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.

Problem solving with fractions and ratios

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

Describing more conversions with ratio

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 {{ }} multiplicative relationship.

Select the bar model that is correctly labelled to solve this problem:  Sam and Jacob share some stickers in the ratio of 3 : 7.  Sam get 168 less than Jacob. How many stickers does Sam get?

Sam and Jacob share some stickers in the ratio of 3 : 7.  Sam get 168 less than Jacob.  How many stickers does Sam get?

The ratio of children to adults in a club is 2 : 3.  If there are 26 children, how many are in the club in total?

A bag contains red, green and yellow sweets.  $$1\over4$$ of them are red. The rest of the sweets are either green or yellow, in the ratio 4 : 5. There are 72 sweets in the bag. How many are yellow? 

Andeep’s older sister Belle is 3 times his age.   His brother Charlie is $$5\over6$$ of Belle's age. The total of Andeep’s and Belle’s ages is 48. How old is Charlie?

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

1 km = 1000 m, 1 m = 100 cm.  What is 5 400 000 cm in kilometres?

The scale on a map is 1:5 000 000. 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 1:500 000. The distance between two places is 86 km. What is the distance on the map?

The length of a pencil is 2.5 inches.  Convert this into centimetres given that 1 inch = 2.54 cm.

The distance between London and Manchester is 200 miles.  Convert this into kilometres given that 5 miles = 8 km.

Problem solving with fractions and ratios

Lesson outcome