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Students learn how to generate and describe sequences on a term-to-term and position-to-term basis.Ā 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 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}.

June 5, 2019

Students should be able to represent the solutions to an inequality on a number line, using set notation or as a list of integer values. Here’s how I teach using the balance method for solving inequalities using a number line. Matching inequalities, Number sets and Number Lines At the start of the lesson students recap […]

May 1, 2019

In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]

April 17, 2019

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]