Two-Way Frequency Tables
I can read a two-way table and compute the relative frequency the question actually asks for.
The problem this sheet solves
Conditional relative frequency is computed against the grand total, because the grand total is the number students can see. The same cell gives three honest answers — 18 per cent of everyone, 30 per cent of the athletes, 45 per cent of the job-holders — and none of them is a mistake. And raw counts cannot show association at all when the groups are different sizes. This is taught as a READING instruction rather than a rule about tables: the words after of the name the group, and that group's total is the denominator. Underlining them ends the error. One anatomy tile is the three fractions side by side, which is what to point at when a student asks which per cent is the real one. Two tables are given on purpose — one with an association and one with none — so no association is a finding rather than a failure.
The key rule
The words after "of the" name the group, and that group's total is the denominator. Read those words before writing the fraction.
Of the what?
Watch out
The mistake: A student answers 18 per cent, dividing by 100.
The fix: The question says of the athletes, and there are 60 of them. 18 out of 60 is 30 per cent. Dividing by 100 answers a question nobody asked.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
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.