Comparing Functions: Which Changes Faster?
Grade 8 Mathematics Understanding Rate of Change 20-minute lesson
I Can... Statement
I can compare two functions and explain which one changes faster I can describe rate of change in my own words I can identify which function changes faster using simple data I can explain my thinking using a complete sentence
Warm-Up: Who's Faster?
Person A walks 1 mile in 10 minutes Person B walks 1 mile in 20 minutes Who is faster? How do you know? Think-Pair-Share with your neighbor
What is Rate of Change?
Rate of change = how much y changes when x increases by 1 Think of it as the 'speed' of a function Steeper lines change faster We can find this in tables, graphs, and equations
Comparing Function Tables
{"left":"Function A: When x increases by 1, y increases by 3\nFunction B: When x increases by 1, y increases by 5","right":"Function B changes faster!\nLook for the pattern in the y-values"}
Comparing Graphs
Steeper lines change faster Look at the slope of each line The line that rises more quickly has a greater rate of change Use your finger to trace the steepness
Practice Question
Look at these two functions: Function 1: y = 2x + 1 Function 2: y = 5x + 1 Which function changes faster? Explain your thinking using a complete sentence.
Success Check & Next Steps
Can you find rate of change from tables, graphs, and equations? Can you explain which function changes faster using complete sentences? Tomorrow: We'll practice with more complex comparisons Extension: Create your own real-world function examples