CCSS.Math.Content.HSS-CP.A.4
The standard
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
Common Core State Standards for Mathematics
What this standard means
Students need to organize counts for two categorical variables in a two-way table, then use the table to find totals, joint probabilities, conditional probabilities, and decide whether two events look independent. They should read phrases like “given that” as a signal to restrict the group first.
Mastery looks like choosing the right denominator every time and explaining results in context, not just writing a fraction. Students often use the grand total when they should use a row or column total. They also mix up independence with “not related at all” instead of comparing conditional probabilities to overall probabilities.
Ways to teach it
- Have students survey 30 classmates on grade level and preferred lunch item, then build a two-way frequency table with row and column totals.
- Ask students to write: How does the probability of liking pizza change when we only look at juniors?
- Give a completed two-way table and ask for one joint probability, one conditional probability, and one independence decision.
- Use school club sign-up data by grade and activity type to discuss whether grade level seems related to club choice.
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