CCSS.Math.Content.HSG-GMD.A
The standard
Explain volume formulas and use them to solve problems
Common Core State Standards for Mathematics · High School — Geometry
What this standard means
Students need to connect volume formulas to the shapes they describe, not just plug in numbers. They should explain why a prism, cylinder, pyramid, cone, or sphere formula makes sense using layers, cross-sections, or comparisons between solids.
Mastery means students choose the right formula, identify the needed measurements, keep units straight, and explain their reasoning. Common sticking points are confusing radius and diameter, mixing area and volume, forgetting the one-third factor, and treating formulas as unrelated facts.
Ways to teach it
- Build a prism and a matching pyramid with rice or water, then compare how many pyramid fills make one prism fill.
- Prompt students: Explain why a cone’s volume is not the same as a cylinder’s volume with the same base and height.
- Give three solids with extra measurements and ask students to circle only the needed values before calculating volume.
- Use a shipping box, soup can, and party hat to estimate packaging volume and compare which holds the most.
Plan a lesson for CCSS.Math.Content.HSG-GMD.A
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Related standards
- CCSS.Math.Content.8.G.C
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
- CCSS.Math.Content.5.MD.C.5
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
- CCSS.Math.Content.HSG-GMD.A.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
- CCSS.Math.Content.8.G.C.9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.