MAFS.8.F.2.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
General Information
Subject Area: Mathematics
Grade: 8
Domain-Subdomain: Functions
Cluster: Level 3: Strategic Thinking & Complex Reasoning
Cluster: Use functions to model relationships between quantities. (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

  • Assessment Limits :
    Function notation may not be used. Functions must be linear.
  • Calculator :

    Neutral

  • Context :

    Allowable

Sample Test Items (3)
  • Test Item #: Sample Item 1
  • Question:

    The cost, C, to rent a car for d days is shown in the table.

    Write an equation that represents this function?

  • Difficulty: N/A
  • Type: EE: Equation Editor

  • Test Item #: Sample Item 2
  • Question:

    A rental car company has a linear pricing plan. The total cost, C, to rent a car for 2, 4, 6, and 10 days, d, is shown.

    A. What is the daily rate for the pricing plan?

    B. Write an equation that represents the pricing plan.

  • Difficulty: N/A
  • Type: EE: Equation Editor

  • Test Item #: Sample Item 3
  • Question:

    This question has two parts.

    Suzie's Plumbing uses a linear model to determine the total cost, in dollars, of a service call.

    Part A. Using the table below, create an equation to represent the linear model that Suzie's Plumbing uses to determine the total cost, C, in terms of hours worked, h.

    Part B. Select the phrases and values to make accurate statements about the service fee and the hourly charge.

    The one-time fee is represented by the ___________ of the function and is ____.

    The hourly charge is represented by the _______ of the function and is _____ per hour.

  • Difficulty: N/A
  • Type: : Multiple Types

Related Courses

This benchmark is part of these courses.
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200410: Mathematics for College Success (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
1200700: Mathematics for College Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.8.F.2.AP.4a: Identify rise/run (m) as slope and identify the coordinates of the y-intercept.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

3D Modeling

Wind Farm Design Challenge:

This  lesson is a problem-based learning activity aligned to Florida's math and science standards. In this middle-school engineering design challenge, students are asked to create the most efficient wind turbine while balancing cost constraints. Students will apply their knowledge of surface area and graphing while testing 3D-printed wind farm blades. In the end, students are challenged to design and test their own wind farm blades, using Tinkercad to model a 3D-printable blade.

Type: 3D Modeling

Assessments

Sample 4 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 2 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 1 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Formative Assessments

Profitable Functions:

Students are asked to write a function to model a linear relationship given its graph.

Type: Formative Assessment

Trekking Functions:

Students are asked to construct a function to model a linear relationship between two quantities given a table of values.

Type: Formative Assessment

Smart TV:

Students are asked to determine the rate of change and initial value of a linear function given a table of values, and interpret the rate of change and initial value in terms of the situation it models.

Type: Formative Assessment

Construction Function:

Students are asked to construct a function to model a linear relationship between two quantities given two ordered pairs in context.

Type: Formative Assessment

Drain the Pool:

Students are asked to determine the rate of change and initial value of a linear function when given a graph, and to interpret the rate of change and initial value in terms of the situation it models.

Type: Formative Assessment

Interpreting Distance-Time Graphs:

This lesson unit is intended to help you assess how well students are able to interpret distance-time graphs and, in particular, to help you identify students who:

  • Interpret distance-time graphs as if they are pictures of situations rather than abstract representations of them.
  • Have difficulty relating speeds to slopes of these graphs.

Type: Formative Assessment

Lines and Linear Equations:

This lesson is intended to help you assess how well students are able to:

  • Interpret speed as the slope of a linear graph.
  • Translate between the equation of a line and its graphical representation.

Type: Formative Assessment

Lesson Plans

Rockets To Pluto:

Students will explore current space technology and explore the possibilities of traveling to Pluto. Students will participate in an Engineering Design Challenge in which they will construct and test their rockets to see how far they can go!

An Engineering Design Challenge is a combination of project-based learning, design thinking, and the engineering design process that develops the innovator's mindset through iteration. This lets students use their own imaginations to design projects according to science and engineering processes.

Type: Lesson Plan

Fast Food Frenzy:

In this activity, students will engage critically with nutritional information and macronutrient content of several fast food meals. This is an MEA that requires students to build on prior knowledge of nutrition and working with percentages.

Type: Lesson Plan

What's My Function?:

Students will determine function rules that have been written on cards taped to their backs. They will suggest input values and peers will provide output values to help them determine their function. They will then graph their functions for additional practice.

Type: Lesson Plan

Lines and Linear Equations:

This lesson unit is intended to help you assess how well students are able to interpret speed as the slope of a linear graph and translate between the equation of a line and its graphical representation.

Type: Lesson Plan

Interpreting Distance-Time Graphs:

This lesson takes a formative assessment approach to assessing whether students can interpret distance-time graphs. Whole-class discussion, group work, and individual activities help students interpret distance-time graphs related to real-world scenarios.

Type: Lesson Plan

Discovering Kepler's Law for the Periods of Planets:

Students listen to a video that describes Kepler's determination that planetary orbits are elliptical and then will use data for the solar distance and periods of several of the planets in the solar system, then investigate several hypotheses to determine which is supported by the data.

Type: Lesson Plan

Getting Graphic with Linear Functions:

Students will learn how to construct a linear function to model a linear relationship, determine the rates of change and initial value from a table and graph as well as be able to interpret what the rate of change means as it relates to a situation.

Type: Lesson Plan

In the Real World:

This resource provides a Lesson Plan for teaching students how to analyze word problems to look for clearly identified values and determine which of them is a constant value and which of them is subject to change (will increase or decrease per unit of time, weight, length, etc.). The students will also be taught how to determine the correct units for each value in the equation.

Type: Lesson Plan

Are We There Yet?:

Students will learn to write and interpret linear functions that represent real world situations, noting the importance of slope and y-intercept.

Type: Lesson Plan

Original Student Tutorials

Constructing Functions From Two Points:

Learn to construct a function to model a linear relationship between two quantities and determine the slope and y-intercept given two points that represent the function with this interactive tutorial.

Type: Original Student Tutorial

Scatterplots Part 5: Interpreting the Equation of the Trend Line :

Explore how to interpret the slope and y-intercept of a linear trend line when bivariate data is graphed on a scatterplot in this interactive tutorial.

This is part 5 in 6-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Scatterplots Part 4: Equation of the Trend Line:

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 in 6-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Constructing Linear Functions from Tables:

Learn to construct linear functions from tables that contain sets of data that relate to each other in special ways as you complete this interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Professional/Enthusiast

Slope and Deep Sea Sharks:

Shark researcher, Chip Cotton, discusses the use of regression lines, slope, and determining the strength of the models he uses in his research.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Tasks

High School Graduation:

This task does address some aspects of modeling as described in Florida Standard for Mathematical Practice 4. Also, students often think that time must always be the independent variable and so may need some help understanding that one chooses the independent and dependent variable based on the way one wants to view a situation.

Type: Problem-Solving Task

Baseball Cards:

This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.

Type: Problem-Solving Task

Modeling with a Linear Function:

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

Type: Problem-Solving Task

Downhill:

This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.

Type: Problem-Solving Task

Chicken and Steak, Variation 1:

In this problem-solving task students are challenged to apply their understanding of linear relationships to determine the amount of chicken and steak needed for a barbecue, which will include creating an equation, sketching a graph, and interpreting both. This resource also includes standards alignment commentary and annotated solutions.

Type: Problem-Solving Task

Video Streaming:

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Type: Problem-Solving Task

Chicken and Steak, Variation 2:

In this problem-solving task students are challenged to apply their understanding of linear relationships to determine the amount of chicken and steak needed for a barbecue, which will include creating an equation, sketching a graph, and interpreting both. This resource also includes standards alignment commentary and annotated solutions.

Type: Problem-Solving Task

Delivering the Mail:

This problem-solving task involves constructing a linear function and interpreting its parameters in a mail delivery context. It includes standards alignment commentary and annotated solutions.

Type: Problem-Solving Task

Distance Across the Channel:

This problem-solving task asks students to find a linear function that models something in the real world. After finding the equation of the linear relationship between the depth of the water and the distance across the channel, students have to verbalize the meaning of the slope and intercept of the line in the context of this situation. Commentary on standards alignment and illustrated solutions are also included.

Type: Problem-Solving Task

Drip, Drop, Drip, Drop:

Students design an experiment to model a leaky faucet and determine the amount of water wasted due to the leak. Using the data they gather in a table, students graph and write an equation for a line of best fit. Students then use their derived equation to make predictions about the amount of water that would be wasted from one leak over a long period of time or the amount wasted by several leaks during a specific time period.

Type: Problem-Solving Task

Professional Development

Mathematical Modeling: Insights into Algebra, Teaching for Learning:

This professional development resource provides a rich collection of information to help teachers engage students more effectively in mathematical modeling. It features videos of two complete lessons with commentary, background information on effective teaching, modeling, and lesson study, full lesson plans to teach both example lessons, examples of student work from the lessons, tips for effective teaching strategies, and list of helpful resources.

  • In Lesson 1 students use mathematical models (tables and equations) to represent the relationship between the number of revolutions made by a "driver" and a "follower" (two connected gears in a system), and they will explain the significance of the radii of the gears in regard to this relationship.
  • In Lesson 2 students mathematically model the growth of populations and use exponential functions to represent that growth.

Type: Professional Development

Student Center Activity

Edcite: Mathematics Grade 8:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

Teaching Idea

Learning About Rate of Change in Linear Functions Using Interactive Graphs:

This resource features two pairs of interactive graphs to help students explore rate of change and linear relationships. "Users can drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modifications in that rate affect the linear graph displaying accumulation (the total cost of calls). In this first part, Constant Cost per Minute, the cost per minute for phone use remains constant over time. In the second part, Changing Cost per Minute, the cost per minute for phone use changes after the first sixty minutes of calls." (from NCTM's Illuminations)

Type: Teaching Idea

Tutorials

Finding and Interpreting Slope from a Table:

In this video, you will practice finding the slope of a line from data in a table, and interpret what the slope means in the problem.

Type: Tutorial

Interpreting Linear Graphs: Cats, Cats and More Cats!:

In this video, you will use a linear graph to determine the y-intercept (starting point) and slope (rate of change), as well as interpret what these mean in the given scenario.

Type: Tutorial

Slope-Intercept Form from a Table:

In this video, you will practice writing the slope-intercept form for a line, given a table of x and y values.

Type: Tutorial

Slope-Intercept Equation from Two Solutions:

Given two points on a line, you will find the slope and the y-intercept. You will then write the equation of the line in slope-intercept form.

Type: Tutorial

Slope-Intercept Equation from Slope and Point:

Given the slope of a line and a point on the line, you will write the equation of the line in slope-intercept form.

Type: Tutorial

Determining a linear equation by checking solutions:

Students will learn how to determine an equation by checking solutions. Students will be given a table and 4 linear equations and they will have to determine which equation created the table.

Type: Tutorial

Using the Slope-Intercept Form of a Line:

In this video, you will practice writing the equations of lines in slope-intercept form from graphs. You will then practice graphing lines from equations in slope-intercept form.

Type: Tutorial

Dependent and Independent Variables Exercise: Express the Graph as an Equation:

Given a graph, we will be able to find the equation it represents.

Type: Tutorial

Unit/Lesson Sequences

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.

Type: Unit/Lesson Sequence

Proportional Reasoning:

In this resource, a special kind of functional relationship is explored: the proportional relationship. Teachers may find the resource useful for professional development, especially the videos. Students develop proportional reasoning skills by comparing quantities, looking at the relative ways numbers change, and thinking about proportional relationships in linear functions.
This resource has four objectives. Students learn to differentiate between relative and absolute meanings of "more" and determine which of these is a proportional relationship, compare ratios without using common denominator algorithms, differentiate between additive and multiplicative processes and their effects on scale and proportionality, and interpret graphs that represent proportional relationships or direct variation.

Type: Unit/Lesson Sequence

Direct and Inverse Variation:

"Lesson 1 of two lessons teaches students about direct variation by allowing them to explore a simulated oil spill using toilet paper tissues (to represent land) and drops of vegetable oil (to simulate a volume of oil). Lesson 2 teaches students about inverse variation by exploring the relationship between the heights of a fixed amount of water poured into cylindrical containers of different sizes as compared to the area of the containers' bases." from Insights into Algebra 1 - Annenberg Foundation.

Type: Unit/Lesson Sequence

Virtual Manipulatives

Linear Equations:

This resource provides guided practice for writing and graphing linear functions.

Type: Virtual Manipulative

Linear Function Machine:

In this activity, students plug values into the independent variable to see what the output is for that function. Then based on that information, they have to determine the coefficient (slope) and constant(y-intercept) for the linear function. This activity allows students to explore linear functions and what input values are useful in determining the linear 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

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.

Type: Virtual Manipulative

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.

Type: Virtual Manipulative

Number Cruncher:

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

Worksheet

Mass vs. Weight:

This laboratory activity worksheet engages students in an exploration of mass and weight. Students use a balance and spring scale to measure the masses and weights of a several of objects. Students will analyze the data and determine the the relationship between mass and weight using graphing skills. An answer key is attached to assist the use of this resource.

Type: Worksheet

STEM Lessons - Model Eliciting Activity

Fast Food Frenzy:

In this activity, students will engage critically with nutritional information and macronutrient content of several fast food meals. This is an MEA that requires students to build on prior knowledge of nutrition and working with percentages.

MFAS Formative Assessments

Construction Function:

Students are asked to construct a function to model a linear relationship between two quantities given two ordered pairs in context.

Drain the Pool:

Students are asked to determine the rate of change and initial value of a linear function when given a graph, and to interpret the rate of change and initial value in terms of the situation it models.

Profitable Functions:

Students are asked to write a function to model a linear relationship given its graph.

Smart TV:

Students are asked to determine the rate of change and initial value of a linear function given a table of values, and interpret the rate of change and initial value in terms of the situation it models.

Trekking Functions:

Students are asked to construct a function to model a linear relationship between two quantities given a table of values.

Original Student Tutorials Mathematics - Grades 6-8

Constructing Functions From Two Points:

Learn to construct a function to model a linear relationship between two quantities and determine the slope and y-intercept given two points that represent the function with this interactive tutorial.

Constructing Linear Functions from Tables:

Learn to construct linear functions from tables that contain sets of data that relate to each other in special ways as you complete this interactive tutorial.

Scatterplots Part 4: Equation of the Trend Line:

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 in 6-part series. Click below to open the other tutorials in the series.

Scatterplots Part 5: Interpreting the Equation of the Trend Line :

Explore how to interpret the slope and y-intercept of a linear trend line when bivariate data is graphed on a scatterplot in this interactive tutorial.

This is part 5 in 6-part series. Click below to open the other tutorials in the series.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorials

Constructing Functions From Two Points:

Learn to construct a function to model a linear relationship between two quantities and determine the slope and y-intercept given two points that represent the function with this interactive tutorial.

Type: Original Student Tutorial

Scatterplots Part 5: Interpreting the Equation of the Trend Line :

Explore how to interpret the slope and y-intercept of a linear trend line when bivariate data is graphed on a scatterplot in this interactive tutorial.

This is part 5 in 6-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Scatterplots Part 4: Equation of the Trend Line:

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 in 6-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Constructing Linear Functions from Tables:

Learn to construct linear functions from tables that contain sets of data that relate to each other in special ways as you complete this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Tasks

Modeling with a Linear Function:

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

Type: Problem-Solving Task

Downhill:

This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.

Type: Problem-Solving Task

Chicken and Steak, Variation 1:

In this problem-solving task students are challenged to apply their understanding of linear relationships to determine the amount of chicken and steak needed for a barbecue, which will include creating an equation, sketching a graph, and interpreting both. This resource also includes standards alignment commentary and annotated solutions.

Type: Problem-Solving Task

Video Streaming:

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Type: Problem-Solving Task

Chicken and Steak, Variation 2:

In this problem-solving task students are challenged to apply their understanding of linear relationships to determine the amount of chicken and steak needed for a barbecue, which will include creating an equation, sketching a graph, and interpreting both. This resource also includes standards alignment commentary and annotated solutions.

Type: Problem-Solving Task

Distance Across the Channel:

This problem-solving task asks students to find a linear function that models something in the real world. After finding the equation of the linear relationship between the depth of the water and the distance across the channel, students have to verbalize the meaning of the slope and intercept of the line in the context of this situation. Commentary on standards alignment and illustrated solutions are also included.

Type: Problem-Solving Task

Student Center Activity

Edcite: Mathematics Grade 8:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

Tutorials

Finding and Interpreting Slope from a Table:

In this video, you will practice finding the slope of a line from data in a table, and interpret what the slope means in the problem.

Type: Tutorial

Interpreting Linear Graphs: Cats, Cats and More Cats!:

In this video, you will use a linear graph to determine the y-intercept (starting point) and slope (rate of change), as well as interpret what these mean in the given scenario.

Type: Tutorial

Slope-Intercept Form from a Table:

In this video, you will practice writing the slope-intercept form for a line, given a table of x and y values.

Type: Tutorial

Slope-Intercept Equation from Two Solutions:

Given two points on a line, you will find the slope and the y-intercept. You will then write the equation of the line in slope-intercept form.

Type: Tutorial

Slope-Intercept Equation from Slope and Point:

Given the slope of a line and a point on the line, you will write the equation of the line in slope-intercept form.

Type: Tutorial

Determining a linear equation by checking solutions:

Students will learn how to determine an equation by checking solutions. Students will be given a table and 4 linear equations and they will have to determine which equation created the table.

Type: Tutorial

Using the Slope-Intercept Form of a Line:

In this video, you will practice writing the equations of lines in slope-intercept form from graphs. You will then practice graphing lines from equations in slope-intercept form.

Type: Tutorial

Dependent and Independent Variables Exercise: Express the Graph as an Equation:

Given a graph, we will be able to find the equation it represents.

Type: Tutorial

Virtual Manipulatives

Linear Function Machine:

In this activity, students plug values into the independent variable to see what the output is for that function. Then based on that information, they have to determine the coefficient (slope) and constant(y-intercept) for the linear function. This activity allows students to explore linear functions and what input values are useful in determining the linear 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

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.

Type: Virtual Manipulative

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.

Type: Virtual Manipulative

Number Cruncher:

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

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Tasks

High School Graduation:

This task does address some aspects of modeling as described in Florida Standard for Mathematical Practice 4. Also, students often think that time must always be the independent variable and so may need some help understanding that one chooses the independent and dependent variable based on the way one wants to view a situation.

Type: Problem-Solving Task

Baseball Cards:

This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.

Type: Problem-Solving Task

Modeling with a Linear Function:

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

Type: Problem-Solving Task

Downhill:

This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.

Type: Problem-Solving Task

Chicken and Steak, Variation 1:

In this problem-solving task students are challenged to apply their understanding of linear relationships to determine the amount of chicken and steak needed for a barbecue, which will include creating an equation, sketching a graph, and interpreting both. This resource also includes standards alignment commentary and annotated solutions.

Type: Problem-Solving Task

Video Streaming:

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Type: Problem-Solving Task

Chicken and Steak, Variation 2:

In this problem-solving task students are challenged to apply their understanding of linear relationships to determine the amount of chicken and steak needed for a barbecue, which will include creating an equation, sketching a graph, and interpreting both. This resource also includes standards alignment commentary and annotated solutions.

Type: Problem-Solving Task

Distance Across the Channel:

This problem-solving task asks students to find a linear function that models something in the real world. After finding the equation of the linear relationship between the depth of the water and the distance across the channel, students have to verbalize the meaning of the slope and intercept of the line in the context of this situation. Commentary on standards alignment and illustrated solutions are also included.

Type: Problem-Solving Task

Teaching Idea

Learning About Rate of Change in Linear Functions Using Interactive Graphs:

This resource features two pairs of interactive graphs to help students explore rate of change and linear relationships. "Users can drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modifications in that rate affect the linear graph displaying accumulation (the total cost of calls). In this first part, Constant Cost per Minute, the cost per minute for phone use remains constant over time. In the second part, Changing Cost per Minute, the cost per minute for phone use changes after the first sixty minutes of calls." (from NCTM's Illuminations)

Type: Teaching Idea

Virtual Manipulative

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.

Type: Virtual Manipulative