Step 9 Objective

Show some insight into mathematical structure by using pattern and symmetry to justify generalisations, arguments or solutions.


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.

From results generated describes in words how to work out the number of pegs inside or outside.

METHOD

The number on the outside goes up by 4 each time. You can work out the middle by if it was 6 by 6 it would take 2 off so it would be 4 by 4. Then you would times 4 by 4 and that would give you the answer.

<< Previous Step | Next Step >>

Printable version