means when variables are in proportion if they have a constant multiplicative relationship.

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

shows us how many equal parts in a whole.

Expressing multiplicative relationships as ratios and fractions

Maths

Checking understanding of multiplicative relationships

Securing understanding of ratio as a multiplicative relationship

Multiplicative relationships in context

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

For every 1 t-shirt, there is 1 pair of shorts.

For every 1 t-shirt, there are 2 pairs of shorts.

Number of pairs of shorts × 1 = Number of t-shirts

Number of pairs of shorts × 0.5 = Number of t-shirts

Number of houses $$\times \frac{3}{4}=$$ Number of phones

Number of phones $$\times \frac{3}{4}=$$ Number of houses

Number of phones $$\times \frac{4}{3}=$$ Number of houses

A quantity is divided into two parts: A and B. Match each ratio with the correct fraction.

A quantity is divided into two parts: A and B. Match each ratio with the correct formula.

A quantity is divided into two parts: A and B. Match each fraction with the correct formula to find B.

If two things are proportional then the ratio of part to whole is maintained and the __________ relationship between parts is also maintained.

The ratio table shows a recipe for a  pizza topping sauce. Complete this statement: Pizza sauce $$\times$$ {{ }} = Puree.

The ratio table shows a recipe for a  pizza topping sauce. Complete this statement:  Garlic $$\times$$ {{ }} = Puree.

A bowl of fruit contains apples and bananas. For every 3 apples, there are 5 bananas. There are 15 apples in the bowl. There are {{}} bananas in the bowl. 

A box of fruit contains apples and bananas. For every 3 apples, there are 5 bananas. There are 80 pieces of fruit in total. How many bananas are there? {{ }} bananas.

"For every 9 circles there are 14 squares."

"For every 9 circles there are 15 squares."

"For every 36 circles there are 60 squares."

"For every 1.5 circles there are 2.5 squares."

"For every 1 circle there are 1.5 squares."

Which are equivalent ratios to: "For every 3 circles there are 5 squares."

Expressing multiplicative relationships as ratios and fractions

Lesson outcome