Title of Unit Quadratic Equations – Characteristics and Solving

Grade Level

10th and 11th Grade

Curriculum Area Mathematics – Algebra II Time Frame

2 weeks

Stage 1 – Identify Desired ResultsContent Standards:

MM2A4. Students will solve quadratic equations and inequalities in one variable.

a. Solve equations graphically using appropriate technology.

b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

Understandings

Students will understand that:

Quadratic equations can be solved graphically and/or algebraically There is a reason why you have real and complex roots Quadratic equations are an essential part of the banking system within the

United States and around the world. There are various important uses for quadratic equations

Related Misconceptions:

Solving quadratic equations are very difficult to accomplish. There is no way to tell if the roots of a quadratic equation is suppose to be

real or complex. Quadratic equations have no relevance in real world application.

Essential Questions

Overarching Questions:

To what extent are quadratic equations used in real world applications?

Why do complex roots exist within quadratic equations?

How many possible roots can a quadratic equation have?

Are there other possible ways for solving a quadratic equation?

Topical Questions:

What are the methods for solving quadratic equations graphically?

What are the methods for solving quadratic equations algebraically?

What are the methods for solving quadratic inequalities?

Are the methods for solving quadratic inequalities and quadratic equations similar?

How can the solution of quadratic inequalities be described with linear inequalities?

Knowledge and Skills

Knowledge

Students will know:

Key Terms - Real and complex roots, quadratic formula, determinant. completing the square, factorization.

How to determine and interpret the discriminant.

How to find the roots of a quadratic equation.

How to describe the roots to a quadratic equation

How to describe the solution to a quadratic inequality

How to utilize the quadratic formula. How to utilize the taking square roots

method.

Skills

Students will be able to:

Solve a quadratic equation and inequality graphically.

Solve a quadratic equation and inequality algebraically.

How to utilize the quadratic formula.

Apply appropriate methods (completing the square, bussing the b factoring, and taking square roots) to solve a quadratic equation algebraically.

Calculate interest on an amount of money using quadratic

How to apply quadratic equations to real life applications.

equations.

Stage 2 – Assessment Evidence

Performance Task

The Construction Project

Goal & Role: You are in charge of the financial team at Mipro Inc. The company is doing well financially and The Board of Directors has decided to construct a new office building. Your job is to prepare a report detailing which bank’s Certificate of Deposit, if any, will be most beneficial to the company. (Application)

Audience: You need to convince the Board of Directors of how to proceed with financing the building project (Perspective).

Situation: This construction project must be completed in 2 years as the current lease on the building will expire in 2 years. The construction team has estimated that the cost of the building project is $2,000,000. The Board of Directors stated the company has committed a principle of $750,000 for the building project and would like to not invest anymore. The principle will be placed into a Certificate of Deposit in hopes that enough interest can be made to pay for the building project in 2 years (Empathy). The following are the bank rates and promotions on Certificate of Deposits(Interpretation):

Discovery Bank: 2 Year CD: APY: 2.76% + 20% bonus matching at the end of the 2nd year;

Capitol Two Bank: 2 Year CD: APY 2.85% + 5% bonus matching at the end of the 2nd year;

StarTrust Bank: 2 Year CD: APY 3.00% + 1% bonus matching at the end of each year.

Product Performance and Purpose: You will need to prepare a professional presentation (Explanation) which will provide all of the necessary information for the Board of Directors to make an informed decision. Your presentation must be in Microsoft Powerpoint and must include all performed calculations. If you find that neither bank will be sufficient, then you must provide what criteria the company should be looking for in a Certificate of Deposit that will be sufficient for the building project (Self-Knowledge). The following formula is used to calculate the interest on a Certificate of Deposit: Principle * (1+APY)2 = Future Amount

Standards and Criteria for Success: Your presentation will be judged by 5 of your classmates chosen at random. Their scores will make up 20% of the final grade in the class. The remaining 80% will come from the rubrics associated with the tasks. A successful presentation will score at minimum an 80%. Any presentation with a score less than 80% will be required to repeat the presentation.

Performance Task Rubric

Math - Problem Solving : The Construction Project

Teacher Name: Mr. Maxwell

Student Name: ________________________________________

CATEGORY 4 3 2 1Mathematical Concepts

Explanation shows complete understanding of the mathematical concepts used to solve the problem(s).

Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s).

Explanation shows some understanding of the mathematical concepts needed to solve the problem(s).

Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written.

Explanation Explanation is detailed and clear.

Explanation is clear.

Explanation is a little difficult to understand, but includes critical components.

Explanation is difficult to understand and is missing several components OR was not included.

Strategy/Procedures

Typically, uses an efficient and effective strategy to solve the problem(s).

Typically, uses an effective strategy to solve the problem(s).

Sometimes uses an effective strategy to solve problems, but does not do it consistently.

Rarely uses an effective strategy to solve problems.

Neatness and Organization

The work is presented in a neat, clear, organized fashion that is easy to read.

The work is presented in a neat and organized fashion that is usually easy to read.

The work is presented in an organized fashion but may be hard to read at times.

The work appears sloppy and unorganized. It is hard to know what information goes together.

Completion All problems are completed.

All but one of the problems are completed.

All but two of the problems are completed.

Several of the problems are not completed.

Mathematical Terminology and Notation

Correct terminology and notation are always used, making it easy to understand what was done.

Correct terminology and notation are usually used, making it fairly easy to understand what was done.

Correct terminology and notation are used, but it is sometimes not easy to understand what was done.

There is little use, or a lot of inappropriate use, of terminology and notation.

Mathematical Errors

90-100% of the steps and solutions have no mathematical errors.

Almost all (85-89%) of the steps and solutions have no mathematical errors.

Most (75-84%) of the steps and solutions have no mathematical errors.

More than 75% of the steps and solutions have mathematical errors.

PowerPointPresentation

No errors found in grammar, spelling or usage that distract the reader. Required format used

A few errors found in grammar, spelling or usage that distract the reader.

Most of the formatting requirements have been satisfied

A significant amount of errors found in grammar, spelling, or usage that distracts the reader.Very Little of the formatting requirements have been satisfied

Numerous errors found in grammar, spelling or usage that distract the reader.

Required format has not been used

Total Teacher Evaluation = ___ / 28 * .80 = _____

4 3 2 1Presentation was

excellentPresentation was

very goodPresentation was

satisfactoryPresentation was

poor

Total Peer Evaluation = ____ / 20 * .20 = _____

Total Score: ______

Other Evidence

(e.g. tests, quizzes, work samples, observations)

Students will take examinations regarding solving quadratic equations. Students will be required to work out and explain homework problems on the board

during class (Explanation). Students will complete online quiz, covering the previous lesson. Students will work groups solving quadratic equations and provide explanations of

solutions to the class (Explanation). Students will provide a one page written summary of each guest speaker’s discussion

about real life applications of quadratic equations (Perspective). Students will open an in-class savings account and will calculate compound interest

earned using a quadratic equation (Application).

Student Self-Assessment and Reflection

Each examination will have a section for students to discuss their accomplishments and weaknesses on the examination.

At the conclusion of the semester, each student will send an e-mail to next year’s math teacher to discuss what they learned within the class and to find out how their knowledge will be utilized within the next class.

Students will keep a journal and write about the math class during the last 5 minutes of each class.

At the conclusion of the semester, students will be asked to complete an evaluation tool to assess their feeling about the current math class and ability to perform adequately in the next level math class.

Stage 3: Plan Learning Experiences

Week 1

· Begin with each student taking the Pre-Test to gain insight into current knowledge base. W

· Direct student to Video Podcast on Characteristics of Quadratic Equations Part 1 to teach students about the Vertex and Axis of Symmetry. W, E

· Display and utilize online graphing calculator to reinforce Podcast lesson: http://www.coolmath.com/graphit/ E

· Have students practice finding the vertex and Axis of Symmetry of a quadratic equation. solving quadratic equations graphically using a worksheet. E2, O

· Conduct online tutoring session W, E

· Give a quiz on finding axis of symmetry and Vertex. E-2

Week 2

· Follow-up: Review Definition and graph of a Quadratic Equation. R

· Follow-up: Review Axis of Symmetry and Vertex Characteristics. R, O

· Direct student to Video Podcast on Characteristics of Quadratic Equations Part 2 to teach students about the Domain and Range. W, E

· Display and utilize online graphing calculator to reinforce Podcast lesson: http://www.coolmath.com/graphit/ E

· Have students practice finding the domain and range of problems. E2, O

· Have student post solutions to characteristics of quadratic equation problems via online mechanism and have peer review sessions. E2,O,R

· Give online quiz on Characteristics of Quadratic Equations.

· Direct students to Video Podcast on Solving Quadratic Equations. W,E

· Practice factoring method of quadratic equations. E-2

· Direct students to Practice Problem 1 and Practice Problem 2 Podcast for practical application of solving quadratic equations.

· Have students practice solving quadratic equations graphically using a worksheet. E2, R

· Demonstrate the use of the Quadratic Equation Solver: http://www.webgraphing.com/quadraticequation_quadraticformula.jsp E

· Demonstrate the use of the The Quadratic Solver: http://zonalandeducation.com/mmts/miscellaneousMath/quadraticRealSolver/quadraticRealSolver.html E

· Give an online quiz on solving quadratic equations algebraically, using factoring and the quadratic formula methods, and graphically. E2

Week 3

· Follow-up: Review solving quadratic equations algebraically. R,O

· Follow-up: Ask students about the process of solving linear inequalities. W

· Follow-up: Review solving linear inequalities. R,O

· Have banker webcast with students to discuss the importance of quadratic equation within the banking system and to present real world problem to be solved by students (from Stage 2) E-2,T, O

· Have students’ present solutions to real world problem.