Urban and Civil

Nov 26, 2013 (4 years and 6 months ago)

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Gloria Turnpaugh

Math Lesson

Pythagorean Theorem

Standards:

MA.A1.9.1 2000

Use a variety of problem solving strategies, such as drawing a diagram, making a chart,
guess
-
and
-
check, solving a simpler problem, writing an equation, and working backwards.

MA.G.5.1 2000

Prove and use the Pythagorean
Theorem.

MA.G.5.2 2000

State and apply the relationships that exist when the altitude is drawn to the hypotenuse
of a right triangle.

MA.G.5.6 2000

Solve word problems involving right triangles.

Learning Objectives:

Students will be able to solve
for a third unknown side on a right triangle using the Pythagorean
theorem.

Students will be able to describe and define the Pythagorean Theorem when asked from memory.

Students will be able to identify a right triangle and the corresponding sides

(being

the legs and
hypotenuse)

that fit the Pythagorean Theorem.

Students will be able to define and differentiate between when they are and are not supposed to use
the Pythagorean Theorem.

Lesson Development:

Engage:

Discern between acute, obtuse, and right triangle

Images will be shown on overhead for classroom.

Have students identify each type of triangle.

Have students identify the sides of a right triangle.

*acute

all angles smaller than 90 degrees

Gloria Turnpaugh

Math Lesson

Pythagorean Theorem

*obtuse

one angle larger than 90 degrees

*right

angle of 90 degrees

*Hypotenuse

the side opposite the right angle, is always the
longest side of a right triangle.

*Sides(legs)

refers to the two side that are not the
hypotenuse,
the two sides which make up the right angle.

Define the Pythagorean Theorem for the students

*Rule about sides of a right triangle: a proved geometric proposition stating that the square of the
longest side (hypotenuse) of a right tria
n
gle
is equal to the sum of the squares of the other two
sides

*

a
2
+b
2
=c
2

where a and b are legs and c is the hypotenuse

*Address the proper way to state this equation

*A squared plus B squared is equal to C squared.

Explore
:

Present two triangles on the
board.

Have students identify sides and hypotenuse.

Have students create the Pythagorean equations.

Gloria Turnpaugh

Math Lesson

Pythagorean Theorem

*First problem:

*The legs A and B (12 and 9) squared and added together equal the length of the
hypotenuse C squared.

*Second problem:

*The legs A and
B (5 and b) squared and added together equal the length of the
hypotenuse C (13) squared.

Have students work the problems.

Explain:

Present short power point presentation of Pythagorean Theorem Proof using algebra.

Discuss slides with students as
the proof progresses, have students explain each step.

Gloria Turnpaugh

Math Lesson

Pythagorean Theorem

Gloria Turnpaugh

Math Lesson

Pythagorean Theorem

Gloria Turnpaugh

Math Lesson

Pythagorean Theorem

Gloria Turnpaugh

Math Lesson

Pythagorean Theorem

Elaborate:

Display three “real life” problems on overhead
.

Have students identify the necessary information in each problem and construct an equation to
satisfy the problem.

Have

students work the equations created from the “real life” example problems.

1)

A 25
-
foot ladder leans against a building such that the
base of the ladder is 7 feet away from the building. How
far up the building does the top of the ladder reach?
(

2) A 13
-
foot guy
-
wire is connected to a telephone pole 12
feet up from its base. How far away from the base of the
telephone pole is the guy wire connected to the ground?

3) A rectangular section of concrete to be pour
ed requires
a steel beam to support it across the diagonal. The
rectangular section is 8
-
ft by 15
-
ft. How long must the
diagonal support be? (answer: 17 feet)

Evaluate:

Present a triangle on the board for the
students.

Have students identify
the trian
gle, sides,
and determine the Pythagorean equation.

Have students compute the problem and
solve the triangle for the remaining side.

Review process and solution with students.

Gloria Turnpaugh

Math Lesson

Pythagorean Theorem

Give homework assignment over materials.

Homework is a two
-
page handout. The first page has nine triangles with a missing side. Using
the Pythagorean theorem, solve for the missing side. Solve the problems without the use of a calculator,
and show all work. The second page has five short answe
r questions. Please complete this assignment for
the following class period.

Images compliments of Bing Image Search

http://www.ehow.com/info_8572047_real
-
problems
-
based
-
pythagorean
-
theory.html

http://www.math
-
aids.com/Pythagorean_Theorem/

http://www.juliantrubin.com/encyclopedia/mathematics/pythagorean_theorem.html

http://www.slideshare.net/yaherglanite/algebraic
-
proof
-
of
-
py
thagoras
-
theorem

Gloria Turnpaugh

Math Lesson

Pythagorean Theorem

10)

Write the Pythagorean theorem math equation: ____________________________

11)

Explain the steps of the Pythagorean Theorem with
complete sentences

using
language

(or what you think academic language sounds like.)

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

_________________________________________________
_________________

12)

Explain the steps of the Pythagorean Theorem using
every day language.

(For example,
how would you talk if you were explaining it on a children’s tv show?)

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

13)

Explain the steps of the Pythagorean Theorem
using
informal language

or
texting
language/spelling.

(For example, how would you talk if you were hanging out with your friends
or writing a note to them?)

__________________________________________________________________

____________________________
______________________________________

__________________________________________________________________

__________________________________________________________________

14)

A suitcase measures 24 inches long and 18 inches high. What is the diago
nal length of the
suitcase? (Use an exact square root answer.)

Gloria Turnpaugh

Math Lesson

Pythagorean Theorem

1)

c = √
(
45
) cm

2)

c = 13 cm

3)

c = √(29) m

4)

x = 7 m

5)

x = √(75) cm

6)

x = √(336) cm

7)

c = √(50) m

8)

c = √(4100) m

9)

x = √(21) cm

10)

a
2
+b
2
=c
2

11)

The sum of the two sides of a right triangle squared
is equal to the square of the
hypotenuse.

12)

A variation of 11

13)

A variation of 11

14)

30 inches