A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.

Securing understanding of ratio as a multiplicative relationship

Maths

Checking understanding of multiplicative relationships

Multiplicative relationships in context

Expressing multiplicative relationships as ratios and fractions

Multiplicative relationships

Equivalent multiplicative relationships

Representing a multiplicative relationship

Ratio language and notation

Checking and securing finding a fraction of a given amount

Deepening understanding with fractions of a given amount

Expressing one number as a fraction of another

Dividing a quantity into a given ratio

Determining the whole

Determining the part

Describing exchange rates with ratio

Describing more conversions with ratio

Problem solving with fractions and ratios

The multiplicative relationship is extended in the future unit by considering percentages and the connections between multiplicative relationships and direct proportion. By building on a secure understanding of fractions and ratio, pupils can see their understanding of multiplicative relationships being extended.

In the prior unit, pupils generalised and developed their fluency of multiplying with fractions. In this unit, this understanding is extended to ratio and connections between ratios and fractions are explored.

This unit introduces the concept of multiplicative relationsihps, and connects fractions to the idea of ratios. Ratios are then explored in depth and used to solve contextual problems such as those involving exchange rates and general conversions.

Understanding multiplicative relationships: fractions and ratio

A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole. The relationship between parts and/or the whole is always {{}}.

This means the robot is fully protected and quick. 

This means the robot is quick but not fully protected.

A robot in travelling around a toxic planet. The protective clothing is heavy, so for every 6 protective items, there must be 2 batteries. Match the equipment list to its effect on the robot.

To make a "Sunrise" orange paint, 2 cans of yellow paint for every 1 can of red paint is used. Match the paint shades to the recipes.

To make lemonade, 1 lemon and 2 tablespoons of sugar are used for every 500 ml of water. Jun uses 750 ml of water to make lemonade. Jun should use {{ }} tablespoons of sugar. 

A ratio describes the relationship between values.

Adding the same amount to each part in a ratio keeps the ratio the same.

Multiplying the same amount to each part in a ratio keeps the ratio the same.

Select all the statements that are correct.

18 parts cocoa, 45 parts milk powder and 10 parts sugar.

15 parts cocoa, 35 parts milk powder and 7 parts sugar.

10 parts cocoa, 25 parts milk powder and 5 parts sugar.

20 parts cocoa, 55 parts milk powder and 10 parts sugar.

"Choko Milk chocolate" bars are made with 2 parts cocoa, 5 parts milk powder and 1 part sugar.  Too much cocoa makes it too bitter, too much sugar makes it too sweet. Match each result with its recipe

Use the ratio table to work out how many slices of cheese are needed to make 7 sandwiches. {{ }} slices.

Use the ratio table to work out how many slices of cheese are needed when there are 12 slices of tomato. {{ }} slices.

Here is a recipe for vanilla cake. How much sugar is needed if you use 6 eggs? {{}} grams of sugar.

Here is a recipe for vanilla cake. How much vanilla is needed if you use 125 g of flour? {{}} ml of vanilla.

Lucas has some red and blue marbles. For every 4 red marbles, he has 5 blue marbles. Lucas has 20 red marbles altogether. Lucas has {{ }} blue marbles.

Laura has some red and blue marbles. For every 4 red marbles, she has 5 blue marbles. She has 36 marbles altogether. Laura has {{ }} blue marbles.

Securing understanding of ratio as a multiplicative relationship

Lesson outcome