Activity 01
Inquiry Circle: The Spaghetti Fit
Groups are given scatter plots and pieces of uncooked spaghetti. They must place the spaghetti to represent the 'best fit' for the data, then use two points on their spaghetti line to calculate the slope and write the equation, comparing their line's 'fit' with other groups.
Analyze what the strength and direction of a correlation tell us about the relationship between two variables.
Facilitation TipDuring the Spaghetti Fit, walk around with a long strand of spaghetti in hand to model how to position it over the points without forcing it through any single dot.
What to look forProvide students with 2-3 different scatter plots. Ask them to write one sentence describing the association (positive, negative, or none) for each plot and identify any obvious outliers.
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Activity 02
Think-Pair-Share: Predicting the Future
Give students a scatter plot of Canadian Olympic medal counts over time with a line of best fit. Students use the line to predict the count for the next Olympics (extrapolation). They pair up to discuss how reliable they think that prediction is and what factors might change it.
Explain how outliers influence our interpretation of a data set.
Facilitation TipFor Predicting the Future, provide sentence stems like 'If the trend continues, then…' to support students in articulating predictions clearly.
What to look forGive students a scatter plot showing student study hours versus test scores. Ask them to explain in their own words what the pattern on the plot suggests about the relationship between these two variables and to identify one outlier if present.
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Activity 03
Peer Teaching: Slope in the Real World
Pairs are given different trend lines (e.g., 'fuel used vs. distance' or 'height vs. age'). They must explain to another pair what the slope and intercept mean in that specific context (e.g., 'the slope is the liters per kilometer').
Differentiate between positive, negative, and no association in scatter plots.
Facilitation TipIn Slope in the Real World, assign each pair a different real-world context so they can teach their peers about slope using relatable examples.
What to look forPresent a scatter plot with a clear outlier. Ask students: 'How does this single data point affect our understanding of the overall relationship between the two variables? What might this outlier represent in the real world?'
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Generate Complete Lesson→A few notes on teaching this unit
Start with concrete examples—like age versus height—where the line of best fit clearly does not start at zero. Avoid formal equations at first; focus on visual balance and verbal reasoning. Research shows that informal fitting builds intuition before formal methods are introduced, so resist the urge to rush to formulas.
Students will confidently describe the direction and strength of an association, sketch a line of best fit with roughly equal points above and below it, and use that line to make simple predictions. They will also explain how outliers can shift or clarify trends in real data.
Watch Out for These Misconceptions
During the Collaborative Investigation: The Spaghetti Fit, watch for students who anchor their spaghetti line to the origin, especially when the data does not start at zero.
Ask students to place their spaghetti over the first point they see in the data set and explain why that point might not be (0,0). Have them adjust their line to better match the trend.
During the Collaborative Investigation: The Spaghetti Fit, watch for students who try to connect the dots with a jagged line.
Have students compare their spaghetti line to a 'dot-to-dot' line drawn by a peer. Ask which line helps us see the overall trend and which one gets lost in individual points.
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