# Expressions, Equations and Formulae

Students continue to develop their algebraic reasoning skills by expanding a pair or brackets, factorising expressions, solving equations and formulae and changing the subject of a formula.

This unit takes place in Term 4 of Year 8 and follows on from setting up and solving equations.

##### 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)

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