Mathematics · Grade 8 · Patterns in Data · Term 3

Constructing Scatter Plots

Constructing scatter plots for bivariate measurement data to observe patterns.

• Ontario Curriculum Expectations
• 8.SP.A.1

About This Topic

Scatter plots are a powerful tool for visualizing the relationship between two variables. In the Ontario Grade 8 curriculum, students move from simple bar graphs to analyzing bivariate data. They learn to construct scatter plots and look for associations, such as positive, negative, or no correlation. This is the foundation for data-driven decision-making.

Students also learn to identify clusters and outliers, data points that fall far away from the general trend. Understanding why an outlier exists (is it an error or a unique case?) is a key part of statistical literacy. This topic connects math to real-world issues like climate change, health trends, and sports statistics, helping students become critical consumers of information.

This topic comes alive when students can physically model the patterns. By collecting their own data, such as height vs. arm span or study time vs. test scores, students become invested in the 'story' the data is telling and are more likely to notice the nuances in the patterns.

Key Questions

1. Explain how to accurately represent bivariate data on a scatter plot.
2. Differentiate between independent and dependent variables when creating a scatter plot.
3. Construct a scatter plot from a given data set.

Learning Objectives

• Construct a scatter plot accurately representing bivariate measurement data from a given set.
• Identify and differentiate between independent and dependent variables for a scatter plot.
• Analyze a scatter plot to identify patterns, including linear trends, clusters, and outliers.
• Explain the meaning of positive, negative, and no correlation as observed on a scatter plot.

Before You Start

Representing Data on Coordinate Grids

Why: Students must be able to plot points accurately on a Cartesian coordinate system to construct a scatter plot.

Understanding Variables

Why: Students need a basic understanding of what a variable is and how it can change to grasp the concept of bivariate data.

Key Vocabulary

Bivariate Data	A set of data that consists of two variables for each individual observation. For example, a student's height and weight.
Scatter Plot	A graph that uses dots to represent the values obtained for two different variables being observed. It shows the relationship between the two variables.
Independent Variable	The variable that is changed or controlled in an experiment to test its effects on the dependent variable. It is typically plotted on the horizontal axis (x-axis).
Dependent Variable	The variable being tested and measured in an experiment. Its value is expected to change in response to a change in the independent variable. It is typically plotted on the vertical axis (y-axis).
Correlation	A statistical measure that describes the extent to which two variables change together. It can be positive, negative, or show no relationship.
Outlier	A data point that differs significantly from other observations in the data set. It may indicate a measurement error or a unique case.

Watch Out for These Misconceptions

Common Misconception

Students often think 'negative correlation' means there is no relationship.

What to Teach Instead

Clarify that a negative correlation is a strong relationship where one value goes up as the other goes down. Use the analogy of 'more time spent gaming' vs. 'less time spent sleeping' to show a clear negative trend.

Common Misconception

Students may believe that an outlier should always be deleted from the data.

What to Teach Instead

In a collaborative discussion, explore why outliers are important. They might represent a breakthrough in science or a specific event. Teaching students to investigate outliers rather than ignore them is key to good data science.

Active Learning Ideas

Inquiry Circle: The Human Scatter Plot

Students collect data on two variables (e.g., shoe size vs. height) from their classmates. They then 'become' the data points by standing on a large grid on the floor or using sticky notes on a giant wall-grid to create a live scatter plot and discuss the trend they see.

45 min·Whole Class

Gallery Walk: Spot the Outlier

Post several scatter plots around the room showing different Canadian data (e.g., temperature vs. latitude, population vs. area). Students move in groups to identify the type of association and circle any outliers, writing a possible 'story' for why that outlier exists.

35 min·Small Groups

Think-Pair-Share: Correlation vs. Causation

Show a scatter plot with a strong correlation but no logical link (e.g., ice cream sales vs. shark attacks). Students think about whether one causes the other, pair up to find the 'hidden variable' (summer heat), and share why correlation doesn't always mean causation.

25 min·Pairs

Real-World Connections

• Environmental scientists use scatter plots to examine the relationship between air pollution levels (independent variable) and respiratory illness rates (dependent variable) in different cities, informing public health policies.
• Sports analysts create scatter plots to visualize the connection between practice time (independent variable) and game performance metrics like points scored (dependent variable) for athletes, helping to optimize training regimens.
• Economists might plot a country's GDP growth (independent variable) against its unemployment rate (dependent variable) to identify economic trends and forecast future conditions.

Assessment Ideas

Quick Check

Provide students with a small data set (e.g., hours studied vs. test score). Ask them to identify the independent and dependent variables, then sketch a scatter plot on mini-whiteboards. Observe their plotting accuracy and variable assignment.

Exit Ticket

Give students a scatter plot showing a clear trend. Ask them to write one sentence describing the relationship (e.g., positive correlation) and one sentence explaining what an outlier might represent in this context.

Discussion Prompt

Present two different scatter plots, one showing a strong positive correlation and another showing no correlation. Ask students: 'How do these plots differ visually? What does each type of pattern tell us about the relationship between the two variables?'

Frequently Asked Questions

What is a scatter plot?

A scatter plot is a graph that uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. They are used to observe relationships between variables.

What is the difference between positive and negative association?

In a positive association, both variables tend to increase together (like height and weight). In a negative association, as one variable increases, the other tends to decrease (like altitude and temperature).

How can active learning help students understand scatter plots?

Active learning, like the 'Human Scatter Plot,' makes data personal. When students are the data points, they see how their individual 'dot' contributes to the overall trend. This kinesthetic experience makes concepts like 'clusters' and 'outliers' much more intuitive than just looking at a small graph in a book.

Does correlation mean that one thing caused the other?

No! This is a common mistake. Just because two things happen together (correlation) doesn't mean one caused the other (causation). There is often a third 'lurking' variable that affects both, or it could just be a coincidence.