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Math lesson plan · 8th grade (Year 9 in England) · 45 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 · 5 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 · 5 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 · 10 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 · 10 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) → (x, −y)? (Rotation of 90° anticlockwise about the origin / Translation / Reflection in the x-axis / Rotation of 180° about the origin) → Reflection in the x-axisPrompt: Try it on a point such as (2, 1) and sketch the result.
  2. After a reflection, 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.

You do: independent practice · 10 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 · 5 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) → (x + 2, y)? (Translation / Dilation with scale factor 3 / Rotation of 90° anticlockwise about the origin / Reflection in the x-axis) → TranslationPrompt: Try it on a point such as (2, 1) and sketch the result.
  2. After a translation, 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

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

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

  2. Question 2

    After a dilation with scale factor 1/2, is the image congruent to the original (same size and shape)?

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

  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 − 4, y)?

    • A. Dilation with scale factor 4
    • B. Translation
    • C. Rotation of 180° about the origin
    • D. Rotation of 90° anticlockwise about the origin

  5. Question 5

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

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

  6. Question 6

    After a translation, 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. Dilation with scale factor 3
    • C. Reflection in the x-axis
    • D. Reflection in the y-axis

  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. D. Reflection in the x-axis

  2. 2. B. No, only similar

  3. 3. A. Yes, congruent

  4. 4. B. Translation

  5. 5. A. Yes, congruent

  6. 6. A. Yes, congruent

  7. 7. D. Reflection in the y-axis

  8. 8. B. No, only similar