Plotting the End Exit Ticket Plotting the End
Final Check: Interpreting the Journey
Exit Ticket
Student Name: __________________________________
Date: ________________________
1 The Mystery Journey
Study the graph below. It represents a student's walk from home to school. Write a brief narrative that explains what happened during their journey.
Distance
Time
Your Story
2 Graphical Vocabulary
Match the graphical feature to its meaning in a "Distance-Time" story.
Horizontal Line
A. The person is moving home.
Steepest Slope
B. The person has stopped moving.
Downward Slope
C. The point where the story starts.
y-intercept
D. The person is at their fastest speed.
Self-Assessment
How comfortable do you feel translating graphs?
Lost
Getting There
Expert
Graph Storytellers Slides Graph Storytellers
Turning Data into Narrative
The Mystery Plot
Look at the graph below. If this represented someone's morning, what happened?
Think-Pair-Share:
Where did they start?
When were they fastest?
Did they stop?
Today's Mission
Interpret
Read a graph and explain exactly what is happening in the real world.
Sketch
Listen to a story and draw a graph that captures every twist and turn.
Vocabulary of Motion
Steep Slope
Fast, consistent movement away or toward a point.
Flat (Zero) Slope
Stopping. Time passes, but distance does not change.
Curved Line
Changing speed. Accelerating or decelerating.
The "Returning" Line
On a Distance-Time Graph:
Line going UP = Moving AWAY from the start.
Line going DOWN = Moving TOWARD the start (Returning).
Story to Graph: Maya's Walk
1. Maya leaves home and walks at a steady pace to the park.
2. She sits on a bench for 10 minutes to watch the ducks.
3. She realizes she forgot her keys and runs back home twice as fast.
Distance Time Steady Pace Stopped Returning Fast
Your Turn
Grab the Graph Matchmaker handout. Work with your partner to decode the stories behind the lines!
Graph Storytellers Answer Key Graph Storytellers
Master Answer Key & Teacher Reference
Teacher Resource
Algebra 1 • Grade 9
Graph Matchmaker
Story 1
B
Returns to start (returns home) at the fastest speed.
Story 2
C
Fast start, slows down, then stops entirely.
Story 3
A
Steady, stop, steady, continues away from start.
Teacher Tip: Verify that students recognize the x-axis represents "home" or "distance = 0". Graph B is the only one where the journey concludes back at the start point.
Sketch Your Story: Jax the Courier
Correct Graph Profile
Critical Checkpoints:
Segment 1: Steep line from 0 to 3 miles (at 15 mins).
Segment 2: Flat horizontal line from 15 to 20 minutes.
Segment 3: Gentler slope from 3 to 5 miles (ends at 40 mins).
Segment 4: Very steep return line back to distance 0 (at 50 mins).
Exit Ticket Solutions
1. Mystery Story Sample Answer:
"The student walked quickly away from home for a few minutes. They stopped for a while (perhaps at a friend's house or a stoplight). Finally, they realized they forgot something and sprinted back home as fast as possible."
Horizontal Line B
Steepest Slope D
Downward Slope A
y-intercept C
Graph Storytellers Teacher Guide Graph Storytellers
Comprehensive Instruction Guide
Grade 9 • Algebra 1
65 Minutes Duration
Learning Objective
Students will translate between qualitative narratives and distance-time graphs, interpreting slopes as rates of speed and intercepts as starting/ending points.
Key Vocabulary
Qualitative Graph Rate of Change Intercept Segment
Lesson Materials
Class Slides
Worksheet Set
Exit Ticket
Answer Key
Teacher Insight
Watch for students who interpret a "downward slope" as physically walking down a hill. Emphasize that in distance-time, this means moving toward the reference point.
Ensure students use straight edges for sketching; it reinforces the concept of constant speed.
The Instructional Arc
10
Minutes
Hook: The Mystery Commute
Slides 1–3
Display the "mystery graph." Ask: "If this graph represents a student's morning, what happened?"
Introduce the lesson's goal: Becoming "Graph Translators" who can read pictures and write stories.
15
Minutes
Direct Instruction: The Graph’s Anatomy
Slides 4–8
Slope as Speed: Steeper = faster. Flat = stopped. Downward = returning.Turning Points: Explain that sharp corners represent sudden changes (instataneous stops or reversals).
15
Minutes
Guided Practice: Graph Matchmaker
Handout 1
Students work in pairs to match stories to graphs. Focus on "clue words" like steady, stopped, fast, and returned.
15
Minutes
Independent Practice: Sketching Jax
Handout 2
Students create a graph from scratch based on the story of Jax the Courier. Walk around and prompt: "Where did Jax stop?" "How do we show he went back home?"
10
Minutes
Exit Ticket: Plotting the End
Handout 3
Final individual check. Collect for assessment of student's ability to identify key graphical features and their meanings.
Sketch Your Story Worksheet Sketch Your Story
Translating Words into Graphs
Activity
Student Name
Date
The Courier's Busy Afternoon
"Jax the bike courier starts at the central warehouse. He pedals at a fast, steady speed for 15 minutes to deliver a package to a building 3 miles away. He spends 5 minutes inside getting a signature. Then, he bikes at a slower, relaxed pace for 20 minutes to reach a coffee shop 2 miles further from the warehouse. Finally, he gets an emergency call and sprints back to the central warehouse, arriving in just 10 minutes."
Sketch Jax's distance from the warehouse over time:
Use a ruler for straight lines!
Distance (Miles)
Time (Minutes)
0
5
10
0
15
30
45
60
1 Which segment is the steepest? Why?
2 How many "stops" are in the story?
Graph Matchmaker Worksheet Graph Matchmaker
Connecting Stories to Slopes
Worksheet
Student Name
Date
Your Mission
Match each story to its correct distance-time graph. Look for "clues" about speed (slope) and direction (movement away or towards the start).
01
Leo walked to the library at a steady pace. He spent an hour doing research. On the way home, he realized he was late for dinner and ran as fast as he could.
Graph Match:
02
Sara started biking quickly away from her house. She hit a steep hill and slowed down significantly. Once she reached the top, she stopped for a break.
Graph Match:
03
Marcus walked half a block, stopped to sniff a tree, walked another half block, and then walked back home at the same steady pace.
Graph Match:
Graph A
Graph B
Graph C
Justify Your Choice
Explain which "clue words" led you to pick one of your matches.
Sketch Your Story Worksheet Sketch Your Story
Translating Words into Graphs
Activity
Student Name
Date
The Courier's Busy Afternoon
"Jax the bike courier starts at the central warehouse. He pedals at a fast, steady speed for 15 minutes to deliver a package to a building 3 miles away. He spends 5 minutes inside getting a signature. Then, he bikes at a slower, relaxed pace for 20 minutes to reach a coffee shop 2 miles further from the warehouse. Finally, he gets an emergency call and sprints back to the central warehouse, arriving in just 10 minutes."
Sketch Jax's distance from the warehouse over time:
Use a ruler!
Distance (Miles)
Time (Minutes)
0
5
10
0
15
30
45
60
1 Which segment is the steepest? Why?
2 How many "stops" are in the story?
