# MAFS.7.G.2.6Archived Standard

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

### Remarks

Examples of Opportunities for In-Depth Focus

Work toward meeting this standard draws together grades 3–6 work with geometric measurement.
General Information
Subject Area: Mathematics
Domain-Subdomain: Geometry
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. (Additional 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 of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Three-dimensional shapes may include right prisms and right pyramids. When the base of a figure has more than four sides, the area of the base must be given.
• Calculator :

Yes

• Context :

allowable

Sample Test Items (3)
• Test Item #: Sample Item 1
• Question: The surface area of a cube is 6 square centimeters. What is its volume, in cubic centimeters?
• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 2
• Question:

A cube with a surface area of 96 square centimeters is shown.

Eight cubes like the one shown are combined to create a larger cube. What is the volume, in cubic centimeters, of the new cube?

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 3
• Question:

Mitzi has a rectangular swimming pool. She fills it with water to a depth of 5 feet. The water has a volume of 1200 cubic feet.

Use the Connect Line tool to draw a rectangle that represents the possible dimensions of the swimming pool.

• Difficulty: N/A
• Type: GRID: Graphic Response Item Display

## Related Courses

This benchmark is part of these courses.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
0101060: M/J Three-Dimensional Studio Art 3 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912115: Fundamental Explorations in Mathematics 2 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

## Related Resources

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

## 3D Modeling

Wind Farm Design Challenge:

In this engineering design challenge, students are asked to create the most efficient wind turbine while balancing cost constraints. Students will apply their knowledge of surface area and graphing while testing 3D-printed wind farm blades. In the end, students are challenged to design and test their own wind farm blades, using Tinkercad to model a 3D-printable blade.

Type: 3D Modeling

## Formative Assessments

Prismatic Surface Area:

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

Type: Formative Assessment

Octagon Area:

Students are asked to find the area of a composite figure.

Type: Formative Assessment

Cube Volume and Surface Area:

Students are asked to calculate the volume and surface area of a cube.

Type: Formative Assessment

Composite Surface Area:

Students are asked to find the surface area of a composite figure.

Type: Formative Assessment

Composite Polygon Area:

Students are asked to find the area of a composite figure.

Type: Formative Assessment

Chilling Volumes:

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

Type: Formative Assessment

Estimations and Approximations: The Money Munchers:

The context: There is 24,400 in 1 bills under a mattress. How far will the mattress lower if the money is deposited in the bank? Complete with worksheets, student examples, student mistakes for analysis. This lesson unit is intended to help you assess how well students are able to:

• Model a situation.
• Make sensible, realistic assumptions and estimates.
• Use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem.

Type: Formative Assessment

Estimations and Approximations: The Money Munchers:

This lesson unit is intended to help you assess how well students are able to:

• Model a situation.
• Make sensible, realistic assumptions and estimates.
• Use assumptions and estimates to create a chain of reasoning in order to solve a practical problem.

Type: Formative Assessment

Designing a Sports Bag:

This lesson unit is intended to help you assess how well students are able to:

• Recognize and use common 2D representations of 3D objects.
• Identify and use the appropriate formula for finding the circumference of a circle.

Type: Formative Assessment

## Lesson Plans

Clean It Up:

Students will help a volunteer coordinator choose cleanup projects that will have the greatest positive impact on the environment and the community.  They will apply their knowledge of how litter can impact ecosystems along with some math skills to make recommendations for cleanup zones to prioritize.  Students will explore the responsibilities of citizens to maintain a clean environment and the impact that litter can have on society in this integrated Model Eliciting Activity.

Type: Lesson Plan

Coding Geometry Challenge # 16, 18 & 19:

This set of geometry challenges focuses on creating a variety of polygons using the coordinate plane as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

Egg-Cellent Transport:

This lesson addresses the topic of limiting factors looking specifically at maintaining wildlife populations. There is an engineering design challenge included in which students will have to take on the role of a wildlife conservation officer and create a container for the egg of an endangered species that will protect it in the field until he/she can get it back to the lab.

Type: Lesson Plan

Three Dimensions Unfolded:

Students will use nets of prisms to find the surface area of composite three-dimensional (3-D) figures. Students will learn to identify the faces of 3-D figures that are needed to find the surface areas.

Type: Lesson Plan

STEM-Designing an Organ Transport Container:

This is a STEM-Engineering Design Challenge lesson. Students will go through the process of creating an organ transport container using their knowledge of human body systems, heat flow, and volume.

Type: Lesson Plan

Density of Solids and Liquids:

In this Lab, students create their own definition for the term density and calculate the densities of different substances- solids and liquids. Students will learn that every substance has its own unique density, depending on how tightly atoms or molecules of the materials are packed. Students gather data about known samples to infer the identity of an unknown sample.

Note: This lesson will only cover the density portion of benchmark SC.8.P.8.4

Type: Lesson Plan

Using Nets to Find the Surface Area of Pyramids:

In this lesson, students will explore and apply the use of nets to find the surface area of pyramids.

Type: Lesson Plan

Estimating: Counting Trees:

This lesson unit is intended to help you assess how well students are able to solve simple problems involving ratio and direct proportion, choose an appropriate sampling method, collect discrete data, and record their data using a frequency table.

Type: Lesson Plan

Aquarium Splash:

Students explore how the formulas for surface area and volume were derived and apply this knowledge to solve problems. Students will be presented with a problem-solving task that incorporates finding the surface area and volume when designing an aquarium.

Type: Lesson Plan

Using Dimensions: Designing a Sports Bag:

This lesson unit is intended to help you assess how well students are able to recognize and use common 2D representations of 3D objects, as well as identify and use the appropriate formula for finding the circumference of a circle.

Type: Lesson Plan

Netty People and Pets:

Students will learn what a "net" is, draw nets of three dimensional shapes, accurately calculate the surface area of their nets, and put them together to create an original person or pet.

Type: Lesson Plan

Hands-On! Rectangular Prisms:

Students create surface area nets with graph paper and work with manipulative cubes to decide if there is a relationship between surface area and volume in rectangular prisms.

Type: Lesson Plan

Manipulating Mathematics (Volume and Surface Area):

This is a lesson designed to teach students how to find the volume and surface areas of right rectangular prisms. It provides an interactive lesson where students get to learn hands-on with cereal boxes and on the computer with a GeoGebra activity.

Type: Lesson Plan

Installing Tile Floor:

This MEA requires students to formulate a comparison-based solution to a problem involving finding the best plan for installing tile floor considering different aspects. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client.

Type: Lesson Plan

Makeover, Home Edition Part II:

This is the second part of the lesson, "Makeover, Home Edition." This lesson will continue focusing on unit prices, but also incorporates area and volume. Part I (Makeover, Home Edition #48705) is based on creating backyard dimensions for fencing. Part III (Makeover, Home Edition #49025) will deal with creating a scale drawing of this backyard. Part IV (Makeover, Home Edition Final #49090) will focus on inserting a window and painting walls inside the house.

Type: Lesson Plan

Survival Journal Part Two: Outdoor Gardening:

In this lesson, students will design two outdoor gardens, 1) a raised garden bed and 2) a ground level garden (traditional). Students will, with help of the teacher, till the ground with removal of ground cover, build border for garden, add soil, attach poles with string to create a life size graph all so they can grow tomatoes and plot the data easily in their survival journals.This is Part 2 of a 4-Part Project on Survival.

Type: Lesson Plan

Raising Your Garden MEA provides students with a real world engineering problem in which they must work as a team to design a procedure to select the best material for building raised garden beds. The main focus of this MEA is to recognize the importance of choosing the correct material for building a raised garden bed, what information is needed before starting a gardening project, and to consider the environmental and economic impact the garden will have on the school. Students will conduct individual and team investigations in order to arrive at a scientifically sound solution to the problem.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations.

Type: Lesson Plan

Sweet Surface Area:

In this lesson, students will explore the relationship between volume and surface area through real-world problem solving. They will work with a partner as they are tasked with finding the least expensive packaging (smallest surface area) for a given number of caramels (volume). Students will justify their packaging strategy in a group discussion.

Type: Lesson Plan

Wallpaper Woes Money Math: Lessons for Life:

Students hear a story about a middle-school student who wants to redecorate his bedroom. They measure the classroom wall dimensions, draw a scale model, and incorporate measurements for windows and doors to determine the area that could be covered by wallpaper. Students then hear more about the student's redecorating adventure and learn about expenses, budget constraints, and tradeoffs.

Type: Lesson Plan

Cylinder Volume Lesson Plan:

Using volume in the real world

Type: Lesson Plan

All wrapped up in surface area fun!:

This lesson allows a hands-on approach for students to use real- life problem solving. Students will apply their measurement skills to the concept of surface area. This lesson provides opportunities for students to work cooperatively with others as a team.

Type: Lesson Plan

Boxing Candles:

In this MEA, students select jars for candles based on a variety of factors and then design boxes to contain the jars.

Type: Lesson Plan

How Much Surface Area Does Your Skin Take Up?:

Students relate their body parts to six cylinders. They adjust the surface area of a cylinder formula, and then measure, record, and compute the approximate surface area of their skin. Students will develop a better understanding of how much skin covers up their body when they calculate how much surface area their skin takes up.

Type: Lesson Plan

Relating Surface Area and Volume:

Students will recognize that while the surface area may change, the volume can remain the same. This lesson is enhanced through the multimedia CPALMS Perspectives Video, which introduces students to the relationship between surface area and volume.

Type: Lesson Plan

## Perspectives Video: Professional/Enthusiasts

Volume and Surface Area of Pizza Dough:

<p>Michael&nbsp;McKinnon&nbsp;of Gaines Street Pies explains how when making pizza the volume is conserved but the&nbsp;surface area changes.</p>

Type: Perspectives Video: Professional/Enthusiast

Modeling with Polygons for 3D Printers:

<p>Understand 3D modeling from a new angle when you learn about surface geometry and 3D printing.</p>

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

## 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

Maximizing Area: Gold Rush:

Before the lesson, students attempt the Gold Rush task individually. You then look at their responses and formulate questions for students to think about as they review their work. At the start of the lesson, students reflect on their individual responses and use the questions posed to think of ways to improve their work. Next, students work collaboratively in small groups to produce, in the form of a poster, a better solution to the Gold Rush task than they did individually. In a whole-class discussion students compare and evaluate the different methods they used. Working in small groups, students analyze sample responses to the Gold Rush task, then, in a whole-class discussion, review the methods they have seen. Finally, students reflect on their work.

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. Multiple solution processes are presented.

sandundertheswingset2024:

The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started. The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set?

In this problem solving task, students investigate Shamu Stadium at Sea World. They will use knowledge of geometric shapes to solve problems involving area and volume and examine as well as analyze a diagram making calculations. Students will also be challenged to design an advertising poster using the measurements they mind.

Surface Area and Volume:

In this activity, students adjust the dimensions of either a rectangular or triangular prism and the surface area and volume are calculated for those dimensions. Students can also switch into compute mode where they are given a prism with certain dimensions and they must compute the surface area and volume. The application keeps score so students can track their progress. This application allows students to explore the surface area and volume of rectangular and triangular prisms and how changing dimensions affect these measurements. This activity also includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

## Project

Classroom Floor Plan:

This resource guides the learner step-by-step in creating a scale floor plan of a classroom. The instructions include sample drawings of student work. The activity includes sketching a map of the classroom, measuring the room and calculating the area and perimeter, creating a scale drawing, and drafting a CAD (computer-aided design) floor plan. The lesson provides students with hands-on, real world practice solving problems of measurement, ratio, and scale.

Type: Project

## Teaching Ideas

Modeling: Making Matchsticks:

This lesson unit is intended to help you assess how well students are able to:

• Interpret a situation and represent the variables mathematically.
• Select appropriate mathematical methods.
• Interpret and evaluate the data generated.
• Communicate their reasoning clearly.
The context is estimating how many matchsticks (rectangular prisms) can be made from this tree (conic).

Type: Teaching Idea

Packing For A L-o-o-o-ng Trip To Mars:

In this engineering task, students will apply concepts of volume to decide what they will need to take on a 2-1/2 year journey to Mars. Then plan how to fit everything into a 1-cubic-meter box, using only a measuring tape, pencil and paper, and math.

Type: Teaching Idea

## Tutorials

Find the Volume of an Object in a Rectangular Prism:

Find the volume of an object, given dimensions of a rectangular prism filled with water, and the incremental volume after the object is dropped into the water.

Type: Tutorial

Volume of a Rectangular Prism Problem:

This video involves packing a larger rectangular prism with smaller ones which is solved in two different ways.

Type: 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

## Virtual Manipulatives

Area Builder:

This manipulative allows you to create shapes using colorful blocks to explore the relationship between perimeter and area. The game screen challenges you to build shapes or find the area of figures.

Type: Virtual Manipulative

Surface Area of Prisms:

This lesson is designed to develop students' knowledge of surface area and introduce them to calculating the surface area of a triangular prism. This lesson provides links to discussions and activities related to surface area as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Virtual Manipulative

Surface Area of Rectangular Prisms:

This lesson is designed to introduce students to the concept of surface area and how to find the surface area of a rectangular prism. This lesson provides links to discussions and activities related to surface area as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Virtual Manipulative

## WebQuest

Volume of Prisms:

This lesson is designed to develop students' understanding of volume and ability to find volumes of triangular prisms. It provides links to discussions and activities related to volume as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: WebQuest

## STEM Lessons - Model Eliciting Activity

Boxing Candles:

In this MEA, students select jars for candles based on a variety of factors and then design boxes to contain the jars.

Installing Tile Floor:

This MEA requires students to formulate a comparison-based solution to a problem involving finding the best plan for installing tile floor considering different aspects. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client.

Raising Your Garden MEA provides students with a real world engineering problem in which they must work as a team to design a procedure to select the best material for building raised garden beds. The main focus of this MEA is to recognize the importance of choosing the correct material for building a raised garden bed, what information is needed before starting a gardening project, and to consider the environmental and economic impact the garden will have on the school. Students will conduct individual and team investigations in order to arrive at a scientifically sound solution to the problem.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations.

## MFAS Formative Assessments

Chilling Volumes:

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

Composite Polygon Area:

Students are asked to find the area of a composite figure.

Composite Surface Area:

Students are asked to find the surface area of a composite figure.

Cube Volume and Surface Area:

Students are asked to calculate the volume and surface area of a cube.

Octagon Area:

Students are asked to find the area of a composite figure.

Prismatic Surface Area:

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

## Student Resources

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

## Perspectives Video: Professional/Enthusiast

Modeling with Polygons for 3D Printers:

<p>Understand 3D modeling from a new angle when you learn about surface geometry and 3D printing.</p>

Type: Perspectives Video: Professional/Enthusiast

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. Multiple solution processes are presented.

sandundertheswingset2024:

The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started. The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set?

## Tutorials

Find the Volume of an Object in a Rectangular Prism:

Find the volume of an object, given dimensions of a rectangular prism filled with water, and the incremental volume after the object is dropped into the water.

Type: Tutorial

Volume of a Rectangular Prism Problem:

This video involves packing a larger rectangular prism with smaller ones which is solved in two different ways.

Type: 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 benchmark.

## Perspectives Video: Professional/Enthusiast

Modeling with Polygons for 3D Printers:

<p>Understand 3D modeling from a new angle when you learn about surface geometry and 3D printing.</p>

Type: Perspectives Video: Professional/Enthusiast