Unit 5, Lesson 1
Proportional Relationships and Equations
Accelerated 6
Preparation
Lesson Narrative
In this lesson, students represent proportional relationships using equations of the form . They examine tables of equivalent ratios and see that the relationship in each table can be represented by an equation of the form , where is the constant of proportionality that relates the two quantities. As students calculate values in the tables and write equations relating the quantities, they practice looking for and expressing regularity in repeated reasoning (MP8).
The last activity is optional because it provides an opportunity for additional practice using a different context.
The activities in this lesson say that the contexts were seen in earlier lessons. Those lessons are not included in this course, so these instructions do not apply. Use some time in the Launch of each activity to familiarize students with the contexts, as needed.
- Generalize a process for finding missing values in a proportional relationship, and justify (orally) why this can be abstracted as $y=kx$, where $k$ is the constant of proportionality.
- Generate an equation of the form $y=kx$ to represent a proportional relationship in a familiar context.
- Write the constant of proportionality to complete a row in the table of a proportional relationship where the value for the first quantity is 1.
Let’s write equations describing proportional relationships.
Required Preparation
None
In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity. This number is called the constant of proportionality.
In this example, the constant of proportionality is 3.
In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity.
This table shows a proportional relationship between and . Each value of is 4 times a value of . This relationship can be written as .
| 2 | 8 |
| 3 | 12 |
| 5 | 20 |
| 10 | 40 |