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*NB: This is my third attempt to post this question due to technical hitches. Please forgive if this results in multiple posts.
Bill, I’d like to revisit the discussion we had about products at http://commoncoretools.me/forums/topic/the-meaning-of-product-3-oa-1/
A related standard, 3.MD.7b asks students to “represent whole-number products as rectangular areas…” In light of the use of product you described previously, I’m not sure whether students are faced with tasks such as “Draw a rectangle to match dimensions of 3 x 4” or ones such as “Draw a rectangle that has an area of 12 sq units” or both.
The relevant progressions doc on page 17 states that “Students might then solve numerous problems…[such as] designing a house with rooms that fit specific area criteria” and also “finding all the rectangular regions with whole-number side lengths that have an area of 12 area-units”. In both cases, the students start with a figure such as 12 sq meters, and then they have to identify the two dimensions of a rectangle that matches.
On the other hand, factor pairs are not addressed until Grade 4 (4.OA.4) and the example provided in 4.MD.3 of the Standards is that students “find the width of a rectangular room given the area of the flooring and the length”. Giving one of the dimensions in this example seems like an easier problem than the one suggested for Grade 3 where students have to identify both dimensions.
So, two questions arise:
– Are Grade 3 students expected to both draw a rectangle given dimensions and also calculate the dimensions of a rectangle given the area?
– If students are to find factor pairs in Grade 3 does the difference between Grade 3 and 4 largely rest on pictorial vs symbolic calculation?
An astute question as usual, Duane. I have time for a brief answer, which is that the activities for Grade 3 described in the progressions document (finding possible dimensions given the area) seem less systematic than the Grade 4 standard requiring systematic listing of all the factor pairs. Granted, the document mentions “finding all the rectangular regions with whole-number side lengths that have an area of 12 area-units,” but this seems more of a classroom activity that is paving the way for Grade 4, rather than a direct substituted for the Grade 4 standard. The answer to your first question is “yes.” The answer to the second question is “close, but not quite.” I would say the distinction is between exploratory and systematic work, rather than between pictorial and symbolic work, although there is obviously some parallel between the two dichotomies.
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