Math Probability Lesson Plans

In mathematics, the probability of something happening has a numerical value assigned to it - usually expressed in ratio or percentage form. This concept can be confusing.  Luckily, a pair of dice is all you need to introduce and explore the concept of probability. For many years I have played a game called "Defy the Pig" with my classes. They love this game because they get to "gamble," or take a chance that a certain number will not come up on either of the dice when rolled. That number is 1 - also known as the "pig" in this game.

Before beginning the game, I introduce the concept of probabililty.  Once we've established that probability is the chance of something happening, I ask, "What are the chances that a 1 will appear each time I roll the dice?"  I lead the them to realize that, mathematically speaking, there is a 1 in 6 chance that I will roll a 1 each time I roll the dice. You can take this a bit further, and convert the ratio into a percentage, which is easier for many students to visualize.  If you divide 6 into 1, you get just about a 17% chance of rolling a 1 each time. 

But here's the catch. Just because the probability of rolling a 1 is 1 in every 6 rolls, that doesn't mean that this is what will happen once we begin rolling the dice. The great thing about probability is that you can never be sure what will happen, because there is the element of chance. It's also important to point out that they will be rolling two dice at the same time. I ask them, "Now what's the probability of a 1 coming up?" Eventually, they will realize that the chances are now 2 out of 12 - which is the same as 1 out of 6!  It's great fun to help them understand that these two ratios represent exactly the same level of probability. Now.....on to the game!

On the whiteboard, I draw five small boxes in a vertical column. Underneath the bottom box, I draw a horizontal line, then another box underneath that.  I put a plus sign to the left of the five boxes. Each person should each have a piece of paper and a marker or crayon (I discourage the use of pencils in this game), and they copy what I have put on the board.  To the right of the five boxes, I draw a circle.  They don't have to put the circle on their papers. 

I roll the dice.  I add the value of the dice and write that number in the circle on the board.  For this first roll, the 1 or "pig" doesn't come into play. I roll the dice, and a total of 8 comes up.  I write the number 8 in the circle on the board.  They now have to make a decision.  Either they can accept the number in the circle, and put it in their top box, or they can raise their hands and "gamble" that the next roll will not result in a 1 coming up on either die.  They are trying to "Defy the Pig."  A few will write the 8 in their top box, but most will raise their hands. Once a student has written a number in one of their boxes, he observes until that round is over.  They cannot change the number once it's put in the box - no matter how high the number becomes in the circle on the board.

Once everyone has made their decision (either hands up, or a number in their box), I roll the dice again.  Let's say a total of 11 comes up.  I now add the 11 to the 8 that's already in the circle on the board.  I erase the 8 and write 19.  Now, they have to make a decision again.  Either they write 19 in their top box, or they raise their hands to gamble again.  Once everyone has made up their mind, I roll the dice again.  This time, a 1 (the pig!) appears.  Everyone who had their hand up must put a 0 in their top box!  They gambled, and lost this time.  Once the "pig" has appeared, and everyone has either a 0 or higher value in their top box, I put an X in the top box, erase the number in the circle, and begin round two.  Each of the five boxes represents a round (1 - 5 ) going from top to bottom. 

The game continues in this fashion until all five rounds have been played. It's amazing how high a single round can go until the "pig" appears.  Believe it or not, in 1991, I had a single round score of 190 before the "pig" finally appeared!  Once all the rounds have been played, each person adds up the scores in each of his 5 boxes. The person with the highest score wins!

This game has always been quite popular with my classes, and makes a great "sponge activity" if you happen to have 10 -15 minutes of time to fill during any part of the day. Below, you will find some other excellent lesson plans on probability that will enhance further exploration of this important mathematical concept.

Math Probability Lesson Plans:

Probability Polly

This lesson is ideal for younger learners. They respond to a series of statements made by the teacher by using the words certain, possible, impossible, sometimes, always, and never. Then, they design a spinner that has eight differently-colored sections in order to gain more practice using these important words associated with probability.

Probability Popsicle Pop-Ups

Decorate and utilize popsicle sticks to help understand probability. Each person receives 12 popscicle sticks, which they paint red on one side and yellow on the other.  They work in groups, and take turns dropping their popsicle sticks - recording how many of each color come up each time. This fun lesson can also be used to introduce the concepts of mean, median, and mode.

M&M Graphing and Probability

M&M's are such a fun manipulative tool!  This innovative lesson facilitates working in  pairs to determine the probability of choosing a certain color M&M out of a large bag. First, each pair creates graphs and charts based on how many M&M's of each color are in their small bags.  As an extension, they can research why there was a period of time that no red M&M's were made , and when they re-introduced.

Probability: The Study of Chance

This lesson is designed for upper elementary grades, but can be used all the way through high school. They play the classic game, "Rock, Scissors, Paper" in order to study concepts of probability as well as mean, median, mode and range. This interesting lesson requires individuals to determine if the game is "fair," even when more than two players are participating at the same time.

Discussion Question:

 What's your favorite probablity game to play in the classroom?