options: Recognize and represent proportional relationships between quantities.

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
problem_activity: In science class, you measure the mass and volume of different pieces of aluminum. You determine that there is a proportional relationship between mass and volume. The data on four samples of aluminum is shown in the table.
| **           Volume (cm                       $$^3$$                      )          ** | **           Mass (g)          ** |
|-----------------------------------------------------------------------------------------|-----------------------------------|
|                                            4                                            |               10.8                |
|                                            7                                            |               18.9                |
|                                           12                                            |               32.4                |
|                                           18                                            |               48.6                |
After you put your scale away, you realize that you forgot to find the mass of one more piece of aluminum. The volume of the piece of aluminum is 10 cm
$${^3}$$
. Can you determine the mass without taking your scale back out?


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