Step 6 Objective

Draw simple conclusions and explain reasoning; suggest extensions to problems; conjecture and generalise.


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.

Makes a table of results systematically with most of results correct, may notice that the number of pegs in the hollow increases by two more each time.

There are 16 pegs on the outside. The hollow is 9 pegs

Area of hollow square.
  • 3 x 3
  • 4 x 4
  • 5 x 5
  • 6 x 6
  • 7 x 7
  • 8 x 8
  • 9 x 9
  • 10 x 10
Number of pegs on outside.
  • 8
  • 12
  • 16
  • 20
  • 24
  • 28
  • 32
  • 36
Number of pegs in hollow.
  • 1
  • 4
  • 9
  • 16
  • 25
  • 36
  • 49
  • 64

Outside goes up in fours

Hollow goes up in twos


<< Previous Step | Next Step >>

Printable version