Common Core Math
High School Geometry Teaching and Learning Resources
Domain: MG: Modeling with Geometry
Select the cluster for resources on this page:
MG-A: Apply geometric concepts in modeling situations
- MG-A.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).
- MG-A.2. Apply concepts of density based on
area and volume in modeling situations (e.g., persons per square
mile, BTUs per cubic foot).
- MG-A.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).
MIT BLOSSOMS: Video lessons with additional teacher
and learner resources. Descriptions are from the video summaries.
Building Cryptosystems: "This video module presents an
introduction to cryptography – the method of sending messages in
such a way that only the intended recipients can understand
them. In this very interactive lesson, students will build three
different devices for cryptography and will learn how to encrypt
and decrytp messages." Aligns with MG-A.3.
Engineering Innovation and Entrepreneurship: "This video
lesson introduces students to the worlds of engineering
innovation and entrepreneurship. ... The video will familiarize
students with all the steps in the innovation process: from
conception to launch. By the end of this lesson, students will
be prepared for an optional long-term innovation project."
Aligns with MG-A.3.
Using Geometry to Design Simple Machines: "This video is
meant to be a fun, hands-on session that gets students to think
hard about how machines work. It teaches them the connection
between the geometry that they study and the kinematics that
engineers use -- explaining that kinematics is simply geometry
in motion. In this lesson, geometry will be used in a way that
students are not used to." Aligns with MG-A.3.
National Math and Science Initiative: Lesson:
Using Linear Equations to Define Geometric Solids: Use
this lesson for geometry within a unit on volume applications. Students
write the equations of lines and graph linear equations that define
bounded regions, calculate the areas and perimeters of the regions,
revolve the planar regions about horizontal and vertical lines to create
solids, and calculate the volumes of the resulting solids; they use
technology (virtual manipulatives) to create and revolve planar figures
about horizontal and vertical lines and model the conceptual
understanding using a real world situation. Targeted standards
include GMD-A.3, GMD-B.4, GPE-B.7 and MG-A.1. Common Core Math
Practice standards 1-7 are also addressed.
Geometric Solids: Use this virtual manipulative to "learn about
various geometric solids and their properties. You can manipulate and
color each shape to explore the number of faces, edges, and vertices."
View the solid or its net. You can also use this tool to help determine
the relationship between the number faces, vertices, and edges.
Wolfram Demonstrations Project:
Download the free Wolfram CDF player to interact with the following
- US Common Core State Standard Math HSG-MG.A.1:
57 manipulatives--all are worth viewing. Among those:
Interlocking disks, wooden bucket, throw a hammer, telescopic
tower, ball in a box, collapsible cup, collapsible umbrella,
dome frames made of arches, Jefferson National Expansion
Memorial, deploying and steering a parabolic antenna, modeling a
simple roller coaster, controlling airplane flight, perspective
drawing of billiards table, basic views in technical drawing,
potter's wheel, Hello Block world, motion of planet around a
star, and more.
- US Common Core State Standard Math HSG-MG.A.2:
2 manipulatives: Truck packing (aligns with MG-A.2, MG-A.3) and
US Common Core State Standard Math HSG-MG.A.3:
28 manipulatives. Among those:
Louisiana Department of Education:
Multiple choice and constructed response
Sample Test Items: Geometry (from 2016-2017): Constructed Response
samples: Population Density aligns with MG-A.2;
Soybean Yield aligns with MG-A.3; Wheelchair Ramp aligns with SRT-C.8.
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