Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

There are **118** NRICH Mathematical resources connected to **Fractions**, you may find related items under Fractions, decimals, percentages, ratio and proportion.

Problem
Primary curriculum
Secondary curriculum
### Terminating or Not

Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tumbling Down

Watch this animation. What do you see? Can you explain why this happens?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Almost One

Choose some fractions and add them together. Can you get close to 1?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractions Rectangle

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Extending Fraction Bars

Can you compare these bars with each other and express their lengths as fractions of the black bar?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Fraction Bars

What fraction of the black bar are the other bars? Have a go at this challenging task!

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A4 Fraction Subtraction

This task offers opportunities to subtract fractions using A4 paper.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Same Answer

Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tangling and Untangling

Twisting and turning with ropes can be encoded mathematically using fractions. Can you find a way to get back to zero?

Problem
Primary curriculum
Secondary curriculum
### Matching Fractions

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Jumping

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bryony's Triangle

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fraction Match

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

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Diminishing Returns

How much of the square is coloured blue? How will the pattern continue?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Countdown Fractions

Here is a chance to play a fractions version of the classic Countdown Game.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Greedy Algorithm

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Keep it Simple

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Twisting and Turning

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Twisting and Turning

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Chance to Win?

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Making Longer, Making Shorter

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Equal Temperament

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractions Jigsaw

A jigsaw where pieces only go together if the fractions are equivalent.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fraction Fascination

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Harmonic Triangle

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractional Wall

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

Age 7 to 11

Challenge Level

Interactive
Primary curriculum
Secondary curriculum
### Cuisenaire Environment

An environment which simulates working with Cuisenaire rods.

Age 5 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractions and Percentages Card Game

Can you find the pairs that represent the same amount of money?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Andy's Marbles

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Orange Drink

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ben's Game

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fair Feast

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Peaches Today, Peaches Tomorrow...

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractional Triangles

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Farey Sequences

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tiny Nines

What do you notice about these families of recurring decimals?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Halving

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Matching Fractions, Decimals and Percentages

Can you match pairs of fractions, decimals and percentages, and beat your previous scores?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Egyptian Fractions

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractions in a Box

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rectangle Tangle

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pumpkin Pie Problem

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fair Shares?

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### There's a Limit

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Bowl of Fruit

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Happy Halving

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Chocolate

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?

Age 7 to 14

Challenge Level