CCSS.Math.Content.8.G.C
The standard
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Common Core State Standards for Mathematics
What this standard means
Students need to choose the right formula, identify the radius, diameter, height, or slant-free information given, and calculate volume with correct units. They should also compare shapes, work backward from a volume, and handle answers in terms of pi or as decimals.
Mastery looks like a student explaining why a formula fits the object, not just plugging in numbers. Common trouble spots are using diameter as radius, mixing up surface area and volume, using cone and sphere formulas incorrectly, and forgetting cubic units.
Ways to teach it
- Give students cans, paper cones, and plastic balls with rulers, then have them measure, calculate, and compare estimated volumes.
- Ask students to write which container holds more, a cylinder or cone with the same radius and height, and justify without calculating.
- Post three problems with one cylinder, one cone, and one sphere, then have students circle needed measurements before solving.
- Have students compare the volume of two drink cups from a cafeteria menu using posted dimensions and decide which is the better buy.
Plan a lesson for CCSS.Math.Content.8.G.C
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Related standards
- CCSS.Math.Content.HSG-GMD.A.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
- CCSS.Math.Content.7.G.B
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
- 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.
- CCSS.Math.Content.6.G.A
Solve real-world and mathematical problems involving area, surface area, and volume.