Square numbers

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

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

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?

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

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

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

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?

Can you find a rule which relates triangular numbers to square numbers?

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?

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?