Math 1 · Unit 2 · Lesson 6
Average Rate of Change: How Fast It Is Changing
Steeper means faster, and now it gets a number. Pick two points. The average rate of change is the change in the output divided by the change in the input: how much it went up or down for each step to the right. Find it from a table, from a graph, and from a rule, then read it back into the story.
The big idea
The average rate of change is one fraction: the change in the output on top, the change in the input on the bottom. Pick two points on the interval you care about, subtract the outputs, subtract the inputs in the same order, and divide. The number says how much the output goes up or down for each single step of the input, on average across that stretch. Positive means climbing, negative means falling, zero means flat, and bigger means steeper. It works the same from a table, from two points read off a graph, or from a rule after you evaluate at the two inputs. Say the interval and the units, and read the number back into the story. Next unit, this same fraction gets its real name, slope, and pairs up with the equation of a line.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the fraction, the three moves, the three ways (table, graph, rule), the sign rule, and a worked example. Plus a worksheet with an answer key and a short lesson plan.