Have a go at balancing this equation. Can you find different ways of doing it?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Can you work out some different ways to balance this equation?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

What happens when you round these three-digit numbers to the nearest 100?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Can you replace the letters with numbers? Is there only one solution in each case?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Can you substitute numbers for the letters in these sums?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Number problems at primary level that require careful consideration.

What could the half time scores have been in these Olympic hockey matches?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

You have 5 darts and your target score is 44. How many different ways could you score 44?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?