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This task is a great task to use as a wrap up of the Ratios and Proportion skills taught in the seventh grade math standards. I have used this as a small group task in my classroom after I have covered Rates, Unit Rates, Proportional Relationships, Constant of Proportionality, Constant Rate of Change, etc.
This task highlights student understanding of what proportional and non-proportional relationships are and the differences. It also does a great job of showing if students understand the connection between Unit Rate, Constant of Proportionality, and Constant Rate of Change. You are also able to identify their deep understanding of the relationship of using the Constant of Proportionality in a linear relationship in the y=kx format, where k is the Constant of Proportionality.
I do not give any instruction to this task. I just give them a overview and read the initial introduction of the task and what they need to accomplish. Then as they work, I circulate to the groups questioning rather than answering.
After groups have finished the task, (30 minutes) We go through it together and they explain their thinking and why they did what they did and how they arrived at their answer. I then have the other groups ask clarifying questions beginning with "I wonder.." of "I noticed....." This then allows their peers critique the reasoning of others and justify their thinking.

Material Type:
Learning Task

Author:
Illustrative Mathematics