Title of Lesson: Where are parabolas in the real world?

Author: Jenni Darlow

Grade Level: Algebra I

Date to be taught: 5^th six weeks

Length of lesson: 1 class period

Objectives:

After this lesson the student will be able to:

Identify the relationship between a parabola and its focus and directrix,

Identify examples of some real world parabolas,

Identify the function of some real world parabolas

Identify how the focus of a parabola is used in its real world function,

Identify if a curve is a parabola

TEKS addressed:

(b)  Knowledge and skills.

(A.1)  Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways.

The student is expected to:

(D) represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities

(A.2)  Foundations for functions. The student uses the properties and attributes of functions.

The student is expected to:

(C) interpret situations in terms of given graphs or creates situations that fit given graphs

Engagement:

Teacher does	Student does
Have students sit in groups of 3. Give each student a worksheet with a straight line (directrix) and a point (focus) and rulers. Tell students they should be familiar with parabola’s by this point, but there is another way to construct a parabola besides with a quadratic formula. Tell students they are able to construct a parabola using this point and line and that they have 5 minutes to discuss and try ideas within their groups.	Students will discuss ideas with each other and attempt to construct parabolas on the worksheets they have been given
Call on various students to show their parabola and tell how they constructed it.	Students will show their constructions and explain what they did.

Evaluate:

Teacher should note if students have identified a relationship between the parabola, point and line and if it is the correct relationship.

Explore:

Teacher does	Student does
Direct students to the keymath website with the applet that shows the relationship between the parabola, focus and directrix	Students will explore the applet at www.keymath.com/x6928.xml
Teacher will call on a student to explain the relationship between the point, line and parabola as they have discovered it	Students will explain the relationship between focus, directrix and parabola, introducing the new vocabulary
Assign each student in the group an example of a real world parabola: car headlights, satellite dish, parabolic reflector to ignite a flammable material. Give students worksheets with unlabeled pictures of these, not identifying what they are. Have students think about and discuss what they might be and how the focus might relate to their function	Students will look at the pictures and analyze their function. They will discuss with their groups what they think they pictures are, how the different things in the pictures function, and what role the focus of the parabola plays in the specific function of each.

Evaluate:

Teacher will walk around while students are working to see if they are on the right track and help guide them onto the correct track if necessary

Explain:

Teacher does	Student does
Have various students present what they came up with	Students will tell the class what they have come up with. They will describe the applications of the parabola pictured and how the focus in involved in the functioning
Tell students to think about other examples similar to these of parabolas they have come across in the world and if they can identify the focus and function of the focus if there is one (this will help with their project for the final assessment)	Students will begin to think about other real world applications of the parabola and its properties

Evaluate:

Teacher will see if students have identified the function of the focus in the application of the parabolas

Extend:

Teacher does	Student does
Teacher poses the question: How can you determine if a curved shape is a parabola? And shows pictures of various shapes	Students will discuss amongst themselves answers to the question
Teacher calls on students to answer for each picture if it is a parabola, or if they cannot tell from just looking at the picture, how they might tell if they had other tools	Students should identify that a parabola has to have a focus and directrix that are equidistant from every point on the parabola and if those can be identified for a curve, it is a parabola, but if they do not exist, then the curve is not a parabola

Evaluate: Teacher will hand out worksheets like the ones at the beginning of class with a line and a point, and rulers and ask students to construct a parabola. Teacher will evaluate whether students have understood the relationship between the directrix, focus and parabola by assessing the accuracy and construction of the parabolas.