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4/6
Week 02 · Rates and Speed

Thursday

The timing log
// A ratio with two different units
⏱ about 20 min

Thursday: The Timing Log

Raven spreads the Field Day timing log across the Numbers Desk. Four runners, four distances, four times.

"Helper 1 ran 56 meters," Rocket says. "Longest run. Helper 1 is fastest."

"What do you notice about the seconds column?" Raven asks.

"They are all different," Rocket says. "Oh. Different distances and different times. I need unit rates."

Nova dims her light to a soft glow. "Four divisions. Then the ranking will be fair."

Rocket works down the table. "Rocket 5. Raven 6. Helper 1 is 7. Helper 2 is 4."

"Helper 1 is still fastest," he says, "but now I can prove it."

Read the log

These times are the crew's own made-up Field Day log. Each runner ran a different distance, so the raw numbers cannot be compared.

Divide meters by seconds for each runner. The unit rates can be compared, because every one is for exactly 1 second.

Rocket fell for a trap. A longer run is not a faster run, and a shorter time is not a faster run either.

Only the unit rate tells you about speed. Once you have it, the ranking is just putting four numbers in order.

RunnerMetersSecondsMeters per second
Rocket4085
Raven3056
Helper 15687
Helper 23694
A double number line for Helper 1, meters over seconds: 7 over 1, 14 over 2, 21 over 3, 28 over 4

The double number line shows Helper 1's rate. Every second adds 7 meters, so 8 seconds reach 56 meters.

UNIT RATES FROM THE LOG
  • Read the question.
  • Tap your answer.
Helper 1 ran 56 meters in 8 seconds. How many meters per second?
Helper 2 ran 36 meters in 9 seconds. How many meters per second?
Who was the slowest runner in the log?
Who was the fastest runner in the log?
RUNNERS FROM SLOWEST TO FASTEST
  • ?Helper 1, 7 meters per second
  • ?Raven, 6 meters per second
  • ?Rocket, 5 meters per second
  • ?Helper 2, 4 meters per second
WHY THIS EXERCISERanking by unit rate is fair even when every runner went a different distance.
PLAN THE RELAY
  • Read the question.
  • Tap your answer.
Raven runs 6 meters per second. How far does she go in 20 seconds?
How many seconds does Raven need for 60 meters at 6 meters per second?
The relay lasted 2 minutes in all. How many seconds is that?
Helper 1 runs 7 meters per second. How many meters in 12 seconds?
Raven's speed in meters per second
Seconds Raven would need for 60 meters at that speed
Meters Helper 2 would run in 3 seconds
How many more meters per second Helper 1 ran than Rocket
Try it
Time yourself reading a page of a book. Count the lines and divide to get lines per minute.
Predict how long 5 pages would take. Then try it and compare.
Draw a bar for each runner showing meters per second. Label the fastest.

Fair ranking. Tomorrow you find rates all around you and review the week.

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