The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.

Checking and securing finding a fraction of a given amount

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

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

Which of the following is not the reciprocal of 4?

Use a bar model to calculate $$3\over8$$ of 48

Which of the following are equivalent calculations for $$5\over9$$ of 72?

Calculate $$2 {{3} \over {5}}$$ × $$2\over7$$

What symbol separates the parts of a ratio?  E.g. the mathematical notation for writing 4 to 5.

Alex "60 triangles, so there are 20 squares because of the ratio is 3 : 1"

Laura "180 triangles, so there are 40 squares because of the ratio is 3 : 1"

Andeep "20 triangles, so there are 40 squares because of the ratio is 4 : 1"

Sofia "45 triangles, so there are 15 squares because of the ratio is 4 : 1"

Jun "34 triangles, so there are 26 squares because of the ratio is 4 : 1"

In a bag there are only triangles and squares. The ratio of triangles to squares is 3 : 1. There are 60 shapes in total. Who correctly worked out the number of squares?

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

Chocolates in a box either have red or blue wrappers.  The ratio of red to blue is 3 : 2. Andeep eats 2 blue chocolates and now the ratio is 12 : 7. How many blues were in the box originally?

Checking and securing finding a fraction of a given amount

Lesson outcome