MAT-HS Targeted Standards (F) Concept: Function (LE) Domain: Linear, Quadratic and Exponential Models Cluster: Construct and compare linear and exponential models and solve problems

MAT-HS.F-LE.04 Use logarithms to express the solution to ab^{ct}=d where a, c, and d are real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.

Student Learning Targets:

Knowledge Targets

I can define a logarithm.

I can recall properties of logarithms and exponents.

I can recognize common logarithms and natural logarithms.

I can identify an asymptote.

I can recall the change of base formula.

Reasoning Targets

I can convert from a logarithm to exponential expressions.

I can identify an asymptote.

I can expand and condense logarithms.

I can evaluate logarithms and exponential expressions.

I can distinguish between a natural log and common log.

Skills (Performance) Targets

I can apply basic properties of exponents and logarithms to rewrite algebraic expressions.

I can graph logarithmic and exponential functions.

I can solve logarithmic and exponential equations.

I can graph and determine the equation of an asymptote.

I can express the solution to an exponential function as a logarithm.

I can evaluate logarithms using technology.

Product Targets

I can

I can

Alg II Solve Exponential Equations Proficiency Scale

Score

Description

Sample Activity

4.0

(advanced)

In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations.

Describe the error in the following work:

3.5

In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

The student can:

solve an exponential equation using logarithms.

The student exhibits no major errors or omissions.

Solve the following equation.

2.5

The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

There are no major errors or omissions regarding the simpler details and processes as the student can:

recognize and recall specific terminology such as :

exponent

logarithm

Euler number (e)

base

identify an exponential equation.

use inverse operations.

evaluate a logarithmic expression.

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Which of the following is an exponential equation?

4^{3x-2}=1

2x+1=8

3. 3x^{2}-2=45

1.5

The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).

0.5

With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).

0.0

Even with help, the student demonstrates no understanding or skill.