tag:blogger.com,1999:blog-38826907707432397082024-03-18T12:32:15.523-07:00Hands On MathBurn The Textbooks, Shred The Worksheets, Teach Math.Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.comBlogger251125tag:blogger.com,1999:blog-3882690770743239708.post-32586211342326471042018-05-30T07:37:00.000-07:002018-05-30T07:37:02.264-07:00Percentages, Decimals, Fractions Diamond Blocks In Minecraft<div dir="ltr" style="text-align: left;" trbidi="on">
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com295tag:blogger.com,1999:blog-3882690770743239708.post-84952311121659919022018-05-21T08:19:00.000-07:002018-05-21T08:19:07.639-07:00Practicing Integer Addition w/ Paper Football Game<div dir="ltr" style="text-align: left;" trbidi="on">
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com110tag:blogger.com,1999:blog-3882690770743239708.post-73022140329291502112018-05-21T07:40:00.000-07:002018-05-21T07:40:17.619-07:00Memorization Tool For Integer Multiplication & Division Using Emoji's<div dir="ltr" style="text-align: left;" trbidi="on">
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com30tag:blogger.com,1999:blog-3882690770743239708.post-16339965301555553332018-05-16T08:00:00.005-07:002018-05-16T08:01:44.932-07:00Math Checkers Board Game<div dir="ltr" style="text-align: left;" trbidi="on">
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com25tag:blogger.com,1999:blog-3882690770743239708.post-46218578394187961602018-05-08T16:05:00.002-07:002018-05-08T16:05:43.049-07:00Driving Blind? <div dir="ltr" style="text-align: left;" trbidi="on">
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com29tag:blogger.com,1999:blog-3882690770743239708.post-43501039694728049922014-12-13T08:35:00.000-08:002014-12-13T08:35:45.787-08:00Building a Wheelchair Ramp Model With Slope 1/12<div dir="ltr" style="text-align: left;" trbidi="on">
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<h2 class="MsoNormal" style="margin: 0in 0in 0pt; text-align: center;">
Building a Wheelchair Ramp Model With Slope 1/12</h2>
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The scenario was the following. </div>
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Grandma wanted to come see her grandson play high school
football but the bleachers were not wheelchair accessible. The students were
asked to build a model wheelchair ramp that was accessible to the top bleacher
while also staying within ADAs (Americans With Disabilities) building code—the slope
must be exactly 1/12 throughout the ramp. </div>
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The students were giving the following model conversion
scale</div>
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<h3 class="MsoNormal" style="margin: 0in 0in 0pt; text-align: left;">
5 yards = 1 inch.</h3>
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Using this, they modeled a 120 x 50 yards football field into
a 24’’ x 10’’ football field.</div>
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<o:p> </o:p></div>
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Next, using the bleachers my six year old son built for
them, they measured the height at 2’’. </div>
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Using the 1/12 slope, they built a 24’’
incline wheelchair ramp. </div>
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</div>
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Then converted these scaled numbers to real life. 5 yards =
1 inch. Meaning a 2’’ height = 10 yards of actual height and 24’’ ramp = 120
yards. </div>
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com23tag:blogger.com,1999:blog-3882690770743239708.post-36425045621874659032014-11-01T09:16:00.000-07:002014-11-01T09:16:22.747-07:00Miles Per Hour with Toy Cars (Converting Units w/ Dimensional Analysis) <div dir="ltr" style="text-align: left;" trbidi="on">
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<h2 style="text-align: center;">
How Fast is a Toy Car Really
Traveling? </h2>
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<div class="MsoNormal" style="margin: 12pt 0in 0pt;">
To examine this question and teach
dimensional analysis we converted feet per second to miles per hour using a toy
car.</div>
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<div class="MsoNormal" style="margin: 12pt 0in 0pt;">
<b style="mso-bidi-font-weight: normal;">Step 1:</b> Using a stop watch, yard stick and a windup toy car we
calculated the average feet per second to be </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDIi88MofRg5XoUHVciC8-GRUkOdhIb5ctu3aWJ-h3M60kKIu09Vf4MkuWm14B3_PooIg9by8itNi16KN6FW77n1W8oAekPkH9P4J_3L9a-uajQUej2I9LBzu1G6oW4gwR2MWO8ABXywgc/s1600/IMG_4013.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDIi88MofRg5XoUHVciC8-GRUkOdhIb5ctu3aWJ-h3M60kKIu09Vf4MkuWm14B3_PooIg9by8itNi16KN6FW77n1W8oAekPkH9P4J_3L9a-uajQUej2I9LBzu1G6oW4gwR2MWO8ABXywgc/s1600/IMG_4013.PNG" height="320" width="213" /></a></div>
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<o:p> </o:p></div>
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<div class="MsoNormal" style="margin: 12pt 0in 0pt;">
22.5ft/6.8sec</div>
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<b style="mso-bidi-font-weight: normal;">Step 2:</b> We set up the problem </div>
<br />
<div class="MsoNormal" style="margin: 12pt 0in 0pt;">
<o:p> </o:p></div>
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<div class="MsoNormal" style="margin: 12pt 0in 0pt;">
<b style="mso-bidi-font-weight: normal;">Step 3:</b> We used conversion techniques to translate ft/sec to
miles/hour.<span style="mso-spacerun: yes;"> </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgo_ZY7PVvlsNxRwl0iQCTU48LUPg_UsT-mO4bgZwPx1-oGKyhGNgTr0g7RS0j6jfFFC8A1qN3QdtziTVkDzPfM9MuDluq5Yd4tG2ZzN5LgN9_IPJ6Oa9jXymKfxjzRV-e31LYKGpsMB3vW/s1600/IMG_4015.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgo_ZY7PVvlsNxRwl0iQCTU48LUPg_UsT-mO4bgZwPx1-oGKyhGNgTr0g7RS0j6jfFFC8A1qN3QdtziTVkDzPfM9MuDluq5Yd4tG2ZzN5LgN9_IPJ6Oa9jXymKfxjzRV-e31LYKGpsMB3vW/s1600/IMG_4015.JPG" height="240" width="320" /></a></div>
<br />
<div class="MsoNormal" style="margin: 12pt 0in 0pt;">
<o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 12pt 0in 0pt;">
This little car was traveling
approximately 2.26 miles/hour</div>
</div>
Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com16tag:blogger.com,1999:blog-3882690770743239708.post-88101754045476102972014-10-18T04:18:00.000-07:002014-10-18T04:18:43.568-07:00Proportionality & Grasshoppers<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
Proportionality
& Grasshoppers</div>
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
<o:p> </o:p><div class="separator" style="clear: both; text-align: center;">
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<br />
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
What would it
mean if students could jump proportionally as far grasshoppers? To find out, I
brought in some grasshoppers. </div>
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
<o:p> </o:p></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw6SHrAoB0LE5QQemAfb2x6b9999g1gm1xsphQfiEeNJOrrhNANiQaDd9YVHORJWCIznf4pNaSJ0MYGZgS_A0dQCR_pI3p0UvRdOw0o9bgx5MGXOs1x6ToqWx0BjCHyvDnG4V0-YegIjHt/s1600/photo+3.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw6SHrAoB0LE5QQemAfb2x6b9999g1gm1xsphQfiEeNJOrrhNANiQaDd9YVHORJWCIznf4pNaSJ0MYGZgS_A0dQCR_pI3p0UvRdOw0o9bgx5MGXOs1x6ToqWx0BjCHyvDnG4V0-YegIjHt/s1600/photo+3.JPG" height="320" width="240" /></a></div>
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
First we
measured the length of two grasshoppers to be approximately 1 inch. Next, we
measured the distance of three jumps (in inches) from two grasshoppers I found
in my backyard and took the average of all three jumps for an average of 43
inches. </div>
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
<o:p> </o:p><div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghtj8PcphLDo6Wv3ayut2Uvh98qSDyXuIaf24Tmu3jaf1OTGftJiARkl-8qdnIhenY0KCkGxiSzy-8JrhvNWjHijBY7LIOe0NSEPOMk5AHjX8l3npBNxB4KC92QLSlNaEWAb-hOKGTUUoY/s1600/photo+1.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/AVvXsEghtj8PcphLDo6Wv3ayut2Uvh98qSDyXuIaf24Tmu3jaf1OTGftJiARkl-8qdnIhenY0KCkGxiSzy-8JrhvNWjHijBY7LIOe0NSEPOMk5AHjX8l3npBNxB4KC92QLSlNaEWAb-hOKGTUUoY/s1600/photo+1.JPG" height="320" width="240" /></a></div>
<br />
<br />
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
Next, we
measured the height of two students in inches and took the average for a result
of 62 inches.</div>
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
<o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
Finally we
formed the proportion </div>
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
<o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
<span style="font-size: x-large;">1/43 = 62/x</span></div>
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
<o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
x = 2,666
inches which is roughly 74 yards. </div>
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
</div>
<div class="MsoNormal" style="margin: 5pt 0in; mso-layout-grid-align: none;">
In essence, if students could jump proportional to grasshoppers we could nearly jump 3/4 of a football field. </div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
</div>
</div>
</div>
Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com9tag:blogger.com,1999:blog-3882690770743239708.post-88146340220254849752014-10-04T09:41:00.002-07:002014-10-04T09:50:00.898-07:00How Matrices Can Help When You’re Dating On A Budget. <div dir="ltr" style="text-align: left;" trbidi="on">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsGNe_ukmOjl16LqPfgqGmh4sMZTJAZGCDZT8ato541pQJxEpIWDZDGf73-QF_sSTbak64hPEpAtb1tihOemaXL3d6iBzLMQ4X8hd1V7wUhrnyvLrGxnVErxAsBmcQsqr5MKZAhalehuJE/s1600/IMG_3844.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsGNe_ukmOjl16LqPfgqGmh4sMZTJAZGCDZT8ato541pQJxEpIWDZDGf73-QF_sSTbak64hPEpAtb1tihOemaXL3d6iBzLMQ4X8hd1V7wUhrnyvLrGxnVErxAsBmcQsqr5MKZAhalehuJE/s1600/IMG_3844.JPG" height="240" width="320" /></a></div>
<br />
<br />
<h2 style="text-align: center;">
How Matrices Can Help When You’re Dating On A Budget. </h2>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
The scenario was that each student was treating their
partner out on a date for pizza with the only caveat being they were on a tight
budget and needed to find the cheapest place to take their date. </div>
<br />
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
I first had my student draw a picture of their dates! </div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
</div>
<div style="text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMNG_pjy70gRa7_Y4QlNf-gRWcceqovbvJJF8xtA2a_SEF2KB8vuA3FFPnH_lo2rPREen7z5TH2cra5kDbSb5eS4JjRuQgZCPALObLMhJo47InA7i1NGun4qECMd2m2dkwMwreYXHjljx0/s1600/IMG_3846.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMNG_pjy70gRa7_Y4QlNf-gRWcceqovbvJJF8xtA2a_SEF2KB8vuA3FFPnH_lo2rPREen7z5TH2cra5kDbSb5eS4JjRuQgZCPALObLMhJo47InA7i1NGun4qECMd2m2dkwMwreYXHjljx0/s1600/IMG_3846.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">(Eva didn't talk much)</td></tr>
</tbody></table>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgidj48DcQYz3WN_PSqioq_G7en54uSZ4rXyzubmLuSyTKIvc_Zo1YMMmqVqa0rC8FbqCD3Nb2INPhu1sBToXwRW808PL_GTYg1sNBO0cCSVIgHi1zvTNpvpEPGltAdRsrpERcn9oXvm34z/s1600/IMG_3845.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgidj48DcQYz3WN_PSqioq_G7en54uSZ4rXyzubmLuSyTKIvc_Zo1YMMmqVqa0rC8FbqCD3Nb2INPhu1sBToXwRW808PL_GTYg1sNBO0cCSVIgHi1zvTNpvpEPGltAdRsrpERcn9oXvm34z/s1600/IMG_3845.JPG" height="320" width="240" /></a><br />
<div align="left" class="separator" style="clear: both; text-align: center;">
</div>
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<div class="MsoNormal" style="margin: 0in 0in 0pt;">
</div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
The students were asked to skim through three restaurant
take-out menus to find the price of a large pizza and placed the prices inside a
1 x 3 matrix (Matrix A). </div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
</div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
</div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
Next, the students were asked to skim through three
restaurant take-out menus to find the price of additional toppings for a large
pizza and placed the prices inside another 1 x 3 matrix (Matrix B).</div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
</div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCkVR1oxi5u00gJ2MHp3YKvkvDWoeOjtj6GjsU7UafzYbJEtWPa2bYiacCO94mviEVtNPwG0YXgCAp_SGmG6zgyRhdDvhUSvqtxOBJQgsUov6eorqs6vncepW1yPx_vsO6v0vbP5OfxadN/s1600/IMG_3834.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCkVR1oxi5u00gJ2MHp3YKvkvDWoeOjtj6GjsU7UafzYbJEtWPa2bYiacCO94mviEVtNPwG0YXgCAp_SGmG6zgyRhdDvhUSvqtxOBJQgsUov6eorqs6vncepW1yPx_vsO6v0vbP5OfxadN/s1600/IMG_3834.JPG" height="320" width="240" /></a></div>
<br />
<br />
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<div class="MsoNormal" style="margin: 0in 0in 0pt;">
Next, I had each student ask their date how many toppings
they wanted on their large pizza (I answered for their dates of course). </div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
The students then multiplied matrix B by the number of
toppings they wanted on their pizza and placed the prices inside another 1 x 3
matrix (Matrix C). </div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
Finally, the students were asked to add Matrix A to Matrix C
to find the total price at three restaurants for a large pizza with a specified
number of toppings and choose the cheapest restaurant. </div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
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</div>
Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com12tag:blogger.com,1999:blog-3882690770743239708.post-81080888857746259682014-09-27T07:03:00.000-07:002014-09-27T07:03:17.405-07:00Estimating, Error Rates & Plotting <div dir="ltr" style="text-align: left;" trbidi="on">
<h2 style="text-align: center;">
Estimating, Error Rates & Plotting </h2>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
</div>
<br />
<div class="separator" style="clear: both; text-align: center;">
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<br />
<div class="separator" style="clear: both; text-align: center;">
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<br />
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<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
Take your class outside and designate a single starting
point. From that point throw 5 or 6 objects at various distances. Next, ask
your students to estimate how many feet each object is from the starting point.
After they have estimated each object have them measure the length to the
nearest foot and record their data in a table such as that below. </div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGC5sJgFHbnyjPu0n43rukDkHbiRpirEFoEclJiMCBrax3jnz_yttszTVJGhEKA4knNSsSDqo_ds8WlagTW23sShzLYWCfSnFlxapsYEef5_mc_FTaSIfrU9hWNyNkqGF67VOIJvcB_HFo/s1600/photo+5.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/AVvXsEjGC5sJgFHbnyjPu0n43rukDkHbiRpirEFoEclJiMCBrax3jnz_yttszTVJGhEKA4knNSsSDqo_ds8WlagTW23sShzLYWCfSnFlxapsYEef5_mc_FTaSIfrU9hWNyNkqGF67VOIJvcB_HFo/s1600/photo+5.JPG" height="240" width="320" /></a></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbUua-l-NBWY34DmxIibT7ovYEfDWtHY-NELw61vhEckTWsLx4ewaZOOAQuUQAohoPG2MBsaz9e4KMEvuCFsqo2tTLyBRMub2XENKkWaqcOqScQ0ppujFsFL6B_B2zZkDYM8ayeNfu81D1/s1600/photo+6.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/AVvXsEhbUua-l-NBWY34DmxIibT7ovYEfDWtHY-NELw61vhEckTWsLx4ewaZOOAQuUQAohoPG2MBsaz9e4KMEvuCFsqo2tTLyBRMub2XENKkWaqcOqScQ0ppujFsFL6B_B2zZkDYM8ayeNfu81D1/s1600/photo+6.JPG" height="320" width="240" /></a><o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
Next, have each student calculate their error rate using the
formula (actual) – (estimate) / (actual) and change their decimal to a percent.
</div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
Finally, have the students plot the points on a coordinate
(x,y) plane and form a scatter plot. It’s best to have them graph the equation
y = x so that they can see their error rates. <span style="mso-spacerun: yes;"> </span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
<br />
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
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<o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
</div>
Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com4tag:blogger.com,1999:blog-3882690770743239708.post-43588860034073796312014-09-19T22:42:00.002-07:002014-09-19T22:42:36.314-07:00Scatter Plots With Ramps<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
Scatter plots move in two dimensions which allow students to see changes in
slope as well as the relationship of the two data sets. The study of scatter
plots lends to a lot of fun experiments and can also serve as a great segue to
discussions on proportionality or the coordinate system. <br />
<br />
Ramp Height & Distance Traveled. <br />
<br />
We decided to build ramps and plot the height verses distance traveled. We
increased the ramp in (approximately) one inch blocks and rolled a golf ball
off the ramp to measure the distance traveled. See Below. To get better results we took the average of three rolls. Lots of FUN!<span style="mso-spacerun: yes;"> </span><o:p></o:p><br />
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com4tag:blogger.com,1999:blog-3882690770743239708.post-18409001997007274522014-09-13T05:18:00.001-07:002014-09-13T05:18:18.230-07:00What To DO With a Handful of Pennies? Measures of Central Tendency<div dir="ltr" style="text-align: left;" trbidi="on">
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A good icebreaker to use when introducing Measures of
Central Tendency (Mean, Median, Mode, etc) is to grab a handful of pennies from
your vehicle and lay them out on a table and have your students work in groups to place them in order
of date from least to greatest (if you have a large class you may need multiple handfuls of pennies). </div>
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Next, start collecting data.</div>
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Mode can easily be seen by the largest stack. </div>
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Median, Range, Q1, Q3, IQR can also easily be found</div>
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Mean is slightly tougher unless you allow your students access to a calculator</div>
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Next, have your students create a dot plot of the data</div>
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Finally, have your students pick 5 pennies for their homework. Tape the pennies to their worksheet so that they can read the date (see pic below). </div>
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com13tag:blogger.com,1999:blog-3882690770743239708.post-29085240362765074882013-11-21T10:14:00.000-08:002013-11-21T10:14:32.884-08:00Prime Number Challenge!<div dir="ltr" style="text-align: left;" trbidi="on">
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<span class="Apple-style-span" style="font-family: Arial;"><span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; border-collapse: separate; color: black; font-family: Times; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><br /></span></span>
<span class="Apple-style-span" style="font-family: Arial;"><span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; border-collapse: separate; color: black; font-family: Times; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><br /></span></span>
<span class="Apple-style-span" style="font-family: Arial;"><span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; border-collapse: separate; color: black; font-family: Times; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">An integer <a href="http://primes.utm.edu/notes/faq/one.html" style="background-color: #f0f9ff; color: #000033; text-decoration: underline;">greater than one</a> is called a <strong>prime number</strong> if its only positive divisors (factors) are one and itself.</span></span><br />
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<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; border-collapse: separate; color: black; font-family: Times; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><br /></span></div>
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<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; border-collapse: separate; color: black; font-family: Times; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Here is a chart detailing the all Primes from 1 - 100</span></div>
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<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; border-collapse: separate; color: black; font-family: Times; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><br /></span></div>
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<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; border-collapse: separate; color: black; font-family: Times; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">We know via the proof-by-contradiction by Euclid that there are an infinite number of prime numbers, yet, this doesn't reveal them. Unlike a standard integer (whereupon whatever number you can come up with, for example n, i can surpass this number with the simple exercise of n+1), large prime numbers are incredible difficult to find. There is no formula for churning out prime numbers, they must be found :)</span></div>
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<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; border-collapse: separate; color: black; font-family: Times; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><br /></span></div>
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<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; border-collapse: separate; color: black; font-family: Times; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">In 2008, a mathematician won $100,000 for finding the next highest prime number (the largest known to date)</span></div>
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<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; border-collapse: separate; color: black; font-family: Times; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><br /></span></div>
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<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; border-collapse: separate; color: black; font-family: Times; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">The number is </span><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; font-family: Times;"><b>2<sup>43112609</sup>-1</b></span></div>
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<span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; font-family: Times;"><b><br /></b></span></div>
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<span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; font-family: Times;">Most likely you students won't be able to grasp how big this number really is, but, for intents and purposes, if you were to sum up all the atoms in the entire universe you would get a number roughly 10^80 (vastly smaller than the one shown here)</span></div>
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<span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; font-family: Times;"><br /></span></div>
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<span class="Apple-style-span" style="font-family: Times;"><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; font-size: medium;">If you would like to see how big this number really is i suggest you download it from here </span></span><a href="http://prime.isthe.com/chongo/tech/math/prime/m43112609/prime-c.html">http://prime.isthe.com/chongo/tech/math/prime/m43112609/prime-c.html</a> </div>
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I will produce a tiny fraction of the full number for you here, but if you want the full thing, you must go to the prime site <a href="http://prime.isthe.com/chongo/tech/math/prime/m43112609/prime.html">http://prime.isthe.com/chongo/tech/math/prime/m43112609/prime.html</a></div>
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<span class="Apple-style-span" style="font-family: Arial;"><span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; border-collapse: separate; color: black; font-family: Times; font-size: small; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><blockquote>
<pre><span class="Apple-style-span" style="font-size: xx-small;">three hundred sixteen quattuormilliamilliatrecensexviginmilliaunsexagintillion,
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nine hundred seventy two quattuormilliamilliatrecenquinviginmillianongendononagintillion,
nine hundred eighty four quattuormilliamilliatrecenquinviginmillianongenunnonagintillion,
seven hundred sixty one quattuormilliamilliatrecenquinviginmillianongennonagintillion,
one hundred fifty nine quattuormilliamilliatrecenquinviginmillianongennovemoctogintillion,
sixty quattuormilliamilliatrecenquinviginmillianongenoctooctogintillion,
eight hundred seventy three quattuormilliamilliatrecenquinviginmillianongenseptenoctogintillion,
two hundred fifty quattuormilliamilliatrecenquinviginmillianongensexoctogintillion,
nine hundred thirty nine quattuormilliamilliatrecenquinviginmillianongenquinoctogintillion,
four hundred sixty two quattuormilliamilliatrecenquinviginmillianongenquattuoroctogintillion,
eighty five quattuormilliamilliatrecenquinviginmillianongentreoctogintillion,
five hundred seventy five quattuormilliamilliatrecenquinviginmillianongendooctogintillion,
seven hundred forty quattuormilliamilliatrecenquinviginmillianongenunoctogintillion,
seven hundred fifty four quattuormilliamilliatrecenquinviginmillianongenoctogintillion,
five hundred seventy seven quattuormilliamilliatrecenquinviginmillianongennovemseptuagintillion,
ninety eight quattuormilliamilliatrecenquinviginmillianongenoctoseptuagintillion,
six hundred twenty quattuormilliamilliatrecenquinviginmillianongenseptenseptuagintillion,
five hundred fifty eight quattuormilliamilliatrecenquinviginmillianongensexseptuagintillion,
eleven quattuormilliamilliatrecenquinviginmillianongenquinseptuagintillion,
seven hundred seventy nine quattuormilliamilliatrecenquinviginmillianongenquattuorseptuagintillion,
five hundred twenty nine quattuormilliamilliatrecenquinviginmillianongentreseptuagintillion,
eight hundred eighty four quattuormilliamilliatrecenquinviginmillianongendoseptuagintillion,
forty two quattuormilliamilliatrecenquinviginmillianongenunseptuagintillion,
one hundred ninety eight quattuormilliamilliatrecenquinviginmillianongenseptuagintillion,
two hundred eighty seven quattuormilliamilliatrecenquinviginmillianongennovemsexagintillion,
six hundred forty three quattuormilliamilliatrecenquinviginmillianongenoctosexagintillion,
three hundred nineteen quattuormilliamilliatrecenquinviginmillianongenseptensexagintillion,
three hundred thirty quattuormilliamilliatrecenquinviginmillianongensexsexagintillion,
four hundred sixty five quattuormilliamilliatrecenquinviginmillianongenquinsexagintillion,
sixty four quattuormilliamilliatrecenquinviginmillianongenquattuorsexagintillion,
four hundred fifty five quattuormilliamilliatrecenquinviginmillianongentresexagintillion,
two hundred thirty four quattuormilliamilliatrecenquinviginmillianongendosexagintillion,
nine hundred eighty eight quattuormilliamilliatrecenquinviginmillianongenunsexagintillion,
one hundred forty two quattuormilliamilliatrecenquinviginmillianongensexagintillion,
one hundred thirty nine quattuormilliamilliatrecenquinviginmillianongennovemquinquagintillion,
five hundred sixty five quattuormilliamilliatrecenquinviginmillianongenoctoquinquagintillion,
seven hundred eighty five quattuormilliamilliatrecenquinviginmillianongenseptenquinquagintillion,
four hundred forty seven quattuormilliamilliatrecenquinviginmillianongensexquinquagintillion,
four hundred seventy four quattuormilliamilliatrecenquinviginmillianongenquinquinquagintillion,
twenty three quattuormilliamilliatrecenquinviginmillianongenquattuorquinquagintillion,
five hundred forty six quattuormilliamilliatrecenquinviginmillianongentrequinquagintillion,
three hundred fifty three quattuormilliamilliatrecenquinviginmillianongendoquinquagintillion,
seven hundred fifty eight quattuormilliamilliatrecenquinviginmillianongenunquinquagintillion,
five hundred thirty seven quattuormilliamilliatrecenquinviginmillianongenquinquagintillion,
three hundred twenty four quattuormilliamilliatrecenquinviginmillianongennovemquadragintillion,
eight hundred one quattuormilliamilliatrecenquinviginmillianongenoctoquadragintillion,
eight hundred thirty eight quattuormilliamilliatrecenquinviginmillianongenseptenquadragintillion,
one hundred twenty quattuormilliamilliatrecenquinviginmillianongensexquadragintillion,
three hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenquinquadragintillion,
six hundred quattuormilliamilliatrecenquinviginmillianongenquattuorquadragintillion,
eight hundred sixty eight quattuormilliamilliatrecenquinviginmillianongentrequadragintillion,
four hundred sixteen quattuormilliamilliatrecenquinviginmillianongendoquadragintillion,
five hundred twenty five quattuormilliamilliatrecenquinviginmillianongenunquadragintillion,
four hundred quattuormilliamilliatrecenquinviginmillianongenquadragintillion,
seven hundred ninety quattuormilliamilliatrecenquinviginmillianongennovemtrigintillion,
three hundred eighty one quattuormilliamilliatrecenquinviginmillianongenoctotrigintillion,
two hundred eighty five quattuormilliamilliatrecenquinviginmillianongenseptentrigintillion,
eight hundred eighty eight quattuormilliamilliatrecenquinviginmillianongensextrigintillion,
two hundred fifty six quattuormilliamilliatrecenquinviginmillianongenquintrigintillion,
six hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenquattuortrigintillion,
eighty five quattuormilliamilliatrecenquinviginmillianongentretrigintillion,
eight hundred fifty five quattuormilliamilliatrecenquinviginmillianongendotrigintillion,
four hundred fifty six quattuormilliamilliatrecenquinviginmillianongenuntrigintillion,
two hundred thirty one quattuormilliamilliatrecenquinviginmillianongentrigintillion,
five hundred seventy seven quattuormilliamilliatrecenquinviginmillianongennovemvigintillion,
five hundred twenty seven quattuormilliamilliatrecenquinviginmillianongenoctovigintillion,
nine hundred thirty nine quattuormilliamilliatrecenquinviginmillianongenseptenvigintillion,
three hundred five quattuormilliamilliatrecenquinviginmillianongensexvigintillion,
nine hundred twenty quattuormilliamilliatrecenquinviginmillianongenquinvigintillion,
eight hundred eleven quattuormilliamilliatrecenquinviginmillianongenquattuorvigintillion,
seven hundred sixty six quattuormilliamilliatrecenquinviginmillianongentrevigintillion,
five hundred eighty five quattuormilliamilliatrecenquinviginmillianongendovigintillion,
three hundred eight quattuormilliamilliatrecenquinviginmillianongenunvigintillion,
six hundred seventy quattuormilliamilliatrecenquinviginmillianongenvigintillion,
one hundred thirty two quattuormilliamilliatrecenquinviginmillianongennovemdecillion,
one hundred twenty nine quattuormilliamilliatrecenquinviginmillianongenoctodecillion,
one hundred fifty five quattuormilliamilliatrecenquinviginmillianongenseptendecillion,
two hundred twenty one quattuormilliamilliatrecenquinviginmillianongensexdecillion,
eight hundred four quattuormilliamilliatrecenquinviginmillianongenquindecillion,
three hundred eighty one quattuormilliamilliatrecenquinviginmillianongenquattuordecillion,
five hundred forty eight quattuormilliamilliatrecenquinviginmillianongentredecillion,
six hundred twenty five quattuormilliamilliatrecenquinviginmillianongendodecillion,
seven hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenundecillion,
nine hundred forty three quattuormilliamilliatrecenquinviginmillianongendecillion,
twenty quattuormilliamilliatrecenquinviginmillianongennovemtillion,
six hundred ninety four quattuormilliamilliatrecenquinviginmillianongenoctotillion,
five hundred twenty eight quattuormilliamilliatrecenquinviginmillianongenseptentillion,
fifteen quattuormilliamilliatrecenquinviginmillianongensextillion,
nine hundred ninety nine quattuormilliamilliatrecenquinviginmillianongenquintillion,
two hundred twenty one quattuormilliamilliatrecenquinviginmillianongenquattuortillion,
seven hundred eighteen quattuormilliamilliatrecenquinviginmillianongentretillion,
one hundred ninety one quattuormilliamilliatrecenquinviginmillianongendotillion,
five hundred fifty seven quattuormilliamilliatrecenquinviginmillianongenuntillion,
seven hundred sixty one quattuormilliamilliatrecenquinviginmillianongentillion,
seven hundred eighty nine quattuormilliamilliatrecenquinviginmilliaoctingennovemnonagintillion,
thirty eight quattuormilliamilliatrecenquinviginmilliaoctingenoctononagintillion,
five hundred thirty nine quattuormilliamilliatrecenquinviginmilliaoctingenseptennonagintillion,
five hundred twenty two quattuormilliamilliatrecenquinviginmilliaoctingensexnonagintillion,
three hundred forty nine quattuormilliamilliatrecenquinviginmilliaoctingenquinnonagintillion,
seven hundred forty six quattuormilliamilliatrecenquinviginmilliaoctingenquattuornonagintillion,
eight hundred eight quattuormilliamilliatrecenquinviginmilliaoctingentrenonagintillion,
seven hundred ninety seven quattuormilliamilliatrecenquinviginmilliaoctingendononagintillion,
four hundred seventy six quattuormilliamilliatrecenquinviginmilliaoctingenunnonagintillion,
nine hundred seven quattuormilliamilliatrecenquinviginmilliaoctingennonagintillion,
six hundred sixty four quattuormilliamilliatrecenquinviginmilliaoctingennovemoctogintillion,
fifty quattuormilliamilliatrecenquinviginmilliaoctingenoctooctogintillion,
six hundred one quattuormilliamilliatrecenquinviginmilliaoctingenseptenoctogintillion,
two hundred forty eight quattuormilliamilliatrecenquinviginmilliaoctingensexoctogintillion,
four hundred seventy three quattuormilliamilliatrecenquinviginmilliaoctingenquinoctogintillion,
two hundred six quattuormilliamilliatrecenquinviginmilliaoctingenquattuoroctogintillion,
eight hundred seventy four quattuormilliamilliatrecenquinviginmilliaoctingentreoctogintillion,
one hundred thirty three quattuormilliamilliatrecenquinviginmilliaoctingendooctogintillion,
one hundred ninety four quattuormilliamilliatrecenquinviginmilliaoctingenunoctogintillion,
six hundred sixty three quattuormilliamilliatrecenquinviginmilliaoctingenoctogintillion,
five hundred eighty five quattuormilliamilliatrecenquinviginmilliaoctingennovemseptuagintillion,
three hundred thirty four quattuormilliamilliatrecenquinviginmilliaoctingenoctoseptuagintillion,
nine hundred eighty three quattuormilliamilliatrecenquinviginmilliaoctingenseptenseptuagintillion,
eight hundred five quattuormilliamilliatrecenquinviginmilliaoctingensexseptuagintillion,
seven hundred thirty four quattuormilliamilliatrecenquinviginmilliaoctingenquinseptuagintillion,
eight hundred three quattuormilliamilliatrecenquinviginmilliaoctingenquattuorseptuagintillion,
six hundred twenty quattuormilliamilliatrecenquinviginmilliaoctingentreseptuagintillion,
seven hundred five quattuormilliamilliatrecenquinviginmilliaoctingendoseptuagintillion,
seven hundred seventy eight quattuormilliamilliatrecenquinviginmilliaoctingenunseptuagintillion,
two hundred seventy quattuormilliamilliatrecenquinviginmilliaoctingenseptuagintillion,
nine hundred ten quattuormilliamilliatrecenquinviginmilliaoctingennovemsexagintillion,
five hundred sixty one quattuormilliamilliatrecenquinviginmilliaoctingenoctosexagintillion,
seven hundred sixteen quattuormilliamilliatrecenquinviginmilliaoctingenseptensexagintillion,
seven hundred sixty seven quattuormilliamilliatrecenquinviginmilliaoctingensexsexagintillion,
six hundred eighty quattuormilliamilliatrecenquinviginmilliaoctingenquinsexagintillion,
nine hundred fifty four quattuormilliamilliatrecenquinviginmilliaoctingenquattuorsexagintillion,
eight hundred fourteen quattuormilliamilliatrecenquinviginmilliaoctingentresexagintillion,
four hundred fifteen quattuormilliamilliatrecenquinviginmilliaoctingendosexagintillion,</span> </pre>
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<span class="Apple-style-span" style="font-family: Times;"><b><a href="http://www.blogger.com/" name="middle">BUT, with all that (using about 150 lines) there were over 4,321,381 lines omitted ...</a></b></span></div>
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What a mouth full!!!!</div>
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So, here is the goal. Using a large fake check made out for $100,000 and a small bag of candy, pose the challenge to see who can come up with the largest prime number using only paper, pencil and calculator (don't let them cheat on their cell phones by Googling) </div>
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com8tag:blogger.com,1999:blog-3882690770743239708.post-29209255357472415522013-11-19T10:17:00.002-08:002013-11-19T10:17:41.925-08:00The eBay Experiment (Math & Business)<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsgLz0v2fmVcz9BfcoyC_DAlQXbQJi-mqib0zIX7g3gwIXpmqI0Ul5r3RR6T5MYOrkG8dhDuf8RJGTvQNb9cJ8VcYjcu9pdZ0hE3I9WZeo-U_xF68IUXj-0Uz1fdX4zQuw3_wh36ZrRD4q/s1600/ebay.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" closure_lm_740990="null" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsgLz0v2fmVcz9BfcoyC_DAlQXbQJi-mqib0zIX7g3gwIXpmqI0Ul5r3RR6T5MYOrkG8dhDuf8RJGTvQNb9cJ8VcYjcu9pdZ0hE3I9WZeo-U_xF68IUXj-0Uz1fdX4zQuw3_wh36ZrRD4q/s1600/ebay.jpg" wta="true" /></a></div>
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The eBay Experiment (Math & Business)<br />
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This is the perfect project for the educator who is familiar with selling on eBay! Those educators who are not acquainted with selling on eBay can also use this project but they should either take precaution that the project goes smoothly and everything is accounted for or have their students go through the motions of the exercise without actually listing the items. <br />
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This project involves asking each student to pick one item from their home that they wish to sell on eBay. The student will snap their pictures, write their product description and calculate their profit. This experiment could easily reach across disciplines and act as a writing assignment in their English class. (It's a good idea to get a permission slip signed by their parents to allow them to sell this item). <br />
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What You Will Need<br />
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An eBay Account<br />
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Paypal Account<br />
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1 Product To Sell<br />
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Camera To Snap Pics of Product<br />
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Permission Slip From Parents to Sell Product<br />
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Activity Sheet (see below)<br />
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Overview<br />
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Students will bring in their product to sell. The teacher will help the student take a picture of the product from multiple angles, fill out a description of the product and calculate the profits based on the activity sheet below. Students will learn the basics of revenue and cost by selling an item, subtracting the shipping and fees (students will need to calculate these fees by using percentages). And finally, calculate their profit. <br />
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Steps<br />
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1) Setup an eBay and Paypal account (can use your own or set up one specific for this assignment).<br />
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2) Designate a camera to use for all pictures<br />
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3) Have students bring a product into class to sell (with permission slip signed to sell it)<br />
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4) Hand out the activity sheet below to each student while at their desk and have them fill it out while you walk around the room taking pictures of each product.<br />
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Note: You will have lots of pics in your phone, so you should have a system to categorize each product with each student. <br />
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5) Have students turn in their worksheets<br />
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6) Have students begin writing a description of their product on a piece of paper.<br />
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7) If available, have each student turn in their description paper to their English teacher to be edited.<br />
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8) After receiving back their edited descriptions, have student type each description up and email them to you.<br />
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9) Use all the information to list each item. I would make this a classroom project. Using an overhead projector or smartboard, I would have each student come to the front of the class and fill out the eBay template to list their item. This will teach them the basics of eBay while also showing off what they are selling.<br />
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Note: There is no real rush here. You don't need to do auctions, you could opt for a fixed rate auction and use their study hall time to fill out these eBay forms. Additionally, you could have other projects going on while each student comes up individually to fill out their form. Just give it some thought on how to maximize your time. <br />
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10) After the product sells, each student should fill out a profit statement where they subtract their costs from their revenue (see form below)<br />
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Added Notes:<br />
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1) To make things simple, I would narrow the shipping options to Small, Medium or Large flat-rate boxes. The costs for these options can be found via the United States Post Offices website.<br />
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2) To make things simple, I would limit the size of each item to that it fits in the small, medium or large flat-rate boxes. To be sure of this, I would swing by my local post office and pick up some free priority flat-rate boxes so that they have an idea of size.<br />
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3) Although not as fun, it would be a lot easier if the students went through the motions of this exercise but didn't actually list the items<br />
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Listing Sheet:<br />
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Name of Item______________________________________________________<br />
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Category of Item______________________________________________________<br />
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Listing Prices______________________________________________________<br />
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Estimated Shipping______________________________________________________<br />
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Used/New______________________________________________________<br />
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If Used, Tell About The Condition_____________________________________________________________________________________________________________________________________________________________<br />
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Profit Sheet<br />
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Total Revenue:<br />
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Listing Price ________(A)<br />
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Total Cost:<br />
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Shipping Price ________(B)<br />
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Listing Fee (0.10) ________(C)<br />
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Final Value Fee (5% selling price) ________(D)<br />
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PayPal Fee (3% selling price) ________(E)<br />
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Misc Costs (Avg of tape, packagin, etc) ________(F)<br />
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Profit ________(A) minus ________(B-->F) = _________ (G)<br />
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com6tag:blogger.com,1999:blog-3882690770743239708.post-39755670546374928622013-08-01T01:00:00.000-07:002013-08-01T01:00:07.552-07:00Commutative, Associative and Distributive Comic Book<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-size: x-large;">Commutative, Associative and Distributive</span><br />
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Math definitions rank up there with fractions as some of the most dreaded material for students to study. Here is a cute way to lighten up the classroom a bit. <br />
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Have students create their own super hero’s labeled Commutative Man, Associative Man and Distributive Man. The only catch is that the super powers must be related to the math properties. For example, Associative man may use parenthesis for force fields or since order doesn’t matter commutative man may be able to use his powers from both hands.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKfpjDm3lQH1ihSudvQ1g53g02yf-NqUNi8LF7QunXoGBrdFS2AKDQlgZSrSnvUejdJq__uZYae-RHdheaah5RTI3iJY5hf1u2RwLWkU0zbwg6ZJLfXpRwR605Ts-Du_D7M_005AHFnRIY/s1600/img012.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKfpjDm3lQH1ihSudvQ1g53g02yf-NqUNi8LF7QunXoGBrdFS2AKDQlgZSrSnvUejdJq__uZYae-RHdheaah5RTI3iJY5hf1u2RwLWkU0zbwg6ZJLfXpRwR605Ts-Du_D7M_005AHFnRIY/s400/img012.jpg" width="308" /></a></div>
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com3tag:blogger.com,1999:blog-3882690770743239708.post-74580122452769758192013-07-31T15:11:00.000-07:002013-07-31T15:11:34.723-07:00Teaching Percentages By Going On A Math-Class-Date<div dir="ltr" style="text-align: left;" trbidi="on">
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No need for elaborate drill and kill percentage worksheets. One good problem is worth 10 worksheets. The goal is for your students to be able to calculate a 15% tip in a real life scenario.</div>
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You need a menu, a candle.</div>
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Split up your classroom in groups of 5 students. two will be on a date the other will be the waitress. </div>
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Have each couple order from the menu. The waitress will add up the order by hand and bring them each couple the bill. The couple will then calculate a 15% tip. </div>
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com2tag:blogger.com,1999:blog-3882690770743239708.post-22916918184334867042013-07-18T10:59:00.001-07:002013-07-18T10:59:36.287-07:00Bee Hives & Hexagonal Shapes<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjI5hvWKCI9Sxd4RUNtxloM1EDuoPatpJ5IXWccZsFW6fqDa2aSgf1YAGvqJX-0zX8EV-OW9lY8-OrqM95k5iJ8rKYGrbZneT10AW7I9239LF6Xtsi2Q50YCG6yQux0q-r00uUmRb0y9_Lu/s1600/1016725_10101074517989287_162914951_n.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjI5hvWKCI9Sxd4RUNtxloM1EDuoPatpJ5IXWccZsFW6fqDa2aSgf1YAGvqJX-0zX8EV-OW9lY8-OrqM95k5iJ8rKYGrbZneT10AW7I9239LF6Xtsi2Q50YCG6yQux0q-r00uUmRb0y9_Lu/s320/1016725_10101074517989287_162914951_n.jpg" width="320" /></a></div>
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It's very neat to see how evolution discards waste. Here we have constraints on resources forcing bees to to create the<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: 12px; line-height: 16px;"> "maximum amount of space with a minimal amount of material." The result is the use of hexagons. </span><br />
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com1tag:blogger.com,1999:blog-3882690770743239708.post-26470059013618971802013-06-26T09:59:00.001-07:002013-06-26T09:59:12.978-07:00Scaling Models With Sabertooth Tiger Teeth.<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmg_4jjBe8g_-GP3KNPBy2r6_lRxRWn_sCgYPeKrURJM9it14FonKCzZPd_WFg_HlzBJNP8B7jT3_MQZyYgUIq0_BkF1mpWLJyFM-fJgVr-rIhWUFbx8UT90dl45p3BCMleZ32rEVBYQT1/s1600/947143_10101037579374567_1475582075_n.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmg_4jjBe8g_-GP3KNPBy2r6_lRxRWn_sCgYPeKrURJM9it14FonKCzZPd_WFg_HlzBJNP8B7jT3_MQZyYgUIq0_BkF1mpWLJyFM-fJgVr-rIhWUFbx8UT90dl45p3BCMleZ32rEVBYQT1/s320/947143_10101037579374567_1475582075_n.jpg" width="297" /></a></div>
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Scaling Models With Sabertooth Tiger
Teeth.
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As many of you know I homeschool my two
sons (nothing like doing math in your pajamas). I'm going to be
posting some stuff that we do with my five-year old. It's basic but
it may spark some ideas to use in your classroom.
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In this lesson we talked about
Sabertooth Tigers and how their two large teeth measured 12inches in
length. I wanted to compare this to our teeth. So we measured and
figured our that our teeth were about <span style="color: #0e1928;"><span style="font-family: Times-Roman, serif;"><span style="font-size: medium;">7
tenths of an inch. The goal was to let him figure out what he would
look like if he had sabertooth size teeth. This was the result. </span></span></span></div>
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com0tag:blogger.com,1999:blog-3882690770743239708.post-57045516946478968902013-05-11T07:56:00.003-07:002013-05-11T07:56:50.603-07:00A Fancy Way of Adding Zero & The Additive Identity<div dir="ltr" style="text-align: left;" trbidi="on">
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I have a love/hate relationship with riddles. I love them when I can solve them quickly, hate them when they keep me up at night for something that is normally too obvious for me to notice.</div>
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Here is an older riddle, if I can call it that, which your students may love. <br />
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<em>“Take any number. Now add 5 to it. Multiply that by 2. Subtract 6. Divide by 2 and finally subtract 2 and you back to your original number. Why does this work?” </em></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhouPiI88n4r5tr7-ZAmwlu9Qezr9BBAEVCc008xGEUMigfsdhUv9iXWB6EIQ2YSLGIVhhoHafP8AwBbZdX28PKeubjC5z4qbDr2I7in099kF1SUMXqKY-Jy0KWw1UBaQJ5C5_-qKfEu80s/s1600/zero+addition.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="165" mwa="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhouPiI88n4r5tr7-ZAmwlu9Qezr9BBAEVCc008xGEUMigfsdhUv9iXWB6EIQ2YSLGIVhhoHafP8AwBbZdX28PKeubjC5z4qbDr2I7in099kF1SUMXqKY-Jy0KWw1UBaQJ5C5_-qKfEu80s/s320/zero+addition.jpg" width="320" /></a></div>
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1) Let your students try it first on a couple of different numbers</div>
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2) Now let them try to figure out why it works on their own. </div>
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3) Have them write down the whole operation, paying special attention to order of operations. (((((x + 5) * 2) – 6) / 2) – 2)<br />
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4) Again, let them try to figure out why it works on their own. <br />
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5) Ask them to go through the following operation ((((5 * 2) – 6) / 2) – 2) and see what number they get (zero is the answer)<br />
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6) Ask them to restate the <a href="http://www.mathsisfun.com/definitions/additive-identity.html">Additive Identity </a><br />
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7) Thus, this whole problem is simply a fancy way of adding zero to your initial number. <br />
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com7tag:blogger.com,1999:blog-3882690770743239708.post-46912599740053625492013-05-06T07:48:00.003-07:002013-05-06T07:48:36.757-07:00In Pursuit of Perfection of Form<div dir="ltr" style="text-align: left;" trbidi="on">
Our students often never understand how they misplaced a negative symbol or added instead of subtracting. They often think of this is a part of the math process, and it is, to an extent. Many times, to my own embarrassment, I've stood in front of a classroom and butchered a problem on the white board. My only self-medication for these "duh" moments was knowing that we deal in an unforgiving science.<br />
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But still, I often wonder why our students are so sloppy in their work. I once pulled a young man, who was an incredible basketball player, off to the side to ask how he perfected is form so well in the sport. His response was of course practice. If I would have thought about it at that time I would have paralleled his form in basketball with his form in my lecture hall, but I didn't. I'm writing this now so that you may draw this parallel with your students.<br />
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Analyzing this<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhc5esFijrafi4gq2ULQbdzCMjx3vRQhcNOaoLvlj9uvL2a7NZdbSePS-kfRdnEC9pva2HsDctXD93lJuNwmrsWXDStmVrwUhW64m3-iy1Zvhv2KUneM7aexIKQmXA9zdX15rdGDZOB7id1/s1600/Unknown.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="113" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhc5esFijrafi4gq2ULQbdzCMjx3vRQhcNOaoLvlj9uvL2a7NZdbSePS-kfRdnEC9pva2HsDctXD93lJuNwmrsWXDStmVrwUhW64m3-iy1Zvhv2KUneM7aexIKQmXA9zdX15rdGDZOB7id1/s400/Unknown.jpeg" width="400" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQw85h3YgeyJFsyeNaewYELn0BX0pG6yQypr3DtvBk7qTBs3u2c8DvS7UOnjDTu_u8mRpJ8doQ0SykXShnlDE4SPuO-XF3E-3qavMecDSqxyQUG0GLkMQwIKHtj4uqnvNHW2y9Zh1rDt1L/s1600/images-1.jpeg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="249" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQw85h3YgeyJFsyeNaewYELn0BX0pG6yQypr3DtvBk7qTBs3u2c8DvS7UOnjDTu_u8mRpJ8doQ0SykXShnlDE4SPuO-XF3E-3qavMecDSqxyQUG0GLkMQwIKHtj4uqnvNHW2y9Zh1rDt1L/s400/images-1.jpeg" width="400" /></a></div>
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May be the key to helping your students perform this </div>
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com2tag:blogger.com,1999:blog-3882690770743239708.post-65316062681183015012013-02-28T15:30:00.003-08:002013-02-28T15:30:46.562-08:00Coffee Taste Test Using Same Filter (Blind Sampling & Data Collection)<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikluov8F0CCJg-1eJG7r5QzmF4JQfDJOHi-YwF827pgRIbFo5LHdtr9SWVtpoF8NRGCClU8mJ45-Dp6cWfp15NSIm3hVIS_iYNbuc21XNnPUnAbTfwZIAs_Ci_R0DBRsHJyYe-vpPTJ4Nd/s1600/images-1.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikluov8F0CCJg-1eJG7r5QzmF4JQfDJOHi-YwF827pgRIbFo5LHdtr9SWVtpoF8NRGCClU8mJ45-Dp6cWfp15NSIm3hVIS_iYNbuc21XNnPUnAbTfwZIAs_Ci_R0DBRsHJyYe-vpPTJ4Nd/s1600/images-1.jpeg" /></a></div>
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A question occurred to me today. As
normal, I need my afternoon coffee. However, feeling excessively
lazy, instead of making a new pot of coffee, I decided to simply fill
the coffee pot back up and use the same filter from earlier this
morning. As you can imagine, it wasn't exactly indulgent. Yet, I
began to wonder if the coffee I was drinking was actually weaker, or
was it my anticipation of it being weaker that made it so. Project!</div>
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Have your students conduct a blind
taste test with other faculty members being their dummies. I would
even let your students call them dummies...at least for the day. The
taste test will involve each faculty to sample 3 small cups of coffee
and record their data without knowing which cup of coffee is which.</div>
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Cup 1: First pot of coffee.
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Cup 2: Same filter, same coffee, 2nd
pot of water</div>
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Cup 3: Same filter, same coffee, 3<sup>rd</sup>
pot of water</div>
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The survey should be something simple,
but measurable. For example, have them rank each cup of coffee on a
scale of 1-10 with 10 being the highest.
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<b><u>Things to account for</u></b></div>
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<li><div style="margin-bottom: 0in;">
When ranking, will the dummy be
comparing the tastes of one cup to the other cups only, or will they
be comparing them to previous cups of coffee. For example, if the
dummy loves a White Chocolate Mocha from Starbucks as their number
10, they may rank all three of your cups a 1's or 2's. Thus, to
account for this, you may want to raise the ranking system from 1-10
to something like 1-100.</div>
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Will the cups be served black or
with sweater and cream? If the latter, you shuld make sure that each
cup receives nearly the same amount.
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<u><b>After Results:</b></u></div>
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Have each student calculate some
descriptive statistics (mean, median, mode, standard deviation, etc)
and draw some conclusions. Does using the same filter and same coffee
really make the coffee noticeably weaker? Or is it in our
imagination?</div>
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Finally, the most important part of the
activity is the after-activity discussion. Why might the tests be
inaccurate? Was are sample size appropriate? What could we have done
better? How might a double-blind test affect the results? Why might companies use blind taste tests when comparing their product to their competitors</div>
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Have fun...send me some pics if you
decide to do the project! </div>
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com2tag:blogger.com,1999:blog-3882690770743239708.post-28262901445342635222013-02-19T13:33:00.000-08:002013-02-19T13:33:37.113-08:00Representation & Modeling: Getting Your Students To Draw A Math Picture<div dir="ltr" style="text-align: left;" trbidi="on">
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A simple picture can go along way in helping your students solve an application problem. This is as true in pre-algebra as it is in calculus, however, representing the problem with a picture or diagram is often an overlooked step by students. The goal of the blog post is to help students see the value.<br />
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<blockquote class="tr_bq">
Drawing a diagram or other type of visual representation is often a good starting point for solving all kinds of word problems. It is an intermediate step between language-as-text and the symbolic language of mathematics. By representing units of measurement and other objects visually, students can begin to think about the problem mathematically. Pictures and diagrams are also good ways of describing solutions to problems; therefore they are an important part of mathematical communication. <a href="http://www.teachervision.fen.com/math/problem-solving/48931.html">From Teacher Vision </a></blockquote>
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<strong>Activity: </strong><br />
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Take one full class and introduce nothing but word problem with the emphasis on using pictures to capture the problem. Next, quiz students on this vary concept. Read aloud to them a word problem and have them represent it in a picture while at the same time labeling everything they know. Use some variation the following rubric when grading their work.<br />
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Quality of Representation 1 2 3 4 5<br />
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Proper Labeling of Parts 1 2 3 4 5 <br />
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Unneeded Detail 1 2 3 4 5<br />
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Lets Call Upon Another Example From The Teacher Vision Article<br />
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<blockquote class="tr_bq">
Question: A frog is at the bottom of a 10-meter well. Each day he climbs up 3 meters. Each night he slides down 1 meter. On what day will he reach the top of the well and escape--<a href="http://www.teachervision.fen.com/math/problem-solving/48931.html">From Teacher Vision</a></blockquote>
Here is a possible representation of this problem. <br />
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<a href="http://www.teachervision.fen.com/math/problem-solving/48931.html"><img border="0" height="320" mea="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiczhRB4F5d_6Wxlxz-yWzsISIZbdD4dRw0XxXEOOkwTsf_CJTyYag-xFYPXBx9cIk5DHf8F_StE_AkZ7k_Y2AsMVn-zq_1ClvdGoz6ZTCOKCXMtfoYO2tWZvMYeP_sI3GTObc9RcrEC4On/s320/PAS_draw-pic-frog.jpg" width="240" /></a></div>
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com5tag:blogger.com,1999:blog-3882690770743239708.post-58589308755493416352013-01-31T13:40:00.004-08:002013-01-31T13:40:33.774-08:00Using Geometric Formulas To Simplify Life.<div dir="ltr" style="text-align: left;" trbidi="on">
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Bring in a nicely wound cord or garden hose (see below)<br />
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Explain to your students that you want them to determine the length of the cord or garden hose with the only condition being that they cannot stretch it out; they must find another way to measure the length.<br />
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Notice that the wound cord or garden hose is simply a bunch of circles stacked on top of one another. What if we calculated the circumference of the top circle and multiplied it by how many circles are formed by the winding process? Certainly you will be dealing with a margin of error here but it will at least get you in the ball park.<br />
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Note: be careful not to count a circle more than one time.
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com79tag:blogger.com,1999:blog-3882690770743239708.post-49294664431666753772013-01-22T13:24:00.002-08:002013-01-22T13:27:59.345-08:00Area of Irregular Shapes Using Roman Tortoise Formation<div dir="ltr" style="text-align: left;" trbidi="on">
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Out of curiosity, I decided to estimate the how effective the Roman Tortoise Formation was against opposing archery fire. Having only a few minutes during my morning coffee, I decided to limit my estimation to simply the front of the Tortoise Formation. Such an exercise would be fun for a classroom as well. Here was my thought ‘quick-an-easy’ process, feel free to point-out something more scientific or any potential mistakes.<br />
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The Goal: To estimate the area prone to archery fire with the Tortoise Formation. <br />
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Given: Google tells me that the Roman shield <i>Scutum</i> had the following dimensions<br />
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Height of Shield: 42 inches <br />
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Width of Shield: 26 inches. <br />
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Average Height of Roman man was 5 feet, 6 inches<br />
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Converting to feet, here is a general idea of the shape from the reference point of an archer standing directly in front of the formation.<br />
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Noting the rectangular shape and multiplying the average height by the width of six Scutum shields gives us an approximate area of<br />
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5.5ft x 13ft = 71.5ft^2<br />
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A = 71.5ft^2<br />
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The obvious areas prone to archery attack are the legs below the shield and within the semi-ellipsis surrounding their heads. To estimate these areas we could subtract the height of the shield from the average height of the man (5.5ft – 3.5ft = 2ft) and multiply this by the width of the six Scutum shields.<br />
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2ft x 13ft = 26ft^2<br />
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L = 26ft^2<br />
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As for the area’s within the six semi-ellipsis surrounding their heads, we could use the width of the concave shields (2.17ft) as half the circumference of the ellipsis and approximate the height of the radius as .5 feet. This would give us an approximate area of 1.7 ft^2 per ellipse (multiplied by all six would yield 10.2ft^2).<br />
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E = 10.2ft^2<br />
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Thus, for an opposing archer standing in front of the Roman Tortoise Formation would have approximately<br />
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• Area Prone to Attack = Area below the shield (L) plus semicircle areas above their shield (E).<br />
• Area Prone To Attack = L + E<br />
• Area Prone To Attack = 26ft^2 + 10.2ft^2<br />
• Area Prone To Attack = 36.2ft^2<br />
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Or, approximately 51% of their body is exposed.<br />
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**Note: This seems a little high so I might have made a wrong approximation in length somewhere. Also, the roman soldiers body does not encompass the entire exposed area, so one would need to account for that as well. Nevertheless, this was just for fun.<br />
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com4tag:blogger.com,1999:blog-3882690770743239708.post-36309634475856614072013-01-17T13:38:00.000-08:002013-01-17T13:39:01.384-08:00Incorporating Puzzles (Homeschooling Our Two Boys) <div dir="ltr" style="text-align: left;" trbidi="on">
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<blockquote class="tr_bq">
Puzzles are excellent brain training and co-ordination improvement
tools and are quite fun! In particular, they develop your abilities
to reason, analyze, sequence, deduce, logical thought processes and
problem solving skills. These types of puzzles also improve hand-eye
co-ordination and develop a good working sense of spatial
arrangements. See <a href="http://www.brainhealthandpuzzles.com/jigsaw_puzzle.html">Full Article</a></blockquote>
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Jeremiah Dykehttp://www.blogger.com/profile/03596847096401481529noreply@blogger.com1