Setting up and Solving Equations

Scheme of work: Key Stage 3: Year 7: Term 6: Setting up and Solving Equations

use and interpret algebraic notation, including:
- ab in place of a x b
- 3y in place of y + y + y and 3 x y
- a² in place of a x a, a³ in place of a x a x a; a²b in place of a x a x b
- a/b in place of a x b
- Coefficients are written as fractions rather than decimals
simplify and manipulate algebraic expressions to maintain equivalence by:
- collecting like terms
- taking out common factors

Students should use a scale to visualise how it remains balanced when solving equations.
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.

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.

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)