tag:blogger.com,1999:blog-74894929008037941392024-03-13T00:47:23.318-05:00.@MrSchwen<b>@MrSchwen:</b> Let's make learning meaningful.mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.comBlogger128125tag:blogger.com,1999:blog-7489492900803794139.post-85734000608626176712016-12-02T12:08:00.002-06:002016-12-02T12:08:56.498-06:00Less clutter and more interestingToday is an end of the trimester work day. On my to-do list I set aside some time to make my classroom less cluttered with stuff kids don't actually look at and to have more creative visual examples of what we actually do in math class. There is also a shout-out to one of my favorite shows, Lost, as a metaphor for our standards based learning cycle.<br />
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<b>Wall of sequences</b><br />
I invited students to participate in this as well. Top 3 most creative sequences from each class will have the opportunity to be put up on the wall as well.<br />
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<b>Standards based grading and student reflection visual</b></div>
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We reference these ideas on our assessments and in conversations in class. I wanted a visual in class so I made this. The messages below the pictures are in <a href="https://docs.google.com/presentation/d/1NlP9vcmvCwWZfkX5I5mNVk-IAjVVs95uSXfgtQbuzgY/edit?usp=sharing">this slideshow</a> if you can't read them in the picture.</div>
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<br />mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-5355269190751095422016-11-29T08:46:00.000-06:002016-11-29T08:46:47.057-06:00Live student agenda<div class="separator" style="clear: both; text-align: center;">
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A practice I've been doing this year that I've found really helpful for students is updating a live student agenda that is displayed on the board and shared with students. I use the same Google Presentation for an entire unit and just update the first slide to be the current day agenda. I move old agendas to the bottom of the presentation for reference and use for next year...assuming most things are similar for next year.<br />
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I push the agenda out at the beginning of the unit through Google Classroom and encourage kids to bookmark it. It sets up a flow for the day and I try to be as visual with what is displayed as possible. All activities referenced for kids are live links and take away the hassle of what they need to be doing next. I use emojis in class to hint at expectations (teacher led, working as a class, ticket out the door, extension).<br />
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In the slideshow I'm also having slides for essential class notes (in case a student is absent...or didn't write down what I asked them to a few days back) and a rolling list of the main practice activities that should be completed up to this point.mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-33465251233853232412016-11-03T12:31:00.003-05:002016-11-03T12:31:49.612-05:00Google spreadsheet function machineAs an extension, I challenged some students to make a spreadsheet (with formulas) that would write a function for any linear function values they put into their table.<br />
I had a couple of boys excited about the task and it was great to see some of their misconceptions drawn out through the activity.<br />
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<b>Misconception #1: Rate of change is always just the difference in output values</b><br />
Their initial table had x values increasing by 1. When they finally got a working function I congratulated them...and then asked, "What if the x's increased by 2 and didn't start at 1?". I even changed their table values and they realized their function now didn't work in this new situation. Motivated by a new layer of challenge they went back to work.<br />
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<b>Misconception #2: Zero term is always the term before the first term in the table</b><br />
Prior to the experience they thought the zero term (connected to arithmetic sequence concept we'd been doing) was the term before the values represented in the table. For the table above that may have been for them the x = 4 or even x = 3 value rather than thinking of when x = 0.<br />
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Being nerdy and excited about spreadsheets myself I completed the challenge as well and made it a fun visual function machine. <a href="https://docs.google.com/spreadsheets/d/1P4bwRE9C9ZETiOpqJFgVScpy9_VOSGj1Ihen4zVp2XY/edit?usp=sharing">Here's the link to mine.</a><br />
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<br />mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-60501217179798256212016-10-13T14:51:00.002-05:002016-10-13T14:51:11.570-05:00Shifting Times Tables from @nrichmaths<br />
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One of my favorite summer finds was the <a href="https://nrich.maths.org/6713">Shifting Times Tables activity on nrichmaths</a> for helping kids to see the connection between proportional and non-proportional sequences in building toward writing linear equations in slope-intercept (<i>y</i> = m<i>x</i> + b) form.<br />
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In keeping with the same idea of the activity, I wanted to have students making connections to graphs and have access to things like sliders so I converted it to <a href="https://teacher.desmos.com/activitybuilder/custom/57fe6dcd968cd7e605be1f51">this Desmos Classroom activity</a>.<br />
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I do make the assumption that students in this activity have previous experience with proportional relationships in graph and table form.<br />
I'd love feedback or ideas of what I could do to make it better or have students make stronger connections.<br />
<br />mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-34964679204288272212016-10-11T14:50:00.002-05:002016-10-11T14:50:33.925-05:00Independent and dependent variables with @Desmos classroom card sort<div class="separator" style="clear: both; text-align: left;">
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Today we did something cool with the <a href="http://learn.desmos.com/cardsort/">Desmos classroom card sort lab</a>. I wanted students to be able to identify an independent and dependent variable pair relationship and then determine which one was the independent (IV) and dependent (DV) by dragging each card onto the appropriate label.<br />
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I quickly realized how a tool like this can be used for a formative assessment when I displayed the teacher page on the screen for students while they were working. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzPRM3Cw-E6pSxuKTuRahzgdU1F_NDLj1SsmnQbAPZUxcGlcl4U9shv_pxLMuCrUzZxa11SCrJWVqGmkXL8BUmfWCmPXA1hQU1F1hrLB8B_RFzrxXKJV1FRT1VMQB16UoQWYp9O2GNVNO1/s1600/Screen+Shot+2016-10-11+at+2.37.35+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="185" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzPRM3Cw-E6pSxuKTuRahzgdU1F_NDLj1SsmnQbAPZUxcGlcl4U9shv_pxLMuCrUzZxa11SCrJWVqGmkXL8BUmfWCmPXA1hQU1F1hrLB8B_RFzrxXKJV1FRT1VMQB16UoQWYp9O2GNVNO1/s320/Screen+Shot+2016-10-11+at+2.37.35+PM.png" width="320" /></a></div>
It doesn't tell them how they are incorrect but they were working hard to analyze where they were going wrong to try and get their name on the screen to go from red to green. Students either self-corrected or asked for help while others that completed the task moved on to the next screen in the activity.<br />
On the next screen I had them move the pair relationship to a potential graph for the situation--same thing, anticipating a correct stack and giving feedback to kids that weren't there yet.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg55Z2wY_7NkLX1UlvW3VCUbkAd1O7fS22zqVBpOKrI-mCj5relR8pDQtWKfPHRGLLdEt01Hj54ON3FDAv1y0vAL9TnoYfehQeeNUP-9SZ3Zm1Nw2_iXjnOm8LJ5IYwFaqtM93ZhIj7cD61/s1600/Screen+Shot+2016-10-11+at+2.39.36+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="152" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg55Z2wY_7NkLX1UlvW3VCUbkAd1O7fS22zqVBpOKrI-mCj5relR8pDQtWKfPHRGLLdEt01Hj54ON3FDAv1y0vAL9TnoYfehQeeNUP-9SZ3Zm1Nw2_iXjnOm8LJ5IYwFaqtM93ZhIj7cD61/s320/Screen+Shot+2016-10-11+at+2.39.36+PM.png" width="320" /></a></div>
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And finally, using the draw tool giving students a voice to disagree with the predetermined graph for each set of cards if they feel like it doesn't fit with how they see the situation.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgibUVin-dJgekacYrCHmY6L_OJEq093NILTkIWvCAVc5n9QszAZR02oJv9uNRNeQyHuuu_bD-kwImfKcbm9rAgGoc1FuS-hVDjTQq9NaaOUzN-8FCvLWFJOKCH9gxNoMm0xe46HpXyeVYk/s1600/Screen+Shot+2016-10-11+at+2.43.27+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="170" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgibUVin-dJgekacYrCHmY6L_OJEq093NILTkIWvCAVc5n9QszAZR02oJv9uNRNeQyHuuu_bD-kwImfKcbm9rAgGoc1FuS-hVDjTQq9NaaOUzN-8FCvLWFJOKCH9gxNoMm0xe46HpXyeVYk/s320/Screen+Shot+2016-10-11+at+2.43.27+PM.png" width="320" /></a></div>
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And of course this can always happen but you address it with those kids and continue to provide fun opportunities like this for kids to think deeper and interact on a more personal level with math.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4zFR1gddBeVfXJC0L6CnqOMwc91ET7JtPanpHWM1sZuSQdVtfYs5bCxXruIM-JjxzmJZBS-9FqhRsqkMPnR97sid_z3bqFHhkv2peXlybt4IoX84aR8AkuH4cg2rus1Ex1wpSVlkVZhwI/s1600/Screen+Shot+2016-10-11+at+2.45.17+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="176" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4zFR1gddBeVfXJC0L6CnqOMwc91ET7JtPanpHWM1sZuSQdVtfYs5bCxXruIM-JjxzmJZBS-9FqhRsqkMPnR97sid_z3bqFHhkv2peXlybt4IoX84aR8AkuH4cg2rus1Ex1wpSVlkVZhwI/s320/Screen+Shot+2016-10-11+at+2.45.17+PM.png" width="320" /></a></div>
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<a href="https://teacher.desmos.com/activitybuilder/custom/57fd19652abc90e30529e138">Here is a link to the classroom activity in Desmos if you want to check it out.</a></div>
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<br />mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-18572063197834966962016-10-04T12:34:00.001-05:002016-10-04T12:34:16.608-05:00Using @Desmos to generate pythagorean triples<div class="separator tr_bq" style="clear: both; text-align: center;">
<a href="https://www.desmos.com/calculator/zfofrhsdjw"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqO6nc9gcxMonLRULt8oycI7tgRnPASWBAUZAtcwYnjf5ClJhSMb9CExKQmTFZ-OkyiOG3Wrtl9jacwhUCHqYS-VUKskskNKHfhgUHrbuHjhVNTIHLmDG8daMSUgbXgEUu01HVg5lnapgg/s320/Screen+Shot+2016-10-04+at+12.24.48+PM.png" width="320" /></a></div>
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Early stages as far as how I'd use this with students but definitely some fun math to <a href="https://www.desmos.com/calculator/zfofrhsdjw">investigate here</a> through Desmos related to generating pythagorean triples in a coordinate grid.<br />
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<u>Things I notice</u>:<br />When gcd(m,n) = 1 we have the primitive pythagorean triple, when gcd(m,n) > 1 we get a triple similar to a primitive triple.<br /><u>Things I wonder</u>:<br />How could I get spirals to show up in desmos like those in this <a href="https://en.wikipedia.org/wiki/Pythagorean_triple">wikipedia article</a>?</blockquote>
mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com1tag:blogger.com,1999:blog-7489492900803794139.post-52715003063979383072016-10-03T14:44:00.002-05:002016-10-04T08:43:52.611-05:00blog reboot and getting outside<script async="" src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>
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I'm trying a reboot of my blog. My goal is to keep posts short, update what is going on with what I'm doing as a teacher and to make up for the years of blog posts that I spewed disgusting technology and data focused ideas...</div>
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This year I've made it a goal to get students out of the classroom on a weekly basis to see the math that we are learning appearing in the world around us. </div>
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We walked the perimeter of the school grounds which I learned (after being here for 14 school years) is actually about a mile. Our shoes got wet but we now have a good memory to connect with perimeter!</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-XeC6iqkygpVNaiLn1uF_vgTRorNDCy8SGTkqXS7dj2hnyqa7YA9AbEvieB86q1_n-d0c-Dz5MR9-RjGEO82Ood_fDE_sxmEHrfO2SlL8kweUrJEmgaZBn6OPJjgLmreq9jwAdwwBUNLR/s1600/perimeterWalk.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-XeC6iqkygpVNaiLn1uF_vgTRorNDCy8SGTkqXS7dj2hnyqa7YA9AbEvieB86q1_n-d0c-Dz5MR9-RjGEO82Ood_fDE_sxmEHrfO2SlL8kweUrJEmgaZBn6OPJjgLmreq9jwAdwwBUNLR/s320/perimeterWalk.jpg" width="320" /></a></div>
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We went into the cafeteria to find the area and that looked like counting floor tiles and subtracting areas of the room that had closets or protruding sections of wall. </div>
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We went outside to look for right triangles and determine if objects being measured represented right angles.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkH8ySIYRSgs-BikaWePuPiqMH-VXfmQ9pKGHSwArEuJkocxRFO4TtYKHHHxXb5cLSQZlklMTJ4uTbxnmFsaZXw5KbkJs1Ryw2496dzO3x76AI7ZqrN4L07sm3R63DXF48iaKaApeTksuW/s1600/pythagorean.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkH8ySIYRSgs-BikaWePuPiqMH-VXfmQ9pKGHSwArEuJkocxRFO4TtYKHHHxXb5cLSQZlklMTJ4uTbxnmFsaZXw5KbkJs1Ryw2496dzO3x76AI7ZqrN4L07sm3R63DXF48iaKaApeTksuW/s320/pythagorean.jpg" width="320" /></a></div>
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I'm finding the students are enjoying getting out to be active and the more often we do this I'm able to see the students' creativity in finding ideas present I wouldn't have thought of. </div>
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<br />mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-60518089942443340942015-05-22T11:25:00.003-05:002015-05-22T11:25:53.234-05:00#codemath: Student created code on simplifying square root expressionsToday as an extension activity for students that have already mastered <i>simplifying square root expressions</i>, I offered students a chance to complete a symbolic example using my #codemaths structure.<br />
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Here was the minimal prompt given to students in a unit google document:<br />
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<span id="docs-internal-guid-2e0f8786-7c5c-c3da-27df-21b2633174ed"><span style="background-color: white; color: #1155cc; font-family: Arial; font-size: 15px; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><a href="https://goo.gl/Y1MUAX" style="text-decoration: none;">Fill in the gaps in the worked out solution in this #codemaths project</a></span></span></blockquote>
I gave a short explanation of how the variable "<i><b>a</b></i>" is randomly generated and when they type <b>[a]</b> it will output that value instead of the letter <b>"a"</b>. <i>(I recently switched from <a> to [a] to allow for simple html formatting to be used in code output. <b></b> for bold, etc.)</i><br />
Students only needed to "<i>fill in the gap</i>" of the potential worked out solution from their perspective on how they would solve it--filling in enough detail that would help a fictional struggling student viewing it as a potential worked out solution.<br />
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The existing code in the worked out section looks like this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhP7NLos8-X5qjpWZFcWMvCqLxnrSNWPH4bmyLo8Zbuir8ChTPHwXB6xT4hFcdXZPUFRe3Jdt6KPK5DoSv02khLQVjEsbJ4Ey5TpVXxlcOLHsLcXFUTGZj6kF1yRm5DBQuWPA_GtkOkj4s/s1600/Screen+Shot+2015-05-22+at+11.05.45+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="222" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhP7NLos8-X5qjpWZFcWMvCqLxnrSNWPH4bmyLo8Zbuir8ChTPHwXB6xT4hFcdXZPUFRe3Jdt6KPK5DoSv02khLQVjEsbJ4Ey5TpVXxlcOLHsLcXFUTGZj6kF1yRm5DBQuWPA_GtkOkj4s/s320/Screen+Shot+2015-05-22+at+11.05.45+AM.png" width="320" /></a></div>
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And will print out:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZXog91rmrXwCPQN601OnP0X3tMQ7USSt_SZpzbyW25w-R7RYW6ytkto8cK7gWiAQU4DiFrqbhpDneKQ-8LtWOTMTRBhd0jxXg64gDXxURlzrkq-EtFc4dOFEr2WCu6T-8ZImDOYPKyRD_/s1600/Screen+Shot+2015-05-22+at+11.06.32+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="126" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZXog91rmrXwCPQN601OnP0X3tMQ7USSt_SZpzbyW25w-R7RYW6ytkto8cK7gWiAQU4DiFrqbhpDneKQ-8LtWOTMTRBhd0jxXg64gDXxURlzrkq-EtFc4dOFEr2WCu6T-8ZImDOYPKyRD_/s320/Screen+Shot+2015-05-22+at+11.06.32+AM.png" width="320" /></a></div>
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For the sake of not giving away the solution to the problem, I will just share screenshots of the student output from the #codemaths worked out solutions they wrote and emailed to me:<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjpFIabGc3QSKQbdo-4H3RCZ4j62tgzRUr2OymEkd7_JfDrRb2P1ZlGUsI1Q8vyU5yAyIQ8vCu-Y9FXZtroYq_Pn40C8XSW94jJSDcW7z-wFsstW2Rr6Q2yUjsZ1E_T7T7wE4Y1QwCBaDC/s1600/Screen+Shot+2015-05-22+at+10.59.37+AM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="208" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjpFIabGc3QSKQbdo-4H3RCZ4j62tgzRUr2OymEkd7_JfDrRb2P1ZlGUsI1Q8vyU5yAyIQ8vCu-Y9FXZtroYq_Pn40C8XSW94jJSDcW7z-wFsstW2Rr6Q2yUjsZ1E_T7T7wE4Y1QwCBaDC/s320/Screen+Shot+2015-05-22+at+10.59.37+AM.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small; text-align: start;"><i>"Remember to give credit to the makers!!!"</i>--Melissa and Katelyn<br /></span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3og2hKc0sf3wjdQIRL198Aior-U6KhGIhcdBdgrb5_O9mCZbFEIJhQFJ94ltnwWysEfrV8m576VArhu9O_PYquRCM0GfnyDkAngba23aAfl_0fWx2ziLo0IVLBwzS85exXbUu8KG59e9N/s1600/Screen+Shot+2015-05-22+at+10.58.53+AM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="242" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3og2hKc0sf3wjdQIRL198Aior-U6KhGIhcdBdgrb5_O9mCZbFEIJhQFJ94ltnwWysEfrV8m576VArhu9O_PYquRCM0GfnyDkAngba23aAfl_0fWx2ziLo0IVLBwzS85exXbUu8KG59e9N/s320/Screen+Shot+2015-05-22+at+10.58.53+AM.png" width="320" /></a></td></tr>
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<i><span style="font-size: small;">"Here mr. schwen this is my super awesome code"</span></i><span style="font-size: small;">--Ken</span></div>
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Pretty fun application for the kids and little time is spent explaining writing code because of the simplified process and kids are thinking more deeply about the mathematics embedded in an activity like this at a pretty highly symbolic level.<br />
One student, wide-eyed and excited, said to me after getting his to work that <i>"This is really fun!"</i> I like too that there is a trial and error aspect to this as they refine and revise what they think will output and what actually does show up when they test it out.<br />
In all honesty, not all my students are doing this but for the kids that are ready for it, it turned out to be a great discussion and application of where we had been in our mathematics and a good preview as to how math can be used in an increasingly more coded world.<br />
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<br />mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-75779174569163320222015-04-23T21:09:00.003-05:002015-04-23T21:09:41.395-05:00#codemaths:Programming math practice for students<h4>
//Checking in</h4>
I feel like I need to start the first paragraph of every post with a quick paragraph for those who will judge my whole classroom based on one blog post (not that anyone has every voiced judgement but I don't want to give the wrong impression either). As part of any good math classroom I believe there needs to be a balance of conceptual development, investigation and then, in turn, developing mathematical fluency and efficiency. This post will focus on how I am using computers to develop efficient math students, and will not focus on the conceptual development that has taken place prior to students doing this practice work (think textbook problems).<br />
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<h3>
//Learning Cycle, Conversations and Self-Reflection</h3>
I have chromebooks in my classroom, two students to each device, which I actually love in promoting math conversations and collaboration. If offered one device for every student I'm not even sure that I'd want it as an option...seriously. I've spent many (seriously, MANY) more hours than I care to admit developing an electronic form of practice for my classroom that works for my situation and I feel like I'm at a new place personally, thus this blog post.<br />
A few years back I was doing the traditional assign homework, quiz the students and look at the data myself. Big Data in education, we all know the drill. I had all kinds of charts and electronic analyzing going on but I was doing all the analysis, not the kids, <i>and it was after the learning cycle was to have been completed</i>. There are actually quite a few blog posts and processes I've written on electronic student data that I'm actually not even doing now in my own classroom now.<br />
I dabbled in writing rubrics for each learning target for my students which I really actually liked but, for the sake of time and curriculum development, that has been pushed to the back-burner and saved for a year when my course content has fewer changes. In class we don't have "homework" but "practice" and as it is electronic there is an unlimited amount available to students at any time, along with help videos that are an option for kids wanting to review where we've been.<br />
We have dedicated class time for practice (<a href="https://script.google.com/macros/s/AKfycbxURuV9eiZFYwJhjv-bGKiWOKwWrUi4UooJE2nG5TipVvH7VNU/exec">example here</a>) and it keeps individual learners at the focus rather than the pace of the whole class. I actually think it's tragic to hear that many 12, 13 and 14 year old kids are having to do 3-5 hours of homework every night before bed rather than spending time with their family and I don't want to be a contributor to that any longer.<br />
I've done the whole clicker thing and what I didn't like with that was there was a lot of down-time and waiting and a lot more focus on the right answer than the process and conversations. Maybe that's because we were gathering data and in education we want it to be "valid" and "formative". No thanks, I'd rather have my kids talking about the math they are wrestling with than getting pure data from them.<br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1TqHE5AVzWGz99g4QB0eiJmiuazOTiCkG2cjEgUaylRjwAXSccdDjvF8q5jx4wpuoRKaveYiZfqVOs1h5fXPwMmyM3sxVax4YHKLhv5k9-4tv9s1rxh7Q0ELHEhzHGWsTCRfK1zX-1c_E/s1600/Screen+Shot+2015-04-23+at+2.34.17+PM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1TqHE5AVzWGz99g4QB0eiJmiuazOTiCkG2cjEgUaylRjwAXSccdDjvF8q5jx4wpuoRKaveYiZfqVOs1h5fXPwMmyM3sxVax4YHKLhv5k9-4tv9s1rxh7Q0ELHEhzHGWsTCRfK1zX-1c_E/s1600/Screen+Shot+2015-04-23+at+2.34.17+PM.png" height="232" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8000001907349px;"><a href="https://script.google.com/macros/s/AKfycbxURuV9eiZFYwJhjv-bGKiWOKwWrUi4UooJE2nG5TipVvH7VNU/exec">Properties of Exponents Review</a><br />
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//codemaths</h3>
I've written some about this in the past and wanted to highlight some of the changes I've put together. I'm <a href="https://drive.google.com/folderview?id=0B5fEUqF5qtzJbFhfdW02bFpURTA&usp=sharing">presenting on this</a> at the NCTM Regional Conference in Minneapolis, Fall of 2015 from both a teacher perspective as well as using it as a tool to challenge students to think more deeply about the math concepts they are learning while applying them in a pseudo-code environment. I tried going full-blown javascript with a class a few years ago and realized so much time is lost in so many of the small details of just writing code that we would never ramp up soon enough to get to applying the math we were currently learning. Today for example in class I found a couple of side-tracked girls that had clicked on the code link from a practice set they were working on and I think I have them hooked on a code challenge to write a system of equations and an algebraic solution based on three randomly generated variables.<br />
<h4>
//Screen</h4>
Kind of a sneaky teacher thing but I have it programmed to go through a subtle gradient of background color (starting at white). If a student continues to get consecutive questions correct their screen will move through shades of green toward blue. As they get consecutive questions wrong it will move through through yellow shades toward red. For a student looking directly at the screen they may not even notice it but as I'm walking around the room it is easier to see and it helps as a visual cue even from across the room for me to go check in with a pair of students if they aren't already calling for help.<br />
<h4>
//Stars</h4>
Far from gamification but after a set number of correct questions, based on quantity and percent correct they can get 1, 2 or 3 stars to show up. It doesn't save to their profile, record it anywhere or even go in as a grade book but it's laughable at how that actually motivates some kids to try harder and not rush through their thinking. Occasionally I'll hack my own code and pictures of my face will show up as they get more questions right. I thought it was funny--some thought it was creepy but deep down I think that means it's awesome so I keep doing it.<br />
<h4>
//Auto Math Formatting</h4>
<a href="https://script.google.com/macros/s/AKfycbzqApd4mCflS2KpVocOLM5Hp3hpemj0hQO2Jrk4TI2_iYip_Zc/exec">This has been the latest project</a> with many times where I almost gave up and it turned out I had literally one character in the wrong "else if" loop. I didn't want students to get hung up on understanding what 2x^3 represented mathematically so after the code is printed it will go through and format text (like in in the image above) as <span style="font-family: inherit;">2<i>x</i><span style="background-color: white; line-height: 16px; white-space: nowrap;">³ while also formatting fractions and subscript labels, all based on order of operations so 1/2x will be </span></span><br />
<span style="font-family: inherit;"><span style="background-color: white; line-height: 16px; white-space: nowrap;">shown differently than 1/(2x) for example. As students type their responses in a text box they will also see a math </span></span><br />
<span style="font-family: inherit;"><span style="background-color: white; line-height: 16px; white-space: nowrap;">formatted preview of what they are entering.</span></span><br />
<h4>
<b>//Makers</b></h4>
I've tried hard to make this all in a way that can be shared and duplicated but I recognize at this level you really need to have some level of javascript understanding to make something like this work for you. What I've found to be true for me though is that it has become easier for me to make specifically what I need for a lesson rather than trying to find something that is close to what I need. <a href="https://drive.google.com/open?id=1EdNamTkgXoxeey1W2tOjjMPmhqfc_E-jqFFwm7MZ2VQ&authuser=0">Here's a link</a> to a getting started guide I've put together and I'd appreciate any feedback if there are steps or parts of the process that are confusing. <i>I can't believe you've read this far, you must be pretty nerdy too.</i>mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com2tag:blogger.com,1999:blog-7489492900803794139.post-21396333464288361782015-03-12T12:59:00.001-05:002015-03-12T12:59:34.679-05:00Sparkfun Inventor's Kit: Choice activity in math class<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/hlG0oWFGUISvkw3pezmisUo1u6wgvEQ8Y36vvywlFrZhGfni7A0IVoNsDdnzpFH8gngPMg=s400" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/hlG0oWFGUISvkw3pezmisUo1u6wgvEQ8Y36vvywlFrZhGfni7A0IVoNsDdnzpFH8gngPMg=s400" height="240" width="320" /></a></div>
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After seeing a tweet from <a href="https://twitter.com/rutherfordcasey">Casey Rutherford</a> last week, I looked into the <a href="https://www.sparkfun.com/products/12060">Sparkfun Inventor's Kit</a> for my math students. It's a physical circuit board that allows students to play with code that causes the board to interact in the real world<i>--LED lights, displays, sounds, motors, sensors, etc</i>. The kit arrived this morning and rather than get it all figured out myself I threw it (figuratively) to the kids and let them try it out.<br />
My initial concerns was, "<i>I have chromebooks, do I need to install anything to get it to work?</i>" Early into <a href="http://forum.arduino.cc/index.php?topic=61652.0">this thread</a> that started in 2011 the answer would have been "No" but then this guy named Casey Halverson created a Chrome Webstore app called <a href="https://chrome.google.com/webstore/detail/chromeduino/dmkincdpchiadkhhocmbpjljebfifgbl?utm_source=gmail">ChromeDuino</a> that turns it into a plug and play device with Chromebooks. My students had the app installed in a minute and before 3 minutes were starting to follow the instructions in the user manual in getting starting on some of the beginner activities.<br />
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<a href="http://2.bp.blogspot.com/eBN9a6Fp0e4VM8myv7YqFsOFXfIlPyD2Fj_Cr_BNBizf2DuhBXIQ_1is4T7IrKGbG4eFZw=s400" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/eBN9a6Fp0e4VM8myv7YqFsOFXfIlPyD2Fj_Cr_BNBizf2DuhBXIQ_1is4T7IrKGbG4eFZw=s400" height="240" width="320" /></a></div>
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<i>Before the kids got to school I actually plugged it into my Mac desktop running OSX and had trouble getting it to recognize the device. I had to install an application and then decide which serial device port was connected...blah blah blah. I never actually got it to connect properly but it didn't matter because the Chromebooks were the intended device.</i><br />
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<a href="http://4.bp.blogspot.com/7jBvPUMUBIvQn2TrQdg0qDi93utbDxrBC9rkzV1_jC4eLtxMhnmXZppjNd_NbOfp_-mVMA=s400" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/7jBvPUMUBIvQn2TrQdg0qDi93utbDxrBC9rkzV1_jC4eLtxMhnmXZppjNd_NbOfp_-mVMA=s400" height="240" width="320" /></a></div>
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This just might be one of the coolest uses for Chromebooks in a STEM application I have seen yet and it gets the creativity going when kids begin to think about the connections between computer programming and the physical world. I often hope and wonder if having experiences like this in the classroom can be moments where my students years from now will look back and say "That is when I became more interested in __________ and look at where I am today!"<br />
<br />mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-26145280906411701482015-02-27T14:41:00.001-06:002015-02-27T14:41:10.410-06:00Learning, falling down and less testing<div class="separator" style="clear: both; text-align: center;">
<iframe width="320" height="266" class="YOUTUBE-iframe-video" data-thumbnail-src="https://ytimg.googleusercontent.com/vi/B7KMLe8H8Rs/0.jpg" src="http://www.youtube.com/embed/B7KMLe8H8Rs?feature=player_embedded" frameborder="0" allowfullscreen></iframe></div>
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<br />
My students are stressed out this week.<br />
<br />
We are in a two week period where they are taking a final in any one of their given classes every day because it is the end of the trimester and that is what we do here.<br />
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<b>6 weeks</b> (2 weeks x 3 trimesters)</blockquote>
We have state tests coming up in a month, which, for our 8th graders means that they will have one week in a computer lab for each subject area (math, language arts and science)<br />
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<b>3 weeks</b></blockquote>
Our 8th graders have already taken the 8th grade version of the ACT, the EXPLORE test over two class periods, mandated by the state.<br />
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<b>2 days</b></blockquote>
We do two weeks of school district computerized testing in the fall to...gather data for math and language arts.<br />
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<b>2 weeks</b></blockquote>
Plus the regular assessments for grade that classroom teachers give students on a weekly or bi-weekly basis.<br />
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<b>3.5-7 weeks </b>(5 days a week for 36 weeks in a school year)</blockquote>
For a grand total of 18 weeks out of 36 in a school year where my kids are taking a test. Kids. Tests. Tests....kids.<br />
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<b>50% of the school year</b></blockquote>
So we needed a reminder today about what learning and being a kid looks like and feels like: Puppies and Stairs. It was fun to be able to watch the kids laugh and relate to the dogs learning to do something as basic as going up or down stairs and I could see it in their eyes that they understood that this is what learning really is. Sometimes we fall down and <i>often</i> something that feels difficult at first becomes automatic later. The struggle is important (and fun to reflect on) and because of the struggle the learning can have more meaning to us if we persist and don't give up.<br />
<br />
I needed this reminder today too. These are still kids in front of me. They still need time with their families. They have feelings. They, like me, like watching videos sometimes about puppies learning to use stairs.<br />
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mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-65974941893111507062014-12-04T11:43:00.000-06:002014-12-04T11:43:25.870-06:00Breaking my silence: Where I am todayThe title probably makes it sound like I'm going to talk about some controversial topic that I've just been holding back on for beyond my limits. Maybe it would have been a good title to boost my statistics had I actually be making any money on these posts. Where it is actually coming from is, for the past year I've spent a lot of my time keeping closer with the students in my classroom, my family and in collaborating with the teachers in my building. I became a little turned off from the self-promotion and "making a name for myself" attitude that I was seeing more of in the edu sphere and creeping up in myself as well.<br />
I had a chance to catch up with a good friend last night on the phone that also happens to be in education. Talking with him some about this he reminded me that it is still important to share our experiences with other teachers for the sake of the kids and improving our schools for them. So that being said, even after 12 years of teaching, I still feel like I don't know what I'm doing but will share a new post on where I am today and the journey that I hope is ahead for my classroom.<br />
I'd like to believe that my classroom is centered more this year and last on conversations between students 70% of the time each day. That as often as I can I'm providing activities that first help them to explore and build their understanding that at some point tip toward developing efficient and meaningful math skills development and solid mathematical thinking. I am thankful for the continual improvement of resources like <a href="https://www.google.com/url?q=https%3A%2F%2Fstudent.desmos.com%2F&sa=D&sntz=1&usg=AFQjCNEn3dF-F-WO_x3UQOZDdK_irTVgGw">Desmos' Function Carnival</a> in having some engaging ways of doing that in a way that is fun for kids. I also like the idea that it isn't just the typical edtech garbage--that there are good math people I know under the hood developing it in a thoughtful way.<br />
This year in my professional reflection process I'm desiring to make a better connection to activities like this and what we are learning rather than just having isolated fun, engaging things that don't really move my students to a better understanding of the other class stuff we do.<br />
Today we are unpacking what we did yesterday through function carnival and my hope in this activity was to lead kids to develop the skills necessary for future success based on what they explored yesterday. <a href="https://docs.google.com/presentation/d/1Kb6Ht9jjz-7H-wNpBUcQBdzkFPsaXf-mFB0EYMr12Co/present?slide=id.p">This lesson</a> started with students thinking individually, sharing with their partner and then having a large class discussion for the first 10 minutes of class and then partners moving forward at their own pace, discussing and writing their responses. I was free to talk with groups as the need came up and pulled us together as a group as it seemed necessary.<br />
I think this is an area that we need to get better at as teachers--myself included. Yes, still trying to incorporate explorations and investigations but then getting better at connecting those activities to learning and use of those skills learned in future learning opportunities. Maybe in sites like Function Carnival there could be a teacher lesson pool that we could start sharing ways of getting to that with students?mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-41231528695120147502014-05-09T12:57:00.000-05:002014-05-09T12:57:01.825-05:00Number of moves to beat 2048 activity<div class="separator" style="clear: both; text-align: center;">
<a href="http://static.wapmaker.net/7409/2048.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://static.wapmaker.net/7409/2048.png" height="200" width="200" /></a></div>
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I'm early on in developing this activity for my class and who knows--I may even be thinking about it incorrectly but what I do know is this game is both addicting and very relevant to my students right now. What I'm considering posing to them as a question in our exponent unit is:<br />
<blockquote class="tr_bq">
<i>"What is the best and worst case scenario of the amount of time I would need to 'beat' the game and get to the 2048 tile if I take 5 seconds with each move?"</i></blockquote>
If you don't know the game you can check out <a href="https://www.youtube.com/watch?v=soRVwjDmmkA&safety_mode=true&persist_safety_mode=1">this video</a> but I'll warn you--while you are playing this game life happens around you without you being aware of anything going on (very addicting).<br />
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During the game you continue to get new <i>2</i> and <i>4</i> tiles that you must push together to try and build up to a tile of value 2048 (<span style="background-color: white; font-family: arial, sans-serif;">2</span><sup style="background-color: white; font-family: arial, sans-serif;">11</sup>). In a worst case scenario you would continue to get all 2's as new tiles or best case scenario all 4 tiles (neither happens but it sets up a range of what could).<br />
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Here are some scenarios that could give you a range of values for acquiring the 8 tile and the 16 tile:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy2SWR8QTbAiqdMHg2ZfrKQmc8EM7WW6yD6L6CodQlIudPaIhSZZjNpf4bmh-DxeNNMtdwgkMhyphenhypheniPyCaghAsY2xIL_zQoNLmuhiHyO7ClyN3pRWwl7mYEc4jl7l8462qbQtTT9HgwVT7Ly/s1600/Screen+Shot+2014-05-09+at+12.48.48+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy2SWR8QTbAiqdMHg2ZfrKQmc8EM7WW6yD6L6CodQlIudPaIhSZZjNpf4bmh-DxeNNMtdwgkMhyphenhypheniPyCaghAsY2xIL_zQoNLmuhiHyO7ClyN3pRWwl7mYEc4jl7l8462qbQtTT9HgwVT7Ly/s1600/Screen+Shot+2014-05-09+at+12.48.48+PM.png" height="142" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_uk877bvm2rKMvOWhs98OU3VQmUv0kVvT19oNmWh6AnGa7We7JLj1YDqGm1sRC2rJmKh86y1nutMQDVmoDS4mEUvpGBEmFWts6EU4fEJH-gj9lvQMEcaug2LvBNdO4NfhsHRA_jO98wN6/s1600/Screen+Shot+2014-05-09+at+12.48.53+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_uk877bvm2rKMvOWhs98OU3VQmUv0kVvT19oNmWh6AnGa7We7JLj1YDqGm1sRC2rJmKh86y1nutMQDVmoDS4mEUvpGBEmFWts6EU4fEJH-gj9lvQMEcaug2LvBNdO4NfhsHRA_jO98wN6/s1600/Screen+Shot+2014-05-09+at+12.48.53+PM.png" height="148" width="640" /></a></div>
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What I like about the idea of this problem is there is real motivation in wanting to get to an equation but the student will need to be sure that the range of moves can all be generated. I haven't presented it to students yet so more may be following on how that goes.</div>
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I will leave the 4 tile graphic out to allow students the opportunity to consider it on their own and maybe I won't even present them with these scenarios early on in the problem either. Comments or suggestions welcome as always in the comments below. If there is a better example of this somewhere else too please let me know!</div>
<br />mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-36606275999520113152014-05-07T12:39:00.002-05:002014-05-07T12:39:37.517-05:00Open-ended discussion on "Rules of exponents"<div class="tr_bq">
So earlier this week I read <a href="http://mr-stadel.blogspot.com/2013/04/thank-you-math-mistakes.html">this post</a> by Andrew Stadel and was challenged to approach the rules of exponents in a more perplexing way. First of all, starting with the mistakes and what kids already know about exponents was a great launching point for this lesson. I made my own 4 question mistakes not really wanting to get into exponents of zero, negative values or fractions just yet.</div>
<blockquote>
<span style="background-color: transparent; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The following statements are all INCORRECT.</span><span style="background-color: transparent; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">1. Identify the mistake(s).</span><span style="background-color: transparent; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">2. Correct.</span><span style="background-color: transparent; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">3. Justify (show) your reasoning.</span><b id="docs-internal-guid-b350b247-d7ac-5b4d-3a8f-00a39e9b1c3b" style="font-weight: normal;"><br /></b><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">1. </span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="background-color: transparent; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">4</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super; white-space: pre-wrap;">3</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> · 4</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super; white-space: pre-wrap;">2</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> = 16</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super; white-space: pre-wrap;">5</span><b style="font-weight: normal;"><br /></b><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">2. </span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">(3</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super; white-space: pre-wrap;">4</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super; white-space: pre-wrap;">2</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> = 3</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super; white-space: pre-wrap;">6</span><b style="font-weight: normal;"><br /></b><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">3. </span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">x</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super; white-space: pre-wrap;">3</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> · x</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super; white-space: pre-wrap;">2</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> = x</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super; white-space: pre-wrap;">6</span><br /><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">4. </span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">x</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super; white-space: pre-wrap;">2</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">y</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super; white-space: pre-wrap;">3</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> = (xy)</span><span style="background-color: white; color: black; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: super; white-space: pre-wrap;">5</span></blockquote>
We spend a large majority of the time on question 1 in the last hour and somehow managed to get to fractional exponents. Different from earlier classes today, I started my last class by saying there are two levels of answering these questions:<br />
<blockquote class="tr_bq">
<i>1) You grab a calculator and find the value of each side and say "These numbers are different, so it's wrong".<br />2) You apply what you already know about exponents and come up with an explanation that someone who knows less </i><i>than you </i><i>about exponents can understand. </i></blockquote>
For number 1 I had students say that the value should be 4<span style="background-color: white; font-family: Arial; vertical-align: super; white-space: pre-wrap;">5</span>, <span style="background-color: white; font-family: Arial; vertical-align: baseline; white-space: pre-wrap;">2</span><span style="background-color: white; font-family: Arial; vertical-align: super; white-space: pre-wrap;">10</span> and 32<span style="background-color: white; font-family: Arial; vertical-align: super; white-space: pre-wrap;">2</span><br />
<span style="background-color: white; font-family: Arial; vertical-align: super; white-space: pre-wrap;">The fun came in asking students to explain why <span style="font-family: Times; white-space: normal;">4</span><span style="vertical-align: super;">5</span> was the same as <span style="vertical-align: baseline;">2</span><span style="vertical-align: super;">10</span> in visual form. Most at first said that because you take half the base number you must double the exponent but we needed to know why to develop their understanding. </span><br />
<span style="background-color: white; font-family: Arial; vertical-align: super; white-space: pre-wrap;">One student explained by pairing up the two's to make 4's by multiplication and stating there were 5 groups of these pairs--the whole class applauded his explanation after gasping that they got it.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyjmJ1Czhamamqq9NpB2ZBbU9egCRgZefc0B7_B6nS8E22QschHlhBVg74WuLW5afvmJhfgHGpDossSM3fwAQFDL7PluYxhWt6JDB3Z06NfUbxXngQq9FvwjhMoWTsNcWGb9BqmmyYDcAj/s1600/Screen+Shot+2014-05-07+at+12.22.53+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyjmJ1Czhamamqq9NpB2ZBbU9egCRgZefc0B7_B6nS8E22QschHlhBVg74WuLW5afvmJhfgHGpDossSM3fwAQFDL7PluYxhWt6JDB3Z06NfUbxXngQq9FvwjhMoWTsNcWGb9BqmmyYDcAj/s1600/Screen+Shot+2014-05-07+at+12.22.53+PM.png" height="145" width="200" /></a></div>
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So then we went to why 4<span style="font-family: Arial; vertical-align: super; white-space: pre-wrap;">5</span> was the same as 32<span style="background-color: white; font-family: Arial; vertical-align: super; white-space: pre-wrap;">2 </span>and a girl student did this (again applause from the class followed):</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkZfZXc9Mgo6nLTDnQD1R6p_nbkPou5mVOGk1YRlGjLPk11O5h6uHqP8ktNFEPhtV9k6-3ExIQjF3ieA5ymupgyfjI06N9rhyphenhyphenXxaR3xGv0e8YAJDiid4dQYl_LxtOVOL-ubdpjL4dJ_qrB/s1600/Screen+Shot+2014-05-07+at+12.25.04+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkZfZXc9Mgo6nLTDnQD1R6p_nbkPou5mVOGk1YRlGjLPk11O5h6uHqP8ktNFEPhtV9k6-3ExIQjF3ieA5ymupgyfjI06N9rhyphenhyphenXxaR3xGv0e8YAJDiid4dQYl_LxtOVOL-ubdpjL4dJ_qrB/s1600/Screen+Shot+2014-05-07+at+12.25.04+PM.png" height="129" width="200" /></a></div>
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Realizing we were getting dangerously close to logarithms in my 6th grade Algebra class I pushed the envelope and asked what the exponent would be in <span style="background-color: white; font-family: arial, sans-serif;">8</span><sup style="background-color: white; font-family: arial, sans-serif;">x</sup> = 4<span style="font-family: Arial; vertical-align: super; white-space: pre-wrap;">5</span> and they jumped right in!! Some students naturally assumed it was 2.5 and stopped but others weren't satisfied. </div>
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A girl student in class offered to come up and draw a picture of what she thought was happening and we got this to look at as a class:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixYBA8u-rNmzdIOsZ7Dc9ipu_oFcXJbpTIgS6CmAx9xVXWrgMrbTcUD2MJomnXjrheW6KZaCG7cfMP6xVYjCXtXRKzNn5V8K_EKJEA_W8sItDoE0qb_YycQkRtBmbBCd7sg8ONNh2mwFtC/s1600/Screen+Shot+2014-05-07+at+12.29.09+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixYBA8u-rNmzdIOsZ7Dc9ipu_oFcXJbpTIgS6CmAx9xVXWrgMrbTcUD2MJomnXjrheW6KZaCG7cfMP6xVYjCXtXRKzNn5V8K_EKJEA_W8sItDoE0qb_YycQkRtBmbBCd7sg8ONNh2mwFtC/s1600/Screen+Shot+2014-05-07+at+12.29.09+PM.png" height="170" width="200" /></a></div>
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Her picture was an excellent launching point for discussion in thinking about what to do with left-over factors when we try to group to get factors of 8. Her mistake actually brought out a big difference in fractions vs fractions as exponents when another student tried what she said in his calculator. The class came to consensus that for the exponent, since it would take 3-2's to make another factor of eight the exponent should actually be 3 1/3 instead of 3 1/4. </div>
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Wow. Great class, fully engaged students and some great thinking going on driven by the students.</div>
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<span style="background-color: white; font-family: Arial; vertical-align: super; white-space: pre-wrap;"><br /></span>mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com1tag:blogger.com,1999:blog-7489492900803794139.post-55840355301811614712014-05-01T09:42:00.000-05:002014-05-01T09:42:27.030-05:00Reverse it to see what they knowWe are working on solving systems of equations in Algebra class right now. As a class warmup today I asked students to do this:<br />
<blockquote class="tr_bq">
<span id="docs-internal-guid-28cd11b9-b828-216c-a9bf-ecc226c37b4a"><span style="font-family: Arial; vertical-align: baseline; white-space: pre-wrap;"><i>Write a system of equations that has a solution of (3,-2) that you think most (all) students would think it is easiest solved using the linear combination [elimination] method.</i></span></span></blockquote>
It was really fun to see their thinking and push back on them a little bit with--"<i>Hmm...I'm not sure if I'd solve that one with linear combinations. You haven't made it appealing enough to me yet.</i>" What I love about tasks like this is some students do it exactly in the way I was hoping based on what we've already done in class and others do something more intuitive (and sometimes simpler) than what I had in mind.<br />
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We started our unit of solving linear systems with <a href="https://docs.google.com/presentation/d/1FDsTUnMmeEvgq40iI_6oG3AnFcBDgXOE0zGMVo6-6fc/present#slide=id.p">this activity</a> and I have been really happy with the deeper understanding students have had because of the greater focus on the properties of equality. In a couple classes we even looked at doing similar operations using matrices and ideas from my college linear algebra class. (<i><span style="color: #666666;">I think I went through that course hardly knowing why I could do what I did to those matrices and hated how much notebook paper it took to do it...</span></i>)<br />
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Here are a couple of examples of what students said in class today when I talked with them and asked them to share their process with the class:<br />
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<b>Hayden: </b><br />
I started with 3x = 9 because I wanted x=3 and then I made the equation x + y = 1 because that equation was easy to have the correct solution.<br />
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3x = 9 (starts in the middle of the problem in a way)</blockquote>
<blockquote class="tr_bq">
x = 3 </blockquote>
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x + y = 1 (back to the beginning)</blockquote>
Then I made 2x - y = 8 because the 2x would give me the 3x I needed and the 8 would make the 9 when I combine the equations.<br />
<blockquote class="tr_bq">
x + y = 1 </blockquote>
<blockquote class="tr_bq">
2x - y = 8 (manipulating the y's to cancel and to get his 3x = 9 situation)</blockquote>
The y's would also make zero to make someone want to use the combinations method.<br />
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<b>Lucy: </b><br />
I just made up some numbers on the left side and put in the coordinates to see what they would evaluate to:<br />
<blockquote class="tr_bq">
2x + 3y --> 2(3) + 3(-2) = 0 so the equation 2x + 3y = 0 has a solution of (3,-2).</blockquote>
Then I made the next equation to have a -2x because I wanted the x's to cancel when I do combinations and the y-term could be anything. I put in the coordinate again to see what the number on the right side of the equation had to be:<br />
<blockquote class="tr_bq">
-2x + (anything)y = whatever you get back</blockquote>
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-2x + 4y --> -2(3) + 4(-2) = -14 so then the equation -2x + 4y = -14 also has a solution of (3,-2).</blockquote>
I wasn't sure how well the activity would go but the student seemed very engaged from the start and those that I talked to had great strategies in how to go about solving the problem.<br />
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It didn't take a whole lot of planning up front and it gave the students the opportunity to be creative and come up with unique products that demonstrate their understanding of the concept in the reverse direction. </blockquote>
I believe that in doing so students will also have a better understanding of when to use the combinations method instead of the substitution or graphing method when appropriate.<br />
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mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com2tag:blogger.com,1999:blog-7489492900803794139.post-77588201372439093582014-04-28T10:03:00.002-05:002015-05-20T07:52:22.795-05:00#codemaths: Mathish generator <div class="separator" style="clear: both; text-align: center;">
<img border="0" height="148" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9mlTfKDevtQ-bYLW-iIEnr5zmi2yGsgHYCL-WG7TyIvzo80-cX8_YtQ94UuXcoVk-hn07suZRV4T_DH1eYwzcR_k1UKD7XgRFL3_kDtgQ94hXj_RIF-epl6kDQnxHhKPj8h4v41FEB8ta/s1600/Screen+Shot+2014-04-28+at+9.54.11+AM.png" width="640" /></div>
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I realize there are things out there like this that are much better but with our exponent unit coming up I wanted my students to be able to see what they were typing using the "^" to denote exponential form and I wanted order of operations to be considered with how they were typing it in the preview. In our practice material (<a href="https://script.google.com/macros/s/AKfycbwdaweDdUo7ZSqtJv3nY9blHOnPFQn8fNC6KXfykEqit8x3_2Y/exec">here for example</a>) I have it set up to preview as kids type. It can also be copied and pasted into a document if I wanted to use what I have typed for a quiz of some sort instead of using an equation generator that is sometimes hard to format (or is a picture in some cases).<br />
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<a href="https://script.google.com/macros/s/AKfycbzqApd4mCflS2KpVocOLM5Hp3hpemj0hQO2Jrk4TI2_iYip_Zc/exec">Here is the link to the work in progress.</a><br />
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I've been thinking for future in wanting it to format complex fractions but have run into a limitation with Google Apps Scripts in not allowing the <u> tag in html or for me to specify what sides of a cell to show a border. I have a hard time believing this would cause a security risk for them but they do not seem to allow that at this time.<br />
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<b><span style="color: red;">**An update as of 5/20/15 now includes fractions with exponential and radical expressions if you type sqrt to represent the square root symbol. Formatting and appearance is still based on order of operations.**</span></b>mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-49899972027007302482014-04-16T13:07:00.000-05:002014-04-16T13:07:05.698-05:00Differentiated Lesson: Systems of Equations<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLbW4VRHyOQMpZJpdnk35MWDgTvM9-no_b4ekM51YPtD8sePjQHhj0Ed97PBa5el8u3gwMggDol6h-1h98osXYI9iB6hLr96Xn487F3mT7pQSxVbzmOtGRp4NxTrTDY6xhQCk5tp9bfLwn/s1600/Screen+Shot+2014-04-16+at+12.58.21+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLbW4VRHyOQMpZJpdnk35MWDgTvM9-no_b4ekM51YPtD8sePjQHhj0Ed97PBa5el8u3gwMggDol6h-1h98osXYI9iB6hLr96Xn487F3mT7pQSxVbzmOtGRp4NxTrTDY6xhQCk5tp9bfLwn/s1600/Screen+Shot+2014-04-16+at+12.58.21+PM.png" height="311" width="320" /></a></div>
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Today in class I anticipated I'd have a range of abilities with what we are doing in wrapping up a multi-day lesson. I have become fully dependent on the half class set of chromebooks on days like today. I would even say that I am happy that I do not have a 1:1 ratio in my classroom because of the conversations rooted in the need to share and discuss their thinking. </div>
<blockquote class="tr_bq">
<i>Regular access to classroom technology is crucial for this day to happen in the way that it does.</i></blockquote>
We have been working toward solving systems of equations in algebra, the last 2-3 days have been spent on <a href="https://docs.google.com/presentation/d/1FDsTUnMmeEvgq40iI_6oG3AnFcBDgXOE0zGMVo6-6fc/present#slide=id.p">this algebra-like investigation.</a><br />
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As part of the review day, students were checking graphical solutions to a system of equations on <a href="https://docs.google.com/file/d/1WHBs2XWH_kEAheaPlHodcKBmWNexNLdRFyH1MHEYSL_fcw0ZcKqpOVJnoX-7_1qsbriMUiVMj5KYF_dI/edit">this worksheet</a> ("websheet"?) from <a href="http://www.mathematicsvisionproject.org/">http://www.mathematicsvisionproject.org</a>. I asked students to do their algebra check on paper but I wanted them to graph (mostly) on <a href="http://www.desmos.com/">Desmos</a> (yay!) and at least once on a graphing calculator (...for future college board tests...meh). <br />
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On the second page of the MVP math sheet, #5 says:<br />
<blockquote>
<i>"A theater wants to take in at least $2000 for a certain matinee. Children’s tickets cost $5 each and adult tickets cost $10 each. The theater can seat up to 350 people. Find five combinations of children and adult tickets that will make their goal."</i></blockquote>
I challenged the class to also come up with some equations that represented the situation and to think about what could be replaced by variables. I did not expect everyone at this point in our learning cycle to do so but was very pleased with some results I will share below. Other students in the class that weren't ready just found the 5 possible combinations, still laying the groundwork for next class when we discuss the problem as a group. Students could also get additional practice on <a href="https://script.google.com/macros/s/AKfycbwPs35GHEogBmZXfLjg54ZBv88Q8VuvxGNypqdt-hBtI0BWCps/exec">this web app</a> if they felt they needed it.<br />
I was most pleased with a group that not only went to <a href="http://www.desmos.com/">desmos</a>, I was able to start talking to them about the <u>inequalities</u> they had written, which regions created contained points that were considered solutions and if they needed to add any (constraints) to better define the solution region. At the end of class they were excited and were going to continue working on it tonight even though they did not have to. (<a href="https://www.desmos.com/calculator/hadxteqy67">Here is what they made as an extension to the word problem shown above.</a>)<br />
Thank you Desmos for making free tools like this for math teachers. I really like that students can graph equations in standard form (not just in the form y=mx+b). It helped in building understanding for these students as they were looking at the solution area of their graph. On a related note, you should also check out their <a href="https://teacher.desmos.com/">classroom activities page</a>.mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-54841039491669771342014-03-26T14:58:00.000-05:002014-03-26T14:58:05.071-05:00Messing with major educational giants: Early April Fool's Day mischiefSo today as I was working on making a test for my algebra class I came across a site that had an equation editor...naturally drawing me in of course.<br />
While there for no more than 10 seconds a chat window popped up asking if I wanted any math help. I could have ignored it but I needed a diversion and below is the result.<br />
I was surprised I got as far as I did before they asked for a payment since I started by saying I needed help on a test I was taking...this being a company I know for a fact already makes a lot of money through the educational system.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiV31Wk97PPkYFOS5X1JGZm9HKxZW_VWtSLqYW_JSOZcfnK7bFWgrxNemEAxus9v3CsyIKVGw8Db03pzASPr_Sg2bzZHWgAgdi2ydOKpuOh5LNMciujmBdFWOEmlQMxuLywBU9ujYbL7VON/s1600/Screen+Shot+2014-03-26+at+2.17.51+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiV31Wk97PPkYFOS5X1JGZm9HKxZW_VWtSLqYW_JSOZcfnK7bFWgrxNemEAxus9v3CsyIKVGw8Db03pzASPr_Sg2bzZHWgAgdi2ydOKpuOh5LNMciujmBdFWOEmlQMxuLywBU9ujYbL7VON/s1600/Screen+Shot+2014-03-26+at+2.17.51+PM.png" height="504" width="640" /></a></div>
<br />mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com1tag:blogger.com,1999:blog-7489492900803794139.post-76613059305951597842014-03-21T09:50:00.000-05:002014-03-21T09:50:37.086-05:00#codemaths: Considering different solutions as variables change<b>A symbolic extension to our current learning in class</b><br />
I presented this as a challenge for my students today that were ready to move on from the review that others were still doing in class. All students worked on the initial question and a handful moved on to try to program the solution in #codemaths. I was happy to see that a couple of my female students were working on this and I talked to them about the movement to try and get more girls into programming in what is typically seen as a male career path--they thought that was pretty cool.<br />
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<blockquote class="twitter-tweet" lang="en">
"You cannot be what you cannot see!" -<a href="https://twitter.com/reshmasaujani">@reshmasaujani</a> on <a href="https://twitter.com/msnbc">@msnbc</a>. Great segment! <a href="http://t.co/hH4VzVZ1vl">pic.twitter.com/hH4VzVZ1vl</a><br />
— Girls Who Code (@GirlsWhoCode) <a href="https://twitter.com/GirlsWhoCode/statuses/446314419073859584">March 19, 2014</a></blockquote>
<b>Here is the example the class worked on and the skills I went over to prepare students for what they would need to do in order to connect the Javascript to the mathematics they were applying:</b><br />
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<span style="background-color: white; color: blue; font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">What is the solution to ax+b≥c where a, b and c are any value? </span><span style="background-color: white; color: #666666; font-family: Arial; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Are there any circumstances that cause your solution to be different? </span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"></span></div>
<b id="docs-internal-guid-bb366534-e51a-777b-412a-443e6b984856" style="font-weight: normal;"><br /><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"></span></b>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Javascript skills needed:</span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> using the eval() function and joining a string with variable expressions.</span></div>
<b style="font-weight: normal;"><br /><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"></span></b>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Joining strings with variable values:</span></div>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">“This sentence includes the value “+b; </span></div>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">displays as </span></div>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">“This sentence includes the value 3”</span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span></div>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">when b = 3.</span></div>
<b style="font-weight: normal;"><br /><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"></span></b>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Using the eval() function: </span></div>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">You can do math using the eval() function as well:</span></div>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">“x>”+eval(a*b-c) </span></div>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">would display as </span></div>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">“x>-1” </span></div>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">when a=1, b=2 and c=3.</span></div>
<b style="font-weight: normal;"><br /><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"></span></b>
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<a href="https://script.google.com/macros/s/AKfycbxa9d1543kySk9wnS_cTZ3KfZV5Prl9QPkD9VW6Ugu3LMuR1Yo/exec?constraints=if(a%3D%3D0)%7Ba%20%3D%203%3B%7D%0Avar%20Gsymbol%20%3D%20%22%3E%22%3B%0Avar%20Lsymbol%20%3D%20%22%3C%22%3B%0Aif(a%3C0)%0A%7B%0Avar%20solved%20%3D%20%22type%20your%20solution%20to%20include%20values%20like%20x%22%2BLsymbol%2Bc%2B%22%20here%22%3B%0A%7D%0Aelse%0A%7B%0Avar%20solved%20%3D%20%22type%20your%20solution%20to%20include%20other%20values%20like%20x%22%2BLsymbol%2Bb%2B%22%20here%22%3B%0A%7D&tableCheck=unchecked&graphCheck=unchecked&question=Solve%20the%20inequality%20%3Ca%3Ex%2B%3Cb%3E%3CLsymbol%3E%3Cc%3E&solution=solved&workedout=Try%20and%20have%20a%20worked%20out%20explanation%20here.%20Remember%20you%20can't%20use%20less%20than%20or%20greater%20than%20symbols%20in%20this%20section%2C%20instead%20use%20the%20variables%20from%20above%20like%20%3CLsymbol%3E.&equation=&inputType=textbox&inputList=" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">In this #codemaths challenge</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, you will want to change the variable ‘solved’ in the constraints section to output a correct solution for any inequality that may result for random variables a, b and c that is programmed in the question section. </span></div>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Notice in the first line of code</span></div>
<div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">if(a==0){a = 3;}</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">that a will be changed to 3 if it is ever equal to 0.</span></div>
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mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com1tag:blogger.com,1999:blog-7489492900803794139.post-59262576392072495732014-03-07T09:47:00.001-06:002014-03-07T12:17:53.277-06:00Triangle Inequality: Introducing a learning target in contextIn starting a new unit today I wanted to give context to students for writing inequalities. In our algebra class students have not yet learned the triangle inequality theorem which states that:<br />
<blockquote class="tr_bq">
<i>The sum of any two sides in a triangle must be greater than the third side.</i></blockquote>
Seems like a great opportunity for some 'ruler math'. I kept the rulers on my desk until after the bell because spring break starts after today and I know how middle schoolers can we with unstructured time and these tools...<br />
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In anticipating the pacing to be different for each student I made the activity as a Google presentation and provided students <a href="https://docs.google.com/presentation/d/1xQJniCtBmzKPD-qyxh0jeChXRbi6hdJyGnYtgtQDZx4/present#slide=id.p">the link</a>, instructing them to do their work on paper and answer completely any questions asked of them in the activity--noting that I would be breaking in periodically to the whole class and facilitating some discussion.<br />
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/laoEt8qpoMk?feature=player_embedded' frameborder='0'></iframe></div>
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My favorite part was #4 of the first drawing where many of them grew frustrated with not being able to construct a 1 cm, 2 cm, 5 cm triangle--thinking it was something they were doing wrong. Kind of a fun way to watch them squirm and I know I'm not the first math teacher to have ever done this.<br />
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I had some awesome conversations with students while they were working. One student changed what he said mid-sentence. He went from saying<br />
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<i>"The two lengths need to be <u>at least</u> the length of the third...The two lengths need to be <u>more than</u> the third length..." </i></blockquote>
I asked him why he changed his wording and he explained the difference between the two correctly. Pretty cool--I made sure to highlight that to the class in our whole group time. This kind of mathematics is so much more fun to teach than the traditional "do this, copy me, don't think" style. I overheard the same student above before leaving say to his neighbor<br />
<blockquote class="tr_bq">
<i>"Math is my hardest class because you can't just memorize stuff and copy it down. You actually have to understand the concepts to do well." </i></blockquote>
I told him I will take that as a compliment.<br />
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I am not expecting all students to go here but I am hoping that some make some connections to they pythagorean theorem and how it relates to acute and obtuse triangles in the last slide.<br />
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I've already made some revisions to the activity since teaching it one period and I wouldn't be surprised if it changed a little more as the day goes on. As always I'm open to other ideas or revisions to make it a better experience for my students.mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-45969015929849092132014-02-26T10:02:00.000-06:002014-02-26T10:02:31.437-06:00Another (low prep) open ended set of questionsAgain--nothing fancy here and hopefully that is the point. We did another set of tiered questions for a lesson warmup today to pre assess and to scaffold on their existing knowledge. Students could choose which question they wanted to do and we made connections along the way through each one.<br />
Here is the set of questions:<br />
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<span id="docs-internal-guid-28ce04ec-6ee8-9720-21ca-fcc9f0658534"><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: Arial; vertical-align: baseline; white-space: pre-wrap;"><u>Choose one of the following examples to do</u>:</span></div>
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<span style="font-family: Arial; vertical-align: baseline; white-space: pre-wrap;">1. In the equation 4x + 3y = 13, what is the value of y when x=1.5?</span></div>
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<span style="font-family: Arial; vertical-align: baseline; white-space: pre-wrap;">2. Rewrite the equation </span><span style="font-family: Arial; line-height: 1.15; text-indent: 36pt; white-space: pre-wrap;">4x + 3y = 13 in y=mx+b form.</span></div>
</span><span><span style="font-family: Arial; vertical-align: baseline; white-space: pre-wrap;">3. Rewrite the equation y-c=c(x+3) in y=mx+b form.</span></span></blockquote>
I flat out told students that the easiest is #1 and the most challenging is #3. We have not done any work to this point with solving an equation for a variable when more than 1 variable is present. The student that solved and explained #1 lays the groundwork for what the class will hear for the student that chose #2 and so on. Before the activity students were not ready to answer any question related to #3 but by the end of the discussion the whole class had something to build on for determining the slope and y-intercept present in #3.<br />
Students overall appreciate being able to choose and will often go for the more challenging level (at their ability) when that choice is present. It also helps in leading the lesson more naturally and organically than just a teacher lecture prepared in advance.mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-61010214506047615962014-02-25T09:56:00.001-06:002014-02-25T13:16:30.717-06:00#codemaths: algebra functions and image URLsI've added some function (for my own benefit really) that saves time in anticipating many scenarios in generating random questions--<b>reduce()</b> and <b>coeff()</b> functions using the <a href="https://script.google.com/macros/s/AKfycbxa9d1543kySk9wnS_cTZ3KfZV5Prl9QPkD9VW6Ugu3LMuR1Yo/exec">#codemaths</a> application.<br />
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When used, the reduce function can simplify fractions. For example, for random variables a and b, reduce(a,b) would simplify a=4 and b=1 to 4 and a=2 and b=4 to 1/2. <i>It is still your job to make sure b is not zero with the constraints.</i><br />
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The coefficient function allows expressions to be simplified--most helpful for anticipating the best final answer. There are some specific options to differentiate how it is used.<br />
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If I have the expression ax+by=c using random values for a,b and c (again making sure 'a' and 'b' aren't zero in the constraints), if I use the coeff function I can programmatically simplify the scenario 1x+-4y=5 to x-4y=5. </blockquote>
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To code it you need to use "lead" for a coefficient like a that is the lead coefficient in the expression and "constant" if a term you want to simplify is just a constant term with no variable. </blockquote>
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In the example above you would code <i><coeff(a,"lead")>x<coeff(b)>y=<c></i>. In this case you don't need the "constant" or coeff fuction for c. <i>The equation 1x+-1y=3 would simplify to x-y=3.</i></blockquote>
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That could be used in this example however: ax+b=c: <i><coeff(a,"lead")>x<coeff(b,"constant")>=<c></i>. <i>The equation 1x+-1=3 would simplify to x-1=3.</i></blockquote>
You can also now use a url of an image to be included in a question such as this one:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhT1JFU0vzc8K518DrgFUNJX78QE6jnnf_g-FcBOCeG044hVYwplaDbb7gOlgO-X2RjIPY8VZcwtL-dG7wRbSn2gAdfZri2w1qQWbprJhfEJLp9zYxaf2ikzqvRZUIfOkv6A07fALYauGSd/s1600/Screen+Shot+2014-02-25+at+9.44.32+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhT1JFU0vzc8K518DrgFUNJX78QE6jnnf_g-FcBOCeG044hVYwplaDbb7gOlgO-X2RjIPY8VZcwtL-dG7wRbSn2gAdfZri2w1qQWbprJhfEJLp9zYxaf2ikzqvRZUIfOkv6A07fALYauGSd/s1600/Screen+Shot+2014-02-25+at+9.44.32+AM.png" height="205" width="320" /></a></div>
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<a href="https://script.google.com/macros/s/AKfycbxIfla7beanUkl_11RONMJ5M5yEFZUVGSHSpFbTgfYBZjxXDAs/exec">Here is an example of a question set using pythagorean triples and this diagram.</a></div>
<br />mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-69715442800500052982014-02-12T13:28:00.004-06:002014-02-12T13:28:37.983-06:00Displaying student work (quickly and for free)For the past year I've wanted to get <a href="http://www.airserver.com/">Air Server</a> going in my classroom but due to circumstances out of my pay grade I am not allowed to make it work (well) in my classroom. A week or so ago it occurred to me that there was a simple workaround I could be using that may actually work better.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXmSU2vMKzcqTMdff5rq6xLYmnCh5BoZwJad3Wc3yjMZdgEjfaPJhmAURAgZ8UHy7alQe257nN2ILoful4qW5IApo1e1Eq2y3OMrZDyVnjmUjQH7FGVf5_b8jAnkyyfYD5d_iNtEJY0WXj/s1600/Screen+Shot+2014-02-12+at+1.22.48+PM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXmSU2vMKzcqTMdff5rq6xLYmnCh5BoZwJad3Wc3yjMZdgEjfaPJhmAURAgZ8UHy7alQe257nN2ILoful4qW5IApo1e1Eq2y3OMrZDyVnjmUjQH7FGVf5_b8jAnkyyfYD5d_iNtEJY0WXj/s1600/Screen+Shot+2014-02-12+at+1.22.48+PM.png" height="200" width="141" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Add a new file menu</td></tr>
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I have <a href="https://itunes.apple.com/us/app/google-drive/id507874739?mt=8">Google Drive's app</a> on my phone and iPad and there is an option to take a photo and add it directly to a folder. I have a folder in my Google Drive titled "Student Work". When I see student work that I want to discuss with the class I navigate to that folder in my app, select "Use Camera" in the new document menu and I'm on to the next student.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfPkh6Pc5hRWn12CtdfnD8PIeSiC6vD1-9P3px1etdl5k6KSKI5x5KqhvgAHRVohWvTL36k_wctPm7LfoE9KZ0U68s2keI6vEzCP9Vre0uKBGhGLGwbNCDtsCyQCtL9m6RI_cHOIIxdR0M/s1600/Screen+Shot+2014-02-12+at+1.21.52+PM.png" imageanchor="1" style="margin-left: auto; margin-right: auto; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfPkh6Pc5hRWn12CtdfnD8PIeSiC6vD1-9P3px1etdl5k6KSKI5x5KqhvgAHRVohWvTL36k_wctPm7LfoE9KZ0U68s2keI6vEzCP9Vre0uKBGhGLGwbNCDtsCyQCtL9m6RI_cHOIIxdR0M/s1600/Screen+Shot+2014-02-12+at+1.21.52+PM.png" height="210" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">View from within the app</td></tr>
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When we are ready to regroup I have that folder displayed on my projector and can easily annotate on them when needed through my computer software.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggpz0Px13HeltxtZtb5VzHr_F0tM7OoqPkXp-a0HxBmeh8UiarCUWZkWCfLBLyxslQK4fW9j8KC7NhER62daDo_D0cf2nH0Joi7odzYUoqRXOgbqOZnI3MnJgscVRlePgUZfZHgTZnoZDF/s1600/Screen+Shot+2014-02-12+at+1.27.33+PM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggpz0Px13HeltxtZtb5VzHr_F0tM7OoqPkXp-a0HxBmeh8UiarCUWZkWCfLBLyxslQK4fW9j8KC7NhER62daDo_D0cf2nH0Joi7odzYUoqRXOgbqOZnI3MnJgscVRlePgUZfZHgTZnoZDF/s1600/Screen+Shot+2014-02-12+at+1.27.33+PM.png" height="207" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">View from my computer</td></tr>
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mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com0tag:blogger.com,1999:blog-7489492900803794139.post-91040279745819449622014-02-11T09:40:00.000-06:002014-02-11T09:43:27.060-06:00Desmos' Function Carnival!<blockquote class="twitter-tweet" lang="en">
Thanks Dan Meyer and Desmos! Start playing <a href="https://twitter.com/search?q=%23hwdsb&src=hash">#hwdsb</a> math teachers and students!<br />
<a href="https://t.co/sfXqNX42wt">https://t.co/sfXqNX42wt</a> <a href="https://twitter.com/search?q=%23storygraphs&src=hash">#storygraphs</a><br />
— Christine Chan (@chanland) <a href="https://twitter.com/chanland/statuses/431786942942822402">February 7, 2014</a></blockquote>
I came across <a href="https://class.desmos.com/carnival">Function Carnival </a>on twitter a couple nights ago and instantly knew it was going to be great in class. This is what technology in a math class should look like. We aren't throwing <i>more practice</i> at kids but are instead slowing it down, providing them a tool that creates the conversations more naturally and motivates them to explore the '<i>what ifs'</i> when factors are changed. Embedded is also a reflection tool that shows students an example of another (fictional) student and asks them what the student is thinking or saying with the graph they have created.<br />
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/2WHbxOa-Fxs?feature=player_embedded' frameborder='0'></iframe></div>
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On the teacher side I get a dashboard of every student computer, what graphs they have created and even their short response answers to those reflection questions. I had so many kids today talking about what they saw and <i>wanting</i> to show me their work and how well they did. This is what math education should look like as we begin to acquire more classroom technology. It is not (as I've heard in staff development) having a bin of worksheets available for students that finish the basic stuff early. It is conversations, exploration and connections to potential real life situations.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjABd7uOq-WA0IT_FPAYB6TdDxKNvvxaZI8tCc36abi5Z9p5baLcwKVUMr_g4k3Z8whQQrtz6O_FSyNBJCACM8npUsPeTIF52qG5I6Nx4zod01c91sGskX39PxdVddvdpZYC2IXAlMuBuIU/s1600/Screen+Shot+2014-02-11+at+9.17.38+AM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjABd7uOq-WA0IT_FPAYB6TdDxKNvvxaZI8tCc36abi5Z9p5baLcwKVUMr_g4k3Z8whQQrtz6O_FSyNBJCACM8npUsPeTIF52qG5I6Nx4zod01c91sGskX39PxdVddvdpZYC2IXAlMuBuIU/s1600/Screen+Shot+2014-02-11+at+9.17.38+AM.png" height="55" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Student graphs after completion</td></tr>
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I don't know much of the background as to how this came about but if it was truly a collaboration between <a href="http://desmos.com/">Desmos.com</a> and <a href="http://blog.mrmeyer.com/?p=18462">Dan Meyer</a> I'm very excited for the work to come from that relationship! Thanks so much and looking forward to the future work to come!mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com2tag:blogger.com,1999:blog-7489492900803794139.post-27114543495098317672014-01-30T09:49:00.000-06:002014-01-30T09:49:27.078-06:00Example of choice and a tiered activity to start classA continued focus of my classroom this year has been to promote open ended questions that allow for student choice and creativity (yes in math class this is possible!). A learning target we have been working on recently has been <u>determine if the coordinates of a given figure are vertices of a parallelogram or rectangle</u>. Today in class I gave students three options and told them to choose the one that is the most challenging to them. (Some students did more than one)<br />
<u>Here were the three questions</u>:<br />
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<ol>
<li style="line-height: 1.15;"><span style="font-family: Arial; line-height: 1.15; white-space: pre-wrap;">Write 4 coordinates that will make a parallelogram that is NOT a rectangle</span></li>
<li><span style="font-family: Arial; line-height: 1.15; white-space: pre-wrap;">Write 4 coordinates that make a rectangle that has NO horizontal lines.</span></li>
<li><span style="font-family: Arial; white-space: pre-wrap;">Including the point (0,0), use variables a, b and c to symbolically write coordinates that will always make a parallelogram for any given values. For example maybe your coordinates would look like (0,0) (a,2b) (a,c), etc.</span></li>
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I used <a href="https://script.google.com/macros/s/AKfycbzRVmtB48nHV7AexFmSkDBlrsIlMqF4s1kvKvPX0J3QQipgjyw/exec">this web app</a> to check the points and get them displayed quickly as students shared them. As we moved through student work on each one it naturally sequenced our discussion to the higher level task #3 that some students chose to do. One kid even did the 'mind blown' motion with his hands when we substituted concrete values in for a and b in the student example below to show that it works. It was a pretty simple activity but at the same time a good motivator for some higher level discussions in math class that didn't take a whole lot of time to prepare.<br />
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Here is the follow up discussion we had on #3, including the example a student came up with:<br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-style: italic; vertical-align: baseline; white-space: pre-wrap;"><u>Student example</u>: </span><span style="font-style: italic; vertical-align: baseline; white-space: pre-wrap;">(0,0) (2a,b) (2a,0) (0,b)</span><span style="vertical-align: baseline; white-space: pre-wrap;">How did you come up with these?</span><span style="vertical-align: baseline; white-space: pre-wrap;">Choose values for the variables a,b, and c to show it works.</span><span style="vertical-align: baseline; white-space: pre-wrap;">What if we made a bigger or smaller? </span><span style="vertical-align: baseline; white-space: pre-wrap;">What would it do to the parallelogram?</span><span style="white-space: pre-wrap;">Would it still work if a or b were negative? How would it change it?</span></span></blockquote>
<a href="https://docs.google.com/document/d/19pQPFsDEoO-ICeuPxNg2VjwtBHUm2DNto72AOVfbJWM/edit?usp=sharing">Here is a link to the document of the activity.</a><br />
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mrschwenhttp://www.blogger.com/profile/16852738457317452044noreply@blogger.com1