Read more about the purpose of the MAP *Classroom Challenges*…

## Solving Quadratic Equations: Cutting Corners

### 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

This lesson is structured in the following way:

- 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.
- Finally, students review what they have learned.

### Materials required

- Each student will need a copy of the task,
*Cutting Corners*, and the questionnaire,*How Did You Work?* - Each small group of students will need an enlarged copy of the task,
*Cutting Corners*, 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 45-minute lessons), and 10 minutes in a follow-up lesson (or for homework). Exact timings will depend on the needs of the class.

### 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

### Mathematical Content

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

- H.A-REI: Solve equations and inequalities in one variable
- H.G-SRT: Define trigonometric ratios and solve problems involving right triangles
- H.G-MG: Apply geometric concepts in modeling situations

### Resources

#### Lesson (complete)

- solving_quadratic_equations_complete.pdf ( 3312K PDF/Acrobat 24 Feb 2014)

#### Projector Resources

- solving_quadratic_equations_slides_ms.ppt ( 3915K MS PowerPoint 24 Feb 2014)

A draft Brief Guide for teachers and administrators (PDF) is now available, and is recommended for anybody using the MAP *Classroom Challenges* for the first time.

We have assigned lessons to grades based on the Common Core State Standards for Mathematical Content. During this transition period, you should use your judgement as to where they fit in your current course.

The Beta versions of the MAP Lesson Units may be distributed, unmodified, under the Creative Commons Attribution, Non-commercial, No Derivatives License 3.0. All other rights reserved. Please send any enquiries about commercial use or derived works to map.info@mathshell.org.

Can you help us by sending samples of students' work on the *Classroom Challenges?*