## Wednesday, August 18, 2010

The following lesson plan focuses on probability and the use of Excel spreadsheets to record data and display the data visually.

Essential Question: What is the real world probability of rolling certain outcomes with two dice?

Given two six sided dice, what is the probability of rolling the number 7 with the two dice? What is the probability of rolling 8? How do you know?

Lesson Steps:

1. In groups of either two or three students, roll a pair of dice 36 times and record the results on a sheet of paper.
2. Create a three column spreadsheet within Microsoft Excel. Column 1 should contain the numbers 2 through 12. Column 2 should contain the theoretical probability of rolling each number when rolling the two dice 36 times. Column 3 should contain the actual results when rolling the two dice 36 times.
3. Create a graph of your own choosing comparing the true mathematical probability with the actual results of the experiment.
4. Answer the following questions: Are the results the same or different? If different, why are they different? How would you expect the results to change when rolling the dice 10 times? 100 times? 1000 times? Why?

Ticket Out the Door:

1. The math of chance, as expressed in your lesson, is both accessible and interesting, and the steps will lead to its investigation. I would add a "hook" at the start - some sort of "natural" question before the math question. Dan Meyer talked about hooks yesterday, with illustrations: http://blog.mrmeyer.com/?p=7728

For example:
- If you win at 7 and your partner at 8, is the game fair?

2. Doug,
It is my feeling that the study of probability and statistics at the high school level does not receive sufficient emphasis. The only time we address this area of mathematics is when we are engaged in PSSA review. To do justice to the study of probability and statistics we need to at least develop a unit within the algebra 1 or 2 curriculum. I realize that some students do eventually have access to a probability and statistics course but for most of them this course is taken in the senior year after they have taken the PSSA exams. At any rate it is no wonder students do not gain sufficient understanding in this area when they really only get limited exposure to the material.
That point aside I have listed some web resources for your topic. Some of the interactive ones could be used as a learning center activity.
http://www.edcollins.com/backgammon/diceprob.htm
http://mathforum.org/library/drmath/view/56688.html
http://www.knowyourluck.com/dice2t.html
http://gwydir.demon.co.uk/jo/probability/dice.htm

3. Week 5- Probability
Response to Doug Snyder's probability assignment:
My suggestions for reducing anxiety in this assignment are as follows:
Step 1. As an introduction to this topic it may reduce student anxiety to show the real world connections to the concept of probability. Creating a "classroom casino" may engage students and lower their affective filters. Perhaps a field trip to Las Vegas may also help students and teachers to embrace this wonderful area of mathematics.
Step 2. The use of the spreadsheet in step 2 may prove problematic for some students. Here it may be necessary to spend extra time and energy to avoid undo math anxiety with this part of the lesson. Once again a group approach may help to allay any unwanted fears.
Step 3. The graphing section of the assignment (step 3) may also need to be clarified. Here it may be necessary to provide some examples for students as well as an explanation of the mathematical formulas that are needed.
An excellent article on the topic of math anxiety can be found at: