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

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

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

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

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

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?

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

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

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

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?

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

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?

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. . . .

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?

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?

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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

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

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

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

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

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

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

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?

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?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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

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?

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 players. Practises subtraction or other maths operations knowledge.

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?

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

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?

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?

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

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.

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

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

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?

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?

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

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!

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?