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• #### Credits 165-166

in all the schools in the town or city, or even all the schools in the state. This would involve the use of almanacs or atlases to find out the appropriate numbers to use, depending on the question. Similarly, students might explore how the number of buttons that people wear varies from one section of the country to another. Thus, the students would want to communicate with at least one other school of the same size in some other region and compare data.

#### Protorubric

Characteristics of the high response:

The response appropriately takes into consideration the following aspects of the problem: (a) the data collected from the day before; (b) some estimate of the number of children per classroom; (c) the number of classes in the school; (d) variation of buttons among children of various ages; and (e) adults' buttons (which the pair may choose to disregard entirely).

Reasonable justifications are given for how each numerical value was chosen or calculated.

The numerical values are put together with appropriate arithmetic processes. (For example, if the students decided there were an average of 90 buttons in each of the 12 upper grade classrooms and an average of 60 buttons in each of the 8 lower grade classrooms, they would calculate with these values so that their result would be (90 × 12) + (60 × 8), not in some invalid way, such as adding 90 and 60, then multiplying by the total number of classrooms.)

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