Unit 5, Lesson 10
How Well Can You Measure?
Accelerated 6
10.1
Warm-up
Perimeter of a Triangle
Measure the perimeter of the triangle to the nearest tenth of a centimeter.
Sign in to view assessments and invite other educators
Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.
Measure the perimeter of the triangle to the nearest tenth of a centimeter.
Your teacher will give you a picture of 9 different squares and will assign your group 3 of these squares to examine more closely.
For each of your assigned squares, measure the length of the diagonal and the perimeter of the square in centimeters. Check your measurements with your group. After you come to an agreement, record your measurements in the table.
| diagonal (cm) |
perimeter (cm) |
|
|---|---|---|
| square A | ||
| square B | ||
| square C | ||
| square D | ||
| square E | ||
| square F | ||
| square G | ||
| square H | ||
| square I |
Plot the diagonal and perimeter values from the table on the coordinate plane.
What do you notice about the points on the graph?
Pause here so your teacher can review your work.
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
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
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
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.
Help us improve by sharing suggestions or reporting issues.