# Building and Solving Complex Equations

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to create and solve linear and non-linear equations. In particular, the lesson will help identify and help students who have the following difficulties:

- Solving equations where the unknown appears once or more than once.
- Solving equations in more than one way.

## Introduction

The unit is structured in the following way:

- Before the lesson, students work individually on an assessment task that is designed to reveal their current levels of understanding and difficulties. You then review their work and create questions for students to consider when improving their solutions.
- Students work collaboratively building and solving equations in which the unknown appears more than once in the equation.
- During a final whole-class discussion students review the main mathematical concepts of the lesson.
- In a follow-up lesson, students review their initial solutions and then use what they have learned to either revise the same introductory assessment task or complete a different task.

## Materials required

- Each student will need a copy of the assessment tasks,
*Building and Solving Equations*and*Building and Solving Equations (revisited),*the cut-up sheet*Building Equations*, the cut-up sheet*Solving Equations*, a sheet of paper, a mini-whiteboard, a pen, and an eraser*.*Some students may need extra copies of the sheets*Building Equations*and*Solving Equations*. - There is a projector resource to support whole-class discussions.

## Time needed

15 minutes before the lesson, a 70-minute lesson (or two shorter lessons), and 15 minutes in a follow-up lesson. Exact timings will depend on the needs of your class.

## Lesson Type

## Mathematical Practices

This lesson involves a range of *mathematical practices* from the standards, with emphasis on:

- MP1: Make sense of problems and persevere in solving them
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and make use of structure
- MP8: Look for and express regularity in repeated reasoning

## Mathematical Content Standards

This lesson asks students to select and apply mathematical content from across the grades, including the *content standards:*

- H.A-REI: Understand solving equations as a process of reasoning and explain the reasoning
- H.A-REI: Solve equations and inequalities in one variable