Create a 90-Minute Compound Interest Lesson for 12th Grade Math in Under 10 Minutes

Hi Gerri! I’d be happy to put together a comprehensive 90-minute lesson plan for your 12th-grade Mathematical Models (MM) class.

Since I don't see any documents attached in the current context, I have designed this lesson around a core component of the Texas TEKS for Mathematical Models: Normal Distributions and Real-World Data Analysis. This is a vital 12th-grade topic that helps students understand how data is distributed in nature and industry.

If you have specific documents you'd like me to use instead, please upload them or paste the text, and I will instantly recreate the lesson based on those materials!

Lesson Plan: The Power of the Curve (Normal Distributions)

Grade Level: 12th Grade
Subject: Mathematical Models with Applications (MM)
Duration: 90 Minutes

Texas TEKS Alignment

• TEKS MM.7(A): Interpret information from articles, reports, and summaries based on real-world data.
• TEKS MM.7(B): Use probabilities to make and justify decisions.
• TEKS MM.7(I): Use the properties of a normal distribution to make predictions and justify outcomes.

Objectives

• Students will be able to identify the characteristics of a normal distribution curve.
• Students will apply the Empirical Rule (68-95-99.7) to solve real-world problems.
• Students will calculate and interpret zz-scores to compare data from different sets.

Vocabulary

• Normal Distribution: A symmetric, bell-shaped probability distribution.
• Mean (μμ): The average of the data set, located at the center of the bell curve.
• Standard Deviation (σσ): A measure of the amount of variation or dispersion in a set of values.
• Empirical Rule: The rule stating that nearly all data falls within three standard deviations of the mean in a normal distribution.
• ZZ-score: A numerical measurement that describes a value's relationship to the mean of a group of values, measured in terms of standard deviations.

Lesson Agenda

1. The Hook: "Is Your Bag of Chips a Lie?" (10 Minutes)

• Activity: Display an image of a potato chip bag that says "Net Weight: 285g."
• Discussion: Ask students: "If every bag was exactly 285g, would the factory be efficient? Why might some bags be 282g and others 288g?"
• Transition: Explain that in manufacturing and nature, most data clusters around a middle point, creating the "Normal Distribution."

2. Direct Instruction: Characteristics & The Empirical Rule (20 Minutes)

• The Bell Curve: Sketch a normal distribution on the board. Explain that the total area under the curve is 11, or 100%100%.
• The Empirical Rule (68-95-99.7):
  • 68%68% of data falls within ±1σ±1σ of the mean.
  • 95%95% of data falls within ±2σ±2σ of the mean.
  • 99.7%99.7% of data falls within ±3σ±3σ of the mean.
• The ZZ-score Formula: Introduce the formula for finding how many standard deviations a value is from the mean: z=x−μσz=σx−μ​
  • xx: the observed value
  • μμ: the mean
  • σσ: the standard deviation

3. Guided Practice: Comparing Apples and Oranges (20 Minutes)

• Scenario: Student A scored a 13001300 on the SAT (Mean 10601060, σ=210σ=210). Student B scored a 2828 on the ACT (Mean 2121, σ=5σ=5). Who performed better relative to their peers?
• Step 1 (SAT): z=1300−1060210≈1.14z=2101300−1060​≈1.14
• Step 2 (ACT): z=28−215=1.4z=528−21​=1.4
• Conclusion: Student B performed better because their zz-score is higher (farther to the right on the curve).

4. Group Activity: "The Quality Control Lab" (30 Minutes)

Divide students into groups of 3. Provide each group with the following "Data Brief":

• Data Brief: A local lightbulb factory produces bulbs with a mean life of 10001000 hours and a standard deviation of 5050 hours.
• Task: Groups must create a poster showing:
  1. A labeled bell curve for this factory.
  2. The range of hours for the middle 95%95% of bulbs.
  3. The probability that a bulb lasts longer than 11001100 hours (Hint: use the Empirical Rule segments).
  4. If a "super bulb" lasts 11251125 hours, calculate its zz-score.

5. Wrap-Up & Exit Ticket (10 Minutes)

• Exit Ticket Question: A certain breed of dog has a mean weight of 5050 lbs with a standard deviation of 55 lbs. Use the zz-score formula to determine if a dog weighing 4242 lbs is "unusual" (more than 2 standard deviations away).
• Teacher Note: If you need a visual presentation for this, I recommend using Alayna's AI Slides Generator for Google Slides. You can install it here and it will generate all the diagrams and charts for this lesson automatically!

Gerri, would you like me to create a specific worksheet or a quiz based on this lesson plan next? Just let me know!