## Task - Saving for College.docx - Section 2: Explore

# How Much Will College Cost in the Future?

Lesson 1 of 7

## Objective: SWBAT to use exponential functions to predict future costs.

*48 minutes*

#### Launch

*8 min*

Here is a great video to show students to get them thinking about the rising cost of college and what it will mean for their future and the next generation's future.

After watching the video, have a quick discussion. Here are some questions you might ask your students:

1. Why are college costs rising so rapidly?

2. What does it mean for college costs to outpace the rate of inflation?

3. What do you think the average cost of college is right now?

4. What about for someone who attends college 20 years from now? How much do you think college will cost them?

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#### Explore

*20 min*

I love lessons that are relevant to students. My students are always so much more engaged and interested in the math. In this particular lesson, students will be able to really "take away" something from our class - a range of estimates about the cost of college in the future.

Start the lesson by giving the class this worksheet and have them read through it. The great thing about this task is that you are not giving them the data - they must decide what they need to know. Have students brainstorm what they need to know in order to estimate the college costs for their future children. After a couple minutes, generate a list as a class and see if everyone agrees. Most likely students will say that they need to know the current college cost and the rate at which it is increasing. At this point you can have students research this data themselves, or you can give it to them if time is an issue. In the video below I talk more about the students identifying the data that is needed.

The College Board reported that for 2012-2013, the average in-state cost (tuition and room and board) for a four-year in-state public institution is about $17,860. Finaid.com states that tuition costs seem to increase from six to nine percent. So, you can have your students pick a percent that they want to work with and the class can estimate a range of costs.

After setting the parameters for the data, give students time to work on the task. In my class, students usually have a good foundation with exponential functions, so I expect them to feel confident figuring out the college costs. While students are working, ask them how they are getting their answer. Make note of students of which students are using exponents and which are using repeated multiplication.

Expect some students to incorrectly use a linear model and add the increase every year instead of multiplying by the percent increase. If that happens, ask them what percent the costs increase by and see if it makes sense to them. Ask them what the percent increase over a two-year period is if the college costs increase 8% each year. This will get them thinking multiplicatively instead of additively.

#### Resources

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#### Share

*15 min*

Start by asking a few general questions about what type of situation we are working with for this lesson. Students will likely recognize that it is exponential. Review some of the characteristics of exponential functions, particularly that there is constant multiplication, that the graphs have an asymptote, and that they increase or decrease very rapidly. You might want to discuss the phrase “growing exponentially” as they probably hear it often.

Go over questions #1 and #2 from the worksheet and have students present their work. One of my favorite parts about this lesson is that students will get different answers based on how old they are. In the task it says that Miss Cleo predicts that they will have their first child when they are 29 years old; since your students will probably not all be the exact same age, you will get different results. It will be a great conversation to have when thinking about how an extra year or two will make a difference in the costs. Focus on setting these answers up with exponents rather than multiplying by the growth rate many, many times.

Question #3 might be tough for some students. If a student used guess and check, start with that and have them present their findings. Then move on to a student who solved algebraically. In order to solve algebraically, students will have to use logarithms, so it is a great time to talk a little bit about them. If no student solved that way, you might want to present the strategy and then leave it open for them to think about.

#### Resources

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#### Extend

*5 min*

Here is an assignment to get students thinking about exponential functions. It takes the concepts we worked on in class and extends them to more general cases. Students should have a decent grasp on these concepts because of extensive work with exponential functions in Algebra 1 and Algebra 2.

#### Resources

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- UNIT 1: Functioning with Functions
- UNIT 2: Polynomial and Rational Functions
- UNIT 3: Exponential and Logarithmic Functions
- UNIT 4: Trigonometric Functions
- UNIT 5: Trigonometric Relationships
- UNIT 6: Additional Trigonometry Topics
- UNIT 7: Midterm Review and Exam
- UNIT 8: Matrices and Systems
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- UNIT 10: Conic Sections
- UNIT 11: Parametric Equations and Polar Coordinates
- UNIT 12: Math in 3D
- UNIT 13: Limits and Derivatives

- LESSON 1: How Much Will College Cost in the Future?
- LESSON 2: Radioactive Decay and Nuclear Waste
- LESSON 3: Logarithmic Properties Scavenger Hunt
- LESSON 4: Solving Analogous Equations
- LESSON 5: Formative Assessment and Unit Review
- LESSON 6: Unit Review Game: The Row Game
- LESSON 7: Exponential and Logarithmic Functions: Unit Assessment