Common Core and Sketchpad - DeKalb High School Math

I love what I get to do. This week I was invited to DeKalb High School to work with my former Math Department colleagues. What a great time!

After a few minutes of letting my computer download newest drivers for the SMART Board 800, we were off and running. (Note: if the green status light on the SMART Board pen tray is flashing green, you probably need to update hardware drivers for the SMART Board. My computer actually did this on its own, after I checked the SMART Hardware Settings in the Notebook Tools.)

Like most schools, DHS is hard at work integrating Common Core Standards into math classes. One topic being re-emphasized is transformations in the plane, representing them with physical tools and software.

Bisect an angle with compass and straightedge	Bisect an angle with Geometer's Sketchpad

We will use Geometer's Sketchpad to investigate translations, reflections, rotations and dilations, but first we begin with a review of basic constructions, with SMART Notebook software's compass and straightedge tools. It takes some practice to do this at the SMART Board, so don't try it for the first time in front of a classroom of students. It is a good visual when students are also using paper, compass and straightedge. Compare those constructions with the use of full circles in GSP. It's a good thinking exercise.

Now to really exploit the power of dynamic geometry software, we look at translations, reflections and rotations using Geometer's Sketchpad. These commands use rigid motions to create congruent figures or superimpose a figure onto itself. Students need to know precise definitions of basic geometric figures (segment, angle, circle, etc.) and congruence of figures. "Two figures are congruent, if and only if there is a transformation or combination of transformations that causes one figure to be superimposed onto the other."

Show properties of isosceles triangle with GSP	Reflect rectangle with GSP

What type of questions should be asked to verify that students are grasping these concepts?

• What types of symmetry exist in the given figure - line symmetry, point (rotational) symmetry?
• Where are lines of symmetry in the figure, those that cause the figure to be superimposed onto itself? Do all figures have this symmetry?
• Where are centers of rotation in the figure, those that cause the figure to be superimposed onto itself? Do all figures have this symmetry?
• What properties of the figure are shown from the reflections or rotations that superimpose the figure onto itself?
• What transformation shows two given figures are congruent? Is there more than one way to accomplish this?
• What happens when the line of reflection moves?
• What happens when the angle of rotation changes?

As students become familiar with geometric definitions and methods of GSP, you should ask them how to create more complex figures.

• How do you use a triangle to make a parallelogram? Is there more than one way?
• How do you make a rhombus? Can you do it using reflection or rotation? 
• Can you use these transformations to create regular polygons?

To see more ideas, you can turn to online videos and tutorials. There are some features in Sketchpad Version 5 that are not in Version 4, but you can usually accomplish the task with a few more steps.

Enjoy!

YouTube playlists and videos

Sketchpad in the Classroom playlist by Key Curriculum Press

Sketchpad - Common Core Curriculum videos by Key Curriculum Press

Free Webinars by Key Curriculum Press

TeacherTube Math videos

iPad app - Geometer's Sketchpad SketchExplorer

Most high school math teachers are familiar with The Geometer's Sketchpad (GSP), dynamic geometry and mathematics visualization and exploration software, published by Key Curriculum Press.  Of course, it can be used from 3-12 grades and beyond. It is not just for geometry.

http://www.dynamicgeometry.com

You can now use your iPad to interact with and explore a document created in GSP.  Search SketchExplorer in the App Store, or go to The Geometer's Sketchpad Resource Center General Resources and click on Sketchpad Explorer for iPad to download the app to your iPad. For now, the app is free, but the price is expected to go to about $4.00 US.

The app downloads with links to several documents. To see these links, click on the book icon at the bottom right corner. You can choose to search the Sketch Exchange site directly from the app. Most fit nicely on the iPad screen, but you can choose the iPad tag to find documents that are sized to be compatible with SketchExplorer. This app will interact with most GSP documents, but you cannot create new items on the document or create a new document.

Check out the linked documents, but remember to search Sketch Exchange for more. Here are a few excellent GSP documents from the Sketch Exchange site that work well in SketchExplorer.

• Excercise Machines - This document is amazing, creating exercises for topics from polygon angle sums to special right triangles and circles. Most of these exercises create infinite versions of the same type of problem, with appropriate diagrams. Yes, the solutions are also given.
• Addition on the Open Number Line -  Students add 2- and 3-digit numbers with arcs on the open number line. Strategies for composing and decomposing numbers are developed, such as 32+48 = 32+50-2.
• Cutting up a Pi - This document shows two dissections of the circle to demonstrate why the area formula works. This document has very cool animations.
• Dancing Factors - Choose a number from 1-36 and watch the factors circle ("dance") around it. Great fun, especially for younger students. Be sure to check out the "More Activities" link on the KCP Technologies tab. This GSP document is part of The Dynamic Number Project.
• Unfolding 3-D objects - Watch a cube, square pyramid and cylinder unfold into their 2-D nets, then fold back up. You can show the vertices and change the shape of faces.
• Quadrilateral Tree - This is a nice visualization of the relationships between quadrilaterals, listing properties of each. Vertices can be manipulated to verify properties.
• Why not SSA? - This is an excellent animation to show why two sides and the non-included angle are not sufficient to show congruent triangles. Any student learning about the ways to prove two triangles are congruent will appreciate this demonstration.
• The Unit Circle - Graphs of basic trig functions are shown, as generated by the unit circle, using degrees and radians.
• Player Piano - This is a very cool document that plays Beethoven's Ode to Joy from a GSP document. Transpose the tune up or down, speed it up or slow it down. Download the document into Sketchpad 5 and follow the included instructions to create your own melody.

The Geometer's Sketchpad Resource Center is a tremendous resource for math teachers. 

http://www.dynamicgeometry.com/

Sketch Exchange is a free online community for sharing Sketchpad activities, tips, questions, and ideas.  Upload your activities or download activities created by others.

http://sketchexchange.keypress.com/

The Sketchpad LessonLink is a subscription service, providing access to Sketchpad activities and how-to videos.    http://www.keypress.com/x26771.xml