Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
This challenge extends the Plants investigation so now four or more children are involved.
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?
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.
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?
Use the number weights to find different ways of balancing the equaliser.
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 substitute numbers for the letters in these sums?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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 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!
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
An environment which simulates working with Cuisenaire rods.
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 make square numbers by adding two prime numbers together?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Ben has five coins in his pocket. How much money might he have?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
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?
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?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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 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.
Can you hang weights in the right place to make the equaliser balance?
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?
Find all the numbers that can be made by adding the dots on two dice.
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?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
There are nasty versions of this dice game but we'll start with the nice ones...
Choose a symbol to put into the number sentence.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Here is a chance to play a version of the classic Countdown Game.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
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?