CCSS.Math.Content.8.SP.A.4
The Standard
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.
Common Core State Standards for Mathematics · Statistics and Probability
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students organize paired categorical data from the same people in a two-way table. They calculate relative frequencies by row or column, then compare the percentages to identify a possible association.
What Mastery Looks Like
- Students complete a two-way table accurately and calculate row or column relative frequencies. They compare percentages using the same base group and describe an association without claiming causation.
Common Misconceptions
- Students compare raw counts even when the groups have different sizes. They divide by the grand total instead of the correct row or column total. They may treat any percentage difference as proof of causation.
How to Assess It
- Exit ticket: Of 24 bus riders, 18 buy lunch; of 16 car riders, 6 buy lunch. Have students calculate row percentages and write one sentence describing the association.
Lesson moves
Ways to Teach It
Survey classmates about two yes-or-no questions, place sticky notes in a four-cell table, and calculate row percentages.
Ask students to write: “Which percentages should we compare, and what do they suggest about the relationship between these variables?”
Run a card sort matching two-way tables, relative-frequency tables, and accurate claims about association.
Analyze school lunch and transportation data to see whether lunch choice differs between bus riders, walkers, and car riders.
Learning progression
Where This Standard Sits
See the whole path on the Statistics & Probability progression map.
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.6.RP.A.1
Relative frequencies in two-way tables are ratios of counts, so ratio language supports calculating and comparing row or column percentages.
- CCSS.Math.Content.6.RP.A.3c
Percent as a rate per 100 supports calculating and interpreting row or column relative frequencies in two-way tables.
- CCSS.Math.Content.6.SP.A.1
Recognizing questions with variable data supports understanding why two categorical variables are collected and compared for association.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSS-CP.A.4
Students extend two-way table counts and relative frequencies to conditional probability and independence judgments.
- CCSS.Math.Content.HSS-ID.B.5
High school work extends two-way tables from row and column relative frequencies to joint, marginal, and conditional interpretations.
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