- Year 8
Overestimating vs underestimating
I can determine whether calculations using rounding or truncating will give an underestimate or overestimate.
- Year 8
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.
Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.
These resources were created for remote use during the pandemic and are not designed for classroom teaching.
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 under or overestimate.
- Calculations using rounding or truncating will give an over or underestimate.
- By careful consideration of the calculation, it is possible to tell if an answer is an over or underestimate.
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.
Equipment
Licence
Lesson video
Loading...
Prior knowledge starter quiz
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.
Q2.Which of the following are good, quick estimate calculations for 577 ÷ 19.57?
Q3.Which of the following are a correct estimate for $${11.239\times3.12}\over{0.488}$$?
Q4.Match each calculation to its approximate answer.
$$\frac{9.8}{0.120}$$ -
$$100$$
$$\frac{98}{0.111}$$ -
$$1000$$
$$\frac{9.8}{0.2003}$$ -
$$50$$
$$\frac{980}{0.199}$$ -
$$5000$$
$$\frac{980}{0.498}$$ -
$$2000$$
$$\frac{9}{0.51}$$ -
$$18$$
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.
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
Assessment exit quiz
6 Questions
Q1.An __________ is an estimate for a calculation which is greater than the exact answer.
Q2.An __________ is an estimate for a calculation which is less than the exact answer.
Q3.Match each calculation with a calculation that gives its overestimate.
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
Q4.Match the following calculations which give an overestimated area.
$$\approx \text{ }$$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
Q5.Match which calculations are an overestimate, underestimate or hard to tell.
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 -
$$\frac{37.4}{4.49+6.41}\approx\frac{40}{5+6}$$
Q6.Match which calculations are an overestimate, underestimate or hard to tell.
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 -
$$\frac{59-42}{3.67+1.23}\approx\frac{60-50}{4+2}$$