Correlation Coefficient and Causation
I can read a correlation coefficient, and say why it cannot show that one thing causes another.
The problem this sheet solves
A correlation is a statement about two columns of numbers. Causation is a claim about what would happen if you CHANGED one, and no amount of watching can establish it. The other half of the trouble is what r does not measure: a set where y is exactly x squared — no noise anywhere — has a correlation of exactly zero. The habit taught here is three sentences said out loud in order: x causes y, y causes x, something else causes both. The third gets skipped and is usually the answer. Contexts run from the obviously silly to the genuinely hard — shoe size and reading level in young children, where the lurking variable is age and neither column mentions it. It closes with what does settle causation: an experiment with random assignment, and why nothing observed can substitute.
The key rule
A correlation says two columns of numbers move together. Causation says changing one would change the other, and only an experiment can show that.
What else could explain it?
Watch out
The mistake: A student concludes that buying ice cream causes drownings.
The fix: Hot weather causes both: more ice cream sold, and more people swimming. The two columns move together because a third thing is moving them.
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.