Last Snowman Standing Game

The snowmen face off in this game of addition facts. But beware! A toss of the die may mean the sun melts a snowman. Students practice addition facts as they try to be the last snowman standing because in this game the first person to remove all of his/her snowmen loses the game!

Download the  Last Snowman Standing Game for directions and game mats for three different versions of the game:

• Sum of Two Dice Version to practice addition facts
• Difference of Two Dice Version to practice subtraction facts
• One Die Toss for a simplified version to analyze the probability of a die toss

Data Collection: The directions for each version also include directions for data collection and analysis of the outcomes of the games. Be sure to incorporate these activities, if at all possible, as games offer a highly motivational study in probability. Students love to "play games" to collect data. They're also eager to analyze games so that they learn how the game works and what strategies they can use to improve their odds of winning.

Differentiation: This game offers many opportunities to differentiate the activity. First of all, teachers are able to select from three different versions. Secondly, each teacher should differentiate the game analysis to meet the instructional level of his/her students. Most students can handle the questions with teacher guidance. Older students and talented primary students may be challenged to analyze the game and answer the questions in small groups.


Read about the Last Snowman Standing game on Mathwire.

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

Free the Animals Game

Who will free their animals first?   Students toss two dice, calculate the difference and free an animal from that number cage.   Younger students will enjoy this animal version of the Release the Prisoners game and learn subtraction facts as well.   Both the 6-sided dice game mat and the 12-sided dice game mat are included with directions. 

• Download the Free the Animals game directions and game mats for 6-sided dice to practice easier subtraction facts or 12-sided dice to practice harder subtraction facts. 
• Download the Free the Animals game recording sheet designed so that students can track how many animals each player places in his/her cages and who wins.   Hopefully, students will learn something about probability while mastering subtraction facts.

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 M&M Game

M and M Game: 2-dice Version 

Students place M&M markers on the numbers 2-12.   Students may place one M&M marker on each number or place several on some numbers and leave other numbers blank.   Next, students toss two 6-sided dice, find the sum, and remove an M&M marker from that number, if there is still one.   The first player to remove all markers wins the game. 

This game helps students develop an understanding of the probability of a two-dice throw.  As students play the game, they practice addition facts, but they also learn that some sums are tossed more frequently than others.  This hands-on experience is then solidified with a discussion of all of the possible outcomes, creating a chart to visually capture the data.

Next, students play the game again with this mathematical knowledge and discuss how this information impacts the placement of M&Ms.  Couple this game-playing with class data collection and students may then compare theoretical and experimental probability of a larger sample.

This is just one example of how a simple game may be used as a data collection activity to develop student understanding of theoretical and experimental probability concepts.  Some teachers question the use of games in the classroom pressed for time.  In my experience, this rich use of games to practice basic facts AND as a data collection activity is time well-spent and students respond positively to both the practice and the discussion of these hands-on, fun experiences.

NOTE:  This game, created by Susie Siegel as a grad school project, uses a sentence strip as the number line.  The M&M pieces were created using PowerPoint.  Teachers may choose to laminate the pieces for use in a classroom math center.

MATERIALS:

• Download Ms. Siegel's M&M Game directions and recording sheet.
• Download a picture, alternate recording sheet and directions for using that recording sheet.  NOTE:  This recording sheet was designed to fit into a sheet protector so that students may use dry erase markers to play and record data.  This option may be used without the M&M game pieces.
• Download the 2-dice toss recording sheet for a discussion of the theoretical probability of tossing two dice.  Students write one outcome that produces that sum in each box to create a visual display.   NOTE:  use different colored dice for this activity so that students are able to see that tossing 4 on the red die and 3 on the blue die is different from tossing 3 on the red die and 4 on the blue die.  Both must be counted as outcomes.  Students might benefit from actually using two different color markers to record these outcomes as well.
• Download M&M pieces for use in playing the game.