Exploring Diversity with Math (9-12)
Diversity Beans - Exploring Diversity with Math Lesson Plan (Grades 9-12)
Objective: Use math to explore diversity.
Materials Required: Approx. 1.5 oz of Diversity Beans per student.
Procedure:
A. Introduce the Diversity Beans to the class, explain that there are 6 different colors (black, white, orange, green, yellow, and red) and twelve flavors (cinnamon, orange, root beer, coconut, sour apple, licorice, pineapple, grape, huckleberry, cherry, lemon, and lime).
B. Divide the class into six groups. Count the beans and have the students determine how many beans should be given to each group to evenly divide the beans.
C. Divide the beans by making six piles that are approximately equal in size and give each group a pile.
D. Have each group count their beans and determine the fraction of the original beans that they have.
E. Have each group calculate the probability of a bean being a certain color or flavor. Discuss the concept of probability and that each color should be 1/6 th of the total.
F. Have each group count the number of beans in each color for their pile.
G. Have them express the number of each color bean as a fraction of the total number of beans their group received and as a fraction of the original total amount of beans (Note: fractions should be reduced where possible). Have the class add the fractions of each color per group together to get the original fraction of each color out of the total amount.
H. Ask the class to match color to flavor for the beans.
I. Have the class choose a color/flavor that they want to taste.
J. Have each student take a bean of the chosen color and taste it.
K. Record the results of the flavors tasted as fractions of the total amount tasted.
L. Repeat for the other five colors and record the results as fractions.
M. Add the flavors by fraction to determine the fraction for each flavor of all the beans tasted.
N. Make a 6x12 matrix on the board and fill in the spaces with the fraction of total beans tasted for each possibility.
O. Bring up the concept of statistics and compare statistics to probability.
P. Explain the difference between a priori calculations and post experiment calculations.
Q. Ask the class for other examples where probability and statistics would pertain (such as flipping a coin, rolling a dice, or drawing a card from a deck of cards).
R. Discuss the possible reasons for any discrepancies between expected values and observed outcomes (randomness, chance, small sample size, etc).
S. Have the students determine what the possible outcomes and expected values for each combination are, and compare the expected values to the actual results obtained.
T. Lead the class in a discussion of expected values versus experimentally obtained values, reinforce the concepts of probability and statistics.
U. Ask the class to write a list of how many different ways people can be classified (sex, color, nationality, ethnicity, religious beliefs, age, marital status, tall, short, brown hair, blue eyed, extroverted, shy, talkative, etc).
V. Ask the class to try to put together a matrix that would cover all the possibilities.
W. Discuss with the class the fact that the appearance of people does not relate to the behavior and attitudes of the people. Define diversity in terms of the discussion. Relate how a group of people who appear the same on the outside may be very different on the inside, like the beans. Explain that diversity means accepting the fact that people are all different and that we need to get to know people before judging them on appearance.
X. Relate this to probability and statistics, explaining that judging someone based on appearance, background, or stereotypes is like rolling the dice- the probability of success is low. Discuss that in the case of people, the possible outcomes can not even be determined.
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