Lesson By: Kelly Swain

__Teachers__ =>What do the standards say
about connections?

Standard 9: Connections

Mathematics instructional programs
should

emphasize connections to foster

understanding of mathematics so that all

students-

recognize and use connections
among

different mathematical ideas;

understand how mathematical ideas build

on one another to produce a coherent

whole;

recognize, use, and learn about

mathematics in contexts outside of

mathematics.

*This lesson includes the use
of technology (Geometer's Sketchpad), which is also emphasized
in the standards!

__Objective:__ To explore and make connections between
the Pythagorean Theorem, the real world, and other areas of mathematics.

__Overview:__

Briefly review special right triangles and go over any homework from the previous day, answering any questions. (15 min)

Ask questions to stimulate thought and discussion. (5 min)

Do student guided examples (two). (10 min)

Introduce and begin activity. (20 min, remainder of the period)

Assign Homework

__Teachers__ => This lesson is planned
for a 50 minute class period. Some modications may have to be
made (i.e., may only have time for one example). This lesson could
easily be expanded to fit a block-scheduled class period--allowing
more time for discussion, examples, and the activity.

Questions to Stimulate Thought and Discussion:

Do you think we really use this?

What are some ways we might use the Pythagorean Theorem outside of school?

Student Guided Examples:

Baseball and the Pythagorean Theorem

__Teachers __=> In examples like this one,
try to find ways to include your students. Maybe some of them
love baseball or even play for the school, use them in your example
because they love it, and it increases interest.

The Distance Formula Revisited:

We've already seen and practiced the distance formula. Now, let's see if we can use the Pythagorean Theorem to understand why it works.

What should we try first?

(Hopefully, the students will suggest finding the distance between each of the points.--Think of them in terms of a triangle.)

Now, what?

(Maybe they'll try putting these distances into the Pythagorean Theorem.)

So, by squaring both sides we get...

So, now, we see the relationship between the distance formula and the pythagorean theorem.

__ACTIVITY ( using technology
)__

Homework assignment:

Come up with a problem that you may encounter on a day to day basis in which you could relate the Pythagorean Theorem to.

__Teachers__ => You can find several interesting
activities and examples of the Pythagorean Theorem in Math Forum.