# Lesson 7

Comparing Relationships with Tables

### Lesson Narrative

In the next two lessons students compare proportional and non-proportional relationships. In this lesson, students examine tables and explain whether the relationships represented are proportional, not proportional, or possibly proportional. At this point in the unit, students should be comfortable using the terms “proportional relationship,” "is proportional to," and “constant of proportionality.” By the end of the next lesson, students should understand that equations of the form $$y = k x$$ with $$k > 0$$ characterize proportional relationships.

As students look at data from a context and reason about whether it makes sense quantitatively for the data to represent a proportional relationship, they are engaging in making viable arguments (MP3).

### Learning Goals

Teacher Facing

• Calculate and compare the quotients of the values in each row of a given table.
• Generate a different recipe for lemonade and describe (orally) how it would taste in comparison to a given recipe.
• Justify (orally) whether the values in a given table could or could not represent a proportional relationship.

### Student Facing

Let’s explore how proportional relationships are different from other relationships.

### Required Preparation

Calculators can optionally be made available to take the focus off computation.

### Student Facing

• I can decide if a relationship represented by a table could be proportional and when it is definitely not proportional.

Building On