Fractions, Decimals, Percentages and Ratio

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.

Round and Round and Round

Stage: 3 Challenge Level: Challenge Level:1

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

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.

Keep it Simple

Stage: 3 Challenge Level: Challenge Level:1

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

Fractions Jigsaw

Stage: 3 Challenge Level: Challenge Level:1

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

Mixing Lemonade

Stage: 3 Challenge Level: Challenge Level:1

Can you work out which drink has the stronger flavour?

Triathlon and Fitness

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

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

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.

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...

Mixing Paints

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

A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.

Repetitiously

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

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

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?

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.

Ben's Game

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

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Mixing More Paints

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

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

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.

A Chance to Win?

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

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

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?

Tiny Nines

Stage: 4 Challenge Level: Challenge Level:1

Find the decimal equivalents of the fractions one ninth, one ninety ninth, one nine hundred and ninety ninth etc. Explain the pattern you get and generalise.

Fair Shares?

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

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?

Areas and Ratios

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

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

Fractions - Short Problems

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

A collection of short Stage 3 and 4 problems on fractions, decimals, percentages and ratio.

Ratios and Dilutions

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

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions