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.

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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

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

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?

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

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

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

This task combines spatial awareness with addition and multiplication.

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

What happens when you round these numbers to the nearest whole number?

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.

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

This challenge combines addition, multiplication, perseverance and even proof.

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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?

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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?

Take turns to place a decimal number on the spiral. Can you get three consecutive numbers?

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?

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

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?

In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water?

Can you go through this maze so that the numbers you pass add to exactly 100?

A game in which players take it in turns to choose a number. Can you block your opponent?

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?