 Secondary Mathematics III

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.3�4).
• Absolute Value
This array of resources teaching absolute value includes warm-up problems, a video introducing the topic, worked examples, practice problems, and a review.
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Applications of Quadratic Functions video
This video introduces and explains the topic.
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
This video introduces and explains the topic.
• Applying Rational Equations
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Applying Rational Equations video
This video introduces and explains the topic.
• Exponentials and Logarithms II
This task and its companion, F-BF Exponentials and Logarithms I, is designed to help students gain facility with properties of exponential and logarithm functions resulting from the fact that they are inverses.
• 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.
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
This video introduces and explains the topic.
• Inductive Reasoning video
This video introduces and explains the topic.
• 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.
• Invertible or Not?
This task illustrates several components of standard F-BF.B.4.c: Find Inverse Functions. Here, instead of presenting two functions and asking the students to decide which one is invertible, students are asked to complete a table of input-output pairs for the functions in such a way that one of the functions is invertible and the other one is not.
• Latitude
This task requires students to use data to generate understanding of an invertible function. Some brief notes: First, the table has data ordered by percentage, not latitude, so students will have to reorder the data in order to generate a graph of N(ℓ). Second, students are asked to interpret statements about inverse functions, for which an understanding of the quantities' units is particularly helpful.
• Modeling: Rolling Cups
This lesson unit is intended to help educators assess how well students are able to choose appropriate mathematics to solve a non-routine problem, generate useful data by systematically controlling variables, and develop experimental and analytical models of a physical situation.
• Module 1: Functions and Their Inverses - Student Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 1, Functions and Their Inverses, reviews the features of linear, exponential, and quadratic functions and general inverse relationships. The idea that the inputs and outputs are reversed in inverse functions is reinforced in the module using tables, graphs, equations, and story context.
• Module 1: Functions and Their Inverses - Teacher Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 1, Functions and Their Inverses, reviews the features of linear, exponential, and quadratic functions and general inverse relationships. The idea that the inputs and outputs are reversed in inverse functions is reinforced in the module using tables, graphs, equations, and story context.
• 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.
• Parabolas and Inverse Functions
This task assumes students have an understanding of the relationship between functions and equations. Using this knowledge, the students are prompted to try to solve equations in order to find the inverse of a function given in equation form: when no such solution is possible, this means that the function does not have an inverse.
• Proportional Functions
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Rainfall
In this task students are asked to analyze a function and its inverse when the function is given as a table of values. In addition to finding values of the inverse function from the table, they also have to explain why the given function is invertible.
Through this lesson students will understand how to graph functions.
• Solve Quadratic Expressions by Factoring video
This video introduces and explains the concept.
• Solving Absolute Value Equations
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving Absolute Value Equations video
This video explains how to solve absolute value expressions.
• Solving Equations video
Answers the questions "what are equations?" and "how do we solve them?"
• Solving Quadratic Equations by Completing the Square
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
This video introduces and explains the topic.
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
This video introduces and explains the topic.
• Solving Rational Equations
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving Rational Expressions video
This video introduces and explains the topic.
• Systems of Non-Linear Equations
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Systems of Non-Linear Equations video
This video introduces and explains the topic.
• Temperature Conversions
Unit conversion problems provide a rich source of examples both for composition of functions (when several successive conversions are required) and inverses (units can always be converted in either of two directions).
• Temperatures in degrees Fahrenheit and Celsius
Temperature conversions provide a rich source of linear functions which are encountered not only in science but also in our every day lives when we travel abroad. The first part of this task provides an opportunity to construct a linear function given two input-output pairs. The second part investigates the inverse of a linear function while the third part requires reasoning about quantities and/or solving a linear equation.
• US Households
The purpose of this task is to construct and use inverse functions to model a a real-life context. Students choose a linear function to model the given data, and then use the inverse function to interpolate a data point. 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 materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.