Introducing Proportional Relationships with Tables
Student Summary
If the ratios between two corresponding quantities are always equivalent, the relationship between the quantities is called a proportional relationship.
This table shows different amounts of milk and chocolate syrup. The ingredients in each row, when mixed together, would make a different total amount of chocolate milk, but these mixtures would all taste the same.
Notice that each row in the table shows a ratio of tablespoons of chocolate syrup to cups of milk that is equivalent to 4:1.
About the relationship between these quantities, we could say:
| tablespoons of chocolate syrup |
cups of milk |
|---|---|
| 4 | 1 |
| 6 | 121 |
| 8 | 2 |
| 21 | 81 |
| 12 | 3 |
| 1 | 41 |
- The relationship between the amount of chocolate syrup and the amount of milk is proportional.
- The table represents a proportional relationship between the amount of chocolate syrup and amount of milk.
- The amount of milk is proportional to the amount of chocolate syrup.
We could multiply any value in the chocolate syrup column by 41 to get the value in the milk column. We might call 41 a unit rate, because 41 cup of milk is needed for 1 tablespoon of chocolate syrup. We also say that 41 is the constant of proportionality for this relationship. It tells us how many cups of milk we would need to mix with 1 tablespoon of chocolate syrup.
Visual / Anchor Chart
