LESSON PLAN

Name: Elise Briseno

Title of lesson: Quadratic Functions: Graphing and Solving Equations

Date of lesson:

Length of lesson: 45 – 50 minutes

Description of the class:

Name of course: Algebra II

Grade level: 10th

Honors or regular: Honors

TEKS addressed:

111.33, d, 1, A: For given contexts, the student determines the reasonable domain and range values of quadratic functions, as well as interprets and determines the reasonableness of solutions to quadratic equations and inequalities.

111.33 d, 1, B: The student relates representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions.

111.33 d, 3, A: The student analyzes situations involving quadratic functions and formulates quadratic equations or inequalities to solve problems.

111.33 d, 3, C: The student compares and translates between algebraic and graphical solutions of quadratic equations.

111.33 d, 3, D: The student solves a quadratic equation.

I. Overview

The concept of parametric equation develops from the previous day’s activity. . The students should understand the concept of parametric equation for both a linear and nonlinear motion.

II. Performance or learner outcomes

Students will be able to:

- learn and explain the relationship between two equations

- use a calculator to get a quadratics regression line.

- solve equations that are based on real world situations.

III. Resources, materials, and supplies

Calculators, group folders, and writing paper

Five-E Organization

Teacher Does Probing Questions Student Does

Engage: -Have students form back into their groups. -Begin the day with the homework assigned the previous day. -Make sure to give a similar, but different problem to insure the students understand the concept. The engagement should take five minutes.

-Ask one student to use the teacher’s calculator that displays the screen on the overhead and ask another student to give their directions to explain to the class what they did and to show the class how they did it. -Have a set of two different students do the alternate problem.

-Students turn in assignment except for the two doing the demonstration. -The two students explain and show their work for the homework assignment. -The other two students explain and show their work for the alternate additional problem.

Explore: -The students are ask how to write the two equations of the water balloon’s position, x, as a function of time, t and the water balloon’s vertical position, y, as a function of time, t. -Explain to the students that writing a pair of equations that express x and y in terms of a third variable, t, are called parametric equations. (To ensure that the students are understanding this extension for Algebra II we will have already reviewed the concepts earlier in the school year and I will give then homework problems that we review the concept prior to this lesson and after this assignment.)  The exploration should take ten minutes.

-The questions are placed in the Teacher Does column so that I can use this space to continue with the lesson. -Define to the students that the water balloon moves with a constant speed, v, along a straight line making an angle q. The position of the water balloon at any time may be represented by the parametric equations x=(v cos q)t +x° and y=(y sin q)t +y° where (x°, y°) is the water balloon’s location at t=0. -Have a student draw the picture on the board that illustrates this idea and concept.

-The students share their ideas on how to write the two equations. -The students are listening and taking notes. -The student volunteer is drawing a detailed picture (graph) of the parametric equations of a water balloon in a linear path.

Explain & Extend: -Parametric equations can also be used to model nonlinear motion as in the parabolic path of a water balloon being thrown by a catapult. -Instruct the students that the new parametric equations are x=(v cosq)t +x° and y=-1/2gt^2 + (v sinq)t + y°. -The students are shown a pre-made picture of the parametric equations above.  -Inform the students by knowing the angle at which their water balloon will be shot from, the velocity it will have, and the initial position of the catapult they can calculate the distance traveled by the water balloon. This is what they might want to consider when constructing their catapults, since I will be at a given distance for them to shoot at. -Give a few examples so students can practice the calculations of the equations.  The explanation and extension should take twenty minutes.

-Ask the to explain in writing and verbally the change in the y parametric equation. What is g representing and why is it negative? -Ask the students to write a couple of difference that the two different graphs (the student’s linear graph and my nonlinear graph) possess. -Ask students to work in their groups to solve the examples below. -Example 1: Let v = 158ft/sec, the angle =30°, and (x, y)= (0,10), how far does the water balloon travel? -Example 2: Let v=128ft/sec, the angle =45°, and (x, y)= (10, 15). How far does the water balloon travel? -Example 3: Use the following numbers only v=125ft/sec and (x, y) = (0,0). Find the angle that gives you the longest distance traveled by the water balloon. Does the same angle work if we can v to 250ft/sec? Does the same angle work if we change (x, y) to (0, 15)? Explain.

-The students explain and write down the reason the y equation has changed. The g is the acceleration due to gravity which is 9.8 m/sec^2 or 32 ft/sec^2. -The students should write down the visual differences that the two graphs have. -Students then work in groups the work out problems, but must turn in individual papers.

Evaluate: -I must make sure to circulate around the room and listen to the students reasoning and steps to catch any mistakes or misconceptions. If there are many miscalculations then work out one problem in front of the class. -Instruct students to turn in all group members’ sheets into the project folder. -Inform students that the last problem will be reviewed the next day and should have a paragraph (four to six sentences) that explains the end result. They may want to copy to problem to hand in the next day if they did not complete it with their group in class. The evaluation should take ten minutes.

–Ask students to participate in class discussion on solving a problem.

-Students listen and give suggestions on how to solve the problem as a class. -Students turn in assignment and if needed copy the last problem.

Percent effort each team member contributed to this lesson plan:

___%___ ____Name of group member_____________________

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