Curriculum Hub → Maths Lessons → Number → Accuracy and Rounding → Estimating Solutions by Rounding
Ready-to-teach lesson. Includes PowerPoint, printable worksheet and fully worked solutions. Saves 2+ hours of planning.
Master estimating solutions by rounding with this ready-to-teach GCSE number lesson. Students round every value to 1 significant figure before calculating, estimate square roots using nearby square numbers, and combine both skills in multi-step calculations. The lesson includes editable slides, a printable worksheet, a video tutorial, and exam-style practice with fully worked solutions.
Estimating looks simple but trips students up in exams, usually because they round too late or skip a number entirely. Building the skill in layers, rounding first and calculating second, gives students a reliable routine they can apply to any unfamiliar calculation.
Watch this tutorial first to see how to round each value to 1 significant figure, estimate square roots using square numbers, and set out multi-step estimates clearly. Then try the free worksheet below.
Key topics: rounding to 1 significant figure, rounding first then calculating, estimating square roots, and combining rounding rules in longer calculations.
Download the free GCSE worksheet. It includes exam-style estimation questions, space for working, and fully worked solutions in the accordions below.
Free download: no membership required
Members get complete estimation lessons for KS3 and GCSE: editable slides, differentiated worksheets and teaching examples, plus 1000+ more KS3 and GCSE resources.
This section walks through the full lesson: a rounding recap starter, estimating by rounding to 1 significant figure, estimating square roots, and combining both skills for harder calculations.
Below you will find differentiated learning objectives, a step-by-step teaching approach, common student errors, and tips for support and extension. For simpler approximations, use the KS3 Making Rough Approximations pack. For the full GCSE lesson, use Estimating Solutions by Rounding.
Give students a mix of numbers, large, small and decimal, and ask them to round each to 1 significant figure.
If rounding is not fluent, everything later in the lesson will be slower and more error-prone. Mini-whiteboards work well here so you can scan the room quickly.
Tip: include a number starting with a 9, such as 9.99, since rounding these up often catches students out.
To estimate a calculation, round every number to 1 significant figure first, then calculate with the rounded values.
Demonstrate with a worked example, showing rounding and calculating as two separate steps. Keeping “round first” and “calculate second” apart stops students losing track of what has already been rounded.
Area problems work well here because the estimate is easy to sense-check against the original measurements.
Best for: products, quotients and simple sums or differences.
Best for: square roots, powers and multi-step exam questions.
Once rounding is secure, bring in square roots. Instead of rounding to 1 significant figure, round the number under the root to the nearest square number so the root becomes whole.
\sqrt{48} \approx \sqrt{49} = 7Students already know their square numbers, so this reframes an unfamiliar root as a fact they already have. Display the first fifteen square numbers on the board while they practise.
For calculations with more than one operation, combine both approaches: 1 significant figure where appropriate, and nearest square or cube number wherever a root appears.
Ask students to identify each part of the calculation, decide which rounding rule applies, then combine the estimates. Insist on writing the rounded calculation in full before any arithmetic.
Students who need more support
More able students
Give students three calculations, each missing its rounded values, plus a bank of numbers to choose from. Students pick the correct values so the calculation matches the given estimated answer.
There are three levels of challenge, one per learning objective, so students can work at the level that matches their progress.
Working backwards from the answer checks understanding more rigorously than estimating forwards. Allow about ten minutes.
| Phase | Focus | Time |
|---|---|---|
| Starter | Recap rounding to 1 significant figure | 5 to 10 min |
| Development | Estimating solutions by rounding to 1 s.f. | 10 to 15 min |
| Main | Estimating square roots using square numbers | 10 to 15 min |
| Stretch | Combining rounding, square and cube numbers, and roots | Ongoing |
| Plenary | Complete the estimated calculations, three levels | 10 min |
Use this checklist after the lesson or as a revision self-check. Each skill is covered on this page or linked to the next lesson in the sequence.
Try these 4 GCSE-style questions, then reveal the solutions to check your working.
How to use these questions in class
Q1: Estimate with a square root
\frac{\sqrt{104.3}}{8.72 - 7.389}
\approx \frac{\sqrt{100}}{9 - 7}
= \frac{10}{2}
= 5
Q2: Estimate a product and quotient
\frac{71 \times 32.4}{4.92^2}
\approx \frac{70 \times 30}{5^2}
= \frac{2100}{25}
= 84Q3: Estimate with a power
\frac{1.6 + 9.6^2}{5.9 - 4.3}
\approx \frac{2 + 10^2}{6 - 4}
= \frac{102}{2}
= 51Q4: Estimate a multi-step calculation
\frac{37.8 \times 13.2}{28.5 + 22.1}
\approx \frac{40 \times 10}{30 + 20}
= \frac{400}{50}
= 8Mr Mathematics Membership includes ready-to-teach lessons, differentiated worksheets and exam-ready resources across KS3 and GCSE.
Planning for a whole department? Download the school membership flyer (PDF).
Estimating means rounding every number in a calculation to 1 significant figure, then calculating with those rounded values. The result is close to the true answer and can be worked out without a calculator.
Keep the first non-zero digit and look at the digit after it. If that digit is 5 or more, round up. Then replace the remaining digits with zeros, keeping the place value correct. For example, 578 rounds to 600 and 0.0472 rounds to 0.05.
Always round first, then calculate. Rounding after doing the arithmetic is not estimating, and exam questions asking for an estimate expect to see the rounded calculation written out.
Round the number under the root to the nearest square number so the root is whole. For example, the square root of 48 is about the square root of 49, which is 7.
Rounding to 1 significant figure often leaves a number that is not a square, so the root is still hard to work out. Rounding 48 to 50 does not help, but rounding it to 49 gives an exact root of 7.
Round every value in the numerator and the denominator, work out each part separately, then divide. For example, 37.8 times 13.2 divided by the sum of 28.5 and 22.1 becomes 40 times 10 divided by 50, which is 8.
An estimate is a quick check that your calculator answer is sensible. If the two are very different, you have probably mistyped a value or misplaced a decimal point.
Download the free printable worksheet from this page. It includes exam-style estimation questions with fully worked solutions in the accordions above. No membership is required.
Build a coherent accuracy and rounding unit with these related resources. For the full topic hub, visit All Accuracy and Rounding Lessons.
A Mr Mathematics membership gives you 1000+ ready-to-teach lessons, differentiated worksheets and question generators for KS3 and GCSE.
Schools can also download the school membership flyer (PDF).
A research-backed case exploring why over-reliance on automated math homework platforms and repetitive worksheets lowers student expectations, and how departments can build genuine mathematical thinking.
How to teach converting between fractions, decimals and percentages.
Four problem solving lessons to develop student’s mathematical reasoning and communication skills.