Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .
One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Can you compare these bars with each other and express their lengths as fractions of the black bar?
An activity for teachers to initiate that adds to learners' developing understanding of fractions.
Investigate the successive areas of light blue in these diagrams.
Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?
An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.
Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Calculate the fractional amounts of money to match pairs of cards with the same value.
How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?
This task offers opportunities to subtract fractions using A4 paper.
An article describing activities which will help develop young children's concept of fractions.
Here is a chance to play a fractions version of the classic Countdown Game.
My friends and I love pizza. Can you help us share these pizzas equally?
This article, written for primary teachers, links to rich tasks which will help develop the underlying concepts associated with fractions and offers some suggestions for models and images that help. . . .
What fraction of the black bar are the other bars? Have a go at this challenging task!
On Saturday, Asha and Kishan's grandad took them to a Theme Park. Use the information to work out how long were they in the theme park.
Try adding fractions using A4 paper.
In how many ways can you halve a piece of A4 paper? How do you know they are halves?
Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?
Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be so. . . .
This challenge asks you to imagine a snake coiling on itself.
A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?
Can you find ways to make twenty-link chains from these smaller chains? This gives opportunities for different approaches.
Can you find combinations of strips of paper which equal the length of the black strip? If the length of the black is 1, how could you write the sum of the strips?
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
An environment which simulates working with Cuisenaire rods.
Can you work out how many lengths I swim each day?
A Sudoku with clues as ratios or fractions.
Pick two rods of different colours. Given an unlimited supply of rods of each of the two colours, how can we work out what fraction the shorter rod is of the longer one?
Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?
Can you find the pairs that represent the same amount of money?
It would be nice to have a strategy for disentangling any tangled ropes...
Can all unit fractions be written as the sum of two unit fractions?
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.
Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.
This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
How much of the square is coloured blue? How will the pattern continue?
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?