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

Equivalent multiplicative relationships

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

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

How many equivalent ratios are there to "For every 1 apple, there are 2 bananas."?

Select the equivalent ratios to "For every 10 stars, there are 2 moons."

For every 1 pair of shorts, there are 3 t-shirts.

For every 1 t-shirt, there are 3 pairs of shorts.

For every 5 t-shirts, there are 15 pairs of shorts.

For every 4 t-shirts, there are 5 pairs of shorts.

For every 9 shaded, there are 16 not shaded.

For every 3 shaded, there are 2 not shaded.

For every 2 shaded, there are 3 not shaded.

For every 1 shaded, there is 1 not shaded.

What is the ratio of shaded to not shaded?

For every 10 shaded, there are 15 not shaded.

For every 2 shaded, there are 5 not shaded.

Three pieces of wood are cut so that length of piece A × 3 = length of piece B, length of piece B × 2 = length of piece C. Find the length of piece C in cm if the total length of all 3 pieces is 65 cm

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

For every 2 apples, there are 5 bananas. If there are 10 apples, how many bananas are there?

For every 2 apples, there are 9 bananas. If there are 33 pieces of fruit in total, how many bananas are there?

Packs of fruit are in the ratio of 2 apples to 3 pears to 5 bananas. When there are 27 pears, how many apples and bananas are needs to make as many packs of fruit as possible?

Packs of fruit are in the ratio of 2 apples to 3 pears to 5 bananas. When there are 48 pears, how many apples and bananas are needs to make as many packs of fruit as possible?

Equivalent multiplicative relationships

Lesson outcome