tag:blogger.com,1999:blog-79409549298278992702024-03-12T16:48:54.054-07:00 Mathematical!Mathematical!Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.comBlogger95125tag:blogger.com,1999:blog-7940954929827899270.post-47835209559554519082014-06-09T07:47:00.002-07:002014-06-09T07:47:36.050-07:00test post<div dir="ltr" style="text-align: left;" trbidi="on">
Submit your pictures</div>
Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com4tag:blogger.com,1999:blog-7940954929827899270.post-45018875534597102812014-03-14T17:43:00.000-07:002014-03-15T06:55:57.117-07:00Functions black box<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSWvswlP8bPMKqH336nG25XVXypx0PmDv4H9W_UeZ1FZtBNYoeYSlWRxMZMYb4oxMrBi90KfnAVjSRN7dJ-5UADFlYeK12NYZLUXcNUdNFABvul5g6shJ-nwUKWGEBZh8kaodqqH2yIGY/s1600/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSWvswlP8bPMKqH336nG25XVXypx0PmDv4H9W_UeZ1FZtBNYoeYSlWRxMZMYb4oxMrBi90KfnAVjSRN7dJ-5UADFlYeK12NYZLUXcNUdNFABvul5g6shJ-nwUKWGEBZh8kaodqqH2yIGY/s1600/Capture.JPG" height="164" width="320" /></a></div>
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Directions:<br />
1. Load one of the following problems with a Geogebra-enabled Ipad. <br />
2. Then, play around with the input in order to determine what the function is. <br />
3. Keep track of your inputs and outputs, creating a table and graph with your data.<br />
4. When putting inputs in don't press enter to engage the machine, instead put your desired input into the Geogebra "input bar" button and press enter.<br />
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Parent Functions:<br />
<a href="https://www.dropbox.com/s/997dtnqst558nu8/Function%20Machine%20parent%20problem%201-ipad.ggb">Function Machine Problem 1</a><br />
<a href="https://www.dropbox.com/s/gcherio20w233hi/Function%20Machine%20parent%20problem%202.ggb">Function Machine Problem 2</a><br />
<a href="https://www.dropbox.com/s/ssieimwkf9v38m0/Function%20Machine%20parent%20problem%203.ggb">Function Machine Problem 3</a><br />
<a href="https://www.dropbox.com/s/0zdukont3npo88u/Function%20Machine%20parent%20problem%204.ggb">Function Machine Problem 4</a><br />
<a href="https://www.dropbox.com/s/f2hnrbw4uqm9ahk/Function%20Machine%20parent%20problem%205.ggb">Function Machine Problem 5</a><br />
<a href="https://www.dropbox.com/s/5gtt4iene2d2iyr/Function%20Machine%20parent%20problem%206.ggb">Function Machine Problem 6</a><br />
<a href="https://www.dropbox.com/s/9llnx98936iqo4k/Function%20Machine%20parent%20problem%207.ggb">Function Machine Problem 7</a><br />
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Transformations:Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-13232768078270218032014-03-14T17:30:00.002-07:002014-03-14T17:30:41.299-07:00Permutations and combinationsI like this warm up because Students will take a variety of methods to represent it. There are only two shapes, and its a quick problem that gets down to the idea of choosing. <div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR8cSUfJLjj_99Q6_6gZ0aHTHH1htnWIRIQj62Vt3jap_XqLHQoa54w78lJkKTrKXAHQA39UiNUsNKLvvjbgonBG8ZYTZjkq7WdTh8JfQQ3ZwD4Yf7_4DpLGTtAth_R8yVldBSY8W_bq0/s1600/Capture.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR8cSUfJLjj_99Q6_6gZ0aHTHH1htnWIRIQj62Vt3jap_XqLHQoa54w78lJkKTrKXAHQA39UiNUsNKLvvjbgonBG8ZYTZjkq7WdTh8JfQQ3ZwD4Yf7_4DpLGTtAth_R8yVldBSY8W_bq0/s1600/Capture.JPG" height="224" width="320" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlUiynoh1BQBtro9P5HiSFUIys1g7mdMtzLo_IUKbyD1zTSLvyL1YqAMlMSJG4gg0tW7ReMX1cu2e6ybSWvm7_fldx-LyFzNUn4gJLE2lCzx1igw7Kz1ZU1-nqiHH8bTGefFAUzH8j_uU/s1600/Capture.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlUiynoh1BQBtro9P5HiSFUIys1g7mdMtzLo_IUKbyD1zTSLvyL1YqAMlMSJG4gg0tW7ReMX1cu2e6ybSWvm7_fldx-LyFzNUn4gJLE2lCzx1igw7Kz1ZU1-nqiHH8bTGefFAUzH8j_uU/s1600/Capture.JPG" height="232" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWK-Aqe1wGwwFf3skCqQEwfuJBKtk4pDQpLBo5xuX-q2DNXMXGofUvTIsJXJ0OLJE6MZWrARvHg79FHcA0YddRiQxKtEEzTwSnhaUao7zKIlxQ7Cl02iKARftB2lVUSm1A1Qv92M2DidM/s1600/Capture.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWK-Aqe1wGwwFf3skCqQEwfuJBKtk4pDQpLBo5xuX-q2DNXMXGofUvTIsJXJ0OLJE6MZWrARvHg79FHcA0YddRiQxKtEEzTwSnhaUao7zKIlxQ7Cl02iKARftB2lVUSm1A1Qv92M2DidM/s1600/Capture.JPG" height="113" width="200" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRraW8gILyr8zHGIs9t-7rUnY2jRbsMXNFMZSY4TWfCn9xIV__wHVd8Hpd7O-7QlnMqSNLwRum2BCXewUCtGEn-mUYPX_nNBKZmZUdsQMf3Vq_wFTiIRTtCJGb1TxNlq4OZmguXUYGMC0/s1600/Capture.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRraW8gILyr8zHGIs9t-7rUnY2jRbsMXNFMZSY4TWfCn9xIV__wHVd8Hpd7O-7QlnMqSNLwRum2BCXewUCtGEn-mUYPX_nNBKZmZUdsQMf3Vq_wFTiIRTtCJGb1TxNlq4OZmguXUYGMC0/s1600/Capture.JPG" height="139" width="320" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXvrT75GI7J3ap6RbDL-P_05tQpanw5ydIU1dKfWh54KNs4RsnO-ALBCqGq5LjHMK1Te5SWJKMiIsGHlelMl7sODFRFON7smpbriMAeqL8BGt2fV1eLTS-B1TpFvWmPsg6pIaaDVhTLlc/s1600/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXvrT75GI7J3ap6RbDL-P_05tQpanw5ydIU1dKfWh54KNs4RsnO-ALBCqGq5LjHMK1Te5SWJKMiIsGHlelMl7sODFRFON7smpbriMAeqL8BGt2fV1eLTS-B1TpFvWmPsg6pIaaDVhTLlc/s1600/Capture.JPG" height="135" width="320" /></a></div>
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After this I ask them to extend their thinking with this ordered horse race problem:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6e0DyQ7wxE0HUpjVShnOI1vnvzo3syIxYp21ultOJMLGfYJ41hQggZobUbOPTq-Tn22vlHs8OOXv_Ghfg-mxtlKYqIm3p6Ln3sJmLmkw_n_MijdfIdLRTDK9GYbK37FHZA5rjYCzNzsM/s1600/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6e0DyQ7wxE0HUpjVShnOI1vnvzo3syIxYp21ultOJMLGfYJ41hQggZobUbOPTq-Tn22vlHs8OOXv_Ghfg-mxtlKYqIm3p6Ln3sJmLmkw_n_MijdfIdLRTDK9GYbK37FHZA5rjYCzNzsM/s1600/Capture.JPG" height="174" width="320" /></a></div>
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common student responses include 3*8, 8^3, 8*7*6</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbVFhV5HEySSeSIrORCu47kK9UjhIzwehx3OTKyPMgRSrWxAyxOq8KRcAPDE_azjbo9UFQPvGIAh-Ln6bmZKrvCVC3KnoN-Ec-qxqyN1ZuDtI5yxEaGSPufNvca4XqU6_VgJ-n-b9Tc6I/s1600/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbVFhV5HEySSeSIrORCu47kK9UjhIzwehx3OTKyPMgRSrWxAyxOq8KRcAPDE_azjbo9UFQPvGIAh-Ln6bmZKrvCVC3KnoN-Ec-qxqyN1ZuDtI5yxEaGSPufNvca4XqU6_VgJ-n-b9Tc6I/s1600/Capture.JPG" height="180" width="320" /></a></div>
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and most student responses are "its the same" </div>
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<br />Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-8181422075145813352014-03-14T16:56:00.002-07:002014-03-14T17:33:06.217-07:00Venn Diagrams, Probability and RouletteThis is one of my favorite days during the probability unit. It isn't often I get to gamble with my students and say its educational. <br />
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I begin this day with a quick warm up involving placing cards in the right parts of the Venn diagram. Then, I ask them a few questions about it, just as review of the notation.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMXi2dEOe7C6ZjDKluSkOb_upZH3o7qeTQNix7NwN-IAqrkdHuzS09ZfPA4TpAz5rX9hgv_ztgm6dVx7ElHmBdYrb2ToiaNeeaAn6Au8qXuQEyTAUbuBDdYmN-Nn92hWgofaAmvH4cEb4/s1600/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMXi2dEOe7C6ZjDKluSkOb_upZH3o7qeTQNix7NwN-IAqrkdHuzS09ZfPA4TpAz5rX9hgv_ztgm6dVx7ElHmBdYrb2ToiaNeeaAn6Au8qXuQEyTAUbuBDdYmN-Nn92hWgofaAmvH4cEb4/s1600/Capture.JPG" height="272" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHr_XeoBeHgw04hcAm9ZixdJrOZzod5jdp4tEpvyqyhqme9R51pXN3IzZtLmuytJdWpQDooMnLtuRgDbWFCD9Ox-1vxZk8NB74hQUEfCBV2WWjx_f9GdcG04rZtIPZQkQ09IyqhoA6V7w/s1600/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHr_XeoBeHgw04hcAm9ZixdJrOZzod5jdp4tEpvyqyhqme9R51pXN3IzZtLmuytJdWpQDooMnLtuRgDbWFCD9Ox-1vxZk8NB74hQUEfCBV2WWjx_f9GdcG04rZtIPZQkQ09IyqhoA6V7w/s1600/Capture.JPG" height="320" width="237" /></a></div>
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The last one I stop myself and ask the students how to even say that and inevitably someone says not A or B, to which I have to make a point.<br />
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After everyone is okay with the basic of the Venn diagram I preface the next activity with "Don't tell you parents we're playing this but does anyone recognize this game?<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPohLR0P_sRoxw8LDwVawBXnnkOyIcqlonMmwm2BI7RvxOPqkjL09ZOw08Cl_dkHnhb-6dcNXHLnrU5phQXGdOI8JsYcRfYTBTmzOQ7yow4dsFeGf8h7AZnhx31RzKe4IxM77XSDVNEGM/s1600/Capture.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPohLR0P_sRoxw8LDwVawBXnnkOyIcqlonMmwm2BI7RvxOPqkjL09ZOw08Cl_dkHnhb-6dcNXHLnrU5phQXGdOI8JsYcRfYTBTmzOQ7yow4dsFeGf8h7AZnhx31RzKe4IxM77XSDVNEGM/s1600/Capture.JPG" height="219" width="320" /></a></div>
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Then I start taking bets. I draw two student names at random, inform them what they could bet on and place their bets. Before I spin we have to model the situation with a Venn diagram and talk about intersections, unions, and compliments.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEBq1UKm0b7CuPRfNS2_X4uFDYgYSU3ciX4lCsggcPbl6T8010wx6Aak67PPoy-qKpsJe4D3ycXmRNQ2R5vPK28sFTpUXlQTE1ZU2OY96UGXxFUCT1pAF5b2lsOylzSCH757C8Wk8XO-Q/s1600/031314-1352.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEBq1UKm0b7CuPRfNS2_X4uFDYgYSU3ciX4lCsggcPbl6T8010wx6Aak67PPoy-qKpsJe4D3ycXmRNQ2R5vPK28sFTpUXlQTE1ZU2OY96UGXxFUCT1pAF5b2lsOylzSCH757C8Wk8XO-Q/s1600/031314-1352.png" height="240" width="320" /></a></div>
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Here is the graphic organizerMr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-48238516019909732592014-02-10T13:55:00.000-08:002014-02-10T13:55:35.262-08:00Imaginary numbers<div dir="ltr" style="text-align: left;" trbidi="on">
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Day 1: take notes on what imaginary numbers are. Boring, but it is a topic that always gets the students riled up. Their feather get ruffled once they know that their 7th grade teacher was mistaken when they were told "you can't take the square root of an negative number." in one such instance I got to pull out my Star Wars quotes and tell a student to "let go of their hatred." Most of the students thought imaginary numbers were kind of cool, some thought I was making it all up and playing a trick on them, and unfortunately some through it was the dumbest thing ever and they should be learning something "useful."</div>
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On day two <i>i</i> show most of this video, and put it in the context of a robotic arm rotating to pick things up at various points.</div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwslItC9X5IQuk9lB9Pr0FudZ4mGbTEZSby95fTS7vZmhlDG54GuNWo4nLwNdrPEUI7VdkTsDOfRalBPh1N6w' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
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Then we get to the good stuff. I give students a little packet and have them do the top problem, they double check with me and if they did it right and get a quick "yep" or "not yet," they get to crumple up their paper and shoot it from the free throw line if they're correct, otherwise they have to keep working on the problem. There is only get the one shot per correct answer and if they miss then they have to go fetch their shot and put it in by hand. For all but one of my hours this was a great alternative to a worksheet, and I really saw them asking each other how to get the answer. Who knew throwing the piece of paper would be such a great motivator?!<br />
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The questions increase in difficulty, making for great differentiation. Students can go at their own pace and can know that they are right before continuing. The pace is fast, and I was relatively surprised at how hard students tried on something that they had just the previous day been questioning the relevance of.<br />
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<a href="https://www.dropbox.com/s/9f868g2hdw8plku/complex%20number%20opperations%20flipbook.docx">Here is the template</a>, just photocopy it in order and put the staples in and you'll be ready to go after its cut up, no need to organize the booklets.<br />
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<iframe allowfullscreen="" frameborder="0" height="400" mozallowfullscreen="" msallowfullscreen="" oallowfullscreen="" src="https://app.box.com/embed_widget/hsy4moii9elm/s/fy90933nlzoueph37yem?view=list&sort=name&direction=ASC&theme=blue" webkitallowfullscreen="" width="500"></iframe></div>
Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com1tag:blogger.com,1999:blog-7940954929827899270.post-39962058008283951342014-01-24T09:22:00.002-08:002014-01-24T09:22:49.688-08:00Quadratic patterns<div dir="ltr" style="text-align: left;" trbidi="on">
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For this lesson I hand students a slip of paper as they enter in the door, one that has a quadratic pattern printed on it. Their 1st task is to make a guess, no calculations, how many squares/circles/shaded squares with the 50th term have?<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-gv4U0gC_dpo6LWoC7xFOpT-lEoqu-QvDt0CYH6Zzyak5uTxjdWptCs_wmByIfHEmJ5Vy5VMXPGE8A1VK0C5QTJu80U-T6xtCVCcH8-GFEmpEKQwY-W7vQm2Md1CvaSRP88pISEX249M/s1600/Quad+1&2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-gv4U0gC_dpo6LWoC7xFOpT-lEoqu-QvDt0CYH6Zzyak5uTxjdWptCs_wmByIfHEmJ5Vy5VMXPGE8A1VK0C5QTJu80U-T6xtCVCcH8-GFEmpEKQwY-W7vQm2Md1CvaSRP88pISEX249M/s1600/Quad+1&2.jpg" height="256" width="320" /></a></div>
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All the patterns used for this lesson were taken from <a href="http://www.visualpatterns.org/">http://www.visualpatterns.org/</a></div>
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Then I will take a few answers and put them up on the board to incite some competition and buy-in from the students. <br />
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At this point I may show them how to do it, or remind them if they already know.<br />
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They have some time to work, most of the students can accurately find the equation using the table and the process I trained them with to find the equation from the table, but fewer of them can look at the pictures and write an equation relating x to side lengths and so forth.<br />
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Here are the patterns that we have been using:<br />
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<iframe allowfullscreen="" frameborder="0" height="400" mozallowfullscreen="" msallowfullscreen="" oallowfullscreen="" src="https://app.box.com/embed_widget/b297xjl81wsr/s/vahrc9eji7rrupgx2u87?view=list&sort=name&direction=ASC&theme=blue" webkitallowfullscreen="" width="500"></iframe><br />
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Here is some student work that shows the process of finding the equations:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEEKRSpbfgdnQaReVa2IK3LbGU11ub_Fu_sba3Bkqxk6f7nPHNBjKEr3lIYDb6XaF2ZRVNhtqaf5f_0mq7neWhSgRBBT-ir5H2DmfX2VemW6X8l-Tiji247aaJ6u-Pty4gjq_98RT1uK8/s1600/quad+patterns+5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEEKRSpbfgdnQaReVa2IK3LbGU11ub_Fu_sba3Bkqxk6f7nPHNBjKEr3lIYDb6XaF2ZRVNhtqaf5f_0mq7neWhSgRBBT-ir5H2DmfX2VemW6X8l-Tiji247aaJ6u-Pty4gjq_98RT1uK8/s1600/quad+patterns+5.jpg" height="256" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMd_o6sI91U41lFGa6OXWv-pvwFfW_KA6YsEsQAmjVc__bQdDx4-gAMtW4KbtoNdxWW3PtX8kyfyDdS6YndDlnPN1nUJOTHsibCFDiytK6hAwe-urb_l4Z-sPx_GPoNHNed2eJZEC3o-4/s1600/quad+patterns+6.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMd_o6sI91U41lFGa6OXWv-pvwFfW_KA6YsEsQAmjVc__bQdDx4-gAMtW4KbtoNdxWW3PtX8kyfyDdS6YndDlnPN1nUJOTHsibCFDiytK6hAwe-urb_l4Z-sPx_GPoNHNed2eJZEC3o-4/s1600/quad+patterns+6.jpg" height="256" width="320" /></a>some students can look as the figures and relate the parts to x, but it is more common that they use the table approach as it is more formulaic.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg93nZwGSRcAaFHikwrQJCfvWi5hvFcBcG5mK3g6U77UF0VeBMX16Ewg6nI3sy3QscOzq8FKJD5aIP_Cj5V62cp7QzE0lExdzcBbwevDJgoXFs-k2Uns5yUsOHZgks_HgvYaBrhOiEZn8/s1600/quad+patterns+1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg93nZwGSRcAaFHikwrQJCfvWi5hvFcBcG5mK3g6U77UF0VeBMX16Ewg6nI3sy3QscOzq8FKJD5aIP_Cj5V62cp7QzE0lExdzcBbwevDJgoXFs-k2Uns5yUsOHZgks_HgvYaBrhOiEZn8/s1600/quad+patterns+1.jpg" height="256" width="320" /></a>Drawing the next picture is crucial to getting enough data for using a table. It allows students to get the 2nd differences and work backwards to find the y-intercept.</div>
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Most of the questions that I received, or the students that I helped that were stuck had miscounted the squares, thus finding no pattern. <br />
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After they have done the work to generate the equation they use it to find the value of the 5th term, and at the end of the hour we look to see whose guess was the closest.<br />
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Students then go home with this practice Hw. The first pattern is actually linear, and although it confuses students because that's not the unit we're in it is a good connection to make.<br />
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<iframe allowfullscreen="" frameborder="0" height="400" mozallowfullscreen="" msallowfullscreen="" oallowfullscreen="" src="https://app.box.com/embed_widget/nanuuscd9zr3/s/isdk3ggbldafm9m5y6dk?view=list&sort=name&direction=ASC&theme=blue" webkitallowfullscreen="" width="500"></iframe></div>
Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-17865569007714191032013-12-18T08:34:00.001-08:002013-12-18T08:34:44.759-08:00Graphing non-linear inequalities<div dir="ltr" style="text-align: left;" trbidi="on">
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Learning target: students can graph non-linear inequalities.<br />
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This is a multiple day lesson, where students first start with a game of graphing pictionary. I hand students this packet and tell them that the person holding it must<br />
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<iframe allowfullscreen="" frameborder="0" height="550" mozallowfullscreen="" msallowfullscreen="" oallowfullscreen="" src="https://app.box.com/embed_widget/x0rf1nul553l/s/gue1cnheqh2zeiibrd99?view=list&sort=name&direction=ASC&theme=blue" webkitallowfullscreen="" width="800"></iframe>
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Students have to complete the 4 problems<br />
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I've also learned that these types of activities work great but they have to be accompanied by practice almost immediately after in order to cement the ideas down so students can actually apply the concepts.<br />
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The second day I open with a warm up that requires students to write the equations for a system of inequalities based off of a graph. Then I hand them a sheet, tell them to figure out what the equations are. the most important part is that they are going to double check themselves on their own calculator. I've learned by now that with my 11th grade students activities always run smoother if the lesson is student centered. They must be able to check their own work.</div>
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<iframe allowfullscreen="" frameborder="0" height="550" mozallowfullscreen="" msallowfullscreen="" oallowfullscreen="" src="https://app.box.com/embed_widget/pz43oqyzl5hz/s/grf9gn3038rysncrrbq0?view=list&sort=name&direction=ASC&theme=blue" webkitallowfullscreen="" width="800"></iframe><br />
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This turns out to be a great review of function transformations as well<br />
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Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-63062029972705149492013-12-12T14:21:00.000-08:002013-12-18T08:50:16.587-08:00Linear Programming high challenge<div dir="ltr" style="text-align: left;" trbidi="on">
Learning target: students can solve linear programming problems unassisted.<br />
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students get to pick from one of the three problems and make a poster about it. I show a poster of previous student work of Joe's coffee shop, which is a problem all of them have already solved.:<br />
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(most of the students choose the juice problem)<br />
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<iframe allowfullscreen="" frameborder="0" height="550" mozallowfullscreen="" msallowfullscreen="" oallowfullscreen="" src="https://app.box.com/embed_widget/6a97jxvr4gbr/s/uqg3q2d7ubziq4doyeci?view=list&sort=name&direction=ASC&theme=blue" webkitallowfullscreen="" width="800"></iframe>
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One thing that could make this activity better is if these same students had to complete one problem of the high support, where there is no context.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXY7hl_YM_Vuauida2W3-M9fuLyOlCVyzwblNh77LUKnU2J5pPFGSWKCMdOu040DkjuU9GT24flRXS0HDuZ-fvLNOmDPjlzaxtHTKP09mnUyhp6VKFHGkihV-ZOFWCuLQ41TiCBdeDndk/s1600/poster-file+cabinets+1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXY7hl_YM_Vuauida2W3-M9fuLyOlCVyzwblNh77LUKnU2J5pPFGSWKCMdOu040DkjuU9GT24flRXS0HDuZ-fvLNOmDPjlzaxtHTKP09mnUyhp6VKFHGkihV-ZOFWCuLQ41TiCBdeDndk/s320/poster-file+cabinets+1.JPG" width="246" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhm8VHMB_9EaJgtZZN63hf9VtTiK8JYVA97rLsGkW7U_6p3QB42-9qmOplUCMBR2zSctX6QWTZA9p0aG3kYizB_ZRRWEZ4Je25iKJzx45K4K2pTNurhdwCkUMFccvP1_26dO5DyV5tw4sU/s1600/poster-file+cabinets+2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="251" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhm8VHMB_9EaJgtZZN63hf9VtTiK8JYVA97rLsGkW7U_6p3QB42-9qmOplUCMBR2zSctX6QWTZA9p0aG3kYizB_ZRRWEZ4Je25iKJzx45K4K2pTNurhdwCkUMFccvP1_26dO5DyV5tw4sU/s320/poster-file+cabinets+2.JPG" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvNnpTGh4gykNYFOJZjqmPWk9p2IL8EW0DbQUkbPMxraCKjv-aEoZFZ1t2tEyloiDJ2J9yhkg1EWKdrZ2HrrZTmC3FP5HGSUuTFi8EITCizjh0RAiD2dWfEwYgwr80o-rjxAnF8VdxQgg/s1600/Poster-home+canning+1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvNnpTGh4gykNYFOJZjqmPWk9p2IL8EW0DbQUkbPMxraCKjv-aEoZFZ1t2tEyloiDJ2J9yhkg1EWKdrZ2HrrZTmC3FP5HGSUuTFi8EITCizjh0RAiD2dWfEwYgwr80o-rjxAnF8VdxQgg/s320/Poster-home+canning+1.JPG" width="249" /></a>Anticipate students defining their variables half haphazardly, which can lead to confusion latter, especially for the juice problem where students have to convert their unit to be in all quarts or all gallons.</div>
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Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-8211302587064683552013-12-12T13:56:00.002-08:002013-12-12T13:59:53.814-08:00Linear programming<div dir="ltr" style="text-align: left;" trbidi="on">
Learning Target: students can maximize the profit of a system of inequalities.<br />
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The lesson starts off based on the previous walk-though of feasible region and Fred's coffee shop. then, if students understand they move forward, and if not we go back to basics.<br />
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Determining factor: can the students do this problem while using Fred's coffee shop as a guide<br />
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<iframe allowfullscreen="" frameborder="0" height="400" mozallowfullscreen="" msallowfullscreen="" oallowfullscreen="" src="https://app.box.com/embed_widget/wfyalejsokar/s/tarcliwuc7yncs7sbaz1?view=list&sort=name&direction=ASC&theme=blue" webkitallowfullscreen="" width="500"></iframe>
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High challenge:<br />
Students pick on of three problems and make a poster that shows the solution using the template we have been using.<br />
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Anticipate: students not defining x and y well enough.<br />
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High support:<br />
Here are the three questions. Students had to pick one depending on where they think they are at.<br />
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Question 1 student work</div>
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:<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3hDszJuRJVxRme4iScowKXM9Uwc8kV6bEG1MdFlZOv4GjQBQiCQnXvVA5fc3CeyL_51oSLcBKtspMWQ0DT9Ow5MmAETeRDZ_a1gqDxSf5xYkFURkjBcdIKfJuIQk2P8QUeuSlIwTHdFc/s1600/remedial+1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="256" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3hDszJuRJVxRme4iScowKXM9Uwc8kV6bEG1MdFlZOv4GjQBQiCQnXvVA5fc3CeyL_51oSLcBKtspMWQ0DT9Ow5MmAETeRDZ_a1gqDxSf5xYkFURkjBcdIKfJuIQk2P8QUeuSlIwTHdFc/s320/remedial+1.jpg" width="320" /></a></div>
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Question 2 student work</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrXW7Xdtez7ocRJMkEqb14ZfrFtgo1BhqtiwtZTA2DgADmU3k9fZcYhc6xXWj1Xm27kQbRiJ2wxtHciG5zOanqF0xuurd06iQgXaLlxKyCmaweGbLCjm3CyyvHjtWN38thlYvCEx6pwNE/s1600/remedial+2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="256" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrXW7Xdtez7ocRJMkEqb14ZfrFtgo1BhqtiwtZTA2DgADmU3k9fZcYhc6xXWj1Xm27kQbRiJ2wxtHciG5zOanqF0xuurd06iQgXaLlxKyCmaweGbLCjm3CyyvHjtWN38thlYvCEx6pwNE/s320/remedial+2.jpg" width="320" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg94vNI5nBfh-BVOAQ4g04CTJfN9MiPOHG-1_jzoM2PFra9lhc0RzhAoIVcpvQzrQxnCuIhlPlUbeOmxOwH9ZHiCJ2bTSTWrrwimteW8C8b0Ih8BFHeyYEgQGe2DTQ63YEEo9a5SPen334/s1600/remedial+2-7.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="256" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg94vNI5nBfh-BVOAQ4g04CTJfN9MiPOHG-1_jzoM2PFra9lhc0RzhAoIVcpvQzrQxnCuIhlPlUbeOmxOwH9ZHiCJ2bTSTWrrwimteW8C8b0Ih8BFHeyYEgQGe2DTQ63YEEo9a5SPen334/s320/remedial+2-7.jpg" width="320" /></a></div>
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Question 3 student work.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTMNTBXoIo2jzbN-BlWZMs_HjEiWRcx_Bq3Cqvf-aQBewq_S2i-U2kY2nA-CvirINrx-mTlOBjJMnrtEQZOsYVBZKmWZbHj0MoTd0UX66b6XH4_umH7cVGi9e1lLRF-L3K3Qz8sxYJ_Vk/s1600/remedial+3-2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="256" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTMNTBXoIo2jzbN-BlWZMs_HjEiWRcx_Bq3Cqvf-aQBewq_S2i-U2kY2nA-CvirINrx-mTlOBjJMnrtEQZOsYVBZKmWZbHj0MoTd0UX66b6XH4_umH7cVGi9e1lLRF-L3K3Qz8sxYJ_Vk/s320/remedial+3-2.jpg" width="320" /></a></div>
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Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-56117101909271383042013-12-06T14:36:00.000-08:002013-12-18T08:35:12.240-08:00Scavenger Hunt-feasible region and linear programming introduction<div dir="ltr" style="text-align: left;" trbidi="on">
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Learning Target: students can identify points inside and outside of the feasible region.<br />
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Intro: I hand out the problem to each student as they come in the door and most of them can begin without any prompt.<br />
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the idea is that we are going to set up a scavenger hunt and need to set up the boundaries using a system of inequalities. (thank you Google Maps)<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjijnmXwn8l3azMob72i9AYTejEG5oScnaLiEp09WV0hRD5EIxSOjG10YkaWPRNAKhMFmeW_1eRvaI0YkcxaQbNRv6EbpPZRKIVRUg2lMmNlzQ21qU5UCb0OKAEon4dt-NsvGBOaqfR5lQ/s1600/Day+5-washburn+scavenger+hunt+boundaries.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="590" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjijnmXwn8l3azMob72i9AYTejEG5oScnaLiEp09WV0hRD5EIxSOjG10YkaWPRNAKhMFmeW_1eRvaI0YkcxaQbNRv6EbpPZRKIVRUg2lMmNlzQ21qU5UCb0OKAEon4dt-NsvGBOaqfR5lQ/s640/Day+5-washburn+scavenger+hunt+boundaries.JPG" width="640" /></a></div>
Students graph these and label 5 points that would serve as suitable stations for the scavenger hunt. Inevitably, one student will pick some point where x=4, which gives us a good talking point when we review it.<br />
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there is one question about the northern-most point, which students will eyeball from there sometimes haphazard graphs, which gives us an avenue to review solving systems.</div>
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Plugging the point back in and finding the y-location is not always easy to remember.</div>
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Here is a <a href="https://www.dropbox.com/s/sgyn27471cds901/Scavenger%20hunt%2C%20coffee%20beans.pdf">PDF</a> of the lesson, and below is the worksheet.</div>
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Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-58815021875687953082013-12-02T13:52:00.002-08:002013-12-02T13:53:22.133-08:00Scale of the Universe<div dir="ltr" style="text-align: left;" trbidi="on">
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Lesson objective: students can plot data of varying magnitudes on a semi-log scale.<br />
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This is a lab day, and students log on to find this website: <a href="http://htwins.net/scale2/lang.html">http://htwins.net/scale2/lang.html</a><br />
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They then pick 12 objects of various sizes and write down their names and sizes in meters. The interactive website displays data between the two extremes shown below, and naturally student choose some from each side of the spectrum, which makes it hard to graph using a base 10 scale<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEge-MaDSNMdtxlq9BCYGOP47gJsa4irqoRPQCbhWg7jkFEgegoFw4pjWwEtLovq_XgyF0T0xpP2BfWTG_AhPoW_TZMtdAy-Q6082VHbtq_YaDOvbCL5e5G4zKuCQMQzyrhF94b0O4V7i3o/s1600/observable+universe.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="356" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEge-MaDSNMdtxlq9BCYGOP47gJsa4irqoRPQCbhWg7jkFEgegoFw4pjWwEtLovq_XgyF0T0xpP2BfWTG_AhPoW_TZMtdAy-Q6082VHbtq_YaDOvbCL5e5G4zKuCQMQzyrhF94b0O4V7i3o/s640/observable+universe.JPG" width="640" /></a></div>
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As students enter I hand them <a href="https://www.dropbox.com/s/61ry3n9umcawbj3/investigation-scale%20of%20the%20universe.docx">this worksheet</a> that will guide them through the activity. After they pick their 12 objects they plot them on <a href="https://www.dropbox.com/s/ju0s7iq3eqajlli/semi-log%203.pdf">semi-log scale graph paper</a>.<br />
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Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-79621451771869675462013-11-22T07:18:00.000-08:002013-11-22T11:30:15.605-08:00Logarithmic Lions<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="http://t3.gstatic.com/images?q=tbn:ANd9GcTbi8PE3z9mVQSBDq8XGoYTR3BydLZzekRp81afdPov69XtNIMG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="298" src="http://t3.gstatic.com/images?q=tbn:ANd9GcTbi8PE3z9mVQSBDq8XGoYTR3BydLZzekRp81afdPov69XtNIMG" width="400" /></a></div>
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<a href="http://images.nationalgeographic.com/wpf/media-live/photos/000/006/cache/lions-males-botswana_612_600x450.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="http://images.nationalgeographic.com/wpf/media-live/photos/000/006/cache/lions-males-botswana_612_600x450.jpg" width="400" /></a></div>
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Lions: 1,2,...many, logarithmic thinking.<br />
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This lesson was designed after a national geographic article I read some years back, and I wish I had a copy or knew the name of the article.<br />
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Here's the lesson:<br />
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Show <a href="https://www.dropbox.com/s/yfr23qrp9rts89b/logrithmic%20thinking%20%28predators%29.notebook">this flip</a> (its in Smart Notebook, sorry ActiveInspire). Each student has to write down the number of predators they see, but I only show the slide for a fraction of a second.<br />
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<embed allowfullscreen="true" allowscriptaccess="always" height="600" src="https://app.box.com/embed/qsqugw6t8d9f6bc.swf" type="application/x-shockwave-flash" width="900" wmode="opaque"></embed>
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Which leads to the idea that the human brain was wired to think logrithmically. Evolution favored those who could discern the difference between 1 lion, 2 lions and 3 lions, but no favor is granted to those who can tell the difference between 9 and 11, as they are dead meat anyways.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhv0XOdZDVbwqpWKqbz_dOjVjd7BzTmiE45bPxnBv87YX75VTOCKTnWlLBJF6WmXpqyIY0ZT-9In6qUy_fE6Iv6ChCmb3rAFq7LkTxeTvwtFIZ5Er0JuxlTnw9-RMT6YUXoXOpesIWCqvU/s1600/logarithmic+lions.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="446" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhv0XOdZDVbwqpWKqbz_dOjVjd7BzTmiE45bPxnBv87YX75VTOCKTnWlLBJF6WmXpqyIY0ZT-9In6qUy_fE6Iv6ChCmb3rAFq7LkTxeTvwtFIZ5Er0JuxlTnw9-RMT6YUXoXOpesIWCqvU/s640/logarithmic+lions.JPG" width="640" /></a></div>
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This intro is a fun activity and is a non-threatening way to show semi-log scales.</div>
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Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-23440212220481603152013-11-20T10:19:00.002-08:002013-11-22T06:56:52.543-08:00Formal introduction to logarithms<div dir="ltr" style="text-align: left;" trbidi="on">
Learning target: students can apply logarithms<br />
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DAY 1</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIhh8uWX2Hgf_SB7IB4H862E3IfjIDHMFVLQ3xa7ql9-8nfbVVzpMcoklVGCCgsvY08A9tNareLewLyIIkmqEhaq4Y6_9s5Av8Ip0aguyMfh7L2UcmIfWe6hxrQjDknVBUdhMHcG-WqRg/s1600/practice-base+10+slip.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIhh8uWX2Hgf_SB7IB4H862E3IfjIDHMFVLQ3xa7ql9-8nfbVVzpMcoklVGCCgsvY08A9tNareLewLyIIkmqEhaq4Y6_9s5Av8Ip0aguyMfh7L2UcmIfWe6hxrQjDknVBUdhMHcG-WqRg/s320/practice-base+10+slip.JPG" width="97" /></a>1st I throw this puzzle at them, and they try to solve for the unknown with guess and check. I give them about 5 minutes, which allows them to get close on about 3 or 4 of them. One student may even figure out the relationship between 3=10^x and 30=10^x.<br />
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Common questions:<br />
"Can we write on this?"<br />
"How close do we have to be?"<br />
"Is there an easier way to do this?"</div>
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then I introduce the common log as a way to undo a base, while first reminding them that they just learned how to undo a power (raise to the reciprocal power).</div>
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I solve 1=10^x by taking the log of both sides, and show how things reduce. Then students find the rest of the values by using the log function. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZsaDG_zC289TdVN3d_Rh4cbEXu64rdq7PPUj7tUxJHnJE4mM5BBdQ8-oHOJD4pgcFGXYuV58LUPMhqlasxHhMArVK4V3qh0n0cbEiYN3AU3FcUHpVuxZz4erBpx8paLsh6iq16Gci3DU/s1600/Calc+skillz-logs.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="116" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZsaDG_zC289TdVN3d_Rh4cbEXu64rdq7PPUj7tUxJHnJE4mM5BBdQ8-oHOJD4pgcFGXYuV58LUPMhqlasxHhMArVK4V3qh0n0cbEiYN3AU3FcUHpVuxZz4erBpx8paLsh6iq16Gci3DU/s320/Calc+skillz-logs.JPG" width="320" /></a>Then we talk about how this is all in base 10 and the 10 is not written but is implied. Someone, almost on cue, asks "how do you solve if the base isn't 10?" which leads us into the notes on uncommon logs. I hand out a slip (calculator instructions) that students glue into their notebook, and go over this process. then we do one example, base 3.</div>
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At this point I don't have time to prove the rules so I show them were they come from and we write them down in our exponent booklet. for example 2^3*2^5=2^(2+3)=2^8 leads to the log property log(a*b)=log(a)+log(b)</div>
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Exit slip: expand this logarithm</div>
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Day 2: We talk about how the scale they used in the Moore's law activity is a logarithmic scale, increasing by exponents. then we look back on the logarithmic lions, and talk about how the scale is adjusted. then its back to logarithms rules in their booklet. I will on the side also introduce natural logarithms but we wont work much with them. Homework time. This introduction on day 2 was too boring, and needs to be beefed up. Also, I should have done a few more example on the <a href="https://www.dropbox.com/s/tm6jl28lbtmjziy/Hw%20%23%2014%20high%20challenge%2C%20log%20rules.docx">homework packet</a> before letting students loose.</div>
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Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-5616128564399131932013-11-14T10:01:00.000-08:002013-12-03T09:00:11.615-08:00Cowboy Bob vs. Big-City Slick<div dir="ltr" style="text-align: left;" trbidi="on">
Learnign target: students can model multiple years at a time with compound interest.</div>
Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-19117686223270500392013-11-11T18:02:00.002-08:002013-11-11T18:11:32.088-08:00Inverse functions and SneechesLearning target: students can write equations for inverse functions<br />
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First we start out reviewing composition of functions f(g(x)). I've never taught inverses this way before so we'll see.<br />
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<a href="http://www.mathsisfun.com/sets/images/function-apple-banana.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="50" src="http://www.mathsisfun.com/sets/images/function-apple-banana.gif" width="320" /></a></div>
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<a href="http://www.theforum.co.za/ForumNew/Uploads/image/images/Blog%20images/Dr%20Seuss.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://www.theforum.co.za/ForumNew/Uploads/image/images/Blog%20images/Dr%20Seuss.jpg" /></a></div>
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This lesson is partially a tribute to a personal hero of mine.</h3>
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after they've been working for a while we take a break by watching this video, its about 12 minutes and not about math, but students are due for something novel in class, they've been grinding the wheel for a while, so we watch this:<br />
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dzCbteJ-Js2SnQTxCQPsaHgXve6BZg7x9FT71liaPK-EtH8E6ARAMRjExpepKp5vzuqUP8i4I4aKJWr7nHoQA' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
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<a href="http://freelancechristianitydotcom.files.wordpress.com/2013/01/285_top_10_list1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="133" src="http://freelancechristianitydotcom.files.wordpress.com/2013/01/285_top_10_list1.jpg" width="320" /></a></div>
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Here is the worksheet that I've been using:<br />
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<embed allowfullscreen="true" allowscriptaccess="always" height="600" src="https://app.box.com/embed/q94in6chyf9n2df.swf" type="application/x-shockwave-flash" width="900" wmode="opaque"></embed>Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-74156764922798843262013-11-11T17:52:00.001-08:002013-11-11T17:52:17.880-08:00Dead Puppy TheoremI have to say I stole this from a college of mine, Chris Lusto wrote a post about it:<br />
<a href="http://linesoftangency.wordpress.com/2012/01/20/the-dead-puppy-theorem/">http://linesoftangency.wordpress.com/2012/01/20/the-dead-puppy-theorem/</a><br />
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Dead puppy theorem: every time a student distributes an exponent to a binomial a puppy dies. That is...</h2>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpYkhhiPDWs5O0beBljUyNA39KtdM9H8knkPCVy5QPlI4D-TbPuAPlqUYg96EtLCW0KJCByJA49J65j60weY0mKH8Hd1LNVxfFppdqOhiUAcXk9plxxnIDqwL4CvdXNWSSnHIwYtEW09k/s1600/dead+puppy+theorem.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="65" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpYkhhiPDWs5O0beBljUyNA39KtdM9H8knkPCVy5QPlI4D-TbPuAPlqUYg96EtLCW0KJCByJA49J65j60weY0mKH8Hd1LNVxfFppdqOhiUAcXk9plxxnIDqwL4CvdXNWSSnHIwYtEW09k/s320/dead+puppy+theorem.JPG" width="320" /></a></div>
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I introduced the idea during a warm up, and the students really liked it. It always helps to throw up a picture like this:<br />
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<a href="https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcTaVZ5e3Wch-ek4JfMqQq2cZMRr2C4SdT3lELHEW3aVkuSgUwAj" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcTaVZ5e3Wch-ek4JfMqQq2cZMRr2C4SdT3lELHEW3aVkuSgUwAj" /></a></div>
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would you kill this puppy?</div>
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Every so often a student kills a puppy:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmwZdHq87ze27L_Xdt7pfERRXdxTvzqi1Zan0buQQX2HEqImraAmlpu_qt-CUTJQt2r6_bdJ-C_zWMCOQEgbwflhZgCAyLwhYkn4XseXp5J_fSLwef9hTalJax9OJzjb_-kMhMxfE-Iso/s1600/IMAG0075.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="361" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmwZdHq87ze27L_Xdt7pfERRXdxTvzqi1Zan0buQQX2HEqImraAmlpu_qt-CUTJQt2r6_bdJ-C_zWMCOQEgbwflhZgCAyLwhYkn4XseXp5J_fSLwef9hTalJax9OJzjb_-kMhMxfE-Iso/s640/IMAG0075.jpg" width="640" /></a></div>
<br />Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-49205469348576579732013-11-08T17:18:00.002-08:002013-11-11T18:24:17.740-08:00Exponential Alice<div dir="ltr" style="text-align: left;" trbidi="on">
Learning target: students can model exponential situations.<br />
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This was a good lesson for sorting out repeated multiplication issues.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnzggknrRwbVLfmPJM5eYxFNVG__DHzGVh8dBbyWgA8i_VNW3hsOdBwlbePP0bLjVqfmdvgKiaNd_OVxdJXkQIY3MnJCRHh3O-3nrra8EMfUv3cRLyDKfjrTDU1g4O28rJ6BkoiFCCP9A/s1600/Alice1.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnzggknrRwbVLfmPJM5eYxFNVG__DHzGVh8dBbyWgA8i_VNW3hsOdBwlbePP0bLjVqfmdvgKiaNd_OVxdJXkQIY3MnJCRHh3O-3nrra8EMfUv3cRLyDKfjrTDU1g4O28rJ6BkoiFCCP9A/s320/Alice1.JPG" width="257" /></a>Dispite the fact that I;ve been writting equations with ratios like this for some time students still want to multiply the 4 by 30% and add it back on to 4. Aside from the fact that such steps make it hard to see what the pattern is (are we multiplying or adding? Both?) the only problem I see with this is an economy of calculations, if a student makes a mistake they feel like they have to start over because they were balancing so many things in their head at the time.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMSuM5snyyBQYlbEO6ZcCju_E4Dp4qeMF-WbgjHjoIOik_hx3WFkQbohmeOyDm6JKCRjLm8rkMK37HXG3qnW-aCISlNE0w-xsf8eyucFwzkFnI3anFJBDhCtsGTUB5oh6G0Ak2wzqDLDo/s1600/Alice2.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="193" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMSuM5snyyBQYlbEO6ZcCju_E4Dp4qeMF-WbgjHjoIOik_hx3WFkQbohmeOyDm6JKCRjLm8rkMK37HXG3qnW-aCISlNE0w-xsf8eyucFwzkFnI3anFJBDhCtsGTUB5oh6G0Ak2wzqDLDo/s320/Alice2.JPG" width="320" /></a>On the worksheet students are asked to calculate how tall she would be if she ate 2 oz of cake. When students rush to calculate 2 oz without first calculating 1 oz they usually do 4(1.00+.60) because 30%+30%=60%. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2YVUBleab_uzLoAIz42wRJlai1ge7V8lU24piqDkpGb036n9SfG5g6H18njKI8zD_xgfbue9_MCIEcso6BwXeMcdS5EWdhaMgiMUooGvX0S-excdlWAjI1ismVKhRWsTYIihLml9PigM/s1600/Alice+3.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="197" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2YVUBleab_uzLoAIz42wRJlai1ge7V8lU24piqDkpGb036n9SfG5g6H18njKI8zD_xgfbue9_MCIEcso6BwXeMcdS5EWdhaMgiMUooGvX0S-excdlWAjI1ismVKhRWsTYIihLml9PigM/s320/Alice+3.JPG" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjfs3QmlV2zMegaXUDDPwk2JIci4uAVqHarx_wcg8xdW7bZhyjgHe3ZPHtWoILZgKUHR5hCALdmEPEcYFjpzH_bnyciQL7iCVu6-7BL4li_CtR_TRynGchyphenhyphenWs8KD6A35w9wBJLbuAWR1c/s1600/Alice+4.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="190" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjfs3QmlV2zMegaXUDDPwk2JIci4uAVqHarx_wcg8xdW7bZhyjgHe3ZPHtWoILZgKUHR5hCALdmEPEcYFjpzH_bnyciQL7iCVu6-7BL4li_CtR_TRynGchyphenhyphenWs8KD6A35w9wBJLbuAWR1c/s320/Alice+4.JPG" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcOA5p_wPuajKAIAVOd96_fk_Uc9gLtky3xmRzHRpZabpXoagI8dFGAEQyF3L2LCiWLEeczccWlRxQiVRrtu5UjJJ-Lt4FT86A8_kTeQKscilppR9TAJ-aNMmqe_Os1GXCFwZMmB9lpnY/s1600/Alice+5.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="190" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcOA5p_wPuajKAIAVOd96_fk_Uc9gLtky3xmRzHRpZabpXoagI8dFGAEQyF3L2LCiWLEeczccWlRxQiVRrtu5UjJJ-Lt4FT86A8_kTeQKscilppR9TAJ-aNMmqe_Os1GXCFwZMmB9lpnY/s320/Alice+5.JPG" width="320" /></a>When modeling this with an equation a common mistake is for students to write y=x(1.3), mixing up the recursive and explicit method of describing this pattern.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjodoz_dKMz7y3TQs5KdUexfFqBvpLc5aVImf1xYBiZNfgdiEL4zIKPJ3A6NbA7tvAjXR9km1b98_Tyel1QNVaRcqhkCttlTdchoUqliWCthy2Hx7Mfpw8X8-rXnR_6Ohra5T-eGzRqj1k/s1600/11-08-2013-10-13-35.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjodoz_dKMz7y3TQs5KdUexfFqBvpLc5aVImf1xYBiZNfgdiEL4zIKPJ3A6NbA7tvAjXR9km1b98_Tyel1QNVaRcqhkCttlTdchoUqliWCthy2Hx7Mfpw8X8-rXnR_6Ohra5T-eGzRqj1k/s640/11-08-2013-10-13-35.jpg" width="640" /></a></div>
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Then, every so often I can tell that students want to know this stuff. I find evidence of a student putting in EXTRA effort to make sense of a problem. #2 show the meaning of each part of this equation. Beautiful.<br />
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Here is an available version of the worksheet:<br />
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<embed allowfullscreen="true" allowscriptaccess="always" height="600" src="https://app.box.com/embed/m84d8v5r197em2z.swf" type="application/x-shockwave-flash" width="900" wmode="opaque"></embed>Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-2361606904906983542013-11-08T09:43:00.000-08:002013-11-09T15:16:44.162-08:00Moore's Law<div dir="ltr" style="text-align: left;" trbidi="on">
Learning target: students can make predictions based on exponential growth<br />
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Right off the bat I throw <a href="https://www.dropbox.com/s/pn18xlmjm5ngnwk/transistor%20photo%20essay.docx">this packet</a> at them and ask them to read it. Its the MIT photo essay of various computer chips and transistors throughout computer history.<br />
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I ask students what their questions are and I get a range of answers including:<br />
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"What is this?"<br />
"How does this relate to what we are doing in class?"<br />
"Why are we reading this?"<br />
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So I tell them that the first picture is the birth of the digital age, and give them a brief overview of what a transistor is and how it related to computing power.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZHPzEJNvIeR8GEDJ3XJB3ovvzLclz8_3018Oy_Pd3xxK84IKy5sV19wE21PMl3gCXTxViUxtnPd4mgj8IPqyXUe17GpTWsuBN7zgVvwvcVSk-MiVpXFGNkmMoQ4jrT8kP01bqSK6VE94/s1600/first+computer+transistor.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZHPzEJNvIeR8GEDJ3XJB3ovvzLclz8_3018Oy_Pd3xxK84IKy5sV19wE21PMl3gCXTxViUxtnPd4mgj8IPqyXUe17GpTWsuBN7zgVvwvcVSk-MiVpXFGNkmMoQ4jrT8kP01bqSK6VE94/s320/first+computer+transistor.jpg" width="320" /></a></div>
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From their questions it was clear I was not going to get a question that would involve making a prediction so I gave them the task:</div>
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<b>1. how many transistors are their in a computer chip made in 2013/2014? </b></h3>
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(This we can look afterwards and see what reasonable answer would be)</div>
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<b>2. When will the number of transistors pass the trillion transistor mark?</b></h3>
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Step 1: make a guess. I ask students to make a guess, based on what their gut says and the data points. I can steer them a little "what number do you know it has to be bigger than?" Studies show student engagement increases if they make a guess 1st. I had students write down their guesses and I ut them into an excel file.</div>
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Step 2: attack! It took a while for students to even begin to start this problem. Then eventually someone figured out they had better make a table just to get something.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjem9z8eh7da-gWcWgt5cbBttePQjSPB1V3sUUQ57vz8vdGhY_bkDMRzGfs1FBnLB6hybmvqy_qBzTgK5cBQCmEsL9ApZtd7Aqk9z0B6sP1qhFvm-NGCWI0_qntSL8G8O0djmwXN4kudZI/s1600/11-07-2013-13-55-46.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjem9z8eh7da-gWcWgt5cbBttePQjSPB1V3sUUQ57vz8vdGhY_bkDMRzGfs1FBnLB6hybmvqy_qBzTgK5cBQCmEsL9ApZtd7Aqk9z0B6sP1qhFvm-NGCWI0_qntSL8G8O0djmwXN4kudZI/s400/11-07-2013-13-55-46.jpg" width="400" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6ZPlOjYmKk_EY_Ge6sowI9fDPonIl9dnCwe_AAiNc2WThWpw08cfYQoI1SYR2z_CNAZhFR5NRiWNYpXxztW3WB-yvhbUEF-b6Xb969CuGCJM22qTJXnJYPRVEpeRe0Nn5462z5RW3l-E/s1600/11-07-2013-13-52-00.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6ZPlOjYmKk_EY_Ge6sowI9fDPonIl9dnCwe_AAiNc2WThWpw08cfYQoI1SYR2z_CNAZhFR5NRiWNYpXxztW3WB-yvhbUEF-b6Xb969CuGCJM22qTJXnJYPRVEpeRe0Nn5462z5RW3l-E/s400/11-07-2013-13-52-00.jpg" width="400" /></a></div>
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Then they found the common differences and realized that wasn't useful, so to set students up for the next part I told them a graph was another strategy they could try. After some time I got the question "Mr. Olson, what should the scale be? How am I going to fit 1 and 371 million on the same graph?" -this will be a great lead in to logarithms.</div>
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While trying to make an exponential line of best fit students needed to know how to find the average ratio from year to year. This proved difficult since the data isn't pretty and the years aren't uniform.</div>
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Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-1964263254598339482013-11-06T13:48:00.001-08:002013-11-06T19:20:59.013-08:00Exponent rules 4-in-a-row<div dir="ltr" style="text-align: left;" trbidi="on">
Learning target: students can apply exponent rules.<br />
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<a href="http://teachingcollegemath.com/wp-content/uploads/2011/04/Exponent-Block-1-480x287.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="191" src="http://teachingcollegemath.com/wp-content/uploads/2011/04/Exponent-Block-1-480x287.jpg" width="320" /></a></div>
This activity comes from <a href="http://busynessgirl.com/exponent-block-and-factor-pair-block/">http://busynessgirl.com/exponent-block-and-factor-pair-block/</a><br />
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It was a very engaging way to practice exponent rules, which can be a very dry topic.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmYMMJ8Wz33awAOehazO7TKa1U4_HdlaPKTMHuy6kj2Spc1-q9eVpBRSvBQQrF1qWAexfeIph6uDOBtCZZx8CkTonamXXZqqmirAcRK9b2td1pL0c5Q5nnlLIx-fiO5VgYHqi6AxNZ25k/s1600/IMAG0071.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmYMMJ8Wz33awAOehazO7TKa1U4_HdlaPKTMHuy6kj2Spc1-q9eVpBRSvBQQrF1qWAexfeIph6uDOBtCZZx8CkTonamXXZqqmirAcRK9b2td1pL0c5Q5nnlLIx-fiO5VgYHqi6AxNZ25k/s320/IMAG0071.jpg" width="320" /></a>Two students playing one another.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJInEfRvqjpnSfCeVsqy1u1i3zxm302bc3-t8rKIwQGHjpaxQeyJPYWO6BHFSVVh-EQkalahEaifvBUHyj1N0GRPnJWOpwlWf6EfIUkQxEZU3eV1SFOeyiDvr-dm4LuylU09_pEcKneRU/s1600/IMAG0070.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJInEfRvqjpnSfCeVsqy1u1i3zxm302bc3-t8rKIwQGHjpaxQeyJPYWO6BHFSVVh-EQkalahEaifvBUHyj1N0GRPnJWOpwlWf6EfIUkQxEZU3eV1SFOeyiDvr-dm4LuylU09_pEcKneRU/s320/IMAG0070.jpg" width="320" /></a> A veiw of some sample calculations, scratch paper is a must for this activity.</div>
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What I liked about this is none of my students picked up their calculator. </div>
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Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-75774398927510521022013-11-06T13:37:00.001-08:002013-11-08T08:40:28.287-08:00Exponent rules<div dir="ltr" style="text-align: left;" trbidi="on">
Learning target: students can apply exponent rules<br />
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to try to shake up the way we take notes on this we make a little booklet of all the exponent rules. I saves the last page for Logarithms and the second to last for examples of solving.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqx77VF5L__siRkZm8XELnApDFSV0l21JSoRoj3P2KM7MUJIdJgEgoUYz3pLQMRZHSFimpjykHCKZ2PAOYC3V6FcdPrQ3oQ7G9BH_EqHkwApEA_40iJipj3yEoO4LCi9zBhy2wepmatig/s1600/IMAG0069.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqx77VF5L__siRkZm8XELnApDFSV0l21JSoRoj3P2KM7MUJIdJgEgoUYz3pLQMRZHSFimpjykHCKZ2PAOYC3V6FcdPrQ3oQ7G9BH_EqHkwApEA_40iJipj3yEoO4LCi9zBhy2wepmatig/s320/IMAG0069.jpg" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsG93Mt8cFKtbfM0HnJsB9InhlUvGbmvI1EU3bri8EUBoexV4k1sq0L7D19Ni3GuRgt3Soh8InBMq1tvZS40FNyvJ92Ub_-1Yzrvgsw6B60RF1K2TyXXr0tdwB4Dc20QqgRQfjmgdnHc4/s1600/IMAG0068.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsG93Mt8cFKtbfM0HnJsB9InhlUvGbmvI1EU3bri8EUBoexV4k1sq0L7D19Ni3GuRgt3Soh8InBMq1tvZS40FNyvJ92Ub_-1Yzrvgsw6B60RF1K2TyXXr0tdwB4Dc20QqgRQfjmgdnHc4/s320/IMAG0068.jpg" width="320" /></a></div>
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questions to address: if 2^5/2^3=2^2 than what does 2^3/2^5 equal? If all the twos on top cancel out whats left on top? Zero?<br />
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how do you expand (3x^2)^3 with the power to a power rule? We need to talk more about making 3=3^1<br />
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after which I gave out this A-B sheet stolen from <a href="http://function-of-time.blogspot.com/">f(t)</a><br />
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<a href="https://www.dropbox.com/s/ppjzimfcnf83e7q/Practice-Row%20Game%20Exponent%20Rules.docx">Row-game exponent rules</a><br />
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Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-8556991426586967612013-11-05T18:58:00.001-08:002013-11-05T19:33:42.214-08:00Green Ball BounceLearning target: students can compare models and make deductions based on multiple representations.<br />
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This lesson was meant to be a review of sequences and an introduction to exponential functions, but would also be a good introduction to sequences and recursion in and of itself. I gave students 4 clues and asked them to answer the questions on the cards:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicZ2LST7RGC1xFckk7YRsdZuxh6pr0mZC_yFawN9SDyzSviqCg6SWJRlKNhpsnhTV35u1-dL0jYwLT84jbcGU3WYPQXBJA-zueOVKGnZidicyzxMxg6QkYgnpjXN_KmyUe-T5tby3juHE/s1600/Green+Ball+bounce.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicZ2LST7RGC1xFckk7YRsdZuxh6pr0mZC_yFawN9SDyzSviqCg6SWJRlKNhpsnhTV35u1-dL0jYwLT84jbcGU3WYPQXBJA-zueOVKGnZidicyzxMxg6QkYgnpjXN_KmyUe-T5tby3juHE/s1600/Green+Ball+bounce.JPG" /></a></div>
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<a href="https://www.dropbox.com/s/8k4zkr34rk7ppdb/Investigation%20green%20and%20red%20linyaballs%20and%20Proportiaballs.xlsx">Link to the document</a></div>
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It took a while for students to make sense of the problem and in some classes I had to start them out with a problem statement: On what bounce are the balls closest in height? The other questions are important as well: On what bounce is one ball higher? On what bounce is the other ball higher? ...but sometimes too much at once is crippling.<br />
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My goal was for students to create multiple representations according to the LESH model:<br />
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<a href="http://mason.gmu.edu/~jsuh4/pictures/figure%202.leshmodel.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="211" src="http://mason.gmu.edu/~jsuh4/pictures/figure%202.leshmodel.JPG" width="400" /></a></div>
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I tried to get them to draw a picture of what the scenario looked like but was met with a lot of resistance. It would have helped them to determine how many balls and how many people were involved and what questions they had to answer.</div>
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Here are some great examples of student work:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN4iffjewy3UWeqAXcVg5ZyPxSNOYgjj31yn4rE7owlaQRAmldb_YQUDS_A7XZUoAr69kvKL0e93VGUxKIc2kj6A4VNfmbjl4DAELYA5n_U5hHiQ5jiIXAhu_3t3XzK-2e4CE1w2GcnwU/s1600/ball+bounce+1.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN4iffjewy3UWeqAXcVg5ZyPxSNOYgjj31yn4rE7owlaQRAmldb_YQUDS_A7XZUoAr69kvKL0e93VGUxKIc2kj6A4VNfmbjl4DAELYA5n_U5hHiQ5jiIXAhu_3t3XzK-2e4CE1w2GcnwU/s400/ball+bounce+1.jpg" width="400" /></a></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyftgK31tRnO05yfdGku66PiOJ-xMuBCr6NibUYxd1ge89UY6dhmYWCtUo-r8-_c3l284Uxsh6GfV-BV1uRLXlC8Fs2XZRK31IwP8x-lS6krYmPj0OwdoDsoAr98aAnoiPfD0f_KfAsMc/s1600/ball+bounce+4.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyftgK31tRnO05yfdGku66PiOJ-xMuBCr6NibUYxd1ge89UY6dhmYWCtUo-r8-_c3l284Uxsh6GfV-BV1uRLXlC8Fs2XZRK31IwP8x-lS6krYmPj0OwdoDsoAr98aAnoiPfD0f_KfAsMc/s400/ball+bounce+4.jpg" width="400" /></a><br />
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A great table, but I wish they would have defined what x and y represented.<br />
Students who did not make an adequate enough graph said that the balls were the closest on bounce 4, but they are actually closer on bounce 15, reinforcing the need for thoroughness.<br />
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<span style="text-align: left;">A good looking graph, complete with axis labels. Again, its easy to see that their are two spots where the balls could be the same height. Also, its easier to see which ball bounces higher during which bounce. Students who made an inadequate graph said that the Proportiaball bounces higher from 1-3 bounces but left out the second interval from 16 on. This is a good way to seque into domain as well.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4ioLfv7GuM2T4xcc881gQPTN51fm26XdFDMiKTuui7WjPt4q6ursw3LXS7X6277s8v3tvK-E5eNgKejsIettE538JO3zCSiksuCtp4yKV_5HnvpFnPgvfh2bSFptnO5Qwy0Bt-oeD8oM/s1600/Ball+bounce+5.jpg" imageanchor="1" style="clear: left; display: inline !important; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4ioLfv7GuM2T4xcc881gQPTN51fm26XdFDMiKTuui7WjPt4q6ursw3LXS7X6277s8v3tvK-E5eNgKejsIettE538JO3zCSiksuCtp4yKV_5HnvpFnPgvfh2bSFptnO5Qwy0Bt-oeD8oM/s400/Ball+bounce+5.jpg" width="400" /></a><span style="text-align: center;"></span></div>
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Here is one common misake students make for the Proportiaball, they do the first calculation: 120(1.00-.10) and get 12, then assume that the ball decreases by 12 each time.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipolSTuhkFS_XXFVDJnHVWIVjPmyjhWGLyvwVl98Y_RL8SHhf-RlUIBKrQv_4kTXns9lXzHOPSKqfTxeGCBlbYGfkz1Z4PU8IyKOswFRA02dCqYTAQ9ZLdHIsKAPjwPDh_PoPI9VjHg84/s1600/Ball+bounce+7.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipolSTuhkFS_XXFVDJnHVWIVjPmyjhWGLyvwVl98Y_RL8SHhf-RlUIBKrQv_4kTXns9lXzHOPSKqfTxeGCBlbYGfkz1Z4PU8IyKOswFRA02dCqYTAQ9ZLdHIsKAPjwPDh_PoPI9VjHg84/s400/Ball+bounce+7.jpg" width="400" /></a><br />
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<span style="text-align: center;">Here is good student work showing the calculations, where its easy to see the ratio is always going to be (1.00-.10)</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8QH3IoXcg7pdLWOAv8TrbX1r659n0rOIPwiSLwc0lGJBCv8r9qrW5HMKFFaPvN2LQ6IcEBffOSPl1dPFhakOEVB00V4w-z5m-UIfI1cD-EqCW-CYhJnYQvS1AX_MdJSkFmT-I644zINA/s1600/ball+bounce+8.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8QH3IoXcg7pdLWOAv8TrbX1r659n0rOIPwiSLwc0lGJBCv8r9qrW5HMKFFaPvN2LQ6IcEBffOSPl1dPFhakOEVB00V4w-z5m-UIfI1cD-EqCW-CYhJnYQvS1AX_MdJSkFmT-I644zINA/s400/ball+bounce+8.jpg" width="400" /></a></div>
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I caught several students who were going to go until the height of the Proportiaball was zero, when I asked them if they thought it was going to get to zero they said yeah, its going down, eventually it will be zero. This thinking leads right into algebraic limits and asymptotes. I brought this concept up to all of my classes and one student responded: "If I walk half the way to the lunchroom, then walk half the remaining distance, then walk half of that remaining distance, and so I won't ever mathematically reach the lunchroom, there will always be a small distance left."<br />
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To help with the idea that the Proportiaball never reached the ground I made this geogebra file and zoomed in and zoomed in to show them the function never touches the y-axis:<br />
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This student was able to write the recursive equations for each ball. In general, all of my students had a tough time coming up with the explicit exponential equation for this activity.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEih8S2Bd2YJtr9JF49O3xm4z-9dp112rI7phf-Muus9lchqMdxeG3ISl9UKuHA2TCsOS7Jb2WlMMPXhdVLb1dS7djQLIa1qBmRPv96bQAg80nQUTPcXCmIeSSDHzk-W1L07rbPI9L9VPZY/s1600/ball+bounce+9.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEih8S2Bd2YJtr9JF49O3xm4z-9dp112rI7phf-Muus9lchqMdxeG3ISl9UKuHA2TCsOS7Jb2WlMMPXhdVLb1dS7djQLIa1qBmRPv96bQAg80nQUTPcXCmIeSSDHzk-W1L07rbPI9L9VPZY/s640/ball+bounce+9.jpg" width="640" /></a></div>
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As a follow up to describing patterns and anticipating exponent rules I gave this homework out<br />
<a href="https://www.dropbox.com/s/eynbqggv5tcf2rn/Hw%20%2311.docx">describing exponential patterns HW</a>Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-69986287072671393442013-11-05T18:52:00.002-08:002013-11-06T19:19:40.954-08:00Exponents with Tarsia tilesLearning target: students can calculate numbers involving exponents.<br />
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This was a great introduction into exponent rules. Students worked together to try to complete this Tarsia Puzzle<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvdK2V6xpZXZya1ixYgu_BgAay1HjbtIjqgNu3XcknWy3BmKEgPZ2bkh24d4KOBtDvzU3kze_CJAVIoVrghdGDbK-7SShn9RqhXPikHl8k37OzF-tROhJ8A-d532fu4CVMDBrYsDXbqnk/s1600/tarsia+sol.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="280" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvdK2V6xpZXZya1ixYgu_BgAay1HjbtIjqgNu3XcknWy3BmKEgPZ2bkh24d4KOBtDvzU3kze_CJAVIoVrghdGDbK-7SShn9RqhXPikHl8k37OzF-tROhJ8A-d532fu4CVMDBrYsDXbqnk/s320/tarsia+sol.jpg" width="320" /></a></div>
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<a href="https://www.dropbox.com/s/536npun1lybcxh1/tarsia%20sol.jpg">link to the image</a></div>
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This was a good activity to get students back in the exponent mindset and clear up any calculator skills questions. Some students would use the ^2 key on their calculator and then go back and change the 2. Some students quickly figured out how to use the parenthesis effectively. I had just about 100% engagement for the whole activity, and I had students of mixed ability levels working well with each other.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXe8CyHAp1o7Fg8cC-n6J1i3B4itJPx2DWjNE_6IYfGfNq1BGxhJ5zbV3pxoDN2aXPSr_Z8Y1-4TqZ91IMVjbXEjsSSrIsb5GKRuG8OHH-oOWdpQ7zz7TOIZYaL2cKgQ2Fd3oT1WI_aHk/s1600/2013-11-06+14.30.03.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXe8CyHAp1o7Fg8cC-n6J1i3B4itJPx2DWjNE_6IYfGfNq1BGxhJ5zbV3pxoDN2aXPSr_Z8Y1-4TqZ91IMVjbXEjsSSrIsb5GKRuG8OHH-oOWdpQ7zz7TOIZYaL2cKgQ2Fd3oT1WI_aHk/s400/2013-11-06+14.30.03.jpg" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsNdAyKWDLJX0j4_cUVwHZ1yNsrg02n3c43YBjTyu-OFhpDd6lKpz1Pzsw1w8l171zmpOLp_hP9gxa-EqQRdIQTViT_emamPxdGp5CGEnG391MRyp0kE8qJiOaaNB2idq113t2UgwrhVw/s1600/2013-11-05+12.39.14.jpg" imageanchor="1"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsNdAyKWDLJX0j4_cUVwHZ1yNsrg02n3c43YBjTyu-OFhpDd6lKpz1Pzsw1w8l171zmpOLp_hP9gxa-EqQRdIQTViT_emamPxdGp5CGEnG391MRyp0kE8qJiOaaNB2idq113t2UgwrhVw/s400/2013-11-05+12.39.14.jpg" /></a><br />
My 4th hour class trying to figure it out.^<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnY9cYIXOGNp807ewncBhvfI0in9164htH-p3mI_7T2O5Kwf_ItX_JVoROiCcKloVJJUNtWRBxvsQtldF7dzDbPmu9qxIAbgLqpeeF7fgQoD3KKVvRTg68Z4ytzl3Ued2m5g22W01nz1g/s1600/2013-11-04+13.55.29.jpg" imageanchor="1"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnY9cYIXOGNp807ewncBhvfI0in9164htH-p3mI_7T2O5Kwf_ItX_JVoROiCcKloVJJUNtWRBxvsQtldF7dzDbPmu9qxIAbgLqpeeF7fgQoD3KKVvRTg68Z4ytzl3Ued2m5g22W01nz1g/s400/2013-11-04+13.55.29.jpg" /></a><br />
Not all students finished but the ones that did took great pride in figuring it all out. Some of them even asked if they could take a picture of their finished puzzle with their phones. Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com1tag:blogger.com,1999:blog-7940954929827899270.post-3564434822687946162013-10-02T13:41:00.000-07:002014-01-09T09:55:21.670-08:00Geogebra function machine<div dir="ltr" style="text-align: left;" trbidi="on">
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geogebra functions<br />
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Guess the parent:<br />
<a href="https://drive.google.com/folderview?id=0BxjT-thw_52JTThyckFoZDFwbzQ&usp=sharing">https://drive.google.com/folderview?id=0BxjT-thw_52JTThyckFoZDFwbzQ&usp=sharing</a><br />
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Guess the transformation (easier):<br />
https://www.dropbox.com/s/90o1ot7ndx10ps0/Function%20Machine%20parent%20problem%201.ggb<a href="https://www.dropbox.com/s/90o1ot7ndx10ps0/Function%20Machine%20parent%20problem%201.ggb">Function machine problem 1</a><br />
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Guess the transformation (hard):<br />
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From dropbox:<br />
<a href="https://www.dropbox.com/s/90o1ot7ndx10ps0/Function%20Machine%20parent%20problem%201.ggb">Problem 1</a><br />
<a href="https://www.dropbox.com/s/gcherio20w233hi/Function%20Machine%20parent%20problem%202.ggb">Problem 2</a></div>
<iframe height="400px" scrolling="no" src="http://www.geogebratube.org/material/iframe/id/54360/width/400/height/400/border/888888/rc/false/ai/false/sdz/false/smb/false/stb/false/stbh/true/ld/false/sri/false/at/preferjava" style="border: 0px;" width="400px"> </iframe></div>
Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-48437765564859957752013-09-30T13:24:00.001-07:002013-09-30T13:24:11.186-07:00Unit 1 sequence review<div dir="ltr" style="text-align: left;" trbidi="on">
<div dir="ltr" style="text-align: left;" trbidi="on">
Students self corrected the practice test and began work on the review<br />
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Review:<br />
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<embed allowfullscreen="true" allowscriptaccess="always" height="400" src="https://app.box.com/embed/58n3txfhypu3xgo.swf" type="application/x-shockwave-flash" width="466" wmode="opaque"></embed>
Review solutions:<br />
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<embed allowfullscreen="true" allowscriptaccess="always" height="400" src="https://app.box.com/embed/jxfg6ns94b56rd5.swf" type="application/x-shockwave-flash" width="466" wmode="opaque"></embed>
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Practice test student solutions:</div>
<embed allowfullscreen="true" allowscriptaccess="always" height="400" src="https://app.box.com/embed/68lgyee5k6bxeqg.swf" type="application/x-shockwave-flash" width="466" wmode="opaque"></embed></div>
Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0tag:blogger.com,1999:blog-7940954929827899270.post-66173483898549829392013-09-25T14:05:00.000-07:002013-09-26T16:04:19.248-07:00Penny Pyramid<div dir="ltr" style="text-align: left;" trbidi="on">
Learning target: I can add the terms of a sequences and describe it using partial sums<br />
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This lesson was adapted from here:<br />
<a href="http://threeacts.mrmeyer.com/pyramidofpennies/act1/actone.mov">http://threeacts.mrmeyer.com/pyramidofpennies/act1/actone.mov</a><br />
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Mr. Olsonhttp://www.blogger.com/profile/11456492923614438279noreply@blogger.com0