# Indices and Standard Index Form

Scheme of work: GCSE Foundation: Year 11: Term 1: Indices and Standard Index 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 a highest common factor, lowest common multiple, and 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 â‰¤ 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 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 x 10-2 to have a value of -120.

## Indices and Standard Index Form Resources

### Mr Mathematics Blog

#### Interpreting Cumulative Frequency Graphs

Linking cumulative frequency graphs to ratio, percentages and financial mathematics.

#### Higher GCSE Maths Revision Lesson

In this lesson there are five grade 8 and 9 maths problems for higher ability students.