Square numbers

There are 44 NRICH Mathematical resources connected to Square numbers

problem

Favourite

Square subtraction

Age

7 to 11

Challenge level

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

problem

Favourite

Filling the gaps

Age

14 to 16

Challenge level

Which numbers can we write as a sum of square numbers?

problem

Favourite

Generating triples

Age

14 to 16

Challenge level

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

problem

Favourite

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

Favourite

Fractions in a box

Age

7 to 11

Challenge level

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

problem

Favourite

One wasn't square

Age

7 to 11

Challenge level

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

problem

Favourite

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

Favourite

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

Favourite

Two primes make one square

Age

7 to 11

Challenge level

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

problem

Favourite

Cycling squares

Age

7 to 11

Challenge level

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?

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For younger learners

Square numbers

Square subtraction

Filling the gaps

Generating triples

Factors and multiples puzzle

Fractions in a box

One wasn't square

Picture a pyramid

Sticky numbers

Two primes make one square

Cycling squares