Comparing Area and Perimeter

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1 Getting Started
2 Watch and Notice
3 Draw the Two Rectangles in Your Copy
4 Try It Together
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started Here are two rectangles drawn on squared paper.

Rectangle A: a long thin strip, 1 square tall and 6 squares long.
Rectangle B: a chunky block, 2 squares tall and 3 squares long.

Count the squares inside each one.

Now have a think before we work anything out: if an ant walked all the way around the edge of each one, would it walk the same distance both times? Hands up for your guess.

Teacher Notes

Take three hands-up guesses, not open call-outs. Do not settle the question yet — this is a genuine prediction, and pupils should stay unsure.

Both shapes cover 6 squares, so it is tempting to assume the way around must match too. Hold that tension; the lesson exists to test it.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Let's look at these rectangles together. For each one, count the squares that fit inside (that is the area) and then walk right around the edge, adding every side (that is the perimeter). The first two shapes cover the same area, so watch what happens to the distance around. The third one is a bigger shape where both the area and the perimeter are different, so keep an eye on both numbers.

Teacher Notes

Do NOT name the rule yet. Work each shape live: count inside for area, walk the edge adding sides for perimeter. Pause before revealing each perimeter so the class can predict.

1 by 6 — area 6, perimeter 14. Ask the class to notice how much edge is on the outside of a long thin shape.
2 by 3 — same area 6, but perimeter only 10. This is the moment the guess from the hook gets tested.
3 by 3 — a bigger area (9), so pupils don't over-conclude that area is fixed while perimeter changes; here both differ. The description flags this on screen too.

Only after the 2 by 3 lands should you draw the class toward naming what they saw: same area, different distance around. Let a pupil say it before you do.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Draw the Two Rectangles in Your Copy ~3 mins

COPYBOOK MOMENT

Illustration for Draw the Two Rectangles in Your Copy In your squared copy, draw two different rectangles that each cover 8 squares. Write the perimeter beside each one, then ring the rectangle with the longer way around.

Teacher Notes

Walk the room glancing for two genuinely different rectangles (e.g. 1 by 8 and 2 by 4) and correct perimeter sums. This is whole-class copybook practice, not marking — no individual assessment.

+10 XP

4 - Try It Together ~8 mins

Today we build these rectangles on one shape-measurer. We drag the corners to change each shape into the next. We will work three shapes in turn. First a 2 by 4 rectangle. Then a 1 by 8. Then a 3 by 3. For each one, count the area inside. Then add the sides for the perimeter. Say out loud whether the distance around is getting longer or shorter as the shape changes.

Shape Measurer

Teacher Notes

There is one shape-measurer here, seeded with the 2 by 4. Pupils take turns at the board and drag the corners to build each next rectangle from the one before — the class agrees or corrects out loud.

For each rectangle, have the pupil at the board read the area first, then the perimeter. Ask the class to predict the perimeter before the pupil drags to the next shape. The 1 by 8 has the same area as the 2 by 4 (8 squares) but a longer way around — hold out for a pupil to spot that.

Listen for pupils muddling the two words; revoice cleanly — area is the squares inside, perimeter is the walk around the edge.

+15 XP

5 - Class Challenge ~8 mins

Key point

Here is the investigation. Each time, use exactly 12 square tiles. Where you have your own tiles, work on your own; where a group of four shares one set of 12, take turns arranging them. Make as many different rectangles as you can and write down the area and the perimeter of each one.

First, make any rectangle from all 12 tiles and record its area and perimeter.
Then find a second, different rectangle from the same 12 tiles.
Which of your rectangles has the smallest distance around?
Explain why the area stayed 12 every single time while the perimeter kept changing.

Using exactly 12 square tiles each time, how many different rectangles can you make, and what is the area and perimeter of each?

Give each pupil 12 square tiles (or 12 shaded squares on squared paper) where possible; where tiles are short, seat pupils in groups of four sharing one set of 12 and take turns. They arrange all 12 into a rectangle, record the sides, the area and the perimeter, then rearrange into a different rectangle and record again. Repeat to find every rectangle possible from 12 tiles (1 by 12, 2 by 6, 3 by 4). Individual pupils bring one rectangle to the board to record its measurements for the class.

Make any rectangle from all 12 tiles and record its area and perimeter.
Find a second, different rectangle from the same 12 tiles.
Which of your rectangles has the smallest distance around?
Why did the area stay 12 every time while the perimeter changed?

Ways to start:

Lay all 12 tiles in a single long row — what are the sides of that rectangle?
Try two rows of 6 tiles — how does the shape look now?

Stretch:

Put your rectangles in order from the longest way around to the shortest — what do you notice about their shapes?
If you had 16 tiles instead, which rectangle would have the shortest perimeter?

Record: table with columns: sides (e.g. 2 by 6), area (squares), perimeter (units)

Answers & strategies (teacher)

Make any rectangle from all 12 tiles and record its area and perimeter. — For example 2 by 6: area 12 squares, perimeter 2 + 6 + 2 + 6 = 16.
Find a second, different rectangle from the same 12 tiles. — 3 by 4: area 12 squares, perimeter 3 + 4 + 3 + 4 = 14 (or 1 by 12: area 12, perimeter 26).
Which of your rectangles has the smallest distance around? — The 3 by 4 rectangle, with a perimeter of 14 — the chunkiest rectangle has the shortest way around.
Why did the area stay 12 every time while the perimeter changed? — The 12 tiles never went away, so the space covered (area) stayed 12; but spreading them into a long thin shape puts more tile edges on the outside, making the distance around longer.

Teacher Notes

This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.

Grouping: pupils with their own 12 tiles work individually; where tiles are short, seat groups of four sharing one set of 12 and take turns. Either way, each pupil brings one rectangle to the board.

Every pupil enters — anyone can lay 12 tiles into one rectangle. The stretch is finding all three rectangles and ordering them. Circulate and prompt: can you make a different rectangle from the same tiles?

The key one you are steering toward: the long thin 1 by 12 has the longest perimeter (26), the chunky 3 by 4 has the shortest (14), yet every one covers 12 squares. Let a pupil articulate why before you revoice it.

+15 XP

Pupil practice

Module 5 · Area, Perimeter and Volume Measures

Lesson 57 · Comparing Area and Perimeter

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This lesson is copyright of Coding Ireland 2017 - 2025. Unauthorised use, copying or distribution is not allowed.

Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

3 - Draw the Two Rectangles in Your Copy ~3 mins

4 - Try It Together ~8 mins

Shape Measurer

5 - Class Challenge ~8 mins

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