Standard

Essential
Question

Bloom’s
Taxonomy Activities

Vocabulary

Pacing

F.LE.1 Distinguish
between situations that can be modeled
with linear functions and with exponential functions.

What is
the difference between the progression of points on a linear graph and the
progression of points on an exponential graph?

Given a
situation, determine if the model created is linear or exponential based on
the context clues in the equation.

Linear
graph
Exponential
graph

3 days

F.LE.1a Prove that linear functions grow by equal differences over
equal intervals, and that exponential functions grow by equal factors over equal
intervals.

How many
points are needed to create an accurate equation for a linear function and an
accurate equation for an exponential function? Are there exceptions?

Given the
graph of a linear function, defend algebraically or graphically that the
function increases or decreases over equal intervals by equal quantities.
Given the
graph of an exponential function, prove growth occurs over equal intervals.

Interval
Equal
factor
Equal
difference

3 days

F.LE.1b
Recognize situations in which one quantity changes at a constant rate per
unit interval relative to another.

What
context clues suggest that a quantity changes at a constant rate per
interval?

Analyze
several word problems relating to constant rate of change to determine which
qualities or context clues are consistent across the problems.

Constant
rate

3 days

F.LE.1c
Recognize situations in which a quantity grows or decays by a constant
percent rate per unit interval relative to another.

What
context clues suggest that a quantity changes at a constant factor per
interval?

Analyze
several word problems relating to constant factors of change to determine
which qualities or context clues are consistent across the problems.

Constant
factor

3 days

F.LE.2 Construct linear
and exponential functions, including arithmetic and geometric sequences,
given a graph, a description of a relationship, or two inputoutput pairs
(including reading these from a table).

What
information is necessary to create a graphical or algebraic representation of
a described function?

Given
various expressions of information pertaining to a linear or an exponential
function, create a graphical or algebraic representation of the function.

Inputoutput
pairs

3 days

F.LE.3 Observe using
graphs and tables that a quantity increasing exponentially eventually exceeds
a quantity increasing linearly, quadratically, or (more generally) as a
polynomial function.

What is
unique about an exponential function as compared to a linear or quadratic
function?

Analyze
linear, quadratic, and exponential functions to determine unique qualities
between the three types of functions.

Exponential
function
Linear
function
Quadratic
function

3 days

F.LE.4
For exponential models, express as a logarithm the solution to ab^{ct} = d where a, c, and d are numbers and the base b
is 2, 10, or e; evaluate the
logarithm using technology.

In what instances is 2+2 not equal to 4?

Selfguide your understanding of logs using the graphing
calculator; create your own problems and share with the class
http://mathbits.com/mathbits/tisection/Algebra2/logarithms.htm

Logarithm
Base
Exponent
Natural log

3 days

F.LE.5
Interpret the parameters in a linear or exponential function in terms of a
context.

How does
the manipulation of the components of a function relate to its corresponding
graph?

Given a
function, manipulate various components such as slope or intercept to
determine how the function changes under the new conditions.

Parameters

1 day
