Standard #: MAFS.912.F-IF.3.9 (Archived Standard)


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Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.



General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Functions: Interpreting Functions
Cluster: Analyze functions using different representations. (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 Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    Assessed with:

    MAFS.912.F-IF.2.4



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1200385: Algebra 1-B for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
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Related Resources

Formative Assessments

Name Description
Comparing Quadratics

Students are asked to compare two quadratic functions, one given by a table and the other by a function.

Comparing Linear and Exponential Functions

Students are given a linear function represented by an equation and an exponential function represented by a graph in a real-world context and are asked to compare the rates of change of the two functions.

Comparing Linear Functions

Students are given two linear functions, one represented by a graph and the other by an equation, and asked to compare their intercepts in the context of a problem.

Lesson Plans

Name Description
Stop That Arguing

Students will explore representing the movement of objects and the relationship between the various forms of representation: verbal descriptions, value tables, graphs, and equations. These representations include speed, starting position, and direction. This exploration includes brief direct instruction, guided practice in the form of a game, and independent practice in the form of a word problem. Students will demonstrate understanding of this concept through a written commitment of their answer to the word problem supported with evidence from value tables, graphs, and equations.

Linear Functions Representations

Students will compare properties of linear functions when presented in different representations. Students work as pairs within groups to analyze and confirm which representations are best suited for different needs. This lesson focuses on linear functions.

Representing Polynomials This lesson unit is intended to help you assess how well students are able to translate between graphs and algebraic representations of polynomials. In particular, this unit aims to help you identify and assist students who have difficulties in recognizing the connection between the zeros of polynomials when suitable factorizations are available, and graphs of the functions defined by polynomials as well as recognizing the connection between transformations of the graphs and transformations of the functions obtained by replacing f(x) by f(x + k), f(x) + k, -f(x), f(-x).
Forming Quadratics This lesson unit is intended to help you assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation. In particular, the lesson will help you identify and help students who have the following difficulties in understanding how the factored form of the function can identify a graph's roots, how the completed square form of the function can identify a graph's maximum or minimum point, and how the standard form of the function can identify a graph's intercept.

Perspectives Video: Expert

Name Description
Birdsong Series: Mathematically Modeling Birdsong

Richard Bertram discusses his mathematical modeling contribution to the Birdsong project that helps the progress of neuron and ion channel research.

Download the CPALMS Perspectives video student note taking guide.

Problem-Solving Tasks

Name Description
Throwing Baseballs

This task could be used for assessment or for practice. It allows students to compare characteristics of two quadratic functions that are each represented differently, one as the graph of a quadratic function and one written out algebraically. Specifically, students are asked to determine which function has the greatest maximum and the greatest non-negative root.

Kimi and Jordan

In the middle grades, students have lots of experience analyzing and comparing linear functions using graphs, table, symbolic expressions, and verbal descriptions. In this task, students may choose a representation that suits them and then reason from within that representation.

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:

Using this CMAP

To view an introduction on the CMAP tool, please .

To view the CMAP, click on the "Open Resource Page" button above; be sure you are logged in to your iCPALMS account.

To use this CMAP, click on the "Clone" button once the CMAP opens in the "Open Resource Page." Once the CMAP is cloned, you will be able to see it as a class inside your iCPALMS My Planner (CMAPs) app.

To access your My Planner App and the cloned CMAP, click on the iCPALMS tab in the top menu.

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 Manipulative

Name Description
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

Problem-Solving Tasks

Name Description
Throwing Baseballs:

This task could be used for assessment or for practice. It allows students to compare characteristics of two quadratic functions that are each represented differently, one as the graph of a quadratic function and one written out algebraically. Specifically, students are asked to determine which function has the greatest maximum and the greatest non-negative root.

Kimi and Jordan:

In the middle grades, students have lots of experience analyzing and comparing linear functions using graphs, table, symbolic expressions, and verbal descriptions. In this task, students may choose a representation that suits them and then reason from within that representation.

Virtual Manipulative

Name Description
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).



Parent Resources

Problem-Solving Tasks

Name Description
Throwing Baseballs:

This task could be used for assessment or for practice. It allows students to compare characteristics of two quadratic functions that are each represented differently, one as the graph of a quadratic function and one written out algebraically. Specifically, students are asked to determine which function has the greatest maximum and the greatest non-negative root.

Kimi and Jordan:

In the middle grades, students have lots of experience analyzing and comparing linear functions using graphs, table, symbolic expressions, and verbal descriptions. In this task, students may choose a representation that suits them and then reason from within that representation.



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