle-2368593" target="_blank">Tarsia Puzzle</a>.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-JVd50_wXYGo/V-sTfCul-NI/AAAAAAAABmM/dq4tteUG6jY7MxT5OsWNPlgyN-hPuuYrgCEw/s1600/IMG_3513%2B%25281%2529.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-JVd50_wXYGo/V-sTfCul-NI/AAAAAAAABmM/dq4tteUG6jY7MxT5OsWNPlgyN-hPuuYrgCEw/s320/IMG_3513%2B%25281%2529.JPG" width="320" /></a></div><br />I love these collaborative puzzles for practice, especially for something like this where students can easily make little errors. When they don't find their answer, they are forced to re-examine their work or possibly the work of their peer - I hear such great discussions from this, that I never hear when students are working on a worksheet or textbook problems.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-Vj-zvsL2Tx4/V-sTfDuHBlI/AAAAAAAABmQ/fIYPQWxNoqsG7aLRm9RsaTCmaK8RpB52ACEw/s1600/IMG_3563.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-Vj-zvsL2Tx4/V-sTfDuHBlI/AAAAAAAABmQ/fIYPQWxNoqsG7aLRm9RsaTCmaK8RpB52ACEw/s320/IMG_3563.JPG" width="240" /></a></div><br />When they finished, they started on this <a href="https://www.teacherspayteachers.com/Product/Solve-Inequalities-Coloring-Activity-2573917" target="_blank">coloring activity </a>that they finished up for homework. It also helped them to study for their quiz, which was today. From what I have graded so far, they did really well. After the quiz, I had my best lesson yet on compound inequalities. I really wanted to focus on preparing them for writing compound inequalities for domain and range. We did this problem, from Algebra Nation, with an answer bank. Giving students an answer bank really helped them to break down this task and think about how to represent situations with compound inequalities.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-pKz-0fmeLe0/V-sTiAwiwGI/AAAAAAAABmw/AsYE9sngCjgGwetqAB_e2cij-NN_aYSzgCEw/s1600/IMG_3572.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://1.bp.blogspot.com/-pKz-0fmeLe0/V-sTiAwiwGI/AAAAAAAABmw/AsYE9sngCjgGwetqAB_e2cij-NN_aYSzgCEw/s320/IMG_3572.JPG" width="320" /></a></div><br />Then I did this <a href="https://www.teacherspayteachers.com/Product/Algebra-Graphing-and-Writing-Compound-Inequalities-Parking-Sign-Activity-1196123" target="_blank">activity</a>, which may be one of my favorite things yet. They graph compound inequalities from parking signs based on when cars CAN park.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-rcQZbFp974g/V-sUxRBbPzI/AAAAAAAABnU/HZyrFe9b-vwfRDmJbgC6Uig6_nE-UGeGACLcB/s1600/IMG_3566.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://4.bp.blogspot.com/-rcQZbFp974g/V-sUxRBbPzI/AAAAAAAABnU/HZyrFe9b-vwfRDmJbgC6Uig6_nE-UGeGACLcB/s320/IMG_3566.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;"> I loved how this made a concept that is usually tricky for my students into something relevant and fun. Speaking of fun, on to "fun"-ctions next! </span></div>Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com1tag:blogger.com,1999:blog-177420802016800294.post-52045618129576531472016-09-22T20:39:00.000-04:002016-09-22T20:58:14.904-04:00How my students discovered the distance formula<div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-6MRi1gRb21M/V-R89kAFXiI/AAAAAAAABlI/E-YYSUWjWaYXwQSisrQblAOfZWyWYAKwgCLcB/s1600/distance%2Bformula%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-6MRi1gRb21M/V-R89kAFXiI/AAAAAAAABlI/E-YYSUWjWaYXwQSisrQblAOfZWyWYAKwgCLcB/s320/distance%2Bformula%2Bpin.jpg" width="290" /></a></div>My focus in geometry has been on conceptual understanding, so in introducing distance formula, I wanted to make sure students understood the why. It took me two days, but my students have really grasped this concept, so I am very proud of them.<br /><br />I started with a review of Pythagorean Theorem. We reviewed the puzzle and did some practice with this Tarsia puzzle {<a href="https://www.teacherspayteachers.com/Product/Pythagorean-Theorem-Tarsia-Puzzle-1503881" target="_blank">a freebie in my TpT store!</a>}<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-lsPUxEpnqAY/V-Q_uf1h8wI/AAAAAAAABjw/jKtN0x8RkKQTgkAgjsmL0lWJc4DeS2_4gCLcB/s1600/IMG_3416.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-lsPUxEpnqAY/V-Q_uf1h8wI/AAAAAAAABjw/jKtN0x8RkKQTgkAgjsmL0lWJc4DeS2_4gCLcB/s320/IMG_3416.JPG" width="240" /></a></div><br />My students did these <a href="https://www.teacherspayteachers.com/Product/Pythagorean-Theorem-Pennant-2346977" target="_blank">pennants</a> from <a href="http://scaffoldedmath.blogspot.com/" target="_blank">Scaffolded Math and Science</a>, which have awesome questions to get kids thinking about Pythagorean Theorem (and they look great as classroom decor). I love the questions that start my giving students the area of the right triangle a side length and ask them to work backwards to the side lengths. I also love that this student made Pythagoras a red head - like me :)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-lS9Rve4tetY/V-RAP5r5TII/AAAAAAAABj0/r9T7KNGG8hMslUD1J5IajwzS5uA5D3oIACLcB/s1600/IMG_3493.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://3.bp.blogspot.com/-lS9Rve4tetY/V-RAP5r5TII/AAAAAAAABj0/r9T7KNGG8hMslUD1J5IajwzS5uA5D3oIACLcB/s320/IMG_3493.JPG" width="240" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-2cnLc--RvEo/V-R8Zk8IphI/AAAAAAAABlA/FghKWWBl8AYQ-uGzooUShgwGWP_GOw8jgCLcB/s1600/distance%2Binb%2B1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="231" src="https://4.bp.blogspot.com/-2cnLc--RvEo/V-R8Zk8IphI/AAAAAAAABlA/FghKWWBl8AYQ-uGzooUShgwGWP_GOw8jgCLcB/s320/distance%2Binb%2B1.jpg" width="320" /></a></div><br />Once we had the mechanics of the Pythagorean Theorem ironed out, we put it onto a coordinate plane. We graphed two points and I asked students if they could see a way to apply the Pythagorean Theorem. We had a great discussion about how it didn't matter if you drew the right triangle above or below the segment. One student even pointed out, "You are always going to be missing the hypotenuse because you can't count the diagonal distance." (Which I was SO excited to hear a student articulate. I can't tell you how many times I have seen students try to count diagonally across the graph.) We did two examples in their INBs and then I gave them this <a href="https://www.teacherspayteachers.com/Product/Distance-Formula-Maze-2587940" target="_blank">Distance Formula Maze</a>. I printed them one 1/4 of a page and attached graphs to the sheet. I told them to complete the first five problems using Pythagorean Theorem and then stop.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-7cnAmWNs_dY/V-R4xK0IrJI/AAAAAAAABkU/aI1g5AtCnfYJfYtFWvO3y5MEEr1uTfACACLcB/s1600/distance%2Bformula%2Bpt.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="224" src="https://4.bp.blogspot.com/-7cnAmWNs_dY/V-R4xK0IrJI/AAAAAAAABkU/aI1g5AtCnfYJfYtFWvO3y5MEEr1uTfACACLcB/s320/distance%2Bformula%2Bpt.png" width="320" /></a></div><br /><br />As they worked, I asked them to think about whether they could do this problem without a graph and what that would look like. I also told them I would give a Dum-Dum to any really good answers, so that got students extra motivated. One student said, "Draw a graph!" I told him that would be a great strategy on the EOC, but I wanted them to try it without graphing anything, so they went back to thinking.<br /><br />One student called me over and said, "Couldn't you just find the difference between the y-values and x-values in your ordered pairs and then use those numbers to do Pythagorean Theorem?" I asked her to prove this would work with an example she already did, so she looked a problem one, where she found the distance between (4,7) and (8,-5). She said, "Well 7 - (-5) is 12, so ... oh look, that's the same as the length of the leg. And 8-4 is 4 - so I think that would work." Then another student called me over and said, "This reminds me of learning about slope in Algebra class and this formula y2-y1 / x2-x1. Expect you wouldn't want to divide them at the end." I was so excited - here were my students coming up with ideas and connecting to prior knowledge all on their own. We flushed out these ideas with a group discussion and came up with the distance formula. They saw the connection between Pythagorean Theorem and the Distance Formula and my textbook has this cool graphic that helps really make that connection.<br /><a href="https://4.bp.blogspot.com/-ofpoVreWIJc/V-R8aR6iltI/AAAAAAAABlE/He0jkSENrcIpvUn7x1HIsmOgZ8yP-uGMwCLcB/s1600/distance%2Binb%2B2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="198" src="https://4.bp.blogspot.com/-ofpoVreWIJc/V-R8aR6iltI/AAAAAAAABlE/He0jkSENrcIpvUn7x1HIsmOgZ8yP-uGMwCLcB/s320/distance%2Binb%2B2.jpg" width="320" /></a><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />Then we did some examples and I sent them back to their maze. I told them to try our new formula for the next five and then they could finish any way they wanted.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Sws8g_-M1To/V-R5ieopa7I/AAAAAAAABks/FUVTTQaqh8EloRGjoCZoN-CRB5kEUhmQACLcB/s1600/IMG_3522.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-Sws8g_-M1To/V-R5ieopa7I/AAAAAAAABks/FUVTTQaqh8EloRGjoCZoN-CRB5kEUhmQACLcB/s320/IMG_3522.JPG" width="240" /></a></div><br />As students practiced, they started to favor one or the other. A few clever students came up with a hybrid of their own. One student was so proud he called me over and asked if it was OK for him to make up his own distance formula. I was intrigued, so he demonstrated with the points (1, -4) and (7, -1). He drew a table to help him find the distance between the x and y-values and then plugged those numbers into Pythagorean Theorem. Talk about taking ownership of your learning!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-8LH8FC5BkSs/V-R5EryYpaI/AAAAAAAABkc/hREUtRQDX4sWXLl5d0btt4keieq_HVHtACLcB/s1600/distance%2Bformula%2Bhybrid.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="239" src="https://1.bp.blogspot.com/-8LH8FC5BkSs/V-R5EryYpaI/AAAAAAAABkc/hREUtRQDX4sWXLl5d0btt4keieq_HVHtACLcB/s320/distance%2Bformula%2Bhybrid.jpg" width="320" /></a></div><br />Our next lesson was midpoint, which I used my fan lesson that I blogged about here. Again, the students understood what they were doing. Today, I gave them this mini quiz with a tough Check All That Apply problem, and they nailed it! Discovery learning and conceptual understanding <br />for the win!Math Dyalhttp://www.blogger.com/profile/06607190697039229965noreply@blogger.com0