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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
Place the numbers 1 to 6 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.
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.
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.
Ben has five coins in his pocket. How much money might he have?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Find all the numbers that can be made by adding the dots on two dice.
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?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Annie and Ben are playing a game with a calculator. What was Annie's secret number?
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.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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. . . .
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
A game for 2 players. Practises subtraction or other maths operations knowledge.
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?
Use the number weights to find different ways of balancing the equaliser.
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!
Can you substitute numbers for the letters in these sums?
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?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
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?
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?
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?
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?
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.
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you hang weights in the right place to make the equaliser balance?