Proportionality means when 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.

Describing more conversions with 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

Dividing a quantity into a given ratio

Determining the whole

Determining the part

Describing exchange rates 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

In this list of common metric units of length which one is missing?
millimetre, {{ }}, metre, kilometre

1 km = 1000 m, 1 m = 100 cm.  What is 480 000 cm in kilometres?

The scale on a map is 1:300 000. The distance between two places on the map is 5 cm. What is the distance in real life in kilometres?

The scale on a map is 1:50 000. The distance between two places is 4.3 km. What is the distance on the map?

The length of a leaf is 3.5 inches.  Convert this into centimetres given that 1 inch = 2.54 cm.

The distance between London and Edinburgh is 403 miles.  Convert this into kilometres given that 5 miles = 8 km.

Complete the sentence:  The exchange rate shows a {{ }} relationship between 2 currencies.

A graph representing a proportional relationship must go through which point?

Use the graph to convert £100 into dollars ($).

Use the graph to convert $25 into pounds (£).

£1 : ¥182. Use this exchange rate to convert £300 into yen (¥).

£1:¥182  Use this exchange rate to convert ¥31 850 into pounds (£).

Starter Quiz

Complete the sentence: The exchange rate shows a relationship between 2 currencies.