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# MARS: Building and solving linear equations in one variable

The ‘Solving linear equations in one variable’ resource is a concept development lesson from the ‘Mathematics Assessment Resource Service’ (MARS). The resource is intended to help students solve linear equations in one variable, collect like terms, expand expressions, and to categorize linear equations according to the number of solutions. It also aims to encourage discussion on some common misconceptions about algebra.

Sometime before the lesson, students work on the following formative assessment:

In common with other MARS concept development lessons, extensive guidance is included for responding to common issues that students have with this task. These take the form of suggested questions and prompts.

As an example, students sometimes assume that 5 – x = 6 is the same as x – 5 = 6 and give the value x = 11

In this instance suggested questions and prompts are:

• Is 3 – 2 the same as 2 – 3? Try some other numbers. Will it ever be the same?
• Now look at your work. Is 5 – x the same as x – 5? How do you know?
• Check your work by substituting x = 11 back into the equation. What do you notice?

The initial task in the lesson is to consider 4x + 1 = 3 and to find a value of x that makes it false. The next task is to find a value of x that makes the equation true. Some prompting maybe needed if students rely on trial and improvement.

An additional slide is provided to help any students who struggle with the task. The slide shows two alternative approaches to the task: trial and improvement and a more formal reversing method. The task then becomes one of explaining how each approach works.

This introduction provides students with a model of how they should justify their solutions.

There is a collaborative activity in which students must group equations according to whether they are ‘always true’, ‘sometimes true’, or ‘never true’.

It is suggested that there is a class discussion on what each of these means:

• ‘Always true’ meaning the equation is true for any value of x
• ‘Never true’ meaning there are no values of x that make the equation true
• ‘Sometimes true’ meaning students must find two values, one that makes the equation true and one that makes the equation false

The resource includes an assessment for students to complete sometime after the lesson. This is designed to give feedback on how their understanding has improved from the initial assessment.