Lesson Topic: Pythagorean Theorem

Instructional Objectives: / Students will be able to:
· Use the Pythagorean Theorem to solve for the unknown sides of a right triangle.
·
VSC Addressed: / 8.2.A.1.b. Identify and describe the relationship among the parts of a right triangle
ASSESSMENT LIMIT: Use the hypotenuse or the legs of right triangles
8.2.A.2.b. Apply right angle concepts to solve real-world problems
· ASSESSMENT LIMIT: Use the Pythagorean Theorem
Time Frame / 1-2 days
Materials/Equipment: / Markers
Construction Papers
ü Graph paper
ü Cardboard squares of various sizes
ü Scissors
ü Colored pencils
ü Rulers
Document Camera
Computers
LCD Projector
Prior Knowledge: / · Types of triangles
· Describe angles
· Right triangles
· Powers of integers
· Estimating square roots
Vocabulary / right triangle
hypotenuse
leg
right angle
Pythagorean Theorem
formula
substitute
square
square root
Pythagorean triple
LESSON / Warm-up
Mixed exercises on classifications and parts of triangles.
Fluency test on finding the square roots of a number.
Group Investigation Activity:
· Have the students work in groups of 4 to complete this activity.
· Give each group graph paper and have each member draw one
right triangle.
· Students will then find squares that fit on each side of the right triangle
(in other words, three squares, each with side lengths equal to one side of the triangle).
· Measure the sides of the squares.
· Calculate the areas of the squares (l x w).
· Compile the group’s data into the table provided.
· Look for patterns in the calculations done.
· Complete the chart and answer the discussion questions.
Explicit Teaching/Modeling:
· Show a flipchart on Pythagorean Theorem and some examples and have the students identify the parts and the missing side.
· Have a walk through on the steps in finding the missing side of a right triangle using the Pythagorean Theorem.
Guided Practice:
· I do - Using a flipchart, show a real-life application problem and model the procedures in finding the length of the unknown side.
· We do – Have another example and have the students solve the problem either independently or with a partner, while a volunteer student solves on the promethean board.
· You do – For the last example, give another problem and have the students work on their own and check for correctness.
The WORK SESSION
· Differentiation / Think- Tac-Toe
· Have the students complete the Pythagorean Think-Tac-Toe worksheet.
· The Think-Tac-Toe allows for differentiation by readiness, interest, and learning profile.
· Modifications
· Accomodations / · Students with IEP will work with a special educator or co-teacher during the modeling and the group investigation activities. Utilize the following websites during the activity for the students to see the proof and examples of Pythagorean Theorem visually and interactively. Have the students use the promethean board on these websites.
http://www.pbs.org/wgbh/nova/proof/puzzle/theorem.html
http://www.pbs.org/teachers/connect/resources/6329/preview/
· Have the students work with a partner when completing the Think-Tac-Toe
· Use of calculating devices
· Process Chart on Pythagorean Theorem
· Extended Time
· Frequent Breaks
· Reduced Distractions
· Formative Assessment / · Exit Ticket:
Vocabulary Graphic Organizer on Pythagorean Theorem
· Homework: / List Down 5 Pythagorean Triples. Show your work using the Pythagorean Theorem
· Reflection

PROCESS CHART

PYTHAGOREAN THEOREM

· The hypotenuse is the longest side of the right triangle and the side opposite of the right angle. The sides that form the right angle are called legs. For any right triangle, the Pythagorean Theorem is true:

leg + leg = hypotenuse

a + b = c

The square of the hypotenuse equals the sum of the squares of the legs.

WALK-THROUGH STEPS

· Identify the right angle, legs, and hypotenuse of the right triangle.

· Plug in the value of the legs for a and b in the Pythagorean Theorem.

· Evaluate the exponential expressions.

· Take the square root of each side of the equation to solve for c.

GROUP INVESTIGATION WORKSHEET

Directions:

1. Each group has a set of right triangles and squares to sort.

2. For each right triangle, label the shorter leg a, the longer leg b, and the hypotenuse c.

3. Find squares that fit on each side of the right triangle (in other words, three squares, each with side lengths equal to one side of the triangle).

4. Compile your group’s data into the table below by finding the length of each side of the right triangle and the area of each square on each side.

Right
Triangle / Leg (a) / Leg (b) / Hypotenuse
(c) / Area
Leg (a2) / Area
Leg (b2) / Area
Hypotenuse
(c2)
1
2
3

· What do you notice about the values you found for the areas?

· Is there any relationship between the areas of the squares on the legs and the area of the square on the hypotenuse?

PYTHAGOREAN THEOREM THINK-TAC-TOE

Select and complete one activity from each horizontal row to demonstrate your understanding of the Pythagorean Theorem.

WORKSHEET / Complete a Pythagorean Theorem WorD Problems. Draw the figure, label its parts, and show your work. / Complete a BCR on Pythagorean Theorem. / Complete a worksheet on solving for the hypotenuse of a right triangle.
ACTIVITY / Compose a poem on Pythagorean Theorem with emphasis on its real life application and how to solve for the unknown side. / Compose a rap on Pythagorean Theorem with emphasis on its real life application and how to solve for the unknown side. / Create a comic strip on Pythagorean Theorem with emphasis on its real life application and how to solve for the unknown side.
INTERACTIVE / Go to www.ixl.com and complete the problems on solving for the unknown side of a triangle using the Pythagorean Theorem. / Go to www.studyisland.com and complete 15 problems on solving for the unknown side of a triangle using the Pythagorean Theorem. / Research on the life and contributions of Pythagoras and make a powerpoint presentation with 6-10 slides.

Use the Pythagorean Theorem to solve the problems below. Draw a picture to help you!!

1. A ladder is leaning against a house. The base of the ladder is 5 feet from the house. The top of the ladder rests 12 feet up. How long is the ladder?

2. A cable that is 45 feet long is attached to the top of a vertical pole. The cable is anchored to the ground 36 feet from the base of the pole. How tall is the pole?

3. Ms. Walker tells you that she is drawing a right triangle with a hypotenuse of 13 inches and leg of 5 inches. How long is the other leg?

4. Mr. Shoales rests a ladder against a wall with the base 6 feet from the wall. The ladder is 10 feet long. How high is the wall where the pole rests against?

5. Point A is 9 miles from Point B, and 12 miles from Point C, with a right angle at Point A. A road directly connects Points B and C. How many miles is this road?

BCR ON PYTHAGOREAN THEOREM

A. Ms. Reid wants to cover a bulletin board. She puts a boarder on the diagonal of the bulletin board. How many feet of boarder does she need?

______

· Use what you know about triangles to explain how you found your answer. Use numbers, words, and/or symbols in your explanation.

______

SOLVE FOR THE HYPOTENUSE

Complete the Pythagorean Triples by giving the value for the hypotenuse.

3, 4, ___ 7, 24, ___ 9, 12, ___

6, 8, ___ 5, 12, ___ 15, 20, ___

Do the side lengths below form a right triangle? Show your work. If yes, circle the hypotenuse.

a) 9, 12, 15

b) 8, 14, 12

c) 12, 5, 13

d) 11, 7, 9

Solve for the hypotenuse in the right triangles below. Show your work!