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


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

Number

  • 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

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