NCTM 2012 Presentation 1

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This document describes resources for teaching algebra concepts using the TI-Nspire calculator. It focuses on a DVD library titled "Algebra Applications" that contains 10 volumes addressing topics like linear functions, quadratic functions, and systems of equations. One application examines the 2008 housing crisis by modeling different mortgage scenarios, constructing an amortization table, and exploring how the loan balance changes with each payment of principal and interest over time. Graphs and calculations on the TI-Nspire are demonstrated to analyze mortgage data and better understand the factors that contributed to the crisis.

Economy & Finance Business

Algebra Resources for the TN-Nspire

Media4Math includes a variety of free and
premium resources, including short video
tutorials on the Nspire, Math in the News, and
other tutorials.

Algebra Resources for the TN-Nspire

In this presentation we will focus on our DVD
Library, Algebra Applications.

Algebra Resources for the TN-Nspire

Volume 1 Volume 2

1. Linear Functions 6. Functions and

2. Quadratic Functions Relations

3. Variables and 7. Exponential Functions

Equations 8. Logarithmic Functions

4. Inequalities 9. Rational Functions

5. Data Analysis 10. Systems of Equations

Algebra Resources for the TN-Nspire

Algebra Applications: Data Analysis focuses on
the housing crisis of 2008.

Algebra Resources for the TN-Nspire

The impact of the housing crisis was a steep drop
in the stock market.

Algebra Resources for the TN-Nspire

The value of houses on the market began to go
down and some had trouble keeping up with
suddenly higher mortgage payments.

Algebra Resources for the TN-Nspire

As a result, the number of foreclosures began to
increase dramatically.

Algebra Resources for the TN-Nspire

To get a better understanding of the housing
crisis, we start with what a mortgage is.

Algebra Resources for the TN-Nspire

We use the TI-Nspire to explore different
mortgage scenarios and also construct an
amortization table.

Algebra Resources for the TN-Nspire

We start by opening a Spreadsheet window and
labeling three cells for the loan amount, the
interest rate, and the total number of payments.

Algebra Resources for the TN-Nspire

We input the values shown, and we use the
Nspire’s Time Value of Money function to
calculate the mortgage amount.

Algebra Resources for the TN-Nspire

The TVMPMT function takes six values: the
number of payments, interest, loan amount,
future value, and payments and compoundings
per year.

Algebra Resources for the TN-Nspire

The future value is set to zero since
we’re calculating full repayment of
the loan.

Algebra Resources for the TN-Nspire

The result is the monthly mortgage
payment, set as a negative value.

Algebra Resources for the TN-Nspire

We can now calculate the full value
of the loan, principal plus all interest
payments.

Algebra Resources for the TN-Nspire

So, for this mortgage the loan
repayment is nearly twice the value
of the original loan amount.

Algebra Resources for the TN-Nspire

Why is the repayment so much more
than the original loan amount? Each
payment is used to pay interest and
pincipal.

Algebra Resources for the TN-Nspire

So, let’s add a new column to the
spreadsheet to track how the balance
on the loan changes with each
payment.

Algebra Resources for the TN-Nspire

The Current Loan Balance is made up
of these three values.

Algebra Resources for the TN-Nspire

Use this formula to calculate the
Current Loan Balance.

Algebra Resources for the TN-Nspire

The varying balances can be
calculated using the Generate
Sequence feature.

Algebra Resources for the TN-Nspire

U(n-1)*(1+B2/100/12)+B4

Use this Generate Sequence Formula
for Column C.

Algebra Resources for the TN-Nspire

Fill out the Generate Sequence
dialogue box.

Algebra Resources for the TN-Nspire

Column C now has all the Current
Balance amounts for payments 1
through 360.

Algebra Resources for the TN-Nspire

Knowing what the Current Balance is,
we can calculate how much of each
monthly payment is interest only.

Algebra Resources for the TN-Nspire

Use a column-level formula to find the
percentage of the Current Balance is
interest only.

Algebra Resources for the TN-Nspire

Column D shows the amount of the
mortgage payment made up of
interest only. At the start of the loan,
it’s mostly interest.

Algebra Resources for the TN-Nspire

We can now also calculate the
amount of each mortgage payment
that goes to the principal.

Algebra Resources for the TN-Nspire

Creating a Principal-vs.-Interest
scatterplot reveals an interesting
pattern.

Algebra Resources for the TN-Nspire

Let lables “principal” and “interest”
are based on the Spreadsheet column
headings.

Algebra Resources for the TN-Nspire

To see al lof the graph, don’t forget to
change the Window settings to Zoom
Data.

Algebra Resources for the TN-Nspire

This is the graph of Principal vs.
Interest throughout the life of the
loan.

Algebra Resources for the TN-Nspire

Finally, we can calculate the Equity,
as the loan is gradually repaid.

Algebra Resources for the TN-Nspire

Total Equity is found using this
formula. But in 2008, the “increase in
value of the house” was a decrease.

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NCTM 2012 Presentation 1

2. Algebra Resources for the TN-Nspire Media4Math includes a variety of free and premium resources, including short video tutorials on the Nspire, Math in the News, and other tutorials.

3. Algebra Resources for the TN-Nspire In this presentation we will focus on our DVD Library, Algebra Applications.

4. Algebra Resources for the TN-Nspire Volume 1 Volume 2 1. Linear Functions 6. Functions and 2. Quadratic Functions Relations 3. Variables and 7. Exponential Functions Equations 8. Logarithmic Functions 4. Inequalities 9. Rational Functions 5. Data Analysis 10. Systems of Equations

5. Algebra Resources for the TN-Nspire Algebra Applications: Data Analysis focuses on the housing crisis of 2008.

6. Algebra Resources for the TN-Nspire The impact of the housing crisis was a steep drop in the stock market.

7. Algebra Resources for the TN-Nspire The value of houses on the market began to go down and some had trouble keeping up with suddenly higher mortgage payments.

8. Algebra Resources for the TN-Nspire As a result, the number of foreclosures began to increase dramatically.

9. Algebra Resources for the TN-Nspire To get a better understanding of the housing crisis, we start with what a mortgage is.

10. Algebra Resources for the TN-Nspire We use the TI-Nspire to explore different mortgage scenarios and also construct an amortization table.

11. Algebra Resources for the TN-Nspire We start by opening a Spreadsheet window and labeling three cells for the loan amount, the interest rate, and the total number of payments.

12. Algebra Resources for the TN-Nspire We input the values shown, and we use the Nspire’s Time Value of Money function to calculate the mortgage amount.

13. Algebra Resources for the TN-Nspire The TVMPMT function takes six values: the number of payments, interest, loan amount, future value, and payments and compoundings per year.

14. Algebra Resources for the TN-Nspire The future value is set to zero since we’re calculating full repayment of the loan.

15. Algebra Resources for the TN-Nspire The result is the monthly mortgage payment, set as a negative value.

16. Algebra Resources for the TN-Nspire We can now calculate the full value of the loan, principal plus all interest payments.

17. Algebra Resources for the TN-Nspire So, for this mortgage the loan repayment is nearly twice the value of the original loan amount.

18. Algebra Resources for the TN-Nspire Why is the repayment so much more than the original loan amount? Each payment is used to pay interest and pincipal.

19. Algebra Resources for the TN-Nspire So, let’s add a new column to the spreadsheet to track how the balance on the loan changes with each payment.

20. Algebra Resources for the TN-Nspire The Current Loan Balance is made up of these three values.

21. Algebra Resources for the TN-Nspire Use this formula to calculate the Current Loan Balance.

22. Algebra Resources for the TN-Nspire The varying balances can be calculated using the Generate Sequence feature.

23. Algebra Resources for the TN-Nspire U(n-1)*(1+B2/100/12)+B4 Use this Generate Sequence Formula for Column C.

24. Algebra Resources for the TN-Nspire Fill out the Generate Sequence dialogue box.

25. Algebra Resources for the TN-Nspire Column C now has all the Current Balance amounts for payments 1 through 360.

26. Algebra Resources for the TN-Nspire Knowing what the Current Balance is, we can calculate how much of each monthly payment is interest only.

27. Algebra Resources for the TN-Nspire Use a column-level formula to find the percentage of the Current Balance is interest only.

28. Algebra Resources for the TN-Nspire Column D shows the amount of the mortgage payment made up of interest only. At the start of the loan, it’s mostly interest.

29. Algebra Resources for the TN-Nspire We can now also calculate the amount of each mortgage payment that goes to the principal.

30. Algebra Resources for the TN-Nspire Creating a Principal-vs.-Interest scatterplot reveals an interesting pattern.

31. Algebra Resources for the TN-Nspire Let lables “principal” and “interest” are based on the Spreadsheet column headings.

32. Algebra Resources for the TN-Nspire To see al lof the graph, don’t forget to change the Window settings to Zoom Data.

33. Algebra Resources for the TN-Nspire This is the graph of Principal vs. Interest throughout the life of the loan.

34. Algebra Resources for the TN-Nspire Finally, we can calculate the Equity, as the loan is gradually repaid.

35. Algebra Resources for the TN-Nspire Total Equity is found using this formula. But in 2008, the “increase in value of the house” was a decrease.

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