Teacher(s):  Rob Leichner

Date(s):

Subject: Math 3

Grade Level(s): 10 – 12

Time to Complete (in periods):

2

Unit:

Unit 3 – Exponential and Logarithmic Functions

Lesson Topic/Title/Focus:

Solving and Graphing Exponential Equations

BACKGROUND KNOWLEDGE necessary for students before engaging in this lesson:

Students will need to be able to graph functions on a calculator and adjust scale to see values. Students will need to understand solving equations as a means of isolating a variable to find a value.

COMMON CORE STATE STANDARDS to be addressed in this lesson:

School-wide initiatives:      Writing Anchor   2            Math SMP 1, 2, 3, 4, 5, 6, 7, 8

District-wide initiative:           Informational Text

ESSENTIAL QUESTIONS and LESSON ESSENTIAL QUESTIONS for this lesson. They are open-ended, thought-provoking questions that ask students to uncover ideas, problems, controversies, philosophical positions and/or adopt varying perspectives.

1. What are the potential outcomes for the world if the polar sea ice continues to melt?

2. What equation BEST models the current rate of melting for the polar ice caps?

3. Why will a value with an annual percentage rate of decay never reach zero?

OBJECTIVES of this Lesson (Specific, Measurable, Attainable, Realistic, and Timely):

SWBAT create and solve linear, quadratic, exponential, and cubic functions from given data on the polar ice caps.

SWBAT evaluate functions to assess their accuracy on when the polar ice caps will melt.

INSTRUCTIONAL PLANNING—Day 1

Warm-Up

Time: 20 min.

Students watch the first 1:05 of video: “Earth Underwater.” (Link:  https://www.youtube.com/watch?v=1JsTXSPcGUY) Then, students read primary source article “Arctic Sea Ice Decline” from Weather Underground (Link:  http://www.wunderground.com/climate/SeaIce.asp?MR=1). Students highlight words they don’t know or sentences that seem confusing. Also, students answer questions on activity sheet. 

Teacher Input (Introduction)

Time: 15 min.

Teacher leads students through discussion of issue (with lots of turn and talk, some cold call). Why is this an issue? What has led to the problem? Do you believe that it’s an issue?

Then, conversation turns to math. Where in the article did you see math that could relate to determining the problem? Why is this important?

Guided Practice

Time: 25 minutes

Students analyze graph from article in groups to determine potential equations of problem. Activity sheet leads them through this activity. (Teacher might need to review scale of graph, decimal estimations, plotting points, etc. as needed. Students will need TI-83 or higher calculators to calculate the regression equations.)

Independent Practice

Time: 20 min.

On activity sheet, students will use their equations they determined to calculate amount of polar ice in given years. Then, they will guess when the polar ice will reach zero.

Closure: On activity sheet, answer question: When do you think the polar ice levels will reach zero, based on your functions?

Key Vocabulary

Linear function, Quadratic function, Exponential function, polar ice caps, sea ice melt

FORMATIVE ASSESSMENT(S): Indicate how students will be assessed and how these assessments will be used to improve instruction.

Informal assessment observing activity sheets during group work, listening to group discussions, cold call during instruction

Formal assessment in collecting activity sheets after Day 1 to assess functions and answers

POST-LESSON REFLECTION (What worked? What should be changed for the next implementation? How did students react to the lesson?)

INSTRUCTIONAL PLANNING—Day 2

Warm-Up

Time: 5 min.

 Students share their answers to yesterday’s closure activity, teacher records on board to see who is closest after the lesson. 

Teacher Input (Introduction)

Time: 15 min.

1. Teacher writes functions from yesterday (linear, quadratic, exponential, cubic) on the board as a reminder. Then, graph and solve the linear using the calculator. (2^nd-Calc-Zero, NOT the table…the table won’t give decimal answers.) Steps are on the activity sheet as a reference.

2. Teacher leads brief review lesson on solving linear (set = 0 and solve equation), quadratic (quadratic formula), and exponential (rewrite in log form) functions.

Guided Practice

Time: 35 minutes

1. Students graph and solve the quadratic, exponential, and cubic functions using the calculator. The exponential is an error – groups discuss why, then teacher leads class discussion.

2. Students solve linear, quadratic, and exponential equations algebraically on activity sheet. Exponential function again gives an error – groups discuss why, then teacher leads class discussion.

Independent Practice

Time: 30 min.

1. Students calculate when the ice levels will reach 0.1 million square kilometers, based on their exponential functions, to assess if they can solve an actual exponential function not = 0.

2. Students calculate ice levels in the year 2030 based on their equations. Why would scientists make the “zero-level” claim if the exponential equation can never reach zero?

3. Students begin their main task for this activity – a letter to their Congressman/Congresswoman explaining why it is so important to take action to prevent the melting of the polar ice caps, based on their math. Directions/rubric provided on activity sheet.

Closure: On activity sheet, answer question: Did this activity help you understand the difference between linear, quadratic, exponential, and cubic functions and how to solve each?

Key Vocabulary

Linear function, Quadratic function, Exponential function, polar ice caps, sea ice melt

FORMATIVE ASSESSMENT(S): Indicate how students will be assessed and how these assessments will be used to improve instruction.

Informal assessment observing activity sheets during group work, listening to group discussions, cold call during instruction

Formal assessment in collecting activity sheets after Day 2 to assess answers to independent practice and grading letters to assess understanding of math and issue.

POST-LESSON REFLECTION (What worked? What should be changed for the next implementation? How did students react to the lesson?)