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Single Transformations

5 min readGrade 5 · Geometry

Transformations are motions that move shapes without changing their size. A translation slides a shape in a direction; a reflection flips it across a line; a rotation turns it around a point. All three preserve the shape's size and angles: the image is congruent to the original. First Peoples weaving and cedar basket patterns frequently use systematic transformations to create repeating designs, demonstrating that transformation thinking is embedded in artistic practice.

Three transformation types

Translation (slide): every point moves the same distance in the same direction. Reflection (flip): every point moves to the mirror image position across a line. Rotation (turn): every point moves through an angle around a fixed centre point. All three produce a congruent image: same size and shape, different position (and possibly orientation).

Describing transformations precisely

A translation of (3 right, 2 up): every point moves 3 units right and 2 units up. A reflection across the y-axis: each point's x-coordinate changes sign. A 90-degree clockwise rotation about the origin. Precision in description is the competency: not just moved but 3 units right and 2 up; not just flipped but across the vertical line through x=4.

First Peoples weaving and transformation

Cedar basket and Chilkat blanket weaving uses systematic reflections and translations to create complex bilateral and rotational symmetric designs. Each repeated unit is a transformation of the previous one. Students who understand transformations can analyze these patterns mathematically and appreciate the design thinking embedded in the artform. Invite a local weaver to share the design process.

KEY VOCABULARY
TranslationA transformation that slides every point the same distance in the same direction.
ReflectionA transformation that flips a shape across a line, creating a mirror image.
RotationA transformation that turns a shape around a fixed point by a given angle.
ImageThe resulting shape after a transformation is applied.