Teacher Guide: Transformations

Learning Objective 5-10 min lesson

Students will: Identify and describe translations, reflections, rotations, and dilations; use coordinate notation to describe transformations; determine if transformations result in congruent or similar figures; and describe sequences of transformations.

Why this matters for FAST: Transformations are heavily tested on FAST. Students must understand the difference between rigid transformations (which preserve size) and dilations (which change size), and express transformations using coordinate notation.

Materials Needed

Whiteboard/projector
Student Concept Worksheet
Graph paper
Rulers and protractors
Tracing paper (optional)
Coordinate plane handouts

Common Misconceptions to Address

Misconception #1: All transformations change size

Students think all transformations make figures bigger or smaller. They confuse dilations with other transformations.

How to Address:

"Only DILATIONS change size. Translations, reflections, and rotations are RIGID transformations - they preserve size and shape. Remember: Rigid = same size, same shape (congruent). Dilation = same shape, different size (similar)."

Misconception #2: Confusing reflection over x-axis vs y-axis

Students mix up which coordinate changes when reflecting over each axis.

How to Address:

"Think of the axis as a mirror. Reflecting over the x-axis? The y-coordinate changes sign (x, y) to (x, -y). Reflecting over the y-axis? The x-coordinate changes sign (x, y) to (-x, y). The coordinate that shares a letter with the axis stays the same!"

Misconception #3: Rotation direction confusion

Students confuse clockwise vs counterclockwise rotations, or don't know which way is positive.

How to Address:

"Counterclockwise is the POSITIVE direction (like the unit circle). 90 degrees counterclockwise: (x, y) becomes (-y, x). 90 degrees clockwise: (x, y) becomes (y, -x). Remember: clocks go the NEGATIVE direction!"

Lesson Steps

1

Activate Prior Knowledge (1 min)

Review coordinate planes and plotting points. Ask: "If I move a point 3 units right and 2 units up, what happens to its coordinates?"

2

Introduce the Four Transformations (3 min)

SAY THIS:

"There are four main ways to transform a figure: Translation (slide), Reflection (flip), Rotation (turn), and Dilation (resize). The first three keep the figure the same size - we call them RIGID transformations."

The Four Transformations

Translation: (x, y) → (x + a, y + b) - slide every point the same amount

Reflection: over x-axis: (x, y) → (x, -y) | over y-axis: (x, y) → (-x, y)

Rotation 90° CCW about origin: (x, y) → (-y, x)

Dilation: (x, y) → (kx, ky) where k is the scale factor

3

Congruence vs Similarity (2 min)

Rigid Transformations → CONGRUENT figures

Translations, Reflections, Rotations preserve size and shape

Dilations → SIMILAR figures

Same shape, different size (unless scale factor = 1)

4

Coordinate Notation Practice (2 min)

Work through examples together:

Point A(3, 4) translated 5 left, 2 up: A'(3-5, 4+2) = A'(-2, 6)
Point B(2, -3) reflected over x-axis: B'(2, 3)
Point C(4, 1) dilated by scale factor 2: C'(8, 2)

5

Sequences of Transformations (2 min)

Show how to apply multiple transformations in order. Emphasize that order matters! Demonstrate: translate then reflect gives a different result than reflect then translate.

Check for Understanding

Quick Exit Ticket:

"A triangle is reflected over the y-axis, then translated 3 units down. Is the final image congruent or similar to the original?"

Correct answer: Congruent. Both reflection and translation are rigid transformations that preserve size and shape.

IXL Skills to Assign

Recommended IXL Practice:

Translations: find the coordinates Reflections: find the coordinates Rotations: find the coordinates Dilations: find the coordinates Identify transformations Sequences of transformations

Differentiation & Extension

For struggling students: Focus on one transformation at a time. Use tracing paper to physically move figures. Practice with single points before whole shapes.

For advanced students: Challenge them with compositions of transformations, finding the single transformation equivalent to a sequence, or exploring transformations with matrices.

For home: Send Parent Activity sheet. Families can explore symmetry in art and nature.