Gold Seal Lesson:
Rolling A Seven

Copernicus Education Gateway

Subject:

Mathematics

Grade:

5-8

ICLE Standards:

Probability: Modeling situations by devising and carrying out experiments or simulations to determine probabilities; make predictions that are based on experimental or theoretical probabilities.

Problem Solving: Apply concepts of chance and techniques of data handling to evaluate and solve problems in a familiar context.

Performance Task:

You are playing a game with a friend using two dice. To win, you must roll a seven (any combination of the two dice that add to seven). Answer each of the following questions, recording your predictions on a sheet of paper. Justify each prediction.

1. What do you think your chances are of rolling a seven on any one roll of the two dice?

2. How many times do you think you would have to roll the two dice before rolling a seven?

3. If you roll the two dice 30 times, how many times do you think you would roll a seven?

Now you are to conduct experiments to see how close actual results are to your prediction, putting any written work on the sheet of paper used for your predictions to the questions above.

• Experiment 1: Roll 2 dice 50 times, recording the sum of the two dice after each roll. Keep track of your sum for each roll, using a tally, chart, table, etc. How many times did you roll a sum of seven? Compare, in writing, your results with the prediction you made in question 1 above.

• Experiment 2: Roll 2 dice until you get a seven. How many rolls did it take before you rolled a seven? Repeat this experiment 20 time, each time recording the number of times it took you to roll a seven. What is the mean number of times you had to roll the two dice before rolling a seven? Compare your results with your prediction in question 2 above.

• Experiment 3: Roll your two dice 30 times, recording the sum of the two dice for each roll. How many times did you roll a seven? Compare your results with your prediction in question 3 above.

Notes to the teacher: You may wish to have the students combine their individual results to get whole class results. That would give the opportunity to discuss sample size and number of trials needed to close the “gap” between the theoretical and experimental probabilities. This student activity should be followed with a discussion/activity for students to develop an understanding of theoretical probability. They would then be able to answer question 1 from a theoretical point of view and would be able to discuss expectations and other questions related to the task. Students should then compare and contrast the ideas of experimental and theoretical probabilities.

Knowledge / Skills:

Understand the best procedures for statistical data collection, organization, and display. (m5)

Understand the characteristics of measures of central tendency (i.e., mean, median, and mode). (m15)

Understand the characteristic differences between theoretical and empirical probability (e.g., the theoretic probability of rolling a six an a die is 1/6; empirical probability is derived from repeated experimentation or accumulated statistics). (m20)

Determine the probability of single and compound events using the basic premise that the probability of an event is equal to the number of ways it can occur divided by the total number of outcomes. (m25)

Know how to determine combinations (i.e., the various grouping a set may be arranged in without regard to order). (m43)

Rubric:

4 Points = The student works independently on the task. He/she makes good predictions and gives a reasonable justification for all three questions. The student conducts the three experiments correctly, organizing his/her work in a neat and logical manner. The student makes meaningfully comparisons of his/ her experimental results to predictions.

3 Points = The student needs some assistance in performing the task. His/her predictions are fairly reasonable. He/she states justifications, but they are not convincing. The student conducts the three experiments correctly, but the organization and report of data are somewhat difficult to follow. The student makes comparisons of his/her experimental results to predictions, but they are not sound.

2 Points = The student needs a lot of assistance in performing the task. His/her predictions are not well stated and/or the justification of predictions are vague. The student only conducts two of the three experiments. His/her presentation of the data lacks organization and is sloppily recorded.  Comparisons between experimental results and predictions are unclear.

1 Point = Even with considerable assistance, the student does not complete the task. His/her predictions and justifications are incomplete and show little understanding of simple probability concepts. The student conducts at most one of the three experiments. The data are haphazardly recorded, with little attention given to neatness or logical order. Comparisons between experimental results and predictions, when made, are meaningless.

Keywords:

GEOMETRY
CENTRAL TENDENCY STATISTICS
CHARTS
DATA COLLECTION
INFERENCE
PREDICTION
PROBABILITY
PROBLEM SOLVING
COMPUTATION
SAMPLING
TABLES 
MODELS & CONSTRUCTIONS

Grades:

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [x] - 6 [x] - 7 [x] - 8 [x] - 9 [] - 10 [] - 11 [] - 12 []

ICLE Application:

D

© 2000 International Center for Leadership in Education
1587 Route 146 - Rexford - NY - 12148
518.399.2776 Fax: 518.399.7607
97