Cogito
Algebra 1 · Chapter 3 · Lesson 4
Rate of Change
How fast the output moves as the input does.
11 problems · about 22 minutes · F-IF.B.6
What this lesson teaches
The student computes an average rate of change and interprets it with units.
- Rate of change is the change in output divided by the change in input.
- For a line it is constant and equals the slope; for a curve it depends on the interval.
- A rate without units is not an answer.
Warm Up
Straightforward practice. Get the method working first.
4 problemsFrom 5 to 25 over 4 steps. Rate?
Answer 5
Why 5.
From 2 to 14 over 4 steps. Rate?
Answer 3
Why 12 ÷ 4.
From 20 to 8 over 3 steps. Rate?
Answer -4
Why −12 ÷ 3.
From 7 to 7 over 5 steps. Rate?
Answer 0
Why No change.
Build It Up
The same ideas with more to keep track of.
3 problemsIs the rate of change of a straight line constant? 1 for yes, 0 for no.
Answer 1
Why That is what makes it straight.
Through (0, 3) and (4, 19). Rate?
Answer 4
Why 16 ÷ 4.
A negative rate means the output is doing what? 1 for rising, 2 for falling.
Answer 2
Why The sign is direction.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSelect every statement that is true of the rate of change.
Answer It is change in output over change in input.; It should be reported with units.
Why Only a line has one rate throughout.
Through (1, 5) and (3, 11). Rate?
Answer 3
Why 6 ÷ 2.
The Drain: From 40 litres to 10 litres over 6 minutes. What is the rate, in litres per minute?
Answer -5
Why −5.
The Wage: £60 for 5 hours. What is the rate, in pounds per hour?
Answer 12
Why 12.