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August 30, 2009


, 7Solve real-world and mathematical prelboms by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. So, is the example equation on p. 4, x + 5:50 9:20, appropriate for Grade 6? How should we read these examples? Does x + p literally mean the equation of the sum of a variable and one number? Since equations of the form, px + q = r is a Grade 7 expectation, we know that we are not supposed to combine these two types in Grade 6. But, what about x + p + q = r?Still on p. 4,and still in the same paragraph, I am not sure if I like the rather than language in students find greater benefit in representing the problem algebraically by choosing variables to represent quantities, rather than attempting a direct numerical solution, since the former approach provides general methods and relieves demands on working memory. Aren't they (algebraic representations and numerical strategies) obviously related? I'm not sure if I understand the claim about relieves demands on working memory, either. I don't think students will find it any more difficult to think, well, before he paid $9.20, he had 2.30+9.20, $11.50. And this was after he got $5.50 from grandmother It seems like a benefit of an algebraic equation in a complicated process is that it suggests a numerical strategy to find the solution.Now on to p.5, and this is the last comment/question. The draft says, Students in Grade 5 began to move from viewing expressions as actions describing a calculation to viewing them as objects in their own right. This statement made me wonder what 1.OA.7, Understand the meaning of the equal sign means. In general, I wish the document will more clearly articulate the contrast between what we are expecting from students in Grades K-5 from what we should expects in Grades 6-8. As the draft note, students start using letters for unknowns in Grade 3. So, what are some of the specific differences in their understanding we are expecting? I think the more clearly and specifically the document can articulate the contrast, the more useful it will be for teachers and curriculum developers.

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