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Math lesson plan · 8th grade (Year 9 in England) · 30 minutes

Translations, reflections and rotations

Geometry

CCSS 8.G.A.1CCSS 8.G.A.3England: KS3 GeometryEngland: GCSE Foundation Geometry

Objective and success criteria

Students will: Translations, reflections and rotations.

  • 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: Coordinates in all four quadrants

Leads to: Congruent triangles; Vectors; Transformations of functions

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

Warm-up · 4 min

  • Quick retrieval from earlier learning (Coordinates in all four quadrants). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. In which quadrant is the point (−3, 1)? (I / II / III / IV) → IIPrompt: Quadrants are numbered anticlockwise starting top right.
  2. In which quadrant is the point (−4, −2)? (I / II / III / IV) → IIIPrompt: Quadrants are numbered anticlockwise starting top right.
  3. In which quadrant is the point (−6, 6)? (I / II / III / IV) → IIPrompt: Quadrants are numbered anticlockwise starting top right.

Hook · 3 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: Translations, reflections and rotations. Read the success criteria together.

I do: model it · 7 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Model one question from the student sheet, thinking aloud.
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 6 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.

You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.

Exit ticket · 3 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

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: Coordinates in all four quadrants.
  • 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

  • Move on to: Congruent triangles; Vectors; Transformations of functions.
  • 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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Translations, reflections and rotations

Name

Date

Score/ 6

  1. Question 1

    Reflect (1, 5) in the line y = x. Type the image like (2, −1).

    xy−10−8−6−4−2246810−10−8−6−4−22468100y = xP

    Answer

  2. Question 2

    Rotate (7, 3) by 90° anticlockwise (counterclockwise) about the origin. Type the image like (2, −1).

    xy−10−8−6−4−2246810−10−8−6−4−22468100P

    Answer

  3. Question 3

    Translate the point (−7, 7) by 4 left and 5 up. Where does it end up? Type it like (2, −1).

    xy−12−6612−12−66120P

    Answer

  4. Question 4

    Reflect (−1, −4) in the x-axis. Type the image like (2, −1).

    xy−10−8−6−4−2246810−10−8−6−4−22468100P

    Answer

  5. Question 5

    Rotate (−6, 4) by 90° clockwise about the origin. Type the image like (2, −1).

    xy−10−8−6−4−2246810−10−8−6−4−22468100P

    Answer

  6. Question 6

    Translate the point (2, 1) by 1 left and 4 up. Where does it end up? Type it like (2, −1).

    xy−12−6612−12−66120P

    Answer

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Answer key: Translations, reflections and rotations

  1. 1. (5, 1)

  2. 2. (−3, 7)

  3. 3. (−11, 12)

  4. 4. (−1, 4)

  5. 5. (4, 6)

  6. 6. (1, 5)