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Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. ★
Standard #: MAFS.912.F-IF.2.6Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Functions: Interpreting Functions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Interpret functions that arise in applications in terms of the context. (Algebra 1 - Major Cluster) (Algebra 2 - Major 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
Related Courses
Related Resources
Formative Assessments
  • Pizza Palace # Students are given a table of functional values in context and are asked to find the average rate of change over a specific interval.
  • Air Cannon # Students are given a graph of an exponential function and are asked to calculate and compare the average rate of change over two different intervals of time.
  • Estimating the Average Rate of Change # Students are asked to estimate the average rate of change of a nonlinear function over two different intervals given its graph.
  • Identifying Rate of Change # Students are asked to calculate and interpret the rate of change of a linear function given its graph.
Lesson Plans
  • Slide, Slide Away # In this Engineering Design Challenge, student teams will design, calculate, build and then test a tower structure that can successfully hold a slide made from a pool tube. The slide will be placed at three different heights to determine which height is safe yet still fun. Students will be given supply restraints and guidelines as they work in teams to solve the problem.  
  • Compacting Cardboard # Students investigate the amount of space that could be saved by flattening cardboard boxes. The analysis includes linear graphs and regression analysis along with discussions of slope and a direct variation phenomenon.
  • Functions and Everyday Situations # This lesson unit is intended to help you assess how well students are able to articulate verbally the relationships between variables arising in everyday contexts, translate between everyday situations and sketch graphs of relationships between variables, interpret algebraic functions in terms of the contexts in which they arise and reflect on the domains of everyday functions and in particular whether they should be discrete or continuous.
  • Cup-Activity: writing equations from data # This is a great lab activity that allows students to develop a true understanding of slope as a rate of change. Students are active and involved and must use higher order thinking skills in order to answer questions. Students work through an activity, measuring heights of cups that are stacked. Students them determine a "rate of change - slope". Students are then asked to put this into slope-intercept form. The important part here is in their determining the y-intercept of the equation. Students then take this further and finally attempt to create a linear inequality to determine how many cups, stacked vertically, will fit under a table.
  • BIOSCOPES Summer Institute 2013 - Motion # This lesson is the first in a sequence of grade 9-12 physical science lessons that are organized around the big ideas that frame motion, forces, and energy. It directly precedes resource # 52648 "BIOSCOPES Summer Institute 2013 - Forces." This lesson is designed along the lines of an iterative 5-E learning cycle and employs a predict, observe, and explain (POE) activity at the beginning of the "Engage" phase in order to elicit student prior knowledge. The POE is followed by a sequence of inquiry-based activities and class discussions that are geared toward leading the students systematically through the exploration of 1-dimensional motion concepts. Included in this resource is a summative assessment as well as a teacher guide for each activity.

  • Acceleration # In this lesson students will learn to:
    1. Identify changes in motion that produce acceleration.
    2. Describe examples of objects moving with constant acceleration.
    3. Calculate the acceleration of an object, analytically, and graphically.
    4. Interpret velocity-time graph, and explain the meaning of the slope.
    5. Classify acceleration as positive, negative, and zero.
    6. Describe instantaneous acceleration.
Original Student Tutorial
  • Changing Rates # Learn how to calculate and interpret an average rate of change over a specific interval on a graph in this interactive tutorial.
Perspectives Video: Expert
Problem-Solving Task
  • The High School Gym # This task asks students to consider functions in regard to temperatures in a high school gym.
Unit/Lesson Sequences
  • 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
  • Linear Functions and Slope # This session on linear function and slope contains five parts, multiple problems and videos, and interactive activities geared to help students recognize and understand linear relationships, explore slope and dependent and independent variables in graphs of linear relationships, and develop an understanding of rates and how they are related to slopes and equations. Throughout the session, students use spreadsheets to complete the work, and are encouraged to think about the ways technology can aid in teaching and understanding. The solutions for all problems are given, and many allow students to have a hint or tip as they solve. There is even a homework assignment with four problems for students after they have finished all five parts of the session.
Virtual Manipulatives
  • Graphing Lines # Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the slope and various types of line equations can be explored.
  • Function Flyer # In this online tool, students input a function to create a graph where the constants, coefficients, and exponents can be adjusted by slider bars. This tool allows students to explore graphs of functions and how adjusting the numbers in the function affect the graph. Using tabs at the top of the page you can also access 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).
MFAS Formative Assessments
  • Air Cannon # Students are given a graph of an exponential function and are asked to calculate and compare the average rate of change over two different intervals of time.
  • Estimating the Average Rate of Change # Students are asked to estimate the average rate of change of a nonlinear function over two different intervals given its graph.
  • Identifying Rate of Change # Students are asked to calculate and interpret the rate of change of a linear function given its graph.
  • Pizza Palace # Students are given a table of functional values in context and are asked to find the average rate of change over a specific interval.
Original Student Tutorials Mathematics - Grades 9-12
  • Changing Rates # Learn how to calculate and interpret an average rate of change over a specific interval on a graph in this interactive tutorial.
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