Goal: Think like a mathematician! Identify quantities and relationships in problem situations.
An ice cream costs $3.29, including tax, and a soda costs $1.24 less, also including tax. [How much do an ice cream and a soda cost together?]
Source: Kelemanik, Lucenta, Janssen Creighton, Routines for Reasoning Fostering the Mathematical Practice in All Students, Portsmouth, NH: Heinemann, 2016
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I conducted this task with a class of fifth graders as the first task for the Capturing Quantities routine. Fifth grade teachers have expressed frustration with kids jumping right to solving the problem, so I left the question off initially so that we could really focus on quantities and relationships. I started with this task because I thought the math would be easily accessible and we could focus on the structure of the routine. I was mostly right about that, though surprisingly we took several minutes to talk about the tax. Some students were convinced that it was critical information to have. Through a great discussion via student’s diagrams, students were able to come to consensus that because both prices included tax, that it didn’t matter what the tax was. I anticipated that may come up but had convinced myself that they would automatically see that the amount of tax was not an important quantity. The fact that it was included in both prices did turn out to be a relevant relationship to our discussion! I asked students to suggest questions that could be answered with this information, then revealed the actual question and had them complete the problem. It was a great introduction to the routine!