F.1.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

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Formative Assessments
Formative Assessments
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CPALMS: Students are asked to recognize and compare the initial values of two functions represented in different ways.

Competing Functions

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CPALMS: Students are asked to compare a specific value of two functions given in different forms (a graph and a verbal description) within a real-world context.

This House Is Mine

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CPALMS: Students are asked to compare the rates of change of two functions presented in different forms (an expression and a table) within a real-world context.

Innovative Functions

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CPALMS: Students are asked to compare the rate of change of two functions presented in different forms (table and graph) within a real-world context.

Speed Reading

Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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This applet allows the user to input a series of (x,y) ordered pairs and plot them either as a connected function or unconnected data points. Parameters such as minimum and maximum x value, minimum and maximum y value, and x- and y-scale can be set by the user or determined by the applet.
Simple Plot by Shodor Interactivate
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Assessment Questions
Assessment Questions
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Equation Editor
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Video of Expert Instruction
Video of Expert Instruction
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This video (approx. 5:00 min) explains how to compare two functions by analyzing an equation (algebraic) and a graph (visual) and reasons why they each represent a one-to-one function. Misunderstandings about the y-intercept and the coefficient as the rate of change are discussed.

“Comparing Two Functions” by LearnZillion

 

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In this video (approx. 2:35 min), Sal is given a table of values of a linear function and four linear graphs. He explains how to determine which graph has the same rate of change as the function represented in the table.

“Comparing Linear Functions: Table vs. Graph” by Khan Academy

Hook/Performance Tasks
Hook/Performance Tasks
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Illustrative Mathematics: This task is a simple modeling exercise, taking verbal and numerical descriptions of battery life as a function of time and writing down linear models for these quantities. To draw conclusions about quantities, students have to find a common way of describing them.

Battery Charging

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