Unit 4. Data Acquisition
Revision Date: Feb 04, 2017 (Version 2.1)Summary
Students will formulate a hypothesis, run simulations, and analyze the results to determine what needs to be modified in their hypothesis and/or the simulation itself.
Outcomes
Overview
Source
The coin flipping extension is based on a CS10K lesson: https://sites.google.com/site/mobilecsp/lesson-plans/lp-coinflip-miniprojects
Students will be able to:
Student computer usage for this lesson is: required
The PowerPoint "Using Data and Simulations" can be found in the Lesson Resources folder.
Penny Bias article to go with lesson extension: http://mathtourist.blogspot.com/2011/02/penny-bias.html
For the Monty Hall Problem extension:
Online simulation of the problem: http://math.ucsd.edu/~crypto/cgi-bin/MontyKnows/monty2?1+17427
There are several videos on YouTube demonstrating and explaining the Monty Hall Problem.
An animated video: https://www.youtube.com/watch?v=mhlc7peGlGg length is 5:48
Live action video: https://www.youtube.com/watch?v=4Lb-6rxZxx0 length is 5:30
There is sample code for the die Python program in the Lesson Resources Folder called 4-3 Sample Code.py
Journal:
Have students share their answers with the class.
import random
at the top of the coderandom.randint(min,max)
returns a 'random' integer between the min and max values (inclusive).Ask the class: What are the advantages/disadvantages of using a program vs. actual dice? How quickly can the computer generate thousands of test cases? Can the computer be used to analyze the test cases as well as to generate the random numbers?
Journal: Summarize how a program can be used as a simulation to test a hypothesis.
Students can be provided with the code for a function to simulate rolling one die and use it to develop the rest of the program.
After the first group activity, the teacher can swap a student from each group to allow different input into the next group activity.
This extension is based on advanced mini project # 4, which can be found here: https://docs.google.com/a/smcps.org/document/d/1AKHpiQ87bE4W1YzHlAFh2uNAHuEtdMOCQVV6HfxfDzc/edit
Students read an article about the 'randomness' of flipping a penny: http://mathtourist.blogspot.com/2011/02/penny-bias.html
Next, students should hypothesize the results of lining up 10 pennies on edge and knocking them over (as described in the article). Students need to determine how many times to run the experiment, collect data, and analyze the results.
Students should work in pairs to write a computer simulation for the penny experiment. (Note: this is a program based on experimental data, not theoretical.)
Discuss as a class the validity of the simulation written. Can this simulation be used for other coins?
In the game show "Let's Make a Deal", the original host was Monty Hall. Onvery show, Monty would present a player with three doors or curtains to choose from. The contestant was asked to choose a door in search of a prize. After making a selection, Monty Hall would open one of the doors not selected by the contestant to reveal a non-prize (perhaps a goat). Then Monty would ask if the contestant wanted to change their choice.
After explaining the show to the class ask, "Should the contestant change?" Students should propose a hypothesis.
Have the students design a simulation to test their hypothesis (discuss what is the data collected and the number of times the simulation should run to collect data). After running the simulation, students should evaluate their hypothesis and determine whether it needs to be modified or whether the simulation needs to be modified.
If Monty Hall had four doors, what should the contestant do?
What should the contestant do if they know that Monty does not know what is behind each door?
Online simulation of the problem: http://www.math.ucsd.edu/~crypto/Monty/monty.html
There are several videos on YouTube demonstrating and explaining the Monty Hall Problem.
An animated video: https://www.youtube.com/watch?v=mhlc7peGlGg length is 5:48
Live action video: https://www.youtube.com/watch?v=4Lb-6rxZxx0 length is 5:30
Review student journal entries and class discussions to determine students' understanding of simulations, a hypothesis, and the ability to determine a method to test a hypothesis.
Describe an algorithm to simulate drawing an ace of any suit from a standard deck of cards.
Make a hypothesis about drawing cards from a standard deck of cards and determine how to collect data to answer your hypothesis.