Pupils draw various sized rectilinear shapes on a grade, calculate the differences between products in opposite corners, and generalise.

Good knowledge of expanding double brackets, and ability to label other squares in grid relative to a reference square (top left-hand corner used) labelled $n$.

The task should not require much explanation for pupils with requisite prior knowledge. You may however:

1. Want to demonstrate how to calculate the difference on a rectangle of your choosing, and use the opportunity to explain why the product of numbers in the bottom-left and top-right corners will be greater than the product of the other two corners.

2. After this pupils should be able to progress at their own pace through the sheet until the last section.

3. The last section involves some tricky algebraic expansion and you may want to leave some working on the board/prepare your pupils for this.

*Have a copy of the teacher sheet available for reference.