Cogito
Grade 8 Math · Chapter 6 · Lesson 4
Reading a Graph as a Story
Rising, falling, flat.
10 problems · about 18 minutes · 8.F.B.5
What this lesson teaches
The child describes qualitatively how a quantity changes by reading the shape of its graph.
- A rising graph means increasing; a falling graph means decreasing.
- A flat section means the quantity is not changing, not that it is nought.
- The steeper the section, the faster the change.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Rate of Change and Starting Value: Through (0, 7) and (3, 19). What is the rate?
Answer 4
Why 4.
Review — Linear and Nonlinear Functions: 4, 10, 16, 22. Constant rise?
Answer 6
Why 6, so it is linear.
Review — What a Function Is: Rule "multiply by 4 then add 1". What comes out when 5 goes in?
Answer 21
Why 21.
Warm Up
Straightforward practice. Get the method working first.
3 problemsA distance graph falls steadily. Is the person moving away or back? 1 for away, 2 for back.
Answer 2
Why Back towards home.
A rising graph means the quantity is increasing. 1 for yes, 0 for no.
Answer 1
Why Up is more.
Does a flat section mean the quantity is nought? 1 for yes, 0 for no.
Answer 0
Why It means unchanging.
Build It Up
The same ideas with more to keep track of.
2 problemsA slope of −3 means rising or falling? 1 for rising, 2 for falling.
Answer 2
Why Negative slopes fall.
A slope of 0. Is the graph flat? 1 for yes, 0 for no.
Answer 1
Why No rise per run.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Flat Part: On a distance graph, a flat section means the speed is what?
Answer 0
Why Nought — stopped.
The Steeper Line: Of slopes 2 and 5, which section is changing faster? Give the number.
Answer 5
Why 5.