Step 8 Objective

Present a concise reasoned argument, using symbols, diagrams, graphs and related explanatory texts.


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 around 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.

Writes a connected chain of reasoning to explain why the number of pegs on the outside is a multiple of 4.

Or

Notices that the number of pegs in the hollow produces the sequence of square numbers.

Every time the number of dots around the outside increased by 4

After making the table I discovered that the number of squares on the inside of a square was got by squaring the sides of the previous square.

EG square 1 is 2x2 square


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