Virginia SOL 8.MG.2
SOL Standard (Knowledge and Skills Cluster)
The student will investigate and determine the surface area of square-based pyramids and the volume of cones and square-based pyramids.
Virginia Standards of Learning for Mathematics
Cluster contents
Knowledge and Skills in This Standard
8.MG.2 is a Standards of Learning standard. These are the knowledge and skills expectations under it.
- 8.MG.2.a
Determine the surface area of square-based pyramids by using concrete objects, nets, diagrams, and formulas.
- 8.MG.2.b
Determine the volume of cones and square-based pyramids, using concrete objects, diagrams, and formulas.
- 8.MG.2.c
Examine and explain the relationship between the volume of cones and cylinders, and the volume of rectangular prisms and square based pyramids.
- 8.MG.2.d
Solve problems in context involving volume of cones and square-based pyramids and the surface area of square-based pyramids.
Teacher's field guide
What This Cluster Means
What Students Need to Do
- Students find the surface area of square-based pyramids from models, nets, diagrams, and formulas. They find cone and pyramid volumes and explain the one-third relationship to cylinders and prisms. They apply these calculations in context.
What Mastery Looks Like
- Students select the needed dimensions and use slant height, vertical height, and base measurements correctly. They calculate accurately, include proper units, and explain why each volume is one-third of a related prism or cylinder.
Common Misconceptions
- Students often use vertical height instead of slant height when finding triangular face areas. They may omit the one-third factor for volume, add only some faces, or use square units for volume.
How to Assess It
- Give students a labeled square-based pyramid and cone. Ask them to find the pyramid’s surface area, both volumes, and explain where the one-third factor comes from.
Lesson moves
Ways to Teach It
Build a square pyramid from a net, label every dimension, and calculate the base area and four triangular face areas.
Write an explanation of why a cone holds one-third as much as a cylinder with the same base and height.
Run a card sort matching pyramid and cone diagrams with formulas, calculations, units, and completed answers.
Calculate roofing material for a square pyramid roof and the capacity of a cone-shaped paper cup using provided dimensions.
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Printable 8.MG.2 Worksheet
A ready-to-print activity worksheet aligned to 8.MG.2, with an answer key for the teacher on its own page. No account needed.
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