1. km/h
m/s
mph
Photo by Interiot
Calculating Speed

2. Speed
Speed is a comparison between the distance something has traveled and the amount of time it took.
Distance and time are very different things. So when we compare them using division we get a rate.
Depending on how much you want to integrate teaching about rates, you may want to stop here and review the definition of a rate with your students.

3. Speed Speed is the rate of motion.
Speed tells us how fast something is travelling.

4. Speed To calculate speed, we take a distance and divide it by time.
Because we measure distance and time in different ways, we ALWAYS need units when we calculate speed.
Go around and ask students what some units are that we use to measure distance (feet, miles, inches, meters, kilometers, centimeters) and time (hours, minutes, seconds).
What are some units of d and t?

5. The units tell us that we divided meters by seconds!
Speed
Distance = 6 meters
Time = 3 seconds
6 meters
3 seconds
Speed =
The units tell us that we divided meters by seconds!
Speed = 2 m/s

6. You read this rate by saying, “2 meters per second.”
Speed
Speed = 2 m/s
You read this rate by saying, “2 meters per second.”
2 m/s means that the object is traveling a distance of 2 meters every second.
By dividing, we are just simplifying the fraction so that the denominator is always 1. So we are calculating how far something will travel in a single unit of time. That could be 1 seconds, 1 minute, or 1 hour. That is why it is so important to write the units, so that we know what that unit of time is!

7. The units tell us that we divided km by hours!
Speed
Distance = 10 kilometers
Time = 2 hours
10 kilometers
2 hours
Speed =
The units tell us that we divided km by hours!
Speed = 5 km/h

8. You read this rate by saying, “5 kilometers per hour.”
Speed
Speed = 5 km/h
You read this rate by saying, “5 kilometers per hour.”
5 km/h means that the object is traveling a distance of 5 kilometers every hour.
By dividing, we are just simplifying the fraction so that the denominator is always 1. So we are calculating how far something will travel in a single unit of time. That could be 1 seconds, 1 minute, or 1 hour. That is why it is so important to write the units, so that we know what that unit of time is!

9. Which object is traveling at the fastest rate?
Speed
Which object is traveling at the fastest rate?
3 km/h or
3 km/s
The first object takes an hour to travel 3 kilometers, but the second object only takes a second to travel 3 kilometers. The second object is MUCH faster!
This object is moving 3 km every second! Units provide important information!

10. Right now, we will only be calculating average speed.
If you take a road trip and travel 100 miles in 2 hours, what is your average speed?
50 mi/h
Photo by Nepenthes
But does this mean that you travelled 50 mph the entire trip? What about stoplights or bathroom breaks?

11. Average Speed
If you take a road trip and travel 100 miles in 2 hours, what is your average speed?
50 mi/h
Teacher Note: The exact speed that an object is traveling at any given moment is its INSTANTANEOUS speed. When students get to high school, they will use instantaneous speeds to calculate acceleration, but this is far beyond what you need to worry about in 6th grade. But some of your students may ask what we call the speed at an exact moment out of curiosity.
Photo by Nepenthes
Average speed does NOT tell us the exact speed at every second during a trip. It tells us the speed that was averaged over that time.

12. Speed Formula d s t
Use the formula to derive all three ways of expressing this relationship. d t d s
S =
d = s × t
t =
If you can’t get back the original formula, you made your triangle wrong!

13. Don’t forget your units! Don’t forget your units!
140 km
2 h
S = 70 km/h
Don’t forget your units!
S = d t
S =
4.8 m
3.0 s
S = 1.6 m/s
Don’t forget your units!

14. Challenge Question! Can you find the trick?
8 km
0.5 h
S = 16 km/h
Don’t forget your units!
They asked for the speed in kilometers per hour, but gave you minutes!
30 minutes = ½ hour (or 0.5 hour)