# Solving Quadratic Equations

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to solve quadratics in one variable. In particular, the lesson will help you identify and help students who have the following difficulties:

- Making sense of a real life situation and deciding on the math to apply to the problem.
- Solving quadratic equations by taking square roots, completing the square, using the quadratic formula, and factoring.
- Interpreting results in the context of a real life situation.

## Introduction

- Before the lesson students attempt the problem individually. You then review their work and write questions for students to answer to help them improve their solutions.
- At the start of the lesson, students work alone, answering your questions. Students are then grouped and work collaboratively on the same task. In the same small groups, students are given some sample solutions to comment on and evaluate. In a whole-class discussion, students explain and compare the different solution strategies they have seen and used.
- In a follow-up lesson students review what they have learned.

## Materials required

- Each student will need a copy of
*Cutting Corners*and the*How Did You Work?*questionnaire. - Each small group of students will need an enlarged copy of the
*Cutting Corners*task and a copy of each of the*Sample Responses to Discuss*. - Calculators should be available for students who require them.
- There is also a projector resource to help with whole-class discussions.

## Time needed

15 minutes before the lesson, a 90-minute lesson (or two shorter lessons), and 15 minutes in a follow-up lesson. Exact timings will depend on the needs of the 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
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics
- 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-CED: Create equations that describe numbers or relationships
- H.A-REI: Solve equations and inequalities in one variable
- H.G-MG: Apply geometric concepts in modeling situations
- H.G-SRT: Define trigonometric ratios and solve problems involving right triangles