MA.912.F.1.8

Determine whether a linear, quadratic or exponential function best models a given real-world situation.

Clarifications

Clarification 1: Instruction includes recognizing that linear functions model situations in which a quantity changes by a constant amount per unit interval; that quadratic functions model situations in which a quantity increases to a maximum, then begins to decrease or a quantity decreases to a minimum, then begins to increase; and that exponential functions model situations in which a quantity grows or decays by a constant percent per unit interval. 

Clarification 2: Within this benchmark, the expectation is to identify the type of function from a written description or table.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Functions
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1200310: Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200320: Algebra 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200370: Algebra 1-A (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200380: Algebra 1-B (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912070: Access Mathematics for Liberal Arts (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
7912080: Access Algebra 1A (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
7912090: Access Algebra 1B (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1200315: Algebra 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200375: Algebra 1-A for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200385: Algebra 1-B for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912075: Access Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1210305: Mathematics for College Statistics (Specifically in versions: 2022 and beyond (current))
1207350: Mathematics for College Liberal Arts (Specifically in versions: 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.F.1.AP.8: Select whether a linear or quadratic function best models a given real-world situation.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

How Does Your Garden Grow?:

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.

Type: Formative Assessment

Prove Linear:

Students are asked to prove that a linear function grows by equal differences over equal intervals.

Type: Formative Assessment

Prove Exponential:

Students are asked to prove that an exponential function grows by equal factors over equal intervals.

Type: Formative Assessment

Linear or Exponential?:

Students are given four verbal descriptions of functions and asked to identify each as either linear or exponential and to justify their choices.

Type: Formative Assessment

Fit a Function:

Students are given a set of data and are asked to use technology to create a scatter plot and write a function that fits the data set.

Type: Formative Assessment

Lesson Plan

Appreciation for Car Depreciation:

Students will use information from the internet or a car dealership's advertisement to identify a car and determine the future value of the car using different depreciation rates over different intervals of time. Students will graph their data to show exponential decay and compare to a linear decrease on the same graph.

Type: Lesson Plan

Perspectives Video: Professional/Enthusiast

KROS Pacific Ocean Kayak Journey: Water Usage Rates:

A seafaring teacher filters all the good information you need to understand water purification rates for distance traveling.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Type: Perspectives Video: Professional/Enthusiast

MFAS Formative Assessments

Fit a Function:

Students are given a set of data and are asked to use technology to create a scatter plot and write a function that fits the data set.

How Does Your Garden Grow?:

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.

Linear or Exponential?:

Students are given four verbal descriptions of functions and asked to identify each as either linear or exponential and to justify their choices.

Prove Exponential:

Students are asked to prove that an exponential function grows by equal factors over equal intervals.

Prove Linear:

Students are asked to prove that a linear function grows by equal differences over equal intervals.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.