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
Revision Lessons

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.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Teaching in a Bubble

Practical tips and advice for preparing to teach in year group bubbles.

Problem Solving – Perimeter and Area

Students are challenged to apply the rules of arithmetic to a series of real-life, functional problems.

Behaviour Management in a Mathematics Lesson

As we approach the start of the next term I thought I would share some tips on behaviour management in a mathematics lesson. These are things that I have picked up over the years and have worked well for me. I am sure there are opposing viewpoints and you may find some of these tips […]