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?
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?
Can you find all the different ways of lining up these Cuisenaire rods?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Number problems at primary level that require careful consideration.
Find out what a "fault-free" rectangle is and try to make some of your own.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
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 put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
In this matching game, you have to decide how long different events take.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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.
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
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?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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.
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?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Investigate the different ways you could split up these rooms so that you have double the number.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
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!
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
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.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
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?
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?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?