Secondary Mathematics III

Strand: GEOMETRY - Geometric Measurement and Dimension (G.GMD)

Visualize relationships between two-dimensional and three-dimensional objects (Standards G.MD.4).

Standard G.GMD.4

Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

• 2D Representations of 3D Objects
This lesson unit is intended to help educators assess how well students are able to visualize two-dimensional cross-sections of representations of three-dimensional objects.
• Global Positioning System II
Reflective of the modernness of the technology involved, this is a challenging geometric modelling task in which students discover from scratch the geometric principles underlying the software used by GPS systems.
• Introduction to the Materials (Math 3)
Introduction to the Materials in the Mathematics Three of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems.
• Modeling: Rolling Cups
This lesson unit is intended to help educators assess how well students are able to choose appropriate mathematics to solve a non-routine problem, generate useful data by systematically controlling variables, and develop experimental and analytical models of a physical situation.
• Module 5: Modeling with Geometry - Student Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 5, Geometric Modeling, begins with students visualizing two-dimensional cross sections of three-dimensional objects and solids of rotation. They learn to approximate the volume of an irregular solid by decomposing it into cylinders, frustrums, and cones with volumes that can be easily calculated.
• Module 5: Modeling with Geometry - Teacher Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 5, Geometric Modeling, begins with students visualizing two-dimensional cross sections of three-dimensional objects and solids of rotation. They learn to approximate the volume of an irregular solid by decomposing it into cylinders, frustrums, and cones with volumes that can be easily calculated.
• Student Task: Propane Tanks
In this task, students must work out how much you need to change the radius of a propane gas tank in order to double its capacity.
• Tennis Balls in a Can
This task is inspired by the derivation of the volume formula for the sphere.

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.