Sketching Graphs from Stories

Lesson 2 of 2: Turning Words into Graphs

In this lesson:

• Sketch a qualitatively accurate graph from a verbal description
• Analyze and sketch complex, multi-section graphs

What You Will Be Able to Do

By the end of this lesson, you should be able to:

1. Sketch a graph that matches a verbal description — direction, shape, steepness
2. Analyze a complex multi-section graph completely
3. Write a full graph story, accounting for every section

Could You Draw This Runner's Graph?

"A runner starts still, speeds up, holds a steady pace, then slows to a stop."

Could you sketch speed versus time — without any numbers?

Make One Decision per Phase

For the runner's speed, decide just one thing per phase:

• Start still → up? flat? down?
• Steady pace → up? flat? down?
• Slows to a stop → up? flat? down?

The Five-Step Sketching Process to Follow

Build the graph one segment at a time — direction, shape, steepness.

Worked Example: Sketch the Runner

Speed versus time, built segment by segment:

Up from zero → flat plateau → down to zero.

Your Turn: Sketch Along With Me

Same runner, but now you draw it as I describe each segment.

Segment 1: speeds up. Segment 2: steady. Segment 3: slows to stop. Draw each, then advance.

Worked Example: Sketch Cooling Coffee

"Hot coffee sits on a counter and cools toward room temperature."

Decreasing, nonlinear — fast at first, then slowing; never reaches zero.

Worked Example: A Bicycle Ride

"Slow steady climb, then coast faster and faster downhill, then brake to a stop."

Constant low → nonlinear speed-up → steep drop.

Quick Check: Read the Sketch

Look at the bicycle graph again.

Which segment is the steepest? Which segment is curved rather than straight?

Your Turn: Throw a Ball

"A ball is thrown straight up, slows to a peak, then falls back down, faster and faster."

Sketch height vs. time. Remember: the axis is time, not sideways motion.

Worked Example: Gas in the Tank

A car's fuel level over time — six sections:

Each section: name its direction and its shape.

Both Directions, On Harder Graphs

You've now sketched from stories and read a complex graph.

Synthesis means doing both — on graphs with many sections.

Worked Example: A School Day

"Stress is low before school, climbs through classes, spikes before a test, drops after, holds moderate, then eases after school."

Your Turn: Compare Two Runners

Two runners' speed vs. time for the same race:

Describe the qualitative differences — who speeds up faster? who holds pace longer?

Watch Out For These Three Traps

• Cooling drawn straight to zero — it should curve and level off
• Graph as a path — the bottom axis is time, not sideways motion
• Steeper = faster change in the vertical quantity — name what's changing

Quick Check: Sketch a Short Story

"A car waits at a red light, then accelerates, then cruises steadily."

On your own: sketch speed vs. time — three segments. Draw before advancing.

Your Turn: Sketch the Whole Story

"A skydiver falls speeding up, the parachute opens and she slows sharply, then she drifts down at a steady, slow rate."

On your own: sketch speed vs. time. No labels given — you decide everything.

Key Takeaways From This Lesson

✓ Sketch in segments — decide direction, shape, and steepness
✓ Curves flatten toward a limit (cooling) — don't draw straight to zero
✓ Reading and sketching are the two directions of graph literacy

Bottom axis is time, not a path; steeper = vertical quantity changing faster

Coming Up Next In High School

You can now move freely between a situation, its words, and its graph.

Next: high school formalizes this — naming intervals of increase and decrease, maximums and minimums, and end behavior.