Percentages Homework Grid Your aim is to score at least 50 points by choosing different tasks. You must pick one from each row: fluency, reasoning and problem-solving. Bronze Silver Gold Fluency (5 points) Calculate 23% of £160. Reduce £90 by 23%. The price of a coat is reduced by 23% in the sale. It now costs £92.40. What did it cost before the sale? Reasoning (10 points) Which of these gives the larger amount: Explain why the answer to each of these Statistics tell us that female employees in the 17% of £50 or 50% of £17? must be the same: 47% of 9 and 9% of 47. UK earn 9.1% per hour less than their male colleagues. If all female employees were to receive a 10% increase on their pay, would this now mean they were earning more, less or the same as the male employees? ProblemSolving (15 points) Beth visits a large department store during the January sales. She spots these two sale stickers. Which one has the larger percentage reduction? Was £39.99 Now £25! The Big One! (30 points) Normal price £52 Take 35% off! Ellie and Frederic are selling sweets at their respective schools’ tuck shops. Ellie buys 100 sweets for £28 and sells them for £45. Frederic buys 50 sweet for £13 and makes a £7.50 profit. Who makes the bigger percentage profit? I invest some money in a savings account. During the first year, I received 2% interest back, then in the second year I receive 3%. What percentage interest have I received overall? By looking online at “payday loan” lenders, design a short presentation to explain to your classmates why borrowing from one of these is never a good idea. visit twinkl.com Percentages Homework Grid Answers Your aim is to score at least 50 points by choosing different tasks. You must pick one from each row: fluency, reasoning and problem-solving. Fluency (5 points) Reasoning (10 points) Bronze Silver Gold Calculate 23% of £160. Reduce £90 by 23%. 10% is £16 so 20% is £32 1% is £1.60 so 3% is £4.80 In total, 23% is £36.80 23% is £20.70 90 – 20.70 = £69.30 The price of a coat is reduced by 23% in the sale. It now costs £92.40. What did it cost before the sale? Which of these gives the larger amount: 17% of £50 or 50% of £17? Explain why the answer to each of these must be the same: 47% of 9 and 9% of 47. These actually give the same answer: £8.50. We can calculate these using the decimal equivalents: 0.47 × 9 0.09 × 47 To work out why, we can look at the decimal equivalents: 50 × 0.17 or 17 × 0.5. If we were to calculate these by hand, we would work out the answer to the integer problems then divide by 100. ProblemSolving (15 points) Beth visits a large department store during the January sales. She spots these two sale stickers. Which one has the larger percentage reduction? Was £39.99 Now £25! Normal price £52 Take 35% off! The first deal has a percentage reduction of 14.99 39.99 × 100 = 37.5%. Therefore, the first deal has a larger percentage reduction. The Big One! (30 points) A 23% reduction is 77% 92.40 ÷ 0.77 = £120 To calculate the answer in both cases, we would work out 47 × 9 and then divide by 100. Hence they will give the same answer. Ellie and Frederic are selling sweets at their respective schools’ tuck shops. Ellie buys 100 sweets for £28 and sells them for £45. Frederic buys 50 sweet for £13 and makes a £7.50 profit. Who makes the bigger percentage profit? Ellie’s percentage profit is 17 × 28 Frederic’s percentage profit is 100 = 60.7% 7.50 13 Statistics tell us that female employees in the UK earn 9.1% per hour less than their male colleagues. If all female employees were to receive a 10% increase on their pay, would this now mean they were earning more, less or the same as the male employees? Currently, female employees are earning 90.9% of what male employees earn. A 10% increase would be calculated by 90.9 × 1.1 = 99.99%. This would mean they were still earning slightly less than their male colleagues. I invest some money in a savings account. During the first year, I received 2% interest back, then in the second year I receive 3%. What percentage interest have I received overall? 1.02 × 1.03 = 1.0506 This is 5.06% interest. × 100 = 57.7% Therefore, Ellie makes the bigger percentage profit. By looking online at “payday loan” lenders, design a short presentation to explain to your classmates why borrowing from one of these is never a good idea. Responses will vary, but pupils should make reference to inflated interest fees that quickly double the amount that must be paid back. visit twinkl.com