Step 5 Objective

Solve problems and investigate in a range of contexts, explaining and justifying methods and conclusions; begin to generalise and to understand the significance of a counter-example.


Examples of what pupils should know and be able to do

Hollow Squares

Here is a hollow square.

diagram showing the hollow square created by circling dots on squared paper.
  • How many pegs form the square on the outside?
  • How many pegs are there in the hollow?
  • Draw some more hollow squares.
  • Investigate.
diagram showing how the formula 2x+2(x-2) equals number of pegs around the outside of a square and to work out the hollow would be (x-1)squared equals the size of the hollow, where x is equal to the number of pegs along the top side.

Examples drawn from Hollow Squares.

Pupil notices that the number of pegs on the outside increases by four as the number along each side of the square increases by one. Partially explains why the number is a multiple of 4 by referring to the number of sides of a square.

First of all the dots on the outside go up in 4, for example 12, 18, and 20


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