Correlation Coefficient and Causation
I can describe a correlation coefficient and explain why correlation does not show causation.
What students learn
Students learn to read a correlation coefficient r for direction and strength, say what it does not measure, and explain why a correlation does not show that one variable causes another.
See inside
The key rule
Correlation is not causation: a lurking variable may drive both. A randomized experiment can show cause.
−1 ≤ r ≤ 1
On this sheet, ignore the sign: 0.8 or more is strong, 0.5 up to 0.8 is moderate, under 0.5 is weak.
Watch out
In a town, ice cream sales and drownings have r = 0.92. A student says ice cream causes drownings.
The mistake: r = 0.92 is high, so ice cream causes drowningsA correlation alone cannot show cause.
The fix: hot weather drives both: more ice cream, more swimmingA lurking variable moves them together.
The mistakes it targets
- Reads a strong correlation as proof of cause
- Compares signed r values instead of their sizes for strength
- Reads r = 0 as no relationship instead of no linear association
- Names one of the two variables as the lurking variable
- Treats a self-chosen group as proof of cause
- Reads a negative correlation as weak
The interactive Teacher Deck (31 slides, PowerPoint)
- The Learn page taught on screen: 9 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (three 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.