Discuss the meaning of perimeter. Establish how to find the perimeter of a square if you know the width. Set the children the challenge of finding different perimeters and notice the link with the 4x table.
Consider how to find the width if you know the perimeter. Set the challenge of finding widths of different squares, including those where the perimeter is not a multiple of 4. Through investigating this, revise how to quarter a number and express remainders in different ways. (Links are given to earlier investigations to help with this.)
Quiz: Questions involving finding the perimeter from the width and finding the width from the perimeter, including examples where the answer is not a whole number, eg perimeter = 25, width = 6.25 or 6ΒΌ.
Discuss the meaning of perimeter for a rectangle (p1). Speculate on what will happen to the perimeter if you fix the width and made the length go up in ones (p3). What will happen if you fix the width and increase the length by a different amount (pp7/8). Investigate!
Next, consider what will happen if you increase the width and the length at the same time (p10). Suppose you make the width and length increase at different rates. What then (p14)? Investigate!
Next, discuss what happens if you work backwards. Can you find the length if you know the width and the perimeter (p17)? What happens if the perimeter is an odd number (p18)?
What happens if you fix the perimeter and make the width increase (p21)? etc, etc.
Loads to investigate here! Once the pupils have worked through the investigation given, they may have their own ideas for further exploration.