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

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

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?

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

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

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

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

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?

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

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?

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

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

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

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. . . .

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

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!

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

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

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

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?

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?

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?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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?

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

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

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

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?

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

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?

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

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!

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?

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?

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?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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.

This task follows on from Build it Up and takes the ideas into three dimensions!

Can you find all the ways to get 15 at the top of this triangle of numbers?

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?

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

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

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?