Overestimating vs underestimating
I can determine whether calculations using rounding or truncating will give an underestimate or overestimate.
Overestimating vs underestimating
I can determine whether calculations using rounding or truncating will give an underestimate or overestimate.
Lesson details
Key learning points
- When multiplying or adding, using a value which has been rounded up results in an overestimate.
- When dividing or subtracting, using a value which has been rounded up results in an underestimate.
- Calculations using rounding or truncating will give an over or under estimate.
- 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.
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).
Video
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Starter quiz
6 Questions
$$\frac{9.8}{0.120}$$ -
$$100$$
$$\frac{98}{0.111}$$ -
$$1000$$
$$\frac{9.8}{0.2003}$$ -
$$50$$
$$\frac{980}{0.199}$$ -
$$5000$$
$$\frac{980}{0.498}$$ -
$$2000$$
$$\frac{9}{0.51}$$ -
$$18$$
Exit quiz
6 Questions
38.48 + 29.84 -
$$\approx$$ 40 + 30
18.983 + 19.303 -
$$\approx$$ 20 + 20
45.9348 + 39.84 -
$$\approx $$ 50 + 40
8.548 + 2.84 + 19.203 -
$$\approx$$ 9 + 3 + 20
38.48² + 29.84 -
$$\approx$$ 40² + 30
$$\approx \text{ }$$8 × 8 -
Area of a square with lengths 7.89 m
$$\approx \text{ }$$8 + 8 + 8 + 8 -
Perimeter of a square with lengths 7.89 m
$$\approx\text{ }$$ 5 × 5 -
Area of a square with lengths 4.67 m
$$\approx \text{ }$$ 5 + 5 + 5 + 5 -
Perimeter of a square with lengths 4.67 m
$$\approx\text{ }$$ 0.5 × 0.5 -
Area of a square with lengths 0.498 m
$$\approx\text{ }$$0.5 + 0.5 + 0.5 + 0.5 -
Perimeter of a square with lengths 0.498 m
Overestimate -
$$\frac{899}{4.40+6.35}\approx\frac{900}{4+6}$$
Underestimate -
$$\frac{712}{8.98+9.45}\approx\frac{700}{10+10}$$
Hard to tell -
$$\frac{37.4}{4.49+6.41}\approx\frac{40}{5+6}$$
Overestimate -
$$\frac{59-42}{3.67+1.23}\approx\frac{60-40}{3+1}$$
Underestimate -
$$\frac{59-42}{3.67+1.23}\approx\frac{55-45}{4+2}$$
Hard to tell -
$$\frac{59-42}{3.67+1.23}\approx\frac{60-50}{4+2}$$