Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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.
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?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
There were 22 legs creeping across the web. How many flies? How many spiders?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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 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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?
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?
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.
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and diagonal equal to 15.
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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.
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
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!
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
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?
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?
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?
What is happening at each box in these machines?
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?
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?
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?
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!
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?
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.