This review quiz/activity starts with a quick warm up. It is good to think about units and rates before diving into harder problems. The task asks, “A full gallon is 128 ounces, how many 8 ounce cups are there in a half gallon?”
This quick refresher on converting units helps prime students for the next two tasks. Unit conversions will help them model the number of ounces left and then the number of cups left per day.
Students experience how the modeling of the milk differs based on if the unit is ounces or cups. Then, the students are asked to evaluate the reasoning of two hypothetical students, Daria and Amir. Each are modeling the situation correctly but using different units. After doing the task, your student’s responses might look something like this,
This task promotes productive conversations among your students. Ask your students students who answered A or B to elaborate on their good ideas of how to model the situation. It is important to assign competence to students who had some productive thinking. This will help them see they are on track, even if they didn’t recognize both of the correct answers. Hopefully, through a productive conversation, students will come to understand that both Amir and Daria are correct. They are just using different units to model the situation. We recommend you start this discussion with the “reveal answer” button deselected.
The final task is for the students to convert the recursive formulas into explicit ones.