Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Can you hang weights in the right place to make the equaliser balance?

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

If you have only four weights, where could you place them in order to balance this equaliser?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Use the number weights to find different ways of balancing the equaliser.

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?

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?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

Find all the numbers that can be made by adding the dots on two dice.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

A game for 2 players. Practises subtraction or other maths operations knowledge.

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Can you find 2 butterflies to go on each flower so that the numbers on each pair of butterflies adds to the same number as the one on the flower?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

This challenge extends the Plants investigation so now four or more children are involved.

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

In this game for two players, the aim is to make a row of four coins which total one dollar.

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.