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.
- Rectangle A is 2 cm by 9 cm. Rectangle B is 3 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.
- Two rectangles both have a perimeter of 16 cm. One is 1 cm by 7 cm, the other is 4 cm by 4 cm. What is the difference between their areas, in cm²? → 9Prompt: 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.
- Ava says: "If two rectangles have the same area, they must have the same perimeter." True or false? (Think about 4 × 4 and 16 × 1.) (true / false) → falsePrompt: Both have area 16. Work out both perimeters.
- 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? → 4Prompt: 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