Two-Way Frequency Tables
I can find joint, marginal and conditional relative frequencies from a two-way table.
What students learn
Students learn to read a two-way table, find joint, marginal and conditional relative frequencies with the right denominator, and judge association by comparing row percents.
See inside
The key rule
The words after "of the" name the group. Its total is the denominator.
percent = part ÷ whole × 100
Round only at the end, to the place the question names.
Watch out
Of 100 students, 60 play a sport, and 18 of those 60 have a job. A student says 18% of the athletes have a job.
The mistake: 18 ÷ 100 = 0.18, or 18%100 is everyone, not the athletes.
The fix: 18 ÷ 60 = 0.3, or 30%The group is the 60 athletes.
The mistakes it targets
- Divides by the grand total when the question names a group
- Divides a joint frequency by a row total
- Uses a column total for a row group
- Uses a row total for a column group
- Compares raw counts instead of percents to judge association
- Treats the two conditional percents of one cell as equal
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 10 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, six common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.