# Ratio, Proportion & Rates of Change

This is part of ourĀ Secondary Curriculum collection of favourite rich tasks arranged by topic.

##### Stage: 3 Challenge Level:

Can you work out which drink has the stronger flavour?

##### Stage: 3 Challenge Level:

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

### Olympic Measures

##### Stage: 3 Challenge Level:

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

### All in a Jumble

##### Stage: 3 Challenge Level:

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

### Triathlon and Fitness

##### Stage: 3 Challenge Level:

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

### Thousands and Millions

##### Stage: 3 Challenge Level:

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

### Mixing Paints

##### Stage: 3 Challenge Level:

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:

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?

### Nutrition and Cycling

##### Stage: 4 Challenge Level:

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

### Speed-time Problems at the Olympics

##### Stage: 4 Challenge Level:

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

### Speeding Boats

##### Stage: 4 Challenge Level:

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

### The Legacy

##### Stage: 4 Challenge Level:

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?

##### Stage: 4 Challenge Level:

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

### Areas and Ratios

##### Stage: 4 Challenge Level:

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.

### 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:

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?