Focus Plan
Texarkana Independent School District
GRADING
PERIOD:
Teacher:
1st six weeks
PLAN CODE:
M11.1.2
Ronda Jameson
Course/subject:
Math 11
Grade(s):
11
Time allotted
for instruction:
2 class periods on block
Title:
Climbing the Pythagorean Ladder
Lesson TOPIC:
Pythagorean Theorem
TAKS Objective:
Objective 8
The student will demonstrate an understanding of the concepts and uses of
measurement and similarity
G.5 Geometric patterns. The student uses a variety of representations to
describe geometric relationships and solve problems. The student is expected
to:
(D) Identify and apply patterns from right triangles to solve meaningful
problems, including special right triangles (45-45-90 and 30-60-90) and
triangles whose sides are Pythagorean triples.
8.9 (A) The student uses indirect measurement to solve problems. The
student is expected to use the Pythagorean Theorem to solve real-life
problems.
Focus TEKS and
Student Expectation:
Supporting TEKS and
Student Expectation:
8.14 (B) The student is expected to use a problem solving model that
incorporates understanding the problem, making a plan, carrying out the plan,
and evaluating the solution for reasonableness.
Concepts
Pythagorean theorem
Legs/Hypotenuse
Enduring Understandings/Generalizations/Principles
The student will understand that
The Pythagorean Theorem is a relationship among the lengths of the three sides of a
right triangle. The Pythagorean Theorem applies only to right triangles.
In any right triangle with leg lengths a and b and hypotenuse length c, a2 + b2 = c2.
If the side lengths of any triangle satisfy the equation a2 + b2 = c2, then the triangle
is a right triangle, and c is its hypotenuse.
Pythagorean triple
Any set of three whole numbers that satisfy the Pythagorean Theorem is called a
Pythagorean triple. Any multiple of a Pythagorean triple is also a Pythagorean
triple.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
I.
Sequence of Activities (Instructional Strategies)
A.
Focus/connections
The teachers will read the following:
A Brief History of the Pythagorean Theorem
Pythagoras (569-500 B.C.) was born on the island of Samos in Greece, and did much traveling
through Egypt, learning, among other things, mathematics. Not much more is known of his early
years. Pythagoras gained his famous status by founding a group, the Brotherhood of
Pythagoreans, which was devoted to the study of mathematics. The group was almost cult-like in
that it had symbols, rituals and prayers. In addition, Pythagoras believed that “Number rules the
universe,” and the Pythagoreans gave numerical values to many objects and ideas. These
numerical values, in turn, were endowed with mystical and spiritual qualities.
Legend has it that upon completion of his famous theorem, Pythagoras sacrificed 100 oxen.
Although he is credited with the discovery of the famous theorem, it is not possible to tell if
Pythagoras is the actual author. The Pythagoreans wrote many geometric proofs, but it is difficult
to ascertain who proved what, as the group wanted to keep their findings secret. Unfortunately,
this vow of secrecy prevented an important mathematical idea from being made public. The
Pythagoreans had discovered irrational numbers! If we take an isosceles right triangle wit legs of
measure 1, the hypotenuse will measure “the square root of 2”. But this number cannot be
expressed as a length that can be measured with a ruler divided into fractional parts, and that
deeply disturbed the Pythagoreans, who believed that “All is number”. They called these numbers
“alogon,’ which means “unutterable”. So shocked were the Pythagoreans be these numbers, they
put to death a member who dared to mention their existence to the public. It would be 200 years
later that the Greek mathematician Eudoxus developed a way to deal with these unutterable
numbers. Retrieved from: http://www.geom.uiuc.edu/demo5337/Group3/hist.html 12/1/2004
B.
Activity Right Triangles in Egypt
Give each student a length of twine, yarn, or string and a ruler.
Directions:
It is known that the Egyptians used a knotted rope as an aid to constructing right angles in their
buildings. The rope had 12 evenly spaced knots, which could be formed into a 3-4-5 right
triangle, thus giving an angle of exactly 90 degrees. Can you make a rope like this? Tie knots to
create a right triangle with side lengths of 3,4, and 5. Then use your knotted rope to check some
right angles in the room.
C.
Accommodations/modifications
Students requiring modifications may work with a peer during the Right Triangles in Egypt
activity.
D.
Enrichment
Explain why {-3, -4, 5} could not represent the sides of a right triangle. Why could using a
calculator lead you to a wrong answer to this question?
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
II.
iii.
STUDENT PERFORMANCE
A.
Description
Students will review Pythagorean Theorem as teacher displays
and summarizes overhead sheets. Teacher may require students to take notes.
B.
Activity:
Students will create a Pythagorean Theorem problem similar to one they might see on
TAKS. Selected students will come to the front of the room and present their problem.
Class will work that problem. Teacher will facilitate discussion.
C.
Enrichment:
Students are asked to imagine themselves 10 years in the future and to write a paragraph
describing a situation in which they would use the Pythagorean Theorem to solve a problem or
assist in an activity.
Assessment
A.
Assessing the Activity
During the activity, the teacher will perform an informal assessment by circulating through the
classroom, asking questions, and providing feedback.
B.
Assessing the lesson
Students will take Quiz over Pythagorean Theorem
IV.
taks preparation
A. Transition to TAKS context
Overhead sheets demonstrate for students the progression in critical thinking skills from grades 8
through 11 expected to master TAKS questions assessing knowledge of Pythagorean Theorem.
B. Sample TAKS questions
See overhead sheets
V.
VI.
Key Vocabulary
Square root, right triangle, leg, hypotenuse, Pythagorean triples, irrational number, diagonal
Resources
A.
Textbook
Glencoe, Algebra I Section 13-1
Glencoe Geometry Section 5-2
Glencoe Algebra II
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
B.
Supplementary materials/equipment

Overhead Sheets - Pythagorean Theorem

String/yarn/or twine

Rulers – standard and metric

Quiz - Pythagorean Theorem
C.
Technology
Graphing Calculator
VII.
Follow up activities
The teacher should be prepared to “spiral” this content throughout the school year.
VIII.
Teacher notes
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District