Superlesson
Project 1-1
Algebra
Chapter 1, Data and Relationships
Cars, credit cards, banking,... all of these areas can be
confusing for adults. How can you find the best financial deals
as you begin paying for your own purchases? Is credit a good
way to pay for goods and services? Let's investigate using the
Internet and mathematics!
Part A, Interpreting Graphs of Data
1. Decide whether to get a new or used car by looking at the
Which is better: new or used? Web site. Use the default values
which should be set to:
Age of used vehicle: 3 years
Price of new vehicle: $15,000
Future depreciation: Average
Hit the "Calculate" button.
|
New |
Used |
|
| Interest rate (%) |
8 |
10 |
| Loan term (months) |
24 |
24 |
| Down payment ($) |
2,000 |
2,000 |
| Years you own car |
4 |
4 |
| Maintenance costs ($/month) |
30 |
120 |
a. Scroll down and look at the line graph titled "Yearly Cost." Why does the average yearly cost of owning a new vehicle decrease sharply during the first 2 years?
b. What can you tell about the yearly cost of the new and used vehicles after you have owned them for 10 years?
c. Go back to the data box given in a and change the loan term to 5 years. Explain what happens to the graph titled "Yearly Cost."
Hint: Remember to translate years into months.
2. Think about how long it will be before you will have paid off the cost of the car.
a. If you can pay off your car within a few years, will it be cheaper for you to get a new car or a used car?
b. If it will take you more than just a few years to pay off your car, will it be cheaper for you to get a new car or a used car?
Part B, Adding with Integers and Matrices
3. Different credit cards charge different rates of interest and annual fees. To help you decide which factors matter the most, look at the credit card page of the Financial calculator Web site.
a. Use the default values, which should be set to:
Amount Owed Now: $5000
Future Monthly Charges: $275
Future Monthly Payments: $350
Annual Rate: 17%
Annual Fee: $25Scroll down and look at the "Schedule of Payments." Write the first six months as a matrix with the headings Balance Owed, Monthly Purchase, Monthly Payments, Interest and Fees, and Cumulative Interest and Fees. Label your work Matrix A.
b. What is the dimension of Matrix A?
4. Change the interest rate to 6% and hit "Calculate."
a. Now look at the "Schedule of Payments" and write the data for the first 6 months as a matrix with the same headings you used for Matrix A. This time, label your work Matrix B.
b. What is the dimension of Matrix B?
5. Compare Matrices A and B
a. Calculate the Matrix A - B and label it.
b. Explain what Matrix A - B represents.
c. What is the dimension of Matrix A - B?
6. Notice that the dimensions of the matrices in 5, 6, and 7 are all the same. Must this always be the case to add or subtract? Explain.
Part C, Multiplying with Integers and Matrices
7. The nation's money is not always worth exactly the same amount. Compared with the money of other nations, the dollar may be worth more or less.
a. Suppose the U.S. dollar were devalued so that $10 would be worth only $1. How would the devaluation affect the numbers in Matrix A?
b. Write a problem showing how multiplying your matrix by a scalar would account for this devaluation.
c. Find the answer to the problem you wrote in b.
Part D, Measures of Central Tendency
8. Work with a partner to examine the mathematics of the Coin flipping Web site.
a. Flip a coin 10 times for each trial. (You will each have 100 flips.) In the chart, record the number of "tails" for each trial.
Game 1
TRIALS1
2
3
4
5
6
7
8
9
10
Total
You Partner
b. Find the mean, median, and mode for both your scores and your partner's scores.c. Explain which measure of central tendency best reflects your average coin-flipping score.
Part E, Making Connections
9. Work with a partner and the Coin flipping Web site for 10 more flipping trials. Record your scores on a new chart.
|
Game 2 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
Total |
| You | |||||||||||
| Partner |
a. Make a matrix of your first 10 trials from 8a (Game 1).
b. Make a matrix of your second 10 trials from 9 (Game 2).
10. Create a new matrix showing your scores from Game 2 minus your scores from Game 1.
a. Explain what a number of +2 in the eleventh column would indicate.
b. What would a number of 0 in the eleventh column indicate?
c. What would a number of -2 in the eleventh column indicate?
11. Look at the information gathered from the second game you and your partner played.
a. What type of graph could be drawn from this data? Explain.
b. Explain how you could represent both games on the same graph.