## CalculateSimpleInterestUsingFormula_GPS.docx - Section 2: Guided Problem Solving

# Simple Interest

Lesson 12 of 15

## Objective: SWBAT calculate simple interest using a formula

*50 minutes*

#### Introduction

*10 min*

I will begin with the essential question: How can you calculate simple interest?

The notes section begins with a simple paragraph about interest. Either a student, the class, or I will read through the paragraph. We will fill in the blanks as we go. The final version should say:

Money that you save in a bank account can grow. Money that you borrow from a bank is not free.

"Interest is money paid or earned for the use of money. The principle is the amount of money borrowed or deposited. Simple interest is money paid or earned only on the principal. Simple interest can be calculated using a formula."

The formula is then presented in its most common form.

Before going into examples it is probably worth discussing cases where interest can occur. I will ask and/or provide examples of borrowing money - using credit cards, car loans, tuition loans, mortgages. Interest (though often not simple interest!) is paid on these loans. I want students to understand that there is a cost for borrowing money. Conversely, money put in a savings account, mutual funds, retirement accounts, etc can grow based on interest. So it is possible for your money to earn money. Again, I may tell students interest on these types of accounts is not usually simple interest but the concept of simple interest will help us understand the other types when they study them.

I will then read through the first example. After the first reading, I will go through and annotate values in the problem. I will label $500 as the principal, 3% as the rate - written 0.03, and 3 years as the time. Then, in part A I will write p = 500, r = 0.03, and t = 3. The equation will be written, values will be substituted and the equation will be solved.

In part B, students will need to know that "balance" means how much is in the account. In this case it's principal plus interest.

Students have a check for understanding problem. I expect to see annotations and variable assignments in the same manner as the example.

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#### Guided Problem Solving

*15 min*

Before beginning the guided practice it will be helpful to review the steps needed to solve the problems, especially since they are not written in the resource.

I will ask students to discuss and answer:

1) What is the first thing necessary to solving an interest problem?

Answers: Identify which values represent interest, principle, rate, and time/

2) What do we do with these values?

Answer: Substitute them into the simple interest formula.

3) What do we do next?

Answer: Simplify and solve the equation.

Now students will solve the 5 guided practice problems. Problem 1 is meant to see how well students understand simple interest - that is why I chose a variable for years and have an unspecified principal. Students hopefully can say that they would multiply the amount of money placed in the savings account by 0.02 times y to find the interest.

Problems 2 and 3 are most like the example.

Problem requires student to find the unknown interest rate. The steps discussed above will be extremely helpful. Here it is necessary to make sure that students are identifying the correct values. I have provided variables to ensure that students assign the variables correctly. It also helps me quickly assess how well they are solving the problems as I walk the room.

The last question is an explain your thinking problem (**MP3**). I want students to understand that they want the lowest possible interest rate when borrowing, yet they want their investments to yield a high rate of return.

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#### Independent Problem Solving

*20 min*

Students now work independently to solve the next set of problems. The first 5 only require students to find the interest and the balance.

Number 6 is designed to bring out a common error. The time is given in months, but the students need to recognize that time needs to be represented in years.

Problems 7-10 use either provide time in months or require students to find something other than the interest: the principle, the rate, or the time.

Note: Problems 1,2 and 9 are most similar to the exit ticket. As students are working, I will pay especially close attention to these three problems as a gauge on how prepared they are for the exit ticket.

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#### Exit Ticket

*5 min*

Before beginning the exit ticket, we will discuss how to use the simple interest formula. We will also review each term - interest, principle, rate, time, and balance.

I will ask my students to annotate each problem in the manner of the examples. Many of the mistakes my students make are from not carefully reading. Annotating will help them better understand the problems they are solving.

The exit ticket is worth 5 points. Students earning 4-5 points will have successful exit tickets.

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###### The Defining Pi Project, Day 1

*Favorites(4)*

*Resources(31)*

Environment: Urban

- LESSON 1: Multiple Representations of Percents
- LESSON 2: The 10% Benchmark
- LESSON 3: The 1% Benchmark
- LESSON 4: Percent Benchmark Fluency
- LESSON 5: Drawing Bar Models to Represent Percents of Increase and Decrease
- LESSON 6: Solve Problems by Applying Percents of Increase and Decrease
- LESSON 7: Discounts and Sales Tax
- LESSON 8: Finding a Percent of Change
- LESSON 9: Finding an Original Value
- LESSON 10: A Percent Equation
- LESSON 11: Expressions for Percent Increases and Decreases
- LESSON 12: Simple Interest
- LESSON 13: Increasing and Decreasing Quantities by a Percent (Day 1 of 2)
- LESSON 14: Increasing and Decreasing Quantities by a Percent (Day 2 of 2)
- LESSON 15: Percent Assessment