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.

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

Construction Function

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CPALMS: 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.

Smart TV

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CPALMS: 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.

Drain the Pool

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

Trekking Functions

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

Profitable Functions

Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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CPALMS: In this tool, students input a function to create a graph where the constants, coefficients, and exponents can be adjusted by slider bars. This allows them to explore graphs of functions and how adjusting the numbers in the function affect the graph.

Function Flyer

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CPALMS: 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.

Linear Function Machine

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CPALMS: This resource 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.

Graphing Lines

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CPALMS: Students enter inputs into a function machine. By examining the outputs, they determine what function the machine is performing. This allows students to explore functions and what inputs are most useful for determining the function rule.

Number Cruncher

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

Linear Equations

Assessment Questions
Assessment Questions
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Equation Editor 1
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Videos of Expert Instruction
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Hook/Performance Tasks
Hook/Performance Tasks
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Illustrative Mathematics: This task could be used in an instructional sequence designed to develop knowledge related to students’ understanding of linear functions in contexts. Collaboration with peers is more likely to result in the exploration of a range of interpretations.

Baseball Cards

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Illustrative Mathematics: This is one of two assessment tasks illustrating the similarities and differences between the 8th grade standards in Functions and in Statistics and Probability. It involves constructing a linear function and interpreting its parameters in a context.

Delivering the Mail, Assessment Variation

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Illustrative Mathematics: While not a full-blown modeling problem, this task does address some aspects of the SMP 4. Discussion about how one chooses the independent and dependent variable based on the way one wants to view a situation would be appropriate.

High School Graduation

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Illustrative Mathematics: This real world situation can be modeled with a linear function. It's a good opportunity to discuss choosing independent and dependent variables and interpreting slopes, intercepts, and generic point on the graph in context.

Chicken and Steak, Variation 1

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Illustrative Mathematics: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.

Distance Across the Channel

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Illustrative Mathematics: Students are given two monthly plans to consider and are to explain what type of function models the situation, define variables that make sense in the context, and then write an equation with cost as a function of videos viewed. Also, decide which is better plan?

Video Streaming

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Illustrative Mathematics: The goal is to build understanding of linear relationships within meaningful and a somewhat familiar context. Scaffolding with regard to initial interpretations of the graph and transforming the equation into slope-intercept form may be necessary.

Chicken and Steak, Variation 2

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Illustrative Mathematics: In this task, students are to find the slope and intercepts of the graph of this function and explain what they mean in the context of the moving car.

Downhill

Problem Based Lessons
Problem Based Lessons
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