Secondary Mathematics III
Educational Links
Strand: FUNCTIONS  Building Functions (F.BF)
Build a function that models a relationship between two quantities. Develop models for more complex or sophisticated situations
(Standards F.BF.1). Build new functions from existing functions
(Standards F.BF.34).
Standard F.BF.3
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Note the effect of multiple transformations on a single function and the common effect of each transformation across function types. Include functions defined only by a graph. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

FUNCTIONS  Building Functions (F.BF)  Sec Math III Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics III  Building Functions (F.BF).

Generalizing Patterns: Table Tiles
This lesson unit is intended to help educators assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types that are needed for a range of square tabletops.

Introduction to the Materials (Math 3)
Introduction to the Materials in the Mathematics Three of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems.

Modeling: Rolling Cups
This lesson unit is intended to help educators assess how well students are able to choose appropriate mathematics to solve a nonroutine problem, generate useful data by systematically controlling variables, and develop experimental and analytical models of a physical situation.

Module 2: Logarithmic Functions  Student Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 2, Logarithmic Functions, picks up where Module 1 leaves off. Students begin to understand logarithms by drawing upon their experiences with inverses and exponential functions to evaluate, approximate, and order logarithmic expressions such log2 8 and log2 20.

Module 2: Logarithmic Functions  Teacher Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 2, Logarithmic Functions, picks up where Module 1 leaves off. Students begin to understand logarithms by drawing upon their experiences with inverses and exponential functions to evaluate, approximate, and order logarithmic expressions such log2 8 and log2 20.

Module 3: Polynomial Functions  Student Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 3, Polynomial Functions, begins with a task that links linear, quadratic, and cubic functions together by highlighting the rates of change of each function type and using a story context to show that a linear function is the sum of a constant, a quadratic function is the accumulation or sum of a linear function, and a cubic function is the sum of a quadratic function.

Module 3: Polynomial Functions  Teacher Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 3, Polynomial Functions, begins with a task that links linear, quadratic, and cubic functions together by highlighting the rates of change of each function type and using a story context to show that a linear function is the sum of a constant, a quadratic function is the accumulation or sum of a linear function, and a cubic function is the sum of a quadratic function.

Module 4: Rational Expressions and Functions  Student Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 4, Rational Expressions and Functions, students work with the fractions that are ratios of polynomials, rational expressions and functions.

Module 4: Rational Expressions and Functions  Teacher Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 4, Rational Expressions and Functions, students work with the fractions that are ratios of polynomials, rational expressions and functions.

Module 6: Modeling Periodic Behavior  Student Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 6, Modeling Periodic Behavior. In this module students use a Ferris wheel as a context for constructing conceptual understanding of circular trigonometry. They begin by calculating heights on the Ferris wheel, progress to calculating the heights at a given time on the Ferris wheel, and then, graphing the heights to show a sine function.

Module 6: Modeling Periodic Behavior  Teacher Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 6, Modeling Periodic Behavior. In this module students use a Ferris wheel as a context for constructing conceptual understanding of circular trigonometry. They begin by calculating heights on the Ferris wheel, progress to calculating the heights at a given time on the Ferris wheel, and then, graphing the heights to show a sine function.

Module 7: Trig. Functions, Equations & Identities  Student Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 7, Trigonometric Functions, Equations, and Identities, students work with more trigonometric graphs, beginning with the familiar Ferris wheel context.

Module 7: Trig. Functions, Equations & Identities  Teacher Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 7, Trigonometric Functions, Equations, and Identities, students work with more trigonometric graphs, beginning with the familiar Ferris wheel context.

Module 8: Modeling With Functions  Student Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 8, Modeling with Functions, focuses on a big idea of functions: Functions can be combined together (using basic operations or composed) to make new functions, usually retaining some of the features of both functions.

Module 8: Modeling With Functions  Teacher Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 8, Modeling with Functions, focuses on a big idea of functions: Functions can be combined together (using basic operations or composed) to make new functions, usually retaining some of the features of both functions.

Solving Rational Expressions video
This video introduces and explains the topic.
http://www.uen.org  in partnership with Utah State Board of Education
(USBE) and Utah System of Higher Education
(USHE). Send questions or comments to USBE
Specialist 
Lindsey
Henderson
and see the Mathematics  Secondary website. For
general questions about Utah's Core Standards contact the Director

Jennifer
Throndsen.
These materials have been produced by and for the teachers of the
State of Utah. Copies of these materials may be freely reproduced
for teacher and classroom use. When distributing these materials,
credit should be given to Utah State Board of Education. These
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Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah
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