Home → Curriculum Hub → Maths Lessons → Schemes of Work → Key Stage 3 → Indices and Approximation
This Key Stage 3 Indices and Approximation scheme of work is designed for Year 8 work on powers of ten, rounding and estimating, bounds of accuracy, laws of indices and standard form. It sets out prior number fluency, the index and approximation ideas to keep explicit, and how the unit supports calculator use and interpretation of results.
Use this page to sequence the lessons below, align vocabulary for significant figures, error intervals and index laws, and make clear links between rounding for estimation and bounds for possible values.
Last updated: April 2026
For more schemes and topic routes across KS3, GCSE and A-Level, browse the Mr Mathematics Curriculum Hub.
Start with the prerequisite and key-concept cards so place value and the meaning of a power are secure before standard form. Teach the lessons in the order listed unless your department splits approximation and indices across terms—if you reorder, keep significant-figure rounding before bounds and index laws before standard-form calculations.
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If you are comparing options for a department, the membership page sets out exactly what is included so you can align this unit with your wider KS3 number and algebra plan.
Students should be secure with the following before index laws and approximation work accelerate.
Ideas to keep visible while students work with indices, rounding and standard form.
Subject content (Number)
How this unit supports fluency, reasoning and problem solving in Key Stage 3.
Typical slips to challenge while teaching this unit.
Use it to sequence teaching, align vocabulary and connect estimation with bounds. Then use the lessons below as the delivery route for the unit.
They need solid place value, ordering and the four operations on integers and decimals so powers of ten, rounding and standard form are developments of structure, not new notation in isolation.
Each lesson listed below has its own page with downloadable resources and, where available, online tasks. Access depends on your membership level.
Yes if your timetable requires it—keep rounding and one-significant-figure estimation before bounds where possible, and complete core index laws before standard-form arithmetic.
You can find additional revision lessons, exam-style questions and topic-based practice on the GCSE Maths Revision Hub. This is useful for consolidating learning after teaching the unit or for Year 11 exam preparation.
Students learn to use the place-value table and written methods to multiply and divide numbers by 0.1 and 0.01.
As learning progresses, more able students multiply and divide by powers of ten expressed in index form.
Related Blog: Multiplying and Dividing Numbers by 0.1 and 0.001: A Guide for Key Stage 3 Teachers
Students are introduced to rounding numbers to a significant figure.
Learning progresses from rounding whole numbers to one significant figure to rounding decimals to two or more significant figures.
Related Blog: Rounding to a significant figure
Students learn how to make rough approximations by rounding numbers to one significant figure, then use those estimates to judge the size of products, quotients and simple powers.
As learning progresses, students extend to estimating expressions involving square and cube roots.
Related Blog: Estimating Solutions by Rounding to a Significant Figure
Students learn how to find the upper and lower bounds of a rounded number. They begin with measurements and values rounded to the nearest integer, then progress to numbers rounded to a given decimal place or significant figure.
As learning progresses, students represent bounds on a number line, express a range using inequality notation, and apply the same ideas to multi-part problems.
Students learn how to use the multiplication and division rules of indices to simplify numerical expressions in index notation. As learning progresses, they discover and apply the power rule, positive index form, and the power of zero.
Students learn how to write indices with negative powers as fractions.
As learning progresses students are challenged to write unit fractions using index notation.
Students begin by learning how to apply the power rule of indices to simplify and evaluate exponential expressions.
Later, as learning progresses, they expand expressions raised to a power and use the multiplication and division rules of indices to tackle more complex problems.
Key Stage 3: Power Rule of Indices
Students learn how to convert between large numbers written in ordinary and standard form.
As learning progresses more able students are challenged to find the sum and difference of numbers written in standard form.
Related Blog:
Students learn how to convert between ordinary and standard form for numbers less than 1.
As learning progresses, students are challenged to convert between fractions and standard form.
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Students multiply numbers in standard form, applying index laws and simplifying powers of 10. They start with basic multiplication, then advance to whole numbers.
Later, they tackle applied problems like molecular mass and population density, rounding answers as needed.
Additional practice rounding estimating solutions by rounding.
The problem-solving activity challenges students to estimate the time taken to fill a pool when given flowrate.
Rounding to a significant figure
Estimating Solutions by Rounding to a Significant Figure
Students gain additional practice writing small in standard form.
The problem-solving activity challenges students to write the sum of four fractions in standard form.
Students gain additional practice writing large numbers in standard form.
The problem-solving activity challenges students to use ratios to convert between metric units of speed.
Additional practice simplifying expressions using the rules of indices.
The problem-solving activity challenges students to work out the pressure when area and force are given in index notation.
Students are challenged to solve various problems involving calculations with standard form.
Five problems link to volume, substitution and probability.
Students are challenged to apply their understanding of rounding and accuracy to estimate solutions to real-life, functional problems.
Five problems link to the area of a circle, speed, ratio notation and money.
Students learn how to estimate solutions to problems by rounding numbers to the nearest ten, significant figures, or other convenient values. The lesson begins with revision exercises that recap the concept of rounding and estimating products, divisions, and sums.
As the lesson progresses, the problems become more varied and complex. Students start with simple rounding tasks and gradually move on to more involved scenarios, such as verifying calculator results, estimating costs, and determining quantities. They also practice using approximations to validate calculations and make quick, reasonable estimates in real-world contexts.
Rounding to a significant figure
Estimating Solutions by Rounding to a Significant Figure
Revision Hub
Browse the Mr Mathematics Revision Hub for more maths revision lessons organised by topic and GCSE grade.
Students revise solving exam-style problems with standard form, including writing, multiplying, dividing, and converting numbers.
As they progress, they tackle ratios, real-world contexts like ocean and planet sizes, and multi-step problems. More able students apply index rules to simplify expressions, enhancing fluency and problem-solving.
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