Students learn how to calculate square numbers and square roots. They are taught to use visualisation, written methods and calculators. Less able students are encouraged to use a timetable to support their learning and more able are challenged to demonstrate Lagrange's Theorem.

The lesson begins with introducing squares as having an odd number of factors. In the main part students are taught square numbers using diagrams and patterns. Later, they go on to calculate square roots and decimal numbers. At the end of the lesson they are challenge to demonstrate Lagrange's Theorem for a series of numbers.

**Differentiated Learning Objectives**

- All students should be able to calculate the first twelve square numbers using the timetable grid.
- Most students should be able to calculate the square numbers and their roots up to 12.
- Some students should be able to calculate the square of negative, decimals and fractions.