Unit 5, Lesson 10
How Well Can You Measure?
Accelerated 6
10.1
Warm-up
Measure the perimeter of the triangle to the nearest tenth of a centimeter.
Student Lesson Summary
When we measure the values for two related quantities, plotting the measurements in the coordinate plane can help us decide if it makes sense to model them with a proportional relationship. If the points are close to a line through , then a proportional relationship is a good model.
This graph shows the height of the stack for different numbers of stacked coins.
Graph of 7 plotted points, origin O, with grid. Horizontal axis, number of coins, scale 0 to 30, by 5’s. Vertical axis, height of stack in centimeters, scale 0 to 5, by 1’s. Points plotted at 0 comma 0, 5 comma 0.8, 10 comma 1.5, 15 comma 2.5, 20 comma 3.4, 25 comma 4.2, 30 comma 4.9.
These points are close to a straight line through , so the relationship may be proportional.
This graph shows the time it takes for a tennis ball to fall from different starting heights.
Graph of 7 plotted points, origin O, with grid. Horizontal axis, starting height in yards, scale 0 to 7, by 1’s. Vertical axis, fall time in seconds, scale 0 to 1.1, by 0.1’s. Points plotted at 0 comma 0, 1 comma 0.4, 2 comma 0.6, 3 comma 0.75, 4 comma 0.88, 5 comma 0.98, 6 comma 1.05.
These points are not close to a straight line through , so the relationship is not proportional.
Another way to investigate whether or not a relationship is proportional is by making a table and dividing the values on each row. Here are tables that represent the same relationships as the previous graphs.
| number of coins |
height in centimeters |
centimeters per coin |
|---|---|---|
| 5 | 0.8 | 0.16 |
| 10 | 1.5 | 0.15 |
| 15 | 2.5 | 0.167 |
| 20 | 3.4 | 0.17 |
| 25 | 4.2 | 0.168 |
| 30 | 4.9 | 0.163 |
The centimeters of height per coin are close to the same value, so this relationship appears to be proportional.
| starting height (yards) |
fall time (seconds) |
seconds per yard |
|---|---|---|
| 1 | 0.40 | 0.40 |
| 2 | 0.60 | 0.30 |
| 3 | 0.75 | 0.25 |
| 4 | 0.88 | 0.22 |
| 5 | 0.98 | 0.196 |
| 6 | 1.05 | 0.175 |
The seconds of fall time per yard of starting height are not close to the same value, so this relationship is not proportional.
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