MAFS.912.G-MG.1.1

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Modeling with Geometry
Cluster: Level 1: Recall
Cluster: Apply geometric concepts in modeling situations. (Geometry - Major 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 1: Recall - More Information
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

  • Assessment Limits :
    Items may require the student to use knowledge of other Geometry
    standards.

    Items may include composite figures.

    Items must not also assess G-GMD.1.3 or G-MG.1.3.

  • Calculator :

    Neutral

  • Clarification :
    Students will use geometric shapes to describe objects found in the
    real world.

    Students will use measures of geometric shapes to find the area,
    volume, surface area, perimeter, or circumference of a shape found
    in the real world.

    Students will apply properties of geometric shapes to solve real-world
    problems. 

  • Stimulus Attributes :
    Items must be set in a real-world context.
  • Response Attributes :
    Items may require the student to use or choose the correct unit of
    measure.

    Items may require the student to apply the basic modeling cycle.

Sample Test Items (1)

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206300: Informal Geometry (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0104410: Figure Drawing (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated))
7912070: Access Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0102340: Arts Collaboration: Designing Solutions for Art, Work, and Life Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1207300: Liberal Arts Mathematics 1 (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.G-MG.1.AP.1a: Describe the relationship between the attributes of a figure and the changes in the area or volume when one attribute is changed.

Related Resources

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

Assessments

Sample 1 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Sample 3 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Formative Assessments

Size It Up:

Students are asked to name geometric solids that could be used to model several objects.

Type: Formative Assessment

Estimating Volume:

Students are asked to model a tree trunk with geometric solids and to use the model to estimate the volume of the tree trunk.

Type: Formative Assessment

Camping Calculations:

Students are asked to find the measure of an angle formed by the support poles of a tent using the properties of geometric shapes.

Type: Formative Assessment

Estimating Area:

Students are asked to select appropriate geometric shapes to model a lake and then use the model to estimate the surface area of the lake.

Type: Formative Assessment

Lesson Plans

NASA Space Shuttle Mission Patches:

Students apply geometric measures and methods, art knowledge, contextual information, and utilize clear and coherent writing to analyze NASA space shuttle mission patches from both a mathematical design and visual arts perspective.

Type: Lesson Plan

Cape Florida Lighthouse: Lore and Calculations:

The historic Cape Florida Lighthouse, often described as a conical tower, teems with mathematical applications. This lesson focuses on the change in volume and lateral surface area throughout its storied existence.

Type: Lesson Plan

Interchangeable Wristwatch Band:

Students use measures and properties of rectangular prisms and cylinders to model and rank 3D printable designs of interchangeable wristwatch bands that satisfy physical constraints.

Type: Lesson Plan

Building Blocks of Geometry:

Students will be introduced to the undefinable concepts of points, lines, and planes that are the building blocks of geometry and recognize that these three terms become the basis for many other geometric definitions. Students will participate in a Building Block Scavenger Hunt, using cameras to photograph examples of specified terms that they find outside of the math classroom. The students will compose a power point to display their photographs of the required terms.
This lesson is adapted from a presentation that included an activity by Dianne Olix, 1995.

Type: Lesson Plan

Modeling: Rolling Cups:

This lesson unit is intended to help you 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.

Type: Lesson Plan

A Pi-ece of Florida History:

A Pi-ece of Florida History discovers significant dates in Florida History in the first 8 digits after the decimal of the number Pi. Historical people associated with those dates are identified and described. Students then use body measurements to approximate volume.

Type: Lesson Plan

Quadrilaterals using Unit Origami - Sonobe Cube:

This lesson can be used as an introduction - unit attention grabber- or as a final review on quadrilaterals. As the class forms a Sonobe cube, the different quadrilaterals are formed with each new fold. Included is a Power Point introduction, a video I made demonstrating how to fold the unit origami design, a video of my lesson I use as a middle or high school introduction to quadrilaterals and 2 worksheets which accompany the lesson. I enjoy doing this activity each year and am amazed all the prior knowledge the students have retained as the lesson proceeds.

Type: Lesson Plan

Turning Tires Model Eliciting Activity:

The Turning Tires MEA provides students with an engineering problem in which they must work as a team to design a procedure to select the best tire material for certain situations. The main focus of the MEA is applying geometric concepts through modeling.

Type: Lesson Plan

Perspectives Video: Experts

Implications of the Spherical Earth:

To understand atmospheric and oceanic currents, one needs a well-rounded understanding of geometry and the shape of the Earth.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Mathematical Patterns and Folds in the Brain:

A bio-mathematician discusses the folds and the structure of the brain and how they relate to math.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

The Relationship between Wing Shape and Flight Performance:

Ken Blackburn, an aerospace engineer for the United States Air Force, describes the relationship between wing shape and flight performance. 

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

3D Modeling with 3D Shapes:

Complex 3D shapes are often created using simple 3D primitives! Tune in and shape up as you learn about this application of geometry!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Bacteriophage Geometry and Structure:

Viruses aren't alive but they still need to stay in shape! Learn more about the geometric forms of bacteriophages!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Tasks

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.

Type: Problem-Solving Task

Coins in a circular pattern:

Using a chart of diameters of different denominations of coins, students are asked to figure out how many coins fit around a central coin.

Type: Problem-Solving Task

The Lighthouse Problem:

This problem asks students to model phenomena on the surface of the earth by examining the visibility of the lamp in a lighthouse from a boat.

Type: Problem-Solving Task

Solar Eclipse:

This problem solving task encourages students to explore why solar eclipses are rare by examining the radius of the sun and the furthest distance between the moon and the earth.

Type: Problem-Solving Task

Seven Circles III:

This provides an opportunity to model a concrete situation with mathematics. Once a representative picture of the situation described in the problem is drawn (the teacher may provide guidance here as necessary), the solution of the task requires an understanding of the definition of the sine function.

Type: Problem-Solving Task

Running around a track II:

The goal of this task is to model a familiar object, an Olympic track, using geometric shapes. Calculations of perimeters of these shapes explain the staggered start of runners in a 400 meter race.

Type: Problem-Solving Task

Running around a track I:

In this problem, geometry is applied to a 400 meter track to find the perimeter of the track.

Type: Problem-Solving Task

How thick is a soda can? (Variation II):

This problem solving task asks students to explain which measurements are needed to estimate the thickness of a soda can.

Type: Problem-Solving Task

How thick is a soda can? (Variation I):

This problem solving task challenges students to find the surface area of a soda can, calculate how many cubic centimeters of aluminum it contains, and estimate how thick it is.

Type: Problem-Solving Task

How many leaves on a tree? (Version 2):

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

How many cells are in the human body?:

This problem solving task challenges students to apply the concepts of mass, volume, and density in the real-world context to find how many cells are in the human body.

Type: Problem-Solving Task

Hexagonal pattern of beehives:

The goal of this task is to use geometry to study the structure of beehives.

Type: Problem-Solving Task

Global Positioning System II:

Reflective of the modernness of the technology involved, this is a challenging geometric modeling task in which students discover from scratch the geometric principles underlying the software used by GPS systems.

Type: 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

Tennis Balls in a Can:

This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a "double-naped cone" with vertex at the center of the sphere and bases equal to the bases of the cylinder

Type: Problem-Solving Task

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. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

Type: Problem-Solving Task

Text Resource

Math for Hungry Birds:

This informational text resource is intended to support reading in the content area. A new study indicates that the flying patterns of hunting albatrosses may resemble mathematical designs called fractals. This article describes the basics of fractals and why scientists think the albatross may hunt in such patterns. As it turns out, many animals may use math to find food!

Type: Text Resource

STEM Lessons - Model Eliciting Activity

Interchangeable Wristwatch Band:

Students use measures and properties of rectangular prisms and cylinders to model and rank 3D printable designs of interchangeable wristwatch bands that satisfy physical constraints.

NASA Space Shuttle Mission Patches:

Students apply geometric measures and methods, art knowledge, contextual information, and utilize clear and coherent writing to analyze NASA space shuttle mission patches from both a mathematical design and visual arts perspective.

Turning Tires Model Eliciting Activity:

The Turning Tires MEA provides students with an engineering problem in which they must work as a team to design a procedure to select the best tire material for certain situations. The main focus of the MEA is applying geometric concepts through modeling.

MFAS Formative Assessments

Camping Calculations:

Students are asked to find the measure of an angle formed by the support poles of a tent using the properties of geometric shapes.

Estimating Area:

Students are asked to select appropriate geometric shapes to model a lake and then use the model to estimate the surface area of the lake.

Estimating Volume:

Students are asked to model a tree trunk with geometric solids and to use the model to estimate the volume of the tree trunk.

Size It Up:

Students are asked to name geometric solids that could be used to model several objects.

Student Resources

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

Problem-Solving Tasks

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.

Type: Problem-Solving Task

Coins in a circular pattern:

Using a chart of diameters of different denominations of coins, students are asked to figure out how many coins fit around a central coin.

Type: Problem-Solving Task

The Lighthouse Problem:

This problem asks students to model phenomena on the surface of the earth by examining the visibility of the lamp in a lighthouse from a boat.

Type: Problem-Solving Task

Solar Eclipse:

This problem solving task encourages students to explore why solar eclipses are rare by examining the radius of the sun and the furthest distance between the moon and the earth.

Type: Problem-Solving Task

Seven Circles III:

This provides an opportunity to model a concrete situation with mathematics. Once a representative picture of the situation described in the problem is drawn (the teacher may provide guidance here as necessary), the solution of the task requires an understanding of the definition of the sine function.

Type: Problem-Solving Task

Running around a track II:

The goal of this task is to model a familiar object, an Olympic track, using geometric shapes. Calculations of perimeters of these shapes explain the staggered start of runners in a 400 meter race.

Type: Problem-Solving Task

Running around a track I:

In this problem, geometry is applied to a 400 meter track to find the perimeter of the track.

Type: Problem-Solving Task

How thick is a soda can? (Variation II):

This problem solving task asks students to explain which measurements are needed to estimate the thickness of a soda can.

Type: Problem-Solving Task

How thick is a soda can? (Variation I):

This problem solving task challenges students to find the surface area of a soda can, calculate how many cubic centimeters of aluminum it contains, and estimate how thick it is.

Type: Problem-Solving Task

How many leaves on a tree? (Version 2):

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

How many cells are in the human body?:

This problem solving task challenges students to apply the concepts of mass, volume, and density in the real-world context to find how many cells are in the human body.

Type: Problem-Solving Task

Hexagonal pattern of beehives:

The goal of this task is to use geometry to study the structure of beehives.

Type: Problem-Solving Task

Global Positioning System II:

Reflective of the modernness of the technology involved, this is a challenging geometric modeling task in which students discover from scratch the geometric principles underlying the software used by GPS systems.

Type: 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

Tennis Balls in a Can:

This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a "double-naped cone" with vertex at the center of the sphere and bases equal to the bases of the cylinder

Type: Problem-Solving Task

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. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

Type: Problem-Solving Task

Parent Resources

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

Problem-Solving Tasks

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.

Type: Problem-Solving Task

Coins in a circular pattern:

Using a chart of diameters of different denominations of coins, students are asked to figure out how many coins fit around a central coin.

Type: Problem-Solving Task

The Lighthouse Problem:

This problem asks students to model phenomena on the surface of the earth by examining the visibility of the lamp in a lighthouse from a boat.

Type: Problem-Solving Task

Solar Eclipse:

This problem solving task encourages students to explore why solar eclipses are rare by examining the radius of the sun and the furthest distance between the moon and the earth.

Type: Problem-Solving Task

Seven Circles III:

This provides an opportunity to model a concrete situation with mathematics. Once a representative picture of the situation described in the problem is drawn (the teacher may provide guidance here as necessary), the solution of the task requires an understanding of the definition of the sine function.

Type: Problem-Solving Task

Running around a track II:

The goal of this task is to model a familiar object, an Olympic track, using geometric shapes. Calculations of perimeters of these shapes explain the staggered start of runners in a 400 meter race.

Type: Problem-Solving Task

Running around a track I:

In this problem, geometry is applied to a 400 meter track to find the perimeter of the track.

Type: Problem-Solving Task

How thick is a soda can? (Variation II):

This problem solving task asks students to explain which measurements are needed to estimate the thickness of a soda can.

Type: Problem-Solving Task

How thick is a soda can? (Variation I):

This problem solving task challenges students to find the surface area of a soda can, calculate how many cubic centimeters of aluminum it contains, and estimate how thick it is.

Type: Problem-Solving Task

How many leaves on a tree? (Version 2):

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

How many cells are in the human body?:

This problem solving task challenges students to apply the concepts of mass, volume, and density in the real-world context to find how many cells are in the human body.

Type: Problem-Solving Task

Hexagonal pattern of beehives:

The goal of this task is to use geometry to study the structure of beehives.

Type: Problem-Solving Task

Global Positioning System II:

Reflective of the modernness of the technology involved, this is a challenging geometric modeling task in which students discover from scratch the geometric principles underlying the software used by GPS systems.

Type: 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

Tennis Balls in a Can:

This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a "double-naped cone" with vertex at the center of the sphere and bases equal to the bases of the cylinder

Type: Problem-Solving Task

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. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

Type: Problem-Solving Task