Single Transformations
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.
Formalize
Coordinate transformation: shape with vertices at (2,1), (4,1), (4,3). Translate by (3 right, 1 up): new vertices at (5,2), (7,2), (7,4). Reflect across x=0: new vertices at (-5,2), (-7,2), (-7,4). These precise descriptions allow shapes to be reconstructed without diagrams.
Single Transformations
Distinguish transformations: translation preserves orientation (the shape points the same way). Reflection reverses orientation (a right-facing shape becomes a left-facing shape). Rotation can preserve or change apparent orientation depending on the angle. Students identify which transformation was applied from a before/after diagram.
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
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?
Step 1: Draw triangle ABC on the grid: A(1,6), B(3,6), C(2,8) — label the vertices; transformations are tracked vertex by vertex.
Step 2: Apply the translation "5 right, 2 down" to EACH vertex: A(1,6) → A′(6,4); B(3,6) → B′(8,4); C(2,8) → C′(7,6). (Right adds to the first number; down subtracts from the second.)
Step 3: Join A′B′C′ and compare: same side lengths, same angles, same orientation — the triangle didn't turn or flip; every point just took the identical trip. Draw one arrow from A to A′: that ONE arrow is the whole story (all points ride the same arrow).
Step 4: The property to name: translations preserve everything except location. Size ✓ shape ✓ direction it faces ✓.
Check task: "B′ of some translation is (0,0) and B was (4,3) — describe the slide." (4 left, 3 down — read the arrow backwards.)
Step 1: Draw a flag shape left of the vertical mirror line x = 5 (a pole with a triangular pennant pointing RIGHT toward the line).
Step 2: Reflect vertex by vertex — measure each point's distance to the mirror, then walk the SAME distance beyond: a vertex 2 squares left of the line lands 2 squares right; a vertex ON the line stays put.
Step 3: Inspect the image: the pennant now points LEFT. Reflections reverse orientation — the image is the shape's mirror twin, not a slid copy. (Hold the page to a real mirror to confirm the drawing.)
Step 4: The error to catch in the room: students who COPY the flag across (pennant still pointing right) have translated, not reflected. The tell is always orientation.
Step 5: The double-flip surprise: reflect the image over the SAME line — it returns home exactly. Then: reflect over x = 5 and then x = 9 — the flag ends up… translated (8 right)! Two mirrors make a slide; let them discover it and try to explain why (each mirror pushes it 2× its distance).
Step 1: Draw an L-shape with a marked corner P at (4,4), the rotation centre ON the shape's corner. Rotating about a point of the shape itself keeps that point frozen.
Step 2: Rotate 90° clockwise: the trick that makes it precise — for each vertex, walk from P: "3 right" becomes "3 down," "2 up" becomes "2 right" (clockwise quarter-turn swaps the walk's directions: right→down, up→right, left→up, down→left). Map two or three key vertices this way and rebuild the L.
Step 3: Verify with tracing paper: trace the original, pin your pencil at P, turn the paper a quarter turn — the trace should land exactly on your drawn image. Tracing paper is the honest referee for every rotation dispute.
Step 4: Inventory what changed: location of most points ✓ changed; the direction the L faces ✓ changed; size and shape ✗ unchanged; the point P ✗ unmoved.
Step 5: The classification wrap-up across all three lessons: slides, flips, turns — each moves shapes WITHOUT distorting them (congruence movers). Which ones can change orientation? Only the flip. Which leave a point fixed? The turn (its centre) — and the flip (its whole mirror line). Structure, tabulated by the class.