Probability
is an area of mathematics that often doesn't get its fair share of attention
in elementary classrooms. Here are some activities to get you started
that involve students in thinking about probability ideaswhile also providing
practice with mental addition, experience with strategic thinking, and
the opportunity to relate multiplication and geometry. All activities
are adapted from Marilyn Burns's About Teaching Mathematics (Math
Solutions Publications, 1992).
The Game of Pig
(Grades 3–8)
Math concepts: This
game for two or more players gives students practice with mental addition
and experience with thinking strategically.
The object: to be
the first to score 100 points or more.
How to play: Players
take turns rolling two dice and following these rules:
1. On a turn, a player
may roll the dice as many times as he or she wants, mentally keeping a
running total of the sums that come up. When the player stops rolling,
he or she records the total and adds it to the scores from previous rounds.
2. But, if a 1 comes
up on one of the dice before the player decides to stop rolling, the player
scores 0 for that round and it's the next player's turn.
3. Even worse, if
a 1 comes up on both dice, not only does the turn end, but the player's
entire accumulated total returns to 0.
After students have
had the chance to play the game for several days, have a class discussion
about the strategies they used. You may want to list their ideas and have
them test different strategies against each other to try and determine
the best way to play.
TwoDice Sums
(Grades 1–8)
Math concepts: Students
of all ages can play this game, as long as they're able to add the numbers
that come up on two dice. While younger children benefit from the practice
of adding, older students have the opportunity to think about the probability
of the sums from rolling two dice.
The object: to remove
all the counters in the fewest rolls possible.
How to play: Two
or more players can play. Each player needs 11 counters, a game strip
that lists the numbers from 2 to 12 spaced far enough apart so the counters
can fit on top of each number, and a recording sheet. Here are the rules
for playing:
1. Each player arranges
11 counters on the game strip and records the arrangement.
2. Once the counters
are arranged, players take turns rolling the dice.
3. For each roll,
all players can remove one counter if it is on the sum rolled. Players
keep track of the number of rolls of the dice it takes to clear their
game board.
After students have
had the chance to play the game for several days or so, have a class discussion
about the different ways they arranged the counters and the number of
rolls it took. Have them write about the arrangements that are best for
removing the counters in the fewest number of rolls. For an extension,
try Which Number Wins?
Which Number Wins?
(Grades 1–8)
Math concepts: In
this individual activity, students roll two dice and record the results.
Make a recording sheet that is an 11 x 12 block grid with the numbers
2 through 12 across the top. While young children gain practice with addition
facts, older children can examine the data, compare results with other
classmates, and think about why some sums are more likely than others.
To do the activity, students need two dice and a recording sheet.
The object: to roll
the dice and record the number fact in the correct column, stopping when
one number gets to the finish line.
How to play: Post
a class chart that lists the numbers from 2 to 12 and have students make
a tally mark to show the winning sum. Have each child do the experiment
at least twice.
After you've collected
the data, discuss with the class why it seems that some sums "win"
more than others. Young children may not be able to explain it, but older
students often figure out that there is only one way to get the sums of
2 and 12, and six ways to get a sum of 7.
After discussing
the data, return to the game of TwoDice Sums and see if students revise
their strategies. You may want to ask students to write about the game
and the likelihood of twodice sums.
How Long? How
Many? (Grades 3–5)
Math skills: This
twoperson game involves probability and strategy, and gives children
experience with multiplication in a geometric context.
The object: to make
rectangular arrays with Cuisenaire Rods and place them on 10by10centimeter
grids until no more space is available. The game encourages students to
think strategically as they consider where to place their rectangles to
avoid being blocked.
How to play: students
need Cuisenaire Rods, one die, and a grid sheet for each (Make a 10cm
x 10cm grid. Also leave space for students to record how many of their
squares are covered and uncovered.) The rules are:
1. On his or her
turn, a player rolls the die twice to determine which Cuisenaire Rods
to take. The first roll tells "how long" a rod to use. The second
roll tells "how many" rods to take.
2. Players arrange
their rods into a rectangle, place it on their grid, and trace it. They
write the multiplication sentence inside.
3. The game is over
when one player can't place a rectangle because there's no room on the
grid. Then players figure out how many of their squares are covered and
how many are uncovered and check each other's answers.
After students have
had experience playing the game, talk with them about strategies for placing
rectangles and figuring out their final scores.
Adapted from Instructor,
April 1994.
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