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. . . .
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
These two group activities use mathematical reasoning - one is numerical, one geometric.
Place the numbers 1 to 6 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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
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 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!
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Ben has five coins in his pocket. How much money might he have?
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.
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?
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?
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?
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.
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?
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?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
Can you substitute numbers for the letters in these sums?
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?
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?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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!
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?
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?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
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?
Find all the numbers that can be made by adding the dots on two dice.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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.
Can you hang weights in the right place to make the equaliser balance?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.