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	<title>Sine of the Times</title>
	<atom:link href="http://blog.keycurriculum.com/feed/" rel="self" type="application/rss+xml" />
	<link>http://blog.keycurriculum.com</link>
	<description>A Blog for Navigating the Common Core State Standards</description>
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		<title>Exploring Conic Sections with Sketchpad</title>
		<link>http://blog.keycurriculum.com/2012/05/exploring-conic-sections-with-sketchpad/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=exploring-conic-sections-with-sketchpad</link>
		<comments>http://blog.keycurriculum.com/2012/05/exploring-conic-sections-with-sketchpad/#comments</comments>
		<pubDate>Sat, 12 May 2012 16:43:39 +0000</pubDate>
		<dc:creator>Daniel Scher</dc:creator>
				<category><![CDATA[Math Software]]></category>
		<category><![CDATA[Constructions]]></category>
		<category><![CDATA[Dynamic Geometry]]></category>
		<category><![CDATA[Modeling]]></category>
		<category><![CDATA[Sketchpad]]></category>

		<guid isPermaLink="false">http://blog.keycurriculum.com/?p=4948</guid>
		<description><![CDATA[As a student, I didn’t place conic sections on my list of favorite high school topics. The standard textbook treatment of the ellipse, parabola, and hyperbola seemed uninspired. There were messy algebraic equations with multiple square roots. There was lots of &#8230; <a href="http://blog.keycurriculum.com/2012/05/exploring-conic-sections-with-sketchpad/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<!-- Start Shareaholic LikeButtonSetTop Automatic --><!-- End Shareaholic LikeButtonSetTop Automatic --><p>As a student, I didn’t place conic sections on my list of favorite high school topics. The standard textbook treatment of the ellipse, parabola, and hyperbola seemed uninspired. There were messy algebraic equations with multiple square roots. There was lots of terminology. Drawing a conic meant plotting several points on graph paper and connecting them with a wobbly curve.</p>
<p><a href="http://blog.keycurriculum.com/wp-content/uploads/2012/05/Bent-Straw-Construction.jpg" rel="lightbox[4948]"><img class="alignright  wp-image-4995" style="border: 1px solid black" src="http://blog.keycurriculum.com/wp-content/uploads/2012/05/Bent-Straw-Construction.jpg" alt="Bent Straw Ellipse Construction using Sketchpad" width="329" height="239" /></a>I gave little thought to conics until I met <a title="David Dennis" href="http://www.quadrivium.info/math/" target="_blank">David Dennis</a>, then a fellow graduate student in mathematics education at Cornell University.</p>
<p>David had a keen interest in the origins of curve-drawing devices. One historical figure in particular intrigued him: Frans van Schooten (1615–1660), a Dutch mathematician whose translation and commentary for Descartes’ landmark treatise, <em>La Géométrie,</em> led to the popularization of Cartesian geometry.</p>
<p><span id="more-4948"></span></p>
<p>Descartes’ book was available in bookstores, but van Schooten’s work, <em>Sive de Organica Conicarum Sectionum in Plano Descriptione, Tractatus</em> (<em>A Treatise on Devices for Drawing Conic Sections</em>), remained tucked away in rare book collections. Luckily, Cornell’s Kroch Library contained a copy. David made the trip.</p>
<p>When he returned from the library, David could barely contain his enthusiasm. “Go and see it for yourself,” he said. “It’s really something.”</p>
<p>A visit to the library confirmed David’s findings. There in van Schooten’s book were drawing after drawing of devices that drew conics. The illustrations were exquisite, with artistic flourishes adorning many of them.</p>
<div id="attachment_4977" class="wp-caption aligncenter" style="width: 631px"><a href="http://blog.keycurriculum.com/wp-content/uploads/2012/05/SketchpadScreenSnapz0011.jpg" rel="lightbox[4948]"><img class="size-full wp-image-4977" src="http://blog.keycurriculum.com/wp-content/uploads/2012/05/SketchpadScreenSnapz0011.jpg" alt="" width="621" height="293" /></a><p class="wp-caption-text">Two ellipse-drawing devices from Frans van Schooten</p></div>
<p>That was 1991. Today you can view van Schooten’s manuscript <a title="Van Schooten" href="http://echo.mpiwg-berlin.mpg.de/ECHOdocuViewfull?pn=5&amp;ws=1&amp;ww=1&amp;wh=1&amp;start=1&amp;viewMode=images&amp;mode=imagepath&amp;url=/mpiwg/online/permanent/library/EWN480XH/pageimg">online</a>.</p>
<p>As I paged through van Schooten’s book, I wondered whether his ideas could find their way into mathematics classrooms. His models, consisting of hinges and slotted rulers, were not easy to build. How could students replicate them?</p>
<p><a title="The Geometer's Sketchpad" href="http://www.keycurriculum.com/products/sketchpad" target="_blank">Sketchpad</a> provided a large part of the answer. While nothing can substitute for the experience of operating a physical model, a Sketchpad simulation comes close. In fact, Sketchpad betters van Schooten in some ways, allowing students to manipulate the parameters of any model and view their effects on a curve immediately.</p>
<p>It’s been 20 years since I first developed van Schooten’s ideas into a Sketchpad module, <em><a title="Exploring Conic Sections with The Geometer's Sketchpad" href="http://www.keycurriculum.com/resources/sketchpad-resources/activity-modules/high-school-activity-modules-for-the-geometers-sketchpad#conic-sections">Exploring Conic Sections with The Geometer’s Sketchpad</a>,</em> for Key Curriculum. I’ve just updated the book for its third edition. The sketches that accompany the book have received a total makeover for Sketchpad 5.</p>
<p>You can get a preview of the ellipse models by watching the video below. For an in-depth overview, watch my <a title="Conic Sections Webinar" href="http://www.keycurriculum.com/exploring-conic-sections-with-sketchpad">Sketchpad webinar</a> that I conducted earlier this year.</p>
<span style="text-align:center; display: block;"><a href="http://blog.keycurriculum.com/2012/05/exploring-conic-sections-with-sketchpad/"><img src="http://img.youtube.com/vi/L9csTtUmKek/2.jpg" alt="" /></a></span>
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		<title>Moral of the Story: Pineapples Don&#8217;t Have Sleeves</title>
		<link>http://blog.keycurriculum.com/2012/05/moral-of-the-story-pineapples-dont-have-sleeves/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=moral-of-the-story-pineapples-dont-have-sleeves</link>
		<comments>http://blog.keycurriculum.com/2012/05/moral-of-the-story-pineapples-dont-have-sleeves/#comments</comments>
		<pubDate>Tue, 08 May 2012 23:24:59 +0000</pubDate>
		<dc:creator>Josephine Noah</dc:creator>
				<category><![CDATA[Assessment]]></category>
		<category><![CDATA[Standardized Testing]]></category>

		<guid isPermaLink="false">http://blog.keycurriculum.com/?p=4930</guid>
		<description><![CDATA[I intended to start this blog post inspired by this article about &#8220;security breaches&#8221; of the California Standards Test (CST) standardized test. My thoughts about this article were in two directions: how do you ensure integrity of high-stakes tests in &#8230; <a href="http://blog.keycurriculum.com/2012/05/moral-of-the-story-pineapples-dont-have-sleeves/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<!-- Start Shareaholic LikeButtonSetTop Automatic --><!-- End Shareaholic LikeButtonSetTop Automatic --><p><a href="http://blog.keycurriculum.com/wp-content/uploads/2012/05/Pineapples.jpg" rel="lightbox[4930]"><img class="alignright size-medium wp-image-4934" title="Pineapples Don't Have Sleeves" src="http://blog.keycurriculum.com/wp-content/uploads/2012/05/Pineapples-300x213.jpg" alt="" width="300" height="213" /></a>I intended to start this blog post inspired by <a title="Click and post: CST security breach" href="http://toped.svefoundation.org/2012/04/28/click-and-post-cst-security-breach/" target="_blank">this article</a> about &#8220;security breaches&#8221; of the California Standards Test (CST) standardized test. My thoughts about this article were in two directions: how do you ensure integrity of high-stakes tests in our current era of pervasive cell-phone/camera/internet access; and are kids even taking these tests seriously, and what does that say about their value and meaningfulness?</p>
<p>I started to ponder these topics, then got totally derailed when I came across a reference to &#8220;Pineapples Don&#8217;t Have Sleeves&#8221; in the article&#8217;s comments. I was then sucked into a YouTube vortex of videos on the topic of pineapples not having sleeves. In case you don&#8217;t have an hour or more to spend on the topic, I&#8217;ll provide some highlights.  (And if you&#8217;re in New York, this may all be old news; apologies.)</p>
<p><span id="more-4930"></span>First, I came across <a title="hatboy9991's Pineapple and Hare You Tube video" href="http://www.youtube.com/watch?v=coavD_aPZRo&amp;feature=related" target="_blank">this video</a>. It&#8217;s fairly longwinded, but introduced me to the frustration of an 8th grader taking the 2012 New York State ELA standardized test. The stories are horrible and stupid and getting worse every year, he says. This year&#8217;s pineapple and hare fable is particularly lame. A pineapple challenges a hare to a race, and the other forest animals think the pineapple must have a trick up its sleeve, but indeed it loses because it can&#8217;t move, and so the animals eat it. The owl states the moral: Pineapples don&#8217;t have sleeves.</p>
<p>Okay, I have to agree, that&#8217;s pretty ridiculous.</p>
<p>But what I found wonderful, actually, is that this preposterous story inspired lots of discussion on YouTube, Facebook, Twitter, and who knows where else. Much of it is pure venting about the offensiveness of standardized testing, but weaved in is also some discussion about the questions asked—did the animals eat the pineapple because they were annoyed, or hungry? Can we determine which was the wisest animal in the forest? What does it mean to &#8220;make sense&#8221; of a story that&#8217;s nonsense? If students are discussing what they&#8217;ve read, even it&#8217;s because they&#8217;re offended by the silliness of it, that&#8217;s not all bad. Apparently <a title="New York Times article about the Pineapple and Hare" href="http://www.nytimes.com/2012/04/21/nyregion/standardized-testing-is-blamed-for-question-about-a-sleeveless-pineapple.html?pagewanted=all" target="_blank">New York has decided</a> to not count the questions in their scoring because at least two may not have unambiguous answers. And, there has been similar outrage in other states in past years about this same story and its accompanying questions; nonetheless, the test makers have continued using it. By the way, the author of the story, who sold the rights for it to be used on the test, considers himself explicitly to be a writer of nonsense, and notes that it was rewritten for the test to be even more random.</p>
<p>I&#8217;m glad that students are discussing sense-making, and I love, too, that students have been inspired to make some great videos expressing their feelings about this test. Here&#8217;s a mosaic of students <a title="kbutrie's Pineapple and Hare YouTube video" href="http://www.youtube.com/watch?v=wQW6-8pA8rA&amp;feature=related" target="_blank">expressing their thoughts</a> on the ridiculousness of the story. And <a title="jenniieeisneon's Pineapple and Hare YouTube video" href="http://www.youtube.com/watch?v=b1nLI7-iCSE&amp;feature=related" target="_blank">this video</a> is particularly illuminating. This student reads us the story and the questions, which she found on the internet. Her personality shines through loud and clear, and she does a nice video. It&#8217;s neat that students have the tools and skills to be doing this. But the fact that photos of the whole story and question are on the internet demonstrates one of the original points. If this information is on the internet after the fact, there&#8217;s no reason they can&#8217;t be there and accessed by other test takers during the test.</p>
<p>But in case you&#8217;re concerned that the kids are all up in arms and none of them are taking standardized tests seriously, <a title="Friendship Tech Prep's &quot;Proficient and I Know It&quot; YouTube video" href="http://www.youtube.com/watch?v=Y66drwnTiwU&amp;feature=related" target="_blank">here&#8217;s a counterpoint</a>. These kids appear seriously motivated to be &#8220;proficient&#8221; or &#8220;advanced&#8221; on the DC Comprehensive Assessment System test. For me, this vid&#8217;s the winner of the bunch. Gotta love the creativity and effort!</p>
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		<title>Some Suggestions for Math Technology Professional Development</title>
		<link>http://blog.keycurriculum.com/2012/05/some-suggestions-for-math-technology-professional-development/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=some-suggestions-for-math-technology-professional-development</link>
		<comments>http://blog.keycurriculum.com/2012/05/some-suggestions-for-math-technology-professional-development/#comments</comments>
		<pubDate>Fri, 04 May 2012 12:27:23 +0000</pubDate>
		<dc:creator>Karen Greenhaus</dc:creator>
				<category><![CDATA[Professional Development]]></category>
		<category><![CDATA[Fathom]]></category>
		<category><![CDATA[Modeling]]></category>
		<category><![CDATA[Pedagogy]]></category>
		<category><![CDATA[Sketchpad]]></category>
		<category><![CDATA[Standards for Mathematical Practice]]></category>
		<category><![CDATA[Teacher Collaboration]]></category>
		<category><![CDATA[TinkerPlots]]></category>
		<category><![CDATA[Use Appropriate Tools Strategically]]></category>
		<category><![CDATA[Videos]]></category>

		<guid isPermaLink="false">http://blog.keycurriculum.com/?p=4901</guid>
		<description><![CDATA[I have been really focused on math technology professional development lately, which makes sense of course, since that&#8217;s what I do for a living. But after last week&#8217;s NCSM and NCTM conferences (see Karen Coe&#8217;s recent post), where professional development &#8230; <a href="http://blog.keycurriculum.com/2012/05/some-suggestions-for-math-technology-professional-development/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<!-- Start Shareaholic LikeButtonSetTop Automatic --><!-- End Shareaholic LikeButtonSetTop Automatic --><p><img class=" wp-image-4903 alignright" title="Demonstrating TinkerPlots at NCTM 2012" src="http://blog.keycurriculum.com/wp-content/uploads/2012/05/KeyCurriculum_NCTM2012-0388.jpg" alt="Demonstrating TinkerPlots at NCTM 2012" width="362" height="234" />I have been really focused on math technology professional development lately, which makes sense of course, since that&#8217;s what I do for a living. But after last week&#8217;s NCSM and NCTM conferences (see <a href="http://blog.keycurriculum.com/2012/04/behind-the-scenes-at-ncsm-and-nctm/">Karen Coe&#8217;s recent post</a>), where professional development came up often (see <a href="http://greenhauseducation.blogspot.com/" target="_blank">my personal blog</a>), and after responding to numerous email inquiries this week, I decided to share some Key Curriculum Professional Development options and offer my suggestions on how to get the most bang for your buck (luckily, many of these options are free).<strong></strong></p>
<p><span id="more-4901"></span></p>
<p><strong><a href="http://www.keycurriculum.com/training/webinars" target="_blank">Free weekly webinars.</a></strong> Each week we offer a free technology webinar, focused on a specific mathematics content, ranging from elementary concepts through calculus, using one or more of our dynamic mathematics programs:<em> <a href="http://www.keycurriculum.com/products/sketchpad" target="_blank">Sketchpad</a>, <a href="http://www.keycurriculum.com/products/tinkerplots" target="_blank">TinkerPlots,</a></em> or <em><a href="http://www.keycurriculum.com/products/fathom" target="_blank">Fathom</a></em>. The presenters are all current or former mathematics teachers, and they focus not only on using the software, but also on teaching strategies and elucidating the mathematics. All webinars are recorded for on-demand viewing and are posted with downloadable files that you can be use in your classroom. Suggestions for use as professional development:</p>
<ul>
<li>Individual teachers/administrators can attend or watch the recording to improve their knowledge (of technology, mathematics, and/or pedagogical approaches) and gain new ideas to try in the classroom.</li>
<li>Teams of teachers can attend together or watch the recording together (during department time or collaborative planning time), discuss strategies and try the lessons in their own classrooms, then meet again and share experiences.</li>
<li>Teacher leaders, coaches, etc. can use the recordings and documents/lessons to conduct school or site-based training or model in the classroom.  The training might be focused on specific content or teaching strategies and can support technology integration in math classrooms.</li>
</ul>
<p><strong><a href="http://www.keycurriculum.com/training/online-courses" target="_blank">Six-week moderated online courses</a>.</strong> Long-term professional development, where you have time to practice and try things out and get feedback and support, is really the best way to learn and integrate something new. Change takes time. Our online courses allow time to learn new skills slowly, get support and help from both the course resources (videos, tutorials) and from a moderator who is a current or former mathematics teacher and an expert in the software. During the course, you share questions and ideas with an online community of colleagues. These courses teach how to use the software in the context of mathematics—including how dynamic software may change the way you understand mathematical concepts—and provide you with resources to use in your classroom. We have courses for Statistics (<em>Fathom</em>), Elementary Mathematics (<em>Sketchpad</em>), Middle School Mathematics (<em>Sketchpad</em> and <em>TinkerPlots</em>), Algebra (<em>Sketchpad</em>) and Geometry (<em>Sketchpad</em>) and a brand new course coming in June for advanced <em>Sketchpad</em> users, <a href="http://www.keycurriculum.com/training/online-courses/constructing-dynamic-demonstrations-with-sketchpad-online-course" target="_blank">Constructing Dynamic Demonstrations</a>. Suggestions for use as professional development:</p>
<ul>
<li>An individual teacher can take these courses for personal growth and ideas on how to integrate technology in specific math courses. You&#8217;ll gain skill in the software and also review or learn math content, and more importantly, explore ways to help students learn that content.</li>
<li>Schools/districts can support individual teachers/coaches/teams of teacher, using these courses as a train-the-trainer model. After completing the course, the selected teachers can use the course content to train others in their schools or districts, creating internal capacity. When teams of teachers take the course together, it creates a collaborative group of teachers learning together, trying things together, and supporting each other, making change and effective technology integration a sustainable endeavor.</li>
</ul>
<p><a href="http://www.keycurriculum.com/resources" target="_blank"><img class="alignleft  wp-image-4923" title="Sketchpad activity modules at NCTM 2012" src="http://blog.keycurriculum.com/wp-content/uploads/2012/05/KeyCurriculum_NCTM2012-0512.jpg" alt="Sketchpad activity modules at NCTM 2012" width="358" height="238" /><strong>Free tutorials, movies, and lessons</strong></a><strong>.</strong> We have <em><a href="http://www.keycurriculum.com/resources/sketchpad-resources" target="_blank">Sketchpad</a></em>, <em><a href="http://www.keycurriculum.com/resources/tinkerplots-resources" target="_blank">Tinkerplots</a>,</em> and<em><a href="http://www.keycurriculum.com/resources/fathom-resources" target="_blank"> Fathom</a></em> resources designed to help you learn the software in your own time and at your own pace. There are movies that demonstrate how to do specific skills, which can be rewound and played over and over as you play along with the software. The tutorials have step-by-step instructions, with some tips in video form. We also provide ready-to-use lessons, with teacher notes, lesson plans, sketches/files—a complete lesson focused on math but also allowing you to learn the software. Many of these resources are built into each software program or available on our web at no cost. <em>Fathom</em> and <em>TinkerPlots</em> come with hundreds of pre-made, cross-curricular data sets<em>. Sketchpad</em> has an entire <a href="http://learningcenter.dynamicgeometry.com" target="_blank" class="broken_link" rel="nofollow">Learning Center</a> built into its Help menu, with not only the tutorials and sample activities, but also movies of teachers and students sharing their experiences with <em>Sketchpad</em>. Suggestions for professional development:</p>
<ul>
<li>An individual teacher can use these resources to learn and try things in their classroom at their own pace. This allows them to take control of their learning and how they implement technology, slowly, focused.</li>
<li>Teams of teachers (content teams, math departments, etc.) can utilize these resources to learn the software together. Look at specific movies/tutorials at department meetings, or during planning. Do a lesson study with one of the sample activities—focus on the standards and where the activity fits in your curriculum, try it in the classroom, and come back and share results and student work.</li>
<li>Math coaches and math instructional leaders can use these as coaching activities, modeling activities and support for technology integration.</li>
<li>Movies, tutorials, and sample activities can be grouped together and used in focused professional development events sponsored by schools/districts. It&#8217;s possible to use these resources together to introduce the skills of the tool, give teachers time to practice and work through a number of activities, and then choose activities to implement.</li>
</ul>
<p>My suggestions are just a few possibilities of what can be done to create effective math technology professional development. Professional development means developing new skills and strategies and continuing to learn and grow in your profession. Start exploring all the possibilities.</p>
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		<title>Exploring Factor Patterns in an Interactive Array</title>
		<link>http://blog.keycurriculum.com/2012/05/exploring-factor-patterns-in-an-interactive-array/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=exploring-factor-patterns-in-an-interactive-array</link>
		<comments>http://blog.keycurriculum.com/2012/05/exploring-factor-patterns-in-an-interactive-array/#comments</comments>
		<pubDate>Wed, 02 May 2012 16:25:18 +0000</pubDate>
		<dc:creator>Daniel Scher</dc:creator>
				<category><![CDATA[Math Software]]></category>
		<category><![CDATA[Dynamic Number]]></category>
		<category><![CDATA[Problem Solving]]></category>
		<category><![CDATA[Sketchpad]]></category>

		<guid isPermaLink="false">http://blog.keycurriculum.com/?p=4794</guid>
		<description><![CDATA[OK, I admit it: I have factors on the brain. First, I wrote about When Factoring Gets Personal. I followed that with a post describing what happens When Factors Put on Their Dancing Shoes. So what&#8217;s next—When Factors Apply for a Home Equity &#8230; <a href="http://blog.keycurriculum.com/2012/05/exploring-factor-patterns-in-an-interactive-array/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<!-- Start Shareaholic LikeButtonSetTop Automatic --><!-- End Shareaholic LikeButtonSetTop Automatic --><p>OK, I admit it: I have factors on the brain.</p>
<p>First, I wrote about <a title="When Factoring Gets Personal" href="http://blog.keycurriculum.com/2012/02/when-factoring-gets-personal/">When Factoring Gets Personal</a>. I followed that with a post describing what happens <a title="When Factors Put on Their Dancing Shoes" href="http://blog.keycurriculum.com/2012/03/when-factors-put-on-their-dancing-shoes/">When Factors Put on Their Dancing Shoes</a>. So what&#8217;s next—When Factors Apply for a Home Equity Loan? Thankfully no, but I do have an update to share.</p>
<p>Last week I had an idea for a new <a title="Dynamic Number" href="http://www.kcptech.com/dynamicnumber" target="_blank">Dynamic Number</a> Sketchpad model that&#8217;s easy to describe. A rectangular array of numbers from 1 to <em>n</em> appears on screen. Those numbers that are factors of <em>n</em> are shaded blue. The remaining numbers are shaded orange. By dragging a point in the upper-right corner of the array, you can change its dimensions.</p>
<p>With this concept in mind, I created the sketch. Here are two pictures of the array showing the factors of 24 and the factors of 27. Feel free to <a title="Factor Patterns Model" href="http://www.kcptech.com/dynamicnumber/downloads/Factor_Patterns.zip">download</a> the sketch.</p>
<div id="attachment_4839" class="wp-caption aligncenter" style="width: 585px"><a href="http://blog.keycurriculum.com/wp-content/uploads/2012/05/Arrays1.jpg" rel="lightbox[4794]"><img class=" wp-image-4839 " src="http://blog.keycurriculum.com/wp-content/uploads/2012/05/Arrays1.jpg" alt="" width="575" height="168" /></a><p class="wp-caption-text">Factor Arrays showing the factors of 24 and 27</p></div>
<p>What are the mathematical and pedagogical benefits of using this model?</p>
<p><span id="more-4794"></span></p>
<p>If the goal of learning about factors is to recite the factors of any given number, then this model is horrible—it does the work for you! But I think the payoff from factors lies in analyzing the patterns that emerge when viewing the factors of <em>lots</em> of numbers. And that&#8217;s the benefit of this Sketchpad model. It makes the factoring itself easy and allows students to focus on what is interesting in the visual patterns of the blue and orange-shaded numbers.</p>
<p>Here is a partial list of questions and observations that I imagine a group of students might make while exploring the Sketchpad model:</p>
<ul>
<li>The number 1 is always shaded blue.</li>
<li>The number in the bottom-right corner of the array is always shaded blue.</li>
<li> Our array has 11 rows, and I see that the number 11 is shaded blue. In general, if we have <em>n</em> rows in our grid, then the number <em>n</em> will be shaded blue.</li>
<li>What arrays have just two of their numbers shaded blue?</li>
<li>There are only two ways to display the factors of prime numbers in the array—either as a single row of circles or a single column of circles.</li>
<li>If the array has at least 2 columns and 2 rows, then the number it represents isn&#8217;t prime.</li>
<li>If the number of rows and columns in the array are equal and prime, the array will contain exactly three numbers shaded blue.</li>
<li>We found a way to create arrays with exactly four numbers shaded blue. Drag the red point to form a single row of numbers. Make sure the largest number in the row is prime. Then drag the red point straight up to create a prime number of columns. That does the trick.</li>
<li>When our array contains an even number of rows, the rows in the upper half of the array are filled entirely with orange circles. Only the number we’re factoring is shaded blue. Why is that?</li>
<li>We can pair every number that is shaded blue with a partner. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18. Let’s pair 1 and 18, 2 and 9, and 3 and 6 together. In each pair, the product of the numbers is 18.</li>
<li>What happens when we pair the factors of 25? Its factors are 1, 5, and 25. We can pair 1 and 25 together, but can we pair 5 with itself?</li>
<li>In most of our arrays, there are an even number of circles shaded blue. But in some cases, the number of blue circles is odd. Is there a way to predict whether there will be an even or odd number of blue circles?</li>
<li>We dragged the red point so that the numbers from 1-20 all appeared in a single row.  We wanted to find other ways to display those 20 circles in the array. The numbers in blue—1, 2, 4, 5, 10, and 20—gave us a big hint. Since 2 is a factor of 20, we can make a 2 x 10 array. Similarly, we make a 4 x 5, a 5 x 4, and a 10 x 2 array.</li>
<li> If the number of columns is even, the number 2 is always shaded blue. If the number of columns is odd, the number 2 alternates between orange and blue as I drag the red point up to add more rows.</li>
<li>We created a game. We scrolled our sketch window so that you can only see the bottom row of circles. Your challenge is to make an educated guess about the total number of circles in the array.</li>
</ul>
<p>What other questions and discoveries about factors can be made with the Sketchpad factor array? Share your ideas!</p>
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		<title>Behind the Scenes at NCSM and NCTM</title>
		<link>http://blog.keycurriculum.com/2012/04/behind-the-scenes-at-ncsm-and-nctm/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=behind-the-scenes-at-ncsm-and-nctm</link>
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		<pubDate>Mon, 30 Apr 2012 18:20:13 +0000</pubDate>
		<dc:creator>Karen Coe</dc:creator>
				<category><![CDATA[Conferences]]></category>
		<category><![CDATA[Fathom]]></category>
		<category><![CDATA[Ignite]]></category>
		<category><![CDATA[IMP]]></category>
		<category><![CDATA[Interactive Whiteboards]]></category>
		<category><![CDATA[NCTM]]></category>
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		<category><![CDATA[TinkerPlots]]></category>

		<guid isPermaLink="false">http://blog.keycurriculum.com/?p=4739</guid>
		<description><![CDATA[I thought I’d give you a behind-the-scenes view of last week&#8217;s activities in Philadelphia. Karen Greenhaus, Andres Marti, Elizabeth DeCarli, and I were assigned to the first event, NCSM. We were up bright and early on Monday morning to set &#8230; <a href="http://blog.keycurriculum.com/2012/04/behind-the-scenes-at-ncsm-and-nctm/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<!-- Start Shareaholic LikeButtonSetTop Automatic --><!-- End Shareaholic LikeButtonSetTop Automatic --><p><a href="http://blog.keycurriculum.com/wp-content/uploads/2012/04/NCTM-Booth1.jpg" rel="lightbox[4739]"><img class=" wp-image-4765 alignleft" title="NCTM Booth" src="http://blog.keycurriculum.com/wp-content/uploads/2012/04/NCTM-Booth1-1024x607.jpg" alt="NCTM Booth" width="421" height="248" /></a>I thought I’d give you a behind-the-scenes view of last week&#8217;s activities in Philadelphia.</p>
<p><a href="http://blog.keycurriculum.com/author/kgreenhaus">Karen Greenhaus</a>, <a href="http://blog.keycurriculum.com/author/amarti">Andres Marti,</a> <a href="http://blog.keycurriculum.com/author/edecarli">Elizabeth DeCarli</a>, and I were assigned to the first event, NCSM. We were up bright and early on Monday morning to set up our booth, even although it was 4:00 am in our heads, having just flown in from California (Karen from Texas). Our booth was to be delivered at 8:00 am and set up by the opening of the show at 11:00 am. We waited and waited&#8230; and waited.</p>
<p>Finally I called Lainie Johnson, our Marketing Manager in California (I apologize for the VERY early call, Lainie) who gave me the shipping company’s information and the case of the missing booth was opened. I got my first real glimpse of the massive behind-the-scenes logistics of the NCSM and NCTM events after multiple calls between the main hall and the loading dock yielded no results. I asked if I could go down to the loading dock and was told “you don’t want to go down there, it’s dangerous.” So I went anyway&#8230;</p>
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<p>There were 22 loading bays and each had a truck in it. Our booth was in one of those trucks, but which one? One of the guys from Freeman, rather surprised to find me down there, called me over to him and told me to jump on the back of his “golf cart.” Off we went in search of the missing shipment and after a quick tour down the loading bay we found what we were looking for—tucked in the very back of a truck was our crate. The trucking company thought it was due for delivery for NCTM a few days later and thought they were early, by our measure they were now over two hours late. The guys from Freeman were incredibly helpful and we almost had everything in place when the show started. Phew.</p>
<p>We didn’t get a chance to see any of the sessions at NCSM—we rarely do—but we saw many of our friends in the leadership community when they visited our booth. Our friend Arjan Khalsa, from <a href="http://www.conceptuamath.com" target="_blank">Conceptua Math</a>, hosted a wonderful soirée on Tuesday evening where math, specifically fractions, and music were the themes for the evening. Arjan also announced the publication of Nora Ramirez’ new book, <a href="http://www.nctm.org/catalog/product.aspx?id=14118" target="_blank"><em>Beyond Good Teaching</em></a>  and Steve Leinwand signed copies of his book,  <em><a href="http://www.heinemann.com/products/E02656.aspx" target="_blank">Accessible Mathematics</a>,  </em>for 10 lucky winners.</p>
<p>We ended NCSM by hosting an Ignite on Wednesday afternoon. Our amazing speakers filled the room to capacity: Karim Kai Ani, Juli K. Dixon, David Elliott, Tim Kanold, Donna Simpson Leak, Jamila Riser, Scott Steketee, and Steve Weimar, Annie Fetter, and Max Ray from the <a href="http://mathforum.org" target="_blank">Math Forum</a>. Thanks all! The talks will be posted by the end of next week on <a href="http://www.youtube.com/user/KeyCurriculumPress" target="_blank">our YouTube</a> channel and also accessible from <a href="http://www.keycurriculum.com/connect" target="_blank">our website</a>. Many teachers told me they’ve used the Ignite videos for their own professional development and have shared them widely with their colleagues. Good stuff!</p>
<p>With NCSM wrapped up, we turned to NCTM. We had a new booth this year that focused on our learning tools, <a href="http://www.keycurriculum.com/products/sketchpad" target="_blank"><em>Sketchpad</em></a>, <a href="http://www.keycurriculum.com/products/fathom" target="_blank"><em>Fathom</em></a> and <a href="http://www.keycurriculum.com/products/tinkerplots" target="_blank"><em>TinkerPlots</em></a>. The booth set up went very smoothly thanks to Skyline, SMART (who donated two boards) and Lainie, who thought of every possible detail. There was a lot of interest in <em>TinkerPlots</em> this year, due to the new data analysis and probability standards for middle school in the Common Core. And Sherry Fraser, one of our <a href="http://www.keycurriculum.com/products/interactive-mathematics-program"><em>IMP</em></a> authors, spent time in the booth and spoke to teachers about <em>IMP</em> and anything else they asked her! Thank you, Sherry.</p>
<p>Back at home, our team was busy promoting over 30 talks on Twitter that included <em>Sketchpad, TinkerPlots,</em> or <em>Fathom</em>. The first feedback I got about Nick Jackiw’s talk on <em>&#8220;Euclid’s Elements: An Interactive Geometry Perspective&#8221;</em> was that it was “phenomenal.” We videotaped it so you can see it too on <a href="http://www.keycurriculum.com/connect" target="_blank">our Connect page</a> once we edit it.</p>
<p><a href="http://blog.keycurriculum.com/wp-content/uploads/2012/04/NCTM-User-Group.jpg" rel="lightbox[4739]"><img class="alignright  wp-image-4771" title="NCTM User Group" src="http://blog.keycurriculum.com/wp-content/uploads/2012/04/NCTM-User-Group-1024x641.jpg" alt="Michael Bosse and friends at User Group" width="396" height="267" /></a>Thursday night we hosted a User Group for 200+ fans of <em>Sketchpad</em>, <em>Fathom</em>, and <em>TinkerPlots</em>. Over 20 teachers shared short demonstrations with other teachers. Thanks to Rick Gaston and Lainie for organizing and hosting the evening for our user community, and to Karen Greenhaus for emceeing and for not singing! Just kidding, Karen.</p>
<p>Friday morning we were up at 6:30 am to host a breakfast for the Presidential Awardee group, CPAM. At that hour, it must be love, folks. Everyone received <em>TinkerPlots</em> and participated in a short demo using a data set about U.S. Presidents. One President had 15 children! Who knew! You can find which one by downloading the software and exploring the “Presidents” data set.</p>
<p>After the CPAM breakfast, we had four more hours in the booth before the show closed. A busy time as teachers rushed to see some last minute product demos. At noon the show closed and it took a lot less time for us to pack up than it did for us to set up!</p>
<p>The week ended with a lovely lunch in Philly before we all headed for various flights. It was wonderful to see so many friends of Key. Thanks for stopping by. Many thanks to the Key team for all their hard work.</p>
<p>See you in Denver!</p>
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		<title>Philadelphia Freedom</title>
		<link>http://blog.keycurriculum.com/2012/04/philadelphia-freedom/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=philadelphia-freedom</link>
		<comments>http://blog.keycurriculum.com/2012/04/philadelphia-freedom/#comments</comments>
		<pubDate>Mon, 23 Apr 2012 20:07:31 +0000</pubDate>
		<dc:creator>Andres Marti</dc:creator>
				<category><![CDATA[Conferences]]></category>
		<category><![CDATA[Fathom]]></category>
		<category><![CDATA[Ignite]]></category>
		<category><![CDATA[Interactive Whiteboards]]></category>
		<category><![CDATA[NCTM]]></category>
		<category><![CDATA[Sketchpad]]></category>
		<category><![CDATA[Teacher Collaboration]]></category>
		<category><![CDATA[TinkerPlots]]></category>

		<guid isPermaLink="false">http://blog.keycurriculum.com/?p=4718</guid>
		<description><![CDATA[If you&#8217;re around my age, you clearly remember the famous Elton John song. I can&#8217;t help but think of &#8220;Philadelphia Freedom&#8221; whenever someone mentions Philadelphia. It&#8217;s an involuntary response that shoots straight out of my unconscious. And since today is &#8230; <a href="http://blog.keycurriculum.com/2012/04/philadelphia-freedom/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<!-- Start Shareaholic LikeButtonSetTop Automatic --><!-- End Shareaholic LikeButtonSetTop Automatic --><p>If you&#8217;re around my age, you clearly remember the famous Elton John song. I can&#8217;t help but think of &#8220;<a title="&quot;Philadelphia Freedom&quot; by Elton John" href="http://www.youtube.com/watch?v=2sd6P2Tu8rw" target="_blank">Philadelphia Freedom</a>&#8221; whenever someone mentions Philadelphia. It&#8217;s an involuntary response that shoots straight out of my unconscious. And since today is the first day of the <a title="NCSM Annual Conference" href="http://www.mathedleadership.org/events/conferences/PA/index.html" target="_blank">NCSM conference</a> in Philly, that song has been percolating in my head ever since I arrived in town a couple of days ago.</p>
<div id="attachment_4721" class="wp-caption alignright" style="width: 310px"><a href="http://blog.keycurriculum.com/wp-content/uploads/2012/04/EdC-at-NCSM.jpg" rel="lightbox[4718]"><img class="size-medium wp-image-4721 " title="Elizabeth DeCarli at NCSM 2012" src="http://blog.keycurriculum.com/wp-content/uploads/2012/04/EdC-at-NCSM-300x225.jpg" alt="Elizabeth DeCarli at NCSM 2012" width="300" height="225" /></a><p class="wp-caption-text">Elizabeth DeCarli tinkering with her plots at NCSM.</p></div>
<p>It turns out that since I joined Key, I&#8217;ve met many people from Philly, including Scott Steketee, who works for KCP Technologies. Scott is one of the most thoughtful, intelligent, and kind-hearted people I&#8217;ve ever met, and he&#8217;ll be one of our <a title="NCSM Ignite" href="http://www.keycurriculum.com/ignite-at-ncsm" target="_blank">Ignite</a> speakers this Wednesday. (For those of you fortunate to be here this week, Scott has a Sketchpad-based surprise waiting for you!)</p>
<p>Philly is also the home of Drexel University, which houses the <a title="The Math Forum" href="http://mathforum.org" target="_blank">Math Forum</a>, the world&#8217;s largest online math community. As seems appropriate in this historic city of freedom, the Math Forum is completely free, and has been a source of support for math  students seeking help for two decades now. They are currently set up next to us in the exhibit hall, which is great because we love Annie Fetter, Steve Weimar, Max Ray, and the rest of the gang, who will also be presenting talks at the Ignite. In fact, there&#8217;s a long history between the Math Forum and Key, as the Math Forum and Sketchpad both evolved out of the Visual Geometry Project in the late 1980&#8242;s.</p>
<p>Anyway, teachers really seem to love free stuff, so we&#8217;ve got some free technology gifts to give away. First of all, you can download all three of our software products, <a title="The Geometer's Sketchpad" href="http://www.keycurriculum.com/products/sketchpad" target="_blank">Sketchpad</a>, <a title="Fathom Dynamic Data" href="http://www.keycurriculum.com/products/fathom" target="_blank">Fathom</a>, and <a title="TinkerPlots Dynamic Data Exploration" href="http://www.keycurriculum.com/products/tinkerplots" target="_blank">TinkerPlots</a>, for free. Granted, they are in preview mode which prevents saving and printing, but it does allow you to play with the tools and explore the ample free sample activities that come with them. Then we have <a title="Sketchpad Explorer for the iPad" href="http://www.dynamicgeometry.com/General_Resources/Sketchpad_Explorer_for_iPad.html" target="_blank">Sketchpad Explorer</a>, which is a Sketchpad player for the iPad, which you can download for free from the Apple App Store. And finally we have our <a title="Technology User Group" href="http://www.keycurriculum.com/technology-user-group-at-nctm" target="_blank">Technology User Group</a> on Thursday evening, which includes free activities, appetizers, and drinks.</p>
<p>So if you&#8217;re in Philly, stop by and visit our booth or come to our Ignite on Wednesday, or join our User Group on Thursday. We&#8217;d love to see you! And if not, take a look at our technology tools, and watch some videos of <a title="Key's Math Ignite page" href="http://www.youtube.com/playlist?list=PL5CDF98F961F9527D&amp;feature=plcp" target="_blank">previous Ignite speakers</a> while you&#8217;re there.</p>
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		<title>NCSM 2012 Ignite &#8211; It&#8217;s Fast, It&#8217;s Fun, It&#8217;s Math!</title>
		<link>http://blog.keycurriculum.com/2012/04/ncsm-2012-ignite-its-fast-its-fun-its-math/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=ncsm-2012-ignite-its-fast-its-fun-its-math</link>
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		<pubDate>Fri, 20 Apr 2012 15:51:38 +0000</pubDate>
		<dc:creator>Karen Greenhaus</dc:creator>
				<category><![CDATA[Conferences]]></category>
		<category><![CDATA[CMC]]></category>
		<category><![CDATA[Ignite]]></category>
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		<guid isPermaLink="false">http://blog.keycurriculum.com/?p=4684</guid>
		<description><![CDATA[The big annual math conferences are next week in Philadelphia. First up, the National Council of Supervisors of Mathematics (NCSM) conference, April 23–25, followed by the National Council of Teachers of Mathematics (NCTM) conference, April 25–28. Naturally, those of us &#8230; <a href="http://blog.keycurriculum.com/2012/04/ncsm-2012-ignite-its-fast-its-fun-its-math/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<!-- Start Shareaholic LikeButtonSetTop Automatic --><!-- End Shareaholic LikeButtonSetTop Automatic --><p>The big annual math conferences are next week in Philadelphia. First up, the National Council of Supervisors of Mathematics (<a title="NCSM Conference 2012" href="http://www.mathedleadership.org/events/conferences/PA/index.html" target="_blank">NCSM</a>) conference, April 23–25, followed by the National Council of Teachers of Mathematics (<a title="NCTM Conference 2012" href="http://www.nctm.org/conferences/content.aspx?id=29461" target="_blank">NCTM</a>) conference, April 25–28. Naturally, those of us at Key have been gearing up to meet thousands of math teachers and leaders and &#8220;bring math to life&#8221; (to borrow from our new motto!) with all our software and resources. One of the big events we are sponsoring is our <a title="Key Ignite NCSM 2012" href="http://www.keycurriculum.com/ignite-at-ncsm" target="_blank">Ignite!</a> presentation at NCSM, where we bring together math leaders and thinkers to share their thoughts on math education.</p>
<p><a href="http://igniteshow.com/" target="_blank"><img class="size-full wp-image-4687 alignright" title="Ignite Talks Logo" src="http://blog.keycurriculum.com/wp-content/uploads/2012/04/ignite1.png" alt="" width="330" height="104" /></a></p>
<p>If you have never been to an Ignite! event, it&#8217;s really quite a fun, unique, and enlightening experience. Each speaker gets 20 PowerPoint slides to make their point. The slides auto-advance every 15 seconds, so the total talk is five minutes. Not a lot of time, so the challenge is to use visuals and key words to make your point quickly and succinctly. I speak from personal experience when I say planning a five-minute talk is significantly harder than planning for an hour talk or even a day-long workshop—especially when the clock is ticking!</p>
<p><span id="more-4684"></span></p>
<p><a title="Ignite Talks" href="http://igniteshow.com/" target="_blank">Ignite!</a> events started in 2006 in Seattle, Washington and since then, events have occured throughout the world. Key Curriculum hosted our first Ignite event at NCSM 2010 and have been doing it ever since at local, regional and national math conferences. They&#8217;ve been exciting and fun times that brought together innovative math educators who have shared, in various ways, their expertise and insight into math education.  They are never the same and never dull, and there are always surprises, such as Mike Shaughnessy <a href="http://www.youtube.com/watch?v=Ys2azxl0DvQ&amp;list=PL5CDF98F961F9527D&amp;index=17&amp;feature=plpp_video" target="_blank">singing refrains</a> at NCSM 2011, Michael Serra <a href="http://www.youtube.com/watch?v=G57qemxBVoM&amp;list=PL5CDF98F961F9527D&amp;index=19&amp;feature=plpp_video" target="_blank">teaching math anxiety</a> at CMC North 2010, and Ruth Cossey <a href="http://www.youtube.com/watch?v=_JO5-DD1PsQ&amp;list=PL5CDF98F961F9527D&amp;index=10&amp;feature=plpp_video" target="_blank">reciting an Ode to the Common Core</a> at CMC South 2011.</p>
<p>I am looking forward to this year&#8217;s event and I hope those of you who are attending NCSM 2012 this year in Philly will come and spend an hour being &#8216;ignited&#8217; about math. We have some great speakers lined up this year:</p>
<ul>
<li>Karim Kai Ani from Mathalicious</li>
<li>Juli Dixon from The University of Central Florida</li>
<li>David Elliott from Glenbard E. High School in Illinois</li>
<li>Annie Fetter from The Math Forum at Drexel (see Annie&#8217;s previous Ignite in my last post <a href="http://blog.keycurriculum.com/?p=4364&amp;preview=true">&#8220;What do you wonder&#8230;&#8221;</a>)</li>
<li>Tim Kanold from The Common Core Math Learning Group</li>
<li>Donna Leak from Rich Township High School District 227</li>
<li>Max Ray from The Math Forum at Drexel</li>
<li>Jamila Riser from The Delaware Mathematics Coalition</li>
<li>Scott Steketee from KCP Technologies</li>
<li>Steve Weimar from The Math Forum at Drexel</li>
</ul>
<p>As you can see, quite a diverse line-up, from all around the country and from different areas of the math education arena, so it&#8217;s bound to be interesting, exciting and entertaining.  Stop by and join us Wednesday, April 24, from 4–5 p.m. in Room 105 at the Pennsylvania Convention Center. There will be plenty of room and like I said—it&#8217;s fast, it&#8217;s fun, and it&#8217;s math!</p>
<p>For those of you who won&#8217;t be in Philly, we will be recording the speakers and posting them on our <a href="http://www.youtube.com/playlist?list=PL5CDF98F961F9527D&amp;feature=plcp" target="_blank">YouTube channel.</a> To get a taste of Ignite, check out some of our previous presentations. They are all good, but here are a few of my personal favorites.</p>
<p>Patrick Callahan presents his &#8220;Modest Proposal.&#8221;</p>
<p><iframe src="http://www.youtube.com/embed/VlnBRkIOSrM" frameborder="0" width="420" height="315"></iframe></p>
<p>Max Ray explains &#8220;Why 2 &gt; 4.&#8221;</p>
<p><iframe src="http://www.youtube.com/embed/daCtIac24yU" frameborder="0" width="420" height="315"></iframe></p>
<p>Elizabeth DeCarli reflects on &#8220;Making Math Memorable.&#8221;</p>
<p><iframe src="http://www.youtube.com/embed/Rguu1_FtdVQ" frameborder="0" width="420" height="315"></iframe></p>
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		<title>The Dynamic Number Project Comes to NCTM Philadelphia</title>
		<link>http://blog.keycurriculum.com/2012/04/the-dynamic-number-project-comes-to-nctm-philadelphia/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=the-dynamic-number-project-comes-to-nctm-philadelphia</link>
		<comments>http://blog.keycurriculum.com/2012/04/the-dynamic-number-project-comes-to-nctm-philadelphia/#comments</comments>
		<pubDate>Wed, 18 Apr 2012 15:47:08 +0000</pubDate>
		<dc:creator>Daniel Scher</dc:creator>
				<category><![CDATA[Conferences]]></category>
		<category><![CDATA[Dynamic Geometry]]></category>
		<category><![CDATA[Dynamic Number]]></category>
		<category><![CDATA[Fathom]]></category>
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		<guid isPermaLink="false">http://blog.keypress.com/?p=4578</guid>
		<description><![CDATA[It’s time for the NCTM Annual Meeting! For the past two and a half years, my colleague Scott Steketee and I have been collaborating with elementary teachers in New York and Philadelphia as they field test curriculum materials for the &#8230; <a href="http://blog.keycurriculum.com/2012/04/the-dynamic-number-project-comes-to-nctm-philadelphia/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<!-- Start Shareaholic LikeButtonSetTop Automatic --><!-- End Shareaholic LikeButtonSetTop Automatic --><p>It’s time for the <a title="2012 NCTM Annual Meeting" href="http://www.nctm.org/conferences/content.aspx?id=29461" target="_blank">NCTM Annual Meeting</a>!</p>
<p>For the past two and a half years, my colleague Scott Steketee and I have been collaborating with elementary teachers in New York and Philadelphia as they field test curriculum materials for the <a href="http://www.kcptech.com/dynamicnumber" target="_blank">Dynamic Number</a> project. We’ll be showcasing our work at three sessions during the upcoming NCTM conference in Philadelphia.</p>
<div id="attachment_4599" class="wp-caption alignleft" style="width: 600px"><a href="http://blog.keypress.com/wp-content/uploads/2012/04/NCTM-Annual-Conference1.gif" rel="lightbox[4578]"><img class="size-full wp-image-4599 " src="http://blog.keypress.com/wp-content/uploads/2012/04/NCTM-Annual-Conference1.gif" alt="NCTM Annual Meeting 2012" width="590" height="90" /></a><p class="wp-caption-text">Image courtesy of the National Council of Teachers of Mathematics</p></div>
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<p>I’ll be presenting with Janice Manning, Matt Silverman, and Sonal Malpani from the School of Discovery and Exploration in Brooklyn, NY. <a title="Dynamic Fractions in the Elementary School Classroom" href="http://nctm.confex.com/nctm/2012AM/webprogram/Session8140.html" target="_blank">Our talk</a> focuses on students’ understanding of fractions and the impact of using a variety of Sketchpad fraction models. We’ll be bringing classroom videos with us to give the audience an up-close look at students’ conceptual understanding.</p>
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<p>In another session, Scott will be presenting with Kristen Johnson, Anna Varano, and Maryann Milewski-Moskal from the Penn Alexander School in Philadelphia, PA. <a title="A Dynamic Number Approach to Multiplication" href="http://nctm.confex.com/nctm/2012AM/webprogram/Session8145.html" target="_blank">Their talk</a> focuses on another central topic in the elementary curriculum—multiplication—and will also include classroom video.</p>
<p>Separately, Scott is presenting a <a title="Function Composition" href="http://nctm.confex.com/nctm/2012AM/webprogram/Session8861.html" target="_blank">session</a> on function composition that treats this often misunderstood topic by combining a geometric approach with the usual symbolic one.</p>
<p>Finally, you can learn more about the Dynamic Number project and KCP Technologies’ other NSF-funded project, <a title="Data Games" href="http://www.kcptech.com/datagames/" target="_blank">Data Games</a>, at the Technology User Group from 7:00–9:00 on April 26 in Salons H/I/J at the Philadelphia Marriott on 1201 Market Street.</p>
<p>The <a title="Key Curriculum User Group" href="http://www.keycurriculum.com/tech-user-group-at-nctm" target="_blank" class="broken_link" rel="nofollow">User Group</a>, sponsored by Key Curriculum, is a great opportunity to chat with other users of Sketchpad, Fathom, and TinkerPlots and see their latest creations. And if that’s not a big enough selling point, how about this: The Dynamic Number project will unveil at the User Group the most complex Sketchpad model ever made. No kidding!</p>
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		<title>Branding isn’t about math. Are you sure about that?</title>
		<link>http://blog.keycurriculum.com/2012/04/branding-isnt-about-math-are-you-sure-about-that/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=branding-isnt-about-math-are-you-sure-about-that</link>
		<comments>http://blog.keycurriculum.com/2012/04/branding-isnt-about-math-are-you-sure-about-that/#comments</comments>
		<pubDate>Mon, 16 Apr 2012 15:18:16 +0000</pubDate>
		<dc:creator>Karen Coe</dc:creator>
				<category><![CDATA[Math Software]]></category>
		<category><![CDATA[Constructions]]></category>
		<category><![CDATA[Dynamic Geometry]]></category>
		<category><![CDATA[Modeling]]></category>
		<category><![CDATA[Sketchpad]]></category>
		<category><![CDATA[Use Appropriate Tools Strategically]]></category>
		<category><![CDATA[Videos]]></category>

		<guid isPermaLink="false">http://blog.keypress.com/?p=4634</guid>
		<description><![CDATA[At around Pi-hour on Friday afternoon we successfully launched our new website. The night before (the night of the big storm for Bay Area folks), Andres and I were out with a dear former colleague and I mentioned I was &#8230; <a href="http://blog.keycurriculum.com/2012/04/branding-isnt-about-math-are-you-sure-about-that/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<!-- Start Shareaholic LikeButtonSetTop Automatic --><!-- End Shareaholic LikeButtonSetTop Automatic --><p><a href="http://www.keycurriculum.com" target="_blank"><img class="alignnone size-medium wp-image-4636" title="logo_CMYK" src="http://blog.keypress.com/wp-content/uploads/2012/04/logo_CMYK_hires-300x78.jpg" alt="Pi-Petal Rose Logo" width="300" height="78" /></a></p>
<p>At around Pi-hour on Friday afternoon we successfully launched our new <a href="http://www.keycurriculum.com" target="_blank">website</a>. The night before (the night of the big storm for Bay Area folks), Andres and I were out with a dear former colleague and I mentioned I was going to blog about our new branding, new website, and new name. She said, “You can’t do that, it’s a math blog, nobody is interested in branding!” To which I replied, “What other company do you know used their own software to create their logo? Our branding <em>is</em> math.” We then had another drink.</p>
<p>Let me explain. We were working with a very talented designer and trying to communicate we wanted a logo that expressed math in motion to match our new tag line of “bringing math to life.”  He came back with some wonderful designs but none of them felt quite right to us. Our favorite was a design that had eight colored petals but it didn’t deeply resonate. I was talking to Milan, our CFO, about it and as he wandered over to the local coffee shop for his “Milan special” he sent me an email that simply read, “Not fewer petals, more petals, 22 to be exact.” I knew exactly what he meant. The day before he and I were in a business development meeting with Steve Rasmussen, where Steve constructed the “pi-petal rose” by way of introducing construction in <em>Sketchpad</em>. People are always delighted to see a visual representation of Pi for the first time&#8211;something very familiar seen in a new way. With a little finessing by the designer we’ve adopted the pi-petal rose as our new logo.</p>
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<p>You can see a quick animation of our new logo was the end of this <a href="http://www.keycurriculum.com/products/sketchpad" target="_blank">video</a> for the new <em>Sketchpad</em> page, or you can watch this video where Karen Greenhaus takes you through how to construct it step-by-step.</p>
<p><iframe src="http://www.youtube.com/embed/2Mju65kb-dI" frameborder="0" width="560" height="315"></iframe></p>
<p>In addition to the new website and logo we’ve changed our name. We’re dropping Press from our name and just going by Key Curriculum. Press suggests printing and that’s not the trajectory we’re on. Also, our old colophon was an image of an open book so that had to go too. It has been replaced with the pi-petal rose.</p>
<p>The new website was built from scratch—out with the old, in with the new. The site emphasizes our learning tools and also provides many free resources to help you get started with<em> </em><a href="http://www.keycurriculum.com/products/sketchpad" target="_blank"><em>Sketchpad</em></a>, <a href="http://www.keycurriculum.com/products/fathom" target="_blank"><em>Fathom</em></a>, and <a href="http://www.keycurriculum.com/products/tinkerplots" target="_blank"><em>TinkerPlots</em></a>. The number one thing we hear from teachers is “I’d love to use <em>Sketchpad</em> (or <em>Fathom</em>, or <em>TinkerPlots</em>) but I’m not sure how to get started.” With the release of <em>Sketchpad 5</em> we built extensive getting started resources (videos, tutorials, activities, etc.) into the application and we still heard the same thing. We’ve now taken all of those resources and put them on the website for free. Enjoy exploring them at the <a href="http://www.keycurriculum.com/resources" target="_blank">Resource Center</a>.</p>
<p>I hope you like the new site. We’ve tried to make everything easier for you. You can download free trial versions of our software, access free resources, and sign up for our popular Tech Tuesday webinars. No excuses not to get started.</p>
<p>Many thanks to the amazing team at Key who made all this possible in 14 weeks from start to finish!</p>
<p>By the way, the Greek word for rose is triantafillo, or thirty petals. They should change it to ekosidiofillo, or 22 petals.  Archimedes would be pleased if they did!</p>
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		<title>Who survived the Titanic?</title>
		<link>http://blog.keycurriculum.com/2012/04/who-survived-the-titanic/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=who-survived-the-titanic</link>
		<comments>http://blog.keycurriculum.com/2012/04/who-survived-the-titanic/#comments</comments>
		<pubDate>Sat, 14 Apr 2012 23:20:26 +0000</pubDate>
		<dc:creator>Andres Marti</dc:creator>
				<category><![CDATA[Math Software]]></category>
		<category><![CDATA[Data and Statistics]]></category>
		<category><![CDATA[Dynamic Data]]></category>
		<category><![CDATA[TinkerPlots]]></category>
		<category><![CDATA[Videos]]></category>

		<guid isPermaLink="false">http://blog.keypress.com/?p=4614</guid>
		<description><![CDATA[Exactly a century ago, the RMS Titanic struck an iceberg and sank on its maiden voyage. Most people know the story better than me, or at least the Hollywood version of it, as I&#8217;ve never seen the movie. (On the &#8230; <a href="http://blog.keycurriculum.com/2012/04/who-survived-the-titanic/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<!-- Start Shareaholic LikeButtonSetTop Automatic --><!-- End Shareaholic LikeButtonSetTop Automatic --><p>Exactly a century ago, the <em>RMS Titanic</em> struck an iceberg and sank on its maiden voyage. Most people know the story better than me, or at least the Hollywood version of it, as I&#8217;ve never seen the movie. (On the other hand, my daughter just saw it again in 3D and &#8220;cried the whole time.&#8221;)</p>
<p>One of my favorite data sets to demonstrate on <a title="TinkerPlots Dynamic Data Exploration product page" href="http://www.keycurriculum.com/products/tinkerplots" target="_blank">TinkerPlots</a> is a record of the people who were on that tragic journey. There are very few attributes, but precisely those that are the most interesting: gender, class (or crew), adult or child (here numeric age would have been even more interesting), and whether that person survived.</p>
<p>So for this special Saturday blog edition, I&#8217;m going to share a short silent movie (seems era-appropriate) of me visually exploring the main question in my head: Was survival correlated to other variables such class or gender? Take a look and see what you think.</p>
<p><iframe src="http://www.youtube.com/embed/yKY6QW8YIB8?rel=0" frameborder="1" width="560" height="315"></iframe></p>
<p>I was really surprised by the size of the crew given the number of the passengers&#8230;and they certainly took a heavy toll that day. If you want to learn more about the people on the <em>Titanic</em>, I recently read this interesting <a title="Messages from the Titanic" href="http://channel.nationalgeographic.com/channel/titanic/mail-from-the-titanic/" target="_blank">collection of communications</a> from the <em></em> before and after the tragedy. And if you want to see more dynamic data animations, see what we&#8217;ve done at our website to <a title="TinkerPlots Dynamic Data Exploration product page" href="http://www.keycurriculum.com/products/tinkerplots" target="_blank">show TinkerPlots in action!</a></p>
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