Mathematics 6

# Surf for More Math

## Lesson 6 - Creating Designs

To encourage students to have fun on the Web while learning about Creating Designs, here are some games and interactive activities they can do on their own or in pairs.

### Goal

Create a design by performing translations on a basic shape.

### Builds Upon

Student Book pages 432-433

### Instructions for Use

Quiltmaker is an interactive program that allows students to design a quilt by repeating, rotating and reflecting shapes.

To use Quiltmaker, click on the triangles in the workspace. Click the 'Rotate' button to flip the shapes. Click the 'Reflect' or 'Repeat' buttons to extend the pattern in the quilt. Change the colour by clicking on the colour palettes. Click the 'Erase' to start over. Click 'Index' to show different patterns.

Transformation - Rotation lets students create a design by performing transformations of a basic shape.

To change the rotation angle, click and drag the black dot on the side of the angle. The first original is visually connected to its image by the rotation arc. When another object is placed on the workspace, its rotated image appears also. You can move the new original or the translation vector to make the image show in the workspace.

To move the centre of rotation, click and drag the vertex of the rotation angle. The original object remains fixed, and the size of the angle is unchanged. The effect is to shrink or enlarge the circular path from the original to its image. You can also drag the original object, and the rotation angle and rotated image are dragged along.

To place and move new objects in workspace, c lick on any desired shape button. Each piece enters separately. When the first object is placed on the workspace, the rotation angle and a white arc of a circle shows how the original is turned to its image. When more objects are entered, they are rotated through the same angle as the first, but the circular arc is attached only to the first object. You can select, slide, or rotate each original object individually, and its rotated image follows.

To delete objects, select an original object or group by clicking on it (black dots show what is selected), then click the ' Delete ' button.

To group or ungroup original objects, c lick and hold down the mouse button to "lasso" (draw a rectangle around) two or more original objects, then release. The objects grouped now move and rotate (about their common center) together. To ungroup, click on the group to select it, and Shift-Click.

To show axes, click the box at the bottom of the screen. The lattice points in the background of the workspace are for convenience in visualizing the effects of a rotation.