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?

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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 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?

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

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?

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

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

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

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

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?

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

There were 22 legs creeping across the web. How many flies? How many spiders?

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?

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?

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 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?

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

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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.

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

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

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

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?

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!

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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?

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

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.

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.

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.

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?

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?

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

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

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?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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

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

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Can you use the information to find out which cards I have used?

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?