8.6

Math8th Grade

Knowledge and Skills Statement (Standard Cluster)

The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas

Texas Essential Knowledge and Skills for Mathematics

Cluster contents

8.6 is a knowledge and skills statement. These are the student expectations under it.

Teacher's field guide

What Students Need to Do: Students explain cylinder volume as base area multiplied by height. They model why a cone with the same base and height has one-third the cylinder's volume. They use diagrams to explain the Pythagorean theorem for right triangles.
What Mastery Looks Like: Students explain that a cylinder is made of layers of base area B stacked through height h. They show that three matching cones fill one cylinder. They use squares on a right triangle to explain why the leg areas add to the hypotenuse area.
Common Misconceptions: Students may treat B as the radius or circumference instead of the area of the base. They may think a cone has half the volume of its matching cylinder. They may use a² + b² = c² on nonright triangles or write a + b = c.
How to Assess It: Give a cylinder with radius 3 and height 8, plus a cone with the same base and height. Ask students to find both volumes, explain B, and draw a 6-8-10 right triangle with square areas labeled.

Lesson moves

Fill a cone with rice three times and pour it into a cylinder with the same base and height.
Ask students to write why V = Bh works by describing a cylinder as equal circular layers stacked to height h.
Run a card sort matching cylinder, cone, and right triangle diagrams with formulas, dimensions, and calculated values.
Calculate and compare the capacities of a cylindrical grain bin and a cone-shaped hopper with the same base and height.

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