Growth Detectives Slides Investigation #402
Growth Detectives
Analyzing data tables to predict the shape of the graph.
01 // INTRODUCTION
The Mystery Graph
If this graph shows up on your radar, what's happening to the numbers in the data table?
Are the numbers increasing steadily ?
Are they increasing faster and faster ?
What operation might be used in the Y column?
Evidence Review
TIMESTAMPS: 1:37 - 3:00
Embedded media
Watch For:
How does "adding" look on a graph?
How does "multiplying" look on a graph?
Can we tell the difference without grid lines?
Activity: Card Sort
Data Tables
Look for the pattern in the Y column. Are we adding or multiplying?
Visual Graphs
Identify the shape. Is it a straight line or a dramatic curve?
Descriptions
Connect the numbers to words. "Doubles each time" vs "Adds 5".
Group Mission: Match all 3 cards for each data set.
20 MINUTES
The Debrief
1
Which feature was easiest to match: the table numbers or the graph shape? Why?
2
If a graph curves upward, how do we know for sure it's exponential and not just a weird line?
3
What word in a description immediately tips you off that it's exponential?
Final Verdict
"I can tell a table will be a curve if..."
Complete the sentence on your exit ticket.
Pattern Matcher Card Sort Pattern Matcher
Investigation #402: Card Sort Activity
Subject
Algebra 1
Mission: Cut out the 12 cards below. Match each Data Table with its corresponding Visual Graph and Description . There are 4 complete sets.
Table Card #01
Table Card #02
Table Card #03
Graph Card #01
Graph Card #02
Graph Card #03
Description Card #01
"Starting at 2, the total grows by exactly 2 units every single step."
Description Card #02
"Starting at 2, the value doubles every time the step increases by 1."
Description Card #03
"Each new step adds 5 to the previous total, keeping growth constant."
Table Card #04
Graph Card #04
Description Card #04
"The value triples with every step, getting steeper very quickly."
End of Materials
Growth Detective Anchor Chart GROWTH MODELS
Linear
The Pattern
Constant ADDITION
Same amount added every time.
Straight Line
Evidence: Slope
Slope is CONSTANT.
It never changes. The steepness is the same from start to finish.
Exponential
The Pattern
Constant MULTIPLICATION
Common ratio (doubling, tripling).
Curved Line
Evidence: Slope
Slope is INCREASING.
It gets steeper and steeper as you move to the right.
Linear Word
STEADY
The Difference
Exponential Word
ACCELERATING
Growth Gossip Discussion Cards Growth Gossip
Discussion Prompts for Growth Detectives
REF: GD-402-DISC
Prompt #01
The "Big Number" Trap
Imagine you add 1,000,000 to a total every single day. The numbers are getting huge! Is this growth linear or exponential? Why?
Key Concept: Addition vs. Multiplication
Prompt #02
The Slow Curve
If you multiply a number by 1.1 every time, it grows very slowly at first. Does the graph still curve, or does it look like a line?
Key Concept: Constant Ratio
Prompt #03
Predicting the Future
Which model—linear or exponential—is easier to predict 100 steps into the future just by looking at the table? Why do you think so?
Key Concept: Long-term Prediction
Prompt #04
The Steepness Factor
In the video, Justin says "no single slope is enough" for exponential data. What does he mean by that? How many slopes does a line have?
Key Concept: Constant Rate of Change
Prompt #05
Visual Deception
Can an exponential curve ever look like a straight line if you only look at a tiny piece of the data? How can the table help you "see" the truth?
Key Concept: Scale and Perspective
Prompt #06
The "Zero" Mystery
If the Y-value is 0 at Step 0, can growth be exponential? (Think about what happens when you multiply by 0).
Key Concept: Initial Value (y-intercept)
Use these during the Reflection Phase or for fast-finishers.
Growth Boardroom Scenario Cards The Growth Boardroom
Client Scenario Cards // Data Consultant Roleplay
Consultant Name
Client #A1
The Hourly Hero
"I just got a job at a local tech shop! I earn $15 for every hour I work. If I work 0 hours, I earn $0. If I work 1 hour, I earn $15, and so on."
Consultant Mission
"Predict the graph shape and explain why to the client."
Client #B2
Viral Venture
"I posted a funny cat video. On the first day, it had 10 views. Every day since then, the number of views has doubled. I'm worried it's going to crash the site!"
Consultant Mission
"Model the next 3 days of growth and sketch the curve."
Client #C3
Cell Splitters
"We are observing a bacteria culture in the lab. Every 30 minutes, each cell splits into two new cells. We started with 50 cells."
Consultant Mission
"Is this linear or exponential? What happens to the slope over time?"
Client #D4
The Coffee Shop
"Our shop is popular! We serve an average of 40 customers every hour from 8 AM to 5 PM. We want to know how many total customers we've served by 2 PM."
Consultant Mission
"Determine if this is a steady growth or accelerating growth."
Shape Predictor Exit Ticket Final Verdict
Exit Ticket #402
Detective Name
Date
1 Predict the Shape
Look at the table below. Will the graph be a straight line or a curved line?
Straight Line
Curved Line
2 Explain Your Evidence
Complete the sentence below with specific evidence from the table.
"I can tell a table will be a CURVE if..."
End of Assessment
