1
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 4. Inverse Variation; Topic
Notes
STRAND 3: QUADRATIC AND NONLINEAR FUNCTIONS
TOPIC 3.4: INVERSE VARIATIONS
Topic Notes
Mathematical focus
Participants explore inverse variations situations. Participants develop the idea
that in inverse variation, y·x is a constant and compare that to direct variation
where y/x is the constant.
Topic overview
This topic includes two tasks:
Task 3.4.1: Distance and Time
Task 3.4.2: Heat and Pressure
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.
TEKS/TAKS focus
TEKS A.11 Quadratic and other nonlinear functions. The student understands there
are situations modeled by functions that are neither linear nor quadratic and models the
situations. The student is expected to:
(B) analyze data and represent situations involving inverse variation using
concrete models, tables, graphs or other algebraic methods.
Materials
Task
Graphing
Calculator
Copies of
Task
Task 3.4.1
Distance and Time
Task 3.4.2
Heat and Pressure
x
x
x
x
Procedures
Break participants into groups of 3 or 4 and have them complete the task.
Participants then come back together for a whole class discussion of the results.
November 24, 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.
2
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 4. Inverse Variation; Topic
Notes
Teaching notes
Have students investigate the tasks using their graphing calculators.
November 24, 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.