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