Mathematics · Grade 9 · Data, Probability, and Decision Making · Term 3

Scatter Plots and Correlation

Students will create and interpret scatter plots, identifying positive, negative, and no correlation.

• Ontario Curriculum Expectations
• CCSS.MATH.CONTENT.8.SP.A.1
• CCSS.MATH.CONTENT.HSS.ID.B.6.A

About This Topic

Scatter plots display the relationship between two numerical variables, allowing students to visualize patterns in bivariate data. In Grade 9, students create scatter plots from real-world datasets, such as height versus shoe size or study hours versus test scores. They identify positive correlation, where points trend upward; negative correlation, where points trend downward; and no correlation, where points scatter randomly. Interpretation includes describing the strength and direction of trends.

This topic fits within the data management strand, supporting skills in probability and decision making. Students differentiate correlation from causation, recognizing that an association does not imply one variable causes the other, as seen in examples like ice cream sales and drowning rates both rising in summer. Key questions guide analysis of relationships, predictions of correlation direction and strength, and application to everyday scenarios.

Active learning benefits this topic because students collect and plot their own data, like measuring hand spans and plotting against height. This hands-on process reveals patterns firsthand, fosters discussions on outliers and trends, and connects abstract concepts to personal experiences, deepening understanding and retention.

Key Questions

1. Analyze the relationship between two variables as depicted in a scatter plot.
2. Differentiate between correlation and causation using real-world examples.
3. Predict the direction and strength of a correlation from a scatter plot.

Learning Objectives

• Create scatter plots to visually represent the relationship between two quantitative variables from a given dataset.
• Analyze scatter plots to describe the direction (positive, negative) and strength (strong, weak, none) of the correlation between variables.
• Differentiate between correlation and causation by providing and evaluating real-world examples.
• Predict the likely correlation between two variables based on visual patterns in a scatter plot.

Before You Start

Coordinate Geometry and Graphing

Why: Students need to be able to plot points accurately on a Cartesian plane to create scatter plots.

Data Representation

Why: Understanding how to organize and interpret data in tables is foundational for creating scatter plots.

Key Vocabulary

Scatter Plot	A graph that displays the relationship between two quantitative variables. Each point on the graph represents a pair of values for the two variables.
Correlation	A statistical measure that describes the extent to which two variables change together. It indicates the direction and strength of a linear relationship.
Positive Correlation	A relationship where as one variable increases, the other variable also tends to increase. Points on the scatter plot generally trend upwards from left to right.
Negative Correlation	A relationship where as one variable increases, the other variable tends to decrease. Points on the scatter plot generally trend downwards from left to right.
Causation	A relationship where one event directly causes another event to occur. Correlation does not imply causation.

Watch Out for These Misconceptions

Common Misconception

Correlation always means causation.

What to Teach Instead

Students often assume a strong scatter plot trend proves cause and effect. Group debates on real examples, like number of firefighters and fire damage, clarify this through evidence discussion. Active plotting of counterexamples builds critical analysis.

Common Misconception

No correlation means unrelated variables.

What to Teach Instead

Scatter plots with random points may still relate weakly or nonlinearly. Hands-on data collection activities let students explore outliers and clusters, refining their interpretation via peer feedback and revisions.

Common Misconception

All positive correlations form straight lines.

What to Teach Instead

Trends can curve or cluster imperfectly. Station rotations with varied datasets help students sketch trend lines collaboratively, distinguishing strength from linearity through observation and comparison.

Active Learning Ideas

Data Collection: Class Height vs. Jump Height

Students measure each other's heights and vertical jump heights in pairs, record data on charts, then plot points on graph paper or digital tools. Groups discuss trends and label as positive, negative, or none. Share findings with the class.

45 min·Pairs

Stations Rotation: Correlation Scenarios

Set up stations with printed datasets: sports stats, weather data, and consumer habits. At each, students plot data, draw trend lines, and rate correlation strength. Rotate every 10 minutes, then debrief as a class.

50 min·Small Groups

Digital Plotting: Correlation vs. Causation Debate

Provide datasets like TV hours vs. grades. Students use Google Sheets or Desmos to create scatter plots, identify correlations, then debate causation in small groups using evidence from plots. Present arguments whole class.

40 min·Small Groups

Prediction Challenge: Mystery Data

Show unlabeled scatter plots; students predict variables, strength, and direction in pairs. Reveal real contexts like temperature vs. cricket chirps, then create their own plots from new data.

35 min·Pairs

Real-World Connections

• Economists use scatter plots to examine the relationship between variables like advertising spending and sales revenue for a product, helping to inform marketing strategies.
• Environmental scientists might plot air pollution levels against traffic volume in a city to understand potential correlations and inform policy decisions.
• Medical researchers analyze scatter plots to investigate relationships between factors like hours of sleep and reaction times, or diet and blood pressure.

Assessment Ideas

Quick Check

Provide students with three different scatter plots, each showing a different type of correlation (positive, negative, none). Ask them to label each plot with the type of correlation and write one sentence explaining their reasoning for each.

Discussion Prompt

Present the scenario: 'Ice cream sales increase in the summer, and so do drowning incidents.' Ask students: 'Is there a correlation? Is there causation? Explain your answer using the terms correlation and causation.'

Exit Ticket

Give students a small dataset (e.g., 5-7 pairs of numbers). Instruct them to create a scatter plot on a mini-whiteboard or paper. Then, ask them to write one sentence describing the correlation they observe and one sentence explaining why it is not necessarily causation.

Frequently Asked Questions

How do you teach positive, negative, and no correlation in scatter plots?

Start with familiar data like height and weight for positive trends, temperature and clothing layers for negative, and eye color versus favorite food for none. Have students plot and annotate their own examples, then compare in groups to solidify distinctions. Use digital tools for quick iterations and visual feedback.

What is the difference between correlation and causation for grade 9 math?

Correlation shows an association in scatter plots, like more exercise linking to better sleep, but causation requires evidence that one causes the other. Discuss spurious examples, such as summer ice cream sales and shark attacks, through class debates. Students analyze plots to identify lurking variables, building decision-making skills.

How can active learning help students understand scatter plots and correlation?

Active approaches like collecting class data on arm span versus height make plotting personal and engaging. Students rotate through stations interpreting varied datasets, discuss trends in small groups, and predict outcomes, which reveals patterns experientially. This reduces misconceptions and improves prediction accuracy over passive lectures.

How to assess scatter plot interpretation in grade 9?

Use performance tasks where students create plots from provided or self-collected data, describe trends, and explain correlation strength. Rubrics evaluate accuracy in labeling direction, addressing causation pitfalls, and justifying predictions. Peer reviews during activities provide formative insights into understanding.