Secondary Mathematics III

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

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

Standard G.MG.1

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

• Eratosthenes and the circumference of the earth
This task is designed for the student to apply geometric concepts in modeling situations.
• 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).
• 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.
• Hexagonal Pattern of Beehives
The goal of this task is to use geometry study the structure of beehives.
• How far is the horizon?
The purpose of this modeling task is to have students use mathematics to answer a question in a real-world context using mathematical tools that should be very familiar to them. The task gets at particular aspects of the modeling process, namely, it requires them to make reasonable assumptions and find information that is not provided in the task statement.
• How many cells are in the human body?
The purpose of this task is for students to apply the concepts of mass, volume, and density in a real-world context.
• How many leaves on a tree?
This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.
• How many leaves on a tree? (Version 2)
Teachers who use this version of the task will need to bring tree leaves (or prepare a good sketch of a tree leaf) to class so that they can work on and discuss how to approximate the area of an irregular shape like a leaf.
• How thick is a soda can? Variation I
This task's main goal is to provide a familiar context and a straightforward question which require a variety of tools to solve: modeling a situation with geometry, paying close attention to units, and converting units.
• How thick is a soda can? Variation II
This is a variation of ''How thick is a soda can? Variation I'' which allows students to work independently and think about how they can determine how thick a soda can is.
• 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.
• Solar Eclipse
Total solar eclipses are quite rare, so much so that they make the news when they do occur. This task explores some of the reasons why.
• 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.
• Tennis Balls in a Can
This task is inspired by the derivation of the volume formula for the sphere.
• The Lighthouse Problem
In addition to the purely geometric and trigonometric aspects of the task, this problem asks students to model phenomena on the surface of the earth.
• Tilt of earth's axis and the four seasons
This task gives students a chance to relate their weather experiences with a simple geometric model which explains why the seasons occur.
• Toilet Roll
The purpose of this task is to engage students in geometric modeling, and in particular to deduce algebraic relationships between variables stemming from geometric constraints.
• Use Cavalieris 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.

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.