← Back to course
Ratios and Data 6-8 / Week 02 / Monday
1/6
Week 02 · Rates and Speed

Monday

What a rate is
// A ratio with two different units
⏱ about 20 min

Monday: What a Rate Is

Rocket bursts through the back door, out of breath. "Forty meters in 8 seconds. I am the fastest on the street."

Raven looks up from the Numbers Desk. "I ran 30 meters in 5 seconds this morning."

"Forty is more than thirty," Rocket says. "So I win."

"What do you notice about the seconds?" Raven asks. Rocket pauses. "Yours are fewer. But you also ran less."

Nova hovers over the notebook, her light tracing the two lines. "Two numbers each. Hard to compare. What if each run lasted exactly 1 second?"

Rocket grabs a pencil. "Forty divided by eight is 5. Thirty divided by five is 6." He stares.

"Six is more than five," Raven says, and smiles.

Rocket, Raven and Nova on the back path with a tape measure and a timer. Raven writes times in her notebook at the Numbers Desk.

A ratio with two different units

Last week a ratio compared two amounts of the same kind, like spoons of blue to spoons of yellow.

A rate is a ratio of two quantities with different units. Rocket's run is 40 meters to 8 seconds.

A unit rate tells the amount for exactly 1 of the second unit. Divide: 40 ÷ 8 = 5 meters per second.

Per means for each one. Speed is a rate that compares distance to time, so 5 meters per second is a speed.

A double number line, meters over seconds: 0 over 0, 5 over 1, 10 over 2, 15 over 3, 20 over 4

Worked example: compare two runs

Raven ran 30 meters in 5 seconds. Her unit rate is 30 ÷ 5 = 6 meters per second.

Rocket ran 40 meters in 8 seconds. His unit rate is 40 ÷ 8 = 5 meters per second.

Unit rates make the comparison fair. In 1 second, Raven covers 1 meter more than Rocket.

The word per is the signal. Meters per second, pages per minute and steps per minute are all unit rates.

A unit rate also predicts. At 6 meters per second, Raven covers 6 × 10 = 60 meters in 10 seconds.

FIND THE UNIT RATE
  • Read the question.
  • Tap your answer.
40 meters in 8 seconds. How many meters per second?
30 meters in 5 seconds. How many meters per second?
24 pages in 6 minutes. How many pages per minute?
300 steps in 3 minutes. How many steps per minute?
WHO COVERS MORE IN 1 SECOND?
  • Read the question.
  • Tap your answer.
Rocket ran 40 meters in 8 seconds. Raven ran 30 meters in 5 seconds. Who was faster?
A snail model moves 12 centimeters in 6 seconds. A toy car moves 15 centimeters in 3 seconds. Which is faster?
Which of these is a rate?
Number sentenceTrue or false?
40 ÷ 8 = 5?
30 ÷ 5 = 6?
24 ÷ 6 = 3?
300 ÷ 3 = 100?
WHY THIS EXERCISEA unit rate is one division, and a wrong division gives an unfair comparison.
Rocket runs 40 meters in 8 seconds. How many meters is that per second? Type the number.
WHY THIS EXERCISEA unit rate is the one number that lets you compare any two runs.
Try it
Set a timer for 1 minute and walk around a room, counting your steps.
Your count is a unit rate: steps per minute. Write it in your Numbers Notebook.
Predict your steps for 3 minutes. Then test it if you have time.
Safety first
Walk, do not run, indoors. Clear the floor first so nothing trips you.
Stop if you feel out of breath. This is counting, not a contest.
Draw a double number line for Raven's run, meters over seconds, from 0 to 5 seconds.

Fair comparison. Tomorrow you learn the method for unit rates, double number lines and changing units.