Understanding Constant of Proportionality
Grade 7 Mathematics Common Core 7.RP.A.2 60-Minute Lesson
Think About It
Have you ever noticed when you double one thing, another thing doubles too? What does that mean? Can you think of an example from your daily life?
What is a Proportional Relationship?
Two quantities that change at the same rate When one quantity doubles, the other doubles too When one quantity triples, the other triples too The ratio between them stays constant
Real-World Example: Apple Store
Let's explore buying apples at $2 per apple Create a table showing number of apples and total cost Look for patterns in the data What stays the same as we buy more apples?
Key Definition
The constant of proportionality is the number that tells us how much one quantity changes when the other quantity changes by 1 unit.
Finding the Constant of Proportionality
{"left":"From a table: Divide any y-value by its corresponding x-value\nFrom an equation: It's the number multiplied by x (like the 2 in y = 2x)","right":"From a graph: It's the slope of the line through the origin\nFrom a word problem: Find the unit rate or price per item"}
Your Turn: Practice Problems
Work in pairs with scenario cards Determine if each relationship is proportional If proportional, find the constant Be ready to explain your reasoning