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Math lesson plan · 6th grade (Year 7 in England) · 45 minutes

Lengths, perimeters and areas from coordinates

Geometry

CCSS 6.G.A.3CCSS 6.NS.C.8England: KS3 Geometry and measures

Objective and success criteria

Students will: Lengths, perimeters and areas from coordinates.

  • 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; Distance between two integers

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 (Coordinates in all four quadrants; Distance between two integers). 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: Lengths, perimeters and areas from coordinates. 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: Point A is (4, −3). Point B is directly below A, 9 units away. What are the coordinates of B? Type them like (2, −3).
  • Step 1: −3 − 9 = −12
  • Step 2: (4, −12)
  • Answer: (4, −12)
  • 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. Point A is (7, −3). Point B is directly below A, 6 units away. What are the coordinates of B? Type them like (2, −3). → (7, −9)Prompt: Moving straight up or down changes only the y-coordinate.
  2. Point A is (−5, −3). Point B is directly below A, 5 units away. What are the coordinates of B? Type them like (2, −3). → (−5, −8)Prompt: Moving straight up or down changes only the y-coordinate.

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. Point A is (1, −7). Point B is directly above A, 8 units away. What are the coordinates of B? Type them like (2, −3). → (1, 1)Prompt: Moving straight up or down changes only the y-coordinate.
  2. Point A is (5, 0). Point B is directly above A, 4 units away. What are the coordinates of B? Type them like (2, −3). → (5, 4)Prompt: Moving straight up or down changes only the y-coordinate.

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

  • 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-6.

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

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Lengths, perimeters and areas from coordinates

Name

Date

Score/ 8

  1. Question 1

    A rectangle has vertices (−6, −5), (7, −5), (7, 6) and (−6, 6). What is its area, in square units?

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

    Answer

  2. Question 2

    Point A is (0, 0). Point B is directly above A, 4 units away. What are the coordinates of B? Type them like (2, −3).

    Answer

  3. Question 3

    How long is the line segment from (−9, 3) to (1, 3)?

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

    Answer

  4. Question 4

    A rectangle has vertices (−3, −5), (6, −5), (6, 3) and (−3, 3). What is its perimeter, in units?

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

    Answer

  5. Question 5

    Point A is (−6, −7). Point B is directly below A, 5 units away. What are the coordinates of B? Type them like (2, −3).

    Answer

  6. Question 6

    How long is the line segment from (−5, 4) to (5, 4)?

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

    Answer

  7. Question 7

    A rectangle has vertices (−6, −8), (2, −8), (2, 3) and (−6, 3). What is its perimeter, in units?

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

    Answer

  8. Question 8

    Point A is (−4, −3). Point B is directly below A, 7 units away. What are the coordinates of B? Type them like (2, −3).

    Answer

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Answer key: Lengths, perimeters and areas from coordinates

  1. 1. 143

  2. 2. (0, 4)

  3. 3. 10

  4. 4. 34

  5. 5. (−6, −12)

  6. 6. 10

  7. 7. 38

  8. 8. (−4, −10)