Students learn how to calculate both theoretical and experimental probability by rotating through
a series of work stations.

Objectives

Upon completion of this lesson, students will:

be able to calculate both experimental and theoretical probabilities

display probabilities in both graphical and fraction form

Standards Addressed:

Grade 10

Statistics and Probability

The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 6

Statistics and Probability

The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 7

Statistics and Probability

The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 8

Statistics and Probability

The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 9

Statistics and Probability

The student demonstrates a conceptual understanding of probability and counting techniques.

Seventh Grade

Statistics and Probability

Investigate chance processes and develop, use, and evaluate probability models.

Statistics and Probability

Using Probability to Make Decisions

Calculate expected values and use them to solve problems

Use probability to evaluate outcomes of decisions

Grades 3-5

Data Analysis and Probability

Develop and evaluate inferences and predictions that are based on data

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

4th grade

Data Analysis and Probability

Standard 4-6: The student will demonstrate through the mathematical processes an understanding of the impact of data-collection methods, the appropriate graph for categorical or numerical data, and the analysis of possible outcomes for a simple event.

5th grade

Data Analysis and Probability

The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of basic concepts of probability.

The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of b

3rd Grade

Probability and Statistics

3.23 The student will investigate and describe the concept of probability as chance and list possible results of a given situation.

Student Prerequisites

Technological: Students must be able to:

use a browser experimenting with the activities.

Teacher Preparation

enough stations so that each pair of students can be working at an individual station. (You
may want to have multiples of each station because some stations take longer to complete than
others.)

2 race boards and 4 race cars

8 dice

2 pieces of paper numbered 1- 12

10 square pieces of paper or 10 poker chips

an opaque bag

15 white marbles

5 red marbles

a spinner

3 index cards (a mole drawn on the reverse of one card)

2 pennies

a deck of playing cards

access to a browser

paper

pencil

Key Terms

experimental probability

The chances of something happening, based on repeated testing and observing results. It is the ratio of the number of times an event occurred to the number of times tested. For example, to find the experimental probability of winning a game, one must play the game many times, then divide the number of games won by the total number of games played

outcome

Any one of the possible results of an experiment

theoretical probability

The chances of events happening as determined by calculating results that would occur under ideal circumstances. For example, the theoretical probability of rolling a 4 on a four-sided die is 1/4 or 25%, because there is one chance in four to roll a 4, and under ideal circumstances one out of every four rolls would be a 4. Contrast with experimental probability

Lesson Outline

Focus and Review

Introduce the idea of probability through a discussion that they can relate to. Students may be
familiar with winning prizes through cereal boxes or soda cans for instance. Students will be able
to calculate both experimental and theoretical probabilities as well as display probabilities in
both graphical and fraction form.

Objectives

Let the students know what they will be learning and doing today. Say something like this:

Today we are going to explore probability with a number of different activities.

We will be moving around the classroom and using the computer today, but for now I would like
you to remain in your seat with the computer off or closed until I give you further
instructions.

Teacher Input

Work through an example work station with the students.

Fill out the appropriate section on the with the class.

Explain the procedures to be followed at each station:

Penny Flip

Write whether you think the coin is more likely to land on heads or tails and why.

Calculate the theoretical probability.

There should be 2 pennies at the station. Each person should flip the penny and record the
number of times it lands on heads and the number of times it lands on tails.

Make a graph representing the results you obtained from the penny flip.

Each student should number a piece of paper 2-12 and place 10 chips or paper squares on 10
numbers. The pieces of paper do not need to be placed on different numbers.

Players roll the dice and the highest roll goes first.

Player 1: roll the dice, calculate your sum, and record this number on your data sheet. If
you have a marker on that number, remove it.

Player 2: roll the dice, calculate your sum, and record the number on your data sheet. If
you have a marker on that number remove it.

The first player to remove all of his/her markers wins.

You may also want to have a computer station set up for the students to work with several
probability applets that model some of the activities at the various stations.
Some appropriate applets are:

Have each group share the experimental data they collected from one experiment. Ask them if
the experimental probability they calculated is the same as the theoretical probability.

Reinforce the concepts of theoretical verses experimental probability.

Compile the class' data for all the experiments and compare the individual group experimental
results to the collective class results. The compiled class results should be closer to the
theoretical probability than most individual group's results.

Discuss why this is so.

Discuss why computers might be helpful when working with probability experiments.