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.