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.

Ratio language and notation

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

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

Match the ratio tables to the correct simplified ratio notation.

Alex "40 triangles, so there are 10 squares because of the ratio is 4:1"

Laura "160 triangles, so there are 40 squares because of the ratio is 4:1"

Sofia "32 triangles, so there are 8 squares because of the ratio is 4:1"

Andeep "30 triangles, so there are 10 squares because of the ratio is 4:1"

Jun "24 triangles, so there are 16 squares because of the ratio is 4:1"

In a bag there are only triangles and squares. The ratio of triangles to squares is 4 : 1. There are 40 shapes in total. Who correctly worked out the number of squares?

The chocolates in a box either have red or blue wrappers. The ratio of red to blue is 3 : 4. If the difference between the red and blue chocolates is 5, how many chocolates are in the box?

The chocolates in a box either have red or blue wrappers.  The ratio of red to blue is 2 : 1. Andeep eats 3 blue chocolates and now the ratio is 12 : 5. How many blue were originally in the box?

They can be used to represent complex concepts.

It allows mathematical ideas to be communicated more effectively than words.

Why do we use symbols and notation in mathematics?

Which of the following is equivalent to "For every 3 circles, there are 4 squares."?

A number and its reciprocal will always have a product of {{ }}.

For every 5 ml of orange concentrate, use 100 ml of water. What is the multiplier for orange to water?

For every 5 ml of orange concentrate, use 100 ml of water. To make 420 ml of squash, how much concentrate do you need?

For every 2 cups of flour, there are 3 cups of water. If there are 13.5 cups of water, how many cups of flour are there?

Ratio language and notation

Lesson outcome