Algebraic Expressions

Scheme of work: GCSE Foundation: Year 9: Term 2: Algebraic Expressions

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
brackets
simplify and manipulate algebraic expressions by:
collecting like terms
multiplying a single term over a bracket
taking out common factors
expanding products of two or more binomials
factorising quadratic expressions of the form x² + bx + c, including the difference of two squares
simplifying expressions involving sums, products and powers including the laws of indices

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.
The multiplication symbol is omitted when using algebraic notation to avoid confusion and divisions are written as using simplified fractions.
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.

When collecting like terms, students often forget ab = ba = a x b and b + a = + b.
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 – 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.