Data and Dollars

Grade 8 Mathematics: TEKS Reporting Category 4

Scatterplots & Personal Finance

The Investigation Mission

Data Analysis

Construct and interpret scatterplots (TEKS 8.11A/B)
Use trend lines to make predictions (TEKS 8.5D)

Personal Finance

Compare simple and compound interest (TEKS 8.12D)
Analyze loans, savings, and budgeting (TEKS 8.12A-G)

Finding the Pattern

Positive Association

As \(x\) increases, \(y\) increases. They move in the same direction!

Negative Association

As \(x\) increases, \(y\) decreases. They move in opposite directions.

No Association

There is no clear pattern or relationship between the variables.

Trend Lines

A **trend line** (or line of best fit) is a straight line that comes as close as possible to all data points in a scatterplot.

1

About half the points should be above the line, and half below.

2

The line should follow the general direction of the data.

Trend Line in Action

Predicting the Future

If a trend line for "Hours Studied vs. Test Score" is \(y = 5x + 60\)...

Scenario:

"Predict the score of a student who studies for 6 hours."

\(y = 5(6) + 60\)

\(y = 30 + 60 = 90\)

Score: 90

Prediction Success

The Wealth Wizards Toolkit

Managing your money is about understanding how it grows (Savings) and what it costs to use someone else's (Loans).

Saving

Delayed gratification for a better future.

Interest

The price of "renting" money.

Loans

Borrowing money to pay back with interest.

Credit

Borrowing power based on your history.

Simple Interest

"Calculated only on the initial amount (principal)."

\(I = Prt\)

\(I\) = Interest Earned

\(P\) = Principal (Start)

\(r\) = Rate (as decimal)

\(t\) = Time (in years)

Wealth Check

You invest $1,000 at 5% simple interest for 3 years.

\(I = 1,000 \times 0.05 \times 3\)

\(I = 50 \times 3\)

\(I = \$150\)

Total Value: $1,150

Compound Challenge

The same $1,000 at 5% compound interest for 3 years.

\(A = 1,000(1 + 0.05)^3\)

\(A = 1,000(1.05)^3\)

\(A = 1,000(1.157625)\)

\(A = \$1,157.63\)

Interest Earned: $157.63

Compound Interest

"Interest on the interest!"

\(A = P(1 + r)^t\)

\(A\) = Total Account Balance

\(P\) = Principal (Start)

\(r\) = Rate (as decimal)

\(t\) = Time (in years)

The Growth Gap

Year	Simple Value ($1,000)	Compound Value ($1,000)	Difference
0	$1,000	$1,000	$0.00
1	$1,050	$1,050	$0.00
2	$1,100	$1,102.50	$2.50
5	$1,250	$1,276.28	$26.28
10	$1,500	$1,628.89	$128.89

The Cost of Credit

Interest Paid

When you borrow, interest is an **expense**. You pay back more than you borrowed.

Monthly Payments

Total Loan Cost \(\div\) Number of Months.

Reality Check: Auto Loan

Borrow: **$10,000**

Interest Rate: **6% Simple**

Term: **5 Years**

Total Interest: $3,000

Total Cost: $13,000

Monthly Payment: $216.67

Investigation Closed

Scan

Look for trends and associations in data.

Sketch

Draw trend lines to reveal the hidden path.

Save

Use the power of compound interest to build wealth.

Are you ready for the STAAR?

Data and Dollars

Data and Dollars Slides

Data and Dollars Teacher Guide

Data and Dollars Student Packet

Data and Dollars STAAR Challenge

Data and Dollars Solutions Guide

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