Math Concept Reader MCR g3 fun and games

Fun
and Games
Math Concept Reader
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Fun
and Games
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Copyright © Gareth Stevens, Inc. All rights reserved.
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ISBN 13: 978-0-15-360185-9
ISBN 10: 0-15-360185-X
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Fun
and Games
by Linda Bussell
Math Concept Reader
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Thursday is Game Day at Valley Elementary School.

On game day, students play games, such as board games,
after school. There are many different games to play. Each
student finds a game to play.
Sometimes players toss a coin to decide who takes the
first turn. Some games use number cubes to decide game
moves, while other games use spinners.
Aaron and Natalie use number cubes in math class.
They use coins and spinners, too. They use them for
probability experiments. Aaron wonders whether the
result of any toss or spin is as likely as any other.

Chapter 1:
Likely or Unlikely?
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Natalie did an experiment in class this week. She tossed
a coin and recorded which side landed face up. She
repeated the experiment. She made a tally table of the
results.
The result of a toss or spin is called an outcome. A coin
toss has two possible outcomes, heads and tails. Heads
and tails are equally likely to occur, so they have the same
probability.
A fair coin is equally likely to land on heads or tails.
The probability of heads is one out of two times. The
probability of tails is also one out of two.

Chapter 1:
Likely or Unlikely?
Valley Elementary students play games after school.

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Experiment Results for
100 Two-color Counter Tosses
Heads Tails
Aaron says, “I did an experiment with a two-color
counter. The coin toss is just like that.” He pulls a sheet of
paper from his backpack. On the paper is a table that he
made to record the results of the two-color counter
experiment.
Natalie agrees. The possible outcomes for the coin and
counter are the same.
Some students are about to play a game. Aaron and
Natalie join them. “Are you ready to play?” asks Natalie.
“I will toss a coin to see who goes first.”

Chapter 2:
More Likely
A two-color counter has two
possible outcomes.
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Sometimes players toss number cubes to determine
game moves. There is a number on each face of the cube
that tells the players how many spaces to move a game
piece. Some games use one number cube while other
games use two.
Tyler, Tanisha, and Austin play a game that uses one
number cube. The outcome is the number of spaces a
player moves a game piece. A cube has six sides that are

each numbered. The possible outcomes are 1, 2, 3, 4, 5,
and 6. There are no other possible outcomes.

Chapter 2:
More Likely
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Experiment Results for
Tossing One Number Cube 100 Times
Outcome Tally Total
16
15
18
17
16
18
1
2
3
4
5
6
If the number cube is fair, the likelihood of any one outcome
is equal to any other. There are six numbers on each cube. The
likelihood of tossing any number is 1 out of 6.
Austin says, “Let’s toss the number cube 100 times.”
Tanisha draws a tally table. Tyler tosses the number cube, and
it lands on the number 4. Tanisha makes a tally mark in the
row for outcomes of 4.
Tyler tosses the number cube again. Tanisha makes a tally

mark in the row for outcomes of 1. They do this over and
over again.

Tanisha makes a tally table to record outcomes.
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Austin says, “Look at the number of tallies for each
outcome. The numbers are not equal. They are about the
same.” Other students watch. They are interested in
Austin’s experiment. Now they have more questions
about probability.
Mariela and Abigail play a game that uses two number
cubes. Mariela wonders about the probability of tossing 2
sixes.
“Figuring the possible outcomes for one number cube is
easy,” Mariela says. “I can just count the number of sides.
Figuring the possible outcomes with two number cubes is
different. I cannot just count the number of sides.”

Figuring out the possible outcomes of tosses using two number cubes is
different than figuring out the outcomes of tosses using one number cube.
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Experiment Results for
Tossing Two Number Cubes 200 Times
Outcome Tally Total
6
10
16
24

26
36
26
24
16
10
6
2
3
4
5
6
7
8
9
10
11
12
Abigail says, “Let’s do an experiment. We can toss two
number cubes, and record the outcomes in a tally table.”
The table will help us decide whether all possible
outcomes are equally likely.
“The outcome for two number cubes is the sum of the
result for each cube. The possible outcomes are 2, 3, 4, 5,
6, 7, 8, 9, 10, 11, and 12,” Mariela says.
Abigail tosses the number cubes and Mariela records the
toss outcomes. Abigail tosses and tosses. Mariela writes
and writes. Abigail tosses the number cubes 200 times!

Mariela records the outcomes of tosses using two number cubes.

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Outcome of 12
Number
Cube 1
Number
Cube 2
6 6
Outcome of 7
Number
Cube 1
Number
Cube 2
1
6
2
5
3
4
6
1
5
2
4
3
The girls see that some outcomes, like 6, 7, and 8, are
more likely, while other outcomes, like 2 and 12, are less
likely. How can this be?
Mariela says, “There is only one way to have an
outcome of 12. The outcome of both number cubes

must be 6.”
Abigail agrees with her. “There are several possible
outcomes that result in 7. There are six combinations of
two number cubes that give a sum of 7.
“That means an outcome of 7 is six times more likely
than an outcome of 12!” says Abigail.

There is only one possible way to toss a 12 with the number cubes.
There are six possible ways to toss a 7 with the number cubes.
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Some of the games the students play use a spinner with
a pointer on it. The pointer determines where players can
move their pieces on the game board.
Andrew and Jared play a game with a spinner that is
divided into four equal parts. Each part is a different color,
and the colors match the spaces on the game board.
“This is a fair spinner because the colored areas on the
spinner are equal in size,” says Jared. “The chance of the
pointer landing on any color is equally likely.”
10
Chapter 3:
Fair Games
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Andrew has an idea. He wants to make a new spinner
to make the game more fun. He draws a new spinner and
divides it into four equal parts.
Andrew and Jared make two of the equal parts blue and
none of the equal parts red. “We will be twice as likely to

land on blue with this spinner,” says Andrew. “The
probability of landing on blue would be two out of four.”
“Yes, and the probability of landing on red would be
zero out of four since it is impossible to land on red,” says
Jared.
11
Chapter 3:
Fair Games
The probability of landing on blue with this spinner is 2 out of 4.
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Now Jared has an idea. He draws another spinner and
colors the sections. He makes the orange and yellow sec-
tions equal, but makes the blue section much larger than
the other sections.
Jared asks Andrew, “Is it likely that the pointer will land
in the blue section?” Andrew replies, “Yes! The blue sec-
tion is larger than any other section. It is most likely to
land on blue. It is less likely to land on yellow or orange.”
“Yes,” says Jared, “but yellow and orange are equally
likely because their areas are equal.”
1
The pointer is most likely to land on blue with this spinner.
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4. Unlikely
1. Impossible
2. Likely
3. Certain
Jared and Andrew take turns drawing spinners. They

have fun designing new spinners for their game. They
work to decide whether an outcome of blue is certain,
likely, unlikely, or impossible.
This is what they decide:
An outcome of blue is impossible with an all yellow
spinner.
An outcome of blue is likely with a mostly blue spinner.
An outcome of blue is certain with an all blue spinner.
An outcome of blue is unlikely with a spinner that has a
small blue section.
1
The possible outcomes of landing on blue.
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1
start
over
2
3
4
5
6
7
8
9
10
11
12
Other students watch the probability experiments. They
want to try some experiments, too. Mariela says, “Why

don’t we make up our own games? We can use what we
have learned about probability to make our games fair and
fun!”
Jared says, “That’s a great idea, Mariela!”
Austin says, “I want to make a spinner with numbers
instead of colors. It will have 12 equal spaces. If the pointer
lands on 2 through 12, the player’s piece moves that many
spaces. If the pointer lands on 1, the player has to start
over!”
1
This spinner uses numbers to move game pieces.
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Next, Abigail tells everyone about her game idea. It uses
two number cubes. “You get extra points for tossing 2 or
12 since those outcomes are the least likely,” she says.
Mariela says, “We can use the results from our
experiment to decide how many points players should get
for each toss. The first player to score 100 points wins!”
The students agree that this game sounds like fun!
The students have ideas for more games. They decide
to bring their new games next week for Game Day so that
everyone can play!
1
Valley Elementary students will meet again to play math games!
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1
Glossary

certain something that will always happen
coin a piece of metal used as money
equally likely outcomes that have the same chance of
happening
fair when every outcome has an equal chance of
happening
impossible something that will never happen
likely an outcome that has a good chance of
happening
number cube a cube with sides numbered
1 through 6
outcome a possible result of an experiment
pointer a moveable arrow that is spun on a spinner
probability the chance that a given event will occur
result data from conducting a survey or an experiment
spinner a square or round base and pointer used in
board games
unlikely an outcome that does not have a good chance
of happening
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Think and Respond

1. Suppose you have two number cubes. Each cube
has six faces numbered 1 through 6. What are the
possible outcomes that result in 4?
2. Look at the spinner on page 12. Is it certain, likely,
unlikely, or impossible for the pointer to land on
orange?
3.

T
urn to page 13. Look at spinner number 4. If you
were to spin the pointer 100 times, which color is
it likely to land on most often? Why? Which color
is the pointer likely to land on least often? Why?
4.
Suppose you play a game with a spinner that
is

blue, and

yellow. Are the outcomes equally
likely?
How could this spinner be used in a game so that
each person has an equal chance to win?
1
3
2
3
Photo Credits: cover, pp. 3, 15: Kay McKinley; pp. 4, 5, 6, 7 Russell Pickering.
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