Look at the picture. There is a rectangle with its sides labelled, and beside it a little stack of building cubes.
For the rectangle we could ask: how far is it all the way around? Or we could ask: how many squares fit inside it? Those are two different questions about the same shape. And for the cubes there is a third question: how many cubes are stacked here?
Give five seconds of quiet think-time, then take three hands-up answers. You want pupils to feel the difference between 'around', 'inside' and 'cubes' before any method is named. Don't resolve it yet — that is what Watch and Notice does.
Look at each shape in turn. For each one, be ready to say whether we should count around, count inside, or count cubes.
First a 5 by 3 rectangle we measure two ways. Then a 4 by 4 square where around and inside give the same number. Then an L-shape built from two rectangles, a 4 by 2 and a 2 by 2, where we count the squares inside. Then a small cube stack.
Work each shape live on the board. For the 5 × 3 rectangle, do it twice: add the four sides for perimeter (16 cm), then count rows and columns for area (15 squares). Point at each number as it lands, this is the distance around, this is the space inside, so pupils see two different numbers, not a mistake.
For the 4 × 4 square, perimeter is 16 and area is 16, same number, different idea. This is the trap; ask 'so is 16 the perimeter or the area?' and let the class untangle it.
For the L-shape, draw it as two joined rectangles and find the area only (count inside). Bottom piece: 4 squares by 2 squares, so 4 × 2 = 8. Upright piece on the left: 2 squares by 2 squares, so 2 × 2 = 4. Add the two parts: 8 + 4 = 12 squares inside. Check by counting each unit square once so none is double-counted. Slip to watch: pupils who multiply the outer length by the outer width as if the L were a full rectangle.
For the cube stack, count the bottom layer of 4, then the top layer of 4, and stress that we count the 8 cubes even though some are hidden. Keep it to cues, do not read a script.
Today we work through some shapes together on the board, deciding each time what the question is asking — around, inside or cubes?
Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud.
Drag the corners on the board to make each shape in turn (start from the 6 × 2 rectangle already set), and switch to 3D for the cube stack. Ask the pupil at the board to name the method first ('around', 'inside' or 'cubes'), then work it. For the 3 × 3 square, do both perimeter and area so the class hears that one shape can answer two questions. For the cube stack, count the bottom layer, then the top, and add the hidden cubes. Watch for pupils who add sides when the question wants squares, or count squares when it wants the distance around — that mix-up is the whole point of the lesson.
In your maths copy, draw one 4 cm by 2 cm rectangle. On the line under it write its perimeter, and label it perimeter. On the next line write its area, and label it area.
Walk the room glancing at whether pupils have labelled which answer is which — this is whole-class copybook practice, not marking. Watch for anyone whose perimeter and area numbers are swapped.
Today we solve five building jobs. Decide each time, around, inside or cubes?
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.
Before each problem, ask the class to name the method: tape is perimeter, slabs are area, 'more space' is area, packing cubes is volume. The trap is the sign border (3 + 2 + 3 + 2 = 10 m, not 6 m from multiplying). For the two mats, pupils compute both on screen (2 × 5 = 10 squares, 3 × 3 = 9 squares) and see that the 2 by 5 mat covers more. For the box, count 4 cubes in each of the 2 layers (4 × 2 = 8). Let pupils predict which method each job needs before they compute.
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