Variables are in proportion if they have a constant multiplicative relationship.

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

Dividing a quantity into a given ratio

Maths

Checking understanding of multiplicative relationships

Securing understanding of ratio as a multiplicative relationship

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

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

Fill in the missing word:  Variables are in proportion if they have a constant {{ }} relationship.

Share 75 in the ratio 2 : 3. Which is a correct first step in solving this problem?

Alex and Lucas share 75 sweets in the ratio of 2 : 3. How many sweets does Lucas get?

Share 96 in the ratio 2 : 7 : 3. What is the value of the largest share?

The ratio of flour to butter to sugar in a cookie recipe is 3 : 2 : 1. You want to make a giant cookie weighing 720 grams. How much butter will you need?

The perimeter of a triangle is 48 cm.  The sides are in the ratio 7:5:8.  How long is the shortest side?

Which of the following are terminating decimals?

Match each calculation to the correct missing number.

A recipe requires 195 grams of chocolate chips to bake 30 cookies.  What weight of chocolate chips would you need to make 500 cookies? Give your answer in grams.

What fraction of 180 is 55?  Give your answer in its simplest form.

If 525 is $$3\over5$$ of 875, which of the following is true?

Match the following with what needs to go in the box.

Dividing a quantity into a given ratio

Lesson outcome