 Standard #: MAFS.912.F-IF.2.6

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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.

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

TEST ITEM SPECIFICATIONS

Item Type(s): This benchmark may be assessed using: MC item(s)
Also assesses: MAFS.912.S-ID.3.7

Assessment Limits :
Items requiring the student to calculate the rate of change will give a
specified interval that is both continuous and differentiable.

Items should not require the student to find an equation of a line.

Items assessing S-ID.3.7 should include data sets. Data sets must
contain at least six data pairs. The linear function given in the item
should be the regression equation.

For items assessing S-ID.3.7, the rate of change and the y-intercept
should have a value with at least a hundredths place value.

Items assessing F-IF.2.6 should not be linear.

Calculator :

Neutral

Clarification :
Students will calculate the average rate of change of a continuous
function that is represented algebraically, in a table of values, on a
graph, or as a set of data.

Students will interpret the average rate of change of a continuous
function that is represented algebraically, in a table of values, on a
graph, or as a set of data with a real-world context.

Students will interpret the y-intercept of a linear model that
represents a set of data with a real-world context.

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

Items should be set in a real-world context.

Items must use function notation.

Items may require the student to choose and interpret variables.

Response Attributes :
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 graph shows the number of acres, in millions, of farmland in the United States from 1975 to 2008. Which statement describes the average rate of change of the graph? N/A MC: Multiple Choice

Related Courses

 Course Number1111 Course Title222 1200310: Algebra 1 (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1200320: Algebra 1 Honors (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1200330: Algebra 2 (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1200340: Algebra 2 Honors (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1200370: Algebra 1-A (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1200380: Algebra 1-B (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1200400: Intensive Mathematics (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1206330: Analytic Geometry (Specifically in versions: 2014 - 2015 (course terminated)) 1200500: Advanced Algebra with Financial Applications (Specifically in versions: 2014 - 2015 (course terminated)) 1200410: Mathematics for College Success (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1200700: Mathematics for College Readiness (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 7912070: Access Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current)) 7912080: Access Algebra 1A (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current)) 7912090: Access Algebra 1B (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current)) 1200315: Algebra 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1200335: Algebra 2 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2019 (course terminated)) 1200375: Algebra 1-A for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1200385: Algebra 1-B for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1207300: Liberal Arts Mathematics 1 (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 7912075: Access Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))

Access Point

 Access Point Number Access Point Title MAFS.912.F-IF.2.AP.6b Describe the rate of change of a function using numbers. MAFS.912.F-IF.2.AP.6c Pair the rate of change with its graph.

Lesson Plan

 Name Description Acceleration In this lesson students will learn to: Identify changes in motion that produce acceleration. Describe examples of objects moving with constant acceleration. Calculate the acceleration of an object, analytically, and graphically. Interpret velocity-time graph, and explain the meaning of the slope. Classify acceleration as positive, negative, and zero. Describe instantaneous acceleration. 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. Compacting Cardboard Students with 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. 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. 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. 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.

Formative Assessment

 Name Description 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 Tutorial

 Name Description Changing Rates Learn how to calculate and interpret an average rate of change over a specific interval on a graph.

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). 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. Graphing Lines Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.

Perspectives Video: Expert

 Name Description Improving Hurricane Scales Meteorologist, Michael Kozar, discusses the limitations to existing hurricane scales and how he is helping to develop an improved scale.

Unit/Lesson Sequence

Name Description
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.
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

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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

Assessment

 Name Description Sample 1 - High School Algebra 2 State Interim Assessment This is a State Interim Assessment for 9th-12th grades. Sample 2 - High School Algebra 1 State Interim Assessment This is a State Interim Assessment for 9th-12th grades. Sample 2 - High School Algebra 2 State Interim Assessment This is a State Interim Assessment for 9th-12th grades. Sample 3 - High School Algebra 2 State Interim Assessment This is a State Interim Assessment for 9th-12th grades. Sample 4 - High School Algebra 1 State Interim Assessment This is a State Interim Assessment for 9th-12th grades.

Video/Audio/Animation

 Name Description Slope "Slope" is a fundamental concept in mathematics. Slope is often defined as " the rise over the run"....but why?

 Name Description The High School Gym This task asks students to consider functions in regard to temperatures in a high school gym.

Lesson Study Resource Kit

 Name Description The Motion of Objects This 9-12 Lesson study resource kit is designed to engage teachers of physical science and physics in the planning and design of an instructional unit and research lesson pertaining to the motion of objects. Included in this resource kit are unit plans, concept progressions, formative and summative assessments, complex informational texts, and etc. that align to relevant NGSSS science, and the new Florida standards for mathematics and English language arts.

Student Resources

 Name Description Changing Rates Learn how to calculate and interpret an average rate of change over a specific interval on a graph. 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). 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. Graphing Lines Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed. Slope "Slope" is a fundamental concept in mathematics. Slope is often defined as " the rise over the run"....but why? The High School Gym This task asks students to consider functions in regard to temperatures in a high school gym.

Parent Resources

 Name Description Graphing Lines Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed. The High School Gym This task asks students to consider functions in regard to temperatures in a high school gym.

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