Identifying Proportional and Non-Proportional Relationships in Graphs

Author: Great Minds, as featured on EngageNY

  • Description
  • Files

What we like about this lesson


  • Addresses standard 7.RP.A.2a
  • Requires students to make connections between the different representations of a situation, and requires students to create tables from ratios in various formats
  • Requires students to use multiple methods and reasoning to determine whether a relationship is proportional; provides examples and non-examples
  • Allows students to draw conclusions based on mathematical evidence

In the classroom:

  • Offers an engaging exploration that connects students' procedural skill and conceptual understanding to real-live situations
  • Gives students the opportunity to work collaboratively in groups
  • Provides students with an opportunity to critique each other's work
  • Gives formal and informal opportunities for teachers to check for understanding
  • Includes a problem set that can be used for homework or for additional practice, as well as an exit ticket that summarizes the mathematics of the lesson

  • Making the Shifts

    How does this lesson exemplify the instructional Shifts required by CCSSM?

    Focus Belongs to the major work of seventh grade
    Coherence Builds on key understandings of ratios, rates, and unit rates (6.RP.A), and prior understanding of proportional relationships in grade 7

    This lesson touches on all three aspects of rigor: conceptual understanding, procedural skill and fluency, and application.

  • Additional Thoughts

    It’s important to note that this sample lesson is the last of a 6-lesson series on "Proportional Relationships", which is part of a 22-lesson unit on Ratios and Proportional Relationships. This sample lesson lays a strong foundation for the work that is to come in the unit, but it is not intended for students to meet the full expectations of the standards through only this lesson. In subsequent lessons, students explore ratios and rates involving fractions, as well as ratios of scale drawings.

    In this particular lesson, students work in groups to demonstrate their understanding of proportional relationships. The “art gallery” provides an opportunity for students to showcase their work and thinking, as well as to reflect on each other’s representations and reasoning. This lesson could be strengthened by concluding the lesson with questions that ask students to discuss and compare various strategies for determining the proportionality of relationships and having them make connections between the different representations of the situations.

    This activity has students think about the structure of the situations to determine whether a proportional relationship exists, as opposed to using the traditional method of “cross-multiplying” for solving proportions ($a$/$b$ = $c$/$d$). For more insight on the grade-level concepts addressed in this lesson, read page 8 of the progression document, Grade 6–7, Ratios and Proportional Relationships.

    The structure of these lessons and the unit overall have some interesting aspects to highlight. Each unit is divided into topics (a set of lessons) that are connected to prior learning and also point to the lesson that follows in the learning progression. Within individual lessons, there are a number of components that add to their strength including variety in questioning techniques and frequent opportunities for students to debrief about their learning. Through the series of lessons, students have the opportunity to engage in all three aspects of rigor.

Supplemental Resources