Indices and Standard Index Form

March 7, 2023

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

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