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What does “structure” mean in this practice? When I read the details, I see examples of discerning patterns, but the only one that I think might be related to structure is “drawing an auxiliary line.” Are there other examples of using structure?
In addition to geometric structure, there is algebraic structure. For example, seeing $x^4 – y^4$ as a difference of two squares, and therefore being able to factor it as $(x^2 – y^2)(x^2+y^2)$ (this is from A-SSE.2). There are some examples of this on the Illustrative Mathematics website. You can go to the new list of illustrations and search for A-SSE and look in the right column for ones aligned to A-SSE.A.2 (not we are using the new notation which includes an A for the first cluster heading in this domain).
In the Progressions, instances of standards for practice are indicated by “MP.” Here are some examples of MP7.
From the Ratio and Proportional Relationships Progression draft:
“For each,” “for every,” “per,” and similar terms distinguish situations in which two quantities have a proportional relationship from other types of situations. For example, without further information “2 pounds for a dollar” is ambiguous. It may be that pounds and dollars are proportionally related and every two pounds costs a dollar. Or it may be that there is a discount on bulk, so weight and cost do not have a proportional relationship. Thus, recognizing ratios, rates, and proportional relationships involves looking for structure (MP7).
From the high school Statistics and Probability Progression draft:
As with univariate data analysis, students now take a deeper look at bivariate data, using their knowledge of proportions to describe categorical associations and using their knowledge of functions to fit models to quantitative data (MP7, MP4).
From the Geometric Measurement Progression draft:
For example, in later grades, understanding area requires seeing how to decompose shapes into parts and how to move and recombine the parts to make simpler shapes whose areas are already known (MP7).
From the Operations and Algebraic Thinking Progression draft:
MP7 Making use of structure to make computation easier:
13 + 29 + 77 + 11 = (13 + 77) + (29 + 11)
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