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Math lesson plan · 8th grade (Year 9 in England) · 60 minutes

Identify transformations from coordinate rules

Geometry

CCSS 8.G.A.3England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures

Objective and success criteria

Students will: Identify transformations from coordinate rules.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Reflect and rotate points on the coordinate plane; Translate points and describe translations

Leads to: the next skill in this area.

Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 6 min

  • Quick retrieval from earlier learning (Reflect and rotate points on the coordinate plane; Translate points and describe translations). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.

Hook · 6 min

  • Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
  • Share the objective: Identify transformations from coordinate rules. Read the success criteria together.

I do: model it · 12 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: Which transformation is described by (x, y) → (x, −y)?
  • Step 1: Reflection in the x-axis
  • Answer: Reflection in the x-axis
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 12 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. Which transformation is described by (x, y) → (−y, x)? (Dilation with scale factor 3 / Translation / Rotation of 90° anticlockwise about the origin / Rotation of 180° about the origin) → Rotation of 90° anticlockwise about the originPrompt: Try it on a point such as (2, 1) and sketch the result.
  2. After a dilation with scale factor 1/2, is the image congruent to the original (same size and shape)? (Yes, congruent / No, only similar) → No, only similarPrompt: Translations, reflections and rotations keep lengths and angles.

You do: independent practice · 17 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 7 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Which transformation is described by (x, y) → (−y, x)? (Rotation of 90° anticlockwise about the origin / Rotation of 180° about the origin / Reflection in the y-axis / Reflection in the x-axis) → Rotation of 90° anticlockwise about the originPrompt: Try it on a point such as (2, 1) and sketch the result.
  2. After a rotation, is the image congruent to the original (same size and shape)? (Yes, congruent / No, only similar) → Yes, congruentPrompt: Translations, reflections and rotations keep lengths and angles.

Watch out for

  • Thinking a square turned on its corner is no longer a square.
  • Reading the wrong scale on a protractor.

Support and stretch

Support

  • Review first: Reflect and rotate points on the coordinate plane.
  • Use concrete materials: rulers and protractors.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.

Free lesson plan from eurekami.com/lesson-plan-builder

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Identify transformations from coordinate rules

Name

Date

Score/ 8

  1. Question 1

    After a translation, is the image congruent to the original (same size and shape)?

    • A. Yes, congruent
    • B. No, only similar

  2. Question 2

    Which transformation is described by (x, y) → (x + 3, y)?

    • A. Reflection in the x-axis
    • B. Rotation of 180° about the origin
    • C. Reflection in the y-axis
    • D. Translation

  3. Question 3

    After a rotation, is the image congruent to the original (same size and shape)?

    • A. Yes, congruent
    • B. No, only similar

  4. Question 4

    Which transformation is described by (x, y) → (x, −y)?

    • A. Reflection in the x-axis
    • B. Rotation of 90° anticlockwise about the origin
    • C. Translation
    • D. Dilation with scale factor 3

  5. Question 5

    Which transformation is described by (x, y) → (−y, x)?

    • A. Translation
    • B. Rotation of 180° about the origin
    • C. Reflection in the x-axis
    • D. Rotation of 90° anticlockwise about the origin

  6. Question 6

    After a reflection, is the image congruent to the original (same size and shape)?

    • A. Yes, congruent
    • B. No, only similar

  7. Question 7

    Which transformation is described by (x, y) → (−x, −y)?

    • A. Rotation of 90° anticlockwise about the origin
    • B. Translation
    • C. Reflection in the x-axis
    • D. Rotation of 180° about the origin

  8. Question 8

    After a dilation with scale factor 3, is the image congruent to the original (same size and shape)?

    • A. Yes, congruent
    • B. No, only similar

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Answer key: Identify transformations from coordinate rules

  1. 1. A. Yes, congruent

  2. 2. D. Translation

  3. 3. A. Yes, congruent

  4. 4. A. Reflection in the x-axis

  5. 5. D. Rotation of 90° anticlockwise about the origin

  6. 6. A. Yes, congruent

  7. 7. D. Rotation of 180° about the origin

  8. 8. B. No, only similar