Lesson objective: Understand the distinction between additive comparisons and multiplicative comparisons of quantities.

Ratios will be defined as a multiplicative comparison, meaning we use multiplication and division in ratio situations. Students are introduced to ratio language, such as "for every" and the use of fractions to describe comparisons. Ratio concepts are developed through work with a table, which helps students visualize the relationships, both additive and multiplicative, between the quantities.

Students bring prior knowledge of comparing quantities using addition and subtraction from Grade 4** **(4.NBT.A.2). This prior knowledge is extended to comparing quantities using multiplication as students observe similarities and differences between the wording of statements about comparisons. A conceptual challenge students may encounter is shifting their thinking of discussing quantities in terms of "how many more than" and "how many less than" to using multiplicative comparison language, such "times as much", "for each", and "for every."

This work helps students deepen their understanding of operations because students begin to distinguish between additive relationships to multiplicative relationships.

Students engage in Mathematical Practice 3 (construct viable arguments and critique the arguments of others) as they examine claims about relationships between quantities.

**Key vocabulary:**

- quantity
- ratio
- ratio table