Step 10 Objective

Appreciate the difference between mathematical explanation and experimental evidence.


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.

I worked this out by using two formulas or I could have just carried on with the paterns mentioned above.

If a square is 2cm by 2cm there are 3 pegs on each side, to work out how many pegs there are around the outside

an example of how to create hollow square equations

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