Lesson 17 | Geometry | 6th Grade Mathematics

Objective

Find surface area and volume in real-world problems.

Common Core Standards

Core Standards

The core standards covered in this lesson

6.G.A.2 — Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Geometry

6.G.A.2 — Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
6.G.A.4 — Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Geometry

6.G.A.4 — Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Determine if a real-world situation is solved by finding the surface area or by finding the volume.
Solve real-world problems using surface area and volume concepts.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

As students make sense of the problems in this lesson, encourage them to draw a sketch of the situation and to label their sketches with the appropriate measurements (MP.1).
Students encounter problems where they must determine what math skills and/or formulas they need to apply to determine, for example, how to cover a barn with paint or package a toy (MP.4).

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Alexis needs to paint the four exterior walls of a large rectangular barn. The length of the barn is 80 feet, the width is 50 feet, and the height is 30 feet. The paint costs $28 per gallon, and each gallon covers 420 square feet. How much will it cost Alexis to paint the barn? Explain your work.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics Painting a Barn

Painting a Barn, accessed on March 20, 2018, 2:30 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

A toy is packaged in a container that is a rectangular prism with the following measurements: $${7{1\over2}}$$ in $$\times$$ $$6$$ in $$\times$$ $$9$$ in. The toy packaging is then placed in a larger box for shipping. How much space will the toy packaging take up in the shipping box? Give some possible dimensions for a shipping box that could be used to ship the toy.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

A vase in the shape of a rectangular prism measures $$9\frac{1}{2}$$ inches tall, and has a $$4$$ inch square base.

a. If the vase is filled $$\frac{3}{4}$$ of the way with water, how much water is in the vase?

b. The vase came in a cardboard box. Each dimension of the box was $$\frac{1}{2}$$ inch greater than the dimensions of the vase. How much cardboard was used to make the box?

Student Response

Create a free account or sign in to view Student Response

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Example where students are given a 3-D figure with dimensions labeled and a net of a similar figure; students determine which figure would use more material to create and which figure would hold the greater volume (only include rectangular prisms for volume)
Challenge: Can you find dimensions for a three-dimensional figure that has the same numerical value for its surface area as it does for its volume?

MARS Summative Assessment Tasks for Middle School Smoothie Box
101Questions Dandy Candies
Illustrative Mathematics Christo's Building — Challenge
MARS Summative Assessment Tasks for Middle School Designing 3D Products: Candy Cartons — This is a lengthy lesson that could work well as a class project if time allows
Open Up Resources Grade 6 Unit 1 Practice Problems — Lesson 16
EngageNY Mathematics Grade 6 Mathematics > Module 5 > Topic D > Lesson 19 — Exercises and Problem Set
Yummy Math Do I Have Enough Wrapping Paper?

Lesson 16

Lesson Map

Topic A: Area of Triangles, Quadrilaterals, and Polygons

Find the area of parallelograms.

6.G.A.1

Find the area of right triangles.

6.G.A.1

Find the area of acute triangles using height and base.

6.G.A.1

Find the area of any triangle using height and base.

6.G.A.1

Find the area of polygons using composition and decomposition.

6.G.A.1

Solve real-world and mathematical problems involving area of polygons.

6.G.A.1

Topic B: Polygons in the Coordinate Plane

Draw polygons in the coordinate plane and find area and perimeter (Part 1).

6.G.A.3

Draw polygons in the coordinate plane and find area and perimeter (Part 2).

6.G.A.3

Solve real-world problems involving distance, area, and perimeter of polygons on and off the coordinate plane.

6.G.A.1 6.G.A.3

Topic C: Volume of Rectangular Prisms

Find volume of rectangular prisms with whole number and fractional edge lengths using unit and fractional unit cubes.

6.G.A.2

Determine the formulas for finding volume of rectangular prisms and use the formulas to solve for volume.

6.G.A.2

Apply volume concepts to solve real-world and mathematical problems, including finding missing measurements.

6.G.A.2

Apply volume concepts to solve real-world and mathematical problems, including finding volume of figures with composite prisms.

6.G.A.2

Topic D: Nets and Surface Area

Describe features of and identify nets that match prisms and pyramids.

6.G.A.4

Create nets and use them to find surface area of three-dimensional figures.

6.G.A.4

Find the surface area of three-dimensional figures with and without nets.

6.G.A.4

Find surface area and volume in real-world problems.

6.G.A.2 6.G.A.4

Geometry

Objective

Common Core Standards

Core Standards

Geometry

Geometry

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

Request a Demo

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Any other information you would like to provide about your school?

Effective Instruction Made Easy