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Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 1. Topic Notes
STRAND 3: QUADRATIC AND NONLINEAR FUNCTIONS
TOPIC 3.1: PYTHAGOREAN THEOREM
Topic Notes
Mathematical focus
The focus of this topic is the Pythagorean Theorem and the connection between
algebraic and geometric skills associated with it.
Topic overview
This topic contains three tasks:
Task 3.1.1: 45-45 Right Triangles
Task 3.1.2: 30-60 Right Triangles
Task 3.1.3: Diagonal Patterns
Although these ideas are geometric, this topic is designed to study the
functionality of patterns and how they apply in all mathematical subjects.
TExES Standards focus
TExES Standard II.004 Patterns and algebra. The teacher uses patterns to model and
solve problems and formulate conjectures. The beginning teacher:
(A) Recognizes and extends patterns and relationships in data presented in tables,
sequences, or graphs.
TExES Standard II.006 Patterns and algebra. The teacher understands linear and
quadratic functions, analyzes their algebraic and graphical properties, and uses them to
model and solve problems. The beginning teacher:
(A) Understands the concept of slope as a rate of change and interprets the
meaning of slope and intercept in a variety of situations.
TExES Standard III.011 Geometry and measurement. The teacher understands
measurement as a process. The beginning teacher:
(D) Applies the Pythagorean theorem, proportional reasoning, and right triangle
trigonometry to solve measurement problems.
TEKS/TAKS focus
TEKS A.5 Linear functions. The student understands that linear functions can be
represented in different ways and translates among their various representations.
The student is expected to:
(C) use, translate, and make connections among algebraic, tabular, graphical,
or verbal descriptions of linear functions.
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
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Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 1. Topic Notes
TEKS A.6 Linear functions. The student understands the meaning of the slope
and intercepts of the graphs of linear functions and zeros of linear functions and interprets
and describes the effects of changes in parameters of linear functions in real-world and
mathematical situations. The student is expected to:
(A) develop the concept of slope as rate of change and
determine slopes from graphs, tables, and algebraic representations; and
(B) interpret the meaning of slope and intercepts in situations using data,
symbolic representations, or graphs.
High School TAKS Objective 6: The student will demonstrate an understanding of
geometric relationships and spatial reasoning.
High School TAKS Objective 8: The student will demonstrate an understanding of the
concepts and uses of measurement and similarity.
Materials
Handout
Graphing Calculator
Ruler
45-45 Right
Triangles
X
X
X
30-60 Right
Triangles
X
X
X
Diagonal Patterns
X
X
X
Procedure
For each task, have participants work in groups of 3-4. Each group should
discover the patterns first and then prepare for a discussion by the class.
Summary
After completing these tasks, participants should have a better understanding of
the importance of patterning in all areas of mathematics and realize that the
majority of the formulas that are traditionally memorized may be discovered by
examining situations like those provided here.
Extensions
• Given the length of one side of an equilateral triangle, can the height be determined
by the techniques shown here?
• Create rectangles using other Pythagorean triples to use with Task 3.1.3: Diagonal
Patterns.
Assessment/Transition to the Classroom
Participants complete the Teacher’s Journal, recording their responses and making
any modifications necessary to make the tasks completely classroom ready.
November 23, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.