Students will complete various activities to reinforce the concept of probability.
- Probability Pistachio, by Stuart J. Murphy
- Popsicle sticks (three
- Colored markers
- A Stick Game recording
- Six-section spinner,
pencil, and large paper
clip for each person
- Paper bags (one per
- Colored Unifix cubes
(ten per person, two
each of five colors)
- Two 1-6 number cubes
per person (one green
and one red per person)
- 1-6 number cube throw
recording sheet (pdf)
- Transparency of a "tree
- Probably Pistachio, by Stuart J. Murphy; ISBN 0-06-446734-1
- Data, Chance, and Probability (Grades 4-6) (Learning Resources,
Incorporated); ISBN 1-56-911997-X
- Math At Hand, by Great Source Education Group Staff; ISBN 0-669-46922-X
- Yahtzee (Dice game involving probability)
Background for Teachers
It is helpful to know if something is likely or unlikely to happen. It’s
more useful if you can use a number to describe that likelihood.
Probability will help you decide how often something is likely to happen.
However, it usually won’t help you to know exactly when that event will
An event is something that may happen. The probability of an event
can be any number from zero through one. It can be written as a
fraction, a decimal, or a percent. If the probability of an event is zero, it
is impossible. If an event is certain, it has a probability of one. The
more unlikely an event is, the closer its probability is to zero. The more
likely an event is, the closer its probability is to one.
When you flip a penny, two things can happen. These two things are
called outcomes. When using a spinner with eight equal sections, there
are eight possible outcomes. When three of those eight sections are red,
and other colors have less than three sections, there are three favorable
outcomes. When you do an experiment to get an idea about probability,
you are sampling, but you may not get exactly the same number as
finding the ratio of favorable to possible outcomes, and sampling can fool
Intended Learning Outcomes
3. Reason mathematically.
5. Make mathematical connections.
Invitation to Learn
Read Probably Pistachio.
Guiding questions: What are the boy's chances of choosing a bag of
popcorn from the coach's basket? What are some examples of
probability in our own lives?
- Distribute popsicle sticks and ask participants to list three
features of Utah (one feature per stick). Examples: Utah
counties, plants or animals, landmarks, regions, deserts,
wetlands, forests. Leave the back of the sticks plain.
- Before you begin the Native American Stick Game, record all
the different ways the sticks might land. Then write your
prediction of the combination you think will happen most often
on A Stick Game recording sheets.
- Drop the sticks on the floor ten times and record the results.
How close was your prediction?
- Ask: Why would the plain sticks most likely
appear more than the colored ones?
- Show a six-section spinner to explain
probability in the Stick Game. Discuss the
simple ratios (fractions) shown in this
- Demonstrate with "probability bags" (paper bag with ten Unifix
cubes inside). Ask questions about probability:
- What are the chances of my drawing out a red cube?
- If I put the cube back (replacement), what are my chances of
drawing it again? If I don't put the cube back (without
replacement), what are my chances now?
- Using overhead projector, record data as you go.
- Distribute 1-6 number cubes; students experiment with how many
combinations of cube throws to complete the chart. Notice a
pattern (e.g., How many different ways can you throw the cube to
get a total of seven?).
- When teaching about Native American tribes of Utah, teach the
Native American Stick Game as part of the unit.
- What is the probability that a given county in Utah was named
after a mineral? State this as a fraction.
- Tree diagrams are used to find all possible outcomes in a sample
space by drawing a diagram or making an organized list.
- Assign students to choose four of their shirts and four pairs of
pants. Draw pictures to show how many different combinations of
outfits they could wear to school (outcomes) using those items of
- Election outcome: Six people are running for class president; the
person with the most votes will be president. The person who
comes in second will be vice president. How many different pairs
of president and vice president combinations (outcome) are
- What is the probability that a number between one and 50
contains the digit four in it? State this as a fraction.
- What is the probability that a person was born in a summer
month? State this as a fraction.