How to explain it
The anchor students hold onto: Increasing: rises left to right. Decreasing: falls left to right. Linear: straight line. Nonlinear: curved. Turning point: where direction switches.
Qualitative graph reading applies directly in 8.SP.A.1 and 8.SP.A.2 — students describe scatter plot trends as increasing, decreasing, linear, or nonlinear patterns.
Worked examples
Example 1
Describe the Graph
Rise, peak, fall. Describe it.
Step 1Left side: graph is increasing.
Step 2At the peak: turning point.
Step 3After the peak: decreasing.
AnswerIncreases to a turning point; then decreases. Nonlinear.
Example 2
Sketch from Words
Sketch: slow rise, steep fall.
Step 1Slowly uphill = increasing.
Step 2Quickly downhill = decreasing.
Step 3Sketch: gentle rise then sharp fall.
AnswerGentle increase then steep decrease; one turning point.
Example 3
Real-World Mixed
Rises all morning, flat at noon.
Step 1Rising all morning = increasing interval.
Step 2Stays flat = constant (neither).
Step 3Sketch: rise, then horizontal segment.
AnswerIncreasing then constant; no turning point — plateau.
Common mistakes
What students write
Student says "the graph goes up" instead of "the graph is increasing".
The fix
Use output language: the output value increases as the input increases — always describe what the output does.
What students write
Student marks the y-intercept or an endpoint as the turning point.
The fix
A turning point is an interior direction change — where the graph switches from increasing to decreasing (or vice versa).
Teacher tip
Head off the two predictable errors before they happen. First: Use output language: the output value increases as the input increases — always describe what the output does. Second: A turning point is an interior direction change — where the graph switches from increasing to decreasing (or vice versa).