Grade 5 Percentage Change Solve problems involving percentage change, including original value problems. If you have any questions regarding these resources, please contact hpateman@cornwallisacademy.com
Key Vocabulary Percentage Increase Decrease Value Discount Interest Sale
EXAMPLES PRACTICE Percentage Change Difference Old value 100 The price of a classic car increased from 50,000 to 70,000. What was the percentage increase? 1) 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 During January 2012 the number of people visiting Thorpe Park fell from 60,000 to 48,000. What was the percentage decrease? 2) 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 Student Sheet 1
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%
Percentage Decrease Old Value New value Old value During January 2012 the number of people visiting Thorpe Park fell from 60,000 to 48,000. What was the percentage decrease? 100 Percentage Decrease = 60,000 48,000 60,000 100 Percentage Decrease = 12,000 60,000 100 Percentage Decrease = 20%
Practice 1) What are the percentage decrease of these values? a) From 100,000 to 40,000 b) From 32,000 to 24,000 c) From 108,000 to 27,000 d) From 400,000 to 350,000 60% 25% 75% 12.5 2) What are the percentage increase of these values? a) From 100,000 to 120,000 b) From 20,000 to 24,000 c) From 64,000 to 128,000 d) From 36,000 to 54,000 20% 20% 100% 50%
Problem solving and reasoning Q1 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? Q3 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? 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 8573.75 what was the average percentage decrease per year? Student Sheet 2
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
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: 482,000 362,500 362,500 119,500 362,500 100 100 = 32.97% Average Percentage Increase per year: 32.97% Number of years 32.97% (2016-2009) 32.97% 7 = 4.71% = 5% to the nearest percent
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? 1264450 950,000 950,000 314450 950,000 100 100 = 33.1% 33.1% Number of years 33.1% (2003-2000) 33.1% 3 = 11% In 2009 a car was on sale for 10,000. The same car in 2012 was on sale for 8573.75 what was the average percentage decrease per year? 10,000 8573.75 10,000 100 14.26% Number of years 1426.25 10,000 100 = 14.26% 14.26% 3 = 4.74%
Exam Questions Specimen Papers Student Sheet 3
Exam Questions Specimen Papers
Exam Questions Specimen Papers
Grade 5 Section 2: Reverse Percentage Change Solve problems involving percentage change, including original value problems. If you have any questions regarding these resources, please contact holly.pateman@futureschoolstrust.com
Key Vocabulary Sort into 2 groups Percentage Loss Inflation Decline Dropped Increase Rise Gain Discount Depreciated Profit Increment Reduction Interest Marked down Decrease Student Sheet 1
Key Vocabulary Sort into 2 groups Percentage Increase Inflation Gain Rise Profit Increment Interest Decrease Loss Decline Depreciated Dropped Discount Reduction Marked down
s for Increase & Decrease Percentage 6% 3% 12% 8.5% 120% Increase + 100% 100 Decrease 100% 100 106% 1.06 94% 0.94 Student Sheet 2
s for Increase & Decrease Percentage 6% Increase + 100% 100 Decrease 100% 100 106% 1.06 94% 0.94 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
Percentage Increase & Decrease Amount X = New Amount Amount = New Amount
Reverse Percentage Change Rachel s monthly pay increased by 6% to 3710. What was Rachel s pay before the increase? In a sale, normal prices are reduced by 20%. Jane buys a road bike for 440. What is the normal price of the bike? Practice Time Find the original cost of these items. a) A cars price has been reduced by 30% and is now on sale for 7000. b) A laptop has increased in price by 10%. It is now on sale for 550. c) A TV has decreased in price by 25% and is now on sale for 750. Student Sheet 3
Reverse Percentage Change Rachel s monthly pay increased by 6% to 3710. What was Rachel s pay before the increase? In a sale, normal prices are reduced by 20%. Jane buys a road bike for 440. What is the normal price of the bike?? X 1.06 = New Amount 3710? X 0.8 = New Amount 440? = New Amount 3710? = New Amount 440 1.06 0.8 = 3500 = 550
Practice Time Find the original cost of these items. a) A car s price has been reduced by 30% and is now on sale for 7000. 10000 b) A laptop has increased in price by 10%. It is now on sale for 550. 500 c) A TV has decreased in price by 25% and is now on sale for 750. 1000
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 4
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?? X 1.02 x 1.1 = New Amount 39270 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?? = New Amount 39270? X 0.75 x 0.9 = New Amount 405 1.122? = New Amount 405 = 35000 = 600 0.675 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? Yes multiplier 0.9 which means percentage 90% 100% No it s infinite
Exam Questions Specimen Papers Student Sheet 5
Exam Questions Specimen Papers
Exam Questions Specimen Papers
Exam Questions Specimen Papers
Exam Questions Specimen Papers
Exam Questions Specimen Papers