Pupils investigate how many squares a straight line passes through. What might first appear very simple contains subtle depth.

Highest common factor of two numbers.

1. Distribute one copy of A3 pupil sheet to each pupil.

2. Briefly outline the problem, perhaps explaining the 5 x 3 example at the top of the sheet.

3. IMPORTANT:

Pupils need to arrive at a formula which includes highest common factor of (length, width) as one of the terms. This will seem unnatural to pupils, so I suggest preparing them for this.

I have used HCF questions as a warm-up for this task, and gently suggested that HCF might make a contribution to this investigation.

The sheet includes a table for pupils to fill in. One column has been left blank into which HCF(length, width) can be added. If pupils need an extra push I would suggest to them adding this column, and you can either suggest this to the whole group or individuals/pairs.

4. Otherwise, pupils should be able to work through the task at their own pace.

It is strongly recommend to have a copy of the teacher sheet available for your reference whilst pupils work through the tasks.