CCRStandardsAdultEd

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.