ROTHESAY ACADEMY

MATHEMATICS DEPARTMENT

FIRST LEVEL THIRD LEVEL

RATIOPATHWAY 1 BLOCK 4

RATIO

Learning Intention

How to write, then simplify a ratio

Success Criteria

Understand what a written ratio means

Understand how to simplify any ratio

A ratio is used to compare two or more different quantities

WRITING A RATIO

There are 12 girls, 18 boys and 2 adults in a classroom.

Write the ratios of:

(a) girls : boys (b) boys : girls (c) boys : girls : adults

When simplifying a ratio we divide each part by the highest

common factor.

SIMPLIFYING A RATIO

There are 12 girls, 18 boys and 2 adults in a classroom.

In their simplest form, write the ratios of:

(a) girls : boys (b) boys : girls (c) boys : girls : adults

NOW YOUR TURN

TeeJay Level E

Page 176 Q6 – Q10

Page 177 Q1 – Q10

UNITARY RATIO

Learning Intention

How to write any ratio in unitary form

Success Criteria

Understand what a unitary ratio means

Understand how to write a unitary ratio

A ratio that has one of its values as “1” is a unitary ratio.

UNITARY RATIO

White these ratios as unitary ratios:

(a) 𝟏

𝟒: 𝟑 (b)

𝟏

𝟕: 𝟔 (c)

𝟑

𝟒: 𝟑

NOW YOUR TURN

TeeJay Level F

Page 159

Q7 – Q11

RATIO CALCULATIONS

Learning Intention

How to use a ratio in a calculation

Success Criteria

Understand how to use a ratio in a word problem

Show all the correct working

RATIO CALCULATIONS

The ratio of boys to girls to teachers on a school trip is 3:7:1.

(a) If there were 12 boys on the trip, how many girls were there?

(b) If there were 8 teachers on the trip, how many pupils were there?

NOW YOUR TURN

TeeJay Level F

Page 160

Exercise 3

PROPORTIONAL DIVISION

Learning Intention

Share an amount in a given ratio

Success Criteria

Understand how to share an amount in a given ratio

Show all the correct working

This is when we have to share an amount in a given ratio.

PROPORTIONAL DIVISION

Daniel and Lana share a prize of £400 in a ratio of 3:5.

How much do they both receive?

Step 1: Number of parts

Step 2: Each share

Step 3: Split

Step 4: Check

NOW YOUR TURN

TeeJay Level F

Page 161

Exercise 4

UNIT VALUE

Learning Intention

Calculate the value of a single item

Success Criteria

Understand how to calculate the value of a single item

Show all the correct working

UNIT VALUE

The cost of seven bottle of water is £4.20.

What is the cost of one bottle?

If you know the total value of several items you can calculate the

cost of one item (unit value) by dividing.

Be careful to divide the right way!

NOW YOUR TURN

TeeJay Level F

Page 163

Exercise 5

DIRECT PROPORTION

Learning Intention

Use direct proportion to calculate the value of a different quantity

of the same item

Success Criteria

Identify if direct proportion exists

Calculate the value of an unknown quantity of items

DIRECT PROPORTION

The cost of seven bottle of water is £4.20.

What is the cost of nine bottles?

Direct proportion is when one quantity changes in proportion

with another (if you double/triple one, the other doubles/triples).

NOW YOUR TURN

TeeJay Level F

Page 165

Exercise 5

DIRECT PROPORTION

Learning Intention

Use direct proportion to calculate the value of a different quantity

of the same item

Success Criteria

Identify a suitable “base” unit

Calculate the value of an unknown quantity of items

DIRECT PROPORTION

500 pencils cost £19.50

What is the cost of 700 pencils?

Sometimes it is easier to calculate the cost of 10, 100 or 1000

rather than just one item.

NOW YOUR TURN

TeeJay Level F

Page 165

Exercise 6 Q11 onwards

RATIO SUMMARY

There are 12 girls, 18 boys and 2 adults in a classroom.

In their simplest form, write the ratios of:

(a) girls : boys (b) boys : girls (c) boys : girls : adults

White these ratios as unitary

ratios:

(a) 𝟏

𝟒: 𝟑 (b)

𝟑

𝟒: 𝟑

The ratio of boys to girls to

teachers on a school trip is

3:7:1.

If there were 12 boys on the

trip, how many girls were

there?

Daniel and Lana share a prize of

£400 in a ratio of 3:5.

How much do they both receive?

The cost of seven bottle of water

is £4.20.

What is the cost of nine bottles?

500 pencils cost £19.50.

What is the cost of 700 pencils?