Tag Archives: Key Curriculum Press

Fractals in 6th Math with @kkleinNYC, Geometer’s #Sketchpad, @Scratch, and pencils. @The_School #mathchat

I’ve had a deep love and respect for Geometer’s Sketchpad since I was first introduced to it in 1994 as an undergraduate Math major (and aspiring math teacher) at Bryn Mawr College.

Later, I used Geometer’s Sketchpad during my student teaching stint at Strath Haven High School and again as a pre-Algebra/pre-Geometry teacher at The Dalton School.

Today in 6th grade Math at The School at Columbia University, Katie Klein (@KKleinNYC) and her associate teacher, Jazmin Sherwood, facilitated a great lesson on Fractals blending direct instruction, video, and self-paced sketching with and without technology.

1. Homework from the previous night was to watch the first 20 minutes of Fractals, Exploring the Hidden Dimension.

2. Here’s a link to beautiful photos of fractals found in nature:  http://io9.com/incredible-photographs-of-fractals-found-in-the-natural-480626285

3. Here are instructions for drawing Sierpinski Triangles with paper and pencil:

4. Here are instructions for drawing Sierpinksi Triangles using Geometer’s Sketchpad on their laptops:

5. Here’s another resource for making other fractals with Geometer’s Sketchpad:  http://www.gwinnett.k12.ga.us/PhoenixHS/math/GSP-website/17_Fractals(51-61).pdf

6. With additional time, students could explore fractals with Scratch or Snap (both are web-based block-based programming environments). Here are some links I gathered:

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Creating tesselations with 6th graders and Geometer’s Sketchpad


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.

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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. 🙂


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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My takeaways from the #ISTE11 exhibit hall

Saying there’s a lot going on in the Exhibit Hall of ISTE11 is gross understatement. Unlike my Aunt Debbie, I made it out of there without four tote bags overflowing with schwag. For me, the Exhibit Hall is about saying “Hi” to vendors I know and trust, avoiding the awkward hard sell, being wow’d by the next “must have” integrative technology, and summoning the joy of trick-or-treating with all the free candy offered on every table.

Below is an incomplete list of booths and presenters (whether old or new to me) I found compelling enough to write down in order to share with my faculty:

http://Pixologic.com for 3D modeling software (export files to our 3D printer!)
Sculptris – free, lite version
ZBrush – full feature

Wacom Technology
Awesome updates from Wacom

Free bibliography composer
Now let’s you make online notecards!

Finally came out with an iPad tray to charge and sync 10 iPads.
You have to charge it in their case, and they are demo’ing a prototype of the case (which I guess they’ll be packaging with the tray?)

PowerSync Tray for iPad – charges and syncs 10 devices, can be daisychained (but why buy 3 trays and not one cart unless you like the size of the tray)
PowerSync Cart for iPad – charges and syncs 30 devices

UPrint by Dimension
UPrint 3D printing by Stratasys
$15K prints up to 8x6x6″
$20K prints up to 8x8x6
$30K prints up to 8x8x12
$33K prints up to 10x10x12
$110K prints up to 14x16x14

iPevo2 document camera
Chopstakes multitouch styli
Cushi pillow stand for iPad

Epson’s Brightlink 455wi
$1600 without software
$1800 with RM Easiteach
Unlike the eBeam, no additional equipment needed besides projector, surface, computer
Infrared signal links from projector to pen tracks everything, 16:10 ratio throw
Not multi-touch
Projector has built-in wifi and speaker, ports for additional speaker

Gamestar Mechanic
Awesome platform for teaching principles of game design

Besides the Echo Smartpen, I was psyched to learn about Sound Stickers and Sticky Notes.
Sound stickers – circles you can program with specific audio! Put them on pages of books and kids can tap it with pen to make audio play
Sticky notes – sticky notes with dot patterns just like the notebooks
They are partnering with http://Harvardsquareacademy.org – not public yet – and getting a community of minds from Harvard and MIT sharing content and lessons to give expertise to students in the classroom

PBS TeacherLine
Online PD, free resources and lessons

Library of Congress
How and why to use primary resources, suggested tools for gathering primary resources

Lego Education
Jason Yount at Tech Support shared a ton of information
http://tiltedtwister.com – can get the building plans and compiled code (Java) for Rubiks Cube solving robot
http://tetrixrobotics.com for pics and plans of robots using tetrix pieces (claw design)
Labview – industry standard software, $500-600 site license. Has help feature to assist you as you translate from RoboLab or Mindstorms into LabView
WeDo – LabView for little kids – pretty basic looking programming language
Renewable Energy Add-on and Activity Pack – need to purchase the new Simple Machines kit 

Eno Play turns Eno board (the whole board!) into a speaker!
Fuse – document camera, web camera, and scanner in one

Vernier is the developer of Logger and tons of sensors
$1.99 Video Physics app – capture or import video with iPad (basketball, swing set, cars, conveyor belt) graph, share to Logger Pro and measure away

Use iPad to control interactive whiteboard screen, write over and edit and play back

Ladibug wireless document camera

One More Story
Online library
Child chooses a book and can experience it in one of three ways: either fully animated and controlled by computer, read by narrator, or read independently
$1.20 per child per year – 100 student minimum
$44 for a home license
Will be available in the fall as an app

Top reseller of Arduino projects
Program with Modkit – upgraded version of Scratch (modulation code)
They bundle an Inventor’s Guide
As an educator – email education@sparkfun.com and get digital or paper educator guides with worksheets for teaching with Arduino!!!!

Fablevision is developing the software for the 3D printer made by Cornell University
Prints models with hard plastic, silicon, latex, cheese whiz, frosting
Printer will be about $1000 or less
Comes in a kit to built
Hopefully available to purchase by september.

Powerful Learning Practice
Sheryl Nussbaum-Beach (@snbeach) and Will Richardson(@willrich45)
Year long, job-embedded PD versus workshops and keynote

2Bot physical modeling technologies
3D classroom modeling, Uses a drill bit to cut through blocks of approved materials (foam, wax, wood) 12x12x2 blocks but separate “printouts” can be pieced together. Under $10K

Key Curriculum Press
“Dynamic Number Project” and The Geometer’s Sketchpad app which will be out in a few weeks
Daniel Scher is the man!


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