South Carolina ETV

South Carolina ETV
1101 George Rogers Boulevard
Columbia, SC 29201-4761
Phone: 803-737-3545

Theoretically Speaking (Grades 6-8)

Master Teacher

Erin E. Greiner

Time Allotment

Two 50-minute classes

Subject Matter

Mathematics: Probability

(Experimental and Theoretical Probability)

Overview

The students will be introduced to Probability and learn to create data to analyze.

Learning Objectives

The students will be able to:

define probability
determine outcome from a given situation based on simple probability
create experimental data using a coin and a number cube
write how theoretical and experimental prob ability are different

South Carolina Standards

(These Standards are found at http://www.state.sc.us/sde/educator/crindex.htm.)

Mathematics—Grade 7

VI.B. Make inferences and convincing arguments based on an analysis to theoretical or experimental probability.

1. The students will determine the probability of a given simple event and express that probability as a fraction, decimal, or a percent as appropriate for the given situation.

2. The student will investigate and describe the difference between the probability of an event found through simulation versus the theoretical probability of that same event.

4. The student will use the results of simulations to determine experimental probability of events and compare the results to theoretical probabilities.

VI.C. Collect, organize, analyze, describe, and make predictions with data, using technology whenever appropriate.

3. The student will analyze theoretical or experimental data.

Media Components

Video

Algebra in Simplest Terms, Lesson 26: Probability

Web Sites

The National Basketball League site includes team specifics and statistics that will be used in the lesson.

The National Collegiate Athletic Association site includes college-level team specifics and statistics which will be used in lesson activities.

Materials

Per student:

a pencil
one sheet of notebook paper
pennies
number cubes (dice)
"paper balls"

Whole class:

one trash can or container

Prep for Teachers

Bookmark the specified Web sites needed and their specific stat pages, teams, players, etc. Pick a specific team(s) and specific player(s) for the class to follow.
Cue the video to the first clip and cue the PowerPoint presentation.*

Introductory Activity: Setting the Stage

Step One

Establish the Difference Between Control and Luck. Briefly discuss the probability of events. For example, getting an A on a test, scoring in a basketball game, flipping a coin and getting heads/tails, winning on a game show like The Price Is Right, Wheel of Fortune, or Who Wants to Be a Millionaire? What determines each outcome?

Are the determining factors able to be changed? Can you fix the outcome?

Tell students that sometimes you can affect the outcome, but there are also outcomes of chance. Make a list of activities that are either controlled outcomes or chance outcomes.

Learning Activity

Step 1

Focus for Media Interaction: Provide students with a focus by asking them if a basketball player's first shot affects the second shot. Ask them: "After a series of misses or makes, is the outcome of the next shot affected?"

FAST FORWARD the tape to the point where you hear the man on the screen say, "many events aren't independent." PLAY the tape and then STOP the tape when the man says, "we would get four, five heads in a row." (Hint: Rewind the tape to the next clip.)

After students have viewed the video, review the focus question. Then ask if it is possible to have a "good day" or a "bad day" affecting the outcome of a shot. What are outside influences? Does the first shot affect the second shot?

Step 2

Establish a Realistic Example of Outcome. Log on to either the The National Basketball League (go to team specific/statistics or The National Collegiate Athletic Association (go to college-level specifics/statistics) Web sites and look at your bookmarked team and player to check their statistics.

Focus for Media Interaction: Ask what can cause them to change. Then compare the specific players on a team. Ask if something can cause these statistics to change. Does the shot of one player affect the shot of another? Does one person's "good day" or "bad day" affect the shot of another?

Culminating Activity 1

Step 1

Each student is to create a "paper ball." Use one sheet of notebook paper to crumble into a ball. Each student is to have only one.

Step 2

Remind students to think whether or not outcomes have a cause or not. Group students and have each student toss/shoot their "paper ball" into a trash can, container, or designated area one at a time. Keep track of who makes and who misses shots for each team. Discuss the causes of the outcome. Are the boys better than the girls? Is it because some play basketball? Or, is it pure luck? Does one shot affect another?

Introductory/Transitional Activity

Step 1

Theoretical versus Experimental Probability. Continue the "paper ball" shots and emphasize the idea of pure luck.

Step 2

Begin PowerPoint presentation. Define Probability and ask what the actual chance is of shooting the "paper ball" into the container. (Show slides one and two.)

Step 3

Create the fraction of the outcome divided by the total possibilities. Let the students see that one half is the same as a 50 percent chance. Explain the slang "50-50."

Learning Activity 2

Step 1

Discuss and explain what theories are. Relate to science and how they are close to a fact.

Ask how an experiment is like a theory. Can it prove or disprove a theory? What are outcomes from an experiment? What if the same experiment is conducted by different people…. can you get different conclusions? Why?

Step 2

Focus for Media Interaction: Ask students to figure out the difference between theoretical and experimental probability.

FAST FORWARD the videotape and PLAY the tape when you see a man sitting by a poker table and he says, "try a coin toss." STOP the video after you see a row of coins with the THINKER sculpture and monkey.

Show PowerPoint Slide 3 and ask students what determines theoretical probability. Can the outcome be different?

Show PowerPoint Slide 4 and ask students what determines experimental probability. Can the outcome be different?

What are the major differences between theoretical and experimental probability?

Explain that theoretical probability is an unchanging fraction of the outcome divided by the total possible outcomes. This differs from experimental probability in that in an experiment, you get a personal outcome that is based on chance or several outside factors.

Culminating Activity 2

Step 1

Each student receives a coin. Review the theoretical outcome of flipping the coin and getting a head or flipping the coin and getting a tail.

Step 2

Each student is to toss the coin 10 times and record the number of heads and the number of tails they get.

Step 3

Each student is to write the form they used while flipping (i.e., let it hit the ground, caught it, caught and turned into hand, etc). In addition, they need to write their experimental probability of rolling—

(A) a one;

(B) a two;

(D) a four;

(E) a five;

(F) a six;

(G) an even;

(H) an odd.

Step 4

Have students write how their experimental data differs from the theoretical data.

Show PowerPoint Slide 5 and have students work the problem based on basic probability.

Cross-Curricular Extensions

Social Studies: Discuss the lottery in terms of probability: Is it partial to one group—theoretically or experimentally?

Voting: Polls are taken. Are these theories or experiments? Does voter turnout have a cause like weather, close running, interest, etc.

Science: Physics: Can someone have a trick coin or trick number cube to change outcome? How? Create such a thing.

Experiments: Can two people come up with different conclusions while doing the same experiment? How?

Assessment

Define probability.
Determine outcome from a given situation based on simple probability.
Create experimental data using a coin and a number cube.
Write how theoretical and experimental prob- ability is different.

Community Connections

Gain information from South Carolina state government about how the new state lottery will be conducted.
Figure out the probability for each event (de- pending on the different lottery activities).
Interview officials asking if it is a fair game.
Debate the issue of the lottery and its fairness according to probability. Or research different state lotteries and debate their fairness or report on which state has the most fair lottery system.

Power Point

Power Point Presentation