Step 4 Objective

Make general statements, based on evidence produced, and explain reasoning.


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 is in the four times table.

I noticed that all outside numbers belong to the 4 times table. In this investigation I found out that every square you draw gets bigger and there are more dots inside the squares. Also I have found out that the number of pegs in turn go odd, even and so on. I have tried many different shapes for this investigation - squares, triangles, hexagons and pentagons.


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