Essential Questions: What is the relationship between the volumes of cylinders, cones, and spheres? What is the difference between volume and surface area of cylinders, cones, and spheres? If congruent or similar plane figures are stacked, what kinds of solids are formed? How do geometric models describe spatial relationships among the dimensions for cylinders, cones, and spheres? How can volume formulas for cylinders, cones, and spheres be used to solve authentic problems in life? Lesson Plans and Seeds Lesson Plan C.9: Volume of Cylinders, Cones, and Spheres Lesson Seed C.9: Volume Download Seeds, Plans, and Resources (zip) Unit Overview Content Emphasis By Clusters in Grade 8 Progressions from Common Core State Standards in Mathematics Send Feedback to MSDE’s Mathematics Team
Lesson Plan C.9: Volume of Cylinders, Cones, and Spheres
Lesson Seed C.9: Volume
Unit Overview
Content Emphasis By Clusters in Grade 8
Progressions from Common Core State Standards in Mathematics
Send Feedback to MSDE’s Mathematics Team
Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.
Lesson Plan: 8.G.C. 9 Volume of Cylinders, Cones and Spheres
Unit/Cluster: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Lesson Topic: Calculate the volume of cylinders, cones, and spheres in real-world situations.
Focus Standard(s)
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.
It is critical that the Standards for Mathematical Practices are incorporated in ALL lesson activities throughout the unit as appropriate. It is not the expectation that all eight Mathematical Practices will be evident in every lesson. The Standards for Mathematical Practices make an excellent framework on which to plan your instruction. Look for the infusion of the Mathematical Practices throughout this unit.
Coherence of Standards Across-Grade Coherence: Content Knowledge from Earlier Grades
7.G.B.4: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Within-Grade Coherence: Content from Other Standards in the Same Grade that Provide Reinforcement
8.NS.A.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
RIGOR
Procedural Skill Students will be using addition, multiplication, squaring and cubing rational numbers as they find the area of cylinders, cones and spheres.
Conceptual Understanding Students will be using a method that will help them understand the meaning of volume for a cylinder, cone and sphere.
Modeling/Application Students will be using models of cones, cylinders and spheres to find the formulas their area.
Enduring Understandings:
Student Outcomes
Method for Determining Student Readiness for the Lesson Given two different sized circles with the center labeled the students should find the radius of the first and then find the diameter of the second. After finding those they should find the area of each circle with the appropriate unit designation. The students discuss the difference between a radius, diameter, circumference, and the area.
Learning Experience
