# Setting up and Solving Equations

Students learn how to use the balance to form and solve linear equations.  Learning progresses from solving one step equations to setting up equations where the unknown appears on both side.

This unit takes place in Term 6 of Year 7 and follows on from writing with algebraic notation.

##### 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
• taking out common factors
##### Key Concepts
• When solving equations students should use a scale to visualise how it remains balanced.
• A secure understanding of the order of operations and inverse operations is needed to keep an equation balanced.
• By solving the equation you find the value of the unknown number.
• When forming equations students often become confused with using brackets.
• An equation can have a positive or negative solution which could be presented as a simplified fraction rather than a decimal.
##### Working mathematically

Develop fluency

• Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]
• Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions

Reason mathematically

• Identify variables and express relations between variables algebraically
• Make and test conjectures about patterns and relationships; look for proofs or counter-examples

Solve problems

• Begin to model situations mathematically and express the results using a range of formal mathematical representations
##### Subject Content

Algebra

• Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
• Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

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