Lesson Objective: Understand that there are multiple ways to maintain a given proportional relationship.

Some of these ways include: using multiplication or division to scale quantities up or down, finding a unit rate, or using other multiplicative reasoning strategies.

This lesson helps build conceptual understanding of proportional relationships as they work with quantities that vary together to categorize items ordered from the company Robots, Inc. The concept is developed through work with a table of values.

Students bring prior knowledge of unit rates from Unit 1 of this grade and the connection between multiplication and division developed over grades 3-6. This knowledge helps students as they now come to understand that they can use the multiplicative structure of proportional relationship, specifically the idea as the number of items increases, the total prices increases by a multiple of the unit rate.

This lesson builds on students’ work with ratio tables and calculating unit rate. An employee has recorded some information in a table, but forgot to record whether customers ordered widgets or sprockets. Students may use unit rates to determine which items were ordered, building toward students’ future work with a constant of proportionality.

NOTE: This lesson introduces the idea of comparing quantities by comparing the price of one of each type of item. Students are not expected to learn the procedure for finding unit rate until the next lesson. This lesson establishes the idea of a possible comparison using either multiplication or division, but does not requiring fluency in calculating unit rate.

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they use a variety of strategies to categorize orders into either "widgets" or "sprockets". This supports students as they deepen their understanding that the cost for each order can be derived from the number of items ordered (which varies) and the price of one of each item (which remains constant). Mathematical Practice 2 (Construct viable arguments and critique the arguments of others) also figures prominently in this lesson as students make the case that their strategy works to make the categorization.

Vocabulary:

- proportional relationship
- unit rate