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

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.

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?

Stage: 2 Challenge Level:

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

Exploring 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. . . .

Farey Sequences

Stage: 3 Challenge Level:

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

Matching Fractions, Decimals and Percentages

Stage: 3 Challenge Level:

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

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?

Cuisenaire Without Grid

Stage: 1 and 2 Challenge Level:

An environment which simulates working with Cuisenaire rods.

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?

Keep it Simple

Stage: 3 Challenge Level:

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

Fractional Wall

Stage: 2 Challenge Level:

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

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.

Peaches Today, Peaches Tomorrow....

Stage: 3 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?

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?

Fractions and Coins Game

Stage: 2 Challenge Level:

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

More Twisting and Turning

Stage: 3 Challenge Level:

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

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.

Stage: 3 Challenge Level:

Can you work out which drink has the stronger flavour?

Cuisenaire Environment

Stage: 1 and 2 Challenge Level:

An environment which simulates working with Cuisenaire rods.

Fraction Lengths

Stage: 2 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?

Paper Halving

Stage: 1 and 2 Challenge Level:

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

What Do You See Here?

Stage: 2 Challenge Level:

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

Stage: 2 Challenge Level:

Can you find ways to make twenty-link chains from these smaller chains?

Matching Fractions

Stage: 2 Challenge Level:

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

Fraction Match

Stage: 1 and 2 Challenge Level:

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

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?

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?

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?

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.

Doughnut

Stage: 2 Challenge Level:

How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?

Ratio Sudoku 3

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios or fractions.

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?

Dividing a Cake

Stage: 2 Challenge Level:

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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?

Unit Fractions

Stage: 3 Challenge Level:

Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.

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.

Mathematical Swimmer

Stage: 3 Challenge Level:

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .

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?

F'arc'tion

Stage: 3 Challenge Level:

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .

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.

Bull's Eye

Stage: 3 Challenge Level:

What fractions of the largest circle are the two shaded regions?

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?

Chocolate Bars

Stage: 2 Challenge Level:

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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.

3388

Stage: 3 Challenge Level:

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

Racing Odds

Stage: 3 Challenge Level:

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

Plutarch's Boxes

Stage: 3 Challenge Level:

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have. . . .