Tag Archives: Geometry

Playing with the #SketchpadExplorer app. Download it for free until 11/1/11 via @keypress

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 numberin 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 Derivativeswhich 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. ­čÖé


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

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Daniel Scher of @keypress is helping us integrate GSP and The Dynamic Number Project


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┬áThe Geometer’s Sketchpad┬«and Fathom Dynamic DataÔäó SoftwareI’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

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Tessellations with Geometer’s Sketchpad in 6th grade Math


I spent a few days this week with the 6th grade math teachers/students. At The School at Columbia University, 6th graders study Islam and Mecca as part of the grade-wide theme: How History Shapes my Identity. For the last few years, I’ve worked with the math teachers to show the kids how to design tessellations on the computer. Then, the students take their creations to Art class and build a physical model out of clay and/or paper. It is one of my favorite integrated projects. (All of our K-8 Themes and Concepts can be found here: http://theschool.columbia.edu/about/curriculum.)

Katie Hildebrandt, often confused from behind for one of her students (à la Macaulay Culkin), is an energetic and supportive member of the 6th grade team and has a natural gift for breaking down mathematical concepts for her students. Before Winter Break, we met and planned a 3-day mini unit for our first week back; It bridged a unit on solving equations with her next unit on the Cartesian Plane. We briefly went over how to make transformations and use specific menu options in Geometer’s Sketchpad, as Katie is one of those independent teachers that initially explores on her own rather than rely on my tutelage. Power to the people!

On the first day of the mini-unit, Katie led a class on reflecting a polygon over the x-axis and y-axis. Students explored the resulting coordinates and stated the formula as an algebraic expression. For example, reflecting over the x-axis means (x,y) becomes (x, -y).

The second day, Katie showed how to rotate a polygon 90, 180, 270, and 360 degrees around the origin. Again, students analyzed how rotating the figure affected the coordinates of the original shape. For example, rotating 90 degrees meant that (x,y) become (-y, x).

On the third day, I stepped in, and we talked about how a tessellation is a pattern of repeating shapes that do not overlap and have no gaps in between. I showed them some of M.C. Escher’s artwork, and we talked about how classic Islamic art would rely on geometric patterns rather than animal or human forms. Because of the nature of our curriculum, the students had similar discussions in Art and Spanish among other subject areas. I showed the kids how to use Geometer’s Sketchpad to build an equilateral triangle, alter one side, and rotate that side 60 degrees to create a new shape. Then we rotated this altered triangle 60 degrees 6 times to form a hexagon before we tessellated the whole hexagon.

For my tessellation activities, I use two online lesson plans that I located years ago:
http://ww3.wpunj.edu/icip/itm/Lessonpl/sketch/rotate.htm – Triangle Rotations by Janet Mae Zahumeny of Roselle Park High School
http://mathforum.org/sum95/suzanne/tess.gsp.tutorial.html – Parallelogram Translations by Cathi Sanders of Punahou School

I started exploring/playing with Geometer’s Sketchpad in 1994 as an undergrad at Bryn Mawr College. To this day, it remains my favorite piece of educational software. Not too long after, I learned about The Math Forum – an amazing resource for math teachers and students founded at Swarthmore College and now seems to be hosted by Drexel University. There is a great link about Exploring and Creating Tessellations: http://www.teacherlink.org/content/math/activities/skpv4-tessellation/home.html

Geometer’s Sketchpad resources:
General Resources: http://www.dynamicgeometry.com/General_Resources.html
Resource Center: http://www.dynamicgeometry.com/
Sketch Exchange: http://sketchexchange.keypress.com/
Workshop Guide: http://www.dynamicgeometry.com/Instructor_Resources/Workshop_Guide.html


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