In this lesson, students examine situations that involve ratios. They identify features that can be described with equivalent ratios. There are opportunities to review work from grade 6 in representing ratios with tables and diagrams. This is intended to support initial, informal conversations about the key ideas in proportional relationships before those ideas are formally introduced.

The tasks are intentionally not well-posed, that is, they do not have exact solutions. They are designed to prompt students to think about how we can use mathematical models to make sense of common perceptual experiences, such as things that taste or look the same or different (MP4). The focus is on examination of a feature that can be represented as a unit rate.

In the first activity, students are given the relevant measurements needed to compare the situations. In the second activity, they are asked to think about how to quantify what they see, in particular, what measurements might help describe the picture. The work of describing observations qualitatively and quantitatively encourages students to communicate with precision (MP6).

Math Community
Today’s math community building time has two goals. The first is for students to make a personal connection to the math actions chart and to share on their Cool-down the math action that is most important to them. The second is to introduce the idea that the math actions that students have identified will be used to create norms for their mathematical community in upcoming lessons.