Activity Plan, Math 2
How Do Your Marbles Roll?
Lesson Summary: Probabilities, rations, and percentages can be found all around us. In this activity, the students will participate in a hands-on project dealing with probability and statistics in which they discover how increasing the sample size affects the accuracy of their predictions. They then use the proportions of the different colored marbles to determine the probability of different outcomes.
Subject: Math: Probability
- Target Grade: 8
- Upper Bound: 8
- Lower Bound: 6
Time Required: One class period.
- colored marbles/vase stones in 4 different colors - need 40 marbles for each group in the class - jellybeans may be substituted
- lunch-sized brown paper bags
- Before class begins, take four bags of differently-colored marbles/vase stones and mix them together. Draw 40 marbles from your stock and place them in the paper bag. Make sure you have at least 40 marbles for each group.
- Divide the class into groups of four and assign each student in the group one of the following jobs: Selector, Scribe, Analyst, and Collector.
- Hand out one copy of Worksheet 1 to each group. The Scribe will be responsible for filling out the designated parts of the worksheet.
- Tell the student groups that they must make a prediction about the percentage compositions of each of the four marble colors found in the opaque bag. Write the hypothesis on the worksheet.
- To begin, the Selector takes out one marble from the bag.
- The Analyst will call out the color of the marble, which will be recorded by the Scribe in the appropriate cell of the table. The numbers in each cell of each row should sum up to the total number of marbles in each row.
- The Collector will then place the recorded marble in a second bag.
- Repeat steps 3-5 until a total of ten marbles have been drawn and recorded.
- As a group, come up with the percentages of each marble color that has been drawn and record the four colors observed thus far. Add the percentage together to make sure they equal 100%.
- Pick and record ten more marbles, record these numbers and then recalculate the percentages of each marble color based on which colors have been drawn thus far. Note that the numbers in each cell are cumulative totals. For example, for the second set of 10-marbles, if there are two red marbles, then add 2 to the number of red marbles for the first second of 10-marbles and record the new red marble total for Marbles 1-20. The instructor should ensure the groups are keeping track of the up-to-date probabilities. Before continuing to the next step, the appropriate boxes on the worksheet should be completely filled in.
- Continue until all marbles have been drawn.
- Determine and record the actual percentages of each marble color in the bag in the last row of the data table.
- At this point, the instructor should survey the marble color data from all the groups in the class and write the totals on the board. The teacher and the class should together calculate the total numbers of each color marble and then find the total class percentages for each color. Have all the students record the class percentage for each color on their own worksheet data table on the last row.
- Have the class answer and discuss the following questions:
- Did the percentages each time you calculated follow a trend?
- Did percentages shift greatly during any part of the activity? If so, when did it happen: beginning, middle, or end?
- What did you notice about your percentages as you removed more and more marbles from the bag?
- How close was your groupís calculated percentage for each colored marble compared to the class percentage for each color?
- Are probabilities more or less accurate when using data from more objects? Why?
- Do you need to count every single marble to get a good estimate of the color percentages?
- Hand out Worksheet 2 to every student and have them answer the questions and turn it in to be graded.
8.3 (A) Compare and contrast proportional and non-proportional relationships
8.3 (B) Find solutions to problems involving percents and rates
8.11 (B) Use probabilities and experimental results to predict and make decisions
8.11 (C) Use different models to simulate an event
8.13 (A) Evaluate methods of sampling for validity of inferences from the data set
8.2 (B) Collect data by observing and measuring
8.2 (C) Organize, analyze, evaluate, make inferences, and predict trends
8.4 (B) Extrapolate from collected information to make predictions