Ratio, Proportion & Rates of Change

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.

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.

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?

Dating Made Easier

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

If a sum invested gains 10% each year how long before it has doubled its value?

The Legacy

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

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

All in a Jumble

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

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Thousands and Millions

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

Here's a chance to work with large numbers...

Speeding Boats

Stage: 4 Challenge Level: Challenge Level:1

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

Mixing Lemonade

Stage: 3 Challenge Level: Challenge Level:1

Can you work out which drink has the stronger flavour?

Speed-time Problems at the Olympics

Stage: 4 Challenge Level: Challenge Level:1

Have you ever wondered what it would be like to race against Usain Bolt?

Place Your Orders

Stage: 3 Challenge Level: Challenge Level:1

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Nutrition and Cycling

Stage: 4 Challenge Level: Challenge Level:1

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

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?

Olympic Measures

Stage: 3 Challenge Level: Challenge Level:1

These Olympic quantities have been jumbled up! Can you put them back together again?

Ratio, Proportion and Rates of Change - Short Problems

Stage: 3 and 4

A collection of short problems on ratio, proportion and rates of change.

Fractions Rectangle

Stage: 3 Challenge Level: Challenge Level:1

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?