Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
You have 5 darts and your target score is 44. How many different ways could you score 44?
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Choose a symbol to put into the number sentence.
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. . . .
Here is a chance to play a version of the classic Countdown Game.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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 put the numbers 1 to 8 into the circles so that the four calculations are correct?
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.
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?
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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 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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
Got It game for an adult and child. How can you play so that you know you will always win?
This task follows on from Build it Up and takes the ideas into three dimensions!
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
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 this game for two players, the aim is to make a row of four coins which total one dollar.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
A game for 2 players. Practises subtraction or other maths operations knowledge.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
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?
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?
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?