Which Function?

This activity has students apply their knowledge to distinguish between numerical data that can be modeled in linear or exponential forms. Students will create mathematical models (graph, equation) that represent the data and compare these models in terms of the information they show and their limitations. Students will use the models to compute additional information to predict future outcomes and make conjectures based on these predictions.

Resource ID#: 46875 Type: Lesson Plan

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Resource Information
Aligned Standards

7

General Information

Subject(s): Mathematics

Grade Level(s): 9, 10, 11, 12

Intended Audience: Educators

Suggested Technology: Graphing Calculators, Internet Connection, Interactive Whiteboard, LCD Projector

Instructional Time: 2 Hour(s)

Keywords: linear functions, exponential functions, graphs, equations, table of values, numerical data, predication, surprise, money

Instructional Component Type(s): Lesson Plan, Worksheet, Project, Text Resource, Teaching Idea, Data Set, Student Center Activity, Learning Goal

Instructional Design Framework(s): Predict-Explain-Observe-Explain

Resource Collection: CPALMS Lesson Plan Development Initiative

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Aligned Standards

This vetted resource aligns to concepts or skills in these benchmarks.

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Benchmark(s) of focus

The benchmark(s) of focus is the primary focus for student learning and instruction to be taught or reinforced and provides an intentional opportunity for students to work with that concept or skill.

MA.912.AR.2.5 Solve and graph mathematical and real-world problems that are modeled with linear functions. Interpret key fea...

Clarifications:

Clarification 1: Key features are limited to domain, range, intercepts and rate of change.

Clarification 2: Instruction includes the use of standard form, slope-intercept form and point-slope form.

Clarification 3: Instruction includes representing the domain, range and constraints with inequality notation, interval notation or set-builder notation.

Clarification 4: Within the Algebra 1 course, notations for domain, range and constraints are limited to inequality and set-builder.

Clarification 5: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.

28

Resources

MA.912.AR.5.7 Solve and graph mathematical and real-world problems that are modeled with exponential functions. Interpret ke...

Clarifications:

Clarification 1: Key features are limited to domain; range; intercepts; intervals where the function is increasing, decreasing, positive or negative; constant percent rate of change; end behavior and asymptotes.

Clarification 2: Instruction includes representing the domain, range and constraints with inequality notation, interval notation or set-builder notation.

Clarification 3: Instruction includes understanding that when the logarithm of the dependent variable is taken and graphed, the exponential function will be transformed into a linear function.

Clarification 4: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.

18

Resources

MA.912.F.1.3 Calculate and interpret the average rate of change of a real-world situation represented graphically, algebrai...

Clarifications:

Clarification 1: Instruction includes making the connection to determining the slope of a particular line segment.

11

Resources

Supporting Benchmark(s)

Supporting benchmarks either make a connection or may help students achieve the focus benchmark(s) and increase students’ opportunities to make connections within the subject or to other subjects. The information included in this section is not a comprehensive list, and educators are encouraged to find other supporting benchmarks.

MA.912.AR.2.2 Write a linear two-variable equation to represent the relationship between two quantities from a graph, a writ...

Clarifications:

Clarification 1: Instruction includes the use of standard form, slope-intercept form and point-slope form, and the conversion between these forms.

35

Resources

MA.912.AR.2.4 Given a table, equation or written description of a linear function, graph that function, and determine and in...

Clarifications:

Clarification 1: Key features are limited to domain, range, intercepts and rate of change.

Clarification 2: Instruction includes the use of standard form, slope-intercept form and point-slope form.

Clarification 3: Instruction includes cases where one variable has a coefficient of zero.

Clarification 4: Instruction includes representing the domain and range with inequality notation, interval notation or set-builder notation.

Clarification 5: Within the Algebra 1 course, notations for domain and range are limited to inequality and set-builder notations.

12

Resources

MA.912.AR.5.4 Write an exponential function to represent a relationship between two quantities from a graph, a written descr...

Clarifications:

Clarification 1: Within the Algebra 1 course, exponential functions are limited to the forms

begin mathsize 12px style f open parentheses x close parentheses equals a b to the power of x end style

, where b is a whole number greater than 1 or a unit fraction, or

begin mathsize 12px style f open parentheses x close parentheses equals a open parentheses 1 plus-or-minus r close parentheses to the power of x end style

, where

begin mathsize 12px style 0 less than r less than 1 end style

Clarification 2: Within the Algebra 1 course, tables are limited to having successive nonnegative integer inputs so that the function may be determined by finding ratios between successive outputs.

18

Resources

MA.912.AR.5.6 Given a table, equation or written description of an exponential function, graph that function and determine i...

Clarifications:

Clarification 1: Key features are limited to domain; range; intercepts; intervals where the function is increasing, decreasing, positive or negative; constant percent rate of change; end behavior and asymptotes.

Clarification 2: Instruction includes representing the domain and range with inequality notation, interval notation or set-builder notation.

Clarification 3: Within the Algebra 1 course, notations for domain and range are limited to inequality and set-builder.

Clarification 4: Within the Algebra 1 course, exponential functions are limited to the forms $begin mathsize 12px style f open parentheses x close parentheses equals a b to the power of x end style$ , where b is a whole number greater than 1 or a unit fraction or $begin mathsize 12px style f open parentheses x close parentheses equals a open parentheses 1 plus-or-minus r close parentheses to the power of x end style$ , where $begin mathsize 12px style 0 less than r less than 1 end style$ .

13

Resources

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