LESSON PLAN

Single Transformations

Apothem Team

Grade 5 · Geometry

LESSON AT A GLANCE

Warm-up

5 min

Explore

15 min

Consolidate

10 min

Practice

12 min

Exit ticket

3 min

Warm-up

Show a shape on a grid. Slide it 4 squares right. Where are the new vertices? (Add 4 to every x-coordinate.) Now reflect it across a vertical line. Where are the new vertices? (Change the x-sign relative to the line.) Now rotate 90 degrees clockwise. (Switch x and y, then negate the new x.) All three transformations produce a congruent image.

Explore

Weaving pattern analysis: show a cedar basket design. Identify: which transformation takes one design unit to the next? (Translation? Reflection? Rotation? Glide reflection?) Students identify the transformation and describe it precisely. Then attempt to replicate a simplified version of the pattern using the identified transformation.

Consolidate

Practice

Students perform each of the three transformations on 2 shapes, describe each transformation precisely, and identify transformations in 3 weaving pattern samples. Exit ticket: translate the point (5, -2) by (-3 right, 4 up). What is the image?

Exit ticket

TIP Use concrete materials for initial exploration: tracing paper for rotation, a Mira for reflection, a sliding template for translation. The physical experience must precede the coordinate description.

WORKED EXAMPLES

A triangle has vertices at (1,2), (3,2), (2,4). Translate by (2 right, -3 down). Find new vertices.

Add 2 to x and -3 to y for each vertex. (3,-1), (5,-1), (4,1).

A shape is reflected across the y-axis. Its vertex was at (4,3). Where is the image vertex?

(-4,3). Reflection across the y-axis negates the x-coordinate, keeping the y-coordinate unchanged.

MATERIALS

•Dot paper and grid paper

•Transparent mirrors (Miras)

•Tracing paper for rotations

•First Peoples weaving pattern images

•Coordinate grid paper

WATCH FOR

!Students may confuse reflection (mirror image) and rotation (turned). A reflected shape has reversed orientation (like a handprint flipped); a rotated shape has the same orientation just turned.

!Students may translate only some vertices and not all. All vertices of a shape must undergo the same translation vector.