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APPENDIX C. RATIONALES FOR THE SELECTION OF THE COMMON CORE 114 formulas was important, as demonstrated in their selection of 5.MD.3 through 5.MD.5. Both address an understanding of volume and applications using volume formulas for right rectangular prisms. Continuing with that line of reasoning, G.GMD.3 was selected (Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems) in lieu of 8.G.9 (Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems). The high school standard subsumes 8.G.9, as it requires understanding and using volume formulas for pyramids in addition to cones, cylinders, and spheres, whereas 8.G.9 implies only memorization of the mathematical formulas. Several standards requiring transformations (translations, reflections, rotations, dilations) were also selected, with a focus on important concepts of congruence and similarity (8.G.2 and 8.G.4). However, 8.G.1 (requiring transformation experimentation) and 8.G.3 (requiring that students describe the effect of transformations) were not considered central enough to the concepts of congruence and similarity. Rather than requiring formal proof (e.g., G.CO.9 through G.CO.11), panelists agreed that more informal reasoning—constructing viable arguments and evaluating the reasoning of others—was more important as a core requirement for adult learners. For this reason, 8.G.5 (Use informal arguments to establish facts about…) and G.SRT.5 (Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures) both were selected. Formal construction also was downplayed in the selected standards, since it takes time and specialized tools, with little pay-off for most adult students. For this reason, neither G.CO.12 (Make formal geometric constructions with a variety of tools and methods…) nor G.CO.13 (Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle) were selected. This content is picked up in more expert training for professional drafters or industrial or architectural engineering. Standards requiring students more informally to “draw” a geometric figure—particularly on a coordinate plane, such as 4.G.1 (Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines…) and 6.G.3 (Draw polygons in the coordinate plane…) were selected. Based on suggestions from the CCSS mathematics writers and the postsecondary faculty survey, G.MG.2 (Apply concepts of density based on area and volume in modeling situations…) was added to the selections in the final round. While panelists did not originally select this standard, they agreed that this concept would provide adult learners with relevant opportunities to apply ratio and proportional reasoning.

APPENDIX C. RATIONALES FOR THE SELECTION OF THE COMMON CORE 115 Rationales for Selecting Data, Statistics and Probability Standards The national trend emphasizing data-driven mathematics in K–12 education is reflected in the selection of nearly all CCSS standards in Measurement and Data (MD) for grades 1 through 5 that are related to the collection, organization, display, and interpretation of data. These complement and progress to the CCSS requirements in Statistics and Probability (SP) for grades 6 through 12. While some MD standards overlap with geometry, there is at least one in each grade level (grades 1–5) relating to the collection, organization, display, and interpretation of data. Panelists selected all of those standards except one (4.MD.4, which is subsumed by the Level C standard 5.MD.2). In the selected CCSS, the number of Statistics and Probability standards gradually increases with the progression from Level A to D, with more than half of all selected data-related standards falling in Level D. Panelists considered some conflicting recommendations from the postsecondary survey and the CCSS writers, such as those received about S.ID.5 (Summarize categorical data for two categories in two-way frequency tables…) and S.ID.9 (Distinguish between correlation and causation). While multiple stakeholders suggested that S.ID.5 be deleted from the selections, describing it as “not essential to understanding needed statistical concepts that follow,” 64 percent of postsecondary survey respondents indicated the content of S.ID.5 was a prerequisite to their course, and the PARCC Frameworks have this as a first priority. In addition, this high school standard shows a progression from concepts in selected standards from grades 7 and 8 that address an understanding of frequency and two-way tables (7.SP.6, 7.SP.7, 7.SP.7b, and 8.SP.4). For these reasons panelists selected this standard. With regard to S.ID.9, while only 3.4 percent of faculty believed that students must be able to distinguish correlation from causation, the CCSS writers believed (and panelists agreed) that this concept was crucially important in our data-driven world.

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