Graph Sketchers Practice Worksheet
Algebra 1 • Functions CCSS 8.F.B.5 / HSF-IF.B.4
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SKETCHING GRAPHS FROM STORIES
Translate qualitative descriptions and rate-of-change relationships into accurate graphs.
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The Graph Sketcher's Toolkit: Key Qualitative Behaviors
Constant Increase Straight line sloping up
Stationary / Flat Horizontal line (rate = 0)
Accelerating Curve steepens upward
Decelerating / Level Curve flattens out
Modeled Example: Maya's Morning Commute Reference Model
Scenario: Maya leaves home walking at a steady speed. She stops at a red crosswalk signal for 2 minutes. When the light turns green, she jogs at a faster constant speed until she reaches school.
• Seg A (Walk): Steady positive slope.
• Seg B (Stop): Flat horizontal line.
• Seg C (Jog): Steeper slope than A.
A B C Time Distance
1 Drone Altitude Mission Variables: Altitude vs. Time
A delivery drone performs the following flight path from ground level:
- Climbs at a constant rate for 20 seconds.
- Hovers in place at peak height for 15 seconds.
- Descends rapidly halfway down in 5 seconds.
- Smoothly decelerates until gentle pad touchdown.
Analysis Question:
Why does stage 4 curve rather than form a straight line?
Sketch Graph Below 0 Time (seconds) Altitude (m)
2 Cooling Campfire Cocoa Variables: Temperature vs. Time
Boiling cocoa (200°F) sits on a table. The air temperature is a steady 50°F.
• Liquids cool fastest when hottest (greatest temp difference).
• Near 50°F, the cooling rate flattens significantly.
• The cocoa levels out at 50°F and never drops below it.
Feature Check:
Where does the curve begin, and what horizontal line does it approach?
Sketch Graph Below 50°F 200° 0 Time Elapsed Temp (°F)
Turn page for Container Fill Rates & Reverse Story Challenge → Graph Sketchers Worksheet • Page 1 of 2
Part II: Depth Analysis & Story Construction
Student Name:
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3 Filling the Mystery Beakers (Constant Water Flow Rate) Rate of Change
Water is poured into each container at a constant flow rate. Sketch the curve showing Water Height (h) vs. Time (t) until completely full.
Container A: Cylinder Equal Width Time Height
Slope: Constant / Straight
Container B: Conical Flask Wide → Narrow Time Height
Slope: Slower → Faster curve
Container C: Stepped Bottle 2-Stage Body Time Height
Slope: Gentle slope → Steep slope
4 The Skateboard Half-Pipe: Comparing Two Variables Same event • Different perspectives
Leo drops in from the top of a half-pipe, rolls back and forth 3 times without kicking, and slows to a stop at the bottom.
Graph A: Height vs. Time Time Height Hint: Starts at max height, dips to zero, oscillates with smaller peaks.
Graph B: Speed vs. Time Time Speed Hint: Starts at 0 speed at release, max speed at the very bottom!
5 Reverse Engineering: Write the Matching Story Constructive Explanation
Trip from Home Graph 1 2 3 4 Time (hours) Distance from Home (mi)
Write a clear real-life story explaining what happens during each phase:
Segment 1 (Climb):
Segment 2 (Flat):
Segment 3 (Climb):
Segment 4 (Steep drop):
Self-Check: Correct Axes Labeled Rates Distinguish Straight vs. Curved Rest/Stops are Flat
Graph Sketchers Worksheet • Page 2 of 2
