Algebraic Expressions

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

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 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.

Common Misconceptions

  • 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.

Algebraic Expressions Resources

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