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 this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

Can you make five differently sized squares from the tangram pieces?

This activity investigates how you might make squares and pentominoes from Polydron.

Here are some ideas to try in the classroom for using counters to investigate number patterns.

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Can you make square numbers by adding two prime numbers together?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.

Learn how to use Excel to create triangular arrays.

Use Excel to investigate the effect of translations around a number grid.

This spreadsheet highlights multiples of numbers up to 20 in Pascal's triangle. What patterns can you see?

Use Excel to create some number pyramids. How are the numbers in the base line related to each other? Investigate using the spreadsheet.

Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree has. . . .

Sketch the graphs for this implicitly defined family of functions.

Try to move the knight to visit each square once and return to the starting point on this unusual chessboard.