Indices and Standard Index Form

In this unit of work students learn how to work with numbers and terms written using index notation.  Learning progresses from understanding the multiplication and division rules of indices to performing calculations with numbers written in standard form.

This unit takes place in Term 3 of Year 10 and follows fractions and mixed numbers.


Indices and Standard Index Form Lessons
4 Part Lesson
Adding and Subtracting in Standard form
4 Part Lesson
Simplifying Surds
4 Part Lesson
Writing Numbers in Standard Index Form
4 Part Lesson
Calculations With Standard Index Form
4 Part Lesson
Rules of Indices
4 Part Lesson
Prime Factor Decomposition
4 Part Lesson
Indices with Negative Powers
4 Part Lesson
Highest Common Factor and Lowest Common Multiple
Problem Solving and Revision Lessons
Extended Learning
Standard Form – Small Numbers
Extended Learning
Rules of Indices
Extended Learning
Standard Form – Large Numbers
Problem Solving
Working with Standard Form
Revision
Primes and Prime Factors
Revision
Calculations with Standard Form
Revision
Prime Factors, Highest Common Factor and Lowest Common Multiple
Revision
Rules of Indices
Revision
Writing Numbers in Standard Form

Prerequisite Knowledge

  • Apply the four operations, including formal written methods, to integers
  • use and interpret algebraic notation
  • count backwards through zero to include negative numbers
  • use negative numbers in context, and calculate intervals across zero

Success Criteria

  • use the concepts and vocabulary of highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem
  • calculate with roots, and with integer indices
  • calculate with and interpret standard form A x 10n, where 1 ≤ A < 10 and n is an integer.
  • simplify and manipulate algebraic expressions
  • simplifying expressions involving sums, products and powers, including the laws of indices

Key Concepts

  • To decompose integers into their prime factors students may need to review the definition of a prime.
  • A base raised to a power of zero has a value of one.
  • Students need to have a secure understanding in the difference between a highest common factor and lowest common multiple.
  • Standard index form is a way of writing and calculating with very large and small numbers. Students need to have a secure understanding of place value to access this.

Common Misconceptions

  • One is not a prime number since it only has one factor.
  • x2 is often incorrectly taken as 2x.
  • Students often have difficulty when dealing with negative powers. For instance, they assume, 1.2 × 10-2 to have a value of -120.

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