Comparing Functions: Rate of Change
Grade 8 Mathematics Understanding How Functions Change Over Time 30-Minute Interactive Lesson
Learning Objectives: I Can Statements
I can define rate of change in my own words I can compare two functions to determine which changes faster I can explain why one function changes faster than another using structured reasoning I can use sentence frames to communicate mathematical thinking clearly
Hook Activity: Walking Scenarios
Scenario A: Tom walks 3 miles every hour Scenario B: Sara walks 5 miles every hour Quick Question: Who is changing distance faster? Turn and talk with your partner for 1 minute
What is Rate of Change?
Rate of change tells us how fast something is changing over time Like walking speed: miles per hour In functions: how quickly the output (y) changes when the input (x) changes Steeper lines = faster rate of change
Comparing Our Walking Functions
{"left":"Tom: 3 miles per hour\nSara: 5 miles per hour\nTom's function: y = 3x","right":"Sara's function: y = 5x\nSara changes distance faster\nHer rate of change is greater"}
Sentence Frame for Mathematical Reasoning
Function _____ changes faster than Function _____ because _____. Use this frame to explain your mathematical thinking clearly! Include specific numbers and evidence in your reasoning
Independent Practice: Apply Your Learning
New scenario: Anna walks 4 miles per hour, Mike walks 6 miles per hour Use the sentence frame to compare their rates of change Include specific evidence in your explanation Extension: Create your own walking scenario and comparison
Exit Ticket: Show What You Know
In your own words, what does 'changes faster' mean when comparing functions? Share one sentence frame response with the class What questions do you still have about rate of change?