Expressions, Equations and Formulae

Expanding a pair of brackets

Factorising expressions

Expanding Brackets and Collecting Like Terms

Equations with the unknown on both sides

Substitution into formulae

Changing the Subject of a Formula

Prerequisite Knowledge

• Use and interpret algebraic notation, including:
  • ab in place of a × b
  • 3y in place of y + y + y and 3 × y
  • a² in place of a × a, a³ in place of a × a × a; a²b in place of a × a × b
  • a/b in place of a ÷ b
• coefficients written as fractions rather than decimals
• simplify and manipulate algebraic expressions to maintain equivalence by collecting like terms

Key Concepts

• Expanding brackets means to take out of brackets.  Factorising an expression is put in brackets.
• When expanding brackets by a negative students often forget to multiply every term inside the bracket by the negative.
• When factorising expressions the highest common factor of each term.  A common misconception is to only partially factorise. For example 9a + 12a² is fully factorised as 3a(3 + 4a) not a(9 + 12a).
• When solving equations involving brackets it is not always necessary to expand the bracket first.  It is often possible to divide both sides by the number outside the bracket.
• To solve an equation you have to get the letter on its own on one side of the equation.  Begin by collecting like terms so all the letters are together.
• When substituting known values into a formula remember to use the correct order of operations.  Students often make mistakes when substituting in negative and fractional numbers.
• Formulae have an unknown on its own.  This is the subject of the formula.  Use the balance method and order of operations to change the subject of the formula.

Working mathematically

Develop fluency

• Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
• Substitute values in expressions, rearrange and simplify expressions, and solve equations

Reason mathematically

• Identify variables and express relations between variables algebraically and graphically

Solve problems

• Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content

Algebra

• Substitute numerical values into formulae and expressions, including scientific formulae;
• Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors;
• Simplify and manipulate algebraic expressions to maintain equivalence by:
  • Collecting like terms
  • Multiplying a single term over a bracket
  • Taking out common factors
  • Expanding products of two or more binomials
• Understand and use standard mathematical formulae; rearrange formulae to change the subject
• Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)