The Pythagorean Theorem

Lesson 4--Conncections

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;
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.