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This unit takes place in Term 4 of Year 10 and is followed by the equations of straight line graphs.

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

- 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<sup<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.
- Whereas a geometric and arithmetic sequence depends on the position of the number in the sequence a recurrence relation depends on the preceding terms.

- Students often show a lack of understanding for what ānā represents.
- A sequence such as 1, 4, 7, 10 is often described as n + 3 rather than 3n ā 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}. - Students often struggle understanding the notation of recurrence sequences. In particular, using difference values of n for a given term.

August 9, 2020

Four new problem solving lessons to develop student’s mathematical reasoning and communication skills.

July 28, 2020

Practical tips and advice for preparing to teach in year group bubbles.

July 22, 2020

Students are challenged to apply the rules of arithmetic to a series of real-life, functional problems.