In this lesson, students convert units of measurement by reasoning about ratios. The goal is to see that when a quantity is measured in two different units, the pairs of measurements form equivalent ratios. Students also begin to think about “rates per 1” in this context and consider how these can help with unit conversion. The reasoning here serves as a transition for understanding unit rates more broadly in future lessons.

In earlier grades, conversion work was limited to units in the same system of measurement. Here, students convert units that may be in different systems. In one activity, the context of comparing speeds (in miles per hour and kilometers per hour) motivates the conversion between miles and kilometers. In another activity, students convert between kilograms and pounds.

The last activity is optional. It offers a chance to convert between units of volume—cups and tablespoons—in a cooking context.

In solving problems, students may use double number line diagrams, tables, or no particular representations. They may relate the units in terms of multiplication and division, for instance. Although students can opt for any strategy that makes sense to them, they should have opportunities to see pairs of measurements represented in different ways and to make connections. This would reinforce the idea of equivalent ratios and prompt students to look for and make use of structure (MP7).