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# Mortgages and Geometric Series DAY #1

Lesson 6 of 15

## Objective: Students will be able to apply their knowledge of a geometric series to the calculation of a mortgage payment!

*45 minutes*

#### What is a Mortgage?

*15 min*

Last night the students’ homework was to look up the definition of a mortgage, or ask their parents what they knew about the term. At the start of class, I ask the students to respond to a Web Response poll asking them one fact or definition they learned. This is usually really insightful, and even after a day the student’s knowledge is still very limited. Although all of them claim to know the word, few of them know what it means and nor do many of them know of its mathematical implications. Because of this “intimidation factor” and connection to the real world, the students are immediately hooked on the lesson.

Chances are that at least a few of the students posted responses sound enough to piece together a working definition of a mortgage – a few may even talk about current rates, and/or terms. However, it is not likely that any of the students shed light on how mortgage payments are calculated. In fact, few adults even attempt to grasp this concept because it has long been indoctrinated that calculations of monthly mortgage payments require the use of complex tables and/or a high power computer program. THIS IS FALSE! As we will demonstrate this class period, the calculation of a mortgage payment is relatively simple… just multiple the principal times a geometric series involving the interest!

As we transition into the PowerPoint, I mention to the students that if any point they get confused or need a minute to talk things over with a partner TO PLEASE STOP ME. In fact, I regularly pause in the lesson to ask students talk about what they see with their thinking groups. This ensures student engagement and personalization of the content. It is also a great way to get questions from the kids because they will soon realize that they are not the only ones who are thinking of the particular question.

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On slide #7, you will see the activity that corresponds to this lesson. The students should now be equipped to begin attacking the problem, which involves creating a flier for a bank that they can use to explain mortgage payment calculations to clients. The workshop exposed the general idea behind a mortgage calculation; but it is up to the students to apply it to an appropriate example, portray that information in a flier, and then be able to orally communicate their knowledge with a mock client. This assesses the student’s understanding through a wide variety of modalities. When assembling groups, I would use NO MORE THAN teams of 2 students. This ensures that the students have someone to work with, without having too many students in a group that there is “standing around”. When the students present their results, they will have an opportunity to learn from each other and perhaps see the task from a new perspective.

**NOTE: **I just have my students use a blank piece of computer paper to make the flier. I tell them that they can tri-fold it if they would like, but that I am mostly concerned about HOW they communicate the mathematical concepts that go into a mortgage payment - - not their strategy for arranging the flier.** **

**Timeline: Work time tomorrow, along with a re-run of the workshop (many students will need to see it again). Presentations and fliers due on the following day. **

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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

- LESSON 1: Introduction to Sequences
- LESSON 2: Arithmetic Sequences and Series
- LESSON 3: Geometric Sequences and Series
- LESSON 4: Sequences and Series Battleship!
- LESSON 5: A Double-Dose of Series Application
- LESSON 6: Mortgages and Geometric Series DAY #1
- LESSON 7: Mortgages and Geometric Series DAY #2
- LESSON 8: Mortgages and Geometric Series DAY #3
- LESSON 9: Mortgages Wrap-up and Additional Scaffolding
- LESSON 10: Investigating Infinite Geometric Series
- LESSON 11: Using Sequences and Series to Make Connections
- LESSON 12: The Binomial Theorem
- LESSON 13: Sequences and Series Partial Unit Review
- LESSON 14: Sequences and Series Partial Unit Review II
- LESSON 15: Unit Test: Sequences and Series