In previous grades, students learned how to represent additive comparison situations, with discrete diagrams, tape diagrams, and addition and subtraction equations that use symbols to represent an unknown quantity. They used these representations to find differences.

In this lesson, students interpret the language of “times as many” in multiplicative comparison situations, and connect this language to representations. They learn to recognize the difference between " times as many" and " more." As they create representations, using discrete diagrams in which each piece represents one item, students have opportunities to examine any errors in the representations they create and make necessary revisions. Although students may write equations to represent multiplicative comparisons, it is not required here, as they will have an opportunity to explore equations in depth in future lessons.

In this lesson, students had access to connecting cubes to represent “twice as many” and “times as many.” How did students use the cubes to reason about or explain multiplicative comparison? If students did not use the cubes, how did they explain their reasoning?