Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
Can you make square numbers by adding two prime numbers together?
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.
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
This number has 903 digits. What is the sum of all 903 digits?
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?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
What is happening at each box in these machines?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
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?
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.
There were 22 legs creeping across the web. How many flies? How many spiders?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
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!
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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.
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?
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?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Are these domino games fair? Can you explain why or why not?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Find the next number in this pattern: 3, 7, 19, 55 ...