Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?
Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
An activity making various patterns with 2 x 1 rectangular tiles.
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
How many triangles can you make on the 3 by 3 pegboard?
George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?
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?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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.
Number problems at primary level that require careful consideration.
Can you find all the different ways of lining up these Cuisenaire rods?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
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?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
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!
Can you draw a square in which the perimeter is numerically equal to the area?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
Investigate the different ways you could split up these rooms so that you have double the number.