Unit 4: Sequences, expressions and equations
Planning guidance
Unit objectives
 Recognise and represent number patterns
 Finding an algebraic expression for the 𝑛 th term
 Translate simple real-world situations into algebraic expressions
 Use letters to represent numbers
 Distinguish between terms and coefficients in algebraic expressions
 Distinguish between like and unlike terms in algebraic expressions
 Add and subtract linear algebraic expressions
 Solve linear equations with one unknown
 Formulate a linear equation with one unknown to solve problems
This unit on solving linear equations is introduced using sequences and expressing a sequence algebraically. It is important to remember that the letters used in algebraic notation represent numbers and are not shorthand for words. Language should be used carefully to ensure that this understanding is communicated to the students. Teachers might choose to use unrelated letters in order to avoid confusion.
There are a few planning points to note for this unit. Sequences have been briefly met in Year 7 and will be covered in Year 9 also, affording an opportunity to consolidate the work on finding the 𝑛 th term. The algebra section builds on the work done in Year 7 and should be an opportunity to reinforce key learning points from that unit. Solving linear equations is done through using bar models to support students' conceptual understanding.
This unit should take three weeks. There are three key sections and it is up to the teachers to decide how to split lessons between them. Each section has a number of key department tasks to be completed together. These form the basis of planning individual lesson. Whilst completing the tasks, time should be given to discussing ways in which language and questioning can be used to enhance learning in this unit.
Suggested Structure
The actual number of lessons spent on each section will depend on the individual class and the number of lessons available to teachers. We suggest the following based on a total of 9, 12 or 15 lessons over a fortnight:
Section
Sequences and 𝑛 th term rules
Solving and exploring linear equations
Interpreting and solving worded problems
9 lessons
4-5
3
1-2
12 lessons
5-6
4
2-3
15 lessons
7-8
5
2-3
Copy right © Mathematics Mastery 2014

Sequences and 𝒏 th term rules
Objectives

Recognise and represent number patterns

Describe and continue number patterns

Compare number patterns and sequences

Find an expression for the 𝑛 th term rule

Generate a sequence from a given rule

Use letters to represent numbers
During these lessons students should be encouraged to explore number patterns and to verbalise and describe patterns before moving onto using algebraic notation. There is ample opportunity to consolidate work on multiples during this time. Students need to appreciate the need for an 𝑛 th term rule so it is useful to ask questions such as ‘what would the 25 th term be?’ to enable them to see the need more clearly. The common misconception that the 25 th term is 5 x the 5 th term should also be addressed at this stage.
Students are encouraged to make links between multiplication tables and number patterns where appropriate but should be shown other patterns that are not linear (such as the Fibonacci sequence).
Having just completed a unit on negative numbers, it is important that they do practise negative number arithmetic when possible.
For further guidance, including the Department Tasks for this section, click Sequences and n th term rules
under Planning resources on the main page for this unit.
Solving and exploring linear equations
Objectives:

Use letters to represent numbers

Substitute into expression

Distinguish between terms and coefficients

Distinguish between like and unlike terms

Add and subtract linear expressions

Solve linear equations with one unknown

Use bar models to represent linear equations
Students will have worked with simple expression and linear equations in Year 7, so teachers may wish to refer back to the relevant units for added guidance and support, particularly if they are not familiar with the Year 7 materials.
Students begin by building on the work done in the sequences section of the unit through developing their substitution skills and their conceptual understanding of algebraic notation.
Throughout this section there is an emphasis on the meaning of letters as standing for numbers and not words and this needs to be reinforced. As such, we strongly discourage using examples such as ‘let 𝑎 be
Copy right © Mathematics Mastery 2014

the number of apples…’ since this could lead to confusion. Students are encouraged to use bar models to support their skills, which will be built on in Year 9 when the balance method is formally introduced.
Many of the problems are introduced pictorially to engage students and enrich the experience. Teachers should not worry too much about algebraic procedures at this stage but focus on conceptual understanding, emphasising the language and the difference between expressions and equations.
For further guidance, including the Department Tasks for this section, click Solving and exploring linear
equations under Planning resources on the main page for this unit.
Interpreting and solving worded problems
Objectives:

Translate simple real-world problems into algebraic equations

Use letters to represent numbers

Writing and simplifying simple expressions

Add and subtract linear expressions

Solve linear equations with one unknown

Formulate a linear equation with one unknown to solve problems

Solve simple problems involving perimeter
During the final section students have the opportunity to explore more context-based problems. At this stage, with a limited toolkit of algebraic techniques, the problems are not designed to be complex but to show students the power of mathematical modelling and to enable them to apply their skills in different contexts. In the mean time there is the chance to consolidate work on perimeter and manipulating expressions in general.
For further guidance, including the Department Tasks for this section, click Interpreting and solving
worded problems under Planning resources on the main page for this unit.
Copy right © Mathematics Mastery 2014