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?
This task offers opportunities to subtract fractions using A4 paper.
What fraction of the black bar are the other bars? Have a go at this challenging task!
Who first used fractions? Were they always written in the same way? How did fractions reach us here? These are the sorts of questions which this article will answer for you.
Written for teachers, this article describes four basic approaches children use in understanding fractions as equal parts of a whole.
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.
There are some water lilies in a lake. The area that they cover doubles in size every day. After 17 days the whole lake is covered. How long did it take them to cover half the lake?
In a certain community two thirds of the adult men are married to three quarters of the adult women. How many adults would there be in the smallest community of this type?
A Sudoku with clues as ratios or fractions.
How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?
Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!
My friends and I love pizza. Can you help us share these pizzas equally?
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.
Can you find ways to make twenty-link chains from these smaller chains? This gives opportunities for different approaches.
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. . . .
Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?
An activity for teachers to initiate that adds to learners' developing understanding of fractions.
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?
Try adding fractions using A4 paper.
Can you compare these bars with each other and express their lengths as fractions of the black bar?
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.
An article describing activities which will help develop young children's concept of fractions.
Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?
Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...
Take a look at the video and try to find a sequence of moves that will untangle the ropes.
There are lots of ideas to explore in these sequences of ordered fractions.
Here is a chance to play a fractions version of the classic Countdown Game.
Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?
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?
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.
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 the pairs that represent the same amount of money?
This is a 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.
Can all unit fractions be written as the sum of two unit fractions?
Calculate the fractional amounts of money to match pairs of cards with the same value.
This challenge asks you to imagine a snake coiling on itself.
It would be nice to have a strategy for disentangling any tangled ropes...
Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?
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.
This article, written by Nicky Goulder and Samantha Lodge, reveals how maths and marimbas can go hand-in-hand! Why not try out some of the musical maths activities in your own classroom?
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.
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. . . .
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.
Choose some fractions and add them together. Can you get close to 1?
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?
Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?
An environment which simulates working with Cuisenaire rods.
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 ï¿½ 1 [1/3]. What other numbers have the sum equal to the product and can this be. . . .
One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?
At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the. . . .