Indices and Approximation

Scheme of work: Key Stage 3: Year 8: Term 1: Indices and Approximation

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 =, < and >

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 x nb = n(a+b).  The division rule is 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

  • Number
    • Use conventional notation to prioritise 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<=<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<a<=b
    • Use a calculator and other technologies to calculate results accurately and then interpret them appropriately

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