An investigate quantifying how many ways squares can be drawn onto a larger square grid. Pupils explore a couple of cases, tabulate results, and discover an underlying pattern.

Square numbers, forming and substituting into expressions.

1. Print off one copy of A3 pupil sheet for each pupil, or pair if preferred.

2. I suggest explaining to pupils that they will be investigating how many squares can be drawn onto an $n \times n$ grid, and perhaps demonstrating for them how many unit squares and how many $2 \times 2$ squares can be drawn onto a $4 \times 4$ grid.

3. Pupils can then work through tasks at their own pace and should check with their teacher if their answer to question 8 is correct - they have been instructed to do this on the sheet.

*I suggest having a copy of the teacher sheet available for reference as pupils work.