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.
These resources will be removed by end of Summer Term 2025.
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.
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.
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.
To help you plan your year 8 maths lesson on: Overestimating vs underestimating, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 8 maths lesson on: Overestimating vs underestimating, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 3 maths lessons from the Estimation and rounding unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson 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 -
$$\frac{59-42}{3.67+1.23}\approx\frac{60-50}{4+2}$$