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Ratios and Data 6-8 / Week 09 / Wednesday
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Week 09 · Proportional Relationships

Wednesday

Numbers Lab: steps and meters
// The straight line through zero
⏱ about 20 min

Wednesday: Numbers Lab, Steps and Meters

Rocket stands at one end of the hallway with the tape measure. "Five steps, then measure. Ten steps, then measure. Fifteen."

He walks five even steps. Raven reads the tape. "Three meters."

Ten steps. "Six meters." Fifteen steps. "Nine meters."

"What do you notice?" Raven asks, writing the numbers down.

"Every five steps adds three meters," Rocket says. "And 3 ÷ 5, 6 ÷ 10 and 9 ÷ 15 are all 0.6."

Nova hovers at the start line, her light marking zero. "Zero steps, zero meters," she says. "Does the line go through it?"

"It has to," Rocket says. "Proportional. My step is 0.6 meters. Raven, your turn, and I bet your k is smaller."

Raven laughs and starts walking. "We will let the data decide."

What you need

  • A tape measure or a meter stick.
  • Masking tape to mark a start line and each stopping point.
  • A clear straight path: a hallway, a yard or a cleared room.
  • Your Numbers Notebook and a pencil.
Safety first
A grown-up picks a flat, clear path away from roads and stairs. Wear shoes.
Walk, never run. Look where you are going, not at the tape.
Let the tape measure roll back slowly. A snapping tape can pinch fingers.

Walk and measure

  1. Mark a start line with tape. Stand with your toes on it.
  2. Walk 5 even steps and stop. Mark the spot with tape. Measure from the start line in meters, to one decimal place.
  3. Return to the start. Walk 10 even steps, mark and measure. Then 15 steps.
  4. Record each pair, steps and meters, in a table. Divide meters by steps for each row.
  5. If the three quotients match (or come very close), your walking is proportional, and the quotient is your k.
  6. Use your k to predict 20 steps. Then walk 20 steps and measure to check.

The crew's walks

Here are the crew's own measurements from the hallway. Quotients are meters divided by steps.

WalkerStepsMetersMeters ÷ steps
Rocket530.6
Rocket1060.6
Rocket1590.6
Raven52.50.5
Raven1050.5
Raven157.5?
A table, Steps and Rocket in meters: 5 and 3, 10 and 6, 15 and 9, 20 and a blank
READ THE LAB DATA
  • Read the question.
  • Tap your answer.
Rocket walked 6 meters in 10 steps. How many meters per step is that?
Raven walked 7.5 meters in 15 steps. How many meters per step is that?
Rocket's k is 0.6 meters per step. How far will 20 of his steps reach?
Raven's k is 0.5 meters per step. How far will 30 of her steps reach?
PROPORTIONAL OR NOT?
  • Read the question.
  • Tap your answer.
Rocket, steps and meters: (5, 3), (10, 6), (15, 9). Is y proportional to x?
Raven, steps and meters: (5, 2.5), (10, 5), (15, 7.5). Is y proportional to x?
A tired walker, steps and meters: (5, 3), (10, 5.5), (15, 7.5). Is y proportional to x?
Raven's k is 0.5 meters per step. How many of her steps make 10 meters? Type the number.
WHY THIS EXERCISEA proportional rule works both ways: from steps to meters and from meters back to steps.
Draw your three measurements as dots, steps across and meters up. Add (0, 0). Do they line up?

Great lab work. Your own steps are a proportional relationship. Tomorrow the seedling tray gets a full data check.

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