* * Introduction **

These lessons are designed for introductory statistics classes at almost any level, but specifically 10-12 grade and/or early college. They can, however, be modified to apply to earlier grades (for instance, to teach the concept of modeling without the burden of analytic proofs.

In order to use the lesson to the fullest, the students should have some previous experience in:

• probability (permutations and combinations)
• using the internet (particularly the World Wide Web)
• limited uses of modeling

Materials needed:

• access to the Internet
• Macintosh (preferred, but not absolutely necessary)
• spreadsheet software (preferred, but not necessary)
• dice
• coins
• cards
• any other materials that can be used to make effective models

* Objectives *

• the students will be able to create models for a variety of expected value problems

• the students will be able to discover the expected value of a variety of problems, either through modeling, through analytical means, or both

• the students will be able to articulate the differences between analytical and empirical solutions (both orally and written)

• the students will be able to articulate the connections between probability and expected value (both orally and written)

• the students will be able to articulate the meaning of expected value (both orally and written)

* Expectations *

For all activities the students are expected to work together to come up with shared definitions for each concept.

For all activities the students are expected to formulate these definitions and explain them both orally and on paper.

For all questions the students are expected to write explanations for their answers and describe the methods they used to come up with them.

* How these lessons fit into the NCTM Standards *

Mathematics as Problem Solving: students will learn to model everyday problems into familiar mathematical concepts with which they are familiar

Mathematics as Communication: students will reflect upon stochastic ideas and relationships; they will formulate mathematical definitions and express generalizations discovered through investigations; they will express mathematical ideas both orally and written; they will be exposed to different forms of mathematical notation to help build an appreciation of the power and efficiency of notational language

Mathematics as Reasoning: students will make and test conjectures, follow logical arguments, judge the validity of arguments, and construct simple valid arguments

Mathematics Connections: students will recognize equivalent representations of the same concept (graphical, formulaic, prosaic); relate procedures in one representation to procedures in an equivalent representation

Please continue on to the Day 1 of the daily lesson plan,

or you can skip to:

Day 2

Day 3

Day 4

Day 5

I hope you and your students find these lessons interesting and fun. If you have any suggestions, questions, or comments, please don't hesitate to write me: Jay Hill.