Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Choose a symbol to put into the number sentence.
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 10 in the circles so that each number is the difference between the two numbers just below it.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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.
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?
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?
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?
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
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?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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 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!
If you have only four weights, where could you place them in order to balance this equaliser?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
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?
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. . . .
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
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!
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
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?
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?
In this game for two players, the aim is to make a row of four coins which total one dollar.
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!
This challenge extends the Plants investigation so now four or more children are involved.
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 is an adding game for two players.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
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?
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.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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?