tag:blogger.com,1999:blog-86431944671907285512024-03-16T13:53:09.885-05:00Math Techniques and StrategiesMaking math fun and incorporating math into all ways of daily life!
I update the blog daily on information for math teachers.Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.comBlogger125125tag:blogger.com,1999:blog-8643194467190728551.post-7992575359683145252021-10-03T15:04:00.001-05:002021-10-03T15:04:10.791-05:00Literal Equations: Tweets from #mtbos<p> Literal equations is one of the topics in Algebra that I struggle finding different activities for. Literal equations is one of those topics that is very procedural and not very conceptual. I put together a list of different activities from #mtbos on Twitter. Look through each of these and see which ones you might like. </p><p><br /></p><p><br /></p>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">Ss looking over literal equations today. Walking themselves through a step by step activity to better understand the process of variable isolation! <a href="https://twitter.com/FJHChargers?ref_src=twsrc%5Etfw">@FJHChargers</a> <a href="https://t.co/RYwMJxMSVe">pic.twitter.com/RYwMJxMSVe</a></p>— Mike Gear (@CoachGear) <a href="https://twitter.com/CoachGear/status/1196571716023177217?ref_src=twsrc%5Etfw">November 18, 2019</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">Ss in algebra 1 solve for literal equations first by sorting them by the operations they needed to use solve them. Then, choosing two from each column to solve on their own. <a href="https://twitter.com/BCPSMATH?ref_src=twsrc%5Etfw">@BCPSMATH</a> <a href="https://t.co/0ah3edjl5r">pic.twitter.com/0ah3edjl5r</a></p>— Miss Small (@MissSmallBCPS) <a href="https://twitter.com/MissSmallBCPS/status/1190076184614322176?ref_src=twsrc%5Etfw">November 1, 2019</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr"><a href="https://twitter.com/hashtag/DoubleBubble?src=hash&ref_src=twsrc%5Etfw">#DoubleBubble</a> for the win! Solving literal equations is a breeze when Ss can visualize their thinking with <a href="https://twitter.com/ThinkingMaps?ref_src=twsrc%5Etfw">@ThinkingMaps</a> and practice <a href="https://twitter.com/hashtag/metacognition?src=hash&ref_src=twsrc%5Etfw">#metacognition</a> to set the foundation for new learning! <a href="https://twitter.com/NBMandarin?ref_src=twsrc%5Etfw">@NBMandarin</a> <a href="https://twitter.com/NBMIDDLE?ref_src=twsrc%5Etfw">@NBMIDDLE</a> <a href="https://t.co/q8y4TpnH12">pic.twitter.com/q8y4TpnH12</a></p>— Pilar Forero Taylor (@pilitaylor333) <a href="https://twitter.com/pilitaylor333/status/1172154663556308992?ref_src=twsrc%5Etfw">September 12, 2019</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">algebra 1 students who displayed mastery solving Literal Equations are creating anchor charts to help other students learn <a href="https://twitter.com/hashtag/UtleyWolves?src=hash&ref_src=twsrc%5Etfw">#UtleyWolves</a> π <a href="https://t.co/9jEIkBhakV">pic.twitter.com/9jEIkBhakV</a></p>— π°ππππππ πΌπ’πππ π·πππ (@HuckMath) <a href="https://twitter.com/HuckMath/status/1037759484041551874?ref_src=twsrc%5Etfw">September 6, 2018</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">Quick warmup puzzle matching opposite operations to get them ready for literal equations. <a href="https://twitter.com/hashtag/iteachmath?src=hash&ref_src=twsrc%5Etfw">#iteachmath</a> <a href="https://twitter.com/hashtag/lovepuzzles?src=hash&ref_src=twsrc%5Etfw">#lovepuzzles</a> <a href="https://twitter.com/hashtag/amazonforthewin?src=hash&ref_src=twsrc%5Etfw">#amazonforthewin</a> <a href="https://twitter.com/hashtag/getthebraininthegame?src=hash&ref_src=twsrc%5Etfw">#getthebraininthegame</a> <a href="https://t.co/DQIjmWzZOW">pic.twitter.com/DQIjmWzZOW</a></p>— Karen Curran (@KCMathRocks) <a href="https://twitter.com/KCMathRocks/status/1179712900409253891?ref_src=twsrc%5Etfw">October 3, 2019</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">Too beautiful outside not to examine literal equations in the parking lot π. Good discussion and questioning!@RossRams1 <a href="https://t.co/F4cPeiATDX">pic.twitter.com/F4cPeiATDX</a></p>— Amy Brossart (@brossart_amy) <a href="https://twitter.com/brossart_amy/status/1306387015756378112?ref_src=twsrc%5Etfw">September 17, 2020</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">Physics students employing math skills to solve literal equations. They are challenging each other with equations they create. <a href="https://t.co/Az0UhfA2LJ">pic.twitter.com/Az0UhfA2LJ</a></p>— Ozark Physics (@OzarkPhysics) <a href="https://twitter.com/OzarkPhysics/status/1163813597169905664?ref_src=twsrc%5Etfw">August 20, 2019</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">Incorporating literacy strategies as we delve into multi-variable/literal equations in Algebra 1 today! <a href="https://twitter.com/CraytonMiddle?ref_src=twsrc%5Etfw">@CraytonMiddle</a> <a href="https://twitter.com/hashtag/BestofCMS?src=hash&ref_src=twsrc%5Etfw">#BestofCMS</a> <a href="https://t.co/8RFPnL5ry8">pic.twitter.com/8RFPnL5ry8</a></p>— Brandon Reeder (@MrReederSC) <a href="https://twitter.com/MrReederSC/status/1439939389212274698?ref_src=twsrc%5Etfw">September 20, 2021</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">Aww yeah, the <a href="https://twitter.com/Giants?ref_src=twsrc%5Etfw">@Giants</a> inched out the @Redskins (and the rest of the pack) while solving algebra literal equations today. First team to the end zone got no homework -emphasis on <a href="https://twitter.com/hashtag/team?src=hash&ref_src=twsrc%5Etfw">#team</a>! <a href="https://twitter.com/hashtag/iteachmath?src=hash&ref_src=twsrc%5Etfw">#iteachmath</a> <a href="https://twitter.com/hashtag/teach180?src=hash&ref_src=twsrc%5Etfw">#teach180</a> <a href="https://t.co/LtcIsQUhVG">pic.twitter.com/LtcIsQUhVG</a></p>— Meghan Smeenk (@MrsSmeenk) <a href="https://twitter.com/MrsSmeenk/status/1179168728933654533?ref_src=twsrc%5Etfw">October 1, 2019</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr"><a href="https://twitter.com/GraspableMath?ref_src=twsrc%5Etfw">@GraspableMath</a> for literal equations at <a href="https://twitter.com/CNEMiddle?ref_src=twsrc%5Etfw">@CNEMiddle</a> <a href="https://twitter.com/cneschools?ref_src=twsrc%5Etfw">@cneschools</a> <a href="https://t.co/tYMU8ZTHF7">pic.twitter.com/tYMU8ZTHF7</a></p>— Steve Phelps (@MathTechCoach) <a href="https://twitter.com/MathTechCoach/status/1318599230383063043?ref_src=twsrc%5Etfw">October 20, 2020</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">I used the Literal Equations in Desmos today - I would recommend this one <a href="https://t.co/oDND5GQLhv">https://t.co/oDND5GQLhv</a></p>— Michelle Kessen (@MichelleKessen) <a href="https://twitter.com/MichelleKessen/status/1177023700908040193?ref_src=twsrc%5Etfw">September 26, 2019</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">Today I used <a href="https://twitter.com/NewVisionsNYC?ref_src=twsrc%5Etfw">@NewVisionsNYC</a> literal equations matching task as we wrap up our unit. Loved the placemat and justification space. Enjoy this off guard photo of me taken today on my phone without my knowledge. <a href="https://twitter.com/hashtag/iteachmath?src=hash&ref_src=twsrc%5Etfw">#iteachmath</a> <a href="https://twitter.com/hashtag/teacherlife?src=hash&ref_src=twsrc%5Etfw">#teacherlife</a> <a href="https://t.co/80sDoDj9Nj">pic.twitter.com/80sDoDj9Nj</a></p>— Dwaina Sookhoo (@mathapprentice_) <a href="https://twitter.com/mathapprentice_/status/1216872443681366017?ref_src=twsrc%5Etfw">January 13, 2020</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-3063442103263945302020-07-09T17:49:00.001-05:002020-07-09T17:49:49.472-05:00Teaching Scientific Notation Using Omni<font size="5">A normal resting heart rate is between 60 and 100 heartbeats per minute. Use the following calculator to help answer the following questions.</font><div><div><br /><div class="omni-calculator" data-calculator="math/scientific-notation" data-config="{}" data-currency="USD" data-show-row-controls="false" data-t="1594333419571" data-version="3" data-width="300">
<div class="omni-calculator-header">Scientific Notation Calculator</div>
<div class="omni-calculator-footer">
<a href="https://www.omnicalculator.com/math/scientific-notation" target="_blank"><img alt="Omni" class="omni-calculator-logo" src="https://cdn.omnicalculator.com/embed/omni-calculator-logo-long.svg" /></a>
</div>
</div>
<script async="" src="https://cdn.omnicalculator.com/sdk.js"></script>
</div><div><span> </span></div><div><span><br /></span></div><div><span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> Number<span> </span><span> </span><span> </span><span> </span><span> </span><span> </span><span> Scientific Notation</span></span><br /></span></div><div><span>a. How many heartbeats happen in a day?<span> </span><span> </span><span> </span><span> </span><span> _____________<span> </span><span> </span><span> </span><span> __________________</span></span></span><br /></div></div><div><br /></div><div><span>b. </span>How many heartbeats happen in a week?<span> </span><span> </span><span> </span><span> _____________<span> </span><span> </span><span> </span><span> __________________</span></span></div><div><br /></div><div>c. How many heartbeats happen in a month?<span> </span><span> </span><span> </span><span> _____________<span> </span><span> </span><span> </span><span> __________________</span></span></div><div><br /></div><div>d. How many heartbeats happen in a year?<span> </span><span> </span><span> </span><span> </span><span> ____________<span> </span><span> </span><span> </span><span> ___________________</span></span></div><div><br /></div><div>e. How many heartbeats happen in a lifetime?<span> </span><span> </span><span> _____________<span> </span><span> </span><span> </span><span> ___________________</span></span></div><div><br /></div><div>What are some questions you might have?</div><div><br /></div><div>__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________. </div><div><br /></div><div>Let's draw a number line... how could we put all the data points on a number line?</div><div><br /></div><div><br /></div><div><span> </span><span> <---------------------------------------------------------------------------------------------------></span><br /></div><div><span><br /></span></div><div><span><br /></span></div><div>What do you notice about the scientific notation row? What do you wonder</div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div>What number might you think 2.05x10β΅ might be?</div><div><span><br /></span></div><div><br /></div><div><br /></div><div><br /></div>Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com9tag:blogger.com,1999:blog-8643194467190728551.post-3199766381774401262020-04-12T20:22:00.003-05:002020-04-12T20:22:47.397-05:00Chef's TableI love good food. I love trying new places. I love the idea of curating an experience, especially with my wife. One place she took me on my last birthday was V. Mertz, probably one of the best restaurants I have ever been to right here in Omaha, that includes going to the James Beard Award Winning Zahav. But, one of my big life goals is to go to Alinea in Chicago. I was trying to get my brother-in-law to understand why going there would be so awesome, but words weren't cutting it. So we watched the 55 minute long Grant Achatz episode on Chef's Table.<br />
<br />
Rewatching this episode during this time where education isn't really education and not knowing what education will look like for next year, this one quote stuck with me when Achatz was starting his new restaurant Alinea he said:<br />
<blockquote class="tr_bq">
"We gathered the staff and I say everybody needs to believe the fact that we are about to open the best restaurant in the country. And anything else will be a failure."</blockquote>
Now I think that almost every part of this episode can be dissected and adapted to education, but when we start again in August, September, October, or whenever we start, what are we coming back to? Worksheets? Taking notes? Sitting in rows? Furthering equity gaps?<br />
<br />
What if instead of going back to the same old school in the traditional sense, we came back to school thinking how would the best school in the country open? What would the first lesson be? What would the first unit be? How can we transform the learning of our students?<br />
<br />
Listening to Zaretta Hammond's webinar <a href="https://crtandthebrain.com/covid19-webinar1-recording/" target="_blank">Moving Beyond the Packet: Creating More Culturally Responsive Distance Learning Experiences</a> she went into detail about making connections, using background knowledge, and actual doing. How can we rebuild school, because next year isn't like starting a new year. We have a chance to build a new system?.<br />
<br />
Will we think that this chance is the one chance to be the best and anything else will be a failure?<br />
<br />
<br />Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-90397205437605459802019-12-18T15:40:00.001-06:002019-12-18T15:40:18.764-06:00The End of the Decade<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I vaguely remember they Y2k scare (I was 11). I donβt really remember how the 2010 new year was, but as 2020 comes closer and the end of this decade approaches it has put me in a reflective mood over the past 10 years. For me educationally, I feel like my philosophy of education has changed, especially outside of the teaching math realm. Below are some things I used to think were important or how I thought about education.</span></div>
<b id="docs-internal-guid-a87e1b2a-7fff-289a-b67b-ad0545bce22d" style="font-weight: normal;"><br /></b>
<ul style="margin-bottom: 0; margin-top: 0;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><div dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I used to think that engagement was key and building elaborate learning experiences would help my students make gains and remember the material for the long term. </span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><div dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I used to think that the latest and greatest would help bridge that gap from coming to math class to enjoying math class.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><div dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I used to think that being a teacher was only going to be a part of my life.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><div dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I used to think that I could carry the weight of the class on my shoulders.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><div dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I used to think that content was king.</span></div>
</li>
</ul>
<br />
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">From the end of college, to subbing for a full year, to my first teaching job, to my second, to my third. My first teaching job left some scars that I am still getting over. I feel like I left a home at my second job to become a better teacher. I got my Masters a few years ago and there have been countless people and PLN members that have been influential these past 10 years. There have been countless teachers that have opened their doors for me to come in and look. To mention a couple of people, first off Marty Fetch who is an instructor at Doane University that focused on building classroom culture. Iβd like to thank countless people in #mtbos and #cleartheair specifically Marian Dingle and Val Brown, whose guidance and leadership in these spaces makes it evident of the work that needs to occur in our classrooms. I am thankful for all the experiences this decade and all of the teachers and students I have had. </span></div>
Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-51415140022831626242019-09-02T20:20:00.000-05:002019-09-02T20:20:45.650-05:00Golden Sower and What Needs to ChangeI've been participating in #cleartheair on Twitter for a little more than a year now. It has led to me to know some amazing educators doing amazing things in their classrooms, but more importantly it has showed me what I need to do to be a better educator for every single one of my students. One thing they led me to was the National Antiracist Book Festival, it featured great books that I have read and one of my challenges this summer was to read all of the ones featured, I know that will not happen now. But, one thing I learned from reading some of these texts was to use my privilege to let others, especially people of color, have a voice in the conversation.<br />
<br />
This leads me to one of the things I like to do is read YA, even though I am a math teacher and I haven't read in a while, but I am a part of the golden sower reading committee one of the things we do as a group is narrow down all the choices of books librarians, students, parents, and us submit to 10 titles. Students then read these 10 titles and vote for them and one of them wins. The author is normally invited to the state to speak, sign books, but one of the big things is advertisement in the state for all of the libraries for the 10 selected. Normally each library has a collection of golden sowers and the winners.<br />
<br />
<a href="https://sites.google.com/site/nebraskagoldensower/young-adult-nominees" target="_blank">Here</a> are the 2019-2020 nominees for golden sower.<br />
<br />
One thing I want to bring to light is the number of diverse books we are choosing for this list. You can see the 10 nominated going back a decade an a half <a href="https://drive.google.com/file/d/1Wr9S2PxdEz8XNCQeZk8onJey5NP4gayE/view" target="_blank">here</a>. At most we have 2 diverse books per year. Here is a breakdown of Nebraska Public Schools as a whole. Does 2 books suffice?<br />
<br />
<img src="data:image/png;base64,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" /><br />
<br />
One thing I want to point to you to, if haven't heard about this story is Dr. Ferial Pearson, "<a href="https://medium.com/@FerialP/deceit-wrapped-in-kindness-3498de1dec55" target="_blank">Deceit Wrapped in Kindness</a>." There was an article published in the Omaha World Herald, but it was pay-walled. Read it. Take your time to fully digest it. I will wait.<br />
<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
<br />
<br />
I grew up in Blair, I went to college in Crete, I live in Bennington, taught in Schuyler, taught in Omaha. I've been all of this state and I have never once felt uncomfortable being anywhere and I know that is my white privilege. That I can walk anywhere being a white cis-gendered male and know I will be safe. I am not going to judge, but I do have some questions. How are we as a state educating our youth? What books are they reading? Are they reading about people who don't look like them?<br />
<br />
This just isn't a Mullen problem, it's a Nebraska problem. I believe there is a direct correlation to the books we choose as a part of the Golden Sower and biases and stereotypes that we perpetuate in our state. I have been less vocal in the past about the books chosen for the Golden Sower. That comes to an end today. It is my duty to put books who look like all of my students in front of them as a part of The Golden Sowers reading committee.<br />
<br />
Next year's Golden Sowers are already chosen for 2020-2021 they are not set in stone, but overwhelmingly chosen. My personal goal is to have the 2021-2022 Golden Sower selections to be the most diverse since the beginning of Golden Sower YA in 1993.<br />
<br />Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-62315943108431277722019-04-30T08:00:00.000-05:002019-04-30T08:00:00.722-05:00Exponential Problem<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">It has been a couple of weeks since I taught exponents and logarithms. We do all the normal things we do with them in Algebra 2. We changed from one to the other, we graphed, we looked at their properties, we did half-life and doubling problems. When my students took the test I was happy to see good scores this late in the school year when motivation can run low. </span></div>
<b id="docs-internal-guid-8b7fc6c1-7fff-7584-5042-22f594fff783" style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Today I found a great problem on a site called FiveThirtyEight it has a <a href="https://fivethirtyeight.com/features/how-many-earthlings-would-survive-63-thanos-snaps/" target="_blank">weekly puzzle</a> people can submit to and it was relevant because Avengers EndGame had just come out. The problem looks like this:</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><img height="262" src="https://lh6.googleusercontent.com/EtuftlL1Zf2J-1-61tKQ6KCWSWb1P4HBGZsfMQiJDjd8vJ7-kFjfI7t7AKCp88cHRnuzbjm3HbJItq8ro36Ttow1bu22wJjQaUfKgG29B_eb8nEfXR6-UHhNdgEfC07phK42esV-" style="-webkit-transform: rotate(0.00rad); border: 1pt solid #000000; transform: rotate(0.00rad);" width="594" /></span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I was going to use this as a bell ringer. I thought it would take them about 2-3 minutes to do. I gave them no further instruction than answer the question. They could use their notes from the last chapter, anything that could help them. After 5 minutes, some students had started to give up. Some students were having rich-mathematical conversations with each other. Talking about halving, did the number of Thanoses also halve, does the original Thanos die when he snaps his fingers. This bell ringer that was supposed to be taking 5 minutes at the maximum is now going on 10 minutes. I felt like there were some misconceptions that students about this problem and that more time would help solidify exponential equations.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I let students struggle for the next 25 minutes, working with partners or in groups, using their notes. Some of the students and groups persevered through the problem, other groups were harder to get moving through the question. Here are some examples of the work my students did.</span></div>
<b style="font-weight: normal;"><br /></b>
<div class="separator" style="clear: both; text-align: center;">
<b style="font-weight: normal;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNbIwTMyTacr9Ha_VCgag5phEaArUcGDfbXp95EuTpoGnz0UKVtvbEpnRQSqNP5tANRydCYo0Tc3QdGSuzvOWePseyMFLhwGAp__HqzbRUMHKRX8lNL0VefuiYfRuC5AjN7ntJSkiLT2nj/s1600/IMG_4321.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="958" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNbIwTMyTacr9Ha_VCgag5phEaArUcGDfbXp95EuTpoGnz0UKVtvbEpnRQSqNP5tANRydCYo0Tc3QdGSuzvOWePseyMFLhwGAp__HqzbRUMHKRX8lNL0VefuiYfRuC5AjN7ntJSkiLT2nj/s320/IMG_4321.JPG" width="191" /></a></b></div>
<b style="font-weight: normal;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj5zW19XvUNDDlPr64cveL-s-yo4YS30sJADY_vdgilMxU1fHwWFPR4d4qZ5FlkS2Tax_RPUuDGrl0tT6rbDcpvTUQbeU8C_qKdbQ9HT9gAGxMxRZ_h_P7Q4HdmFrnU7M686Nhu09P1Yqm/s1600/IMG_4318.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1600" data-original-width="1395" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj5zW19XvUNDDlPr64cveL-s-yo4YS30sJADY_vdgilMxU1fHwWFPR4d4qZ5FlkS2Tax_RPUuDGrl0tT6rbDcpvTUQbeU8C_qKdbQ9HT9gAGxMxRZ_h_P7Q4HdmFrnU7M686Nhu09P1Yqm/s320/IMG_4318.JPG" width="279" /></a> </b><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<b style="font-weight: normal;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1968hbRnoQOwc9Fx_MwowM0q-xStIAmxAM2jLLD5IYCNsNtKEsQHi22qE-LZSSm8CfLwwRlt2TXDVCJ7tecP13f1XNqjVeW12t4uYZQNFGSdvXUmmixdPHU-Ta43bjRN-Lz6O1xxdd5KS/s1600/IMG_4320.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1383" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1968hbRnoQOwc9Fx_MwowM0q-xStIAmxAM2jLLD5IYCNsNtKEsQHi22qE-LZSSm8CfLwwRlt2TXDVCJ7tecP13f1XNqjVeW12t4uYZQNFGSdvXUmmixdPHU-Ta43bjRN-Lz6O1xxdd5KS/s320/IMG_4320.JPG" width="276" /></a></b></div>
<div class="separator" style="clear: both; display: inline !important; text-align: center;">
<b style="font-weight: normal;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdEdu8Exut1weFS5thM2bK8taC6-PcW8CSBwqjnNmxinbGZ1P5BFET_9UgCIrwX0PXRGDozBWudjC7iUYmLFEZIEVxMcQuj1pPcoVH8dboKjluRHMT0m8MolQD76z-25IVDH33WcSUiwcY/s1600/IMG_4317.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1581" data-original-width="1600" height="316" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdEdu8Exut1weFS5thM2bK8taC6-PcW8CSBwqjnNmxinbGZ1P5BFET_9UgCIrwX0PXRGDozBWudjC7iUYmLFEZIEVxMcQuj1pPcoVH8dboKjluRHMT0m8MolQD76z-25IVDH33WcSUiwcY/s320/IMG_4317.JPG" width="320" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_PBMG0Fix1xCVvRuvntfOLAqaaP-AzbaSsHgTLft5kkGWSG5iox8DL4ltxNXS_hWigUsWlB92IMV2sc7miLB3ksKbm5tnOAbxE3fud9oU36KTMZFcfzG49996Stj4l7W2YHZSzT5qXdVb/s1600/IMG_4319.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1450" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_PBMG0Fix1xCVvRuvntfOLAqaaP-AzbaSsHgTLft5kkGWSG5iox8DL4ltxNXS_hWigUsWlB92IMV2sc7miLB3ksKbm5tnOAbxE3fud9oU36KTMZFcfzG49996Stj4l7W2YHZSzT5qXdVb/s320/IMG_4319.JPG" width="289" /></a></b></div>
<b style="font-weight: normal;"><br /></b><br />
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I taught this class three times, after the first time I went to some of the teachers that teach the same thing and asked them if this was beyond their thinking, after a while they decided that the students should be able to answer the problems from what we went over in class, but they added that the studentβs wouldnβt be able to get an answer. After two days of sitting on this I went back to them, I wanted to know why they thought the students couldnβt answer the problem and what we could do next year to remedy this.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Here were some of the teachers responses to why the students werenβt able to answer the problem:</span></div>
<ul style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">One teacher said we did exponentials and logarithms too long ago for students to remember. Also students only remember or do what we teach them.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Another teacher said students donβt know how an exponential equation works.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Another teacher said students canβt persevere or formulate questions.</span></div>
</li>
</ul>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Here were some of the teachers responses to what can we do differently for next year so we can solve this problem:</span></div>
<ul style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">One teacher said we need to be more connected across Algebra 2, we should start with a question and answer it over the course of the unit or chapter, it needs to be an expectation that students can problem solve, students need to get use to out of the box problems from the start of the year.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Another teacher said we need more modeling and that students need more practice at it because the capability is there.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Another teacher said we should start off the chapter and year with questions like these, we need to change the way vocabulary is taught especially when it comes to a problem like this, we need to teach students how to use a simpler problem to solve.</span></div>
</li>
</ul>
<br />
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I agreed with all of the responses that we should be doing next year. When you value problem solving over speed and simplicity you help your students become better mathematicians. This was a good problem for my students to work on for a day, this will help me become a better teacher for them in the future. </span></div>
Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-41498241511975218302019-02-04T19:58:00.000-06:002019-02-04T19:59:01.976-06:00Creating a Polynomial FunctionOne thing that I have been looking forward to trying in Advanced Algebra is more tasks. One of my goals for this year is doing more mathematical talking and orchestrating better discussions in the classroom. One task I created recently that still needs work is this creating a polynomial function from zeros task. Previously students have only factored and solved polynomials with P's and Q's. I was thinking they could work their way backwards from the previous days material.<br />
<div>
<br /></div>
<div>
<br /></div>
<iframe height="315" src="https://docs.google.com/document/d/e/2PACX-1vQ8OeeaWiVJM43JarKFA9d5Ys3slK592chrhaiTjxHb7X3ZPqFs9tuFiixnZ3yPMXvhvAVuZSEfA_Hg/pub?embedded=true" width="650"></iframe><br />
<br />
<br />
Here is a <a href="https://docs.google.com/document/d/e/2PACX-1vQ8OeeaWiVJM43JarKFA9d5Ys3slK592chrhaiTjxHb7X3ZPqFs9tuFiixnZ3yPMXvhvAVuZSEfA_Hg/pub" target="_blank">link</a> to a better looking version.<br />
<br />
I gave them the task to work on for 15 minutes and I went around the classroom getting students started and answering questions. If I had more time I would have done a better job of calling students up and presenting their work, but I was running short on time. I was hoping their thinking would help them think backwards especially with day before lesson.<br />
<br />
Some places they might have gotten stuck at that I had posed responses for:<br />
<br />
<ul>
<li>Students will have a hard time getting started (it feels like a high entry task)</li>
<ul>
<li>I will ask them to go through an example problem we have done before, such as x^2-4x+3</li>
</ul>
<li>Multiplying the "i's" together, it has been about a full quarter since they have seen imaginary numbers multiplied together.</li>
<ul>
<li>I will ask them what i squared is? What do they remember about imaginary numbers?</li>
</ul>
<li>Distributing correctly.</li>
<ul>
<li>Ask them how they would distribute (x+2)(x+2)?</li>
</ul>
</ul>
<div>
If you are really digging this lesson, you can view 28 minutes of the lesson <a href="https://cloud.swivl.com/v/d79b737f912a9f1dc0513dfe00630894" target="_blank">here</a>. </div>
<div>
<br /></div>
<div>
I still feel like the entry to the task is too high, I would love comments on how this could be a better lesson.</div>
Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com1tag:blogger.com,1999:blog-8643194467190728551.post-30417692004363376542019-01-16T22:15:00.001-06:002019-01-16T22:15:49.840-06:00Trig Lasers<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsy6zglTbC_2EVTGDbm3g2RvlIInnnS03-uhUyF-UWc-DoRtv9m_eHAF6tvfGqg0s3EAVbq74mlVmTyDKzxXNLn9wvPF-ik8S5DYa1e6v0Yeu3ITHziF5K21fesZTV-e5Cs22CFe6asA7B/s1600/IMG_4238.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1343" data-original-width="1600" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsy6zglTbC_2EVTGDbm3g2RvlIInnnS03-uhUyF-UWc-DoRtv9m_eHAF6tvfGqg0s3EAVbq74mlVmTyDKzxXNLn9wvPF-ik8S5DYa1e6v0Yeu3ITHziF5K21fesZTV-e5Cs22CFe6asA7B/s320/IMG_4238.JPG" width="320" /></a>One of the things I don't get to do often, but love to do is observe other teachers. I get to see how they run the classroom, how their routines are set-up, and sometimes see really cool lessons. In Basic Geometry Mr. Fick and Ms. Groth had a lesson they were talking about that seemed really cool to observe. They had a bunch of different targets printed, lasers, and protractors.<br />
<br />
To review the trigonometry they have been practicing in class. Ms. Groth had one student come up and set a target on the front wall of the classroom. She had already set a piece of tape on the ground, she wanted to know the angle that would make it so a laser would shine and hit the target. She asked the class what angle they thought it would be and students guessed. She then asked what other information is needed to know so they could accurately calculate the angle. A couple of students said the height and the distance. Those two students came up and measured both of those. Students were given a handout to write down and then calculate the given angle.<br />
<br />
Ms. Groth then did another example where she already gave them the angle and height and they had to calculate the distance away.<br />
<br />
I think a great extension to what I saw would to give each pair of students a target, laser, and compass. Then have students calculate their own. Or possibly have some sort of putt-putt kind of station moving from one target to the next.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_iMLTxRWw8h5YGoCsj5LdjHUpXT4ijKoKuVZ1sie3hPETlUrpuEWS8hQtMCZ3NTju57WMcN6JBz4NmVEhOzaUAXjeTqKyxhN_NYCfqs8d4MngWah2I8jCW98PG6lT9GJZNHr5WlP2vi1q/s1600/target-1341379_1920.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1600" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_iMLTxRWw8h5YGoCsj5LdjHUpXT4ijKoKuVZ1sie3hPETlUrpuEWS8hQtMCZ3NTju57WMcN6JBz4NmVEhOzaUAXjeTqKyxhN_NYCfqs8d4MngWah2I8jCW98PG6lT9GJZNHr5WlP2vi1q/s320/target-1341379_1920.png" width="320" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMFr6T3iojX3fdGDtyHk1tyuugAPfP-BZI_PslwtX_gbOmm1Z_mSwJHFJsuUGoKPSHVUs4h7Nsx9A7CAh8ULQpkD8qtc2TqRaMZLrby-OHWK81CCY-j9-nu1zegotsLjE1hEiIExfhtYjM/s1600/IMG_4239.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMFr6T3iojX3fdGDtyHk1tyuugAPfP-BZI_PslwtX_gbOmm1Z_mSwJHFJsuUGoKPSHVUs4h7Nsx9A7CAh8ULQpkD8qtc2TqRaMZLrby-OHWK81CCY-j9-nu1zegotsLjE1hEiIExfhtYjM/s320/IMG_4239.JPG" width="240" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizUFjvj0L2tkvz3bDzJON0k5tBqFhRBgAz-1QHbqMn2yBh3Je6ytlTttwZ1xIFvOXjApfdIRH_ZqpGk1VzxqszupOfC1oAonuvt4pu32aEVGtrOOKsJrgHfyx5YIKszjtEk_PdU3LlvVye/s1600/IMG_4241.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://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizUFjvj0L2tkvz3bDzJON0k5tBqFhRBgAz-1QHbqMn2yBh3Je6ytlTttwZ1xIFvOXjApfdIRH_ZqpGk1VzxqszupOfC1oAonuvt4pu32aEVGtrOOKsJrgHfyx5YIKszjtEk_PdU3LlvVye/s320/IMG_4241.JPG" width="240" /></a></div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGSqbYOFQTQG1ZppYGXqyMOuDwxuGsl64kgBRdmB_gic3eHNy8gSZYza4TuSm6lmpQGQ-GKLtqwLE9ELLm2AcZIjS9KtzSLBUGtWTdnhuPlZSSX71dvlRsCDX1OFl_5K5pxsc4K4ygFqUp/s1600/IMG_4242.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGSqbYOFQTQG1ZppYGXqyMOuDwxuGsl64kgBRdmB_gic3eHNy8gSZYza4TuSm6lmpQGQ-GKLtqwLE9ELLm2AcZIjS9KtzSLBUGtWTdnhuPlZSSX71dvlRsCDX1OFl_5K5pxsc4K4ygFqUp/s320/IMG_4242.JPG" width="320" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9FAlFcrbDJ7wWambROcjyrOsfgArQ58WrGYzFsTpmSZU8QMG_mNFUrLihCF_7eiW2QxCLU89vGV3SvyyMOLdt8J4lmy_Vux0CdpKpKEcSJvRb-bkCCqzpxnpM7-wJt1pB7b4yMsl24Rvc/s1600/IMG_4240.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://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9FAlFcrbDJ7wWambROcjyrOsfgArQ58WrGYzFsTpmSZU8QMG_mNFUrLihCF_7eiW2QxCLU89vGV3SvyyMOLdt8J4lmy_Vux0CdpKpKEcSJvRb-bkCCqzpxnpM7-wJt1pB7b4yMsl24Rvc/s320/IMG_4240.JPG" width="240" /></a></div>
<br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi31iClXICx21fAyB2p7vRKAhQYDQGbJ5jrDFgSloQnaVFgzbHkZ4m0m7pKbgWMm38ba_QroY_8swK0iQTtAIP0XvUt1AlJoAYWZKZoMeIfbSsbgW4SXg-r-gg7S_qmur-kiXv6BFMybUh3/s1600/IMG_4243.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1223" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi31iClXICx21fAyB2p7vRKAhQYDQGbJ5jrDFgSloQnaVFgzbHkZ4m0m7pKbgWMm38ba_QroY_8swK0iQTtAIP0XvUt1AlJoAYWZKZoMeIfbSsbgW4SXg-r-gg7S_qmur-kiXv6BFMybUh3/s320/IMG_4243.JPG" width="244" /></a></div>
<br />
<br />
<br />Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-86883332056472489502018-11-24T21:48:00.000-06:002018-11-24T21:48:22.003-06:00Are You Looking for Piece-wise Functions<blockquote class="twitter-tweet" data-lang="en">
<div dir="ltr" lang="en">
Doing piecewise functions this year? Hereβs my latest <a href="https://twitter.com/Desmos?ref_src=twsrc%5Etfw">@Desmos</a> activity called Lava Piecewise Functions.<a href="https://twitter.com/hashtag/mtbos?src=hash&ref_src=twsrc%5Etfw">#mtbos</a> <a href="https://twitter.com/hashtag/iteachmath?src=hash&ref_src=twsrc%5Etfw">#iteachmath</a> <br />
<br />
Avoid the lava!<a href="https://t.co/TvMm8knYKo">https://t.co/TvMm8knYKo</a> <a href="https://t.co/latZBLBZqt">pic.twitter.com/latZBLBZqt</a></div>
β Andrew Stadel (@mr_stadel) <a href="https://twitter.com/mr_stadel/status/1044949712313376769?ref_src=twsrc%5Etfw">September 26, 2018</a></blockquote>
<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script><br />
<br />
<blockquote class="twitter-tweet" data-lang="en">
<div dir="ltr" lang="en">
In today's <a href="https://twitter.com/Desmos?ref_src=twsrc%5Etfw">@desmos</a> activity, I asked my stus to break my piecewise function - that was fun to watch! Wanted to impress how much engineering goes into making continuous piecewise fn: <a href="https://twitter.com/hashtag/mtbos?src=hash&ref_src=twsrc%5Etfw">#mtbos</a> <a href="https://twitter.com/hashtag/flipclass?src=hash&ref_src=twsrc%5Etfw">#flipclass</a> <a href="https://t.co/pMQ7BKb8qu">https://t.co/pMQ7BKb8qu</a> <a href="https://t.co/gi0CKwZj8C">pic.twitter.com/gi0CKwZj8C</a></div>
β Audrey McLaren (@a_mcsquared) <a href="https://twitter.com/a_mcsquared/status/1065341899127644160?ref_src=twsrc%5Etfw">November 21, 2018</a></blockquote>
<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script><br />
<br />
<blockquote class="twitter-tweet" data-lang="en">
<div dir="ltr" lang="en">
Walking limits! <a href="https://twitter.com/hashtag/amtnys2018?src=hash&ref_src=twsrc%5Etfw">#amtnys2018</a> <a href="https://t.co/aqdjD2NlTB">pic.twitter.com/aqdjD2NlTB</a></div>
β Caitlyn Gironda (@Caitlyn_Gironda) <a href="https://twitter.com/Caitlyn_Gironda/status/1058794477731672066?ref_src=twsrc%5Etfw">November 3, 2018</a></blockquote>
<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script><br />
<br />
<blockquote class="twitter-tweet" data-lang="en">
<div dir="ltr" lang="en">
Algebra 2 Ss applying piecewise functions by creating a coloring book to send to elementary schools to show the amazing things you can do with math! We are interested in sending our book to multiple schools, so if you are interested lmk! <a href="https://twitter.com/hashtag/TMSLeaveATrail?src=hash&ref_src=twsrc%5Etfw">#TMSLeaveATrail</a> <a href="https://twitter.com/hashtag/ITeachMath?src=hash&ref_src=twsrc%5Etfw">#ITeachMath</a> <a href="https://t.co/Bejse3Njr4">pic.twitter.com/Bejse3Njr4</a></div>
β Sarah Plain (@mrs_plain_LCPS) <a href="https://twitter.com/mrs_plain_LCPS/status/1055289045461463041?ref_src=twsrc%5Etfw">October 25, 2018</a></blockquote>
<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script><br />
<br />
<br />
<br />
<br />Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-6720723193982423672018-11-24T20:36:00.000-06:002018-11-24T20:36:15.370-06:00My Struggles With Completing the SquareThis year I have been struggling with this quadratics unit. I feel as if there are no cohesive elements tying one concept from one to the other. The outline from this unit has been as follows:<br />
<br />
<style type="text/css"><!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--></style><br />
<table border="1" cellpadding="0" cellspacing="0" dir="ltr" style="border-collapse: collapse; border: none; font-family: arial,sans,sans-serif; font-size: 10pt; table-layout: fixed; width: 0px;" xmlns="http://www.w3.org/1999/xhtml"><colgroup><col width="66"></col><col width="53"></col><col width="50"></col><col width="325"></col></colgroup><tbody>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43410}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/6</td><td data-sheets-numberformat="[null,5,"m-d",1]" data-sheets-value="{"1":3,"3":43160}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">3-1</td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"Graphing Quadratic Functions"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">Graphing Quadratic Functions</td></tr>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43411}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/7</td><td data-sheets-numberformat="[null,5,"m-d",1]" data-sheets-value="{"1":3,"3":43160}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">3-1</td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"Graphing Quadratic Functions"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">Graphing Quadratic Functions</td></tr>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43412}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/8</td><td data-sheets-numberformat="[null,5,"m-d",1]" data-sheets-value="{"1":3,"3":43161}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">3-2</td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"Solving Quadratic Equations by Graphing"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">Solving Quadratic Equations by Graphing</td></tr>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43413}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/9</td><td data-sheets-numberformat="[null,5,"m-d",1]" data-sheets-value="{"1":3,"3":43163}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">3-4</td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"Solving Quadratic Equations by Factoring"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">Solving Quadratic Equations by Factoring</td></tr>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43416}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/12</td><td data-sheets-numberformat="[null,5,"m-d",1]" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom;"></td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"Review"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">Review</td></tr>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43417}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/13</td><td data-sheets-numberformat="[null,5,"m-d",1]" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom;"></td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"Quiz"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">Quiz</td></tr>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43418}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/14</td><td data-sheets-numberformat="[null,5,"m-d",1]" data-sheets-value="{"1":3,"3":43162}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">3-3</td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"Complex Numbers"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">Complex Numbers</td></tr>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43419}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/15</td><td data-sheets-numberformat="[null,5,"m-d",1]" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom;"></td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"Complex Numbers"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">Complex Numbers</td></tr>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43420}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/16</td><td data-sheets-numberformat="[null,5,"m-d",1]" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom;"></td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"Complex Numbers"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">Complex Numbers</td></tr>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43423}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/19</td><td data-sheets-numberformat="[null,5,"m-d",1]" data-sheets-value="{"1":3,"3":43164}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">3-5</td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"Solving Quadratic Equations by Completing the Square"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">Solving Quadratic Equations by Completing the Square</td></tr>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43424}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/20</td><td data-sheets-numberformat="[null,5,"m-d",1]" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom;"></td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"Solving Quadratic Equations by Completing the Square"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">Solving Quadratic Equations by Completing the Square</td></tr>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43430}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/26</td><td data-sheets-numberformat="[null,5,"m-d",1]" data-sheets-value="{"1":3,"3":43165}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">3-6</td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"The Quadratic Formula and the Discriminant"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">The Quadratic Formula and the Discriminant</td></tr>
<tr style="height: 21px;"><td data-sheets-numberformat="[null,5,"m/d",1]" data-sheets-value="{"1":3,"3":43431}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">11/27</td><td data-sheets-numberformat="[null,5,"m-d",1]" data-sheets-value="{"1":3,"3":43165}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">3-6</td><td data-sheets-value="{"1":3,"3":1}" style="overflow: hidden; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="{"1":2,"2":"The Quadratic Formula and the Discriminant"}" style="overflow: hidden; padding: 2px 3px 2px 3px; vertical-align: bottom; white-space: clip; wrap-strategy: 3;">The Quadratic Formula and the Discriminant</td></tr>
</tbody></table>
<br />
<div>
With 35 minute periods I have been trying to include different strategies, but overall I want them to know that by completing the square we are finding vertex form of a standard form of a parabola. </div>
<div>
<br /></div>
<div>
I had students use a visual model of completing the square with algebra tiles from Bob Lochel's site: <a href="https://mathcoachblog.com/2017/06/05/area-models-and-completing-the-square/" target="_blank">https://mathcoachblog.com/2017/06/05/area-models-and-completing-the-square/</a></div>
<div>
<br /></div>
<div>
They came away from this with the idea that they are actually trying to fill out a square. The next day I borrowed Julie Morgan's ideas and used this tweet.</div>
<div>
<br /></div>
<div>
<br /></div>
<blockquote class="twitter-tweet" data-lang="en">
<div dir="ltr" lang="en">
New blog post: The week that was (no. 12) <a href="https://t.co/KwGqjpdOym">https://t.co/KwGqjpdOym</a> with shout outs to <a href="https://twitter.com/ChrisMcGrane84?ref_src=twsrc%5Etfw">@ChrisMcGrane84</a> and <a href="https://twitter.com/mpcopland?ref_src=twsrc%5Etfw">@mpcopland</a> <a href="https://twitter.com/hashtag/mtbos?src=hash&ref_src=twsrc%5Etfw">#mtbos</a> <a href="https://twitter.com/hashtag/mathschat?src=hash&ref_src=twsrc%5Etfw">#mathschat</a> <a href="https://twitter.com/hashtag/iteachmath?src=hash&ref_src=twsrc%5Etfw">#iteachmath</a></div>
β Julie Morgan (@fractionfanatic) <a href="https://twitter.com/fractionfanatic/status/1063841592090525697?ref_src=twsrc%5Etfw">November 17, 2018</a></blockquote>
<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script><br />
<br />
I felt like it tied it more directly to properties of a parabola, but I feel like I need a better way to assess what they really know about parabolas.<br />
<br />
I think I am going to use Nat Banting's post about writing everything they know about a specific parabola and print out each one for groups or partners to discuss.<br />
<br />
<blockquote class="twitter-tweet" data-lang="en">
<div dir="ltr" lang="en">
Today I showed this image and asked my class to βtell me everything you know about this graph and/or the function that generated this graph.β<br /><br />They were very annoyed when I said I couldnβt zoom out.<br /><br />βI just canβt deal with full Banting this earlyβ <a href="https://twitter.com/hashtag/MTBoS?src=hash&ref_src=twsrc%5Etfw">#MTBoS</a> <a href="https://t.co/nTwgeTlh2W">pic.twitter.com/nTwgeTlh2W</a></div>
β Nat Banting (@NatBanting) <a href="https://twitter.com/NatBanting/status/1065397307481440256?ref_src=twsrc%5Etfw">November 22, 2018</a></blockquote>
<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script><br />
I need to find a better way to teach this where I am developing conceptual and procedural understanding evenly. If you have any thoughts let me know.Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-7934627912977505522018-09-03T15:43:00.000-05:002018-09-03T15:43:21.422-05:00A Flavorful Application of Mean, Median, Mode<a href="https://mail.google.com/mail/u/1?ui=2&ik=b3ca436179&attid=0.1&permmsgid=msg-f:1610620103307009650&th=165a127355b79e72&view=fimg&disp=thd&attbid=ANGjdJ9TDH6f563cov0K8ttzZr-leaCvolJuEIV4O8vFQ06sSTShao4OFjXI7lw-kdll03tK_NLnI5Qget2D8wI1JulIsLZ48sY9RSd6ULZs2aFLW2qfnQS4voPfy0Y&ats=2524608000000&sz=w683-h647" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Displaying IMG_4066.jpg" aria-hidden="true" border="0" class="aLF-aPX-J1-J3" height="400" src="https://mail.google.com/mail/u/1?ui=2&ik=b3ca436179&attid=0.1&permmsgid=msg-f:1610620103307009650&th=165a127355b79e72&view=fimg&disp=thd&attbid=ANGjdJ9TDH6f563cov0K8ttzZr-leaCvolJuEIV4O8vFQ06sSTShao4OFjXI7lw-kdll03tK_NLnI5Qget2D8wI1JulIsLZ48sY9RSd6ULZs2aFLW2qfnQS4voPfy0Y&ats=2524608000000&sz=w683-h647" width="299" /></a>I was looking for a different way for students to apply their knowledge of mean, median, and mode in Algebra 1. I wanted some application where they can use mean, median, and more in a different context. <br />
<br />
I found this article a couple of months ago and found it really interesting.<br />
<br />
<a href="https://qz.com/918008/the-color-distribution-of-mms-as-determined-by-a-phd-in-statistics/" target="_blank">https://qz.com/918008/the-color-distribution-of-mms-as-determined-by-a-phd-in-statistics/</a><br />
<br />
I had students read this article and groups and come up with what they noticed/wondered about the article. I asked the students if I gave them a pack of M&M's what they would be to extrapolate from the pack. They said they needed to know the total M&M's in the package to determine the location where they were made and the color breakdown inside each one.<br />
<br />
Each group of students were given a package of M&M's and had to count how many of each color they had.<br />
<br />
Then we put all of our data on the board. Students had to come up with the mean, median, and mode for each color and had to decide which of the data sets to use if they had an outlier or not.<br />
<br />
<img alt="Displaying IMG_4067.jpg" aria-hidden="true" class="aLF-aPX-J1-J3" src="https://mail.google.com/mail/u/1?ui=2&ik=b3ca436179&attid=0.3&permmsgid=msg-f:1610620103307009650&th=165a127355b79e72&view=fimg&disp=thd&attbid=ANGjdJ-JIR9RgKIUbf5Kl7pxYMsXexBhpIlgl0VuuKraqLc70-LA_2c4-aas1hy8540V6WDNgxT30VQjQep6sHXU6LptEStlLGKsDM3Mza1PcGYWZjTIrOrpcwA3Tr8&ats=2524608000000&sz=w683-h647" /><br />
<br />
They had to look back at their data and examine which factory their set of M&M's came from. We also talked about what might be different from their graphs to ours and how you might be able to tell the difference between each plant.<br />
<br />
This was a great activity for students, they were excited because they got to share and eat their M&M's when they were done.<br />
Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com1tag:blogger.com,1999:blog-8643194467190728551.post-54443234456255108932018-08-12T17:16:00.000-05:002018-08-12T17:16:07.518-05:003 Act Task: Bacteria Growth<h2>
Act 1:</h2>
<div style="text-align: center;">
<span style="text-align: start;">How many bacteria are there in 300 minutes?</span></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dx92hwtnRkhYIMcP-ELUVWeSlQyTQDg917POJQ9PMIDiDASxEu0hVqPmlNXnkz2PDVhScPWMBscRQ44LDztWQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
<h2>
Act 2:</h2>
<br />
<ul>
<li>Pause the video at 0:00 time frame. There is 1 bacteria at 0 minutes.</li>
</ul>
<br />
<br />
<ul>
<li>Pause the video again at 0:01 time frame, when there is 2 bacteria at 38 minutes.</li>
</ul>
<br />
<br />
<ul>
<li>Pause the video again at 0:04 time frame, when there is 4 bacteria at 88 minutes.</li>
</ul>
<br />
<br />
<ul>
<li>Lastly, pause or show a screen shot at 0:05 time frame, when there is 8 bacteria at 114 minutes.</li>
</ul>
<br />
<h2>
Act 3:</h2>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG6D1XjPUfmJFEdIZdbzCQUA0zOZnIoRnFyxrVvu8W4ek4HwhUfdfkKgjthh58Lm5v5_mwRhE-01LY37P9NyRevxamQRnMw71l-iviQ18scpXc06vyJ8K1v-dV_8MBEfsk1f44zwJr5pn9/s1600/Screen+Shot+2018-08-12+at+5.09.37+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="509" data-original-width="535" height="378" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG6D1XjPUfmJFEdIZdbzCQUA0zOZnIoRnFyxrVvu8W4ek4HwhUfdfkKgjthh58Lm5v5_mwRhE-01LY37P9NyRevxamQRnMw71l-iviQ18scpXc06vyJ8K1v-dV_8MBEfsk1f44zwJr5pn9/s400/Screen+Shot+2018-08-12+at+5.09.37+PM.png" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
There are a total of 471 bacteria in 300 minutes.</div>
<h2 style="clear: both; text-align: left;">
Extensions:</h2>
<div class="separator" style="clear: both; text-align: left;">
</div>
<ul>
<li>When does the number of minutes and bacteria the same?</li>
<li>How many bacteria would there be in 500 minutes?</li>
<li>When will there be 1,000,000 bacteria?</li>
<li>How else could we represent this information?</li>
</ul>
<br />
<br />
<br />Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-5827529558713648842018-07-25T18:42:00.000-05:002018-07-25T18:42:22.678-05:00My #1TMCThing<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhs5wQ4vklGid0ErGRbEbg18JJU4KYVHIiYPFcn2Kbi46Y2lsRPAxs8S_6wTVkec4-MaBMsdEu1u8MM298dECwVc4sOKFT9XBFZuX04YUciyP5of1JFhBwEB3SJ8msWbsHFTsEStjDZDAK/s1600/IMG_4002.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="682" data-original-width="1600" height="272" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhs5wQ4vklGid0ErGRbEbg18JJU4KYVHIiYPFcn2Kbi46Y2lsRPAxs8S_6wTVkec4-MaBMsdEu1u8MM298dECwVc4sOKFT9XBFZuX04YUciyP5of1JFhBwEB3SJ8msWbsHFTsEStjDZDAK/s640/IMG_4002.jpg" width="640" /></a></div>
<br />
I've been going back and forth on what my takeaways from the conference were, because every session I went to felt like I took something away. I have been going to quite a few different conferences mostly around the state of Nebraska and went to ISTE last year in San Antonio and felt like I haven't taken away anything in a long time. Since I have to narrow it down I will talk about two big takeaways I felt permeated through my TMC experience.<br />
<br />
1. Using equity and social justice as a way of teaching mathematics. <a href="https://twitter.com/DingleTeach" target="_blank">Marian Dingle</a> and <a href="https://twitter.com/wmukluk" target="_blank">Wendy Menard</a> took us on a path of self discovery and identity to teach students better. Using social justice standards to help frame lessons and discussions to help build classroom activities. The last day we split into small groups and the group I was apart of focused on ideas for classroom activities that promoted social justice, some of the notes taken from that are <a href="https://docs.google.com/document/d/16H7ea_L2T9H6x8uTMdGGRF98_u4DpAN_eJzPWJzWAGk/edit?usp=sharing" target="_blank">here</a>.<br />
<br />
This is a conversation that I have wanted to have with others in my building for four long years. Are we doing what is best for all students? What practices and approaches can we take to include all students? This is a discussion I want to keep having, especially with others in my state.<br />
<br />
Also I want to thank Dr. Robert Berry for being there and representing NCTM, I haven't been a member for three years now, but seeing him there shows the trajectory that I think NCTM will go and I think it is a place that all teachers should evaluate. I will definitely be renewing my membership to NCTM.<br />
<br />
<img height="480" src="https://pbs.twimg.com/media/DirDPZgW0AAEsdi.jpg" width="640" /><br />
<br />
2. My second thing that I took away from TMC was how incredibly nice everyone is. When I showed up that first day early to register I was given my badge and a button to wear that said, "FIRST!" and since I showed up early I thought to myself that this might be a badge of shame, that this would have been my first time there. However, wearing that badge the first day other people came up to me and made connections with me. For one of the first times in the #mtbos community I felt like I belonged, all because of a simple badge.<br />
<br />
I would love to go to #TMC19 in Berkeley, but others deserve a chance to go and I will wait till it makes its way back to the Midwest to go again.Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-11058492100600190282018-07-15T08:00:00.000-05:002018-07-15T08:00:14.132-05:00Reflection: Representations of RelationsThe one thing I am really nervous about when starting this new school year is the bell schedule, 35 minutes for one period. What can I get done in 35 minutes? Can I get a Desmos activity done in 35 minutes? Could we do a class project in 35 minutes? I feel like I will be cutting out important discussions or big "ah-ha" moments with less time.<br />
<br />
So I went back to thinking about when I start the second day of class with mathematics, I want there to be context in what the students see and do in math. In my last <a href="http://new-to-teaching.blogspot.com/2018/06/representations-of-relations.html" target="_blank">post</a> about Representations of Relations I received this comment:<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuNYY6i_Lnij3mwJHO9XUZOymKPO6-7cP9w1rvVjxrgHf2Bd8EjJd_yT87xBVZltS1NjNF3afypfDWukgzNaSIs9kBzlUnuK6WztWwWCi2tKQqnTyAGrzgRxab9gY11Hmp0nBc1FGkxY6S/s1600/Screenshot+2018-07-14+at+10.52.43+PM.png" imageanchor="1"><img border="0" height="145" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuNYY6i_Lnij3mwJHO9XUZOymKPO6-7cP9w1rvVjxrgHf2Bd8EjJd_yT87xBVZltS1NjNF3afypfDWukgzNaSIs9kBzlUnuK6WztWwWCi2tKQqnTyAGrzgRxab9gY11Hmp0nBc1FGkxY6S/s640/Screenshot+2018-07-14+at+10.52.43+PM.png" width="640" /></a><br />
<br />
They changed the focus of that first lesson to make the rest of the year one cohesive goal.<br />
<br />
<img alt="Image result for gif that's what i want" class="rg_ic rg_i" id="gHsnioPoErg3oM:" jsaction="load:str.tbn" src="data:image/jpeg;base64,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" style="height: 200px; margin-left: -5px; margin-right: -4px; margin-top: 0px; width: 245px;" /><br />
<br />
As part of the curriculum group for Advanced Algebra, we set the pacing guide and decided that representations of relations along with the distributive property should be taught first. One thing I want to get across to students that first week is everyone having their voices heard and problem solving.<br />
<br />
So each wall of the classroom will have the same layout from the previous post,<br />
<br />
<ul>
<li>one wall will have ordered pair along with a piece of butcher paper with notice/wonder at the top. </li>
<li>second wall will have a mapping with a different piece of butcher paper with notice/wonder.</li>
<li>third wall will have a table with butcher paper labeled the same way.</li>
<li>fourth wall will have the New York Times graph and butcher paper.</li>
</ul>
<div>
I want to have students stand (and gather by the board) and take 1 minute to look and 2 minutes to discuss with a partner what they see. I will ask what students notice first, then wonder. At the end I want them to discuss what was similar or different with the four different relations.</div>
<div>
<br /></div>
<div>
I still have to cover distributive property at the end, but as an exit ticket I want them to reflect on the experience and answer the following question:</div>
<blockquote class="tr_bq">
Why did the New York Times select a graph to represent this relation? </blockquote>
I want a connection more to relations, what question should I ask that encompasses what they learned and that representing functions is useful?<br />
<div>
<br /></div>
Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-61328263015665286922018-06-30T08:00:00.000-05:002018-06-30T08:00:07.511-05:00Representations of RelationsThis is going to be my fifth year teaching Algebra 2, this year I am changing schools so it will be called Advanced Algebra. I was doing some curriculum writing with my new team of teachers and the first section we are going to cover as a class is Representing Relations my first reaction was...<br />
<br />
<img alt="Image result for why gif" class="rg_ic rg_i" height="476" id="onwYPy-VEOeEMM:" jsaction="load:str.tbn" src="https://media.giphy.com/media/lYKvaJ8EQTzCU/giphy.gif" style="height: 187px; margin-left: -5px; margin-right: -4px; margin-top: 0px; width: 251px;" width="640" /><br />
<br />
At this point with just coming back to school students may not remember what relations are, what functions are, or domain and range.<br />
<br />
I thought back to <a href="https://youtu.be/NWUFjb8w9Ps" target="_blank">Dan Meyer's talk</a> of headaches and aspirin and why do students need to know there are different ways to represent relations: ordered pairs, tables, graphs, and mapping.<br />
<br />
I took the second graph from New York Times: <a href="https://www.nytimes.com/2018/03/08/learning/whats-going-on-in-this-graph-march-13-2018.html" target="_blank">What's Going on in this Graph? </a> and re-organized the information differently.<br />
<u><br />
</u> <u>Give the students the following information:</u><br />
This data is organized from by: <i>country</i> (guns per 100 people , mass shooters per 100 million people).<br />
United States (85, 28)<br />
Canada (26, 9)<br />
Afghanistan (2, 20)<br />
Iraq (37, 4)<br />
France (35, 15)<br />
Yemen (55, 40)<br />
<br />
Ask the students what they notice? what do they wonder? As the teacher write down everything they say. One question I have is what is the data saying? Is there a different way to represent the data?<br />
<br />
Give the students the following information:<br />
<br />
<iframe src="https://docs.google.com/spreadsheets/d/e/2PACX-1vTFRuTwV3xlTdjH-gOCzYfvd7_o63dPhLsYQSh7CO2PjzZSGY6b6wUpb2rCrPer-DC17monl_aG3202/pubhtml?widget=true&headers=false"></iframe><br />
<br />
What do they notice and wonder now? What has changed? You can show them mapping as well, but eventually you will need to introduce other things, but the last one is the graph from The New York Times.<br />
<br />
<br />
<img alt="" class="css-1m50asq" itemid="https://static01.nyt.com/images/2018/03/06/learning/WGOITG03-13-18LN2/WGOITG03-13-18LN2-articleLarge.png?quality=75&auto=webp&disable=upscale" itemprop="url" sizes="((min-width: 600px) and (max-width: 1004px)) 84vw, (min-width: 1005px) 60vw, 100vw" src="https://static01.nyt.com/images/2018/03/06/learning/WGOITG03-13-18LN2/WGOITG03-13-18LN2-articleLarge.png?quality=75&auto=webp&disable=upscale" srcset="https://static01.nyt.com/images/2018/03/06/learning/WGOITG03-13-18LN2/WGOITG03-13-18LN2-articleLarge.png?quality=90&auto=webp 600w,https://static01.nyt.com/images/2018/03/06/learning/WGOITG03-13-18LN2/WGOITG03-13-18LN2-jumbo.png?quality=90&auto=webp 1024w,https://static01.nyt.com/images/2018/03/06/learning/WGOITG03-13-18LN2/WGOITG03-13-18LN2-superJumbo.png?quality=90&auto=webp 1259w" /><br />
<br />
How do the three representations differ, do they all tell the same story? Do some tell the story better? I'm not sure if this is the way to start the year out, but nothing is perfect. I want students to feel that there is some context to mathematics other than its day 1 therefore we do lesson 1.Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com2tag:blogger.com,1999:blog-8643194467190728551.post-38180713329348946822018-06-13T19:53:00.000-05:002018-06-13T19:53:34.642-05:00"The Grasshopper and the Ant" teach Exponents<h3>
<span style="color: orange;">What do you notice, what do you wonder when you see this image?</span></h3>
<a href="https://www.joslyn.org/collections-and-exhibitions/permanent-collections/european/jean-georges-vibert-the-grasshopper-and-the-ant/" target="_blank"><img height="465" src="https://www.joslyn.org/post/sections/56/Files/vibert_grass_ant(3).jpg" width="640" /></a><br />
<br />
It looks cold, how do you know which one is the ant? Which one is the grasshopper? Which one looks warmer? How do you think the discussion is going?<br />
<br />
<h3>
<span style="color: orange;">Next have the students <a href="https://en.wikisource.org/wiki/Fables_(La_Fontaine,_tr._Wright)/The_Grasshopper_and_the_Ant" target="_blank">read the fable</a> that is associated with it:</span></h3>
A Grasshopper gay Sang the summer away,<br />
And found herself poor By the winter's first roar.<br />
Of meat or of bread, Not a morsel she had!<br />
So a begging she went, To her neighbour the ant,<br />
For the loan of some wheat, Which would serve her to eat,<br />
Till the season came round. "I will pay you," she saith,<br />
"On an animal's faith, Double weight in the pound<br />
Ere the harvest be bound." The ant is a friend<br />
(And here she might mend) Little given to lend.<br />
"How spent you the summer?" Quoth she, looking shame<br />
At the borrowing dame. "Night and day to each comer<br />
I sang, if you please." "You sang! I'm at ease;<br />
For 'tis plain at a glance, Now, ma'am, you must dance."<br />
<h4>
What do you notice? What do you wonder now?</h4>
<div>
Where math comes in to play is the idea of where the grasshopper says, "I will pay you, she saith,</div>
On an animal's faith, Double weight in the ." When you can't afford something say, the full price of a car, how do you afford it? Most students will talk about saving money or a loan. If the grasshopper wants to survive, she wants a cut of the ants food savings and next season the grasshopper will give double back. Ask your students is this fair? Is this how a bank works?<br />
<br />
There is a way to calculate it mathematically, but right now I want students getting use to the idea of exponents. The equation I would have them use is the compound interest equation.<br />
<br />
A=P(1+r/n)^(nt)<br />
<br />
Where A is the amount<br />
P is the principle<br />
r is the interest rate<br />
n is the number of times it is compounded per year<br />
t is the time in years.<br />
<br />
I would have students think about what each of them means and how the rate effects how much the grasshopper would way in the long run.Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-67869341061764576352018-04-30T07:00:00.000-05:002018-04-30T07:00:04.230-05:00Ruth and the Taco CartI love Dan Meyer's Taco Cart if you have never heard of it, here is the task it is great it is wonderful.<br />
<br />
<a href="http://threeacts.mrmeyer.com/tacocart/" target="_blank">http://threeacts.mrmeyer.com/tacocart/</a><br />
<br />
We were recently doing this activity in Algebra 2, because I love how it uses the Pythagorean Theorem and one of my students asks, "what if you split the angle in half and walked that, because that is what I would do." I thought that would be a wonderful geometry question.<br />
<br />
<h3>
<u><span style="color: #b45f06;">Ruth and the Taco Cart</span></u></h3>
<div>
I posed this question to my geometry students, we weren't really learning about angle bisectors, but we had already learned it as well as trigonometry. It took them about 15 minutes to use pythagorean theorem and find the time it would take. However, Ruth was much more difficult.</div>
<div>
<br /></div>
<div>
After students completed the time section I asked what they needed to find the angle and the distance Ruth would have to go.</div>
<div>
<br /></div>
<div>
There were lots of good questions. I gave the rest of it as homework and only a few were able to do it completely.</div>
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiMpgypbPbRce52052Q63zZYk6jWosUj5iNU8af_MFDlm6bWW9XKFiIfSetgS5-HSv8UpDFc-3kR_W3CvVIizIdglwCfrwRrF2CYuC-9XoNKVyO0B-8zJIHGNx_Qy5QyvKPm4RCjCF7uww/s1600/Screen+Shot+2018-04-29+at+7.07.10+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="896" data-original-width="1600" height="357" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiMpgypbPbRce52052Q63zZYk6jWosUj5iNU8af_MFDlm6bWW9XKFiIfSetgS5-HSv8UpDFc-3kR_W3CvVIizIdglwCfrwRrF2CYuC-9XoNKVyO0B-8zJIHGNx_Qy5QyvKPm4RCjCF7uww/s640/Screen+Shot+2018-04-29+at+7.07.10+PM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
For students that did the work, I had them work in a group and work on a couple of extension problems:</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
</div>
<ul>
<li>If Ruth didn't want to talk alone, how long would she have to wait for the other to catch up?</li>
<li>What if she took a different angle?</li>
<li>Does changing the angle effect the time it takes for her to get to her destination?</li>
</ul>
<div>
The other students continued to work on the problem and were given some of these extension problems as they got the answer.</div>
<div>
<br /></div>
<div>
I loved the use of geometry, I will definitely use this when we are learning trigonometry.</div>
<br />
<div>
<br /></div>
Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com4tag:blogger.com,1999:blog-8643194467190728551.post-56030437525602728032018-03-31T08:00:00.000-05:002018-03-31T08:00:09.040-05:003 ACT Task: Beat The Freeze: Circumference<blockquote class="twitter-video" data-lang="en">
<div dir="ltr" lang="en">
Midseason form πβοΈ <a href="https://t.co/1i9N8ykeDf">pic.twitter.com/1i9N8ykeDf</a></div>
β The Freeze (@BeatTheFreeze) <a href="https://twitter.com/BeatTheFreeze/status/979478403614232581?ref_src=twsrc%5Etfw">March 29, 2018</a></blockquote>
<script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script><br />
<br />
<span style="color: #b45f06;"><span style="font-size: large;">The Situation:</span> </span><br />
During Atlanta Braves games, one fan has a chance to race "The Freeze." Who is the first to reach the end?<br />
<br />
<br />
<div>
<span style="color: #b45f06; font-size: large;">Act 1: First 10 Second of the Video:</span></div>
<div>
<br /></div>
<div>
The video shows the contestant running the warning track in the outfield. It shows the lead the contestant has over "The Freeze."</div>
<div>
<br /></div>
<div>
Have the students discuss who they think will win.</div>
<div>
<br /></div>
<div>
How can we prove who will win or lose? What would we have to know in order to solve this problem? Are there properties of a baseball field that we need to know before beginning?</div>
<div>
<br /></div>
<div>
<span style="color: #b45f06; font-size: large;">Act 2:</span></div>
<div>
At the beginning of the video it shows the distance to the left field wall. The distance to the right field wall is 325. You can use 335 or round to 330. </div>
<div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUBDrrX_snFSXpl0Im21iAEay6rGDq3ZcuECHHQpUKGnd6ciuPuddII8SruzAJCdYoupQTcgoQGPpVgjcqzxV6EhPbnJeHunBl3AMaEk5B3ZpOsdKJLUtmQ5T6-fobxpkkRt91r-G2rP65/s1600/Screen+Shot+2018-03-30+at+11.06.02+PM.png" imageanchor="1"><img border="0" height="141" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUBDrrX_snFSXpl0Im21iAEay6rGDq3ZcuECHHQpUKGnd6ciuPuddII8SruzAJCdYoupQTcgoQGPpVgjcqzxV6EhPbnJeHunBl3AMaEk5B3ZpOsdKJLUtmQ5T6-fobxpkkRt91r-G2rP65/s320/Screen+Shot+2018-03-30+at+11.06.02+PM.png" width="320" /></a></div>
<div>
<br /></div>
<div>
The Freeze runs at 22.5 ft/sec</div>
<div>
The contestant runs at 19.1 ft/sec</div>
<div>
<br /></div>
<div>
The contestant is given an 70 foot head start.</div>
<div>
<br /></div>
<div>
<span style="color: #b45f06; font-size: large;">Act 3: </span></div>
<div>
Show the full video. </div>
<div>
<br /></div>
<div>
<span style="color: #b45f06; font-size: large;">Extension Questions:</span></div>
<div>
How long can The Freeze wait and still win?</div>
<div>
What if the rates changed at the midway point?</div>
<div>
What is the biggest lead you could give the fan and win?</div>
<div>
If you were the contestant what strategy might you use to win?</div>
<div>
<br /></div>
<div>
<br /></div>
<div>
<br /></div>
Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-82245504517777967862018-03-19T15:45:00.000-05:002018-03-19T15:45:01.777-05:00Peer Teaching with ELL StudentsI have been teaching one student who is an English language learner who came to me at semester how to add and subtract proper fractions for the past three days. Everyday they come in I feel like I am starting from square one each day. I tried teaching by one example at a time, didn't work. I tried teaching using visuals like fraction circles and bars, that failed. The student was getting more and more frustrated, because they weren't moving forward.<br />
<br />
I tried a different way. The other students in my class are to graphing linear inequalities. A majority of students in this class speak limited English and/or struggle with mathematics. One of the students finished early and I asked them to help this student.<br />
<br />
This was their discussion back in forth in Spanish. It was a great way for both students to move forward mathematically and feel confident going forward.<br />
<br />
Link to conversation in Spanish: <a href="https://chirb.it/ntn5mD" target="_blank">https://chirb.it/ntn5mD</a> . The sound byte is a minute and a half of the whole conversation which took about 5 minutes. <br />
<br />
The girl in the audio does an excellent job of breaking down the problem and used fraction bars to represent the fractions in the problem. You can hear her counting out the fraction bar in the first part of the audio, eventually she moves towards release of instruction where they did a problem together, then she watched as the student did one guiding through the entire process.<br />
<br />
I need to find ways of incorporating more peer teaching for my other students, I wonder how I can help guide them through the steps of asking questions and dialogue between each other better?Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-68945220094496150442018-03-06T17:30:00.000-06:002018-03-06T17:30:04.684-06:00Orthographic Projection with Merge Cube<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiy360pyx2VOER-M22S0ritNPvHRHap9uTnfvciL3Q7x4SKXivDOf_-JAwwto0wYyboV9idLw-O8i1Wmy-G4NmqCKZR8i2tK2UBxDM1TEThyVjpry1TeCxj_9Tm25Bxww971cEYHgyRq3Wn/s1600/Screen+Shot+2018-03-06+at+5.01.50+PM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiy360pyx2VOER-M22S0ritNPvHRHap9uTnfvciL3Q7x4SKXivDOf_-JAwwto0wYyboV9idLw-O8i1Wmy-G4NmqCKZR8i2tK2UBxDM1TEThyVjpry1TeCxj_9Tm25Bxww971cEYHgyRq3Wn/s200/Screen+Shot+2018-03-06+at+5.01.50+PM.png" width="195" /></a>Merge Cube has been a hit with stores like Walmart offering the simple flexible cubes for a dollar a piece. Merge cube is a simple way to get students using augmented reality in a QR code way. Students scan the Merge Cube with an app and a magical world appears.<br />
<br />
One of my favorite apps using the Merge Cube is <a href="https://itunes.apple.com/us/app/dig-for-merge-cube/id1253083884?platform=ipad&preserveScrollPosition=true#platform/ipad" target="_blank">Dig!</a><br />
<br />
Using the app changes a simple cube with a bunch of symbols looking like hieroglyphics into another world. You can build and deconstruct the cube that looks almost exactly like Minecraft. The reason I like this app the most is that students can build using the app.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjy_KeHifYI87blHaZ3P4dr6MGCqL87-D2iyvMqaI8nJIR6-dE0sxs7-OSCnbvkxfpU80sth_KgQp2PSIM6yvyk6EwWfW4JtKHSpqGs-9sxRPwa_Alm2jD0pYAnoU_9A-wiPRB-cdqxXj7O/s1600/IMG_0730.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="346" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjy_KeHifYI87blHaZ3P4dr6MGCqL87-D2iyvMqaI8nJIR6-dE0sxs7-OSCnbvkxfpU80sth_KgQp2PSIM6yvyk6EwWfW4JtKHSpqGs-9sxRPwa_Alm2jD0pYAnoU_9A-wiPRB-cdqxXj7O/s400/IMG_0730.jpg" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
My students at the beginning of the year struggle with this concept of orthographic projection and being able to correctly sketch the block layout. Having students use the Merge Cube students can grasp that conceptual understanding that they don't get from a sketch. Last year I borrowed some of the wooden blocks our construction teacher uses and it was a great way for some of the students to see the finished product. The app allows students to see around each object looking at it from the sides and from the top.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
What I would like to see is have students create their own and have stations at each group where students correctly draw the orthographic projection of their groups creation. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt2otDOkFoRnT0lIShgljPMWLr8LoG1x69Wg8YYnJmFVkKIWfkwD0N3iasgjeVO0Y_zJBgFru-dr9xnacrZLRPFj_08isU2RumfflZ7yBE7VbeUTginQRVJmeZeeoHBs3_sc2NpkJ2yUzH/s1600/IMG_0731.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="280" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt2otDOkFoRnT0lIShgljPMWLr8LoG1x69Wg8YYnJmFVkKIWfkwD0N3iasgjeVO0Y_zJBgFru-dr9xnacrZLRPFj_08isU2RumfflZ7yBE7VbeUTginQRVJmeZeeoHBs3_sc2NpkJ2yUzH/s320/IMG_0731.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;">
<span style="background-color: yellow;">TIP: </span>If you can't get a Merge Cube for each student, there is a shortcut. I printed a picture of one side of the Merge Cube and you can't rotate it like a Merge Cube showing each side, but students can use that one side to create especially using the Dig! app.</div>
<br />Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-64003310074407433882017-12-01T05:00:00.000-06:002017-12-01T05:00:09.958-06:00Graphing Polynomials Using Vases ππΊPolynomials is one of the hardest sections to teach, over the past four years I have acquired different handouts, activities, lessons, and tasks for Algebra 2 students and almost no material for the section on polynomials. Adding, subtracting, multiplying, and dividing polynomials always seemed like an algebraic process and not so much visual or hands on.<br />
<br />
Now I have one activity!!! Graphing polynomials was always tricky, but teaching quadratics before made it seem like a piece of cake for them. One of my favorites is graphing polynomials using vases, yes vases.<br />
<br />
So to preface this I with I spent a week searching all the Goodwills in the Omaha metro area for different vases and this is basically what I found when you take all of the repeats out.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFmaorvIOpOLsY-fPY2TCOlz78oOx7ikgHDwghBQJyqfbXNHQ5kmTg77Ocr9tDv79YFii-MIE8nrh_EH1tYI_5C_J1xh3m4cbc41xcNFN2Y35eCLHWSINSVWeuMbxWpThEd4REQBFhS2bE/s1600/IMG_6272.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="481" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFmaorvIOpOLsY-fPY2TCOlz78oOx7ikgHDwghBQJyqfbXNHQ5kmTg77Ocr9tDv79YFii-MIE8nrh_EH1tYI_5C_J1xh3m4cbc41xcNFN2Y35eCLHWSINSVWeuMbxWpThEd4REQBFhS2bE/s640/IMG_6272.JPG" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
I did replace the big one in the middle and the one on the far right, well you can tell why.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The way I set this up is I provided each group a vis-a-vis marker, ruler, set of measuring cups, and a vase. Students were given the following directions:</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
1. they needed to mark off every inch on the outside of the glass </div>
<div class="separator" style="clear: both; text-align: left;">
2. make a table for how many mL in every inch.</div>
<div class="separator" style="clear: both; text-align: left;">
3. Put the table into Desmos</div>
<div class="separator" style="clear: both; text-align: left;">
4. Find the line of best fit on Desmos (I gave them the different equations)</div>
<div class="separator" style="clear: both; text-align: left;">
5. Look at the R squared value to find which one is best.</div>
<div class="separator" style="clear: both; text-align: left;">
6. Present your vase to the class the following day.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
I had students present from their iPads, but having them create a poster would have been better so they could compare and contrast the vase with the graph to identify key attributes.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
What is even better the day before the students presented they practiced with a <a href="https://teacher.desmos.com/waterline" target="_blank">Desmos activity</a>. At the end of the activity students had to create their own vase and graph.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgScSXacCtBFlchBnU2C7j6TqMIqVUxkxsCjUyKp3Fgpdc41_R0yhXZPQLYeosG47f9zUoIfbKb_qTN3hA4xS0lKiTwU3vH7sGfnxvQ_kMd4RfEYFFJqKEfDs4gkACHB_mpa2FkKu-MU13f/s1600/Screen+Shot+2017-11-25+at+8.35.06+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="914" data-original-width="1532" height="381" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgScSXacCtBFlchBnU2C7j6TqMIqVUxkxsCjUyKp3Fgpdc41_R0yhXZPQLYeosG47f9zUoIfbKb_qTN3hA4xS0lKiTwU3vH7sGfnxvQ_kMd4RfEYFFJqKEfDs4gkACHB_mpa2FkKu-MU13f/s640/Screen+Shot+2017-11-25+at+8.35.06+PM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRlaMPeBRUexQHVRU92umtD8FTJ5HBNpgujF-5HLpiKFB-EPMpLG0sv9mc9fxgcfp_WgSFZYAwX1d4Pstqev11CQagZf0_eE-_rBDVLYmuLF61IXIXXLvn-KTAlNhr98lvz15aRWIZqtij/s1600/Screen+Shot+2017-11-25+at+8.34.54+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1040" data-original-width="1472" height="453" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRlaMPeBRUexQHVRU92umtD8FTJ5HBNpgujF-5HLpiKFB-EPMpLG0sv9mc9fxgcfp_WgSFZYAwX1d4Pstqev11CQagZf0_eE-_rBDVLYmuLF61IXIXXLvn-KTAlNhr98lvz15aRWIZqtij/s640/Screen+Shot+2017-11-25+at+8.34.54+PM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
Below are some photos of my students working on their vase.</div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg50NuHacYCikuYVGZ8Vk-dZu9cAEsv5U9Jgg0FXrbRxKQpJIbGcEdjaX5foL-umJ-XTO2YCOHRQhc3DJjGDnjY4AdI7TtFfikEqIpndn5Ihoj85zKjZl9mJQST5Bea8bZMrZnvc82xLCKl/s1600/IMG_2367.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1095" data-original-width="1600" height="435" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg50NuHacYCikuYVGZ8Vk-dZu9cAEsv5U9Jgg0FXrbRxKQpJIbGcEdjaX5foL-umJ-XTO2YCOHRQhc3DJjGDnjY4AdI7TtFfikEqIpndn5Ihoj85zKjZl9mJQST5Bea8bZMrZnvc82xLCKl/s640/IMG_2367.JPG" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMXc0ZKqm8uFQCyobEwlWlADWGyG73wmayQ0yM7jpcoIzCe4Pw3h6ROhHts9XS8Yd4JhnBZ74dRKCW0mT1MQGDxCVYqc4dFzTFUoAt28BUp7jablOuzYWKJWaslgVOqrnC3FVyo3ftmMc8/s1600/IMG_4291.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="991" data-original-width="1600" height="397" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMXc0ZKqm8uFQCyobEwlWlADWGyG73wmayQ0yM7jpcoIzCe4Pw3h6ROhHts9XS8Yd4JhnBZ74dRKCW0mT1MQGDxCVYqc4dFzTFUoAt28BUp7jablOuzYWKJWaslgVOqrnC3FVyo3ftmMc8/s640/IMG_4291.JPG" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTdrWMdhpnxAxrOh7GqsJydvDAZFo80s9tvVpLlU2sFZKI9nzowYBYRL0jgkkYv2AVzlc9s3KA1u2N2qGnjM_QdAF3xPMOeAQWKKq5oQsMPY6d8ATM1soa67MfEePJZGn07ZGa2xjhg-14/s1600/IMG_4746.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="481" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTdrWMdhpnxAxrOh7GqsJydvDAZFo80s9tvVpLlU2sFZKI9nzowYBYRL0jgkkYv2AVzlc9s3KA1u2N2qGnjM_QdAF3xPMOeAQWKKq5oQsMPY6d8ATM1soa67MfEePJZGn07ZGa2xjhg-14/s640/IMG_4746.JPG" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<br />Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-90253245539863774002017-11-30T05:00:00.000-06:002018-01-11T15:58:16.087-06:00Transversal Tag πOne of my favorite geometry activities I did this year was Transversal Tag. I set up the gym so it had the pattern of a transversal, like the picture below:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4T3rnKw0gV-c5xM11jrNMe4j6uTH65khugsYf1ve0LUS_IwwL13mjuUF02C64a2mu1rn7zSYsXsFRIH4cff26KrMRYBQzztNaPdKJCsqsseB5A8b_pGKrSpyurYtQkXmKrGUvnR9_GMSY/s1600/Two_parallel_lines_being_crossed_by_a_third_line.svg.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="763" height="313" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4T3rnKw0gV-c5xM11jrNMe4j6uTH65khugsYf1ve0LUS_IwwL13mjuUF02C64a2mu1rn7zSYsXsFRIH4cff26KrMRYBQzztNaPdKJCsqsseB5A8b_pGKrSpyurYtQkXmKrGUvnR9_GMSY/s400/Two_parallel_lines_being_crossed_by_a_third_line.svg.png" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Students were randomly assigned a number 1-8 and then a tagger was randomly chosen. I am sure this game would have been much better to play with 3-4 taggers and play freeze tag, but we played that if you were tagged you became a tagger as well. Also if you went to the wrong area you could be tagged and become a tagger as well.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The taggers had to decide which angle congruency to say to get the most amount of people. For example, a favorite to choose was alternate exterior angles, because half of them had to run to the other side of the gym. The taggers also had to be smart about choosing ones where the runner will be going. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Especially closer to the end of the game the taggers had to come together to talk about which one would move the most amount of people and get a specific person out.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Students used the following:</div>
<div class="separator" style="clear: both; text-align: left;">
Alternate Exterior</div>
<div class="separator" style="clear: both; text-align: left;">
Alternate Interior</div>
<div class="separator" style="clear: both; text-align: left;">
Corresponding</div>
<div class="separator" style="clear: both; text-align: left;">
Consecutive Interior</div>
<div class="separator" style="clear: both; text-align: left;">
Vertical</div>
<div class="separator" style="clear: both; text-align: left;">
Linear Pair</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
It was a quick fun game that would have lasted longer if it was freeze tag, but the students had fun, used vocabulary, and had fun running around the gym for 20 minutes instead of being in class.</div>
<br />Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-31548914231820923602017-11-28T05:00:00.000-06:002017-11-28T05:00:43.037-06:00Head's Up: Review Game π£οΈ<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg0jAz1y-1bfvIPHDz3aBW1MjuK3GgY1zRftgs_0KOs0ch-9VvPwZEs3yGSYE0TmxY6fv99QeHNX8L_UF_AM2hjJwwPah5ZRfYeKqKeF1kF7AKGc5SelBdT2LACSlvNNBKi9klvBLiQEgq/s1600/Screen+Shot+2017-11-25+at+5.45.48+PM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="383" data-original-width="386" height="316" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg0jAz1y-1bfvIPHDz3aBW1MjuK3GgY1zRftgs_0KOs0ch-9VvPwZEs3yGSYE0TmxY6fv99QeHNX8L_UF_AM2hjJwwPah5ZRfYeKqKeF1kF7AKGc5SelBdT2LACSlvNNBKi9klvBLiQEgq/s320/Screen+Shot+2017-11-25+at+5.45.48+PM.png" width="320" /></a><a href="https://itunes.apple.com/us/app/heads-up/id623592465?mt=8" target="_blank">Head's Up!</a> is a game of charades where the person puts their iPad or iPhone on their head and the audience performs and nods down for correct and backwards for pass. For students this was one of the best review games we used for vocabulary for geometry.<br />
<br />
Students stood up in front of half the class and used my phone to show the students. This was excellent for students coming up with moving actions for such words as vertical angles and supplementary angles. Students were better able to self define vocabulary words better than previous, plus students had more fun reviewing.<br />
<br />
It costs .99$ for the app and an additional .99$ to make your own cards. Well worth the money.Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-70803716942243422812017-11-25T16:59:00.001-06:002017-11-25T16:59:57.664-06:00Coding Inequalities π»Coding in the classroom has always been an interest to me, Hour of Code is a great resource for any teacher especially those just starting out. For the past two years we have been doing Hour of Code during the Hour of Code week and that has been the most coding we do all year. What I wanted in my classroom was more coding, because I think coding could be the future for most of my students. I also believe that coding can be a gateway to other mathematical principles that are taught in the classroom such as: growth mindset, support productive struggle, and promote reasoning and problem solving.<br />
<br />
So we have started in the math classroom is using one day a unit to work on these skills by implementing a way for students to apply their mathematical knowledge and coding. Students are given a task write code to make a calculator to solve an inequality. Students had to write code in Trinket.io to write their inequality.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiovmeg99FwYTT3wOaMO2iYXmYcsd510-0gGa0r5toB25BnT33FjHkxvKJc6ZaQq9JvsN7FtAvv1z5kV455xvQqtH4v4s3Ivt01Ay8aiwqWh3qdSLT_HVcBxCH3e3FwoEJkGPnXnNUN_xF9/s1600/Screen+Shot+2017-11-25+at+4.53.21+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="771" data-original-width="1600" height="304" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiovmeg99FwYTT3wOaMO2iYXmYcsd510-0gGa0r5toB25BnT33FjHkxvKJc6ZaQq9JvsN7FtAvv1z5kV455xvQqtH4v4s3Ivt01Ay8aiwqWh3qdSLT_HVcBxCH3e3FwoEJkGPnXnNUN_xF9/s640/Screen+Shot+2017-11-25+at+4.53.21+PM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
We were going to use Swift by my Seniors do not have the iPads supported to do it, so we decided for everyone to use Trinket. Some students really loved the problem solving aspect of coding, using the blocks to get the numbers to do what they want them to do. Other students were not happy about trial and error process to finding the answer.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5ZVOthTbwGRfDRePwNw38twNaD47KWuEGRjey3H09yMzuqWzfBRcAZmAE-b5MM5R8awdnwP8rjK5b9SVdAOf37gi-bKsUlNCSfqoO59rHaqJgxRFD7kI_6BErPf78p4iVPzFMHZ3ggy-B/s1600/IMG_8591.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="908" data-original-width="1600" height="361" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5ZVOthTbwGRfDRePwNw38twNaD47KWuEGRjey3H09yMzuqWzfBRcAZmAE-b5MM5R8awdnwP8rjK5b9SVdAOf37gi-bKsUlNCSfqoO59rHaqJgxRFD7kI_6BErPf78p4iVPzFMHZ3ggy-B/s640/IMG_8591.JPG" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
I have some other upcoming units to try this out with like Pythagorean Theorem.</div>
<br />Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0tag:blogger.com,1999:blog-8643194467190728551.post-56696363705900270632017-09-15T06:30:00.000-05:002017-09-15T06:30:23.302-05:00How I Teach Direct VariationI use to teach direct variation by having students take notes, but the past few years I have been using <a href="http://mrorr-isageek.com/tag/bottle-flipping/" target="_blank">Jon Orr's Water Bottle Flip</a>.<br />
<br />
<blockquote class="twitter-tweet" data-lang="en">
<div dir="ltr" lang="en">
[New Post] Flippity Flip, Bottle Flip! Volume, rates, equations. <a href="https://t.co/FQ2QyFJ8Rf">https://t.co/FQ2QyFJ8Rf</a> <a href="https://twitter.com/hashtag/mtbos?src=hash">#mtbos</a> <a href="https://twitter.com/hashtag/bottleflipping?src=hash">#bottleflipping</a> <a href="https://t.co/tyMtBtyCX8">pic.twitter.com/tyMtBtyCX8</a></div>
β Jon Orr (@MrOrr_geek) <a href="https://twitter.com/MrOrr_geek/status/784451740359921668">October 7, 2016</a></blockquote>
<script async="" charset="utf-8" src="//platform.twitter.com/widgets.js"></script><br />
There is an excellent Desmos activity that goes along with it. This year I copied and edited my first Desmos activity which was this one.<br />
<br />
<a href="https://teacher.desmos.com/activitybuilder/custom/57f788035db373e705868c8b" target="_blank">https://teacher.desmos.com/activitybuilder/custom/57f788035db373e705868c8b</a><br />
<br />
I added two slides:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyD7QhSRQS9l80RdoSxhXvqCBl2DoaG3lI5WDCPwyTdP80EP1jvFVyiDSND6swFW3LBjgAsxTsWSzxTh4BqipcdPQ3YaNGpiSn2mbWHCM6Q4ohgL-rCvWJbKcKdTqPVTZ8xzSVNEgz5F6x/s1600/Screen+Shot+2017-09-10+at+3.00.31+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="681" data-original-width="1600" height="272" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyD7QhSRQS9l80RdoSxhXvqCBl2DoaG3lI5WDCPwyTdP80EP1jvFVyiDSND6swFW3LBjgAsxTsWSzxTh4BqipcdPQ3YaNGpiSn2mbWHCM6Q4ohgL-rCvWJbKcKdTqPVTZ8xzSVNEgz5F6x/s640/Screen+Shot+2017-09-10+at+3.00.31+PM.png" width="640" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUMGUGJdHCdDsd_Cz1nfJB0vGMqjec8zGz3KbfyyQ5L14ICHHZH41H7HuCq7_LsUJJ7yT2DQCIzmEiXz5DI9xhTMQECt287ZGko6uoYif3UhnEKasa3j0ZiFXQi06B2Is0ho2eAlH6JTqv/s1600/Screen+Shot+2017-09-10+at+3.01.35+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="628" data-original-width="1600" height="246" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUMGUGJdHCdDsd_Cz1nfJB0vGMqjec8zGz3KbfyyQ5L14ICHHZH41H7HuCq7_LsUJJ7yT2DQCIzmEiXz5DI9xhTMQECt287ZGko6uoYif3UhnEKasa3j0ZiFXQi06B2Is0ho2eAlH6JTqv/s640/Screen+Shot+2017-09-10+at+3.01.35+PM.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
I wanted to emphasize direct variation and ask them deep meanings of graphs. One of the questions I asked was looking at the graph on the bottom, what inferences can you draw?</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
On September 8, there was the NATM (Nebraska Association of Teachers of Mathematics) Conference. During Lenny VerMass presentation, <a href="https://docs.google.com/document/d/1xM4Jx5ZbocS_qJyymda5kwiPW-GJnWEvApP2h8TeLjA/edit" target="_blank">Smoke and you Croak or Huffing and Puffing to Understand Slope</a>, he had a very interesting task. </div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Students had to measure how much air filled their lungs. So we exhaled into a balloon and measured (3) breaths and the circumference of the balloon. Then on a big sheet of paper we had to plot all of our data points for the following graphs and interesting things happened. Try it with your students.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAjcNfZPh6gFQ1IMkU5D-EVTXKamM5vGZfKWofi97e9N_2_IKqZeg-PeT-fxRdA6B4Q73N8l-OuheV8Q2tKhgmeVoGNVLWLv9USF-QMcm6SVU1RD4ZEWeJLUkjzBAjPYj6PKurdB2W-BaU/s1600/Screen+Shot+2017-09-10+at+3.47.31+PM.png" imageanchor="1"><img border="0" height="272" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAjcNfZPh6gFQ1IMkU5D-EVTXKamM5vGZfKWofi97e9N_2_IKqZeg-PeT-fxRdA6B4Q73N8l-OuheV8Q2tKhgmeVoGNVLWLv9USF-QMcm6SVU1RD4ZEWeJLUkjzBAjPYj6PKurdB2W-BaU/s640/Screen+Shot+2017-09-10+at+3.47.31+PM.png" width="640" /></a></div>
<br />Trever Reehhttp://www.blogger.com/profile/16317920102232542135noreply@blogger.com0