Step 7 Objective

Use logical argument to establish the truth of a statement; begin to give mathematical justifications and test by checking particular cases.


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.

As in Step 6 but with mathematical explanations about the patterns in the results.