14.1: Which is the Bluest?
- Which group of blocks is the bluest?
- Order the groups of blocks from least blue to bluest.
Let’s contrast relationships that are and are not proportional in four different ways.
Select two things from different lists. Make up a situation where there is a proportional relationship between quantities that involve these things.
creatures
length
time
volume
body parts
area
weight
substance
Your teacher will give you two copies of the “One Scenario, Four Representations” sheet. For each of your situations, describe the relationships in detail. If you get stuck, consider asking your teacher for a copy of the sample response.
The constant of proportionality for a proportional relationship can often be easily identified in a graph, a table, and an equation that represents it. Here is an example of all three representations for the same relationship. The constant of proportionality is circled:
On the other hand, some relationships are not proportional. If the graph of a relationship is not a straight line through the origin, if the equation cannot be expressed in the form $y = kx$, or if the table does not have a constant of proportionality that you can multiply by any number in the first column to get the associated number in the second column, then the relationship between the quantities is not a proportional relationship.