 # Standard #: MAFS.912.F-LE.1.3

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Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

### General Information

Subject Area: Mathematics
Domain-Subdomain: Functions: Linear, Quadratic, & Exponential Models
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Construct and compare linear, quadratic, and exponential models and solve problems. (Algebra 1 - Supporting Cluster) (Algebra 2 - Supporting Cluster) -

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.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

### Test Item Specifications

N/A

Assessment Limits :
Exponential functions represented in graphs or tables should be able to be written in the form a + k.

For exponential relationships, tables or graphs must contain at least one pair of consecutive values.

Calculator :

Neutral

Clarification :
Students will compare a linear function and an exponential function
given in real-world context by interpreting the functions’ graphs.

Students will compare a linear function and an exponential function
given in a real-world context through tables.

Students will compare a quadratic function and an exponential
function given in real-world context by interpreting the functions’
graphs.

Students will compare a quadratic function and an exponential
function given in a real-world context through tables

Stimulus Attributes :
Items should give a graph or a table.

Items should be given in a real-world context.

Items must use function notation

Response Attributes :
Items may require the student to apply the basic modeling cycle.

Items may require the student to choose an appropriate level of
accuracy.

Items may require the student to choose and interpret the scale in a
graph.

Items may require the student to choose and interpret units

### Sample Test Items (1)

 Test Item # Question Difficulty Type Sample Item 1 The function f(x) models the value of goods that are imported into the United States, where x is the number of years since 1990. The function g(x) models the value of goods that are exported from the United States. If f(x) and g(x) continue to model the importing and exporting of goods, then sometime in 2041, which is 51 years after 1990, f(x)=g(x).Determine which function is exponential. Use the table of values to justify your answer.Type your answer in the space provided. Be sure to include your function choice. N/A OR: Open Response

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#### Related Access Points

 Access Point Number Access Point Title MAFS.912.F-LE.1.AP.3a Compare graphs of linear, exponential, and quadratic growth graphed on the same coordinate plane.

#### Formative Assessments

 Name Description Compare Quadratic and Exponential Functions Students are asked to compare a quadratic and an exponential function in context. Compare Linear and Exponential Functions Students are asked to compare a linear function and an exponential function in context.

#### Lesson Plans

 Name Description Population and Food Supply In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (F-LE.2, F-LE.3, A-REI.11). Exponential growth versus linear growth I The purpose of this task it to have students discover how (and how quickly) an exponentially increasing quantity eventually surpasses a linearly increasing quantity. Students' intuitions will probably have them favoring Option A for much longer than is actually the case, especially if they are new to the phenomenon of exponential growth. Teachers might use this surprise as leverage to segue into a more involved task comparing linear and exponential growth. Exponential growth versus polynomial growth This problem solving task shows that an exponential function takes larger values than a cubic polynomial function provided the input is sufficiently large. This resource also includes standards alignment commentary and annotated solutions. Exponential growth versus linear growth II This task asks students to calculate exponential functions with a base larger than one.

#### Unit/Lesson Sequence

Name Description
Sample Algebra 1 Curriculum Plan Using CMAP

This sample Algebra 1 CMAP is a fully customizable resource and curriculum-planning tool that provides a framework for the Algebra 1 Course. The units and standards are customizable and the CMAP allows instructors to add lessons, worksheets, and other resources as needed. This CMAP also includes rows that automatically filter and display Math Formative Assessments System tasks, E-Learning Original Student Tutorials and Perspectives Videos that are aligned to the standards, available on CPALMS.

Learn more about the sample Algebra 1 CMAP, its features and customizability by watching the following video:

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All CMAP tutorials can be found within the iCPALMS Planner App or at the following URL: http://www.cpalms.org/support/tutorials_and_informational_videos.aspx

#### Virtual Manipulatives

 Name Description Data Flyer 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. Equation Grapher This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).

#### Student Resources

 Name Description Population and Food Supply: In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (F-LE.2, F-LE.3, A-REI.11). Exponential growth versus linear growth I: The purpose of this task it to have students discover how (and how quickly) an exponentially increasing quantity eventually surpasses a linearly increasing quantity. Students' intuitions will probably have them favoring Option A for much longer than is actually the case, especially if they are new to the phenomenon of exponential growth. Teachers might use this surprise as leverage to segue into a more involved task comparing linear and exponential growth. Exponential growth versus polynomial growth: This problem solving task shows that an exponential function takes larger values than a cubic polynomial function provided the input is sufficiently large. This resource also includes standards alignment commentary and annotated solutions. Exponential growth versus linear growth II: This task asks students to calculate exponential functions with a base larger than one.

#### Virtual Manipulatives

 Name Description Data Flyer: 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. Equation Grapher: This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).