Mathematical Model of Coin Flips

Descriptors: coin toss, probability, theoretical probability, spinner, Maththematics, mathematical model

Title of resource: Spreadsheet Model of a Coin Toss or Binary Spinner

Author: Bob Sargent

Purpose: Enrichment of probability unit in MathThematics Book 2 demonstrating a mathematical model.

Audience: students grades 7-10

Resource Requirements: I have attached an excel spreadsheet.  You will need a compatible application.

Abstract:

Simulating coin tosses is a classic example of an educational computer program modeling an event.  The attached spreadsheet graphs simulated trials of some sort of 50/50 binary event, a coin flip or a spinner with two equal sides, using the random function.  I am not suggesting that students should not flip real coins or spin real spinners.  The lesson is about the mathematical model.  The question the students must answer is this; “In what ways does the model behave like what is being modeled, and how is it different?”  The lesson assumes the students already know about probability.  The model does not look like a coin flip or a spinner, yet it yields a similar table of results.  Getting students to articulate this, and elaborate on it, is the hoped for outcome of the lesson.  By repeatedly recalculating the spreadsheet (pressing F9 in Excel) it is possible to have many trials in rapid succession.  By comparing the graphs of 10 coins to the graphs of 100 coins in this way one can see that 100 coins more closely approximate the expected result of 50/50 more often than do 10 coins.  This is a graphic way to get at this idea.

Justification:

Mathematical modeling is one of the Vermont Standards that can be difficult to convey to students.  The spreadsheet is part of an enrichment exercise using a simple model of a simple event to illustrate the idea of mathematical modeling.  The spreadsheet could be part of a station among a group of stations in a unit on probability.  Coin flips and spinners is part of the curriculum in MathThematics, Book 2.  Probability and modeling are Vermont Standards.