F-LE.1.1.c

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

c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

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Formative Assessments
Formative Assessments
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Students are given two functions, one represented verbally and the other by a table, and are asked to compare the rate of change in each in the context of the problem.
Exponential Growth
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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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Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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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
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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
Assessment Questions
Assessment Questions
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Hook/Performance Tasks
Hook/Performance Tasks
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The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real world problem with ties to developing financial literacy skills. In particular, students are introduced to the idea of inflation of prices of a single commodity, and are given a very brief introduction to the notion of the Consumer Price Index for measuring inflation of a body of goods.
Rising Gas Prices – Compounding and Inflation
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This context makes for an interesting application of calculating interest.
How Much Did Peterson Lose By Not Cashing His Check?
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In this example, students are asked to write a function describing the population growth of algae. It is implied that this is exponential growth.
Algae Blooms
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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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Students are asked to select the best model for a given context and use the model to make predictions.
Basketball Bounces, Assessment Variation 1