**Probability**

**Definition**: The likelihood that an event will occur.

Probability = Number of specified outcomes

Total number of outcomes

**History & Application**

“Probability is likely to have been started by Blaise Pascal (1623-1662) and Pierre de Fermat (1601-1665) primarily by games of chance.” (Chakravarthy) It was developed even further by the French and Russian schools.

We see probability in our everyday life, and we use it in decision making. It helps us to better understand the world around us. It is found in health and medicine, in business, economics, education, sports and engineering.

It is used at the local grocery store as they keep their shelves stocked. It is also used as your Mom figures out how much she needs to make for dinner. Probability whether we know it or not is a large part of our lives.

Dr Chakravarthy, Srinivas R. (1999) What is Probability? Retrieved December 12, 2008. Website: http://www.gmi.edu/~schakrav/Math205/Applications.pdf

The focus in elementary probability should be experimental.

**Key Tools in Probability**

- Spinners: Provide a variety of spinners divided into different number of parts and students record all of their spins.
- Coins
- Dice
- Two-sided counters
- Color Tiles: Make several bags of different combination of color tiles. Students pull a tile, record their pull, and replace it in the bag.
- Paper Lunch Bags
- Box with colored marbles with a corner cut out to act as a peep hole: Place a different combination of colored marbles in each box, seal it shut and label the boxes
*A, B,*and so on. Students shake a box and record which marble comes to the corner.

**Pedagogy**

Primary Grades

- Focus on using words such as
*certain, likely, unlikely,*and*impossible.*Example: What is the chance of rolling a 2? - There should be a large model drawn somewhere in the classroom that looks like this

- Know the difference between chance and odds. Chance refers to the number of times the event might happen compared to the total number of outcomes. Odds is a ratio of the number of times the event might happen in comparison to the event not happening. For example, the chance of getting heads is one half but the odds are 1:1.
- Students will need to have some way of collecting their data, such as a tally chart or a bar graph.

Upper Grades

- Begin using independent and dependent events. Independent event occurs when one event does not affect the other. A dependent event occurs when the first event does affect the second.
- Third graders can begin by doing experiments on two independent events. For example, tossing two pennies and figuring out what the possible outcome will be. Other examples are one coin toss and one dice roll, two dice roll, two spinners.
- Introduce a couple different models to help students list possible outcomes, such as a matrix and a tree diagram.
- Students should generalize that the total number of outcomes for both events are the product of outcomes for each event.
- Probability can be related to Pascal’s Triangle see page 474 of Elementary Mathematics is Anything but Elementary by Damon L Bahr and Lisa Ann de Garcia.
- Probability games can be used to determine fairness also refer to page 474 for some idea.

**Lesson Plans by grade level:**

**3 ^{rd} grade**

**1. Spinning Odds and Evens: 3 ^{rd} grade Standard 5 Objective 1**

**Summary:** Students will explore probability by playing a game of chance and determining if it is a “fair” game.

Utah Lesson Plans. (2004). Probability. Retrieved December 12, 2008. Utah Education Network.

Web Site: http://www.uen.org/Lessonplan/preview?LPid=11027.

** 2. Take a Chance with Probability: 3 ^{rd} grade Standard 5 Objective 1**

**Summary:** Students will play games to discover different kinds of probability.

Utah Lesson Plans. (2005). Probability. Retrieved December 12, 2008. Utah Education Network.

Web Site: http://www.uen.org/Lessonplan/preview?LPid=14866.

**3. The Study of Chance: 3 ^{rd} grade Probability**

**Summary:** The purpose of this activity, is to begin the process of helping students to learn the basic principles of probability.

Tina. (2001). Probability. Retrieved December 12. 2008. Elementary Mathematics. Web Site:

http://www.lessonplanspage.com/MathProbabilityChance.htm.

** **

**4. A Concrete Approach to Relative Frequency: 3 ^{rd} grade Probability**

**Summary:** Find out what the probability is of steeping on a crack when you walk on a sidewalk.

Spangler, David. (2001). Probability. Retrieved December 12, 2008. Teacher.Net. Web Site:

http://teachers.net/lessons/posts/3.html.

**4**

^{th}grade**Practice with Probability: 4 ^{th} grade Standard 5 Objective 2**

**Summary:** Students will complete various activities to reinforce the concept of probability.

Utah Lesson Plans. (2004). Probability. Retrieved December 12, 2008. Utah Education Network.

Web Site: http://www.uen.org/Lessonplan/preview?LPid=11089.

**M&M Graphing and Probability: 4 ^{th} grade **

**Summary:** To provide students with a hands-on and cooperative learning experience in the process of collecting, analyzing, and interpreting data, and to improve decision making skills through the use of probability.

Stewart, Karen. (1994). M&M Graphing and Probability. Retrieved December 12, 2008. The Educator’s Reference Desk.

Web Site: http://www.eduref.org/cgi-bin/printlessons.cgi/Virtual/Lessons/Mathematics/Probability/PRB0005.html.

**5 ^{th} Grade**

**1. Math 5- Act 26: Dice Sums: 5 ^{th} grade Standard 5 Objective 1**

**Summary:** The activities in this lesson focus the children on investigating the probabilities of the sums that come up when two dice are tossed.

Utah Lesson Plans. (2003). Probability. Retrieved December 12, 2008. Utah Education Network.

Web Site: http://www.uen.org/Lessonplan/preview?LPid=6177.

2. Math 5- Act 28: Dodecahedron Race: 5^{th} grade Standard 5 Objective 2

Summary: Students’ understanding of probability will be strengthened playing the game “Dodecahedron Race” using a dodecahedron die.

Utah Lesson Plans. (2003). Probability. Retrieved December 12, 2008. Utah Education Network.

Web Site: http://www.uen.org/Lessonplan/preview?LPid=6179.

**3. Probability: 5 ^{th} grade Standard 5 Objective 2**

**Summary:** Students will begin to understand the concept of probability through hands on activities.

Utah Lesson Plans. (2007). Probability. Retrieved December 12, 2008. Utah Education Network,

Web Site: http://www.uen.org/Lessonplan/preview?LPid=19007

** **

**4. Probability: The Study of Chance: 5 ^{th} grade**

**Summary: **The purpose of this activity is to begin the process of helping students to learn the basic principles of probability.

LeMoine, Shirley. (1994). Probability. Retrieved December 12, 2008. The Educator’s Reference Desk.

Web Site: http://ericir.syr.edu/cgi-bin/printlessons.cgi/Virtual/Lessons/Mathematics/Probability/PRB0004.html

**6th grade **

**1. Coin Tossing: 6 ^{th} grade Standard 5 Objective 1**

**Summary: **This experiment is designed to help students see that the probability is not the same as reality. However, they should discover that as we do the experiment more times, the results resemble the probability more closely.

** **Utah Lesson Plans. (2003). Probability. Retrieved December 12, 2008. Utah Education Network.

Web Site: http://www.uen.org/Lessonplan/preview?LPid=6404.

**2. Spinning Probability: 6 ^{th} grade Standard 5 Objective 1 **

**Summary: **Students will apply basic concepts of probability to design spinners that match a specific set of clues.

Utah Lesson Plans. (2003). Probability. Retrieved December 12, 2008. Utah Education Network.

Web Site: http://www.uen.org/Lessonplan/preview?LPid=6401.

3. **Drawing Conclusions: 6 ^{th} grade Standard 5 Objective 1**

**Summary**: This activity poses a fun probability problem concerning changing odds.

Utah Lesson Plans. (2003). Probability. Retrieved December 12, 2008. Utah Education Network.

Web Site: http://www.uen.org/Lessonplan/preview?LPid=6403.

4. **E.T. Probability (Experimental/Theoretical): 6 ^{th} grade Standard 5 Objective 2**

**Summary:** This activity explains the difference between experimental and theoretical probability.

Utah Lesson Plans. (2007). Probability. Retrieved December 12, 2008. Utah Education Network.

Web Site: http://www.uen.org/Lessonplan/preview?LPid=18860.

5. **How Likely is it?: 6 ^{th} grade Standard 5 Objective 2**

**Summary:** This activity explores the concept of probability and chance. It will show many different ways of expressing a ratio and what it means when connected with probability.

Utah Lesson Plans. (2007). Probability. Retrieved December 12, 2008. Utah Education Network.

Web Site: http://www.uen.org/Lessonplan/preview?LPid=18859.

6. **The Dice Game: 6 ^{th} grade Standard 5 Objective 2**

**Summary:** This dice game will help students better understand basic concepts of probability

Utah Lesson Plans. (2003). Probability. Retrieved December 12, 2008. Utah Education Network.

Web Site: http://www.uen.org/Lessonplan/preview?LPid=6402.

**7. Probability Invetigators: 6 ^{th} grade Standard 5 Objective 2**

**Summary:** This activity helps students to understand probability more fully and how it affects their daily lives.

Utah Lesson Plans. (2003). Probability. Retrieved December 12, 2008. Utah Education Network.

Web Site: http://www.uen.org/Lessonplan/preview?LPid=18861.

**Games, worksheets, and more information: **

1.edHelper. (2008). Probability. Retrieved December 12, 2008.

edHelper Website: http://www.edhelper.com/probability.htm

**Summary:** This is a great resource for teachers in letting the students put into practice what they have learned about probability. Print off these **practice sheets**, and let them have a great time.

2. Kids Zone. (2008). Chances. Retrieved December 12, 2008.

Kids Zone Website: http://nces.ed.gov/nceskids/chances/

**Summary:** Here is an **interactive game** of probability, choose your number of dice and see how that affects probability.

3. BBC Education. (2008). Fish Tank Probability. Retrieved December 12, 2008.

Website: http://www.bbc.co.uk/education/mathsfile/shockwave/games/fish.html

**Summary:** A **fun game** for younger grades. They can figure out the probability of catching different colored fish, as they add and take away fish from the tank.

4. Kevin McKeen. (1981). Probability Table of Contents. Retrieved December 12, 2008.

Website: http://www.pleasanton.k12.ca.us/pleasanton/MathWeb/Grade7/Probability/ProbabilityTOC.html

**Summary:** This is a sight with several **probability games** for the whole class. Role dice, flip coins, spin spinners and more. Play the games to learn more about probability.