Access Point #: MAFS.912.A-SSE.2.AP.3e

Use properties of exponents (such as power of a power, product of powers, power of a product, and rational exponents, etc.) to write an equivalent form of an exponential function to reveal and explain specific information about its approximate rate of growth or decay.
Clarifications:

Essential Understandings

Concrete:

  • Add and subtract integers (e.g., use manipulatives, a number line or calculator to add 2 + -5).
  • Use manipulatives to demonstrate what an exponent represents begin mathsize 12px style open parentheses e. g. comma space 8 cubed space equals space 8 cross times 8 cross times 8 close parentheses end style.
  • Produce the correct amount of base numbers to be multiplied given a graphic organizer or template.
  • Use manipulatives to simplify expressions using properties of exponents. (such as power of a power, product of powers, power of a product, and rational exponents, etc.).
  • Use manipulatives to demonstrate exponential decay or growth. (i.e., Given a cup of M&M’s, pour them on a plate and remove the M&M’s with the M side up. Collect the remaining M&M’s and put in cup and repeat until there is only 1 M&M left. Record data and graph at each step.)
  • Given a table, identify whether a function is growing exponentially.

    Example table
  • Given an equation, identify whether it is an exponential function.

    Example equation and graph of an exponential function.
  • Identify whether an exponential function is a growth function or a decay function based on its graph.

    Example graphs of a growth function and a decay function.
Representation:
  • Understand the following concepts, symbols, and vocabulary: base number, exponent, integer.
  • Select the correct expanded form of what an exponent represents
    begin mathsize 12px style open parentheses e. g. comma space 8 cubed space equals space 8 cross times 8 cross times 8 close parentheses end style.
  • Identify the number of times the base number will be multiplied based on the exponent.
  • Understand that a negative exponent will result in a fraction with a numerator of 1 begin mathsize 12px style left parenthesis e. g. comma space 5 to the power of negative 2 end exponent space equals space 1 divided by 25 right parenthesis end style.
  • Understand that b determines whether the graph will be increasing (growth) or decreasing (decay).

    Example equation and growth and decay graphs.
  • Understand that b can be written as (1+r) or (1-r) where r is the rate of change.

    Understand that b can be written as (1+r) or (1-r) where r is the rate of change.
  • Teacher Tool: Click Here
General Information
Number: MAFS.912.A-SSE.2.AP.3e
Category: Access Points
Date Adopted or Revised: 07/14
Cluster: Write expressions in equivalent forms to solve problems. (Algebra 1 - Supporting Cluster) (Algebra 2 - Major Cluster)

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Related Standards

This access point is an alternate version of the following benchmark(s).

Related Courses

This access point is part of these courses.
1200310: Algebra 1
1200320: Algebra 1 Honors
1200330: Algebra 2
1200340: Algebra 2 Honors
1200380: Algebra 1-B
1200400: Foundational Skills in Mathematics 9-12
1207310: Liberal Arts Mathematics
1200410: Mathematics for College Success
1200700: Mathematics for College Algebra
7912060: Access Informal Geometry
7912070: Access Liberal Arts Mathematics
7912080: Access Algebra 1A
7912090: Access Algebra 1B
1200315: Algebra 1 for Credit Recovery
1200335: Algebra 2 for Credit Recovery
1200385: Algebra 1-B for Credit Recovery
7912065: Access Geometry
7912075: Access Algebra 1
7912095: Access Algebra 2
1200387: Mathematics for Data and Financial Literacy

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