If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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?

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?

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?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

Can you complete this jigsaw of the multiplication square?

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Are these statements relating to odd and even numbers always true, sometimes true or never true?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

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

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

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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?

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?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

This problem looks at how one example of your choice can show something about the general structure of multiplication.

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

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?

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

Are these statements always true, sometimes true or never true?

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

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.

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

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?

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?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

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.

Find a great variety of ways of asking questions which make 8.

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?