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Exponents and Logs (Regents Review)
keywords: regents review summary exponents logs
Grades/Course: Regents 3
Lesson Number: Review
Time Required: 45 minutes. The amount of time spent on the interest formula derivation/explanation can be cut by 5 minutes by just giving the formula.
Essential Question(s) for this Lesson
How are logs and exponents related?
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!)
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
Students will answer questions in initial exponent review activity. That will help measure understanding of exponents
Worksheets will be examined as I canvas the room, to look for misunderstandings.
Students will be asked to do an interest problem at their seat to be handed in.
Students will be asked for answers to several of the Worksheet problems.
Student Preparation Prior to this Lesson
Students should have already completed unit on logs and exponents. This is a review.
Index cards and transparencies created from the file
Worksheets to do in class and for homework:
Blank formula sheet, that students will fill in:
Interest formula sheet (test for understanding):
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
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)
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.
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