Secondary Mathematics I [2011]
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Understand the concept of a function and use function notation.
Students should experience a variety of types of situations modeled by functions. Detailed analysis of any particular class of function at this stage is not advised. Students should apply these concepts throughout their future mathematics courses.

Draw examples from linear and exponential functions. In F.IF.3, draw connection to F.BF.2, which requires students to write arithmetic and geometric sequences. Emphasize arithmetic and geometric sequences as examples of linear and exponential functions.

• A Water Function - A Solidify Understanding Task
Defining Function (F.IF.1) Features of Functions Module - Task 7
• A Water Function - Teacher Notes
Teacher Notes for "A Water Function" task. Defining Function (F.IF.1) Features of Functions Module - Task 7
• Algebra Why and When video
This video explains why and when algebra is needed instead of arithmetic functions.
• Connecting the Dots: Piggies and Pools - A Develop Understanding Task
Introducing continuous linear and exponential functions (F.IF.3) Linear and Exponential Functions Module - Task 1
• Connecting the Dots: Piggies and Pools - Teacher Notes
Teacher Notes for "Connecting the Dots: Piggies and Pools" task. (F.IF.3) Linear and Exponential Functions Module - Task 1
• Coordinates and the Cartesian Plane
This lesson helps students understand functions and the domain and range of a set of data points.
• Counting the Trains
In this unit of 3 lessons, students will investigate a relationship between recursive functions and exponential functions.
• Derivate
Students may use the applet in this lesson to graph a function and a tangent line and view its equation.
• Function Flyer
The applet on this site allows the students to manipulate the graph of a function by changing the value of exponents, coefficients and constants.
• Functions and the Vertical Line Test
The vertical line test for functions is the focus of this lesson plan.
• Graphit
With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
• Inductive Patterns
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.
• Inductive Reasoning
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.
• Inductive Reasoning video
This video introduces and explains the topic.
• Interpreting Functions - A Practice Understanding Task
Using graphs to solve problems given in function notation (F.BF.1b, F.IF.2, F.IF.4, F.IF. 5, F.IF.7, A.REI.11, A.CED.3) Features of Functions Module - Task 6
• Interpreting Functions - Teacher Notes
Teacher Notes for "Interpreting Functions" task. (F.BF.1b, F.IF.2, F.IF.4, F.IF. 5, F.IF.7, A.REI.11, A.CED.3) Features of Functions Module - Task 6
• Interpreting Functions Curriculum Guide
The Utah State Office of Education (USOE) and educators around the state of Utah developed these guides for the Secondary Mathematics 1 Cluster "Understand the concept of a function and use function notation." / Standards F.IF.1, F.IF.2, F.IF.3 and Cluster "Interpret functions that arise in applications in terms of a context" / Standards F.IF.4, F.IF.5 and F.IF.6 and Cluster "Analyze functions using different representations" / Standards F.IF.7 and F.IF.9.
• Introduction to Functions
This lesson introduces students to functions and how they are represented as rules and data tables. They also learn about dependent and independent variables.
• Linear Functions
The applet in this lesson allows students to manipulate variables and see the changes in the graphed line.
• Making it Happen (NCTM book)
This NCTM publication is designed to help educators interpret and implement the Common Core State Standards for Mathematics.
• Match that Function - A Practice Understanding Task
Matching features and representations of a specific function (F.IF.2, F.IF.4, F.IF. 5, F.IF.7, A.REI.11, A.CED.3) Features of Functions Module - Task 9
• Match that Function - Teacher Notes
Teacher Notes for "Match that Function" task. (F.IF.2, F.IF.4, F.IF. 5, F.IF.7, A.REI.11, A.CED.3) Features of Functions Module - Task 9
• More Complicated Functions: Introduction to Linear Functions
This lesson is designed to reinforce the concept of linear functions and ask students to write functions using English, tables and algebra.
• Pooling it Together - A Solidify Understanding Task
Combining functions and analyzing contexts using functions (F.BF.1b, F.IF.2, F.IF.4, F.IF. 5, F.IF.7, A.REI.11, A.CED.3) Features of Functions Module - Task 5
• Pooling it Together - Teacher Notes
Teacher Notes for "Pooling it Together" task. (F.BF.1b, F.IF.2, F.IF.4, F.IF. 5, F.IF.7, A.REI.11, A.CED.3) Features of Functions Module - Task 5
Through this lesson students will understand how to graph functions.
• Representing Functions and Relations
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.
• Representing Patterns
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.
• Representing Polynomials
This lesson unit is intended to help educators assess how well students are able to translate between graphs and algebraic representations of polynomials.
• Secondary I Textbook
Secondary I Textbook is composed of modules that are aligned with the Utah Core State Standards for Mathematics. Each lesson begins with a worthwhile task that has been designed to develop mathematical understanding, solidify that understanding, or allow for practice of the new concepts, while focusing on the mathematical goals of the chosen learning cycle.
• Sequencer
By using this applet students are able to create sequences by changing the values of starting numbers, multipliers, and add-ons.
• The Water Park - A Solidify Understanding Task
Interpreting functions using notation (F.IF.2, F.IF.4, F.IF. 5, F.IF.7, A.REI.11, A.CED.3) Features of Functions Module - Task 4
• The Water Park - Teacher Notes
Teacher Notes for "The Water Park" task (F.IF.2, F.IF.4, F.IF. 5, F.IF.7, A.REI.11, A.CED.3) Features of Functions Module - Task 4
• To Function or Not to Function - A Practice Understanding Task
Identifying whether or not a relation is a function given various representations (F.IF.1, F.IF.3) Features of Functions Module - Task 8
• To Function or Not to Function - Teacher Notes
Teacher Notes for "To Function or Not to Function" task. (F.IF.1, F.IF.3) Features of Functions Module - Task 8
• Using a Lottery to Illustrate Functions
In this videotaped lesson students use a lottery to see the uniqueness of functional relationships. (5 minutes)
• Vertical Line Test
This interactive applet asks the student to connect points on a plane in order to build a function and then test it to see if it's valid.

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 Office 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 Office of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.