Task# Same and Different

Illustrative MathematicsVaries

The purpose of this task is to analyze some very common contexts that can be represented by ratios and to motivate the idea of equivalent ratios for different kinds of contexts. It can also be used to introduce students to double number line diagrams. If that is the case, we suggest providing students with an example of one along with the task statement for part (a): The first set of questions connects the idea of constant speed with the idea of a ratio. Students should see that when you have equivalent ratios involving time and distance where the objects are each moving at a constant speed, that implies the objects are moving at the same constant speed.