Gold Seal Lesson:
Over/Under Seven

Copernicus Education Gateway

Subject:

Mathematics

Grade:

5-8

ICLE Standards:

Probability: Model situations by developing and carrying out experiments or simulations to determine probabilities; develop an appreciation for the pervasive use of probability in the real world.

Statistics: Collect, organize and represent data using lists, tables and graphs.

Performance Task:

Jeremy went to the State Fair with his family. On the midway, there were many games of chance that seemed very popular with the fairgoers. He wondered about the probability of winning at these games. 

One game, Over/Under Seven, particularly intrigued him. In this game, you put your money on one of three circles: over seven, equal to seven and under seven. The game man would roll two dice and then add the numbers on each die. You won if the sum matched the circle on which you put your money. Jeremy wanted to play this game and wondered which circle gave him the best chance of winning. Your task is to help Jeremy decide where to put his money. To do this you will simulate the game by rolling a pair of dice 72 times. 

Make a chart of all the various sums that are possible, and each time you roll the dice, record the sum of the dice in the appropriate spot in your chart. Make a graph displaying your data. Now combine your data into a new chart, showing the number of times you rolled a sum under seven, over seven and equal to seven. Make a graph of this composite chart. Analyze your composite chart and graph. Write a short paragraph interpreting the results of your experiment. Make a recommendation to Jeremy as to how he should play the game and support your recommendation.

Knowledge / Skills:

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

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).  (m26)

Use the Counting Principle to determine the probability of events occurring jointly (e.g., if one activity can occur in any of m ways and another in any one of n ways, then the total number of ways both activities can occur is mn).  (m56)

Use expository writing skills in subjects other than English language arts.  (ela58)

Rubric:

5 Points  =  The student completes the first chart correctly. All possible sums are included. This chart illustrates the dice were rolled 72 times. The data are combined properly into the required composite chart. Charts are neatly organized and properly labeled. Graphs are correctly made, are neat and accurate, are properly labeled and correctly matched with the charts. The student correctly analyzes and
interprets his/her composite graph and makes an appropriate and well justified recommendation.

3 Points  =  The student completes the first chart correctly, but fails to label it properly. It is not neatly organized/constructed. All possible sums are included. Chart indicates the dice were rolled the correct number of times. The data are combined properly into the required composite chart, but it is not neatly organized, nor properly labeled. Graphs are correctly made, but lack neatness and are not completely labeled. They correctly match with the charts. The student correctly analyzes and interprets his/her graph and makes an appropriate recommendation, but fails to justify the recommendation. 

1 Point  =  The student completes the first chart, but some of the possible sums are missing. Chart illustrates the dice were not rolled the proper number of times. The data are incorrectly combined into the composite chart. Charts are poorly organized and constructed, lack neatness and are improperly labeled. Graphs are made from the table, but they are inaccurate, poorly constructed and unlabeled. Graphs do not match the charts. The student's analysis and interpretation of the composite graph is vague and unclear. No reasonable recommendation is made, and no proper justification is given.

0 Points  =  The student fails to complete the task.

Keywords:

GEOMETRY
EXPOSITION STATISTICS
CHARTS
DATA ANALYSIS
DATA COLLECTION
GRAPHS
INFERENCE
PREDICTION
COMPUTATION
PROBLEM SOLVING
SAMPLING
SIMULATIONS

Grades:

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

ICLE Application:

D

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