MAFS.912.G-GMD.1.2Archived Standard

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Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Geometric Measurement & Dimension
Cluster: Level 3: Strategic Thinking & Complex Reasoning
Cluster: Explain volume formulas and use them to solve problems. (Geometry - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived

Related Courses

This benchmark is part of these courses.
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
1298310: Advanced Topics in Mathematics (formerly 129830A) (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Lesson Plan

Exploring Cavalieri's Principle:

Students will explore Cavalieri's Principle using technology. Students will calculate the volume of oblique solids and determine if Cavalieri's Principle applies.

Students will also perform transformations of a base figure in a 3-dimensional coordinate system to observe the creation of right and oblique solid figures. After these observations, students will create a conjecture about calculating the volume of the oblique solids. Students will use the conjecture to determine situations in which Cavalieri's Principle applies and then calculate the volume of various oblique solids.

Type: Lesson Plan

Problem-Solving Task

Use Cavalieri’s Principle to Compare Aquarium Volumes:

This task presents a context that leads students toward discovery of the formula for calculating the volume of a sphere.

Type: Problem-Solving Task

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Problem-Solving Task

Use Cavalieri’s Principle to Compare Aquarium Volumes:

This task presents a context that leads students toward discovery of the formula for calculating the volume of a sphere.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Task

Use Cavalieri’s Principle to Compare Aquarium Volumes:

This task presents a context that leads students toward discovery of the formula for calculating the volume of a sphere.

Type: Problem-Solving Task