The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?
This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
In how many ways can you halve a piece of A4 paper? How do you know they are halves?
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.
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.
Investigate the successive areas of light blue in these diagrams.
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?
Calculate the fractional amounts of money to match pairs of cards with the same value.
A Sudoku with clues as ratios or fractions.
Can you match pairs of fractions, decimals and percentages, and beat your previous scores?
What fractions of the largest circle are the two shaded regions?
Can all unit fractions be written as the sum of two unit fractions?
How much of the square is coloured blue? How will the pattern continue?
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.
Can you find the pairs that represent the same amount of money?
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?
It would be nice to have a strategy for disentangling any tangled ropes...
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.
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?
Take a look at the video and try to find a sequence of moves that will untangle the ropes.
An environment which simulates working with Cuisenaire rods.
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.
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
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 picture it?
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have. . . .
There are lots of ideas to explore in these sequences of ordered fractions.
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. . . .
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?
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?
In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?
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?
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. . . .
An article describing activities which will help develop young children's concept of fractions.
Can you find ways to make twenty-link chains from these smaller chains? This gives opportunities for different approaches.
Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!
Can you work out which drink has the stronger flavour?
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.
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?
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?
How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?
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?
Written for teachers, this article describes four basic approaches children use in understanding fractions as equal parts of a whole.
Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?
An activity for teachers to initiate that adds to learners' developing understanding of fractions.