Estimation Check calculations using approximation and estimation If

Estimation Check calculations using approximation and estimation If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key vocabulary Approximation Estimation 1 Significant Figure

Approximation / estimation Some calculations can be difficult such as 63 x £ 4. 82. To make life easier and quicker we can estimate this calculation using a suitable approximations. We can do this by rounding each number to one significant figure before calculating. So an approximate answer to 63 x £ 4. 82 is 60 x £ 5 = £ 300. The real answer is £ 303. 66 We can see that this has given us a very accurate estimation. Estimate the answer to (a) 43. 8 x 0. 59 40 x 0. 6 = 24 (b) 607 600 2. 89 3 = 200 To show that values have been rounded the 'approximately equal to' sign is used, ≈. 43. 8 x 0. 59 ≈ 24 607 ≈ 200 2. 89

Practice (1) Q 1: Using suitable approximations, estimate the answers to the following calculations. (a) 623 x 3. 81 600 x 4 = 2400 (b) 27. 93 ÷ 6. 18 30 ÷ 6 = 5 (c) 831 x 0. 19 800 x 0. 2 = 160 (d) 43. 09 ÷ 0. 48 40 ÷ 0. 5 = 80 (remember that dividing by 0. 5 doubles the answer)

Approximation / estimation Estimate the following calculation 309 x 37 0. 496 300 x 40 0. 5 12 000 0. 5 24 000

Approximation / estimation Sometimes one significant figure is not always the best method. For example, estimate √ 48. 5 We are looking for a square root so we need a square number. √ 49 = 7 Using estimates can be in a variety of contexts for calculations. For example, estimate 11% of £ 297 = £ 39. 67 10% of 300 = £ 30 If asked to estimate 24% of £ 324 = £ 77. 76 Could find 25% of £ 300 = £ 75 or 25% of £ 320 = £ 80

Practice (2) & (3) Q 2: For each calculation write down the solution you consider to be the best estimate. (a) 31. 17 x 4. 72 130 140 150 30 x 5 = 150 (b) 412 ÷ 3. 8 80 100 120 400 ÷ 4 = 100 (c) 282 x 0. 211 50 60 70 300 x 0. 2 = 60 (d) 67. 9 ÷ 0. 52 35 70 140 70 ÷ 0. 5 = 140 (e) 8. 91² 70 75 80 9² = 81 so 80 is closest Q 3: Use estimates to show that these answers are correct. (a) 19% of £ 61 = £ 11. 59 20 % of £ 60 = £ 12 (correct) (b) 52% of £ 606 = £ 325. 12 50% of 600 = £ 300 (incorrect) (c) 4. 8% of £ 78 = £ 2. 34 5% of £ 80 = £ 4 (incorrect) (d) 74% of £ 198 =£ 146. 52 75% of £ 200 = £ 150 (correct)

Practice (4) Estimate the answers to the following calculations. (a) 53. 7 x 28. 9 50 x 30 = 1500 (b) 0. 801 x 398. 9 0. 8 x 400 = 320 400 ÷ 8 = 50 (c) 410 ÷ 7. 93 6000 ÷ 10 = 600 (d) 5909 ÷ 11. 81 √ 121 = 11 (e) √ 120 3 3 of 200 = 150 (f) of 201. 9 4 4 2 (g) 2 of 44. 2 of 40 = 16 5 5

Practice (5) 1. 2. 3. 4. 5.

Underestimate or overestimate? A unit of gas costs 4. 2 pence. On average Ria uses 50. 1 units of gas a week. She pays for the gas she uses in 13 weeks. The estimate: 4 x 50 = 200 p (amount per week) 200 p x 10 weeks = 2000 p = £ 20 So could calculate (more accurately) 200 p x 13 weeks = 2600 p = £ 26 Deciding if underestimate or overestimate: Look to see if numbers were rounded up or down. Both rounded down. So this is an underestimate

Underestimate or overestimate? practice Paul organised an event for a charity. Each ticket for the event cost £ 19. 95. Paul sold 395 tickets. Paul paid costs of £ 6000. He gave all money left to the charity. (a) Work out an estimate for the amount of money Paul gave to the charity. (b) Is your answer to (a) an underestimate or an overestimate? Give a reason for your answer. The estimate: 400 x £ 20 = £ 8000 - £ 6000 = £ 2000 Deciding if underestimate or overestimate: Both rounded up. So this is an overestimate

Problem solving and reasoning Q 1: A party bag costs £ 3. 10 to produce. Claire has 22 guests at her daughter’s party. (a) Estimate how much Claire will spend on party bags. (b) Explain whether this is an over estimate or under estimate. (a) 22 x £ 3. 10 20 x £ 3 = £ 60 (b) The calculation is an underestimate. Reason, because £ 3 is smaller than £ 3. 10 and 20 is smaller than 22. Real answer 22 x £ 3. 10 = £ 68. 20 Q 2: A square field has an area 150 km². Estimate the perimeter of the field. We need to find √ 150. So we need a square number close to 150. The closest is 144. √ 144 = 12 Estimated length is each side of square is 12 km Estimated perimeter is 12 x 4 = 48 km

Exam specimen questions [3 marks]

Exam specimen questions

Exam specimen questions

Exam specimen questions

Exam specimen questions [3 marks]

Exam specimen questions

Exam specimen questions