 Determine an explicit expression, a recursive process, or steps for calculation from a context.
 Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
 Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Assessed with:
MAFS.912.FLE.1.2
 Test Item #: Sample Item 1
 Question:
Chantel drew a picture of her dog on a piece of paper that is 12 centimeters long. She used a copy machine to enlarge her drawing. She used the 115% setting to make each new copy. She then used each new copy to generate the next copy, using the same copier setting.
Enter a recursive formula that will give the length of each new copy.
 Difficulty: N/A
 Type: EE: Equation Editor
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Lesson Study Resource Kit
ProblemSolving Tasks
Professional Development
Unit/Lesson Sequence
Video/Audio/Animation
Virtual Manipulatives
STEM Lessons  Model Eliciting Activity
This MEA deals with creating a business plan for a movie theater, based on provided data. Students will first determine the best film to show, and then based on that decision, will create a model of ideal sales. Students will need to create equations and graph them to visually represent relationships.
Model Eliciting Activities, MEAs, are openended, interdisciplinary problemsolving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
Students use information about credit card Annual Percentage Rate (APR), introductory APR, balance transfer fees and APR, and special offers such as frequent flyer miles or "cash back" to determine which card is the best to help a college student pay expenses and begin establishing a credit rating.
Model Eliciting Activities, MEAs, are openended, interdisciplinary problemsolving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
The Plants versus Pollutants MEA provides students with an openended problem in which they must work as a team to design a procedure to select the best plants to clean up certain toxins. This MEA requires students to formulate a phytoremediationbased solution to a problem involving cleaning of a contaminated land site. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client.
Model Eliciting Activities, MEAs, are openended, interdisciplinary problemsolving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
Students will use basic arithmetic, simple functions, averages, and possibly weighted averages to rank 6 Major League Baseball Parks by home field advantage. Students will write a description of their process using correct terminology and appropriate tone.
Model Eliciting Activities, MEAs, are openended, interdisciplinary problemsolving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
Students are asked to write two explicit functions given verbal descriptions in a realworld context, compose the two functions, and explain the meaning in context.
Students are asked to write an explicit function rule given a verbal description of a functional relationship in a realworld context and are then asked to use the function rule to answer a question.
Students are asked to write and combine an exponential and a constant function from a verbal description to use when answering a related context question.
Students are asked to write an explicit function rule given a verbal description of a functional relationship in a realworld context and are then asked to use the function rule to answer specific questions.
Student Resources
ProblemSolving Tasks
This task provides an approximation, and definition, of e, in the context of more and more frequent compounding of interest in a bank account. The approach is computational.
Type: ProblemSolving Task
In this example, students are given the graph of two functions and are asked to sketch the graph of the function that is their sum. The intent is that students develop a conceptual understanding of function addition.
Type: ProblemSolving Task
This task addresses an important issue about inverse functions. In this case the function f is the inverse of the function g but g is not the inverse of f unless the domain of f is restricted.
Type: ProblemSolving Task
This task asks students to write expressions for various problems involving distance per units of volume.
Type: ProblemSolving Task
The context of this example is the spread of a flu virus on campus and the related sale of tissue boxes sold. Students interpret the composite function and determine values simply by using the tables of values.
Type: ProblemSolving Task
This task develops reasoning behind the general formula for balances under continuously compounded interest. While this task itself specifically address the standard (FBF), building functions from a context, an auxiliary purpose is to introduce and motivate the number e, which plays a significant role in the (FLE) domain of tasks.
Type: ProblemSolving Task
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).
Type: ProblemSolving Task
This task asks students to determine a recursive process from a context. Students who study computer programming will make regular use of recursive processes.
Type: ProblemSolving Task
This task asks students to use proportions of mass and volume to create ideal brine for saltwater fish tanks. It also asks students to compare graphs.
Type: ProblemSolving Task
This problem is a quadratic function example. The other tasks in this set illustrate MAFS.912.F.BF.1.1.a in the context of linear, exponential, and rational functions.
Type: ProblemSolving Task
The purpose of this task is to introduce students to exponential growth. While the context presents a classic example of exponential growth, it approaches it from a nonstandard point of view.
Type: ProblemSolving Task
The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function.
Type: ProblemSolving Task
The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of the context. It can be used as either an assessment or a teaching task.
Type: ProblemSolving Task
Video/Audio/Animation
This video demonstrates writing a function that represents a reallife scenario.
Type: Video/Audio/Animation
Virtual Manipulatives
Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
In this activity, students enter inputs into a function machine. Then, by examining the outputs, they must determine what function the machine is performing. This activity allows students to explore functions and what inputs are most useful for determining the function rule. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
Parent Resources
ProblemSolving Tasks
This task provides an approximation, and definition, of e, in the context of more and more frequent compounding of interest in a bank account. The approach is computational.
Type: ProblemSolving Task
In this example, students are given the graph of two functions and are asked to sketch the graph of the function that is their sum. The intent is that students develop a conceptual understanding of function addition.
Type: ProblemSolving Task
This task addresses an important issue about inverse functions. In this case the function f is the inverse of the function g but g is not the inverse of f unless the domain of f is restricted.
Type: ProblemSolving Task
This task asks students to write expressions for various problems involving distance per units of volume.
Type: ProblemSolving Task
The context of this example is the spread of a flu virus on campus and the related sale of tissue boxes sold. Students interpret the composite function and determine values simply by using the tables of values.
Type: ProblemSolving Task
This task develops reasoning behind the general formula for balances under continuously compounded interest. While this task itself specifically address the standard (FBF), building functions from a context, an auxiliary purpose is to introduce and motivate the number e, which plays a significant role in the (FLE) domain of tasks.
Type: ProblemSolving Task
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).
Type: ProblemSolving Task
This task asks students to determine a recursive process from a context. Students who study computer programming will make regular use of recursive processes.
Type: ProblemSolving Task
This task asks students to use proportions of mass and volume to create ideal brine for saltwater fish tanks. It also asks students to compare graphs.
Type: ProblemSolving Task
This problem is a quadratic function example. The other tasks in this set illustrate MAFS.912.F.BF.1.1.a in the context of linear, exponential, and rational functions.
Type: ProblemSolving Task
The purpose of this task is to introduce students to exponential growth. While the context presents a classic example of exponential growth, it approaches it from a nonstandard point of view.
Type: ProblemSolving Task
The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function.
Type: ProblemSolving Task
The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of the context. It can be used as either an assessment or a teaching task.
Type: ProblemSolving Task