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.

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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

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

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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

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

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?

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

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

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?

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?

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

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.

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

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?

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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.

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.

Here is a chance to play a version of the classic Countdown Game.

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

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!

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?

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

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

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

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

You have 5 darts and your target score is 44. How many different ways could you score 44?

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?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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?

These two group activities use mathematical reasoning - one is numerical, one geometric.

This dice train has been made using specific rules. How many different trains can you make?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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