Area and Perimeter: Area or Perimeter? — Year 4 Lesson Plan
National Curriculum: Mathematics — Measurement, Year 4: measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres; find the area of rectilinear shapes by counting squares
Overview
The last of four Area and Perimeter lessons. Pupils decide whether a real-life problem needs area or perimeter, find both the area and the perimeter of rectilinear shapes on squared paper, and compare shapes by each measure. They notice that the shape with the greater area does not always have the greater perimeter.
Area and Perimeter: Area or Perimeter? learning objectives
- Decide whether a problem needs area or perimeter.
- Find both the area and the perimeter of rectilinear shapes on squared paper.
- Compare shapes by their area and by their perimeter.
- Use the correct units: cm or m for perimeter, cm² for area.
Success criteria
- I can decide whether a problem needs area or perimeter.
- I can find the area and the perimeter of a shape on squared paper.
- I can compare shapes by area and by perimeter.
- I can use cm or m for perimeter and cm² for area.
Key Vocabulary
Suggested Lesson Structure
Sort problem cards into area or perimeter: a fence around a field, carpet for a bedroom floor, ribbon around a cake, turf for a lawn, a frame for a picture, tiles for a kitchen wall. Pupils justify each choice: are we going around the edge, or covering the surface?
Recap: perimeter is a length around the edge (cm or m); area is the surface inside, counted in squares (cm²). On squared paper where each square is 1 cm, model finding the perimeter of a shape by counting the square edges around the outside, and its area by counting the squares inside. Show why counting the squares along the edge does not give the perimeter: a corner square has two edges on the outside. Compare a 1 by 8 strip (area 8 cm², perimeter 18 cm) with a 3 by 3 square (area 9 cm², perimeter 12 cm): the strip has the greater perimeter, but the square has the greater area.
Shape detectives: groups find the area and perimeter of six rectilinear shapes on squared paper, then put the shapes in order by area and in order by perimeter. Discuss: are the two orders the same?
Pupils solve mixed problems, choosing area or perimeter for each: edging for a rectangular flower bed 5 m by 3 m (16 m); how many 1 m square paving slabs cover a patio 4 m by 3 m (12 slabs); ribbon to go around a square card with 15 cm sides (60 cm). Challenge: using 6 square tiles joined edge to edge, make as many different shapes as possible and record each one's area and perimeter (this looks ahead to Year 6).
Whole-unit quiz on mini whiteboards: What is perimeter? What is area? What is the perimeter of a 7 cm by 3 cm rectangle? What is the area of a rectangle 5 squares long and 2 squares wide? Would you use area or perimeter to work out how much carpet to buy? Pupils mark their own answers.
Video for this lesson
Area or Perimeter? | Year 4 Area and Perimeter, Lesson 4 | KS2 Maths (No Narration)
Sorting real problems into area or perimeter, finding both on squared paper, why counting edge squares doesn't give the perimeter, a strip and a square compared, and two real-life problems. Ends with a three-question quiz.
Watch on YouTube →Support and extension for area and perimeter: area or perimeter?
Support
- Use a picture prompt on each problem card: a fence for perimeter, a carpet for area.
- Trace the perimeter in one colour and shade the area in another.
- Give a checklist: “Am I going around the edge, or covering the surface?”
Extension
- Using 6 square tiles joined edge to edge, make different shapes and record each one's area and perimeter. What do you notice? (This looks ahead to Year 6.)
- Write your own area problem and perimeter problem about the school grounds for a partner to solve.
- Find a rectangle with a greater perimeter but a smaller area than a 4 by 4 square.
Check for understanding
Quick questions for the plenary or an exit ticket. Tap a question to see the answer.
1. Would you use area or perimeter to work out how much fence goes around a field?
Answer: Perimeter: the fence goes around the edge.
2. Would you use area or perimeter to work out how much carpet covers a floor?
Answer: Area: the carpet covers the surface.
3. A strip is 1 square wide and 8 squares long. What are its area and perimeter?
Answer: Area 8 cm², perimeter 18 cm.
4. Which has the greater area: a 1 by 8 strip or a 3 by 3 square?
Answer: The 3 by 3 square (9 cm² compared with 8 cm²), even though its perimeter is smaller.
Resources you will need
- Area or perimeter sorting cards
- Six rectilinear shapes on centimetre-squared paper for the guided task
- Mixed problem cards
- Square tiles for the challenge
- Mini whiteboards for the whole-unit quiz
Common Misconceptions
- Counting the squares along the edge to find perimeter. Count the square edges around the outside instead; corner squares have two edges on the outside.
- Using cm for area or cm² for perimeter.
- Thinking a shape with a greater perimeter must have a greater area. Compare a long thin strip with a square.
- Choosing area for problems about going around an edge, such as fencing.
Prior Knowledge
Pupils should already be able to:
- Measure and calculate perimeter (lessons 1 and 2).
- Find area by counting squares and using rows (lesson 3).
- Know the difference between cm and m.
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