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**Scheme of work: Key Stage 3: Year 8: Term 4: Expressions, Equations and Formulae**

- Use and interpret algebraic notation, including:
- ab in place of a x b
- 3y in place of y + y + y and 3 x y
- a
^{2}in place of a x a, a^{3}in place of a x a x a; a^{2}b in place of a x a x b - a/b in place of a x b

- coefficients written as fractions rather than decimals
- simplify and manipulate algebraic expressions to maintain equivalence by collecting like terms

- Expanding brackets means taking 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 + 12a
^{2}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.

- 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, partly 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.

- 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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