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

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

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

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?

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?

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

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

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

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?

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

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?

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

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

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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.

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.

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

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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?

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

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

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?

This challenge is about finding the difference between numbers which have the same tens digit.

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!

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.

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?

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?

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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

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?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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

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 players. Practises subtraction or other maths operations knowledge.

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?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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