Marathon Matchup Organizer
MARATHON MATCHUP
Comparing Linear Functions in Different Representations (8.F.A.2)
Name:
Date:
Period:
Task Context: Ethan and Noah are training for a marathon. Ethan uses an equation to track progress, while Noah uses a table. Deconstruct each function, determine rate of change and starting value, compare their training progress, and identify who runs at a greater speed.
1
Ethan's Training
Equation
Model: \(d = \text{distance (mi)}\), \(t = \text{time (hr)}\)
\(d = 7t + 2\)
Rate of Change (Slope, \(m\)):
What does the slope mean in Ethan's running context?
Initial Value (\(y\)-intercept, \(b\)):
What does the \(y\)-intercept mean before he starts?
2
Noah's Training
Table of Values
| Time (\(t\)) | Dist (\(d\)) |
|---|
| 0 hr | 3 mi |
| 1 hr | 9 mi |
| 2 hr | 15 mi |
| 3 hr | 21 mi |
Find Rate of Change:
\(m = \frac{\Delta d}{\Delta t} = \frac{d_2 - d_1}{t_2 - t_1}\)
\(m =\)
Initial Value (\(y\)-intercept at \(t=0\)):
What do Noah's speed and starting value mean?
3
Head-to-Head Comparison Matrix
| Key Feature | Ethan | Noah | Comparison & Evidence |
|---|
| Running Speed (Slope / Rate of Change) | mph | mph | Who has the greater rate? |
| [ ] Ethan [ ] Noah | | | |
|
| Starting Head Start (\(y\)-intercept / Value at \(t=0\)) | mi | mi | Who started farther ahead?
[ ] Ethan [ ] Noah
|
4
Final Synthesis & Official Response
• Describe the similarities between the two functions:
• Describe the differences in their slope, \(y\)-intercept, and progress:
Based on your comparison, does Ethan or Noah have the greater speed during training sessions?
Answer: Greater speed is
Ethan's Equation:
Noah's Equation:
