Title
Lotto Winners (Kim Kendrick)
Goals
(1) Students will examine the concept probability as it relates to real-world applications.
(2) Students will use communication skills and reasoning when describing the solution to a real-world problem.
Abstract
We are going to examine the problem of being absolutely sure that you win a lotto drawing. The lotto is based on selecting 6 numbers from 40, and matching all 6 numbers exactly. The students will have to determine if it is possible, state all assumptions they have made, and explain their reasoning. This project involves devising a plan, mapping out a strategy, and writing a proposal. The students will work in groups to iron out any problems they may have encountered in the proposal.
Problem Statement
Everyone wants to be an instant millionaire, and that's why the lotto is such an attractive game of "chance". It only takes one selection of the correct 6 numbers from the 40 numbers possible to put yourself on easy street. Possibly the most attractive part about this 'investment' is that the cost is almost equivalent to the cost of a hamburger. As the jackpots increase some people have decided to try to sweep the lotto. That is to say that they invest a certain amount of money to buy all of the possible lotto combinations just to ensure that they win the jackpot. Let's examine this more closely. You are hired by an investor to sweep the next lotto. You must devise a plan, including all expenses, suggestions, cautions, and assumptions on the best way to execute it.
Instructor Suggestions
(1) Set the stage by discussing the "Problem Statement" (see above) with the class.
(2) Distribute the "Lotto Winners" activity sheet (see attachment) and allow the students to individually read the first part of the activity.
(3) When all of the students are finished reading, have the class complete the assignment individually. They should have a good understanding and reasoning for the plan they have devised.
(4) Have the students form small groups (3-4 students) to read over each other's work and clear up any general questions.
(5) When the small-groups are finished, ask for volunteers to share their plan and explain their method and reasoning involved in arriving at their solution.
(6) Discuss the students' work as it relates probability and the communicating in the real-world.
Materials
"Lotto Winners" activity sheet, chalk board, Blank paper, Calculators
Time
Introduction of problem statement (5 minutes), Individual work (25 minutes), Small group work (10-15 minutes), Presentation of small-group work (15 minutes), Large group discussion (5 minutes)
Mathematics Concepts
Discrete Mathematics Concepts:
Project modeling, probability.
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections (within mathematics and across disciplines), Algebra, Probability, Discrete Mathematics.
Colorado Model Content Standards Addressed
Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity will be used in the first year of the Integrated Math Program as a separate module in probability. It could also be used in a traditional Algebra I class when the focus is on developing organizational techniques and applications of scientific methods to solve real-world problems.
Variations/Comments
Students may have trouble planning for such a large task. Pay close attention to any misguided reasoning which could affect the outcome of the entire project. Also, the plan could be submitted in business form, with an accompany cover sheet for the proposal.
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete Mathematics Through Applications. New York: W.H. Freeman and Company.