Lesson objective: Understand that the constant of proportionality is a number that describes how one quantity changes when the other quantity changes by one.

Students bring prior knowledge of using equations to express the relationship between two quantities that change together from 6.EE.9. This prior knowledge is extended to relationships that include fractions and mixed numbers as students formalize the concept of the constant of proportionality. A conceptual challenge students may encounter is interpreting the constant of proportionality in terms of the situation.

The concept is developed through work with a table, which allows students to see the multiplication relationships between proportional quantities.

This work helps students deepen their understanding of equivalence because mixtures with the same multiplication relationship will have the same taste.

Students engage in Mathematical Practice 6 (attend to precision) as they compute and interpret the constant of proportionality and write equations.

**Key vocabulary:**

- constant of proportionality
- equation
- variable

**Special materials needed:**