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Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Fractions

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Mixing Lemonade

Stage: 3 Challenge Level: Challenge Level:1

Can you work out which drink has the stronger flavour?

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The Greedy Algorithm

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Keep it Simple

Stage: 3 Challenge Level: Challenge Level:1

Can all unit fractions be written as the sum of two unit fractions?

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More Twisting and Turning

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

It would be nice to have a strategy for disentangling any tangled ropes...

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Twisting and Turning

Stage: 3 Challenge Level: Challenge Level:1

Take a look at the video and try to find a sequence of moves that will take you back to zero.

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Equal Temperament

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Harmonic Triangle

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you see how to build a harmonic triangle? Can you work out the next two rows?

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Cuisenaire Environment

Stage: 1 and 2 Challenge Level: Challenge Level:1

An environment which simulates working with Cuisenaire rods.

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Peaches Today, Peaches Tomorrow....

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Fractional Triangles

Stage: 2 Challenge Level: Challenge Level:1

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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Farey Sequences

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

There are lots of ideas to explore in these sequences of ordered fractions.

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Halving

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

These pictures show squares split into halves. Can you find other ways?

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Matching Fractions Decimals Percentages

Stage: 2 and 3 Challenge Level: Challenge Level:1

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

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Egyptian Fractions

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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A Bowl of Fruit

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Can you work out how many apples there are in this fruit bowl if you know what fraction there are?

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Happy Halving

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you split each of the shapes below in half so that the two parts are exactly the same?

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Chocolate

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Understanding Fractions

Stage: 1 and 2

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. . . .

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Matching Fractions

Stage: 2 Challenge Level: Challenge Level:1

Can you find different ways of showing the same fraction? Try this matching game and see.

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Bryony's Triangle

Stage: 2 Challenge Level: Challenge Level:1

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?

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Fraction Match

Stage: 2 and 3 Challenge Level: Challenge Level:1

A task which depends on members of the group noticing the needs of others and responding.

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Diminishing Returns

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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The Genes of Gilgamesh

Stage: 4 Challenge Level: Challenge Level:1

Can you work out the parentage of the ancient hero Gilgamesh?

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Stretching Fractions: A Discussion

Stage: 4 and 5

This article extends and investigates the ideas in the problem "Stretching Fractions".

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Counting Fish

Stage: 4 Challenge Level: Challenge Level:1

I need a figure for the fish population in a lake, how does it help to catch and mark 40 fish ?

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All Tangled Up

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you tangle yourself up and reach any fraction?

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Tangles

Stage: 3 and 4

A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?

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Ratio Sudoku 3

Stage: 3 and 4 Challenge Level: Challenge Level:1

A Sudoku with clues as ratios or fractions.

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Introduction to Fractions

Stage: 1 and 2 Challenge Level: Challenge Level:1

The resources in this trail aim to enrich the experiences of children who are just being introduced to fractions.

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Pythagoras’ Comma

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Six Notes All Nice Ratios

Stage: 4 Challenge Level: Challenge Level:1

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.

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Count the Beat

Stage: 1 and 2

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?

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How Long Is the Cantor Set?

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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The Cantor Set

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Fraction Fascination

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

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Couples

Stage: 3 Challenge Level: Challenge Level:1

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?

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Fractions Made Faster

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!

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Fractional Wall

Stage: 2 Challenge Level: Challenge Level:1

Using the picture of the fraction wall, can you find equivalent fractions?

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Rod Fractions

Stage: 3 Challenge Level: Challenge Level:1

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?

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Stretching Fractions

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Fractions and Coins Game

Stage: 2 Challenge Level: Challenge Level:1

Work out the fractions to match the cards with the same amount of money.

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Fraction Card Game 1

Stage: 1 Challenge Level: Challenge Level:1

Match the halves.

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Fracmax

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Teaching Fractions with Understanding: Part-whole Concept

Stage: 1, 2 and 3

Written for teachers, this article describes four basic approaches children use in understanding fractions as equal parts of a whole.

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History of Fractions

Stage: 2 and 3

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.

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What a Joke

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

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Circuit Training

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

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Water Lilies

Stage: 3 Challenge Level: Challenge Level:1

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?

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Can it Be

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?

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Light Blue - Dark Blue

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Investigate the successive areas of light blue in these diagrams.