## (solution) Unit Activity Unit: Single-Variable Expressions This activity

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Unit Activity Unit: Single-Variable Expressions

This activity will help you meet these educational goals:

Mathematical Practices? You will make sense of problems and solve them, use mathematics

to model real-world situations, and use appropriate tools strategically. Introduction

Have you ever made a mistake when trying to solve a math problem? It can be pretty easy to

do, and often will result in losing points on an exam. In the real world, such mistakes can

have more serious effects: Miscalculating how much gas you have left in your car will leave

you stranded. Miscalculating how much money you have left in your bank account might cost

you an overdraft fee. Even more serious, miscalculations have resulted in serious accidents

happening many times. Once, as a result of not using the correct units, a satellite sent to

Mars burned up in the atmosphere, wasting over \$300 million dollars.

Fortunately, there are steps you can take to help avoid making errors along the way. One of

these strategies is manipulating formulas so they are solving for the variable you want before

you substitute values for the variables in the formula. This technique is especially useful when

working with large, unwieldy numbers.

__________________________________________________________________________ Directions and Analysis

Task 1: A Journey to Earth

Every moment of every day, light pours out from the Sun at the center of our solar system

and travels to Earth. It does not arrive at Earth instantaneously though; it takes time to get

here. Your task is to figure out how long it takes for light to travel from the Sun to Earth.

d

t a. The formula for the velocity of an object is v , where v is the velocity of the object, d is

the distance traveled, and t is the time elapsed while that distance is traveled. If you had

only this formula to work with, what should your first step be in determining how long it

takes for light to reach Earth from the Sun? What additional information do you need to

calculate this?

Type your response here:

b. Solve for the variable you are looking for. Show your work.

Type your response here:

1

© 2014 EDMENTUM, INC. c. Now search the Internet for the values of the variables you do not know. What are they?

Type your response here:

d. Using the formula you derived and the values you researched, calculate the time it takes

for light to travel from the Sun to Earth.

Type your response here:

e. Felix Baumgartner is a daredevil famous for breaking the sound barrier during a freefall on

October 14, 2012. Aided by a weather balloon, he climbed to a height of 128,100 feet.

More than 24 miles in the air, he was so high up that he could see Earth?s curvature. He

then jumped out of the capsule that carried him. On the way down, he traveled at an

average of 335.92 miles per hour, at one point even going as fast as 720 miles per hour,

breaking the record for the highest skydive ever attempted and breaking the sound barrier

in the process. Using the formula you derived in part b, how long did it take Baumgartner

to reach the ground, in minutes? Be careful about unit conversions, and show your work.

Type your response here: Task 2: Interest in Finance

Interest is a concept familiar to most people: every credit card in existence has a term called

annual percentage rate (APR), which is an interest rate. Suppose you charged \$1,000 to a

credit card that has a minimum payment each month equal to the interest owed. Can you

figure out how much the interest rate is based on this amount?

The formula for simple interest is I r P m, where I is the amount you will pay in interest,

r is the rate at which interest will accrue, P is the principal (amount borrowed), and m is the

number of times the interest is applied.

a. To solve for the interest rate of your credit card, you need to understand which variables in

the above formula you have. If your minimum monthly payment is \$22 on the \$1,000

credit card bill, which variables do you know the values of?

Type your response here:

b. Manipulate the formula so it will calculate the interest rate you are paying instead of the

amount of money you are paying.

Type your response here: 2 c. Now that you have a formula that will give you the interest rate, plug in the values for the

problem and solve for that interest rate. Interest rates are usually represented for a time

period: over what time period does this rate apply? What would the interest rate be if it

were a yearly rate?

Type your response here:

d. Now consider a different situation. Payday loans are a type of loan where you can get

money for a future paycheck, typically two weeks in advance. A typical payday loan

service might charge \$15 for a loan against a paycheck you will receive in two weeks. The

interest rate is 10% of the paycheck over that two-week period. Given this information,

which variables in the interest formula are known? Develop a formula that will solve for

the unknown variable.

Type your response here:

e. Solve for the value of the unknown variable.

Type your response here:

__________________________________________________________________________ Resources

Document any references you used for this project below. At minimum, include a title and

URL for any Internet resource: 3 Evaluation

Your teacher will use this rubric to evaluate the completeness of your work as well as the

clarity of thinking you exhibit.

Total Points: 10

Task 1: A Journey to Earth Task points: 5 a. Identifying known variables 1 b. Manipulating the formula to solve for the desired variable 1 c. Researching for variable amounts 1 d. Calculating time to reach Earth 1 e. Applying formula to a daredevil?s fall 1 Task 2: Interest in Finance Task points: 5 a. Identifying known variables 1 b. Manipulating the formula to solve for the desired variable 1 c. Determining yearly interest rate 1 d. Manipulating the formula for a new situation 1 e. Calculating a paycheck based on a payday loan interest

rate and interest amount 1 4

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