Look at this rectangle. The top is labelled 6 cm and one side is labelled 3 cm. The other two sides have no numbers on them yet.
What must those two sides be? And how can you be so sure without measuring them?
Display the rectangle labelled only along the top (6 cm) and down one side (3 cm). Take three hands-up answers, not open call-outs. Listen for pupils who say the opposite sides must match.
Look at these three shapes. Watch how we count the sides to find the way around each one, and notice which sides match.
6 by 3 rectangle: point to each side as you add, 6 + 3 + 6 + 3. Long sides match, short sides match. Perimeter 18 cm.
Square, side 5: it's a special rectangle, all four sides equal, so 4 lots of 5 = 20 cm.
7 by 2 rectangle: fill in the two missing sides first, then add, 7 + 2 + 7 + 2 = 18 cm.
Each side once, never twice. Ask which sides match before adding.
Let's work through some rectangles together. I'll set the two sides each time, and you fill in the matching opposite sides and read off the perimeter. Each time, check that the two opposite sides really do match before you add.
This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.
The interactive starts on a 4 cm by 3 cm rectangle. After the first pupil reads its perimeter, drag the rectangle's corner handles to re-set new given sides for the next pupil. Run four or five rectangles in turn (for example 4 by 3, then 5 by 2, then 6 by 4, then 3 by 3, then 8 by 2), each time asking the pupil at the board to fill in the matching opposite sides first, then read off the perimeter. Have the class confirm each opposite pair matches before the total is read. Watch for the common slip of measuring all four sides as if they were different.
In your maths copy, draw a 5 cm by 3 cm rectangle. Write the length on all four sides, then write the perimeter sentence with its total underneath.
Walk the room glancing at whether pupils have written a number on every side and added each one once — this is whole-class copybook practice, not marking.
Let's work through these shapes together, one at a time: a 4 cm by 4 cm square, a 6 cm by 3 cm rectangle, a 7 cm by 4 cm rectangle, and an L-shape made from two rectangles. For each shape we look at, find the hidden sides first, then add all the way around.
L-shape worked example first: a 6 cm by 4 cm rectangle with a 2 cm by 2 cm square cut out of the top-right corner. The bottom is 6 cm, the left side is 4 cm, and both cut edges are 2 cm. The top and the right side have no number on them, so take 2 cm off the side each one lines up with: top = 6 − 2 = 4 cm, right = 4 − 2 = 2 cm. Now add all six sides once, going around: 6 + 2 + 2 + 2 + 4 + 4 = 20 cm.
After that model, use the same steps on each board shape that follows.
Find the perimeter of each of these shapes by filling in any missing sides first, then adding all the way around.
Ways to start:
Stretch:
Practice round: pupils take turns at the board, class confirms before moving on. Run the square and two rectangles briskly first. Then stop and model the L-shape fully on the board before any pupil tries it.
L-shape model: Sketch the L. Label known sides: bottom 6 cm, left 4 cm, both cut edges 2 cm. Hidden top = 6 − 2 = 4 cm. Hidden right = 4 − 2 = 2 cm. Point around once: 6 + 2 + 2 + 2 + 4 + 4 = 20 cm. Six sides, each once.
Slip to watch: adding only four outer sides, or counting a cut edge twice. Keep asking: which sides are hidden, and how do you find them? The 7 by 4 rectangle is new practice, give it a moment more.
If you know the long side and the short side of a rectangle, why don't you need to measure the other two sides at all?
Listen for pupils naming the two pairs of matching sides as the reason. Revoice a strong answer: so the opposite sides are always equal, which means two measurements tell us all four. Head off the idea that every side must be measured separately.
Next we move from the way around a shape to the space inside it, counting square units to find area.
Keep this brief. Tie the missing-side idea back to the L-shape in the challenge — finding hidden sides will matter again for more complex shapes.
You're previewing this lesson. Get full access to this lesson and hundreds more — each one ready to teach, with interactive activities, printable resources and pupil progress tracking built in.