# Higher Tier Expressions

Scheme of work: GCSE Higher: Year 9: Term 2: Expressions

#### Prerequisite Knowledge

• Use and interpret algebraic notation, including:
• ab in place of a x b
• 3y in place of 3 x y
• a2 in place of a x a, a3 in place of a x a x a and a2b in place of a x a x b
• a/b in place of a / b
• Coefficients written as fractions rather than decimals

#### Success Criteria

• Multiplying a single term over a bracket
• Taking out common factors
• Expanding products of two or more binomials
• Factorising quadratic expressions of the form ax2 + bx + c, including the difference of two squares
• Simplifying expressions involving sums, products and powers including the laws of indices

#### Key Concepts

• Students need to appreciate that writing with algebra applies the rules of arithmetic to unknown numbers, which are represented as letters.
• It is important to define the difference between an expression, equation and formula.
• Linear (x), quadratic (x2) and cube terms (x3)cannot be collected together.
• Understanding quadratics in the general form x2 + bx + c helps to factorise and expand expressions.
• Developing mental methods to factorise quadratics is key to gaining confidence with quadratics equations later on.

#### Common Misconceptions

• When multiplying out brackets students incorrectly forget to multiply the second term, especially with negative products. E.g., 2(x + 5) = 2x + 10 and -2(x + 5) = -2x â€“ 10
• When factorising expressions a common misconception is to not fully factorise. E.g., 18x + 24y can be written as 9x + 12y
• When expanding the product of two or more brackets students often incorrectly collect the like terms associated to the linear unknown

## Expanding and Factorising 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.