# Standard 4: Use geometric measurement and dimensions to solve problems. Export Print
General Information
Number: MA.912.GR.4
Title: Use geometric measurement and dimensions to solve problems.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.912.GR.4.AP.1
Identify the shape of a two-dimensional cross section of a three-dimensional figure.
MA.912.GR.4.AP.2
Identify a three-dimensional object generated by the rotation of a two-dimensional figure.
MA.912.GR.4.AP.3
Select the effect of a dilation on the area of two-dimensional figures and/or surface area or volume of three-dimensional figures.
MA.912.GR.4.AP.4
Solve mathematical and/or real-world problems involving the area of triangles, squares, circles or rectangles.
MA.912.GR.4.AP.5
Solve mathematical or real-world problems involving the volume of three-dimensional figures limited to cylinders, pyramids, prisms, or cones.
MA.912.GR.4.AP.6
Solve mathematical or real-world problems involving the surface area of three-dimensional figures limited to cylinders, pyramids, prisms, and cones.

## Related Resources

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

## Formative Assessments

Inside the Box:

Students are asked to identify and draw cross sections of a rectangular prism and to describe their dimensions.

Type: Formative Assessment

Volume of a Cylinder:

Students are asked to derive and explain a formula for the volume of a cylinder given a prism with the same height and the same cross-sectional area at every height.

Type: Formative Assessment

Area and Circumference – 1:

This task is the first in a series of three tasks that assess the students’ understanding of informal derivations of the formulas for the area and circumference of a circle. In this task, students are shown a regular n-gon inscribed in a circle. They are asked to use the formula for the area of the n-gon to derive an equation that describes the relationship between the area and circumference of the circle.

Type: Formative Assessment

Softball Complex:

Students are asked to solve a design problem in which a softball complex is to be located on a given tract of land subject to a set of specifications.

Type: Formative Assessment

Slice of a Cone:

Students are asked to sketch, describe, and compare three horizontal cross sections of a cone.

Type: Formative Assessment

Slice It:

Students are asked to identify and describe two-dimensional cross sections of three-dimensional solids.

Type: Formative Assessment

How Many Trees?:

Students are asked to determine an estimate of the density of trees and the total number of trees in a forest.

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

Population of Utah:

Students are asked to determine the population of the state of Utah given the state’s population density and a diagram of the state’s perimeter with boundary distances labeled in miles.

Type: Formative Assessment

Volume of a Cone:

Students are asked to derive and explain a formula for the volume of a cone given a pyramid with the same height and the same cross-sectional area at every height.

Type: Formative Assessment

Mudslide:

Students are asked to create a model to estimate volume and mass.

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

Area and Circumference - 3:

This task is the third in a series of three tasks that assess the students’ understanding of informal derivations of the formulas for the area and circumference of a circle. In this task, students are given the definition of pi as the area of the unit circle, A(1), and are asked to use this representation of pi along with the results from the two previous tasks to generate formulas for the area and circumference of a circle.

Type: Formative Assessment

Area and Circumference - 2:

This task is the second in a series of three tasks that assesses the students’ understanding of informal derivations of the formulas for the area and circumference of a circle. In this task, students show that the area of the circle of radius r, A(r), can be found in terms of the area of the unit circle, A(1) [i.e., A(r) = r2 · A(1)].

Type: Formative Assessment

Volume of a Pyramid:

Students are guided through the process of writing an informal argument for the volume of a pyramid formula using Cavalieri’s Principle.

Type: Formative Assessment

Sugar Cone:

Students are asked to solve a problem that requires calculating the volume of a cone.

Type: Formative Assessment

Louvre Pyramid:

Students are asked to find the height of a square pyramid given the length of a base edge and its volume.

Type: Formative Assessment

Cylinder Formula:

Students are asked to write the formula for the volume of a cylinder, explain what each variable represents, and label the variables on a diagram.

Type: Formative Assessment

Cone Formula:

Students are asked to write the formula for the volume of a cone, explain what each variable represents, and label the variables on a diagram.

Type: Formative Assessment

Burning Sphere:

Students are asked to solve a problem that requires calculating the volume of a sphere.

Type: Formative Assessment

Windy Pyramid:

Students are asked to use a net to find the surface area of a triangular pyramid.

Type: Formative Assessment

Skateboard Ramp:

Students are asked to draw a net of a three-dimensional figure.

Type: Formative Assessment

Square Pyramid Slices:

Students are asked to sketch and describe the two-dimensional figures that result from slicing a square pyramid.

Type: Formative Assessment

Rectangular Prism Slices:

Students are asked to sketch and describe two-dimensional figures that result from slicing a rectangular prism.

Type: Formative Assessment

Prismatic Surface Area:

Students are asked to determine the surface area of a right triangular prism and explain the procedure.

Type: Formative Assessment

Chilling Volumes:

Students are asked to solve a problem involving the volume of a composite figure.

Type: Formative Assessment

Sphere Formula:

Students are asked to write the formula for the volume of a sphere, explain what each variable represents, and label the variables on a diagram.

Type: Formative Assessment

Pyramid Formula:

Students are asked to write the formula for the volume of a pyramid, explain what each variable represents, and label the variables on a diagram.

Type: Formative Assessment

Cylinder Slices:

Students are asked to sketch and describe the two-dimensional figures that result from slicing a cylinder.

Type: Formative Assessment

Cone Slices:

Students are asked to sketch and describe the two-dimensional figures that result from slicing a cone.

Type: Formative Assessment

Snow Cones:

Students are asked to solve a problem that requires calculating the volumes of a cone and a cylinder.

Type: Formative Assessment

Sports Drinks:

Students are asked to solve a problem that requires calculating the volume of a large cylindrical sports drink container and comparing it to the combined volumes of 24 individual containers.

Type: Formative Assessment

The Great Pyramid:

Students are asked to find the height of the Great Pyramid of Giza given its volume and the length of the edge of its square base.

Type: Formative Assessment

Do Not Spill the Water!:

Students are asked to solve a problem that requires calculating the volumes of a sphere and a cylinder.

Type: Formative Assessment

2D Rotations of Triangles:

Students are given the coordinates of the vertices of a right triangle and asked to describe the solid formed by rotating the triangle about a given axis.

Type: Formative Assessment

Working Backwards – 2D Rotations:

Students are given a solid and asked to determine the two-dimensional shape that will create the solid when rotated about the y-axis.

Type: Formative Assessment

2D Rotations of Rectangles:

Students are given the coordinates of the vertices of a rectangle and asked to describe the solid formed by rotating the rectangle about a given axis.

Type: Formative Assessment

## Lesson Plans

Three Dimensions Unfolded:

Students will use nets of prisms to find the surface area of composite 3-D figures. Students will learn to identify the faces of 3-D figures that are needed to find the surface areas, and those that are not needed.

Type: Lesson Plan

Propensity for Density:

Students apply concepts of density to situations that involve area (2-D) and volume (3-D).

Type: Lesson Plan

Pack It Up:

Students use geometry formulas to solve a fruit growing company's dilemma of packing fruit into crates of varying dimensions. Students calculate the volume of the crates and the volume of the given fruit when given certain numerical facts about the fruit and the crates.

Type: Lesson Plan

This lesson explores the formulas for calculating the volume of cylinders, cones, pyramids, and spheres.

Type: Lesson Plan

The Cost of Keeping Cool:

Students will find the volumes of objects. After decomposing a model of a house into basic objects students will determine the cost of running the air conditioning.

Type: Lesson Plan

The Grass is Always Greener:

The lesson introduces area of sectors of circles then uses the areas of circles and sectors to approximate area of 2-D figures. The lesson culminates in using the area of circles and sectors of circles as spray patterns in the design of a sprinkler system between a house and the perimeter of the yard (2-D figure).

Type: Lesson Plan

In this activity, students will utilize measurement data provided in a chart to calculate areas, volumes, and densities of cookies. They will then analyze their data and determine how these values can be used to market a fictitious brand of chocolate chip cookie. Finally, they will integrate cost and taste into their analyses and generate a marketing campaign for a cookie brand of their choosing based upon a set sample data which has been provided to them.

Type: Lesson Plan

St. Pi Day construction with a compass & ruler:

St. Pi Day construction with compass

This activity uses a compass and straight-edge(ruler) to construct a design. The design is then used to complete a worksheet involving perimeter, circumference, area and dimensional changes which affect the scale factor ratio.

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 surface area concepts and algebra through modeling.

Type: Lesson Plan

## Original Student Tutorials

Volume of Spherical Bubble Tea:

Learn how to calculate the volume of spheres while learning how they make Bubble Tea in this interactive tutorial.

Type: Original Student Tutorial

Ninja Nancy Slices:

Learn how to determine the shape of a cross-section created by the intersection of a slicing plane with a pyramid or prism in this ninja-themed, interactive tutorial.

Type: Original Student Tutorial

I Scream! You Scream! We All Scream for... Volume!:

Learn to calculate the volume of a cone as you solve real-world problems in this ice cream-themed, interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Experts

Velocity of the Aucilla River:

Harley Means discusses the mathematical methods hydrologists use to calculate the velocity of rivers.

Type: Perspectives Video: Expert

MicroGravity Sensors & Statistics:

Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.

Type: Perspectives Video: Expert

Carbon Foam and Geometry:

Carbon can take many forms, including foam! Learn more about how geometry and the Monte Carlo Method is important in understanding it.

Type: Perspectives Video: Expert

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.

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

Unit Rate and Florida Cave Formation:

How long does it take to form speleothems in the caves at Florida Caverns State Parks?

Type: Perspectives Video: Professional/Enthusiast

Volume and Surface Area of Pizza Dough:

Michael McKinnon of Gaines Street Pies explains how when making pizza the volume is conserved but the surface area changes.

Type: Perspectives Video: Professional/Enthusiast

Mathematically Optimizing 3D Printing:

Did you know that altering computer code can increase 3D printing efficiency? Check it out!

Type: Perspectives Video: Professional/Enthusiast

Reflections, Rotations, and Translations with Additive Printing:

Transform your understanding of 3D modeling when you learn about how shapes are manipulated to arrive at a final 3D printed form!

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!

Type: Perspectives Video: Professional/Enthusiast

Scale and Proportion for Bird Photography:

Mathematics plays a role in what we perceive as beautiful! Learn more about it while you learn about bird photography! Produced with funding from the Florida Division of Cultural Affairs.

Type: Perspectives Video: Professional/Enthusiast

Design Process for a Science Museum Exhibit:

Go behind the scenes and learn about science museum exhibits, design constraints, and engineering workflow! Produced with funding from the Florida Division of Cultural Affairs.

Type: Perspectives Video: Professional/Enthusiast

Making Candy: Uniform Scaling:

Don't be a shrinking violet. Learn how uniform scaling is important for candy production.

Type: Perspectives Video: Professional/Enthusiast

Using Geometry and Computers to make Art with CNC Machining:

See and see far into the future of arts and manufacturing as a technician explains computer numerically controlled (CNC) machining bit by bit.

Type: Perspectives Video: Professional/Enthusiast

Estimating Oil Seep Production by Bubble Volume:

You'll need to bring your computer skills and math knowledge to estimate oil volume and rate as it seeps from the ocean floor. Dive in!

Type: Perspectives Video: Professional/Enthusiast

KROS Pacific Ocean Kayak Journey: Food Storage Mass and Volume:

What do you do if you don't have room for all your gear on a solo ocean trek? You're gonna need a bigger boat...or pack smarter with math.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Type: Perspectives Video: Professional/Enthusiast

NASA Space Flight Hardware Geometry:

If you want to take things to space, you have to have a place to put them. Just make sure they fit before you send them up.

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Ideas

Ecological Sampling Methods and Population Density:

Dr. David McNutt explains how a simple do-it-yourself quadrat and a transect can be used for ecological sampling to estimate population density in a given area.

Type: Perspectives Video: Teaching Idea

KROS Pacific Ocean Kayak Journey: Kites, Geometry, and Vectors:

Set sail with this math teacher as he explains how kites were used for lessons in the classroom.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Type: Perspectives Video: Teaching Idea

## Tutorial

Find the Volume of a Triangular Prism and Cube:

This video will show to find the volume of a triangular prism, and a cube by applying the formula for volume.

Type: Tutorial

## Unit/Lesson Sequence

Three Dimensional Shapes:

In this interactive, self-guided unit on 3-dimensional shape, students (and teachers) explore 3-dimensional shapes, determine surface area and volume, derive Euler's formula, and investigate Platonic solids. Interactive quizzes and animations are included throughout, including a 15 question quiz for student completion.

Type: Unit/Lesson Sequence

## Student Resources

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

## Original Student Tutorials

Volume of Spherical Bubble Tea:

Learn how to calculate the volume of spheres while learning how they make Bubble Tea in this interactive tutorial.

Type: Original Student Tutorial

Ninja Nancy Slices:

Learn how to determine the shape of a cross-section created by the intersection of a slicing plane with a pyramid or prism in this ninja-themed, interactive tutorial.

Type: Original Student Tutorial

I Scream! You Scream! We All Scream for... Volume!:

Learn to calculate the volume of a cone as you solve real-world problems in this ice cream-themed, interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Expert

MicroGravity Sensors & Statistics:

Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

Making Candy: Uniform Scaling:

Don't be a shrinking violet. Learn how uniform scaling is important for candy production.

Type: Perspectives Video: Professional/Enthusiast

Using Geometry and Computers to make Art with CNC Machining:

See and see far into the future of arts and manufacturing as a technician explains computer numerically controlled (CNC) machining bit by bit.

Type: Perspectives Video: Professional/Enthusiast

Estimating Oil Seep Production by Bubble Volume:

You'll need to bring your computer skills and math knowledge to estimate oil volume and rate as it seeps from the ocean floor. Dive in!

Type: Perspectives Video: Professional/Enthusiast

## Tutorial

Find the Volume of a Triangular Prism and Cube:

This video will show to find the volume of a triangular prism, and a cube by applying the formula for volume.

Type: Tutorial

## Parent Resources

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

## Perspectives Video: Professional/Enthusiasts

Making Candy: Uniform Scaling:

Don't be a shrinking violet. Learn how uniform scaling is important for candy production.

Type: Perspectives Video: Professional/Enthusiast

Using Geometry and Computers to make Art with CNC Machining:

See and see far into the future of arts and manufacturing as a technician explains computer numerically controlled (CNC) machining bit by bit.

Type: Perspectives Video: Professional/Enthusiast

Estimating Oil Seep Production by Bubble Volume:

You'll need to bring your computer skills and math knowledge to estimate oil volume and rate as it seeps from the ocean floor. Dive in!

Type: Perspectives Video: Professional/Enthusiast