Roots+Lesson+Plan


 * __Roots Lesson Plan__**
 * Subject:** Factoring Polynomials
 * Name:** Casey Sarles
 * Date:** September 25, 2011
 * Time Allotted:** 30 minutes


 * Rationale for selected learning outcomes:** A-APR.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Upon completion of this lesson, students should be able to: 1. Differentiate between quadratic polynomial equations with rational and irrational roots. 2. Describe the process of finding the roots of a quadratic polynomial equation. 3. Sketch a rough graph of the polynomial 4. Explain why they took each step of the process.
 * Objectives:**


 * Organization:** Whole Group/Small Group
 * Teaching Mode/Strategy:** Direct
 * Provision for Individual Differences:** Information will be provided both verbally and visually. Students will have access to the practice problems.
 * Teaching Behavior Focus:** None.

**LESSON ACTIVITIES (Complete 1-8)**
 * SET GROUND RULES:** Today we will have a short lecture before breaking up into small groups to work on problems. If there are any questions please raise your hand. When working in groups, lets agree to work cooperatively regardless of who is in your group. If there are disagreements, let each person explain why they believe they are correct and together, as a group, constructively criticize each other to come to an answer you all agree on.

Welcome to class, today we will be going over how to find the roots of quadratic polynomial equations using two methods, guess and check, and the quadratic formula. Set Ground Rules.
 * STEP 1: Anticipatory Set:** - 1 minute

By the end of today each of you will be able to find the roots and sketch a rough graph of a wide variety of second-degree polynomials.
 * STEP 2: Overview of Learning Outcomes:** - 30 seconds

Mini lecture on finding the roots of and sketching quadratic polynomial equations, student should take notes. Review the general form of a quadratic polynomial equation: ax 2 +bx+c=0.
 * STEP 3: Input of Information:** -5 minutes

Explain that this equation can be represented as a function by replacing the 0 with function notation such as f(x) or y. The 0 allows us to solve for the roots of the equation. The roots of the equation tell us where the function crosses the x-axis.

Introduce the quadratic formula: The quadratic formula can always be used to find the roots of an equation. Explain the parts and how one root is the + and one is the -.

Explain that if roots can be found by factoring, the function has rational roots. If the roots can be found ONLY by the quadratic formula, the function had irrational roots.

Show that the equation x=-b/2a will give the x value of the vertex of the parabola and plugging the x-value into the original equation will give you the y-value of the vertex.

Explain that the a value determines the direction of the parabola. If a is positive, the parabola smiles. If a is negative the parabola frowns.

Do the in class example using guess and check and the quadratic formula. Explain how when factoring, the factors must multiply to equal c and add to equal b in guess and check. Sketch a graph of the example Answer any questions the students may have along the way.
 * STEP 4: Modeling/Examples:** -5 minutes

Assign students to groups of three or four and assign them to a problem. Have students work cooperatively to complete the problem using both methods if possible. If only one method is possible, have students explain why the second method could not be used. Have them sketch a graph of the function.
 * STEP 5: Group Practice:** -5 minutes

Go over examples. Randomly select one student from each group to explain their work, what they did and why each step was taken. Explain homework assigned for the night. Show the voice thread example. Have students ask questions that they may have on examples and about homework for the night.
 * STEP 6: Review and Closure:** -15 minutes

Have student create a voice thread for homework due the next day. Give each group a problem to do for homework. Each individual from the group will create a voice thread solving the specific problem either by guess and check (factoring) or the quadratic formula, solve for the vertex of the function, and graph the function. *NOTE* Slides may be done on a webcam, holding up sheets of paper as individual slide and narrating. Rubric still remains the same.
 * STEP 7: Independent Practice:** –at home

**Materials Needed:** 1. Projector to display voice thread 2. Wikispaces page set up by instructor with examples, one example per group.