Patterns and Sequences

August 31, 2023

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 ar^n-1 rather than arⁿ.

Patterns and Sequences Resources

Mr Mathematics Blog

Problem-Solving with Angles in Polygons

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How to teach problem solving with angles in polygons through scaffolding.

The Sum to Infinity of Geometric Series – A-Level Maths Tutorial

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Explore geometric series in our A-Level Maths tutorial. Perfect for students/teachers, with resources to download at mr-mathematics.com.

Sequences and Series

November 21, 2023

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods