Dice in the Classroom

There are so many effective math games and data investigations that involve tossing dice.  One way to help young students toss dice is to place the dice in a clear jar.  Students simply shake the jar, place it down on its lid, and read the dice toss.  Teachers may place 1-4 dice in the jar and they're ready to go.  HINT:  This also works for coin tosses!

Some teachers prefer to use the small trays in which vegetables and fruits are sometimes packed or small boxes or box lids.  The sides stop the dice from rolling off the student desk.  If noise is a concern in the classroom, place a sheet of craft foam in the bottom of the tray and the dice tosses will be silent.

Now check out some activities from the Mathwire collections:

• Data Analysis:  One Die Toss
• Data Analysis:  Two Dice Toss

Fat Bat Game

Students roll a die to see how many insects their bat eats. Students may continue rolling, in this Bat version of Pig, until they elect to stop, or until they roll a 1. But be careful! If your bat is still eating (collecting points) when a one is tossed, you are a Fat Bat and lose all of your points for that round.

This game is designed to provide a fun experience in the experimental probability of a single die toss. However, students get lots of practice adding a string of single digit numbers, as they total up their winning points for each round. A data analysis option is included to formally extend the analysis of the game's probability for older students.

Download Fat Bat for the student recording sheet, directions for whole class play, and data analysis option for extending the game.

Game of Pig

Game of Pig:  one die version

This is best introduced as a class activity.   Students collect points for each toss of the die unless a ONE is tossed, which means they lose all of the points they have collected in the round.   To prevent losing their points, students may elect to stop at any point in the game before a ONE is tossed and they get to keep the points they collected but get no further points.   Students love the game and begin to appreciate that theoretical probability and experimental probability are often quite different! 

Game Analysis:  Once students are familiar with the game, encourage small groups to develop a "winning strategy" and explain it to their classmates. Then play the class game with groups competing to see who has the best strategy in the actual game. Repeat, as necessary, for students to modify strategies.  NOTE:  Some student strategies are:  stopping after 5 tosses, stopping when they have 20 points, stopping after the second toss of a 6 or a 5, etc.  Be sure to ask students to explain the thinking behind the strategy.

Terry's Note:  I have used this with students in Grades 1-12 as well as in teacher training sessions and everyone loves it!  Students record each toss and then must add up a string of numbers providing great practice in mental math.  Students also continue to search for that magic strategy that will help them win.  Along the way, they informally experience, and thus learn, a lot about experimental probability.  I found this game to be a great use of those few minutes at the end of class to keep students actively engaged.  No student ever groaned when I said we were going to play pig!

• Download directions for playing the Pig Game in a whole class setting.
• Download the Pig Template to use as a recording sheet.  Place the sheet in a plastic sheet protector and use dry erase markers to create a reusable recording sheet.
• Have students record each die toss in a Pig Tally Template for easy data collection.  This method also groups data so that students see a visual representation of the frequency of each outcome.
• Use copies of the Pig Handout as a writing activity.  Encourage students to write about the probability in Pig and what they have learned from playing the game.  OR use these sheets for student groups to write out their "winning strategy" and post them on a bulletin board for future reference.  Keep a running total of times each strategy is successful in winning.
• Play Pig online.

  
Game of Pig:  Two dice version

Students should be familiar with the one-die version of Pig before playing the 2-dice version.   Tossing a one on either die means that the player loses all points collected in that round, if he/she has not stopped before the one is thrown.   Any player who is still playing when snake-eyes (double ones) are thrown, loses all points collected thus far in the whole game! 

Game Analysis:  Students need to develop different strategies for playing this 2-dice version of Pig.   After playing several times, student pairs might analyze the two-dice frequency chart to calculate the probability of a one being tossed.   Students can use this information to develop a winning strategy and compete against other teams to see whose strategy is most successful. 

• Download  a two-dice toss frequency chart for students to use in determining the probability of different outcomes.
• See online directions for playing Two-dice Pig.
• Play an online version of Two-dice Pig against the computer.
• See Two Dice Roll for an online simulation of two-dice toss that graphs the outcomes.  This is a great way for students to collect larger samples of data to analyze experimental probability against theoretical probability.  Groups of students might also use this simulator to generate dice tosses to test their winning strategies.

 Game of Skunk

After students have mastered the Pig Game, analyzed the probability of the game and identified winning strategies, introduce the Game of Skunk and challenge students to analyze the probability used in this game and develop a winning strategy.   How are the games alike and how are they different?   Does the same "winning strategy" work for both games?  

• See Skunk Game Lesson Plan from NCTM Illuminations.
• Download a Skunk Game Recording sheet that may be inserted in a plastic sheet protector and used with erasable markers for a renewable recording sheet. 
• Play online Skunk Game at the NCTM Illuminations site.

The Game of Pig

Pig is one of my favorite probability games.  I have played the game with kindergarten through college level students and used it in teacher training sessions.  Everyone LOVES the game and it's fun to watch who plays it safe and who's the risk-taker.  

In my own classroom experience, I have found that this is best introduced as a class activity. Students collect points for each toss of the die unless a ONE is tossed, which means they lose all of the points they have collected in the round. To prevent losing their points, students may elect to stop at any point in the game before a ONE is tossed and they get to keep the points they collected but get no further points. Students love the game and begin to appreciate that theoretical probability and experimental probability are often quite different! 

I devised a method that uses only one die tossed by the teacher, so this is a great transition activity that quiets a class as they strain to hear and record the results of the die toss AND decide if they will stop or continue to play.   It's a win-win because students feel that they're playing, but they're actually learning a lot about the probability of a one-die toss.

• 
  Download Pig directions.
• Download Pig template or Pig Tally template, and place in a sheet protector to record die tosses.  Students may use dry erase markers for a reusable recording sheet.  The Pig Tally template requires students to use tally marks to record each toss of the die.  This recording sheet is a very visual presentation of the results and proves extremely useful when students devise winning strategies, as described below.

Results:  Younger students may use calculators to total each column.  Older students should use mental math to find the sum of the die tosses.  Students should write the total of all 3 columns in the upper right hand corner of the template and circle it.

Extending the Data Collection & Analysis:

• Ask pairs or small groups of students to talk about the game and come up with a winning strategy.  For example, some groups decide to stop once they have 20 points.  Another group decides to stop when they get 3 of any number.
• Have each group share their winning strategy and explain why they think it is a winner.
• Play the game again.  Groups MUST play according to their winning strategy.
• Discuss the results and allow groups to refine their strategies, if desired, before playing 1-2 more times.
• Finally, ask students to write about what they learned from this game.  Is there really a winning strategy that works all the time?  Explain your thinking.