A review lesson on finding linear slope using rise over run and categorizing the four distinct slope orientations. Includes an instructional anchor chart and a structured student practice worksheet.
Case File: Student Sam was asked to find the slope of a line passing through the points (0, 1) and (3, 7). Sam wrote: "The run is 3 and the rise is 6, so the slope is m = 3/6 = 1/2."
A. What specific mistake did Sam make in setting up the slope ratio?
B. What is the CORRECT simplified slope \(m\)?
\(m =\)
C. Which of the 4 slope types is this line?
Self-Reflection: How confident are you finding slope using rise over run?
Need Help Getting There Slope Expert!
Run: +3
\(m = \frac{-6}{+3} = \mathbf{-2}\)
Problem 5 Solution Line \(y = -2\)
Slope Type: Zero
Rise: 0
Run: 4 (or any nonzero)
\(m = \frac{0}{4} = \mathbf{0}\)
Problem 6 Solution Line \(x = 2\)
Slope Type: Undefined
Rise: 4 (or any nonzero)
Run: 0
\(m = \frac{4}{0} = \mathbf{\text{Undefined}}\)
Part 5: Detective Challenge Solutions & Grading Guide
Scoring Rubric
A. What mistake did Sam make?
Model Answer: Sam inverted the slope ratio by putting Run over Rise (\(\frac{\Delta x}{\Delta y} = \frac{3}{6}\)) instead of Rise over Run (\(\frac{\Delta y}{\Delta x} = \frac{6}{3}\)).
Teacher Tip: This is the #1 most frequent slope mistake nationwide! Emphasize the mnemonic "Rise to the skies, Run along the ground."
Confusing Zero vs. Undefined: Remind students that \(\frac{0}{k} = 0\) (Zero slope is like walking on flat floor), while \(\frac{k}{0} = \text{error}\) (Undefined is like falling down a vertical drop).
Counting signs: When moving down, Rise is negative. Ensure students attach the negative sign to the entire fraction.
