LESSON PLAN

 

Name:  Danielle Ortega

 

Title of lesson: Introduction to Parabolas

 

Date of lesson: Unit: Motion in Baseball, Monday of Week 3

 

Length of lesson: 50 minutes

 

Description of the class:

            Name of course: Algebra II

            Grade level: 11th Grade

            Honors or regular: Either

 

Source of the lesson:

            Construction of Parabola Activity:

            http://utopia.utexas.edu/lesson_plans/2005/gallo_algebra_2_parabola.php

 

TEKS addressed:

            §111.32. Algebra I (One Credit).

(d) Quadratic and other nonlinear functions: knowledge and skills and performance descriptions.

(1) The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions.

           

 

I.       I.      Overview

Students will learn basic characteristics of parabolas and that quadratic functions have parabolas as their graphs.

 

II.  Performance or learner outcomes

            Students will be able to:

·   Identify and recognize parabolas as the graphs of quadratic functions.

·  Define a parabola as the set of points which are all equidistant from the focus and directrix.

·   Determine the focus, directrix, vertex, and axis of symmetry of a parabola from its graph.

 

III. Resources, materials and supplies needed

        Overheads:  Satellite dish, cross-section of satellite dish, graphs of various

              quadratic functions.

 

IV. Supplementary materials, handouts.

         Handout/Worksheet:  Construction of a Parabola

 

Five-E Organization

Teacher Does                     Probing Questions                      Student Does       

Engage:

 Teacher will show a picture of a satellite dish and a picture of a cross section of a satellite dish.

     

 

 

 

In a while, we’ll learn a little bit about how algebra makes satellite dishes work.

 

 

Does anyone know the mathematical name for this shape (referring to cross section)?

 

Where else do you see this shape?

 

Parabola (some may already know, most probably not)

 

 

 

Various answers.

                                                   

Explore:

 Students will follow the instructions on the handout to construct two different parabolas and will record their observations.  Teacher will circulate room, asking questions and making sure the students are correctly constructing the parabolas.

 

 

 What do you notice about the shape of the graphs you’ve made?

 

What happened when you placed the horizontal line closer to the center point?

 

What do all of the points for each graph have in common? 

 

 

What happened when you picked a horizontal line above the center point?

 

Curves, U-shaped.

 

 

 

Shape got steeper, skinnier.

 

 

 

All the same distance from the center point and the line. (Teacher may have to lead them to this conclusion).

 

The curve opened downward, upside down U.

    

Explain:

Two students will use the overhead to draw one of their parabolas.  One student should draw an upward facing parabola and the other should draw a downward facing parabola.

 

Teacher will then put up an overhead of the graph of the function y = x2 .  We will use this picture to introduce important vocabulary such as  parabola, focus, directrix, axis of symmetry, and vertex, relating these to the points and lines the encountered in the exploration activity.

 

Teacher will then place several picture of parabolas on the overhead with their respective functions (y =…).  At first, students will verbally identify the parts of the parabolas.

For the last few, students will individually identify the parts of the parabolas and record them on a piece of paper along with the functions.  The teacher will collect these as an evaluation.

 

Teacher will reconvene the class to emphasize that quadratic functions always have parabolas as their graphs.

 

Ask same questions as above to entire class.

 

 

 

 

 

 

 

Does this graph look like the ones you just drew?

 

 

 

 

 

 

 

 

 

 

What is the focus? Directrix?  Axis of symmetry?  Vertex?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

What do you notice about the functions for all of these parabolas?

 

 

 

 

 

 

 

 

 

 

Yes, same shape.

 

 

 

 

 

 

 

 

 

 

 

Students will give focus, directrix, vertex and and axis of symmetry for each parabola..

 

 

 

 

 

 

 

 

 

 

 

 

 

They all have an x2 in them.  All are degree 2. 

                                               

Extend / Elaborate:

Teacher will put the pictures of the satellite dish back up on the overhead.

 

 

 

 

 

 

 

 

 

The teacher will explain that the parabolic shape of the dish reflects all the incoming signals to the receiver and that’s how satellite dishes work.

 

(Showing cross section) What shape is the cross-section of the satellite dish? What part of the parabola is the receiver of the satellite dish?

 

(Showing whole satellite dish) Is the satellite dish made up of just one parabola?

 

Do they all have the same focus?

 

 

 

 

 

The cross section is a parabola.  The focus.

 

 

 

 

 

No, there are lots of parabolas (lots of cross-sections). 

 

 

Yes, all have the receiver as their focus.

   

 

  Evaluate:

 Teacher will check for understanding at various points of the lesson and collect papers from Explanation section. Teacher will ask a few wrap-up questions.

 

 

      

 

 

Name the parts of the parabola we learned today and how they affect the parabola.

 

What kinds of functions have parabolas as their graphs?

 

Students will describe the vertex, focus, directrix, and axis of symmetry.

 

 

Quadratic functions. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Worksheet below:

Construction of a Parabola

 

 

                                                                             

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


  1. Number all of the horizontal lines above from 1 to 25, starting with the bottom line as #1.  Draw a vertical line down the center of the grid.
  2. Assume the width between each line is 1 unit.  Notice that the radius of the innermost circle is 1 unit and the radius for each successive circle increases by 1.
  3. Label the center point of the circles as F.  Note that F should lie on the vertical line you drew in step 1.
  4. Choose any horizontal line below line number 13 and darken in with your pencil.  Hint:  choosing an odd-numbered line makes the construction a little simpler.
  5. Find the midpoint between point F and the horizontal line you chose and label it V.  This point should lie on the vertical line from step 1. 
  6. Identify the next largest circle from the one on which V lies and the line numbered 1 GREATER than the line on which V lies.   Draw in the two intersection points of this circle and line.
  7. Continue performing step 6, moving progressively further and further outward through the grid, until you reach the largest circle, making sure to draw in all the intersection points.
  8. Connect all the points you have just drawn.

 

  1. Now choose a horizontal line above line number 13 and darken it with your pencil.  Again, choosing an odd-numbered line will make things simpler.
  2. Perform step 5 to label a new point V2. 
  3. Perform step 6, except this time, draw in the 2 intersections of the next largest circle with the line numbered 1 LESS than the horizontal line on which your new V2 lies.
  4. Repeat as before until you reach the largest circle.  Connect all the points you have just drawn.