Category Archives: problem solving

Spreadsheets – Part 2

As a reminder, here’s the original project descriptor.

Here’s a report from one pair of students.

Mistakes made: Originally we had started out with a more expensive, brand new car. Our budget was about $100 a month to put towards a car, so it would have taken us 20 years to pay off the car, which is unreasonable. We had to downsize and settle for a less luxurious car, but one that still met almost all of our standards.

Assumptions:

      • 4 weeks is a month.
      • We have enough money saved for the down payment.
      • We take 10 years to pay off the loan
      • annual rate of 2.29% for loan

Mid-size Sedan

2. We have $100 left for a monthly car payment. Income- expenses. 3400-3300=100

3. Typically for a down-payment you would need about 11% of what the car is worth. So for our car that is worth $11,000 we have about $1,210 saved for the downpayment.

4. The requirements that our car has to meet are 4 door, 30 mpg, mid-size, seats 5.

5. We would want our car to have a working air conditioner, heat, sunroof and radio.

6. We decided to get a used Mazda6i Touring for $11,000 but with 10% off it would cost $9,900.

7. We would need to borrow $9,900 and we would get this money by taking out a loan with Bank of America.

8. (On Spreadsheet)

spreadsheet

9. Our dream car was originally a new fully equipped midsize sedan with a sunroof, but after we found that with our budget of $100 dollars a month, it would take 20 years to pay off. So we decided to get a used car. Mazda6 i Touring which still had air conditioning and heat but did not have a sunroof sadly. This car still meets most of our requirements and was much more affordable so we would be able to pay it off in 10 years.

10. Like we said in number 9, one of our problems before was a 20 year long loan. We fixed this problem by selecting a cheaper used car to buy. If the payment stays the same ($100) and the down payment is the same (11%) then the more expensive the car, the longer the duration of a loan.

https://www.google.com/search?q=Stretch+hummer+limo&rlz=1C1CHFA_enUS497US497&sugexp

11. Our dream car is a stretch hummer limo. The cost of this car brand new is $300,000 after the down payment of 11% costs $267,000. This car would be impossible for us to pay off because the interest that we would have to pay is more than we make monthly so the payment would keep increasing and we would never be able to pay it off.

12. To pay off our dream car in six years we would have to earn about $7320 a month. So subtracting expenses that leaves about $4025 a month to put into the dream car, which will pay it off in 72 months. Assuming that the interest rate and bargaining rate are the same.

What I like about this solution:

  • They stated their assumptions.
  • They made decisions.
  • They made adjustments.
  • They analyzed their results.
  • They dreamed big.
  • They used absolute addressing as part of their spreadsheet formulas.
  • They knew the difference between an annual interest rate and a monthly interest rate.
  • They understood that if their payment doesn’t even cover the monthly interest, they’ll never pay off the loan.

There were several solutions like this one. Not enough, though. Something to think about next year.

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Authentic Assessment?

My junior level math classes have begun working on a project called Buying a Car. For the past few classes we’ve been problem solving using spreadsheets. They’ve been working in teams, using Google spreadsheets to solve problems like this and this (which I adapted from our Core-Plus Mathematics text). My teaching colleague and I decided to jump into this spreadsheet mini-unit before our students had to turn in their laptops for the year. (We are a one-to-one school.)

Here are some pictures of my students hard at work.

photo7  photo6

photo3

photo2

Some things I heard as the students were working:

  • Oh, so the bank pays for the car and then you pay the bank. I get it now!
  • How much does gas cost right now?
  • Where’s the best place to get the loan from? What’s the lowest interest rate we can get?
  • Are we going to buy that truck? What’s the gas mileage on it?
  • How do we figure out the payment? What did we do before?
  • So we have to add the interest and then subtract the payment.
  • We can cut back on the money for entertainment. We can be cheap. There’s only two of us, we don’t need that much food. It’s not like we’re feeding any children.
  • How do we determine how much for a downpayment?
  • Can we afford a monthly payment of $875?

Here’s what I really like about this assessment (having never done it before):

  • There is a high degree of choice.
  • There isn’t a definitive solution.
  • Students have to make (and state) some assumptions in order to solve the problem.
  • They have to think about lots of things that go into a household budget and buying a car.
  • Students working together and helping each other to succeed.

What I’m not so sure about:

  • The quality of their results.
  • If they’ll really apply what they’ve learned during the past 4 classes learning about spreadsheets.
  • How much understanding they’ll walk away with.

It will be interesting to see what they produce as a result.

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