Square numbers

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

This activity creates an opportunity to explore all kinds of number-related patterns.

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Can you use this information to work out Charlie's house number?

In 1871 a mathematician called Augustus De Morgan died. De Morgan made a puzzling statement about his age. Can you discover which year De Morgan was born in?

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?