### Examples

*Algebra 1 Example:*There is a strong positive correlation between the number of Nobel prizes won by country and the per capita chocolate consumption by country. Does this mean that increased chocolate consumption in America will increase the United States of America’s chances of a Nobel prize winner?

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**912

**Strand:**Data Analysis and Probability

**Standard:**Summarize, represent and interpret categorical and numerical data with one and two variables.

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Categorical Data
- Numerical Data

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 8, students first analyzed bivariate numerical data using scatter plots. In Algebra I, students study association between variables in bivariate data and learn that there is a difference between two variables being strongly associated and one of them having a causative effect on the other. In later courses, students will learn how to design statistical experiments that can show causation.- The intent of this benchmark includes the ability to informally draw conclusions about whether causation is justified when two variables are correlated.
- Correlation and causation are often misunderstood. It is important for students to understand their relationship. Causation and correlation can exist at the same time; however, correlation does not imply causation. Causation explicitly applies to cases where an action causes an outcome. Correlation is simply a relationship observed in bivariate data. One action may relate to the other, but that action doesn’t necessarily cause the other to happen, because both of them may be the result of a third “hidden variable.”
- Causation is possible, but it is also possible that correlation occurs from a third variable.
- For example, if one states, “On days when I drink coffee, I feel more productive.” it may be that one feels more productive because of the caffeine (causation) or because they spent time in the coffee shop drinking coffee where there are fewer distractions (third variable). Since one cannot determine whether the causation or the third variable results in correlation, then causation is not confirmed.

- Causation seems unlikely and a third variable seems likely.
- For example, there is a strong correlation between the number of Nobel prizes won by country and the per capita chocolate consumption by country. However, there are many possibilities a third variable, such as a strong economy, that can result in this correlation so causation can be ruled out.

- Causation is likely because there is a reasonable explanation for the causation.
- For example, if one states, “After I exercise, I feel physically exhausted.” it is reasonable to consider this to be a cause-and-effect. Causation can be confirmed by the explanation that because one is purposefully pushing their body to physical exhaustion when doing exercise, the muscles used to exercise are exhausted (effect) after they exercise (cause).

- When correlation is apparent in a bivariate data set, students are encouraged to seek a reasonable explanation that either identifies a hidden variable or a reasonable explanation for causation. Further investigation may be required to confirm or disconfirm causation.

- Causation is possible, but it is also possible that correlation occurs from a third variable.
- In Algebra I, the term correlation is used to describe an association between two variables and does not necessarily imply a linear relationship.
- Instruction includes asking the following questions while students investigate correlation and causation.
- Does this correlation make sense? Is there an actual connection between these variables? Will the correlation hold if I look at some new data that I haven’t used in my current analysis?
- Is the relationship between these variables direct, or are they both a result of some other variable?

### Common Misconceptions or Errors

- Even though students may not be able to reasonably explain why a causal relationship exists, they may assume that correlation implies causation.

### Strategies to Support Tiered Instruction

- Instruction includes co-creating and discussing examples and non-examples of causal relationships in numerical and categorical data.
- For example, a non-causal relationship could be a person’s shoe size and approximate number of vocabulary words they know.
- For example, a causal relationship could be a person’s shoe size and their age.

- Teachers provides instruction to increase understanding the relationship between correlation and causation. Teachers provides students with context that demonstrates when both correlation and causation are present. They may also provide context when only correlation is represented in the given context.

### Instructional Tasks

*Instructional Task 1 (MTR.3.1, MTR.4.1)*

- Data from a certain city shows that the size of an individual’s home is positively correlated with the individual's life expectancy. Which of the following factors would best explain why this correlation does not necessarily imply that the size of an individual’s home is the main cause of increased life expectancy?
- a. Larger homes have more safety features and amenities, which lead to increased life expectancy.
- b. The ability to afford a larger home and better healthcare is a direct effect of having more wealth.
- c. The citizens were not selected at random for the study.
- d. There are more people living in small homes than large homes in the city. Some responses may have been lost during the data collection process.

### Instructional Items

*Instructional Item 1*

- Dr. Larry has noticed that when he carries around his lucky rock, his students seem to be nicer to him. Can one conclude that this positive correlation shows a causal relationship?
- a. Yes, because Larry decides whether or not to put his lucky rock in his pocket before he encounters people during the day.
- b. Yes, because it is not a negative correlation.
- c. No, because lucky rocks only work for children.
- d. No, because it is possible that people are nice to Larry because of another factor that also causes him to put the rock in his pocket.

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Perspectives Video: Experts

## Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

## STEM Lessons - Model Eliciting Activity

This MEA gives the students an opportunity to learn about sustainability and then apply that knowledge to help EcoAthletica determine the location for their next sustainable tourism resort. The students will use a variety of criteria and the definition of sustainability and sustainable tourism to create a model for choosing locations.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

## MFAS Formative Assessments

Students are given a scenario describing an association between two variables and are asked to determine if one variable is a cause of the other.

Students are given a statement of association between two variables and are asked to determine if one variable is a cause of the other.

Students are asked to identify all possible causal relationships between two correlated variables.

Students are asked to interpret a correlation coefficient in context and describe a possible causal relationship.

## Student Resources

## Lesson Plan

This lesson introduces the students to the concepts of correlation and causation, and the difference between the two. The main learning objective is to encourage students to think critically about various possible explanations for a correlation, and to evaluate their plausibility, rather than passively taking presented information on faith. To give students the right tools for such analysis, the lesson covers most common reasons behind a correlation, and different possible types of causation.

Type: Lesson Plan

## Perspectives Video: Professional/Enthusiast

Watching this video will cause your critical thinking skills to improve. You might also have a great day, but that's just correlation.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

This is a simple task addressing the distinction between correlation and causation. Students are given information indicating a correlation between two variables, and are asked to reason out whether or not a causation can be inferred.

Type: Problem-Solving Task

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

Type: Problem-Solving Task

This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic using a table of data.

Type: Problem-Solving Task

## Parent Resources

## Perspectives Video: Professional/Enthusiast

Watching this video will cause your critical thinking skills to improve. You might also have a great day, but that's just correlation.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

This is a simple task addressing the distinction between correlation and causation. Students are given information indicating a correlation between two variables, and are asked to reason out whether or not a causation can be inferred.

Type: Problem-Solving Task

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

Type: Problem-Solving Task

This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic using a table of data.

Type: Problem-Solving Task