standard_description: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
problem_activity: Warm-up
The mathematical purpose of this lesson is for students to motivate a conceptual understanding of the
addition rule
. Monitor for students discussing counting people twice.
Launch
Arrange students in groups of 2. Give students quiet work time and then time to share their work with a partner.
Student Facing
The table displays information about people at a neighborhood park.
|                   | wearing sneakers | not wearing sneakers | total |
|-------------------|------------------|----------------------|-------|
|   wearing a hat   |                  |                      |       |
| not wearing a hat |                  |                      |       |
|       total       |                  |                      |       |
Andre says the number of people wearing sneakers or wearing a hat is 21, because there are a total of 10 people wearing a hat and a total of 11 people wearing sneakers. Is Andre correct? Explain your reasoning.
What is the probability that a person selected at random from those in the park is wearing sneakers or wearing a hat?
Student Response
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Activity Synthesis
The goal of this discussion is to use the context as a model to introduce a conceptual understanding of the addition rule. Ask previously identified students to explain why Andre counted some people twice when he stated that the number of people wearing sneakers or wearing a hat is 21.
Here are some questions for discussion.
“Why did Andre need to subtract 8 from 21 to get the correct answer?” (It needs to be subtracted because the 8 people that were wearing sneakers and wearing a hat were counted twice. We counted them twice when adding the column total for wearing sneakers and the row total for wearing a hat.)
“How could the number of people wearing sneakers or wearing a hat be represented using a Venn diagram?” (A Venn diagram could be made using two overlapping circles, one for wearing sneakers and one for wearing a hat. There would be 8 people in the middle where the two circles overlap. There would be an additional 3 people in the wearing sneakers circle representing those wearing sneakers but not a hat. There would also be an additional 2 people in the circle representing those wearing a hat but not sneakers.)
“What is the probability that a person selected at random is not wearing sneakers and not wearing a hat?” (
\(\frac{12}{25}\)
)


aligns: no