1. Percentage change Grade 4
Express percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Solve problems involving percentage change, including original value problems.
Grade 5
Prior Knowledge
Concept of percentage
Multipliers
Associated words for increase and decrease
Duration
The content of this lesson is intended to be covered within 45 minutes. Suggested timings are below for each episode within the lesson.
Resources
Print slides: 3, 5, 9, 13, 16, 19, 21
Equipment
Calculator
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
Words associated with a percentage increases and percentage decrease
Give students slide 3 printed. To work independently to sort the words into two groups (do not necessarily tell them what the two groups are). Discuss how these words will be used in questions to signal whether the context is percentage increase or decrease.
Method for percentage change
Give students slide 5 printed. Use the two example boxes in the blue to model how to use the formula for percentage change. Slides 6 and 7 have been animated to reveal each step of the solution. Ensure that students copy all of the steps. Give 10 minutes to independently practice using this formula by completing the questions in the yellow box. Make sure that students are not confused why which number to subtract from which. To generlise talk about the difference (and ignoring if positive or negative). 15
Applying the method for percentage change in contextualised problems
Give students slide 9. Allow students to attempt question on their own for 5 minutes. Review question together and model answer. Which extracting the information from these types of questions it can be confusing which numbers relate to which year etc. Recommend that students re write the numbers in a form that makes sense to them – have modelled on slide 10 the use of a table to layout the numbers.
How to find a percentage multiplier
Give students slide 13 printed. Show the example with 6%. Students then repeat with different percentages to find the multiplier for increase and decrease. 10
Formula for percentage increase/decrease and how to rearrange for reverse percentage problems
Show slide 15. Students copy the formulae onto their sheet (slide 13). Apply these formulae to questions. Give students slide 16 printed. Model the answers using slide 17. Students complete 3 further questions to practice. Give answers.
Solving reverse percentage change problems involving 2 multipliers in contextualised problems
Give students slide 19. Students attempt independently for 2 minutes. Review and model answer. Show how a “new” multiplier is created from the 2 original multipliers (otherwise the method is the same).
Calculating percentage change in OCR exam questions (from specimen papers)
Give students slide 21. This includes 4 exam questions related to objective. Students need to use notes from lesson to answer the questions. Relate to mark scheme to show how the marks are allocated.
Next Steps
Compound percentage change
Assessment
PLC/Reformed Specification/Target 5/Ratio, proportion and rates of change/percentage change

3. Key Vocabulary – Sort into 2 groups
Percentage Original Multiplier
Inflation
Loss
Decline
Dropped
Increase
Gain
Rise
Discount
Depreciated
Profit
Increment
Reduction
Interest
Marked down
Decrease
Student Sheet 1

4. Key Vocabulary – Sort into 2 groups
Percentage Original Multiplier
Increase
Decrease
Inflation
Loss
Gain
Decline
Depreciated
Rise
Dropped
Profit
Discount
Increment
Reduction
Interest
Marked down

5. What was the percentage decrease?
Percentage Change
𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝑶𝒍𝒅 𝒗𝒂𝒍𝒖𝒆 ×𝟏𝟎𝟎
The price of a classic car increased from £50,000 to £70,000. What was the percentage increase?
What are the percentage decrease of these values?
From 100,000 to 40,000
From 32,000 to 24,000
From 108,000 to 27,000
From 400,000 to 350,000
What are the percentage increase of these values?
From 100,000 to 120,000
From 20,000 to 24,000
From 64,000 to 128,000
From 36,000 to 54,000
EXAMPLES
PRACTICE
During January 2012 the number of people visiting Thorpe Park fell from 60,000 to 48,000.
What was the percentage decrease?
Student Sheet 2

6. Percentage Increase
𝑵𝒆𝒘 𝑽𝒂𝒍𝒖𝒆 −𝑶𝒍𝒅 𝒗𝒂𝒍𝒖𝒆 𝑶𝒍𝒅 𝒗𝒂𝒍𝒖𝒆 ×𝟏𝟎𝟎
The price of a classic car increased from £50,000 to £70,000. What was the percentage increase? Percentage Increase = 𝟕𝟎,𝟎𝟎𝟎 −𝟓𝟎,𝟎𝟎𝟎 𝟓𝟎,𝟎𝟎𝟎 ×100 Percentage Increase = 20,000 𝟓𝟎,𝟎𝟎𝟎 ×100 Percentage Increase = 40%

7. Percentage Decrease
𝑶𝒍𝒅 𝑽𝒂𝒍𝒖𝒆 −𝑵𝒆𝒘 𝒗𝒂𝒍𝒖𝒆 𝑶𝒍𝒅 𝒗𝒂𝒍𝒖𝒆 ×𝟏𝟎𝟎
During January 2012 the number of people visiting Thorpe Park fell from 60,000 to 48,000. What was the percentage decrease? Percentage Decrease = 60,000 −48,000 60,000 ×100 Percentage Decrease = 12,000 60,000 ×100 Percentage Decrease = 20%

8. Practice What are the percentage decrease of these values?
From 100,000 to 40,000
From 32,000 to 24,000
From 108,000 to 27,000
From 400,000 to 350,000
What are the percentage increase of these values?
From 100,000 to 120,000
From 20,000 to 24,000
From 64,000 to 128,000
From 36,000 to 54,000
60%
25%
75%
12.5
20%
100%
50%

9. Problem solving and reasoningQ1
In 2000, Clarke uses 7000 units of electricity.
In 2001, the price of electricity decreased by 5% and Clarke reduced his usage to 5000 units.
Clarke paid £1400 for the units he used in 2000.
How much did he spend on electricity in 2001?
In 2009 the average price of a house in Spain was £362,500.
In 2016 the average price had increased to £482,000.
What was the average percentage increase per year, to the nearest percent? Q3 Q2
The value of a house in 2000 was £950,000. In 2003 the same house had a value of £1,264,450 what was the average percentage increase per year? Q4
In 2009 a car was on sale for 10,000. The same car in 2012 was on sale for £ what was the average percentage decrease per year?
Student Sheet 3

10. Problem solving and reasoning
In 2000, Clarke uses 7000 units of electricity.
In 2001, the price of electricity decreased by 5% and Clarke reduced his usage to 5000 units.
Clarke paid £1400 for the units he used in 2000.
How much did he spend on electricity in 2001?
Year
2000
2001
Units
7000
5000
Price
1400
Dec 5%?
Price per unit in 2000
£1400/7000 = £0.20 per unit
5% decrease = 95% of normal price
95% of £0.20 = 0.95 × £0.20 = £0.19
This is the price per unit in 2001
£0.19 × 5000 = £950

11. Problem solving and reasoning
In 2009 the average price of a house in Spain was £362,500.
In 2016 the average price had increased to £482,000.
What was the average percentage increase per year, to the nearest percent?
Percentage Increase of house:
482,000−362, ,500 ×100
119, ,500 ×100=32.97%
Average Percentage Increase per year:
32.97% ÷ Number of years
32.97% ÷ ( )
32.97% ÷ 7 = 4.71%
= 5% to the nearest percent

12. Reason and explain
The value of a house in 2000 was £950,000. In 2003 the same house had a value of £1,264,450 what was the average percentage increase per year?
In 2009 a car was on sale for 10,000. The same car in 2012 was on sale for £ what was the average percentage decrease per year?
−950, ,000 ×100
,000 ×100=33.1%
33.1% ÷ Number of years
33.1% ÷ ( )
33.1% ÷ 3 = 11%
10,000− ,000 ×100
,000 ×100=14.26%
14.26% ÷ Number of years
14.26% ÷ 3 = 4.75%

13. Multipliers for Increase & Decrease
Percentage
Increase + 100%
Multiplier ÷ 100
Decrease – 100%
Multiplier ÷100 6% 3%
12%
8.5%
120%
106%
1.06
94%
0.94
Student Sheet 4

14. Multipliers for Increase & Decrease
Percentage
Increase + 100%
Multiplier ÷ 100
Decrease – 100%
Multiplier ÷100 6% 3%
103%
1.03
97%
0.97
12%
112%
1.12
88%
0.88
8.5%
108.5%
1.085
91.5%
0.915
120%
220%
2.2
Not possible
106%
1.06
94%
0.94

15. Percentage Increase & Decrease
Original Amount X
Multiplier =
New Amount
Original Amount =
New Amount ÷
Multiplier

16. Reverse Percentage Change
In a sale, normal prices are reduced by 20%.
Jane buys a road bike for £440.
What is the normal price of the bike?
Rachel’s monthly pay increased by 6% to £3710. What was Rachel’s pay before the increase?
Practice Time
Find the original cost of these items.
A cars price has been reduced by 30% and is now on sale for £7000.
A laptop has increased in price by 10%. It is now on sale for £550.
A TV has decreased in price by 25% and is now on sale for £750.
Student Sheet 5

17. Reverse Percentage Change
In a sale, normal prices are reduced by 20%.
Jane buys a road bike for £440.
What is the normal price of the bike?
Rachel’s monthly pay increased by 6% to £3710. What was Rachel’s pay before the increase?
Original ? X
Multiplier
1.06 =
New Amount
3710
Original ? X
Multiplier
0.8 =
New Amount
440
Original ? =
New Amount
3710
Original ? =
New Amount
440 ÷ ÷
Multiplier
1.06
Multiplier
0.8
Original
= 3500
Original
= 550

18. Practice Time Find the original cost of these items.
A car’s price has been reduced by 30% and is now on sale for £7000.
A laptop has increased in price by 10%. It is now on sale for £550.
A TV has decreased in price by 25% and is now on sale for £750.
£10000
£500
£1000

19. Problem Solving and Reasoning
After a 2% increase, followed by a 10% increase, the annual salary of an Engineer was £39,270. What was the original annual salary?
Ola buys a tablet computer for £405.
The store is having a 25% sale and she has a discount voucher for a further 10% off.
What is the normal price of the tablet computer?
Thinking Questions:
A 10% reduction in price = 90% of the original price?
What is the largest percentage decrease you can get?
Is there a largest percentage increase in price?
Student Sheet 6

20. Problem Solving and Reasoning
After a 2% increase, followed by a 10% increase, the annual salary of an Engineer was £39,270. What was the original annual salary?
Ola buys a tablet computer for £405.
The store is having a 25% sale and she has a discount voucher for a further 10% off.
What is the normal price of the tablet computer?
Original ? X
Multiplier
1.02 x 1.1 =
New Amount
39270
Original ? X
Multiplier
0.75 x 0.9 =
New Amount
405
Original ? =
New Amount
39270 ÷
Original ? =
New Amount
405
Multiplier
1.122 ÷
Multiplier
0.675
Original
= 35000
Original
= 600
Yes multiplier 0.9 which means percentage 90%
A 10% reduction in price = 90% of the original price?
What is the largest percentage decrease you can get?
Is there a largest percentage increase in price?
100%
No it’s infinite

21. Exam Questions – Specimen Papers
Student Sheet 7

22. Exam Questions – Specimen Papers

23. Exam Questions – Specimen Papers

24. Exam Questions – Specimen Papers

25. Exam Questions – Specimen Papers