Resources tagged with: Fractions

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There are 66 NRICH Mathematical resources connected to Fractions, you may find related items under Fractions, Decimals, Percentages, Ratio and Proportion.

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

Mixing Lemonade

Age 11 to 14 Challenge Level:

Can you work out which drink has the stronger flavour?

Diminishing Returns

Age 11 to 14 Challenge Level:

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

The Greedy Algorithm

Age 11 to 14 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

Age 11 to 14 Challenge Level:

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

More Twisting and Turning

Age 11 to 16 Challenge Level:

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

Twisting and Turning

Age 11 to 14 Challenge Level:

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

Equal Temperament

Age 14 to 16 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

Age 7 to 11 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

Age 14 to 16 Challenge Level:

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

Cuisenaire Environment

Age 5 to 16 Challenge Level:

An environment which simulates working with Cuisenaire rods.

Fractions and Percentages Card Game

Age 11 to 16 Challenge Level:

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

Peaches Today, Peaches Tomorrow...

Age 11 to 14 Challenge Level:

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?

Farey Sequences

Age 11 to 14 Challenge Level:

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

Repetitiously

Age 14 to 16 Challenge Level:

Can you express every recurring decimal as a fraction?

Tiny Nines

Age 14 to 16 Challenge Level:

What do you notice about these families of recurring decimals?

Matching Fractions, Decimals and Percentages

Age 7 to 14 Challenge Level:

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

Egyptian Fractions

Age 11 to 14 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

Age 7 to 11 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 shapes?

A Bowl of Fruit

Age 5 to 7 Challenge Level:

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

Terminating or Not

Age 11 to 14 Challenge Level:

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

What Do You See Here?

Age 7 to 11 Challenge Level:

An activity for teachers to initiate that adds to learners' developing understanding of fractions.

Paper Halving

Age 5 to 11 Challenge Level:

In how many ways can you halve a piece of A4 paper? How do you know they are halves?

Linked Chains

Age 7 to 11 Challenge Level:

Can you find ways to make twenty-link chains from these smaller chains? This gives opportunities for different approaches.

Fraction Lengths

Age 7 to 11 Challenge Level:

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?

Exploring Fractions

Age 5 to 11

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. . . .

Early Fraction Development

Age 5 to 11

An article describing activities which will help develop young children's concept of fractions.

The Genes of Gilgamesh

Age 14 to 16 Challenge Level:

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

Stretching Fractions: A Discussion

Age 14 to 18

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

Counting Fish

Age 14 to 16 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

Age 14 to 18 Challenge Level:

Can you tangle yourself up and reach any fraction?

Tangles

Age 11 to 16

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

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios or fractions.

Pythagoras’ Comma

Age 14 to 16 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

Age 14 to 16 Challenge Level:

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

Count the Beat

Age 5 to 11

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?

Age 11 to 14 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

Age 11 to 14 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

Age 11 to 14 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?

Fractions Made Faster

Age 7 to 11 Challenge Level:

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

Rod Fractions

Age 7 to 14 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

Age 14 to 16 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

Age 7 to 11 Challenge Level:

Calculate the fractional amounts of money to match pairs of cards with the same value.

Fraction Card Game

Age 5 to 7 Challenge Level:

Can you match the halves in this interactive game?

Fracmax

Age 14 to 16 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

Age 5 to 14

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

History of Fractions

Age 7 to 14

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

Age 14 to 16 Challenge Level:

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

Circuit Training

Age 14 to 16 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

Age 11 to 14 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?

Can it Be

Age 16 to 18 Challenge Level:

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