F-LE.1.1.b

Distinguish between situations that can be modeled with linear functions and with exponential functions.

b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

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Formative Assessments
Formative Assessments
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Students are given a linear and an exponential function, one represented verbally and the other by a table. Then students are asked to compare the rate of change in each in the context of the problem.
How Does Your Garden Grow?
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Students are asked to prove that a linear function grows by equal differences over equal intervals.
Prove Linear
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Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. 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.
Data Flyer
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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.
Function Flyer
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This virtual manipulative allows the user to explore scenarios of a loan repayment by manipulating the amount of the loan, interest rate, payment amount, frequency of payments, and length of the loan in years.
Loan Calculator
Assessment Questions
Assessment Questions
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Videos of Expert Instruction
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Hook/Performance Tasks
Hook/Performance Tasks
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This task requires students to use the fact that on the graph of the linear function h(x) = ax + b, the y-coordinate increases by a when x increases by one. Specific values for a and b were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.
Linear Functions
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This awesomely gross lesson provides students with a real world context for building linear functions.
How Much Does A 100×100 In-N-Out Cheeseburger Cost?
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This task gives a variation of real-life contexts which could be modeled by a linear or exponential function. The key distinguishing feature between the two is whether the change by equal factors over equal intervals (exponential functions), or by a constant increase per unit interval (linear functions). The task could either be used as an assessment problem on this distinction, or used as an introduction to the differences between these very important classes of functions.
Linear or exponential?
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The purpose of the first question is to give students a question that they can sink their teeth into. There are many ways for them to determine that together the pair ate 36 hot dogs in the first four rounds (1 + 2 + … + 8).
How Many Hot Dogs Did They Eat?!
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This problem-solving task asks students to examine if linear modeling would be appropriate to describe and predict population growth from select years.
In the Billions and Linear Modeling