Numbers and operations · Ages 12–13

Planning an estimate worksheet

Part of: Approximation & estimation

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Numbers and operations · Ages 12–13

Numsprite
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Name:Date:Score:／48

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

1.A photo of a crowd is cut into 19 equal squares, and one square has about 26 people. About how many people are in the photo?
Answer:
2.A bag of beans weighs 300 g. 10 g holds about 27 beans. About how many beans are in the bag?
Answer:
3.A tap drips 6 drops every 3 seconds. That is about drops a minute, an hour and a day.
Fill in each blank
Answer:
4.A bag of beans weighs 600 g. 10 g holds about 33 beans. About how many beans are in the bag?
Answer:
5.500 sheets of paper stack 32 mm high. Correct to 2 significant figures, about how thick is one sheet?
Answer:
6.500 sheets of paper stack 78 mm high. Correct to 2 significant figures, about how thick is one sheet?
Answer:

7.In which situation should the estimate err on the big side?
- A. Working out the least you can save each month
- B. Getting chairs ready for 27 guests
- C. Promising to give away what 9 hours of part-time work will earn
- D. Working out the most passengers of about 65 kg a lift can carry
Choose the right answer
Answer:
8.A wall of 66 square metres is to be painted, and a litre of paint covers 10 square metres. 7 litres of paint is surely enough.
True or false?
Answer:
9.Working out 28 × 98 on a calculator, which result is sensible? Check with an estimate first.
- A. 274
- B. 27,440
- C. 2,744
- D. 126
Choose the right answer
Answer:
10.A wall of 85 square metres is to be painted, and a litre of paint covers 12 square metres. 9 litres of paint is surely enough.
True or false?
Answer:
11.Working out 42 × 38 on a calculator, which result is sensible? Check with an estimate first.
- A. 159
- B. 80
- C. 1,596
- D. 15,960
Choose the right answer
Answer:
12.To estimate how many words a 214-page book has, which way is most sensible?
- A. Count every word in the book
- B. Count the words on the cover, then times 214
- C. Count the words on one page, then times 214
- D. Count the words on one line, then times 214
Choose the right answer
Answer:

13.A heart beats 24 times in 15 seconds. About how many times does it beat in an hour?
Working:
Answer:
14.A rectangular seed tray 50 cm long and 20 cm wide is covered in seeds. A square of side 5 cm holds about 19. About how many seeds are in the tray?
Working:
Answer:
15.A novel has 543 pages and Ming reads about 36 a day. At least how many days to finish it?
Working:
Answer:
16.27 friends are coming to a party, each eating about 2 slices of pizza. How should the pizza be estimated?
- A. Get just 2 slices
- B. Allow a little more each: better too much than too little
- C. Get just 27 slices
- D. Allow a little less each: better too little than too much
Choose the right answer
Working:
Answer:
17.A coach costs $2,024, shared by 34 people. Ka-lok estimates 2,000 ÷ 40 = 50, and $50 each is surely enough.
True or false?
Working:
Answer:
18.A wall is 9.4 m long and 2.7 m high, and a can of paint covers 10 square metres. Paint errs on the big side. At least how many cans?
Working:
Answer:

Show the answers and working

Planning an estimate worksheet: Answers and working

1. 494 people
A sample: 19 squares × about 26 a square = 494 people.
2. 810 beans
300 g is 30 times 10 g: 30 × 27 = 810 beans.
3. 120, 7200, 172800
60 ÷ 3 × 6 = 120; 120 × 60 = 7,200; 7,200 × 24 = 172,800.
4. 1980 beans
600 g is 60 times 10 g: 60 × 33 = 1,980 beans.
5. 0.064 mm
32 ÷ 500 = 0.064, which is 0.064 to 2 significant figures. Measuring a stack and dividing is far more accurate than measuring one sheet.
6. 0.16 mm
78 ÷ 500 = 0.156, which is 0.16 to 2 significant figures. Measuring a stack and dividing is far more accurate than measuring one sheet.

7. B. Getting chairs ready for 27 guests
Too few chairs leaves guests standing, so err on the big side; the other three should err small, to be kept or to be safe.
8. True
66 ÷ 10 ≈ 6.6. Paint should err on the big side, so round up: at least 7 litres.
9. C. 2,744
28 × 98 ≈ 30 × 100 = 3,000; only 2,744 is near the estimate.
10. True
85 ÷ 12 ≈ 7.08. Paint should err on the big side, so round up: at least 8 litres.
11. C. 1,596
42 × 38 ≈ 40 × 40 = 1,600; only 1,596 is near the estimate.
12. C. Count the words on one page, then times 214
One page as a sample, times the number of pages: quick and close. Or average a few pages, then times 214.

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

13. 5760 beats
A minute is four 15 seconds: 24 × 4 = 96; an hour is 60 minutes: 96 × 60 = 5,760.
14. 760 seeds
The tray is 1,000 cm², which is 40 times the small square's 25 cm²; 40 × 19 = 760 seeds.
15. 16 days
543 ÷ 36 is rounded up: the last few pages take a day too, so 16.
16. B. Allow a little more each: better too much than too little
About 27 × 2 slices, plus a few: running short is worse than leftovers.
17. False
Only a bigger cost shared by fewer people makes each share too big, surely enough; a smaller cost over more people makes it too small. Compare 50 × 34 with 2,024.
18. 3 cans
The area is 9.4 × 2.7 = 25.38 m²; 25.38 ÷ 10 rounded up is 3 cans.

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