Square numbers

problem
Summing squares

Age

14 to 16

Challenge level

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
problem
Sticky numbers

Age

11 to 14

Challenge level

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
problem
Picture a pyramid

Age

7 to 11

Challenge level

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?
problem
Square sum

Age

14 to 16

Challenge level

One of these numbers is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?
problem
Factors and multiples puzzle

Age

11 to 14

Challenge level

Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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
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
Triangles within squares

Age

14 to 16

Challenge level

Can you find a rule which relates triangular numbers to square numbers?
problem
Up and down staircases

Age

7 to 11

Challenge level

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
problem
Odd squares

Age

7 to 11

Challenge level

Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?