8.F.5: Describe and Sketch Graphs
Also written as 8.F.B.5 and CCSS.MATH.CONTENT.8.F.B.5 · Cluster: Use functions to model relationships between quantities.
The Official Wording
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Common Core State Standards, Grade 8, Functions · Read it at the source · Checked October 14, 2026
What 8.F.5 Means in Plain English
Eighth graders read a graph like a story, without needing numbers. A graph of distance from home that rises steeply, stays flat for ten minutes, then falls tells of a fast ride out, a stop and the trip back. They say where it rises, falls, levels or curves.
They also run it backwards and sketch a graph from a description, like a bath that fills, sits, then drains. That shape reading carries into high school, where students mark intervals of increase, decrease and maximums on any function’s graph (HSF-IF.4).
8.F.5 I Can Statements
- I can say where a graph is increasing, decreasing or constant.
- I can tell a straight piece of a graph from a curved one.
- I can sketch a graph that matches a story told in words.
8.F.5 Worked Example
A bath described in words, turned into a sketch one piece at a time, with no numbers needed beyond the times and the depth.
A tub fills at a steady rate for 8 minutes until the water is 30 cm deep. It stays at 30 cm for 15 minutes. Then the plug is pulled and it empties in 5 minutes, draining fast at first and slowly at the end. Sketch depth against time.
- Label the axes first. Time is the input, and depth depends on it.horizontal axis: time (min), vertical axis: depth (cm)
- A steady rate means equal rises in equal times, so the first piece is a straight line going up.0 to 8 min: straight line rising from (0, 0) to (8, 30)
- Depth that does not change makes a piece that neither rises nor falls.8 to 23 min: flat line at 30 cm
- Draining fast, then slowly, is decreasing but not linear: steep at first, leveling off as it nears the bottom.23 to 28 min: curve falling from (23, 30) to (28, 0), steep, then shallow
Check it: Cover the problem and read the sketch back as a story. It should tell the same events in the same order, and the times should add up: 8 + 15 + 5 = 28 minutes.
Common Mistakes with 8.F.5
Reading the graph as a picture
“The graph goes up and down, so the bike rode up a hill and down again.”
Try this: Name the two quantities on the axes before describing anything. A rising distance graph means moving away from home, not climbing a hill.
Reading a flat piece as zero
The flat stretch at 30 cm described as “the tub is empty”
Try this: Read the height of the flat piece, not just its shape. Flat means not changing, and here the depth holds at 30 cm.
Drawing every change as a straight line
The draining tub sketched as one straight slanted line, though it slowed down at the end
Try this: Underline the speed words, like steady, faster or slower. Steady gets a straight piece, and speeding up or slowing down gets a curve.
Where 8.F.5 Fits
Practice 8.F.5
Quick Check
- A graph of a phone’s battery charge falls in a straight line, then rises in a curve that flattens near 100%. What happened?
- A graph of a student’s distance from school is flat at 0 for 5 minutes, then rises in a straight line. Describe it.
- A ball is thrown straight up, slows down, stops at the top, then falls faster and faster. Describe the graph of its height against time.