Analyzing Graphs Qualitatively
Aligned to 8.F.B.5 — Common Core State Standards for Mathematics.
What this lesson teaches
A graph tells a story: going up means increasing, going down means decreasing, and flat means constant. Steepness shows how fast the change is; straight sections are linear and curved sections are nonlinear.
Worked example
A graph of the water in a tub rises steeply while it fills, stays flat (level) while someone bathes, then drops to zero as it drains. The flat part shows the amount is constant; the steep drop shows a fast decrease.
Practice questions
- Describe what a flat horizontal section of a distance-time graph means.
- Sketch a graph of a runner speeding up, then resting, then slowing to a stop.
- A graph rises, then falls, then rises again — describe a real situation it could model.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Análisis Cualitativo de Gráficas
Una gráfica cuenta una historia: subir significa aumentar, bajar significa disminuir y estar plana significa constante. La inclinación muestra qué tan rápido es el cambio; los tramos rectos son lineales y los tramos curvos son no lineales.
Ejemplo: Una gráfica del agua en una tina sube abruptamente mientras se llena, se mantiene plana (nivelada) mientras alguien se baña, y luego cae a cero al vaciarse. La parte plana muestra que la cantidad es constante; la caída abrupta muestra una disminución rápida.
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