Why this matters for FAST: Scatter plots and data analysis questions appear frequently on FAST. Students must be able to identify the type of association, describe the relationship in context, and use a line of fit to make predictions.
Students think positive association means the y-values are positive, or that negative association involves negative numbers.
"Positive association means as one variable INCREASES, the other INCREASES too - the line goes UP from left to right. Negative association means as one INCREASES, the other DECREASES - the line goes DOWN from left to right. It has nothing to do with whether the numbers themselves are positive or negative."
Students try to connect all the dots or think the line is wrong if it doesn't touch every point.
"The line of best fit shows the TREND - it should have roughly equal points above and below the line. It's like finding the 'average path' through the data, not connecting the dots!"
Students assume that because two variables are associated, one must cause the other.
"Association (correlation) does NOT prove causation! Ice cream sales and drowning both increase in summer - but ice cream doesn't cause drowning! They both increase because of a third factor: warm weather."
Review plotting points on a coordinate plane. Remind students that each point has an x-value (horizontal) and a y-value (vertical).
"A scatter plot shows the relationship between TWO variables. Each point represents one observation with two measurements. When we look at all the points together, we can see if there's a pattern - we call this an ASSOCIATION."
Types of Association:
Positive: Points go up from left to right (both variables increase together)
Negative: Points go down from left to right (one increases as other decreases)
No Association: Points are scattered randomly with no clear pattern
Is the Association Linear?
Linear: Points follow a straight-line pattern
Non-Linear: Points follow a curved pattern
Example: Height vs. age (0-18) is non-linear - growth spurts! Study time vs. test score might be linear.
"For LINEAR associations, we can draw a LINE OF BEST FIT - also called a trend line. This line should: (1) follow the direction of the points, (2) have about the same number of points above and below, (3) pass through the 'middle' of the data."
Demonstrate drawing a line of fit on sample data. Emphasize it's an estimate - there's some flexibility, but it should capture the overall trend.
Show how to use the line of best fit to predict values:
Work through examples together:
"A scatter plot shows the relationship between hours spent studying and test scores. The points form a pattern that goes up from left to right. Describe the association and what it means in context."
Correct answer: There is a positive linear association. This means that as the number of hours spent studying increases, test scores tend to increase as well. More study time is associated with higher scores.
For struggling students: Start with clearly defined examples (strong associations). Use color-coding for positive (green arrows up) and negative (red arrows down). Provide sentence stems for describing associations.
For advanced students: Introduce outliers and their effect on the line of fit. Have them calculate the equation of the line of best fit using two points.
For home: Send Parent Activity sheet. Families can collect data (like temperature and energy bill) and create their own scatter plots.