Jeremy Gibbs

2-2-99

"6.1 Quadratic Functions"

2nd hour

25 min. lesson

Materials:

book for each student, photos found in books (Taj Mahal, buildings, water)

overhead blank sheets (to group categories of common characteristics)

Behavioral Objective: After the lecture, students will write an evaluative essay describing the importance of mathematics. Students will each have three well-supported ideas with 70% accuracy.

Anticipatory Set:

(Teacher shows pictures. 1. 37 - Buildings, 2. 45 - Buildings, 3. 9 Seascapes, 4. 14 Seascapes, 5. 53 Water, 6. 94 Water, 7. Taj Mahal - Book)

Which is similar? Which are different?

Anticipated Responses: Group buildings and water separate, probably differentiate paintings from photos.

(Teacher writes lists on overhead.)

What are the characteristics of those that are similar?

Anticipated student responses: buildings, water, photos, paintings

Of our two (four) categories, can we find one characteristic that is common to all of them?

Possible Answers: No, all have paint, all deal with art

Correct Response: all deal with quadratic equations

Write that term down at the top of your paper and leave about three lines for us to define it later.

Instructional Input/ Modeling:

Does anyone remember the equation for the area of a circle?

Correct response: A = Õ r^2

Does anyone know how to find the area for a square?

Correct response: A = x^2

What do these two equations have in common?

Correct response: both have powers of 2 in their equations.

These are the simplest quadratic functions that we have.

What about a rectangle?

Correct response: A = lw (which is also said to be second degree)

One more common shape - examples include water from a water hose, or the pendulum of a grandfather clock. You have heard of it before. What is it?

Correct Response: a parabola

Let’s come back to that definition of quadratic and give it a better, formalized, definition.

Let’s brainstorm some key traits of quadratics and their functions.

Possible Answers: curvy lines, squares, powers of 2

As a group, come up with a definition. Then, we will look at the official definition.

Quadratic expression - an expression which contains one or more terms in x^2, y^2, or xy, but no higher powers of x or y.

 

Guided Practice:

Now, I want you to try a couple for me, so that I can see if you have it. (see attached sheet)

Independent Practice:

From class today, as well as prior knowledge, write a one-page essay why you believe it is/ is not important to learn mathematics. Be prepared to defend your answer.

Checking for Comprehension/ Closure:

(Teacher may ask two or three of these questions, depending on level achieved of the class.)

1. Why are parabolas symmetric with respect to the axes? What makes them so?

Correct response: (testing for comprehension) because of the power of two, it makes the functions reflect to be equal

2. Determine which could/ could not be results of quadratic values.

  1. y = x^3 (b) water waves © box (d) volume of Jupiter

a - no, b - yes, c - yes, d - no (application)

3. Compare/ Contrast shape of the Arch with a piece of paper.

Arch - curvy, paper - square

both have powers of two in their equations (checking for analysis)
  1. Suppose we didn’t know or use quadratics, what would be different about architecture and art?

Not stable, not well defined curve lines (checking for synthesis)

 

Closure:

Someone give me the definition of quadratics one last time.

Quadratic expression - an expression which contains one or more terms in x^2, y^2, or xy, but no higher powers of x or y.

Three examples of where quadratic equations are found in every day life.

Arch, buildings, waves, etc.

Everyone understand? Anyone have any questions beyond this. Ok, remember to write your one-page paper tonight analyzing why/ why not we should study math. Have a good day.