1. Divide a quantity in a given ratio.
Grade 4
Ratio Sharing
Divide a quantity in a given ratio.
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Divide a quantity in a given ratio
Grade 4
Prior Knowledge
Basic operations
Simplifying ratios
Duration
Suggested duration is 50 minutes for this objective
Resources
Print slides: 4, 7, 12, 16
Equipment
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
Recapping writing ratios in their simplest form
Give students slide 4 printed. To be completely independently. Review answers. Ensure that prior knowledge of ratios is secure (ordering, simplifying) 5
How to set up a ratio. Listing the parts in the correct order and calculating the missing number(s)
Give students slide 7 printed. This contains 4 key ratio questions – all with slight variations but the set up of the information given in the question and finding the missing number is exactly the same. Using slide 8 to 11 explain each question with the students. 15
Give students slide 12 printed. Mixed practice with a more challenging question. 10
Divide a quantity in a given ratio in OCR exam questions (from specimen papers)
Give students slide 16. This includes 6 exam questions related to objective. Students need to use notes from lesson to answer the questions. Ensure that all steps are shown. Relate to mark scheme to show how the marks are allocated. Note that Sine Rule is needed for the second question. 20
Next Steps
Recipe questions
Direct and inverse proportion
Assessment
PLC/Reformed Specification/Target 4/Ratio, Proportion and Rates of Change/Ratio Sharing

3. Key Vocabulary
Change Divide Proportion Quantity Ratio Share

4. Intro 15% 7/10 2:3 £3.40 3:4:6 £2.15 21% 2/3 3/5 1:2:5:6 50p 2:7
15% 7/10 2:3 £3.40
3:4:6 £ % 2/3
3/5 1:2:5:6 50p 2:7
1:4 £ /8 33%
Which are the 5 ratios?
e.g. 8 : 12 = 2 : 3
6 : 18 =
4 : 8 =
10 : 100 =
12 : 8 =
9 : 18 =
5 : 10 =
4 : 16 =
There are 32 pupils in a class. 20 of them are girls. What is the ratio of boys to girls in its simplest form?
There are 50 sweets in a mixed pack. 25 are jellies, 10 are fizzy cola bottles and the rest are boiled. Write the ratio of each type of sweet in its simplest form.
A fruit drink is made by mixing 60ml of orange juice with 180ml of pineapple juice. What is the ratio of orange juice to pineapple juice in its simplest form?
Concrete is made by mixing sand, water and concrete mix in the ratio of 6 parts sand, 3 parts water and 3 parts concrete mix. What ratio is this in its simplest form?
Write ratios in simplest form
e.g. 4 : 8 : 12 = 1 : 2 : 3
1 day : 6 hours =
6 : 8 : 12 =
2 hours : 30 mins =
20cm : 15cm =
£1 : 70p =
50p : £2.50 =
4km : 12km =
Student Sheet 1

5. Which are the 5 ratios? 15% 7/10 2:3 £3.40 3:4:6 £2.15 21% 2/3
15% 7/10 2:3 £3.40
3:4:6 £ % 2/3
3/5 1:2:5:6 50p 2:7
1:4 £0.50 4/8 33%

6. Write ratios in simplest form
e.g. 8 : 12 = 2 : 3
6 : 18 = 1: 3
4 : 8 = 1: 2
10 : 100 = 1: 10
12 : 8 = 3: 2
9 : 18 = 1: 2
5 : 10 = 1: 2
4 : 16 = 1: 4
e.g. 4 : 8 : 12 = 1 : 2 : 3
1 day : 6 hours = 4: 1
6 : 8 : 12 = 3 : 4 : 6
2 hours : 30 mins = 4: 1
20cm : 15cm = 4: 3
£1 : 70p = 10 : 7
50p : £2.50 = 1: 5
4km : 12km = 1: 3
Write ratios in simplest form
There are 32 pupils in a class. 20 of them are girls. What is the ratio of boys to girls in its simplest form?
 3: 5
There are 50 sweets in a mixed pack. 25 are jellies, 10 are fizzy cola bottles and the rest are boiled. Write the ratio of each type of sweet in its simplest form. 5: 2 : 3
A fruit drink is made by mixing 60ml of orange juice with 180ml of pineapple juice. What is the ratio of orange juice to pineapple juice in its simplest form? 1: 3
Concrete is made by mixing sand, water and concrete mix in the ratio of 6 parts sand, 3 parts water and 3 parts concrete mix. What ratio is this in its simplest form? 2: 1 : 1

7. How to work out given ratios
Sandra has a piece of string 150cm long.
She cuts the string into three lengths in the ratio 5:2:3
Work out the length, in cm, of each piece of string.
Paul and Katie share some sweets in the ratio 3:8
Katie gets 32 sweets.
How many sweets does Paul get?
Talil is going to make some concrete mix. He needs to mix cement, sand and gravel in the ratio 1:3:5 by weight. Talil wants to make 180 kg of concrete mix.
Talil has 15kg of cement, 85kg of sand, 100kg of gravel. Does he have enough cement, sand and gravel?
Pat and Julie share some money in the ratio 2:5
Julie gets £45 more than Pat.
How much money did Pat get?
Guide
P: K
3: 8
?: 32
X4 so = 12
Student Sheet 2

8. P : K 32 =4 8 3 : 8 12 : 32 3 x 4 = 12 How to work out given ratios
Paul and Katie share some sweets in the ratio 3:8
Katie gets 32 sweets.
How many sweets does Paul get?
P : K 32 8 =4
3 : 8 12
: 32
Guide
P: K
3: 8
?: 32
X4 so = 12
3 x 4 = 12

9. =10 parts 5 : 2 : 3 =150cm How to work out given ratios 150 = 15 10
Sandra has a piece of string 150cm long.
She cuts the string into three lengths in the ratio 5:2:3
Work out the length, in cm, of each piece of string.
=10 parts
5 : 2 : 3
150 10
= 15
Guide
=150cm
75 : 30 : 45
5 x 15 = 75

10. 5 – 2 = 3 P : J 45 = 15 3 2 : 5 30 : How to work out given ratios
Pat and Julie share some money in the ratio 2:5
Julie gets £45 more than Pat.
How much money did Pat get?
5 – 2 = 3
P : J 45 3
= 15
2 : 5
Guide
30 :
2 x 15 = 30

11. = concrete C : S : G = 9 parts 1 : 3 : 5 = 180 kg
How to work out given ratios
Talil is going to make some concrete mix.
He needs to mix cement, sand and gravel in the ratio 1:3:5 by weight.
Talil wants to make 180 kg of concrete mix.
Talil has 15kg of cement, 85kg of sand, 100kg of gravel
Does he have enough cement, sand and gravel?
C : S : G
= concrete
180 9
= 20
= 9 parts
1 : 3 : 5
Guide
1 x 20 = 20
3 x 20 = 60
5 x 20 = 100
= 180 kg
20 : 60 : 100
No Talil does not have enough cement

12. Practice Student Sheet 3
Tyler and Kate share £91 in the ratio 4 : 3. Work out how much money each person gets.
2) Ryan and Simon share £72 in the ratio 4 : 8. Work out how much money each person gets.
3) Manisha and Alex share £600 in the ratio 62 : 58. Work out how much money each person gets.
4) Aria, Dillan and Adam share 75 ,10p coins in the ratio 9 : 2 : 4. Work out the number of 10p coins that each of them receives.
Kate, Drake and Ed share £350 between them. Kate receives £120 more than Drake. The ratio of Kate’s share to Drake’s share is 13 : 3. Work out the ratio of Ed’s share to Drake’s share. Give your answer in its simplest form.
True or False?
A bag contains 10 yellow balls, 20 red balls and 25 blue balls. The ratio is 2 : 10 : 5
A wallet contains 16, 2p coins, 24, 10p coins and 6, 50p coins. The ratio is 4 : 6 : 3
A jar contains 36 green marbles, 54 orange marbles and 60 pink. The simplified ratio is 18 : 27 : 30
Student Sheet 3

13. Practice 1) Tyler and Kate share £91 in the ratio 4 : 3.
Work out how much money each person gets.
4 + 3 = 7
91/7 = 13
Tyler: 4 × 13 = £52
Kate: 3 × 13 = £39
2) Ryan and Simon share £72 in the ratio 4 : 8.
4 + 8 = 12
72/12 = 6
Ryan: 4 × 6 = £24
Simon: 8 × 6 = £48
3) Manisha and Alex share £600 in the ratio 62 : 58.
= 120
600/120 = 5
Manisha: 62 × 5 = £310
Alex: 58 × 5 = £290
4) Aria, Dillan and Adam share 75 ,10p coins in the ratio 9 : 2 : 4.
Work out the number of 10p coins that each of them receives.
= 15
75/15 = 5 per part
Aria: 9 × 5 = 45 , 10p coins
Dillan: 2 × 5 = 10 , 10p coins
Adam: 4 × 5 = 20 , 10p coins

14. Problem Solving and Reasoning
Kate, Drake and Ed share £350 between them.
Kate receives £120 more than Drake.
The ratio of Kate’s share to Drake’s share is 13 : 3
Work out the ratio of Ed’s share to Drake’s share.
Give your answer in its simplest form.
120 + Drake = Kate
13 – 3 = 10
120 ÷ 10 = £12 = 1 part
13 × £12 = £156 : Kate
3 × £12 = £36 : Drake
£156 + £36 = £192
£350 - £192 = £158
36 : 158
18 : 79
÷ 2
÷ 2

15. Reason and Explain False False False True or False?
A bag contains 10 yellow balls, 20 red balls and 25 blue balls. The ratio is 2 : 10 : 5
A wallet contains 16, 2p coins, 24, 10p coins and 6, 50p coins. The ratio is 4 : 6 : 3
A jar contains 36 green marbles, 54 orange marbles and 60 pink. The simplified ratio is 18 : 27 : 30
False
False
False

16. Exam Questions – Specimen Papers
Student Sheet 4

17. Exam Questions – Specimen Papers

18. Exam Questions – Specimen Papers

19. Exam Questions – Specimen Papers

20. Exam Questions – Specimen Papers

21. Exam Questions – Specimen Papers

22. Exam Questions – Specimen Papers