Higher Tier Expressions

March 12, 2023

Scheme of work: GCSE Higher: Year 9: Term 2: Expressions

Prerequisite Knowledge

Use and interpret algebraic notation, including:
ab in place of a x b
3y in place of 3 x y
a² in place of a x a, a³ in place of a x a x a and a²b in place of a x a x b
a/b in place of a / b
Coefficients written as fractions rather than decimals

Success Criteria

Multiplying a single term over a bracket
Taking out common factors
Expanding products of two or more binomials
Factorising quadratic expressions of the form ax² + bx + c, including the difference of two squares
Simplifying expressions involving sums, products and powers including the laws of indices

Key Concepts

Students need to appreciate that writing with algebra applies the rules of arithmetic to unknown numbers, which are represented as letters.
It is important to define the difference between an expression, equation and formula.
Linear (x), quadratic (x²) and cube terms (x³)cannot be collected together.
Understanding quadratics in the general form x² + bx + c helps to factorise and expand expressions.
Developing mental methods to factorise quadratics is key to gaining confidence with quadratics equations later on.

Common Misconceptions

When multiplying out brackets students incorrectly forget to multiply the second term, especially with negative products. E.g., 2(x + 5) = 2x + 10 and -2(x + 5) = -2x â€“ 10
When factorising expressions a common misconception is to not fully factorise. E.g., 18x + 24y can be written as 9x + 12y
When expanding the product of two or more brackets students often incorrectly collect the like terms associated to the linear unknown

Expanding and Factorising Resources

Mr Mathematics Blog

Sequences and Series

November 21, 2023

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods

T- Formulae

November 5, 2023

Scheme of work: A-Level Further Mathematics: Further Pure 1: The t – formulae

Regression, Correlation and Hypothesis Testing

September 24, 2023

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Statistics: Regression, Correlation and Hypothesis Testing