This lesson introduces students to the idea that probability and geometry are sometimes linked.
Students will practice what they already know about geometry to learn more about probability.

Objectives

Upon completion of this lesson, students will:

have practiced calculating probability

understand how geometry can help solve probability problems

Standards Addressed:

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 3

Statistics, Data Analysis, and Probability

1.0 Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions

Grade 4

Statistics, Data Analysis, and Probability

2.0 Students make predictions for simple probability situations

Seventh Grade

Statistics and Probability

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

Grades 3-5

Data Analysis and Probability

Understand and apply basic concepts of probability

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

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.

4th Grade

Data Analysis & Probability

The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

Geometry

The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures.

5th Grade

Data Analysis & Probability

The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

Geometry

The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures.

Grade 5

Probability and Statistics

12. The student describes and predicts the results of a probability
experiment.

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.

4th Grade

Probability and Statistics

4.19.b The student will determine the probability of a given simple event, using concrete materials.

5th Grade

Probability and Statistics

5.18 The student will, given a problem situation, collect, organize, and display a set of numerical data in a variety of forms, using bar graphs, stem-and-leaf plots, and line graphs, to draw conclusions and make predictions.

Student Prerequisites

Technological: Students must be able to:

perform basic mouse manipulations such as point, click and drag

use a browser for experimenting with the activities

Geometry: Students must be able to:

understand the basics of angles

Arithmetic: Students must be able to:

work with fractions

understand the relationship between fractions and percentages

Teacher Preparation

Access to a browser

Pencil and paper

The
Spinner Game and the
Adjustable Spinner Game require either computer access or a set of materials for building spinners for each group of
students.

Key Terms

estimate

The best guess arrived at after considering all the information given in a problem

probability

The measure of how likely it is for an event to occur. The probability of an event is always a number between zero and 100%. The meaning (interpretation) of probability is the subject of theories of probability. However, any rule for assigning probabilities to events has to satisfy the axioms of probability

Lesson Outline

Focus and Review

Remind students what has been learned in previous lessons that will be pertinent to this lesson
and/or have them begin to think about the words and ideas of this lesson:

Who has ever watched the game wheel of fortune?

Have you ever noticed when they put the $10,000 space on the wheel it is significantly smaller
than the rest of the spaces?

Do you think size of the space affects whether or not you will land on the space?

Objectives

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

Today, class, we are going to begin learning about probability and its relationship to
geometry.

We are going to use the computers to learn about probability, but please do not turn your
computers on until I ask you to. I want to show you a little about this activity first.

Teacher Input

Lead a
discussion about how probability and geometry are related.

Guided Practice

Open the
Spinner Game in your browser and explain how to work the applet.

Ask students which color you're more likely to spin.

Ask students how you could make one color more likely.

Open the
Adjustable Spinner in your browser and explain how to work the applet.

Discuss what the students discovered through the exploration questions.

Ask students how this applies to dice.

Alternate Outline

If only one computer is available, this lesson can be rearranged in the following ways:

Have students construct spinners with different sized sections out of several different
materials, and then compare the results they obtain. Which materials or designs produce
spinners that produce more truly "random" results? Compare the results of many spins with
these spinners with the computer-generated results from the
Spinner Game and the
Adjustable Spinner Game to show students the advantage of using a computer model to produce accurate results.

Give extra time with the applets for students who are having trouble understanding.