# Patterns and Sequences

Scheme of work: GCSE Foundation: Year 10: Term 1: Patterns and Sequences

#### Prerequisite Knowledge

• use simple formulae
• generate and describe linear number sequences
• express missing number problems algebraically
• Pupils need to be able to use symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:
• missing numbers, lengths, coordinates and angles
• formulae in mathematics and science
• equivalent expressions (for example, a + b = b + a)
• generalisations of number patterns

#### Success Criteria

• generate terms of a sequence from either a term-to-term or a position-to-term rule
• recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions ( r n
• where n is an integer, and r is a rational number > 0 or a surd) and other sequences
• deduce expressions to calculate the nth term of linear and quadratic sequences

#### Key Concepts

• The nth term represents a formula to calculate any term in a sequence given its position.
• To describe a sequence it is important to consider the differences between each term as this determines the type of pattern.
• Quadratic sequences have a constant second difference. Linear sequences have a constant first difference.
• Geometric sequences share common multiplying factor rather than common difference.

#### Common Misconceptions

• Students often show a lack of understanding of what â€˜nâ€™ represents.
• A sequence such as 1, 4, 7, 10 is often described as n + 3 rather than 3n â€“ 2.
• Quadratic sequences can involve a linear as well as a quadratic component.
• Calculating the product of negative numbers when producing a table of results can lead to difficulty.
• The nth term for a geometric sequence is in the form arn-1 rather than arn.

## Patterns and Sequences 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.