Unit 2, Lesson 3
More about Constant of Proportionality
Grade 7
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There is a proportional relationship between any length measured in centimeters and the same length measured in millimeters.
A ruler. Centimeters on top. Millimeters on bottom. Centimeters, 0 to 5, by 1's. Millimeters, 0 to 50, by 10's. 1 centimeter = 10 millimeters, 2 centimeters = 20 millimeters, 3 centimeters = 30 millimeters, 4 centimeters = 40 millimeters, 5 centimeters = 50 millimeters.
There are two ways of thinking about this proportional relationship.
If the length of something in centimeters is known, its length in millimeters can be calculated.
| length (cm) | length (mm) |
|---|---|
| 9 | |
| 12.5 | |
| 50 | |
| 88.49 |
If the length of something in millimeters is known, its length in centimeters can be calculated.
| length (mm) | length (cm) |
|---|---|
| 70 | |
| 245 | |
| 4 | |
| 699.1 |
Complete each sentence:
On its way from New York to San Diego, a plane flew over Pittsburgh, Saint Louis, Albuquerque, and Phoenix traveling at a constant speed.
Complete the table as you answer the questions. Be prepared to explain your reasoning.
A United States map with 5 segments representing the distance a plane flew. The segments are New York to Pittsburgh, Pittsburgh to Saint Louis, Saint Louis to Albuquerque, Albuquerque to Phoenix and Phoenix to San Diego.
| segment | time | distance | speed |
|---|---|---|---|
| Pittsburgh to Saint Louis | 1 hour | 550 miles | |
| Saint Louis to Albuquerque | 1 hour 42 minutes | ||
| Albuquerque to Phoenix | 330 miles |
What is the distance between Saint Louis and Albuquerque?
How many minutes did it take to fly between Albuquerque and Phoenix?
When something is traveling at a constant speed, there is a proportional relationship between the time it takes and the distance traveled.
The table shows the distance traveled and elapsed time for a bug crawling on a sidewalk.
We can multiply any number in the first column by
Table with 2 columns and 4 rows of data. The columns are: distance traveled (cm) and elapsed time (sec). The table has the ordered pairs (the fraction 3 over 2 comma 1), (1 comma the fraction 2 over 3), (3 comma 2) and (10 comma the fraction 20 over 3). Each pair has an arrow pointing from the value in the first column to the value in the second column. The arrow represents multiplying the first value by the fraction 2 over 3 to calculate the second value.
This table represents the same situation, except the columns are switched.
We can multiply any number in the first column by
Table with 2 columns and 4 rows of data. The columns are: elapsed time (sec) and distance traveled (cm). The table has the ordered pairs (1 comma the fraction 3 over 2), (the fraction 2 over 3 comma 1), (2 comma 3) and (the fraction 20 over 3 comma 10). Each pair has an arrow pointing from the value in the first column to the value in the second column. Times the fraction three over 2 is below the table.
Notice that