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Math lesson plan · 3rd grade (Year 4 in England) · 60 minutes

Same area, different perimeter (and the other way round)

Geometry

CCSS 3.MD.D.8England: Y4 Measurement

Objective and success criteria

Students will: Same area, different perimeter (and the other way round).

  • 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: Area of rectangles; Perimeter

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 (Area of rectangles; Perimeter). 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: Same area, different perimeter (and the other way round). 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: Rectangle A is 1 cm by 16 cm. Rectangle B is 2 cm by 8 cm. They have the same area. Which has the greater perimeter?
  • Step 1: A: 2 × (1 + 16) = 34 cm
  • Step 2: B: 2 × (2 + 8) = 20 cm
  • Step 3: Rectangle A
  • Answer: Rectangle A
  • 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. Rectangle A is 3 cm by 10 cm. Rectangle B is 5 cm by 6 cm. They have the same area. Which has the greater perimeter? (Rectangle A / Rectangle B) → Rectangle APrompt: Perimeter = add all four sides.
  2. Two rectangles both have a perimeter of 20 cm. One is 4 cm by 6 cm, the other is 5 cm by 5 cm. What is the difference between their areas, in cm²? → 1Prompt: Find each area: length × width.

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. Rectangle A is 3 cm by 6 cm. Rectangle B is 1 cm by 18 cm. They have the same area. Which has the greater perimeter? (Rectangle A / Rectangle B) → Rectangle BPrompt: Perimeter = add all four sides.
  2. Two rectangles both have a perimeter of 16 cm. One is 3 cm by 5 cm, the other is 4 cm by 4 cm. What is the difference between their areas, in cm²? → 1Prompt: Find each area: length × width.

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: Area of rectangles.
  • 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-3.

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

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Same area, different perimeter (and the other way round)

Name

Date

Score/ 8

  1. Question 1

    Rectangle A is 1 cm by 16 cm. Rectangle B is 4 cm by 4 cm. They have the same area. Which has the greater perimeter?

    • A. Rectangle A
    • B. Rectangle B

  2. Question 2

    Two rectangles both have a perimeter of 24 cm. One is 5 cm by 7 cm, the other is 6 cm by 6 cm. What is the difference between their areas, in cm²?

    Answer

  3. Question 3

    Sofia says: "If two rectangles have the same area, they must have the same perimeter." True or false? (Think about 1 × 12 and 12 × 1.)

    • A. true
    • B. false

  4. Question 4

    Rectangle A is 2 cm by 8 cm. Rectangle B is 4 cm by 4 cm. They have the same area. Which has the greater perimeter?

    • A. Rectangle A
    • B. Rectangle B

  5. Question 5

    Two rectangles both have a perimeter of 12 cm. One is 1 cm by 5 cm, the other is 3 cm by 3 cm. What is the difference between their areas, in cm²?

    Answer

  6. Question 6

    Kai says: "If two rectangles have the same area, they must have the same perimeter." True or false? (Think about 3 × 4 and 12 × 1.)

    • A. true
    • B. false

  7. Question 7

    Rectangle A is 2 cm by 9 cm. Rectangle B is 1 cm by 18 cm. They have the same area. Which has the greater perimeter?

    • A. Rectangle A
    • B. Rectangle B

  8. Question 8

    Maya says: "If two rectangles have the same area, they must have the same perimeter." True or false? (Think about 2 × 8 and 16 × 1.)

    • A. true
    • B. false

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Answer key: Same area, different perimeter (and the other way round)

  1. 1. A. Rectangle A

  2. 2. 1

  3. 3. B. false

  4. 4. A. Rectangle A

  5. 5. 4

  6. 6. B. false

  7. 7. B. Rectangle B

  8. 8. B. false