HSS.ID.C.9Common CoreMathStatistics and ProbabilityGrades 9-12
HSS.ID.C.9: Distinguishing Correlation from Causation
In plain English: HSS.ID.C.9 is the Common Core statistics standard that asks students to tell correlation apart from causation. Two variables can be strongly associated because of a lurking variable, because the cause runs the other way, or by chance, so an association alone does not show that one variable changes the other. It is usually taught in Algebra I and introductory Statistics.
Distinguish between correlation and causation.
Common Core State Standards for Mathematics · Domain: Interpreting Categorical and Quantitative Data (ID) · Cluster: Interpret linear models Also written as HSS-ID.C.9 or S-ID.9 · Official standard
Students learn that a correlation, even a strong one, shows only that two variables tend to change together. Causation means that changing one variable would itself change the other. The gap between the two is where many misleading headlines live.
The lesson gives students three alternative explanations to test against any causal claim: a lurking variable that drives both (population size behind libraries and crimes), reverse causation (low grades leading to tutoring visits), and chance (a strong r in a tiny sample). Students then see why a randomized experiment is the usual way to support a causal claim: random assignment spreads lurking variables evenly across the groups. They practice by rewriting headlines so that the claim matches the evidence.
Learning Objectives
By the end of this lesson, students will be able to:
Explain the difference between correlation (variables that change together) and causation (changing one variable changes the other)
Identify a plausible lurking variable that could explain an observed correlation
Recognize reverse causation and chance as other explanations of a correlation
Explain why a randomized experiment can support a causal conclusion and an observational study usually cannot
Rewrite a causal claim so that it matches the evidence behind it
Prior Knowledge Required
Students should already be comfortable with:
Describing positive and negative association in scatter plots 8.SP.A.1
Computing and interpreting the correlation coefficient with technology HSS.ID.C.8
Interpreting the slope of a linear model in context HSS.ID.C.7
Computing a mean and a rate such as "per 1,000 residents"
Display the invented headline and give students three minutes to write before a pair discussion.
Warm-Up Prompt
"A survey of 500 students finds that students who eat breakfast every day have higher average grades than students who skip it. A headline says: Eating Breakfast Raises Your Grades. List at least two other reasons the survey could turn out this way, even if breakfast itself made no difference."
Collect ideas on the board and group them. Students often suggest family routines, sleep, or getting to school on time, which could affect both breakfast and grades. Name this group lurking variables. Keep any idea in which the grades come first, such as students with good grades having more organized mornings, for the reverse-causation discussion.
Direct Instruction20 minutes
Two words, two claims.Correlation (or association) means that two variables tend to move together; r measures it for a linear pattern. Causation means that changing x would change y, all else being equal. Use Diagram 1 to show the three structures, then work through the examples. For every correlation, ask these questions:
Lurking variable? Is there a third variable z that could drive both x and y?
Reverse causation? Could y be causing x instead?
Chance? Is the sample small, or was this one of many pairs of variables that someone checked?
How were the data produced? An observational study records what people already do. A randomized experiment assigns the treatment by chance, which balances lurking variables between groups and can support a causal claim.
Invented data: 8 towns
Town
A
B
C
D
E
F
G
H
Population (thousands)
12
25
40
58
75
96
120
150
Libraries
1
2
2
3
4
4
6
7
Crimes per year
180
365
590
900
1,080
1,500
1,750
2,300
Lurking variable
For the 8 towns in the table, technology gives r between the number of libraries and crimes per year. Then divide to get libraries per 10,000 residents and crimes per 1,000 residents, and compute r again.
Equation: Counts: r ≈ 0.98. Rates: every town has about 14 to 16 crimes per 1,000 residents, and r ≈ -0.36. Population is the lurking variable: bigger towns have more of both. Libraries do not cause crime (Diagram 2).
Reverse causation
A school finds that students who visit the tutoring center often have lower grades than students who never visit. A parent concludes that tutoring hurts grades.
Equation: The arrow likely runs the other way: low grades lead students to seek tutoring. The correlation is real, but it does not show that tutoring lowers grades.
Chance in a small sample
In a group of 6 students, (day of the month of the birthday, quiz score) = (3, 72), (8, 70), (12, 85), (19, 78), (24, 90), (29, 88).
Equation: Technology gives r ≈ 0.82, yet there is no plausible way a birthday date changes a quiz score. With only 6 points, a strong r can appear by chance; a larger sample would be expected to show almost no correlation.
Experiment that supports causation
A class randomly assigns 60 tomato seedlings to two groups of 30. One group gets fertilizer and the other does not; all other care is the same. After 6 weeks the mean heights are 41.2 cm and 36.5 cm.
Equation: Difference in means: 41.2 - 36.5 = 4.7 cm. Because chance, not a person, decided which plants got fertilizer, lurking variables such as sunlight or seed quality should be balanced between the groups, so the difference can reasonably be attributed to the fertilizer.
Stress that a correlation is not useless: it can suggest a cause worth testing, and it can support predictions even when no cause is known. What it cannot do by itself is show that changing x would change y.
Guided Practice15-20 minutes
Pairs read each invented claim, decide which explanation other than causation fits best, and rewrite the claim so it matches the evidence. Share one rewrite per pair.
"Towns with more swimming pools have more cases of heat stroke, so pools cause heat stroke." (Lurking variable: a hot climate. Rewrite: "Hot towns tend to have both more pools and more heat stroke.")
"Students who bring a water bottle to class get higher grades, so water improves learning." (Lurking variables such as being organized or having family support.)
"Neighborhoods with more coffee shops have higher home prices, so opening coffee shops raises home values." (Lurking variable: residents' income; also reverse causation, since shops open where people can pay.)
"Students who own more books score higher on reading tests, so giving every student 50 books will raise scores." (Lurking variables such as family time spent reading; an experiment that randomly assigns book gifts would be needed.)
"People who take more cough medicine cough more often, so cough medicine causes coughing." (Reverse causation and a lurking variable: coughing leads people to take the medicine, and a worse cold drives both.)
Independent Practice15 minutes
Students work alone with technology. The invented data show, for each month of one year in a beach town, the sunscreen sold at one store (hundreds of bottles) and the visits for sunburn to a local clinic.
Invented data: one beach town, January to December
Month
J
F
M
A
M
J
J
A
S
O
N
D
Sunscreen (hundreds)
2
3
5
8
12
16
18
17
11
6
3
2
Sunburn visits
4
9
7
15
25
27
36
28
23
8
7
3
Tasks: (1) Compute r. (Answer: r ≈ 0.97.) (2) A student writes, "Sunscreen causes sunburn." Name a lurking variable that explains the correlation. (Time in strong sun: summer months bring both more sunscreen sales and more sunburns.) (3) Could the causation run the other way? (Partly: people who get burned may buy sunscreen afterward.) (4) Describe what data would be needed to learn whether sunscreen prevents sunburn. (A randomized experiment, for example volunteers randomly assigned to sunscreen or a look-alike lotion on one arm for the same time in the sun.)
Closure5-10 minutes
Exit ticket: (1) In one sentence each, define correlation and causation. (2) Invented data show that teenagers who spend more time on social media report more anxiety. Give one lurking-variable explanation and one reverse-causation explanation. (3) What kind of study could support the claim that social media time causes anxiety, and why? (Sample answers: stress at school or home could drive both; anxious teens may turn to social media more; a randomized experiment in which volunteers are randomly assigned to cut back, because random assignment balances the other variables.)
Differentiation Strategies
For Struggling Students
Give a three-box organizer for each claim: "Could z drive both?", "Could y cause x?", "Could it be chance?", with one sentence starter in each box
Start with claims where the lurking variable is concrete and visible, such as age or city size, before claims about health or behavior
Have students draw the arrows of Diagram 1 for each claim before writing an explanation
For Advanced Students
Ask students to find a real news headline that claims a cause from an observational study and rewrite it to match the evidence
Ask students to explain why a correlation can still be useful for prediction even when it is not causal, using the sunscreen data
Ask students to design a randomized experiment for one claim from Guided Practice and identify any ethical limits on doing it
Assessment Guidance
What to Look For
Strong answers name a specific lurking variable and explain how it affects both variables, instead of simply writing "correlation is not causation". Look for students who recognize when the direction of cause could be reversed, who treat a strong r from a tiny sample with caution, and who point to random assignment, not sample size, as the feature that lets an experiment support a causal claim. Watch for students who conclude that a correlation can never reflect a cause; the point is that the data alone cannot show it.
02
Classroom Activities
3 Activities
1
Headline Detective
20 minGroups of 3-4
Each group gets 8 invented headline cards, each with one sentence about how the data were collected. Groups decide whether the evidence supports a causal claim, name the most likely alternative explanation, and rewrite the headline to match the evidence.
Headline Cards
"Dog Owners Live Longer" (survey of 2,000 adults)
"New Reading Program Raises Scores" (60 classes randomly assigned to the program or the old curriculum)
"Late-Night Snacking Causes Poor Sleep" (survey of 500 adults)
"Kids Who Play Chess Have Higher Test Scores" (school records)
"Standing Desks Boost Focus" (100 volunteers randomly assigned to standing or sitting desks for a week)
"More Ice Rinks, More Broken Wrists" (data from 40 cities)
"Teens Who Text More Sleep Less" (survey of 800 teens)
"Nightly Reading Log Improves Spelling" (40 classes randomly assigned to use the log or not)
Key for the Teacher
Cards 2, 5 and 8 describe randomized experiments, so a causal claim is reasonable (for the conditions studied)
Card 1: lurking variables such as income or activity level; card 3: reverse causation (poor sleepers may snack at night) or stress; card 4: lurking variables such as family support or study habits
Card 6: city size and a cold climate drive both; card 7: lurking variables such as school start times, or reverse causation (teens who cannot sleep text more)
Modification for Distance Learning
Put the 8 cards on a shared slide deck, one per slide. Groups add a sticky note on each slide with their decision, the alternative explanation and the rewritten headline.
2
Randomize It: A Class Experiment
25 minPairs, then whole class
The class tests whether listening to music changes the time it takes to finish a printed maze. First students see why a survey could not answer the question; then they run a small randomized experiment and compare the group means.
Procedure
Ask: "Do people who listen to music while working finish tasks faster?" Discuss why asking people about their habits could be confounded (people who choose music may differ in other ways)
Each student flips a coin: heads means the music group (headphones, the same playlist), tails means the silent group
Every student solves the same maze while a partner times them; record the times in a shared class table by group
Compute the mean time for each group and the difference in means
Discussion Questions
Why did we use a coin instead of letting students choose their group?
If the music group was faster, what can we conclude, and for whom? What if the difference is small?
How would the conclusion change if students who already liked music had chosen the music group?
Challenge Variation
Re-randomize the recorded times into two new groups several times by shuffling cards with the times written on them, and compare the differences you get by chance with the real difference. This goes further than the standard and previews HSS.IC.B.5.
3
Spurious Correlation Hunt
15 minPairs
Pairs get invented yearly data for one county, compute r for every pair of variables, and explain why all three correlations are strong even though no variable plausibly causes another.
Data
Year
2016
2017
2018
2019
2020
2021
2022
2023
Electric cars registered (thousands)
1.2
1.8
2.5
3.4
4.1
5.6
7.0
8.9
Average movie ticket ($)
8.90
9.10
9.20
9.40
9.20
9.90
10.50
10.80
Yoga studios
14
15
17
18
18
21
23
24
Procedure
Enter the three rows into technology and compute r for each of the 3 pairs
For each pair, write a causal claim that a careless reader might make, then explain why it is not supported
Identify the lurking variable that all three share
Key for the Teacher
r ≈ 0.97 (electric cars and tickets), r ≈ 0.98 (electric cars and yoga studios), r ≈ 0.97 (tickets and yoga studios). All three quantities grow over time for unrelated reasons, so time, and the population and price growth that come with it, is a lurking variable.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Three Reasons Two Variables Can Be Correlated
Arrows show what changes what. In panel 1, x causes y. In panel 2, a lurking variable z (population) drives both variables, so libraries and crimes are correlated with no causal link between them (dashed line). In panel 3, the cause runs from y to x: low grades lead to tutoring visits.
Diagram 2: A Lurking Variable Disappears When You Use Rates
The invented 8-town data, drawn to scale. Left: library counts and crime counts have r ≈ 0.98 because bigger towns have more of both. Right: after dividing by population, crime rates stay near 15 per 1,000 residents whatever the number of libraries per resident, and the correlation is weak (r ≈ -0.36).
04
Homework Assignment
~30 min
HSS.ID.C.9 Homework: Correlation or Causation?
Directions: Answer in complete sentences. When you name a lurking variable, explain how it affects both variables. Use technology to compute r, rounded to two decimal places. All data are invented.
Part 1: Explaining a Correlation (Problems 1-3)
Across 50 cities, the number of hospitals and the number of deaths each year are strongly positively correlated. (a) Does this mean hospitals cause deaths? Name a lurking variable. (b) Explain why comparing death rates per 1,000 residents would still not settle the question. (Hint: who travels to a city with many hospitals?)
In one school, students who sit in the front row earn higher grades. The principal proposes moving the lowest-scoring students to the front row to raise their grades. (a) Give one lurking-variable explanation and one reverse-causation explanation of the correlation. (b) Describe how the school could find out whether seat location actually affects grades.
For 8 house fires, (number of fire trucks sent, damage in thousands of dollars): (1, 5), (2, 22), (2, 10), (3, 38), (4, 60), (4, 45), (5, 95), (6, 80). (a) Compute r and describe the association. (b) A reporter concludes that sending more trucks causes more damage. Identify the lurking variable and explain.
Part 2: Evidence for Causation (Problems 4-6)
Two studies ask whether an energy drink speeds up reaction time. Study A surveys 300 students about how often they drink energy drinks and measures their reaction time. Study B randomly assigns 40 volunteers to drink either the energy drink or a flavored water that looks the same; the mean reaction times are 0.262 seconds and 0.281 seconds. (a) Compute the difference in Study B's means. (b) Which study can support a causal conclusion, and why? (c) Name one lurking variable that could affect Study A.
For 6 seasons, the home runs hit by a local minor league team and the pumpkins sold at a nearby farm stand (hundreds) were (88, 31), (95, 36), (79, 30), (102, 33), (110, 38), (97, 35). (a) Compute r. (b) Explain why this correlation is very likely not causal, and give two reasons a strong r can appear here.
A company says its new study app raises vocabulary quiz scores, based on the fact that app users score higher than non-users. (a) Explain why this evidence shows correlation but not causation. (b) Describe a randomized experiment that could support the claim: name the groups, how students are assigned, and what is measured. (c) Explain in one sentence why random assignment helps with lurking variables.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Lurking Variables
Names a specific variable and explains how it affects both variables
Names a variable without explaining its effect on both
No lurking variable or an unrelated one
Reverse Causation and Chance
Recognizes when the direction may be reversed or the result may be chance
Mentions it without applying it to the context
Not addressed
Study Design
Explains why random assignment supports a causal claim and describes a workable experiment
Mentions an experiment without random assignment
Treats any large survey as proof of cause
Computation
Values of r and the difference in means correct
One value wrong
Values missing or incorrect
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Read each situation carefully and ask how the data were produced before you choose. All data are invented. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Which statement about correlation and causation is correct?
Answer: A
Correlation describes an association; causation is a claim about what would happen if x were changed. Choice C is false because a lurking variable or chance can create a strong correlation between unrelated variables. Choice D is false: a huge observational study can still be confounded.
Question 2 of 20 · Multiple Choice
Over 30 invented summer weeks at one beach, ice cream sales and shark sightings have r = 0.91. What is the best explanation?
Answer: B
Hot weather and the crowds it brings form a lurking variable that drives both counts up. Choices A and C each pick one direction of cause with no evidence. A strong r is quite possible here, so Choice D is wrong.
Question 3 of 20 · Multiple Choice
In an invented survey, people who use a sleep-tracking app report worse sleep than people who do not. A blog says, "Sleep apps ruin your sleep." What is the most likely alternative explanation?
Answer: C
The direction of cause may run from poor sleep to app use, not the other way around. Nothing in the question says the sample is small or the correlation weak, so Choices A and B do not fit.
Question 4 of 20 · Multiple Choice
Which kind of study is best for showing that a new running shoe lowers 5K times?
Answer: D
Random assignment makes the groups alike in fitness, training and other lurking variables, so a difference in times can reasonably be attributed to the shoe. Choices A, B and C are observational: runners who buy a new racing shoe may also train more.
Question 5 of 20 · Multiple Choice
Why does random assignment to treatment groups matter in an experiment?
Answer: A
When chance decides who gets the treatment, other variables should be spread about evenly across the groups. Random assignment does not change the sample size (Choice D), and extending results to a larger population depends on how the subjects were selected, not how they were assigned (Choice B).
Question 6 of 20 · Short Answer
In invented data for 200 children aged 5 to 12, shoe size and reading score have r = 0.70. Name the lurking variable and explain how it affects both.
The lurking variable is age. Older children have bigger feet, and older children have had more years of school and reading practice, so both shoe size and reading score tend to rise with age. Bigger feet do not cause better reading.
Question 7 of 20 · Multiple Choice
Invented yearly data for one city from 2015 to 2022, (bubble tea shops, solar panels installed in hundreds): (3, 2.1), (5, 2.9), (6, 3.1), (9, 4.4), (11, 4.6), (14, 5.2), (15, 6.3), (19, 6.9). Use technology to compute r. Which conclusion is justified?
Answer: B
Technology gives r ≈ 0.99, a very strong positive linear association. Both counts grew over time, and time (with the growth that comes with it) is a lurking variable. Choice A makes the causal leap. Choice D gives the slope of the fitted line, about 0.30, instead of r.
Question 8 of 20 · Multiple Choice
Which conclusion is supported by a randomized experiment?
Answer: C
Only Choice C used random assignment, so lurking variables should be balanced and the stretching plausibly caused the difference. The other studies are observational: people chose their own tea, towns and diets, so income, habits or family support could explain the associations.
Question 9 of 20 · Multiple Choice
Two variables have a correlation of r = 0.95 in an observational study. Which statement is true?
Answer: D
A strong correlation is consistent with causation but does not establish it. Choice C overcorrects: correlation does not rule out causation either. Deciding requires a study design, such as a randomized experiment, that can separate x from other variables.
Question 10 of 20 · Short Answer
In your own words, explain the difference between correlation and causation, and give an example of two variables that are correlated without one causing the other.
Correlation means the variables tend to change together; causation means changing one variable would itself change the other. Example: across months of the year, hot chocolate sales and flu cases rise together, but the cold season drives both; hot chocolate does not cause the flu. Any example with a clear lurking variable, reverse cause or chance explanation earns credit.
Question 11 of 20 · Multiple Choice
In invented data, adults who drink more coffee have higher rates of lung disease. Which variable is the most likely confounding (lurking) variable?
Answer: A
A confounding variable must be linked to both variables. If coffee drinkers in the data smoke more often, smoking could explain the higher rate of lung disease. Choices B, C and D are not plausibly linked to lung disease, so they cannot explain the association.
Question 12 of 20 · Multiple Choice
In an experiment, 60 volunteers are randomly assigned to two groups of 30. One group practices a video game for 10 minutes before a reaction test; the other reads. Mean reaction times are 24.1 hundredths of a second (reading) and 22.4 hundredths (game). What is the difference, and what can be concluded?
Answer: B
The difference is 24.1 - 22.4 = 1.7 hundredths of a second. Random assignment lets the difference be attributed to the treatment, although it applies to volunteers like these, not to everyone (Choice D). Choice C adds the means instead of subtracting. Choice A is wrong because causal conclusions come from the design, not from computing r.
Question 13 of 20 · Multiple Choice
Which invented headline overstates what its evidence shows?
Answer: C
Choice C draws a causal conclusion ("make people thinner") from observational city data; cities that build bike lanes may differ in income, climate or age of residents. Choice B reports a link without claiming a cause, and Choices A and D describe randomized experiments.
Question 14 of 20 · Short Answer
Invented data show that towns with more police officers per resident have more crime per resident. Give two explanations of this correlation other than "police cause crime".
Reverse causation: towns with more crime hire more police officers. Lurking variable: something such as population density or a busy downtown could raise both crime and the number of officers needed. Either explanation fits the data without police causing crime.
Question 15 of 20 · Multiple Choice
In an invented group of 6 students, r = 0.80 between the number of siblings and the score on a science quiz. What is the best response?
Answer: D
In very small samples, a strong correlation can arise from chance alone, as in the birthday example. Choice A makes a causal claim from a tiny observational sample, and Choice B also rests on that causal claim.
Question 16 of 20 · Multiple Choice
An observational study finds that students who play a musical instrument have higher math grades. Which additional evidence would best support the claim that learning an instrument improves math grades?
Answer: B
Random assignment is what separates the effect of lessons from lurking variables such as family income or study habits. A bigger survey (Choice A) or a higher r (Choice D) still comes from students who chose music themselves, so the same lurking variables remain.
Question 17 of 20 · Short Answer
A company claims that its sports drink improves endurance. Describe a randomized experiment that could test the claim.
Recruit volunteers and use chance (a coin or a random number generator) to assign each one to the sports drink or a look-alike drink without the active ingredients. Keep everything else the same, measure endurance (for example, minutes until exhaustion on a treadmill), and compare the group means. Random assignment balances fitness and other lurking variables between the groups.
Question 18 of 20 · Multiple Choice
Which of these is NOT a reason that a correlation might not reflect causation?
Answer: D
Random assignment is the feature that helps an experiment support a causal claim, so it is not a reason to doubt one. Choices A, B and C are the three alternative explanations to check for any correlation.
Question 19 of 20 · Short Answer
Invented weekly data for 8 weeks in one city, (umbrellas sold at a store, car accidents): (12, 6), (40, 10), (25, 9), (60, 13), (8, 4), (52, 11), (33, 7), (18, 8). Use technology to compute r. Does buying umbrellas cause car accidents? Explain.
Technology gives r ≈ 0.92, a strong positive linear association. It does not show that umbrellas cause accidents. Rain is a lurking variable: rainy weeks bring both more umbrella sales and more accidents from wet roads and poor visibility.
Question 20 of 20 · Multiple Choice
In an invented observational study of 150 adults, the correlation between weekly hours of exercise and resting heart rate is r = -0.85. Which statement is justified?
Answer: C
The data show a strong negative association. Because the adults chose how much to exercise, age, diet or overall health could affect both, so the study alone cannot establish cause. Choice D confuses a negative correlation with no correlation.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSS.ID.C.9 mean?
It means students can tell the difference between two variables being associated (correlation) and one variable changing the other (causation). Students explain why a correlation can come from a lurking variable, reverse causation or chance, and recognize what kind of evidence supports a causal claim.
Is HSS.ID.C.9 taught in Algebra 1?
Usually, yes. It is typically taught in Algebra I right after correlation coefficients, and again in introductory Statistics, where it connects to the design of experiments and observational studies.
What is a lurking variable?
A lurking (or confounding) variable is a third variable that affects both variables being studied, so they appear related even if neither causes the other. Population size behind the numbers of libraries and crimes in a town is a classic kind of example.
How can you prove causation?
The strongest evidence usually comes from a randomized experiment, in which chance decides who gets the treatment, so lurking variables are balanced between groups. When experiments are impossible or unethical, scientists combine many observational studies, a plausible mechanism, and consistent results, but a single correlation is never enough.
Does correlation ever mean causation?
A correlation can come from a real cause, and it is often the first hint that one exists. The point of the standard is that the correlation alone cannot show it. Students should say "the data are consistent with a cause, but other explanations have not been ruled out."
What is reverse causation?
It is when the cause runs in the opposite direction from the one claimed. For example, students who visit a tutoring center often may have lower grades because low grades send them to tutoring, not because tutoring lowers grades.
Why can a large sample still fail to show causation?
A larger sample reduces the role of chance, but it does not remove lurking variables or reverse causation. A survey of 100,000 people who chose their own habits can be just as confounded as a survey of 100.
What is the difference between an observational study and an experiment?
In an observational study the researcher records what people already do or have. In an experiment the researcher assigns the treatment, ideally at random. Only the experiment controls who gets the treatment, which is why it can support causal conclusions. The details are studied in HSS.IC.B.3.
How is correlation versus causation tested?
Typical questions give a study and a claim and ask whether the claim is justified, what a lurking variable might be, or which study design could support a causal conclusion. Students should always identify how the data were produced before judging the claim.
What are good examples of correlation without causation for students?
Examples with a clear third variable work well: gray hair and blood pressure in adults (age), hot chocolate sales and flu cases (the cold season), sunscreen sales and sunburns (sunny weather), and the number of TVs per home and life expectancy across countries (national wealth). Students can also compute r for unrelated quantities that grow over the same years.
07
Related Standards
6 standards
These standards connect to HSS.ID.C.9: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
8.SP.A.1Prerequisite
Construct and interpret scatter plots and describe patterns of association
