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Probability Student Task

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?

Please Do Now:

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:

- In groups of either two or three students, roll a pair of dice 36 times and record the results on a sheet of paper.
- 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.
- Create a graph of your own choosing comparing the true mathematical probability with the actual results of the experiment.
- 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:

Submit your results, your graph, and your analysis (Question 4 above) for grading.

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

ReplyDeleteFor example:

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

Doug,

ReplyDeleteIt 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

Week 5- Probability

ReplyDeleteResponse 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:

http://www.mathacademy.com/pr/minitext/anxiety/

Bob -

ReplyDeleteGood thoughts here. I have often found that putting students in appropriate groupings is (sometimes) a good way to get them engaged in a project. Sometimes it gets them engaged in chatting with their friends :-)

Doug

Probability- Math Sophistication 7.2

ReplyDeleteThe study of probability requires a solid understanding of numbers and counting principles. For students to comprehend the ideas that form the basis of the study of probability they must be comfortable with the logic that governs the laws of probability. The ability to envision the possible outcome of an event requires a fairly basic level of sophistication. The ability to develop the mathematical formulas and equations for that event requires a much higher level of sophistication. Once again this level of sophistication will develop over time and with lots of practice. The real key to the development of mathematical sophistication is the innate curiosity and desire of the student. Given the right motivation and the necessary support students can reach higher levels of sophistication.

I agree with Bob. The level of sophistication will develop as the kids grow and learn more with guidance and practice. In our article this activity could fit into a few different traits mentioned. Students could look for patterns in their graphs according to the number of rolls etc. Students will also make and test conjectures. They will be making assumptions, guesswork, trial and error, and doing "experiments" to be able to make conclusions.

ReplyDelete