In this lesson, students build on their work with tables and represent proportional relationships using equations of the form \(y = kx\). The activities revisit contexts from the previous two lessons, presenting values in tables and focusing on the idea that for each table, there is a number \(k\) so that all values in the table satisfy the equation \(y = kx\). By expressing the regularity of repeated calculations of values in the table with the equations, students are engaging in MP8.
- 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.
- I can write an equation of the form $y=kx$ to represent a proportional relationship described by a table or a story.
- I can write the constant of proportionality as an entry in a table.
constant of proportionality
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, because \(2 \boldcdot 3 = 6\), \(3 \boldcdot 3 = 9\), and \(5 \boldcdot 3 = 15\). This means that there are 3 apples for every 1 orange in the fruit salad.
number of oranges number of apples 2 6 3 9 5 15
Print Formatted Materials
Teachers with a valid work email address can click here to register or sign in for free access to Cool Down, Teacher Guide, and PowerPoint materials.
|Student Task Statements||docx|
|Cumulative Practice Problem Set||docx|
|Cool Down||(log in)'|
|Teacher Guide||(log in)'|
|Teacher Presentation Materials||docx|
|Google Slides||(log in)'|
|PowerPoint Slides||(log in)'|