Here are two different rectangles. Walk your finger all the way around the edge of each one and you would travel exactly the same distance, twelve centimetres, on both. They have the same perimeter.
So here is our real question for today: if the fence around two gardens is the same length, must the two gardens hold the same amount of space inside? Have a think, then hands up. What is your first guess, yes or no?
Confirm the two rectangles are on screen (or quickly sketch them on the board) before you read the opening line, so you have something to point at. Take three hands-up guesses, not open call-outs, and do not confirm which is right. Some pupils will say "yes, of course" and some "no" — that split is exactly the tension the lesson resolves. Write the two guesses on the board so we can return to them at the wrap.
This is a genuine prediction, not a teaser: the answer is discovered by pupils in Watch and Notice, not revealed by you now.
Three shapes coming up, each with the same 12 cm fence around the outside. Before each one, show me your thumb: up if you think it holds more space than the last, sideways if less. Then we count the squares inside.
Don't name the rule up front. Build the three results first, then ask what they notice.
Keep a table going: perimeter 12 each time, areas 5, 8, 9.
1 x 5: fence 1+5+1+5=12, count inside, only 5 squares. Long and thin, least space.
2 x 4: same fence 2+4+2+4=12, two rows of four, 8 squares. Thumbs before the reveal.
3 x 3 square: 3+3+3+3=12, three rows of three, 9 squares, most of all. Pause here so the pattern lands.
Ask: what's happening to the space inside as we go? Revoice a pupil into the rule, closer to a square holds more space though the fence never changed.
Watch for perimeter/area mix-up: point to the edge for one, the inside squares for the other.
Keep saying same fence so the fixed perimeter stays front of mind. Thumbs are their part, no answering aloud.
In your maths copy, draw two different rectangles that each have a perimeter of 10 cm. Then write the area of each one underneath, and circle the rectangle that holds more space.
Walk the room and glance for the fence adding to 10 cm on both, and for two genuinely different shapes (a 1×4 and a 2×3 both work). This is whole-class copybook practice, not marking — do not correct individually, just prompt "does your fence add to ten?" where a shape is wrong.
Now we keep the fence a bit longer, exactly 16 cm, and we hunt for rectangles. We build these together on the board, in order: first the long thin 1 × 7, then the 2 × 6, then the 3 × 5, and finally the 4 × 4 square. Before each one, show me your thumbs guess for its space, then we build it and read the space inside off the tool.
Keep an eye on that very last one, the 4 × 4 square. Before we build it, tell me with your thumbs, do you think it will hold more space or less than the others? Let's build them all and find out.
This round is for talking it through together — individual pupils take turns at the board and the class agrees or corrects out loud. The watching class shows a thumbs prediction before each build; that is their participation.
Individual pupils come up to drag a rectangle to each named size; the class predicts the area before you read it off. Keep saying the fence is always 16 cm so the fixed perimeter stays anchored. Build strictly in the order 1×7 → 2×6 → 3×5 → 4×4 so the areas climb 7 → 12 → 15 → 16 and the square is the key one. Do not name the areas until each is read off the tool.
This is our investigation. We fix the fence at 12 cm and find every whole-number rectangle that fits, then compare the space each one holds. A whole-number rectangle is one whose sides are a whole number of squares, like 2 by 4 (we don't use half-squares).
We work these in order on the board, one job at a time:
Does the rectangle that holds the most space always turn out to be the one closest to a square?
These are the practice questions — 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. Reveal the three list-items one at a time so only the current job is on screen.
For perimeter 12 cm the full set is 1×5 (area 5), 2×4 (area 8), 3×3 (area 9). A pupil builds each on the tool; the class reads the area and you record it in the board table.
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.