Scatter Plots and Lines of Best Fit
I can draw and judge a line of best fit, and use it to predict inside the data.
The problem this sheet solves
Students judge a fit by how many points it touches, and the fault is invisible until the rest are counted — four above the rival line and one below, so the cloud is sitting above the line it is meant to run through the middle of. Prediction has a range too: the same line predicts 43 marks on a test out of 20. The numbers are built to make the point exactly: the printed line really is the line of best fit, it touches none of the eight points, and its residuals split four above and four below and cancel to zero, while the tempting rival's add up to 8. Residual signs are treated as content rather than bookkeeping, because over eight points a flipped sign is the difference between a test that works and one that cannot.
The key rule
A line of best fit runs through the MIDDLE of the cloud, with points balanced above and below. How many points it happens to touch is not the test.
Count above and below.
Watch out
The mistake: A student picks y = 2x + 2 because it goes exactly through three of the points.
The fix: Count the rest: four are above it and one below. The cloud sits above the line. y = 2x + 3 touches none and splits them four and four.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.