Slope Searchers Presentation Slope Searchers
Decoding the Steepness of a Line
Warm-Up: Sketching Success
Grab your Rise and Run Grid and follow these steps:
1 Plot the point (2, 2)
2 Plot the point (4, 4)
3 Draw a straight line through both points.
Think: How many units do you "rise" and "run" to get from point A to point B?
Slope Secrets Unlocked
Watch carefully from 0:00 to 2:32
Embedded media
The Slope Formula
Handling Negatives
Labeling Points
The Slope Formula
\[m = \frac{y_2 - y_1}{x_2 - x_1}\]
Numerator
"The Rise"
Change in Y (Vertical)
Denominator
"The Run"
Change in X (Horizontal)
Step 1: The Labeling Ritual
Before calculating, always label your points to avoid messy mix-ups!
(2, 5)
x₁
y₁
(6, 13)
x₂
y₂
Main Event: Slope Sort
1
Grab a card from your deck. Each card has a unique pair of points.
2
Label your points and use the formula to find the slope.
3
Place your card in the correct category: Positive, Negative, Zero, or Undefined.
Positive
Negative
Zero
Undefined
Zero vs. Undefined
Zero Slope
\(\frac{0}{2} = 0\)
Horizontal Line
Undefined
\(\frac{-7}{0} = \text{ERROR}\)
Vertical Line
The Golden Rule
Don't Forget!
"Does the order of the points matter?"
As long as you start with the same point for both the top and the bottom, your answer will be correct.
If you mix them up, you'll flip the sign!
Steepness Check
Complete your exit ticket before you leave!
Find the slope of the line passing through:
(3, -4) & (-5, 2)
Show Your Labels
Simplify Completely
Rise and Run Grid Rise and Run Grid
Warm-Up Activity: Graphing the Basics
Name:
Date:
Phase 1: Plotting
1. Plot Point A: (2, 2) (4, 4)
x
y
GRAPH HERE
Phase 2: Analysis
Vertical Change (Rise):
Horizontal Change (Run):
Slope (Rise / Run):
/
Hint: Count how many boxes you go UP and how many you go OVER from Point A to Point B.
Prediction:
If we picked two different points on this same line, would the slope be different? Why or why not?
Slope Sort Cards Slope Sort Cards
Cut along the dotted lines. Calculate the slope for each card and sort them!
CARD #01
(2, 3) & (5, 9)
Workspace Below
CARD #02
(1, 5) & (4, 2)
Workspace Below
CARD #03
(-2, 4) & (6, 4)
Workspace Below
CARD #04
(3, -1) & (3, 8)
Workspace Below
CARD #05
(-1, -2) & (2, 4)
Workspace Below
CARD #06
(0, 0) & (-3, 6)
Workspace Below
CARD #07
(1, 1) & (5, 3)
Workspace Below
CARD #08
(-2, 5) & (2, 2)
Workspace Below
Pile A
Positive
Pile B
Negative
Pile C
Zero
Pile D
Undefined
Steepness Check Exit Ticket Steepness Check
Exit Ticket
Name
Date
Find the slope of the line that passes through the following two points. Show every step of your calculation, including labeling and substituting into the formula.
(3, -4) & (-5, 2)
x₁
y₁
x₂
y₂
Show Your Work:
Final Slope (m) =
How confident do you feel about calculating slope?
Lost
Getting There
Confident
Slope Master
Blueprint Master Teacher Guide Slope Searchers
Instructional Blueprint & Facilitation Guide
Objective
Students will calculate the slope of a line given two points using the slope formula with integers.
Grade Level
8th Grade Math / Algebra 1
Duration
50 Minutes
Materials Needed
Slope Searchers Slide Deck
Rise and Run Grid (Warm-Up)
Slope Sort Cards (1 set per pair)
Steepness Check Exit Ticket
Instructional Flow
5 MIN
Warm-Up: Rise & Run Grid
Students plot (2,2) and (4,4) on the grid. They should visually count the vertical units (rise) and horizontal units (run).
Key Prompt:
"If you had to tell a robot how to get from the first point to the second, what directions would you give?"
10 MIN
Guided Learning: Video & Formula
Play Video (0:00 - 2:32). Focus on the transition from "counting squares" to using the algebraic formula.
Emphasize the labeling process ($x_1, y_1, x_2, y_2$).
Pause at 1:11 to discuss the "double negative" trap when subtracting negative numbers.
20 MIN
Main Activity: Slope Sort
Students work in pairs to calculate the slope for 8 distinct cards. They must categorize them based on the resulting slope.
Teacher Check-In Points:
Watch for students confusing $x$ and $y$ values in the numerator/denominator. Ensure they are keeping the points in the same order (consistency).
10 MIN
Discussion: The Golden Rule
Review the Slope Sort answers. Discuss the Zero vs. Undefined slopes (Cards #3 and #4).
Discussion Spark:
"Why can't we have a zero on the bottom of our slope fraction? What does that line look like on a graph?"
5 MIN
Closure: Steepness Check
Distribute the Exit Ticket. It contains one specific problem involving a negative number to test for common arithmetic misconceptions.
Common Pitfalls to Watch For
Numerator/Denominator Swap: Students often put the change in $x$ on top because $x$ comes first in an ordered pair.
Subtraction Sign Error: Forgetting that the formula is subtraction. \(y_2 - (-y_1)\) becomes \(y_2 + y_1\). Many students will just write \(y_2 - y_1\) and ignore the negative sign of the point.
Slope Searchers Answer Key Answer Key
Slope Searchers Activity & Assessment
Teacher Resource
01 Rise and Run Grid (Warm-Up)
Rise
2
Run
2
Final Slope
1
02 Slope Sort Cards
Positive Slope
Card 01: m = 2
Card 05: m = 2
Card 07: m = 1/2
Negative Slope
Card 02: m = -1
Card 06: m = -2
Card 08: m = -3/4
Zero Slope
Undefined Slope
03 Steepness Check Exit Ticket
Points: (3, -4) & (-5, 2)
The Formula Set-Up:
\[m = \frac{2 - (-4)}{-5 - 3}\]
Step-by-Step:
\[m = \frac{2 + 4}{-5 - 3} = \frac{6}{-8}\]
Final Simplified Answer:
m = -3 / 4
