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

### Cuisenaire Without Grid

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

An environment which simulates working with Cuisenaire rods.

### Matching Fractions

##### Stage: 2 Challenge Level:

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

### Bryony's Triangle

##### Stage: 2 Challenge Level:

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?

### Fraction Match

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

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

##### Stage: 3 Challenge Level:

Can you work out which drink has the stronger flavour?

### The Greedy Algorithm

##### Stage: 3 Challenge Level:

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.

### Keep it Simple

##### Stage: 3 Challenge Level:

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

### More Twisting and Turning

##### Stage: 3 Challenge Level:

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

### Twisting and Turning

##### Stage: 3 Challenge Level:

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

### Equal Temperament

##### Stage: 4 Challenge Level:

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.

### Fraction Fascination

##### Stage: 2 Challenge Level:

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

### Harmonic Triangle

##### Stage: 3 Challenge Level:

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

### Fractional Wall

##### Stage: 2 Challenge Level:

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

### Cuisenaire Environment

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

An environment which simulates working with Cuisenaire rods.

### Peaches Today, Peaches Tomorrow....

##### Stage: 3 and 4 Challenge Level:

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?

### Fractional Triangles

##### Stage: 2 Challenge Level:

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

### Farey Sequences

##### Stage: 3 Challenge Level:

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

### Halving

##### Stage: 1 Challenge Level:

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

### Matching Fractions Decimals Percentages

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

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

### Egyptian Fractions

##### Stage: 3 Challenge Level:

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.

### Rectangle Tangle

##### Stage: 2 Challenge Level:

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 ten numbered shapes?

### A Bowl of Fruit

##### Stage: 1 Challenge Level:

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

### Happy Halving

##### Stage: 1 Challenge Level:

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

### Chocolate

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

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?

### 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. . . .

### Diminishing Returns

##### Stage: 3 Challenge Level:

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?

### The Genes of Gilgamesh

##### Stage: 4 Challenge Level:

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

### Stretching Fractions: A Discussion

##### Stage: 4 and 5

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

### Counting Fish

##### Stage: 4 Challenge Level:

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

### All Tangled Up

##### Stage: 3 Challenge Level:

Can you tangle yourself up and reach any fraction?

### 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?

### Ratio Sudoku 3

##### Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios or fractions.

### Pythagoras’ Comma

##### Stage: 4 Challenge Level:

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.

### Six Notes All Nice Ratios

##### Stage: 4 Challenge Level:

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

### 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?

### How Long Is the Cantor Set?

##### Stage: 3 Challenge Level:

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?

### The Cantor Set

##### Stage: 3 Challenge Level:

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?

### Couples

##### Stage: 3 Challenge Level:

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?

##### Stage: 2 Challenge Level:

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

### Rod Fractions

##### Stage: 3 Challenge Level:

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?

### Stretching Fractions

##### Stage: 4 Challenge Level:

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?

### Fractions and Coins Game

##### Stage: 2 Challenge Level:

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

### Fraction Card Game 1

##### Stage: 1 Challenge Level:

Match the halves.

### Fracmax

##### Stage: 4 Challenge Level:

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.

### 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.

### 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.

### What a Joke

##### Stage: 4 Challenge Level:

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

### Circuit Training

##### Stage: 4 Challenge Level:

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. . . .

### Water Lilies

##### Stage: 3 Challenge Level:

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?