Secondary Mathematics III
Educational Links

Strand: GEOMETRY - Modeling With Geometry (G.MG)

Apply geometric concepts in modeling situations (Standards G.MG.1-3).

Standard G.MG.3

Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).^★

• Access Ramp - Student Task
  This task has students design an access ramp, which complies with the Americans with Disabilities Act (ADA) requirements and include pricing based on local costs.
• Eratosthenes and the circumference of the earth
  This task is designed for the student to apply geometric concepts in modeling situations.
• Fences - student task
  This task has students design a fence that meets the city ordinances and the client's specifications.
• Framing a House - student task
  This task has students recreate house plans on graph paper and then determine how many linear feet of wall plate material will be needed.
• GEOMETRY - Modeling With Geometry (G.MG) - Sec Math III Core Guide
  The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics III - Modeling with Geometry (G.MG).
• Ice Cream Cone
  This rich task is an excellent example of geometric concepts in a modeling situation and is accessible to all students. In this task, students will provide a sketch of a paper ice cream cone wrapper, use the sketch to develop a formula for the surface area of the wrapper, and estimate the maximum number of wrappers that could be cut from a rectangular piece of paper.
• Image Tool
  Students are able to explore scale by measuring angles in various images in this activity in order to better understand ratio and proportion.
• 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.
• Paper Clip
  This high level task is an example of applying geometric methods to solve design problems and satisfy physical constraints.
• Regular Tessellations of the plane
  This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.
• Running around a track I
  This task uses geometry to find the perimeter of the track.
• Running around a track II
  The goal of this task is to model a familiar object, an Olympic track, using geometric shapes.
• Satellite
  This task is an example of applying geometric methods to solve design problems and satisfy physical constraints.
• Solving Quadratic Equations: Cutting Corners
  This lesson unit is intended to help educators assess how well students are able to solve quadratics in one variable.
• Stairway - Student Task
  This task students to design a stairway for a custom home. They will need to gather information regarding design, safety, and the utility of staircases.
• Storage Shed - student task
  Students are going to build storage sheds as a fund raising project, but before they can start they must determine the best dimensions for the shed, make scale drawings and decide on how much to charge for each shed.

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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.