Rhonda Leichliter ROGERS HIGH SCHOOL, ROGERS, AR
Algebra I : Unit #6 - Exponential Functions : Lesson #8

Comparing Investments

Objective: SWBAT compare simple interest I=prt to compound interest A=P(1 +r/n)^nt, and graph each as a linear function or an exponential function.
Standards: 8.EE.A.1 HSA-SSE.B.3 HSF-IF.C.8 MP1 MP2 MP4 MP7
Subject(s): Math
60 minutes
1 Warm Up - 10 minutes

I intend for the Warm Up to take about 10 minutes for students to complete and for me to review with the class.  In this Warm up, I want students to graph Simple Interest and Compound Interest. The goals in this lesson are:

  • for students to be able to find Simple Interest and Compound Interest
  • for students to recognize Simple Interest as a Linear Function
  • for students to recognize Compound Interest as an Exponential Function
  • for students to have an understanding of the meaning of both Interests

Most of the students that complete the chart in the Warm Up on their own discover a pattern in the table that helped them to complete it.  When graphing Simple Interest, it was easy for the students to see that the function was linear.  When graphing Compound Interest in the second graph, it was more difficult to recognize the function.  It is more recognizable as exponential if more years are plotted.  Students do recognize that Compound Interest is growing at a faster rate than Simple Interest.  When reviewing the Warm Up with students I try to focus more on the meaning of Compound Interest instead of the formula.  I will concentrate more on the formula in the Guided Practice.  I review the Warm Up in the video below:

Link 

Great Lesson for Comparison and Common Core!
Problem-based Approaches

Students should already be able to recognize the key characteristics of a linear function. Exponential functions are not as familiar to students, but they have seen them before.  Exponential Functions have been introduced some in 8th grade, and seen in Science as well.  

Students start getting excited when they see money grow so rapidly.  I think few adults or students realize the Power of an Exponential Function, and how quickly money can grow.

When comparing linear to exponential, students should recognize that time is an issue, but the rate of change of an exponential function is amazing. 

2 Guided Practice - 20 minutes

In the Guided Practice I focus more on the formulas of Simple Interest and Compound Interest and their meaning.  Students need to know the formulas, but also understand the meaning of the variables to identify what numbers are substituted for each variable.  I have provided a key to the Guided Practice in the resource section.

In certain sections of the Guided Practice, I have students define each variable in both the Simple Interest and the Compound Interest formula in their own words before applying to the problems.  This helps students develop meaning for the parts of each formula.  Students practice identifying the value for t for both formulas and n for the Compound Interest formula. This provides students with a better understanding of how to find the value for t and n before evaluating the entire formula.

After allowing the students about three or four minutes to define the variables in the Simple Interest formula and to identify the value for given certain information, students begin applying the Simple Interest formula to problems.  I call on students for the definitions and values for time.  I allow three to four minutes for students to work problems one and two, and have them post their answers on their individual whiteboards.  I instruct students to not hold up their boards until I say "show me." This allows all students to respond before sharing.  I then post the different responses on the front board.  As a class we identify the correct answers and the reasoning behind it.  Several students make a mistake on identifying for problem 2. Some students make the mistake of substituting six for t instead of .5. Number two is also a quick check for students to make sure they are converting from percent to decimal correctly(1.25% to .0125) for r.  I then allow students a few more minutes to complete three and four and check their answers. 

The students then work on defining the variables for Compound Interest and identifying n before applying the entire formula.  Then I guide students through five and six as I did previously with Simple Interest, and finally allow them to complete seven and eight and do a quick check for accuracy.  

3 Independent Practice - 15 minutes

The Guided Practice in this lesson helps set students up for success when working the Independent Practice on their own.

I allow students about 10 to 15 minutes to complete the Independent Practice and post the answer key for students to check at the end of the 15 minutes.  I have students grade their own and hand in for me to check.  I walk around to monitor student progress as students are working independently.  Students are still able to ask for assistance with difficulties that they may have while working the problems.  Some students did still struggle with identifying n and t correctly, and writing r in decimal form for the interest rate instead of as a percentage rate.

I have provided a Key to the Independent Practice for students to do a quick self check before completing the Exit Slip.  

 

4 Exit Slip - 5 minutes

I use the Exit slip as a quick formative assessment to measure student progress on being able to apply the Compound Interest Formula.  Students should calculate a balance of $70,409.42 after the two year period of saving in the account for college.  

Some mistakes students make on the Exit Slip are listed below:

  • substituting .08 instead of .08/365 for the interest rate
  • substituting 720 for n instead of 365
  • multiplying 60,000 times the parentheses before applying the power

All students identified the Principal Amount correctly.