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Content Area: Math
Index: 4.4B Grade 6 CPI 4
Standard: 4.4 - Data Analysis, Probability, and Discrete Mathematics
Strand: B - Probability
Cumulative Progress Indicator: 4 - The student will model situations involving probability using simulations (with spinners, dice) and theoretical models.
Grade: 6
Sample Activities:
· Students examine the probability of a family with four children having two boys and two girls by simulating the situation using four coins. They first choose which side of the coin will represent males and which will represent females. They toss the set of coins 50 times and record their results as the number of boys and the number of girls in each "family." They compare the results of their experiment with the prediction based on probability. They also survey a large sample of students in the school and record the family composition of all families with four children. All of these are used to discuss the likelihood of an evenly-matched family.
· A 25-cent "prize" machine in the grocery store contains an equal number of each of six plastic containers with Power Ranger tattoos. Students are asked to determine how many containers they need to buy to have a good chance of getting all six. They simulate this situation with a bag containing an equal number of six different colored marbles. They draw out, record, and replace one marble at a time until they have drawn marbles of all six colors, recording the number of times that took. They repeat the simulation three times. The class results are gathered and discussed. One issue discussed is whether the model is a good one for the situation or whether it should be modified in some way to better represent reality.
· Students read Caps for Sale by Esphyr Slobodkina. The peddler in the story sells caps and wears his entire inventory on his head: a checked cap and four each of identical blue, gray, and brown hats. Students use concrete objects to model some of the different orders in which the hats can be worn. They come to realize that there are many ways and try to discover the total number of different ways. They search for an efficient way to determine the number of permutations.
· Students work through the Two-Toned Towers and Pizza Possibilities lessons. They make a systematic list of all the towers built out of four red and blue cubes (or of all the pizza combinations) and calculate the probability that a tower has three or four blue cubes.
Vignettes (PDF Format):
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