Approximation & estimation · Ages 12–13
Planning an estimate
Big side or small side, which method, how precise.
How to do it
Method
Big side or small side, which method, how precise
20 squares × about 35 people ≈ 700 people
Another way
Estimate with a rate
3 drops every 10 s: 86,400 ÷ 10 × 3 = 25,920 drops
In full
In a real situation you decide how to estimate. First: should it err on the big side or the small side? Ordering chairs, buying paint or allowing time should be too big; income you can promise should be too small. Second: which method? Things too many to count can be sampled: cut a photo of a crowd into 20 squares, count about 35 people in one, and there are about 20 × 35 = 700. Something that repeats can use a rate: a tap drips 3 drops every 10 seconds, and a day has 86,400 seconds, so about 25,920 drops. Third: how precise? Give a sensible number of figures, and check a calculator's answer for its size with an estimate first. One situation can have more than one sensible strategy, as long as you can give the reason.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A photo of a crowd is cut into 25 equal squares, and one square has about 38 people. About how many people are in the photo?
Show the answer and working
Answer: 950 people
A sample: 25 squares × about 38 a square = 950 people.
Example 2
A tap drips 7 drops every 20 seconds. That is about drops a minute, an hour and a day.
Fill in each blank
Show the answer and working
Answer: 21, 1260, 30240
60 ÷ 20 × 7 = 21; 21 × 60 = 1,260; 1,260 × 24 = 30,240.
Example 3
Working out 39 × 27 on a calculator, which result is sensible? Check with an estimate first.
- A. 1,053
- B. 66
- C. 10,530
- D. 105
Choose the right answer
Show the answer and working
Answer: A. 1,053
39 × 27 ≈ 40 × 30 = 1,200; only 1,053 is near the estimate.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.A photo of a crowd is cut into 19 equal squares, and one square has about 34 people. About how many people are in the photo?
Answer:
2.A tap drips 6 drops every 2 seconds. That is about drops a minute, an hour and a day.
Fill in each blank
Answer:
3.A wall of 85 square metres is to be painted, and a litre of paint covers 6 square metres. 15 litres of paint is surely enough.
True or false?
Answer:
4.To estimate how many words a 349-page book has, which way is most sensible?
- A. Count the words on one line, then times 349
- B. Count the words on the cover, then times 349
- C. Count the words on one page, then times 349
- D. Count every word in the book
Choose the right answer
Answer:
5.250 sheets of paper stack 38 mm high. Correct to 2 significant figures, about how thick is one sheet?
Answer:
All the answers
- 1. 646 people
- 2. 180, 10800, 259200
- 3. True
- 4. C. Count the words on one page, then times 349
- 5. 0.15 mm
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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