CCSS.Math.Content.8.G.C

CCSS.Math.Content.8.G.C is a cluster heading. These are the individual standards under it.

• 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.

01

What Students Need to Do

Students identify the solid, choose the matching volume formula, and use radius, height, and pi correctly. They interpret diagrams and word problems, calculate accurately, and report answers in cubic units.

02

What Mastery Looks Like

Students select the correct formula from a diagram or description and substitute the given measurements accurately. They explain their steps, use cubic units, and give exact or rounded answers as requested.

03

Common Misconceptions

Students often use diameter as radius, confuse slant height with vertical height, or forget the one-third factor for cones. They may choose a surface area formula, round too early, or label volume with square units.

04

How to Assess It

Give students a cone with radius 4 cm and height 9 cm. Ask them to write the formula, find the volume in terms of pi, and give a decimal answer with cubic units.

1. 01

   Fill a paper cone with rice, pour it into a matching cylinder, and count how many cone fills are needed.

2. 02

   Ask students to explain why doubling a cylinder's radius changes its volume more than doubling its height.

3. 03

   Run a formula card sort matching cylinders, cones, and spheres to diagrams, measurements, expressions, and cubic-unit answers.

4. 04

   Compare two drink containers by measuring their dimensions, calculating each volume, and deciding which holds more.

• 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.6.G.A

  Solve real-world and mathematical problems involving area, surface area, and volume.