Year level: 7 / 8

Strand: Algebra / Number

Lesson length: 60 min

In this lesson, students use algebra and linear equations to model two real-world scenarios to find information to make the best choice. Students set the aim of saving for a mobile phone (or similar goal) and use linear equations to model the pay rates of two part-time jobs to help make the better decision. This lesson can be taught in tandem with Patterns, rules and graphs, though both can be taught in isolation.

### Achievement standard

• Students use mathematical modelling to solve practical problems involving rational numbers, percentages and ratios, in financial and other applied contexts, justifying choices of representation.
• Students make and test conjectures involving linear relations using digital tools.

### Content descriptions

Students manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables. AC9M7A06

Students use mathematical modelling to solve practical problems, involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation. AC9M7N09

Students graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution. AC9M8A02

### General capabilities

Numeracy

• number patterns and algebraic thinking (PL8)
• interpreting fractions (PL8)
• multiplicative strategies (PL9)
• proportional thinking (PL2)
• understanding money (PL7, PL8)

Critical and Creative Thinking

• draw conclusions and provide reasons (PL5)
• interpret concepts and problems (PL5)
• draw conclusions and provide reasons (PL5)
• create possibilities (PL5).

Digital Literacy

• create, communicate and collaborate (PL5)
• interpret data (PL5)
• select and operate tools (PL5)

Related content

The following formative assessment is suggested for this lesson.

Students complete the exit ticket (either in the remainder of the class or as homework) on finding the linear rule that converts Celsius temperature to Fahrenheit. A milder version is also given, which is to provide the rule and then to practise substituting in values to make the connection between the two temperature scales.

Some students may:

• feel overwhelmed by the problem and have difficulty starting
• be unable to define the variables and question and consider what needs to be considered
• define the goal to answer the question ‘how much a phone would cost?’ to find a solution to the problem.

It is recommended to guide students to breakdown the problem into smaller parts. Use questioning to help identify what they know and what they don’t know. The lesson encourages students to use tables and/or spreadsheets to help students make sense of the relationship between variables and to also recognise patterns.

Some students may:

• not understand coordinate pairs correctly in relation to a linear rule and that x represents any input number, and y is the output; students may also confuse which figure to plug in
• not understand the concept behind linear relationships and that the rule represents a rate of change
• forget the meaning of c as a constant and that it represents the y intercept, and that y can be 0
• find solving for unknowns, substituting or rearranging equations difficult.

Use the skill check to help identify calculation errors that students make. Identify any misconceptions and use graphing tools and digital platforms to help students visualise coordinates. Make small changes to show how they relate to the change in ‘rate’ when visualising the relationship.

Students:

• identify the gradient and initial value of a linear rule
• create and identifies algebraic equations from word problems involving one or more operations
• identify and justifies equivalent algebraic expressions
• interpret a table of values to plot points on a graph
• analyse and visualise data using a range of digital tools to identify patterns and make predictions
• select and use the core features of digital tools to efficiently complete tasks.

Definitions for linear function, linear equation, linear expression, growing patterns and the Cartesian plane can be found at Version 9 mathematics glossary.