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# Credit Cards Investigation: How is interest really calculated? (Day 3 of 4)

Lesson 11 of 14

## Objective: SWBAT derive the compound interest formula and apply it to solve real world problems.

## Big Idea: My balance is what?!? Students develop the compound interest formula completely on their own before applying it to real world problems.

*51 minutes*

#### Warm-up: Homework Discussion

*10 min*

Have students take a moment to reflect on their homework from last night. Each student in every team should think of one thing they learned in the NPR podcast and then share it with their team. Each team should pick the best fact and write it up on the board. Then as a whole class we can review some of the most interesting aspects of the conversation.

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How is interest really calculated?

In this part of the credit card investigation students explore how interest is really calculated. Using a table students will be asked to write a general equation to calculate compound interest. I assume this section will be difficult for students. As students are working, I plan to monitor their progress by checking their answers in the column ‘expression for balance after x years.’ It is important that students have the correct expressions in Questions 3 and 4 if they are going to obtain the interest formula. I may also give students the hint that they can break down the middle column of the table like so: Credit Card Investigation, Scaffold for question 4.

Apply your knowledge

In this section, students will be answering some very straightforward questions about interest calculations. I will encourage my students to self-assess as they work, focusing particular attention on the reasonableness of their answers.

This section offers a great opportunity for students to practice **MP1: Making sense of problems and persevere in solving them. ** As they evaluate the reasonableness of their solutions to these interest problems.

I will also give students some parts to these answers at some point in the lesson to help with their self-checks. Maybe I will give them the whole dollar amount and have students find the change part of the answer.

Something like this:

- $274.__ __
- $1353. __ __
- $4791.__ __
- $6918. __ __

I want students to know right away if they have made a mistake, without providing them with the exact answers so they can check their work.

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
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- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Cat Island (Day 1 of 2): Cats can’t add but they do multiply!
- LESSON 2: Cat Island (Day 2 of 2): Cats can’t add but they do multiply!
- LESSON 3: Graphing Exponential Functions
- LESSON 4: Shifting Exponential Functions
- LESSON 5: Counting the Change: Linear, quadratic, or exponential? (Day 1 of 2)
- LESSON 6: Counting the Change: Linear, quadratic, or exponential? (Day 2 of 2)
- LESSON 7: Sorting out the Change
- LESSON 8: Stretching Exponential Functions (and your mind)
- LESSON 9: Credit Card Investigation: What is interest? (Day 1 of 4)
- LESSON 10: Credit Card Investigation: What is interest? (Day 2 of 4)
- LESSON 11: Credit Cards Investigation: How is interest really calculated? (Day 3 of 4)
- LESSON 12: Credit Card Investigation: A Dastardly Scheme (Day 4 of 4)
- LESSON 13: Exponential Functions Test Review
- LESSON 14: Exponentials Functions Unit Test