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I. Probability Topics:

A.   NCTM Standards addressed

Instructional programs from prekindergarten through grade 12 should enable all students to:

  • Understand the concept of sample space and construct sample spaces in simple cases;

  • Understand the concept of independent events;

  • Know the characteristics of well-designed studies, including the role of randomization in experiments;

  • Use simulations to explore the variability of sample statistics from a known population.

B.  Related Connections

State lotteries, games  

 

II. Assumed Prior Experience With:

percentages, bar graphs, spinners  



III. Rationale

  • Students will use data from simulations to make theoretical generalizations.
  • Students will discuss possible relationships between several given events.
  • Students will gain understanding about their own mathematical intuition about likelihood.  



IV. Learning Objectives:

Students will discuss and gain experience with independent events, sample spaces, equally likely probabilities, and percentages within the context of this simulation.  



V. Materials & Technology Needed: 

Computer lab set up such that:

1. Each computer has Microsoft Excel.

2. Each computer has access to the "Lucky Number" excel file from the "What are the Odds?" website. We have provided tips for you on using spreadsheet simulations.

Preferably a computer monitor large enough for the entire class to see the"Lucky Number" excel file during group discussion.

"Lucky Number" handouts for each student

OPTIONAL:   3 spinners, each equally partitioned with the digits 0 - 9  



VI. Procedure:

1. Pass out a "Lucky Number" handout to each student.

2. Explain the scenario on the top of the handout.  OPTIONAL:  use 3 spinners to demonstrate what is being simulated.

3.Give them time to individually complete the "Before Opening the Lucky Number File" portion of the handout.  Give them a short amount of time, because the object of these predictions is to get an accurate portrayal of their intuitions and misconceptions.

4. Begin by opening up the "Lucky Number" excel file on the classroom monitor.  Explain the set-up that is described in the beginning of the "Before Running Simulations" section of the handout.

5. Again, give them a short amount of time to complete the "Before Running Simulations" section of the handout.

6. Demonstrate for the class what happens when you press F9.  Demonstrate how to enter the your choice numbers into the appropriate cells.

7. Have each student open up the "Lucky Number" excel file at their own computer.

8. Let them begin to work through the remainder of the handout. 

9. Circulate continuously, paying close attention to answers on the worksheet.

10. Once everyone has worked through the handout, display the excel file on the classroom monitor. Have students generalize aloud what they have learned about "lucky numbers".  Ask for volunteers and try out "lucky number" suggestions on the classroom monitor.  Use this time to prove to students that "nice" numbers occur just as often as "more randomly selected" numbers.

11. Show arithmetically that the likelihood of any given 3 digit number occurring in this scenario is 1/1000.    



VII. Assessment:

Thorough examination of the handout both during and after the lesson will allow you to get a feel for what students are thinking about while experimenting with the simulation.