F-LE.1.1.a

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

a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

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Formative Assessments
Formative Assessments
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Students are asked to prove that an exponential function grows by equal factors over equal intervals.
Prove Exponential
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http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/69183
Prove Linear
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Students are given four verbal descriptions of functions and asked to identify each as either linear or exponential and to justify their choices.
Linear or Exponential?
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
Videos of Expert Instruction
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Shark researcher, Chip Cotton, discusses the use of regression lines, slope, and determining the strength of the models he uses in his research.
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Double Sunglasses
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Will Ryan describes how linear regression models contribute towards his research on sea anemones.
Linear Regression for Analysis of Sea Anemone Data
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Fry’s Bank
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Hook/Performance Tasks
Hook/Performance Tasks
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An important property of linear functions is that they grow by equal differences over equal intervals. In F.LE Equal Differences over Equal Intervals 1, students prove this for equal intervals of length one unit, and note that in this case the equal differences have the same value as the slope.
Equal Differences over Equal Intervals 1
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There are three challenges for this problem depending on the whether this is approached as a simple percent increase problem or a compound interest problem
How Did Motel 6 Go From $6 To $66?
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This task assumes that students are familiar with the ?x and ?y notations. Students most likely developed this familiarity in their work with slope.
Equal Differences over Equal Intervals 2
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This problem assumes that students are familiar with the notation x0 and Δx. However, the language ``successive quotient`` may be new.
Equal Factors over Equal Intervals