Numbers and operations · Ages 12–13

Estimation strategies worksheet

Part of: Approximation & estimation

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Numbers and operations · Ages 12–13

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Round each number to the nearest hundred to estimate 764 + 833:
Answer:
2.Take each number to 1 significant figure to estimate 93 × 188:
Answer:
3.A front-end estimate of 131 + 107 + 981: the hundreds first make ; the tens and ones left, added and taken to the nearest hundred, make ; the estimate is .
Fill in each blank
Answer:
4.Estimate 2,993 ÷ 5 with a compatible number: change 2,993 to the nearest whole hundred that 5 divides, and the estimate is .
Answer:
5.Take each number to 1 significant figure to estimate 7,523 ÷ 98:
Answer:
6.Take each number to 1 significant figure to estimate 6,002 ÷ 52:
Answer:

7.92 × 87 is estimated as 100 × 90. How does the estimate, 9,000, compare with the exact value?
- A. Too small
- B. Exactly equal
- C. Too big
- D. Can't tell
Choose the right answer
Answer:
8.Estimating 81 × 13 as 80 × 10 = 800, the exact value is less than 800.
True or false?
Answer:
9.Taking 1 significant figure, about how much is 42 × 856?
- A. 360,000
- B. 3,600
- C. 940
- D. 36,000
Choose the right answer
Answer:
10.Estimating 71 × 19 as 70 × 10 = 700, the exact value is less than 700.
True or false?
Answer:
11.Taking 1 significant figure, about how much is 59 × 850?
- A. 540,000
- B. 960
- C. 54,000
- D. 5,400
Choose the right answer
Answer:
12.Estimating 9,776 ÷ 13 as 10,000 ÷ 10 = 1000, the estimate is too big.
True or false?
Answer:

13.A rectangular field is 775 m long and 65 m wide. Taking 1 significant figure, about what is its area in square metres?
Working:
Answer:
14.62 members go on a trip; each pays $47 for the coach and $44 for lunch. Taking each number to 1 significant figure, about how much is the total?
Working:
Answer:
15.6 people share $2,393 of prize money. Estimate with a compatible number: change 2,393 to the nearest whole hundred that 6 divides, , and each gets about dollars.
Fill in each blank
Working:
Answer:
16.A hall has 59 rows of 61 seats. Taking 1 significant figure, about how many seats are there?
Working:
Answer:
17.To estimate 4,791 ÷ 6 in your head, which way is best?
- A. Long division of 4,791 by 6
- B. 5,000 ÷ 6
- C. 4,800 ÷ 6
- D. 4,000 ÷ 6
Choose the right answer
Working:
Answer:
18.Petrol costs $28.01 a litre and 38 litres were put in. May estimates 28 × 40 = 1120; the real cost is less than $1,120.
True or false?
Working:
Answer:

Show the answers and working

Estimation strategies worksheet: Answers and working

1. 1600
764 ≈ 800 and 833 ≈ 800, so 800 + 800 = 1,600.
2. 18000
93 ≈ 90 and 188 ≈ 200, so 90 × 200 = 18,000.
3. 1100, 100, 1200
The hundreds: 1,100; the rest, 119, is about 100; 1,100 + 100 = 1,200.
4. 600
2,993 ≈ 3,000, and 3,000 ÷ 5 = 600.
5. 80
7,523 ≈ 8,000 and 98 ≈ 100, so 8,000 ÷ 100 = 80.
6. 120
6,002 ≈ 6,000 and 52 ≈ 50, so 6,000 ÷ 50 = 120.

7. C. Too big
92 became 100 and 87 became 90: both moved the same way, so the product moves that way too.
8. False
81 became 80 and 13 became 10: both bigger makes the estimate too big; both smaller, too small.
9. D. 36,000
42 ≈ 40 and 856 ≈ 900, so 40 × 900 = 36,000.
10. False
71 became 70 and 19 became 10: both bigger makes the estimate too big; both smaller, too small.
11. C. 54,000
59 ≈ 60 and 850 ≈ 900, so 60 × 900 = 54,000.
12. True
9,776 became 10,000 and the divisor 13 became 10. A bigger number divided by a smaller divisor makes the quotient too big; the other way round, too small.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 56000 m²
775 ≈ 800 and 65 ≈ 70, so 800 × 70 = 56,000.
14. 5400 dollars
62 ≈ 60, and each pays about 50 + 40 = 90; 60 × 90 = 5,400 dollars.
15. 2,400, 400
2,393 ≈ 2,400, and 2,400 ÷ 6 = 400.
16. 3600 seats
59 ≈ 60 and 61 ≈ 60, so 60 × 60 = 3,600.
17. C. 4,800 ÷ 6
A compatible number: 4,800 is close to 4,791 and 6 divides it, so 4,800 ÷ 6 is quick.
18. True
Exactly: 28.01 × 38 = 1064.38. The numbers weren't both rounded the same way, so the estimate promises nothing; only working it out tells.

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