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.

Determining the part

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

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

Complete the sentence: When using a bar model the parts must be {{ }}.

What number is represented by the question mark in this bar model?

A bunch of flowers contains red and yellow flowers in the ratio 3 : 5. There are 9 red flowers. How many yellow flowers are in the bunch? 

The ratio of flour to butter to sugar in a cookie recipe is 3 : 2 : 1 . You use 180g of flour. How much butter is used?

Andeep, Sam and Sofia share some sweets in the ratio 3 : 8 : 5  Sofia gets 20 sweets, how many does Andeep get?

The lengths of the sides of a triangle are split in the ratio 3 : 8 : 7  The longest side is 4.8 cm, what is the length of the shortest side?

Sam and Aisha share some stickers in the ratio of 3 : 5. Aisha gets 25 stickers, how many stickers are there in total?

Laura, Jacob and Jun share some sweets in the ratio 5 : 6 : 3. Jacob gets 24 sweets, how many sweets are there in total?

Lucas is making necklaces with red, blue and white beads in the ratio 2 : 7 : 5. He uses 15 white beads. How many beads are on each necklace?

The lengths of the sides of a triangle are split in the ratio 3 : 8 : 7. The shortest side is 6.6 cm, what is the perimeter of the triangle?

Determining the part

Lesson outcome