Indices and Approximation

Students use place value to multiply and divide by decimal numbers and round a number to a given significant figure.  As learning progresses they apply this knowledge to evaluate numbers written using standard index form.

This unit takes place in Year 8 Term 1, and follows on from fractions, decimals and percentages.

Indices and Approximation Lessons
Problem Solving Lessons
Prerequisite Knowledge
  • Understand and use place value for decimals, measures and integers of any size
  • Use the four operations, including formal written methods, applied to integers and decimals.
  • Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
Key Concepts
  • 23 , 2 is the base and 3 is the power. A base number is raised to a power.
  • Students should understand the equivalence between dividing by decimals and multiplying by reciprocals as this leads on to dividing with fractions.
  • Any number raised to a power of zero is equal to one.  Students should understand this as dividing a number by itself equals one.
  • The multiplication rule can be defined as na × nb = n(a+b).  The division rule is defined as na÷ nb = n(a-b).
  • The power rule (23)2 = 26 is an extension of the multiplication rule. The power of zero rule is an extension to the division rule.
  • A number raised to a power of negative one is the reciprocal of that number.
  • When rounding 3.5 to one significant figure the 3 is the most significant with the 5 tenths rounding it up to 4.
  • When writing numbers in standard index for the number before the decimal point must be between 1 to 9 inclusive.
Working mathematically

Develop fluency

  • Select and use appropriate calculation strategies to solve increasingly complex problems.

Reason mathematically

  • Extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically.
  • Make and test conjectures about patterns and relationships; look for proofs or counter-examples.

Solve problems

  • Develop their use of formal mathematical knowledge to interpret and solve problems.
Subject Content


  • Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals.
  • Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5
  • Interpret and compare numbers in standard form A × 10n, where 1≤A<10, where n is a positive or negative integer or zero
  • Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
  • Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x≤b
  • Use a calculator and other technologies to calculate results accurately and then interpret them appropriately

Mr Mathematics Blog

Writing a Single Column Vector

Visual and algebraic methods for writing a single column vector.

Teaching Reciprocals of Numbers and Terms

How to teach working out the reciprocal of integers, fractions, decimals and mixed numbers.

Proving Geometrical Relationships using Algebra

How to teach proving geometrical properties using algebra.