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?

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?

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 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?

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

Can you complete this jigsaw of the multiplication square?

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?

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

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?

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

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

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?

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?

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?

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

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

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

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?

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

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?

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

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

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

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

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?

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

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?

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?

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

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?

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

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?

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

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

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

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.

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

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?

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

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

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?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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

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

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?