Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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.
Can all unit fractions be written as the sum of two unit fractions?
It would be nice to have a strategy for disentangling any tangled ropes...
Take a look at the video and try to find a sequence of moves that will take you back to zero.
The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.
Can you see how to build a harmonic triangle? Can you work out the next two rows?
An environment which simulates working with Cuisenaire rods.
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
There are lots of ideas to explore in these sequences of ordered fractions.
These pictures show squares split into halves. Can you find other ways?
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
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.
Can you work out how many apples there are in this fruit bowl if you know what fraction there are?
Can you split each of the shapes below in half so that the two parts are exactly the same?
There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?
Can you find different ways of showing the same fraction? Try this matching game and see.
This list offers an introduction to fractions that will help children to develop an understanding of fractions and approaches to solving problems using them.
Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?
A task which depends on members of the group noticing the needs of others and responding.
In this problem, we have created a pattern from smaller and smaller squares. If we carried on the pattern forever, what proportion of the image would be coloured blue?
Can you work out the parentage of the ancient hero Gilgamesh?
This article extends and investigates the ideas in the problem "Stretching Fractions".
I need a figure for the fish population in a lake, how does it help to catch and mark 40 fish ?
Can you tangle yourself up and reach any fraction?
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?
A Sudoku with clues as ratios or fractions.
The resources in this trail aim to enrich the experiences of children who are just being introduced to fractions.
Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.
The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.
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?
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 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?
This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
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?
Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!
Using the picture of the fraction wall, can you find equivalent 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?
Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?
Work out the fractions to match the cards with the same amount of money.
Match the halves.
Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.
Written for teachers, this article describes four basic approaches children use in understanding fractions as equal parts of a whole.
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.
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .
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?
When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
Investigate the successive areas of light blue in these diagrams.
