Exponential Functions

13 Components
Initial Task
Multiplying Cells
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Selecting a formative assessment lesson for Algebra II Unit 2 Comparing Investments Having Kittens
Re-engagement
Re-engagement for Unit 2
End of Unit Assessments
End of Unit Assessment for Unit 2 End of Unit Assessment Teacher Resources ALG II Unit 2 Find aligned Regents questions with Quiz Banker
A2 U2: Exponential Functions
Unit Outline
Initial Task
Multiplying Cells
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Selecting a formative assessment lesson for Algebra II Unit 2 Comparing Investments Having Kittens
Re-engagement
Re-engagement for Unit 2
End of Unit Assessments
End of Unit Assessment for Unit 2 End of Unit Assessment Teacher Resources ALG II Unit 2 Find aligned Regents questions with Quiz Banker
None
A2 U2:

Exponential Functions

How do we measure change?
6 weeks
See Standards
Common Core: Major Standards:
N-RN.A.1

Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.  For example, we define 5⅓ to be the cube roots of 5 because we want (5 ⅓ )3 = 5(⅓)3 to hold, so (5 ⅓ )3 must equal 5.

N-RN.A.2

 Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

A-SSE.B.3c

Write expressions in equivalent forms to solve problems. Use the properties of exponents to transform expressions for exponential functions. For example the expression (1.15)t can be rewritten as (1.15 1/12)12t ≈ (1.012)12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

F-BF.A.2

Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences recursively and with an explicit formula, use them to model situations, and translate between both forms.*

Common Core: Supporting Standards:
F-IF.C.7e

Analyze functions using different representations. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F-IF.C.8b

Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)ᵗ, y = (0.97)ᵗ, y = (1.01)12ᵗ, y = (1.2)ᵗ/10, and classify them as representing exponential growth or decay.

F-LE.A.2

Linear, Quadratic, & Exponential Models: Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

F-LE.A.4

Construct and compare linear, quadratic, and exponential models and solve problems. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Common Core: Additional Standards:
F-IF.A.3

Understand the concept of a function and use function notation. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1,  f(n+1) = f(n) + f(n–1) for n ≥ 1.

F-BF.B.4a

Build new functions from existing functions. Find inverse functions: Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x3 or f(x) = (x+1)/(x-1) for x ≠ 1.

F-LE.B.5

Interpret expressions for functions in terms of the situation they model. Interpret the parameters in a linear or exponential function in terms of a context.

Common Core: Plus Standards:
F-BF.B.4b(+)

Build new functions from existing functions.  Find inverse functions: Verify by composition that one function is the inverse of another.

F-BF.B.4c(+)

Build new functions from existing functions. Find inverse functions: Read values of an inverse function from a graph or a table, given that the function has an inverse.

F-BF.B.5(+)

Build new functions from existing functions.  Understand the inverse relationship between exponents and logarithms and use it to solve problems involving logarithms and exponents.

The purpose of this unit is to extend students’ understanding of exponential numbers, properties, and functions, and their applications in the real world.  In this unit, we draw upon standards from five clusters: the real number system; seeing structure in expressions; building functions; interpreting functions; and modeling with linear, quadratic, and exponential functions. Students closely examine the relationship between exponential and logarithmic functions.

Essential Questions:

  • How do we measure change?
  • How are different representations of numbers related?
  • How are different representations of functions related?
  • How do we define relationships between functions?
Printable Unit Plan

Unit Outline

13 Components

Every unit begins with an Initial Task and ends with a Balanced Assessment, both focusing on core mathematics of the unit. The core mathematics is developed through a series of resources around Big Ideas; as you move through the unit, keep students focused on how these ideas are connected and how they address mathematical problem solving. Before attempting the Balanced Assessment, students have an opportunity to synthesize their knowledge through a multi-day Formative Assessment Lesson and teacher-designed re-engagement lessons.

Initial Task See 1 itemHide 1 item

Big Ideas See 5 itemsHide 5 items

Formative Assessment Lesson See 3 itemsHide 3 items

Re-engagement See 1 itemHide 1 item

End of Unit Assessments See 3 itemsHide 3 items