Download Lesson Plan: Exponential Modeling

Lesson Title: Exponential Modeling
Date: _____________ Teacher(s): ____________________
Course: Common Core Algebra II, Unit 2
Start/end times: Multiple day lesson
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson
F.LE.B.5 Interpret the parameters in an exponential function in terms of a context.
MP1:
MP2:
MP4:
MP5:
MP6:
MP7:
MP8:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Common Core Algebra II, Unit 2
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Have students complete the first page on the Savings
Account Activity Sheet
(http://illuminations.nctm.org/uploadedFiles/Content/L
essons/Resources/9-12/CompInterest-ASSavingsAccount.pdf).
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.
Part 1
Assessment Options from the ‘Predicting Your Financial
Future’ Activity (MP2, 4)
Consider two investments, Plan A and Plan B:
Plan A: $20,000 investment for 5 years at 10% interest
rate
Plan B: $14,000 investment for 15 years at 15% interest
rate with monthly contributions of $50
Which is the better investment? In what situations would
each of these plans be the best option to choose?
Part 2
PPT Summary on slide 5
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
Part I:
1. After the lesson launch, discuss in a large group, the differences between the first table and the second table. Try
to develop the formula for exponential growth (compounding annually). Have students complete question 1.
2. Regroup and discuss/develop the formula for compounding interest periodically (monthly, weekly, etc). Then
have students complete questions 2 and 3. (The rest of this activity is an optional extension, but does not address
compound interest).
Note: This may be the end of day 1 for a 50-minute class period. Give students the Cost of College Homework and
use it as the lesson launch for the next day.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Exponential Modeling
Course: Common Core Algebra II, Unit 2
Date: _____________ Teacher(s): ____________________
Start/end times: Multiple day lesson
Part II:
1. Have students complete the warm up on the Exponential Modeling PowerPoint practicing with the compound
interest formula.
2. Assign students to pairs. Have pairs complete the Compound Interest Activity (slide 2 and 3). (MP 8)
3. Introduce the continuous growth formula and e (slide 4).
a. There is a link to a video clip on Bacteria Growth.
b. Compare the continuous growth formula to the compound interest formula
c. Complete practice problems.
Note: Another option for Part II is to print the slides, assign each slide to small groups, and have groups complete
and present to the class.
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
Students should be able to determine the future value of an investment using the formula A = P(1 + r/n)nt , and use
that to make sound financial decisions.
Students should be able to determine which compound interest formula to use based on the type of problem, and
information given.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Discuss with students how bacteria growth and chemical decay can be calculated with a given time, but the
growth/decay happens continuously. (The bacteria does not wait an hour, then double in numbers, the growth
happens constantly, and after an hour there is double the amount.)
Resources: What materials or resources are essential for students to
successfully complete the lesson tasks or activities?
Calculators
Page 1 and 2 from Savings Account Activity from NCTM activity.
Homework: Exactly what follow-up
homework tasks, problems, and/or
exercises will be assigned upon the
completion of the lesson?
Cost of College Homework.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Are students able to apply the correct compound interest formula based on the problem?
Are students able to solve for each part of the equation?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.