Algebraic Expressions

Prerequisite Knowledge

• use simple formulae
• generate and describe linear number sequences
• express missing number problems algebraically
• find pairs of numbers that satisfy an equation with two unknowns

Success Criteria

use and interpret algebraic notation, including:

• ab in place of a × b
• 3y in place of 3 × y
• a² in place of a × a, a³ in place of a × a × a and a²b in place of a × a × 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

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.
• The multiplication symbol is omitted when using algebraic notation to avoid confusion between and ×. Quotients 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.

Common Misconceptions

• Students often forget ab = ba = a × b and b + a = + b when collecting like terms.
• 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.