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 with your class. For many years, I have played a game called Defy the Pig with my pupils. 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 one, which is called the "pig" in this game.
The Concept of Probability
Before beginning the game, I introduce the concept of probability. Once we've established that probability is the chance of something happening, I ask, "What are the chances that a one will appear each time I roll the die?" 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.
The Element of Chance
Here's the catch! Just because the probability of rolling a one 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 (perhaps with your help) that the chances are now 11 out of 36. 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 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, 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 his boxes, he observes the game until that round is over. Pupils 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 each person has made his 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. They have to make a decision again. Either they write 19 in their top box, or they raise their hands to gamble. Once all students have made up their minds, I roll the dice again. This time, a 1 (the pig!) appears. Each person who had his hand up must put a 0 in his top box. This time he gambled and lost. Once the "pig" has appeared, and everyone has either a 0 or higher value in the 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 before 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. 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:
Decorate and utilize popsicle sticks to help understand probability. Each person receives 12 popscicle sticks, which he paints red on one side and yellow on the other. Students work in groups, and take turns dropping their popsicle sticks - recording how many of each color come up each time. This can also be used to introduce the concepts of mean, median, and mode.
What's your favorite probablity game to play in the classroom?