# Expressions, Equations and Formulae

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

#### Prerequisite Knowledge

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

#### Key Concepts

• 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 + 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, 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.

#### 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)

## Expressions, Equations and Formulae Resources

### Mr Mathematics Blog

#### Planes of Symmetry in 3D Shapes

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

#### GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.

#### Regions in the Complex Plane

Explore Regions in the Complex Plane with A-Level Further Maths: inequalities, Argand diagrams, and geometric interpretations.