Square numbers

problem

Triangular Triples

Age

14 to 16

Challenge level

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
problem

Relative Powers

Age

14 to 16

Challenge level

The square of a number is 12 more than the number itself. The cube of the number is 9 times the number. What is the number?
problem

Little Squares

Age

5 to 7

Challenge level

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?
problem

Numbers as Shapes

Age

5 to 7

Challenge level

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

Swimming Pool Tiles

Age

7 to 11

Challenge level

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

Graphing Number Patterns

Age

7 to 11

Challenge level

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?
problem

Cuisenaire Squares

Age

7 to 11

Challenge level

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

A Right Charlie

Age

7 to 11

Challenge level

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

Special 24

Age

7 to 11

Challenge level

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
problem

Augustus' Age

Age

7 to 11

Challenge level

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?