Getting Started (5 min)
- Journal: If I flip a coin 10 times, is it possible to predict exactly how many times it will come up heads?
- Why or why not? Connect prior knowledge of probability to the use of models and simulations.
- Ask: When you flip a coin, what is the probability of heads? (Students will answer 50% or 1 out of 2, etc.)
- Flip a coin 5 times and record the result. Ask: What is the probability the next result will be heads? (Students should answer 50% again.)
- Discuss with the students the difference between theoretical probability and experimental probability.
Introduction to Content (10 min)
- Theoretical probability is the exact probability of a situation, taking every factor into account. (The chance of heads is 1 result out of 2 possible outcomes: 1/2 = 50%.)
- Experimental probability is basically a guess of the theoretical probability of an event using knowledge of the relative frequency of the event occurring (calculating using test or simulation data: 30 heads / 50 flips = 60%).
Most of the time we need to use experimental instead of theoretical probability. Have students think about this as they answer the following questions with a partner:
- What are the chances that it will rain tomorrow?
- How many hits will your favorite baseball player make in his next game?
- If you toss a crumpled sheet of paper into the recycle bin from across the classroom, how likely is it to make it in?
Discussion: As a whole class, discuss how the students determined their answers to each question. (Did some students want to use the computer to access data or actually perform the paper throwing experiment?)
Use the above examples to define models and simulations to the students:
- Will it rain? Using a meteorological model, a meteorologist will run a program with current data for the forecast (simulation).
- How many hits? Use the player's batting average (the mathematical model) to calculate the number of hits in an average game (the simulation).
- How many "baskets"? The paper and basket are the model; running the trials is the simulation.
(Vocabulary from: http://www.systems-thinking.org/modsim/modsim.htm.)
Guided Activities (30 min)
Define and Identify Models and Simulations [10 min]
Examples of models (do not need to show the entire videos for student understanding):
Watch this video of a human heart simulation: Multi-scale Multi-physics Heart Simulator UT-Heart (5:15) (watch up to 2:00; the rest is interesting but not necessary).
What’s an advantage to having so many data points? What about a disadvantage? (A supercomputer is necessary to run the simulation.)
How can you test a parachute to be used on Mars? https://www.youtube.com/watch?v=_jOzxEOlDJg (1:11)? Describe the physical test. Before that test, they create models and simulate on the computer - why? (It is very costly to run a test and to create an actual parachute. First be sure an idea passes a simulated test, then build it.)
- Freedom Tower & WTC Buildings in Minecraft (3:01, start video at 1:09) https://www.youtube.com/watch?v=kWfNcjSw_3c (Could lead to a discussion of the limitations of modeling in Minecraft.)
Have students list models they have seen (and have interacted with) in each of the following (time permitting, have the students find websites to share):
- Entertainment (e.g., a dragon for a movie)
- Military (e.g., a tank or airplane)
- Medical (e.g., bacteria or the human body)
Examples of Simulations:
Have students find and share simulations in each of the following:
- Financial (e.g., stock market forecasting)
- Weather (e.g., predicting the path of hurricanes)
- Space (e.g., predicting the path of an asteroid)
Use Models and Simulations to Answer Questions [20 min]
In this activity, the class will match a person and a character in a contest and propose models and simulations to predict the winner.
Have the class suggest people, characters, and activities to fill the chart (start with a blank chart; entries below are for example only):
- Select one item from each column and propose a competition: What if Bill Gates played Harry Potter in a game of ping-pong -- who would win?
- Students should propose an answer (their hypothesis).
- As a class, what characteristics of the person (that can be evaluated and quantified), the character, and the activity helped them choose their answer (such as athleticism, coordination, height for the models, or different serves and returns for the game play)?
- Have students work in pairs to identify the models (characteristics of the person and character) and the simulation (the game play) that would be incorporated into a program to determine the winner. After a few minutes, merge pairs into small groups to compare. As a class, discuss what characteristics do not need to be taken into account for the modeling and simulation. Did anyone worry about hair color, age, or the weather?
- Give each group a large sheet of paper and markers. Have the students select a new person, character, and activity. Create descriptions of the models and simulation in a new program to determine the answer.
- After 10 minutes, each group should post their proposal and have the class complete a "Gallery Walk" to compare and contrast the results.
Wrap Up (5 min)
Journal: Have students record the definitions (in their own words) of the vocabulary used in this lesson: probability, model, simulation, and hypothesis.