What are some good problem solving methods when using logs and exponents?

(There are many more EQ's one could use around logs and exponents.. how they relate to nature, interest, etc, but since this is a review lesson, the goal is to more modest!)

The website from the Jefferson Math Project is a great resource for Regents review material. Though I did find several errors in the worksheets, thus, be careful!

Specific Purpose(s) or Objective(s)

Review Exponents and Logs

Improve Students' problem solving ability involving logs and exponents

Deeper understanding of formulas and identities involving logs and exponents

Lesson Sequence

Hook

Mention that investing money is exponential, and one uses logarithms to solve some many financial problems. Also human hearing is very sensitive to changes in energy, and in fact, decibels are measured using logarithms (db = 10 log (I / 10^(-12)), 0 db means energy is 10^(-12), 120 db means energy is 10^(12).

On Board at Start of Class

Do Now: Write first names on paper, and "tent" in half

Grab Formula Sheet and worksheets. Fill in as much of formula sheet as you remember.

Objective: (see above)

H/W: Finish marked problems on worksheet

Step by Step Explanation of Activities/Strategies

Hook (1 minutes).

Exponent Round-Robin Game. This takes part as a K of KWL. During game, as formulas come up, write them down on board (7 minutes)

Give students a minute to work on problem 3 in Exponential Equations. Coach them to solution. (2 minutes)

Do the same for problem 8. (3 minutes)

Introduce log formulas (8 minutes)

Have students do 4 Log Properties and Equations worksheet problems marked as "In Class" and go over solutions (10 minutes)

Give interest formula on board and explain. Amount=Principle(1+r/n)^(nt). By subsituting k=n/r, this turns into Amount=Principle(1+1/k)^(krt). As k->inf, this turns into Amount=Principle*e^(rt). Discuss with students how to solve for each of the possible unknowns. (10 minutes)

Closure

Reflection - 3 minutes

Query in terms of fingers how well they understand exponents and logs.

Accommodations for Students with Disabilities or Diverse Learning Styles:

Since this is a review, it really doesn't lend itself well to differentiated instruction. THere should have been plenty of opportunity in introducing logs and exponents during the main unit for students to get these big understandings. During the regents, it is all about problem solving and recall. Thus, this review actually gives the teacher an opportunity to observe if students understand well enough to nail the Regents questions on exponents and logs.

During exponent game, questions will be both read aloud and displayed on overhead.

Worksheets done in class can be finished at own pace for H/W.

Plenty of additional problems and optional problems for advanced students.

## Organizational Information

## Big Ideas

## Essential Question(s) for this Lesson

## NYS Standards Addressed for this Lesson

A2.CM.1, A2.CM.5 (and maybe .6), A2.CM.7, A2.CN.4, A2.CN.7, A2.N.1, A2.A.6, A2.A.8-12, A2.A.18-19, A2.A.27-8,A2.A.51,A2.A.53-4## Evidence of Student Understanding (Assessment) for this Lesson

## Lesson Preparation

## Student Preparation Prior to this Lesson

Students should have already completed unit on logs and exponents. This is a review.## Materials Required

## Teacher Resources

The website from the Jefferson Math Project is a great resource for Regents review material. Though I did find several errors in the worksheets, thus, be careful!## Specific Purpose(s) or Objective(s)

## Lesson Sequence

## Hook

## On Board at Start of Class

## Step by Step Explanation of Activities/Strategies

## Closure

## Accommodations for Students with Disabilities or Diverse Learning Styles: