New
New
Year 8

Overestimating vs underestimating

I can determine whether calculations using rounding or truncating will give an underestimate or overestimate.

New
New
Year 8

Overestimating vs underestimating

I can determine whether calculations using rounding or truncating will give an underestimate or overestimate.

Lesson details

Key learning points

  1. When multiplying or adding, using a value which has been rounded up results in an overestimate.
  2. When dividing or subtracting, using a value which has been rounded up results in an underestimate.
  3. Calculations using rounding or truncating will give an over or under estimate.
  4. By careful consideration of the calculation it is possible to tell if an answer is an over or under estimate.

Common misconception

When subtracting or dividing, the largest value is found by subtracting or dividing the largest rounded number by the largest rounded divisor or additive inverse.

Drawing a number line to show the subtraction of the smallest number will help students see how to achieve an overestimate or underestimate. When using division, reiterating the division of number is the same as multiplying by its reciprocal.

Keywords

  • Overestimate - An overestimate is an estimate for a calculation which is greater than the exact answer.

  • Underestimate - An underestimate is an estimate for a calculation which is less than the exact answer.

Give the answer to a calculation, e.g 40, and ask them create calculations where the answer of 40 is an overestimate or underestimate using addition, multiplication, subtraction and division. A spider diagram can be used to collate the answers. For more challenging work, give the answer of 0.8.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
__________ are the digits in a number that contribute to the accuracy of the number. The first significant figure is the first non-zero digit.
Estimated numbers
Important number
Real numbers
Correct answer: Significant figures
Q2.
Which of the following are good, quick estimate calculations for 577 ÷ 19.57?
Correct answer: 580 ÷ 20
Correct answer: 600 ÷ 20
580 ÷ 19.5
600 ÷ 19.5
Q3.
Which of the following are a correct estimate for $${11.239\times3.12}\over{0.488}$$?
$${11\times3} \over {0.5}$$ $$= 16.5$$
$${10\times3} \over {0.5}$$ $$= 15$$
Correct answer: $${11\times3} \over {0.5}$$ $$= 66$$
Correct answer: $${10\times3} \over {0.5}$$ $$= 60$$
Q4.
Match each calculation to its approximate answer.
Correct Answer:$$\frac{9.8}{0.120}$$,$$100$$

$$100$$

Correct Answer:$$\frac{98}{0.111}$$,$$1000$$

$$1000$$

Correct Answer:$$\frac{9.8}{0.2003}$$,$$50$$

$$50$$

Correct Answer:$$\frac{980}{0.199}$$,$$5000$$

$$5000$$

Correct Answer:$$\frac{980}{0.498}$$,$$2000$$

$$2000$$

Correct Answer:$$\frac{9}{0.51}$$,$$18$$

$$18$$

Q5.
A square plot of grass has a length of 7.88 m (2 d.p). Select the correct estimate for the area of the square grass plot.
Correct answer: 8 × 8 = 64 m²
8 × 8 = 16 m²
8 + 8 + 8 + 8 = 32 m²
8 + 8 + 8 + 8 = 32 m
Q6.
Izzy thinks of a number. Truncated to 1 s.f., it is 500. Rounded to the nearest 50, it is 600. It is multiple of 5 and a palindrome . All of its digits are prime numbers. Izzy's number is
Correct Answer: 575

6 Questions

Q1.
An __________ is an estimate for a calculation which is greater than the exact answer.
average
impossible number
integer
Correct answer: overestimate
underestimate
Q2.
An __________ is an estimate for a calculation which is less than the exact answer.
average
impossible number
integer
overestimate
Correct answer: underestimate
Q3.
Match each calculation with a calculation that gives its overestimate.
Correct Answer:38.48 + 29.84,$$\approx$$ 40 + 30

$$\approx$$ 40 + 30

Correct Answer:18.983 + 19.303,$$\approx$$ 20 + 20

$$\approx$$ 20 + 20

Correct Answer:45.9348 + 39.84,$$\approx $$ 50 + 40

$$\approx $$ 50 + 40

Correct Answer:8.548 + 2.84 + 19.203,$$\approx$$ 9 + 3 + 20

$$\approx$$ 9 + 3 + 20

Correct Answer:38.48² + 29.84,$$\approx$$ 40² + 30

$$\approx$$ 40² + 30

Q4.
Match the following calculations which give an overestimated area.
Correct Answer:$$\approx \text{ }$$8 × 8 ,Area of a square with lengths 7.89 m

Area of a square with lengths 7.89 m

Correct Answer:$$\approx \text{ }$$8 + 8 + 8 + 8 ,Perimeter of a square with lengths 7.89 m

Perimeter of a square with lengths 7.89 m

Correct Answer:$$\approx\text{ }$$ 5 × 5 ,Area of a square with lengths 4.67 m

Area of a square with lengths 4.67 m

Correct Answer:$$\approx \text{ }$$ 5 + 5 + 5 + 5 ,Perimeter of a square with lengths 4.67 m

Perimeter of a square with lengths 4.67 m

Correct Answer:$$\approx\text{ }$$ 0.5 × 0.5 ,Area of a square with lengths 0.498 m

Area of a square with lengths 0.498 m

Correct Answer:$$\approx\text{ }$$0.5 + 0.5 + 0.5 + 0.5,Perimeter of a square with lengths 0.498 m

Perimeter of a square with lengths 0.498 m

Q5.
Match which calculations are an overestimate, underestimate or hard to tell.
Correct Answer:Overestimate,$$\frac{899}{4.40+6.35}\approx\frac{900}{4+6}$$

$$\frac{899}{4.40+6.35}\approx\frac{900}{4+6}$$

Correct Answer:Underestimate,$$\frac{712}{8.98+9.45}\approx\frac{700}{10+10}$$

$$\frac{712}{8.98+9.45}\approx\frac{700}{10+10}$$

Correct Answer:Hard to tell ,$$\frac{37.4}{4.49+6.41}\approx\frac{40}{5+6}$$

$$\frac{37.4}{4.49+6.41}\approx\frac{40}{5+6}$$

Q6.
Match which calculations are an overestimate, underestimate or hard to tell.
Correct Answer:Overestimate,$$\frac{59-42}{3.67+1.23}\approx\frac{60-40}{3+1}$$

$$\frac{59-42}{3.67+1.23}\approx\frac{60-40}{3+1}$$

Correct Answer:Underestimate,$$\frac{59-42}{3.67+1.23}\approx\frac{55-45}{4+2}$$

$$\frac{59-42}{3.67+1.23}\approx\frac{55-45}{4+2}$$

Correct Answer:Hard to tell ,$$\frac{59-42}{3.67+1.23}\approx\frac{60-50}{4+2}$$

$$\frac{59-42}{3.67+1.23}\approx\frac{60-50}{4+2}$$