Green 7 - Simulation Models

I. Essential Purpose: In this unit students confront some common misconceptions about probabilistic events including likelihood of same-gender children in a family and rolling doubles. Students construct simulations to model problems, create and interpret frequency tables and probability distributions, and design experiments to investigate the Law of Large Numbers.

II. State/Local Standards: 2.1.8 A Represent and use numbers in equivalent forms.
2.4.8 F Use measurements and statistics to quantify issues.
2.5.8 A Invent, select, use and justify the appropriate methods, materials and strategies to solve \ problems.
2.6.8 F Use graphing calculators to organize and analyze data.
2.7.8 B Present the results of an experiment using tables, charts, graphs.
2.7.8 C Analyze predictions.
2.7.8 D Compare and contrast results from observations and mathematical models.
2.7.8 E Make valid inferences, predictions, and arguments based on probability.

III. Essential Questions: Why is it important to challenge and/or confirm assumptions that we make about random events?
How can mathematics help me to challenge and/or confirm assumptions about random events?

V. Essential Content: 1. Write an organized procedure to simulate random events.
2. Define random integers.
3. Create histograms and frequency tables of experimental data by hand and with graphing calculators.
4. Conduct and record results of a valid experiment to gather data for random events.
5. Compute probability as a decimal, percent, and fraction.

VI. Essential Skills

Lesson 1 (One Investigation): Simulating Chance Situations

Students will be able to write a simulation of situations where the probability of a success is 0.5.
Students will be able to display experimental results of a simulation in a frequency table and histogram.
Students will be able to estimate shape, center, and spread of their outcomes from the histogram.
Students will be able to generalize results of large numbers of trials in a simulation.

Lesson 2 (Two Investigations): Estimating Expected Values and Probabilities

Students will be able to use single random digits to simulate probabilistic situations where the probability of a success is other than 0.5.
Students will be able to use the random digits generator feature of the graphing calculator.
Students will be able to create, conduct, and analyze a simulation of the collector’s problem.
Students will be able to identify and analyze the binomial distribution.
Students will be able to compare shapes of probability distributions.

Lesson 3 (One Investigation): Simulations and the Law of Large Numbers

Students will be able to use paired random digits to simulate probabilistic situatins.
Students will be able to describe the Law of Large Numbers in context of a play-off system.
Students will be able to create and explain simulations to model binomial distributions.

VII. Resources

Teaching Strategies

VIII. Summative Assessment/Performance Task: Assessments

Benchmarks (Not scanned)

Benchmark 1

Benchmark 2

Benchmark 3

Benchmark 4