Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to nctm.org/illuminations. Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on nctm.org.

## Shape Tool

Pre-K-2, 3-5, 6-8
Standards:
Math Content:
Geometry

This tool allows you to create any geometric shape imaginable. Squares, triangles, rhombi, trapezoids and hexagons can be created, colored, enlarged, shrunk, rotated, reflected, sliced, and glued together. What design can you create?
This interactive is optimized for your desktop and tablet.

• You can double-click any of the shapes along the top and it will automatically appear on the canvas, or you can click-and-drag a shape to any location.

### Toolbar

• Scissors – This tool takes 3 clicks to use.
1. Click a location on the canvas.
2. Move the cursor across a shape and click again to complete a cut line.
3. Finally, click on a shape that is covered by the line, and the shape will be cut into two pieces.
• Glue – Click one shape, and then click an overlapping shape. The two will become one.
• Eraser – Click on any shape, and it will be removed from the canvas.
• Rotate – Click on any shape, and it will be rotated 30° clockwise.
• Horizontal Reflect – Click on any shape to reflect it about a horizontal axis.
• Vertical Reflect – Click on any shape to reflect it about a vertical axis.
• Line Reflect – Move the line by adjusting the two dots. Then, click on a shape to reflect it over the line.
• Mirror – Like the Line Reflect, shapes will be reflected about the line. The difference, however, is that a new shape will not be created. This feature is merely to explore what happens with a reflection.
• Plus/Minus – With the +/– buttons turned on, click on a shape to increase or decrease its size.
• Paint – Select a color, and then click on a shape to change its color.
• Snap – Turn this button on to make objects snap in place with other objects.
• ClearThis is a dangerous button! Pressing it will remove all objects from the canvas.

A tessellation is a pattern of shapes that tiles a plane with no gaps and no overlaps. Each of the six shapes available in this tool are able to tessellate. That is, you can arrange multiple copies of any of the shapes to completely cover the plane.

But is it possible to do that with some combination of shapes? The image above shows one possible arrangement of yellow hexagons and red trapezoids.

• Can you use only orange squares and green triangles to create a regular pattern that tessellates?
• What about yellow hexagons and orange squares?
• …red trapezoids and blue parallelograms?
• …blue parallelograms and pink rhombi?