Unit Plan 31 (Grade 8 Math): Two-Way Tables & Associations
8th graders construct and interpret two-way relative frequency tables to explore relationships between categorical variables. They compare conditional percentages, identify possible associations, and write evidence-based conclusions using precise, responsible statistical language.
Focus: Construct and interpret two-way relative frequency tables; describe associations between two categorical variables.
Grade Level: 8
Subject Area: Mathematics (Statistics & Probability • Data Analysis)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week shifts from numerical pairs to categorical pairs. Students collect or use given data about two yes/no or multi-category variables (for example, “plays a sport” vs “honor roll,” “walks to school” vs “on-time arrival,” “prefers texting” vs “has a phone”). They’ll build two-way frequency tables, compute relative frequencies by rows and by columns, and use those percentages to describe whether there is a possible association between the two variables. Emphasis: clean structure (joint, marginal, conditional), clear percent statements, and responsible language (association ≠ causation).
Essential Questions
- What does a two-way table show that a single tally cannot?
- How do row, column, and overall relative frequencies help us compare groups fairly?
- When do differences in conditional percentages suggest a possible association?
- How should we communicate findings precisely and responsibly?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Construct a two-way frequency table from raw categorical data; compute marginal totals.
- Convert counts to relative frequencies: overall, row-wise, and column-wise percentages.
- Compare conditional relative frequencies to describe possible associations between two categorical variables.
- Write brief, evidence-based conclusions, including cautions about sample size, bias, and no causal claims.
Standards Alignment — CCSS Grade 8
- 8.SP.4: Construct and interpret two-way tables of categorical data; use relative frequencies to describe possible association between two variables.
Success Criteria (student-friendly)
- I can build a correct table with joint and marginal totals.
- I can compute and label row/column percentages accurately.
- I can decide if there seems to be a possible association by comparing conditional percentages.
- I can write a clear conclusion with numbers and a sensible caution.