Day 1: Probability

Spinning Wheel

I. Probability Topic(s): sample space, independent events, Law of large numbers, deviation percentage

B. Related Connections : biology

II. Assumed prior experience: reading charts and graphs, ratios and percentages

III. Rationale:

How can we use the mathematical principals backing probability to better understand real life situations such as genetic make-up?  What are the biological, economic, social and ethical explorations that can be made based upon the understanding of this useful mathematics?

IV. Learning Objectives:

Students will be able to explore concepts surrounding probability through the use of a computer program: Spinning Wheel.

Students will be able to hypothesize as to their own definitions of concepts as they work in pairs.

Students will be able to make a connections between previous units on ratios, percents and decimals and this unit on probability.

Students will be able to write about math, discuss their observations, and finally discover the true meanings of concepts surrounding probability.

Students will be able to develop a formula for deviation percentage.

V. Materials & Technology Needed:

Computer lab with one computer per two students, Microsoft Excel (you will need to activate the add on :  Analysis Toolpack), copies of the provided question sheet.  You must download the SPINNER game onto each computer.

VI. Procedure:

CLASSROOM (10-15 MIN)

• Students will be exploring probability via a program on this site called the Spinning Wheel.

• Students will not be required to be silent but expect them to be talking only about the program

• Time may be limited, but if possible allow for about 30 minutes in the lab

• The worksheet of questions is to be provided to students in the classroom prior to leaving for the lab.

• Explain that they may not get all of the answers, but talk to each other and explore as much as you can for the next 25 minutes.

• Remember that we will be discussing the answers back in class.

• Divide  the class into working groups.

COMPUTER LAB (30 MIN)

• Explain that each color represents one possible outcome of the game of "Spinning a Wheel".   The area of each color is representative of the number of times that color was chosen for 10, 100, or 5000 successive spins.

• Directions for using Spinning Wheel:  HIT F9 AND SEE WHAT HAPPENS!  Each time F9 is pressed, the wheel is spun 10, 100 or 5000 times depending on the current sheet.

• Give the students 5 minutes to explore on their own.

• Use the remaining time wisely and explore all three sheets of questions and charts

• Take turns Pressing F9 and being the note taker.

CLASSROOM II (25 MIN)

• Post the concepts listed in (I.) on the board.

• Begin by asking if anybody would like to propose their own explanation of a concept.  Have them give examples relevant to the Spinning Wheel.  Encourage them to use their own language.

• Continue through the list until it is complete.

VII. Assessment:

• HOMEWORK complete the responses to chart.

• Take a chosen PROBABILITY situation from below and write a paragraph about it including explanations with regard to is RESULTS, SAMPLE SPACE, RELIABILITY, DEVIATION PERCENTAGE and FAIRNESS.

1. 4 out of 5 dentists recommend that you use Colgate toothpaste.

2. 8 out of 10 Americans polled said that they were in favor of paying high school teachers \$1 million a year!

3. 2 out of 3 doctors surveyed suggest the use Tylenol to their patients.

4. 9 out of 10 students said that MATH is their favorite subject.

Note:  This lesson was used in a first year algebra class and was very successful.  At one point, a student was explaining the concept of independent events to her peers via this example.  She held her pencil on end and released it many times in a row.  She explained to here friends that the "landing spot" of each fall of the pencil (event) did not rely on a previous fall.  Sometimes all of the technology and methodology in the world cannot replace peer influence!

 Introduction Process Day1-Probability Day2-Genetics Day3-Extensions Advice Resources Notes to Teacher Probability Misconceptions Interactive Quiz Lesson Plans History Problem Bank Topics Explored NCTM Standards Home