# MA.6.GR.2.4

Given a mathematical or real-world context, find the surface area of right rectangular prisms and right rectangular pyramids using the figure’s net.

### Clarifications

Clarification 1: Instruction focuses on representing a right rectangular prism and right rectangular pyramid with its net and on the connection between the surface area of a figure and its net.

Clarification 2: Within this benchmark, the expectation is to find the surface area when given a net or when given a three-dimensional figure.

Clarification 3: Problems involving right rectangular pyramids are limited to cases where the heights of triangles are given.

Clarification 4: Dimensions are limited to positive rational numbers.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 6
Strand: Geometric Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Area
• Net
• Rectangular Prism
• Rectangular Prism

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

Students in grade 5 found the area of a rectangle with fractional or decimal sides. In grade 6, students find the surface area of right rectangular prisms and pyramids. In grade 7, students calculate the surface area of right circular cylinders.
• Instruction includes constructing models and nets of three-dimensional figures and describing them by the number of edges, vertices and faces. Providing these opportunities will allow students to manipulate materials and connect to the symbolic and more abstract aspects of geometry.
• Instruction includes students using formulas and decomposition strategies to find the surface area of figures. Using the dimensions of the individual faces, students should calculate each rectangle or triangle area and add these values together to find the surface area of the figure.
• Instruction includes describing the types of faces needed to create a three-dimensional figure. Students can make and test conjectures by determining what is needed to create a specific three-dimensional figures.
• Students need to practice the language of the problems they are being asked to solve.
• For instance, when being asked how much wrapping paper is needed to wrap a box, they know from experience that they are working with surface area. If they are being asked how many boxes will fit in a shipping container, then they are looking at volume.
• When using rational numbers, instruction should stay within the same form. Students should not be penalized though if they convert from one form to another when performing operations.
• For example, if students are working with fractions, the side lengths will not include decimals. If students are working with decimals, the side lengths will not include fractions.
• Instruction includes representing measurements for surface area as square units, units squared or units².
• Problem types include having students measure lengths using a ruler to determine the surface area.

### Common Misconceptions or Errors

• Students may not be able to determine the difference in the two-dimensional figures that compose three-dimensional figures.
• Students may invert the formulas for surface area and volume.

### Strategies to Support Tiered Instruction

• Teacher provides nets of the three-dimensional figures and model color coding each similar shape. This will help students properly identify each shape to find the area to calculate surface area.
• For example, a right rectangular prism can be modeled by the net shown below.

• Teacher reviews definitions of surface area and volume and co-creates an anchor chart to display in the room explaining the differences between them. Teacher models the use of manipulatives and geometric software to review the concept of area and surface area.
• Teacher breaks down formulas for area of a rectangle and volume of a rectangular prism to show when finding area, we are multiplying two sides which is why we use units², but with the rectangular prism, we are multiplying three sides, so we use units³ to label. Providing flash cards or cue cards with the formulas will help students in place of anchor charts when they are outside the classroom area.

### Instructional Tasks

Instructional Task 1 (MTR.6.1)
The surface area of a rectangular prism is 115 square inches. The net of the prism is shown. What are the possible dimensions of the prism?

### Instructional Items

Instructional Item 1
Carl is shipping a cardboard box that is a rectangular prism. The net of Carl’s box is shown. What is the area of cardboard, in square inches, required for Carl’s box?

Instructional Item 2
Maxwell is making a replica of the Egyptian pyramids. The figures’ dimensions have a square base with a side length of 7.7 cm and a slant height of 6.2 cm. Maxwell wants to cover the model with gold paper. How much paper, in square centimeters, is needed to cover the pyramid?

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (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))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.GR.2.AP.4: Find the surface area of right rectangular prisms by adding the areas of the shapes forming the two-dimensional net.

## Related Resources

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

## Formative Assessments

Rust Protection:

Students are asked to use a net to find the surface area of a rectangular prism.

Type: Formative Assessment

Pyramid Project:

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

## Lesson Plans

Who's Your Match?:

Students will be able to match a 3-D shape with its net, then using the net, they will find the surface area of the shape. They will then be able to apply this knowledge to solve real world application problems, finishing up with a design contest.

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

Wrapping Up Geometry (Lesson 1 of 2):

This lesson is the first of two in a unit on surface area. This lesson provides a foundation for understanding the concept of surface area by introducing nets of right rectangular prisms.

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

What's on the Surface?:

In this activity, students will work in groups to evaluate the measurements of shapes that form three-dimensional composite shapes to compute the surface area.

Type: Lesson Plan

Who's Your Match?:

Students will be able to match a 3-D shape with its net, then using the net, they will find the surface area of the shape. They will then be able to apply this knowledge to solve real world application problems, finishing up with a design contest.

Type: Lesson Plan

Feel the Heat!:

This MEA is a great way to implement Florida State Standards for math and language arts. It also supports cooperative learning groups and encourages student engagement. Students will explore different types of materials to determine which absorbs the least amount of heat. Students will also calculate the surface area to determine the cost for constructing the buildings using the materials.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Surface Area of Prisms and Pyramids:

In this lesson students will find the surface area of three-dimensional figures. Students will use nets to calculate the surface area of right rectangular prisms and right rectangular pyramids.

Type: Lesson Plan

How Much Paint Will It Take?:

This is a guided inquiry lesson to help students gain greater understanding of the relationship between 2-dimensional and 3-dimensional shapes. Students create right rectangular prisms and problem-solve how to find the flat 2-dimensional surface area. Students are asked to figure out how many party favors (prisms) can be painted with a quart of glow-in-the-dark paint.

Type: Lesson Plan

Box It Up, Wrap It Up (Surface Area of Rectangular Prisms):

In this introductory lesson to surface area, students will make connections between area of two-dimensional figures and calculating the surface area of rectangular prisms using nets, within the context of wrapping birthday presents! Math is Fun :)

Type: Lesson Plan

Wrapping Up Geometry (Lesson 2 of 2):

This lesson is 2 of 2 and is primarily formative in nature, but includes a summative assessment for students to take during the following class period.

During the lesson, students will be reviewing for their assessment on the surface area formula for a right rectangular prism.

Type: Lesson Plan

Lola's Landscaping MEA:

In this Model Eliciting Activity, MEA, students are asked to develop a procedure to fit the most amount of rectangular prism plant packages on one sheet of cardboard, using nets and surface area.

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. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Formula Detective: Finding the Surface Area of a 3D Figure:

This lesson allows students to derive the formulas for 3D figures by having them build models for nets.

Type: Lesson Plan

## Problem-Solving Tasks

Painting a Barn:

Students are asked to use the given information to determine the cost of painting a barn.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

## Tutorials

Nets of 3-Dimensional Figures:

This video demonstrates how to construct nets for 3-D shapes.

Type: Tutorial

Finding Surface Area of a Rectangular Prism :

This video demonstrates using a net to find surface area.

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

## STEM Lessons - Model Eliciting Activity

Feel the Heat!:

This MEA is a great way to implement Florida State Standards for math and language arts. It also supports cooperative learning groups and encourages student engagement. Students will explore different types of materials to determine which absorbs the least amount of heat. Students will also calculate the surface area to determine the cost for constructing the buildings using the materials.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Lola's Landscaping MEA:

In this Model Eliciting Activity, MEA, students are asked to develop a procedure to fit the most amount of rectangular prism plant packages on one sheet of cardboard, using nets and surface area.

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. Click here to learn more about MEAs and how they can transform your classroom.

## MFAS Formative Assessments

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.

Pyramid Project:

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

Rust Protection:

Students are asked to use a net to find the surface area of a rectangular prism.

## Student Resources

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

## Problem-Solving Task

Painting a Barn:

Students are asked to use the given information to determine the cost of painting a barn.

Type: Problem-Solving Task

## Tutorials

Nets of 3-Dimensional Figures:

This video demonstrates how to construct nets for 3-D shapes.

Type: Tutorial

Finding Surface Area of a Rectangular Prism :

This video demonstrates using a net to find surface area.

Type: Tutorial

## Parent Resources

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

## Problem-Solving Task

Painting a Barn:

Students are asked to use the given information to determine the cost of painting a barn.

Type: Problem-Solving Task