Table of Contents:
- Overview
- Objectives
- Materials and/or Software Required
- Prerequisites
- Module Description
- National Standards Addressed
- Assessment Techniques
- Areas of Focus
- Appropriate Grade Level(s)
- Relevant Links and Related Resources
Overview:
Students in High School PreAlgebra and Algebra I participated in a Lab Exercise to determine Probability. Students also are able to build a visualization in Excel. Students engage in discussions pertaining to the logic and reasoning behind several games of chance.
Objectives:
Students will learn, discover and explore probability, odds and size of sample spaces.
Students will use logic and reasoning to make deductions concerning games of chance.
Students will use technology to build graphs in Excel.
Materials:
Computer Lab equipped with Excel
Prerequisites:
Some basic knowledge of java applets.
Some basic knowledge of Excel.
Discussion of Probability and Odds.
Module Description:
Students went to computer lab and were directed to open the web site for the java applet "Web Dice". Students rolled the dice 50 times each. While the students were rolling the dice, they were also instructed to open Excel simultaneously. They recorded each roll into the spreadsheet. They made charts with columns numbered 2 through 12 for the possible outcomes from rolling the 2 dice. After they were finished rolling and recording their data, they were instructed to build their graphs. After discussing what the graphs meant, students were then instructed to enter into their spreadsheet the entire sample space of the class, which was 1200 rolls. After discussing the new graphs, students were instructed to enter the true probability ratios into their graphs. The class then discussed why the larger the sample space, the closer the graph is to the true probability ratios. The entire exercise was then duplicated for odds. Discussion then ensued over the differences between probability and odds.
National Standards Addressed:
Develop an understanding of permutations and combinations as counting techniques.
Compute fluently and make reasonable estimates Develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.
Judge the reasonableness of numerical computations and their results.
Understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions.Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations.
Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases.
Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.
Draw reasonable conclusions about a situation being modeled.
Approximate and interpret rates of change from graphical and numerical data.
Make decisions about units and scales that are appropriate for problem situations involving measurement.
Use unit analysis to check measurement computations.
Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each.
Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments.
Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable. Understand histograms, parallel box plots, and scatterplots and use them to display data
for univariate measurement data, be able to display the distribution, describe its shape, and select and calculate summary statistics.
Use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions.
Understand the concepts of sample space and probability distribution and construct sample spaces and distributions in simple cases.
Apply and adapt a variety of appropriate strategies to solve problems.
Monitor and reflect on the process of mathematical problem solving.
Make and investigate mathematical conjectures. Create and use representations to organize, record, and communicate mathematical ideas.
Select, apply, and translate among mathematical representations to solve problems.
Use representations to model and interpret physical, social, and mathematical phenomena.
Assessment Techniques:
Students are graded on their individual graphs that are printed out and tested over their knowledge of Probability and Odds.
Areas of Focus:
PreAlgebraAlgebra I
Appropriate Grade Level(s):
6th - 12th
Relevant Links and Related Resources:
http://www.mste.uiuc.edu/activity/webdice.html
