Katie Hildebrandt (6th grade math teacher) and I just finished a 2-day unit on Tessellations using Geometer's Sketchpad to rotate an equilateral triangle and translate a parallelogram. I can't praise Geometer's Sketchpad (sometimes shortened to Geo Sketchpad, GSP, or simply Sketchpad) enough. It is one of the few pieces of educational software out there that is entirely constructivist. You can actually learn math by using GSP. Just like classical Euclidean Geomtetry breaks down everything in the world to points, lines, and planes, so does GSP; You can quickly learn to construct, animate, and measure a range of sketches, from the simple to the complex.

In this brief unit, we verbally discussed how a vector is a geometric object (in this case, a segment) that has both a direction and distance. They notice the "di" in the beginning of each word. I also tell them that translating is the same as sliding, and both words have an "sl". We talked about angles of rotation, indications of symmetry, interior angles of a triangle, and reinforced vocabulary: equiangular, equilateral, congruent, parallel lines, etc.

I always start off by showing them works by M.C. Escher. On the site, there is a link to a gallery of his symmetry drawings. I marvel at how Escher painstakingly drew his incredibly intricate and fascinating tesselations component by component. I imagine his pile of pencil stubs and eraser shavings, and reinforce for the kids how we can create infinite variations with GSP in a matter of seconds by clicking and dragging.

I posted something about last year's activity here.

There is a great PDF with multiple activities put out by Key Curriculum Press (@keypress) embedded below or you can click here to download it. We use pages 7-8 for the translation activity and pages 9-10 for the rotation activity.

Daniel Scher is a principal investigator for The Dynamic Number Project. He works to create the iPad-compatible constructions for the Sketchpad Explorer app. Sketchpad Explorer is the iPad companion to Geometer's Sketchpad software program - both are published by Key Curriculum Press (@keypress on Twitter).

Daniel will be coming to The School at Columbia University to help me help the 5th grade teachers integrate Sketchpad Explorer into their math curriculum. He's psyched to watch/evalutate how kids learn with the app versus the software versus without either, and I'm excited to get a full grade of teachers to use a tool that I consider to be an industry standard for math educators. I love Geometer's Sketchpad, and I recently gushed about Sketchpad Explorer on Scholastic's Best in Tech Today.

Upon opening the Sketchpad Explorer app, there is an animated proof of the Pythagorian Theorem.

On the bottom right corner is a book icon. This takes you to many options, one of which is to visit the Sketch Exchange community site. From here, you can click Sketch Exchange sketches tagged with ipad, and then you can choose dynamic number in the tag cloud. These sketches open up with the full Geometer's Sketchpad software program as well.

There are four pages of sketches to choose from. I initially chose Balance Scale: Solving for Unknowns Part 1. When you choose a sketch, further down the page you'll find links to download activity notes, worksheets, and the actual sketch with the .gsp suffix. I was super excited to note the CreativeCommons license (!) of Attribution Non-Commercial No Derivatives which translates to: Give me credit, don't make money off it, and don't alter it. I love Creative Commons almost as much as Geometer's Sketchpad. :)

I had a bit of fun playing with this screen trying to figure out the value of the star and other shapes using the fulcrum, and yes, I think I'm smarter than a 5th grader.

Download the Sketchpad Explorer app here: http://itunes.apple.com/us/app/sketchpad-explorer/id452811793?mt=8

I've been a fan of Geometer's Sketchpad (GSP) since 1994 when I first learned about it as a Senior at Bryn Mawr College. It is among the best examples of educational software out there, as you actually learn the math by using the tool. I wrote a post in January about using GSP to do tessellations in 6th grade math, and Daniel Scher* contacted me about maybe collaborating to integrate The Dynamic Number Project and other great resources.

Last week, Daniel came to The School at Columbia University to meet a select group of teachers, technologists, and math liaisons. He'll be showing them how to integrate The Dynamic Number Project and GSP into their curriculum, make constructions with GSP, and use the soon-to-be-launched iPad app of GSP! While the initial GSP app will only run interactive scripts, the next iteration will allow the user to make constructions. By getting the teachers' hands on an iPad2 installed with the GSP app in June, we're hoping to hit the ground running in September.

* Daniel Scher is a Senior Scientest at KCP Technologies. As per their website, KCP Technologies is the software research and development affiliate of Key Curriculum Press. KCP Technologies developed  The Geometer's Sketchpad® and Fathom Dynamic Data™ Software - I've used both, and they are both awesome. More information about Daniel is pasted from his professional vitae below:

Daniel is a principal investigator for the NSF-funded project Introducing Dynamic Number as a Transformative Technology for Number and Early Algebra. Previously, Daniel was a program director at Best Practices in Education, where he specialized in educational technology applications and the adaptation of the Elkonin-Davydov mathematics curriculum for first and second graders. He investigated the epistemology and mathematics of Dynamic Geometry® while a researcher at Education Development Center. He is the author of Exploring Conic Sections with The Geometer's Sketchpad and is the co-author of a geometry textbook and a precalculus Sketchpad module. Daniel received a BA in Mathematics from the University of Pennsylvania in 1989, an MS in Mathematics Education from Cornell University in 1993, and a PhD in Mathematics Education from New York University in 2002. (http://www.kcptech.com/pages/daniel.html)

 

The Dynamic Number Project: http://www.kcptech.com/dynamicnumber/curriculum.html

Key Curriculum Press on Twitter: @keypress

My 6th Grade tessellations project: http://karenblumberg.com/tessellations-with-geometers-sketchpad-in-6th