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Students learn how to generate and describe sequences on a term-to-term and position-to-term basis. Learning progresses from plotting and reading coordinates in the first quadrant to describing geometric sequences using the nth term.

This unit takes place in Term 1 of Year 10 and is followed by the properties of straight line graphs.

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

- 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

- The nth term represents a formula to calculate any term 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.

- Students often show a lack of understanding for what ‘n’ represents.
- A sequence such as 1, 4, 7, 10 is often described as n + 3 rather than 3n – 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 ar^{n}.

July 6, 2019

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

June 30, 2019

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have. Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

June 24, 2019

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out. This is presented to the class as they come into the lesson. Writing Equivalent Ratios A few students immediately go […]