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M A N E U V E R I N G T H E M I D D L E .C O M

PA G E T W O

PAGE TOPIC RESOURCE

4 Sample Pacing Guide

5-6 Ideas for Implementation & Helpful Hints

7-16 Binder Covers, Dividers, and Spine Labels

17-18 Intro to Nets Student Handout 1

19 Intro to Nets Homework 1

21-22 Surface Area of Cubes and Rectangular Prisms Student Handout 2

23 Surface Area of Cubes and Rectangular Prisms Homework 2

25-26 Surface Area of Triangular Prisms Student Handout 3

27 Surface Area of Triangular Prisms Homework 3

29-30 Surface Area of Prisms Quiz Quiz 1

31-32 Surface Area of Pyramids Student Handout 4

33 Surface Area of Pyramids Homework 4

35-36 Problem Solving with Surface Area Student Handout 5

37 Problem Solving with Surface Area Homework 5

39-42 Surface Area Unit Study Guide Study Guide

43-44 Surface Area Unit Test Test

SURFACE AREA UNITTable of Contents

©Maneuvering the Middle LLC, 2016

DAY 1 DAY 2 DAY 3 DAY 4 DAY 5

Intro to Nets Surface Area of Cubes and Rectangular

Prisms

Surface Area of Triangular Prisms

Surface Area of Prisms Quiz

Surface Area of Pyramids

Student Handout 1Homework 1



Quiz 1 Student Handout 4Homework 4

DAY 6 DAY 7 DAY 8 NOTES

Problem Solving with Surface Area

Surface Area Unit Study Guide

Surface Area Unit Test


Unit Study Guide Unit Test


SURFACE AREAPACING GUIDE

*NOTE: This file has been organized for double-sided printing. Any blank pages were left so intentionally to make printing easy.

Ideas for Implementation: This bundle has all of the notes, homework, quizzes, and tests to make your life easier and help your students to be successful with surface area concepts. A sample pacing guide is included for those of you who do not have a district scope and sequence or if it is very general. Additionally, an answer key is included.

If you notice any discrepancies in the documents or have any questions, please email me at: [email protected].

STANDARDS

7.G.6 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.

SURFACE AREAStudent Handouts


HELPFUL HINTS

A few ideas for organizing your curriculum and keeping things nice and neat:

Keep each unit in a separate binder and use the spine labels and covers to keep them looking nice and easy to find. I personally love 1.5” binders.


Student Handouts

BINDERS

I place my originals in page protectors in chronological order. Any extra copies from that lesson, I hole punch and place behind that page. When I need an extra or a student is missing something from weeeeeeeeks ago, I can simply pull out a copy.

PAGE PROTECTORS

I highlight the edges of my answer keys or if I am really good, print them on colored paper. It helps them to stand out and makes them easy to find on my desk, in a binder, by the document camera, etc. Plus, highlighter doesn’t show up if you make a copy.

ANSWER KEYS

Card stock in a page protector makes an awesome divider. When I set up my dividers, I include one for handouts, activities, assessments, and answer keys. Binder covers and spine labels have been included. J

CARD STOCK

Happy Teaching!

SURFACEAREA

s e v e n t h G r a d e C u r r i c u l u m

U n i t e i g h t : 7 . G . 6

©MANEUVERINGTHEMIDDLE,2016

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SURFACEAREA


U n i t e i g h t : A N S W E R K E Y S


SURFACEAREA


U n i t e i g h t : A C T I V I T I E S


SURFACEAREA


U n i t e i g h t : A S S E S S M E N T S


Name _____________________________________Date ______________________________Pd______

Unit: Surface AreaStudent Handout 1

INTRO TO NETS


NETS OF 3D FIGURES

• A net is a two dimensional _____________________ ____________.

• When folded, a net creates a ________________________________

object.

• All solid figures have specific nets.

Determine which of the following shapes would create the cube below. Explain why or why not.

______________________________________________________________________________________

______________________________________________________________________________________

I IVIIIII V

FACE • Faces of a three-dimensional figure are any of the __________________,

including the bases.

BASE• The base of a three-dimensional figure ______________ the shape.

• A prism has two bases, which are _________________to each other and

______________touch.

VERTEX • The vertex is the ______________of a three-dimensional figure.

EDGE • The edge is the ______________________________that joins two faces.

Label the various parts of the rectangular prism and rectangular pyramid below. What do you notice that differentiates the prism from the pyramid?

Sketch a net for each of the shapes below. Think through the process of unfolding the object, as well as the different characteristics of each object (faces and bases).

How is the net of the pyramid different from that of the prisms?

________________________________________________________________________________________

________________________________________________________________________________________

1. 2. 3.

Use the measurements from the nets below to label the solid figures.

10ft

Summarize today’s lesson:


15 ft

5 ft

5 ft

15 ft

5 ft

6 ft

10 ft

6 ft

6 ft

2 ft

2 ft

6 ft6 ft

5 ft

9 ft

12 ft

7 ft

7 ft

NET 3D FIGURE

1

2

3

4

5

Name _____________________________________Date ____________________________Pd ______

Unit: Surface Area Homework 1

Sketch the 3D figure or net below. Then, record the dimensions on the corresponding object.


3.5 in

12 in6 in

5 cm 5 cm

10 cm

3.8 cm3 cm

8.9 cm

15 c

m

16 cm

INTRO TO NETS

3.5 in

Rewrite the dimensions of the rectangular prism on the net below.

Use the information to determine the area of each rectangle. Then, find the sum of all six faces.

A: ____________B: ____________ C: ____________ D: ____________

E: ____________F: ____________Total Surface Area: ____________

TOTALSURFACE

AREA

• Total surface area is the ______________ of the areas of all faces,

including the ___________ .

Name _____________________________________Date ______________________________Pd______



Surface area is the total _______________on the ____________________ of a three-

dimensional object.

A

B

C

DE F

SHAPE 1 SHAPE 2 SHAPE 3

FORMULA

PLUG IN VALUES

AREA

TOTAL SURFACE AREA8 m

15 m

6 m

1. Decompose each net into different congruent figures. Then, find the area of each figure.

SURFACE AREA OF CUBES AND RECTANGULAR PRISMS

11 cm

4 cm

3 cm

LATERALSURFACE

AREA

• Lateral surface area is the ______________of the areas of the

surfaces of a solid except the ______________.

2. Find the lateral surface area of the rectangular prism.

3. Find the total surface area of the rectangular prism.

4. All of the surfaces of the cube below are being painted. How many square inches will be covered?

5. Find the lateral surface area of the cube.


Use your understanding of surface area to answer the questions below.


5 c

m

4.2 cm

2.9 cm

4 in

4 in

2.5

in

8 in

Name _____________________________________Date ____________________________Pd ______

Unit: Surface AreaHomework 2

Match each correct answer to a letter and complete the riddle below.


________________________

1

Find the total surface area of the cubic box below.

4

How many square centimeters of wrapping paper will be used to wrap the shoe box?

2

Find the lateral surface area of the prism.

5

Find the lateral surface area of the net of the cube below.

3

Find the total surface area of the cube.

6

A label is placed around the juice box below, not including the bases. Determine the surface area of the label.

WHAT IS THE KING OF THE PENCIL CASE?

D: 12 ft2 R: 29.04 cm2 P: 32.18 cm2 L: 36 ft2

T: 1,624 cm2 B: 45 ft2 E: 24 ft2 O: 16.4 cm2

H: 28 in2 M: 34 in2 I: 54 in2 U: 12.96 cm2

4 6 1 3 5 2 1 3

1.5 ft

2 ft

4 f

t

3 ft

2.2 cm

10 c

m

14 cm

1.8 cm

4 in

2 in

1.5 in

SURFACE AREA OF CUBES AND RECTANGULAR PRISMS

Determine the area of the two figures below.

Describe what is different about the two shapes and their areas.

________________________________________________________________________________________

________________________________________________________________________________________

1. 2.

Name _____________________________________Date ______________________________Pd______



SHAPE 1 SHAPE 2

FORMULA

PLUG IN VALUES

AREA

TOTAL SURFACE AREA

3. Decompose each net into different congruent figures. Then, find the area of each figure.

1

SURFACE AREA OF TRIANGULAR PRISMS

TRAINGULARPRISMS

• A triangular prism is composed of:

- three _____________________ faces

- two _____________________ bases

• Remember, the bases of a three-dimensional object ____________touch.

6 in

5.2

in

8.5

in

12 ft

7 ft

12 ft

7 ft

Shade the base of each of the figures below.

4. Find the lateral surface area of the triangular prism.

5. The chocolate candy below is being wrapped in a cardboard box. How many square centimeters are needed for the box?

6. A carpenter is building a unique jewelry box in the shape of a right triangular prism. The base has measurements of 4 inches, 3 inches, and 5 inches. How much wood will it take to complete the project if it is 6 inches tall?

7. Find the total surface area of the triangular prism.


Use your understanding of surface area to answer the questions below.


3.5

ft

7 ft

4 ft

4 ft

4 ft

2.2 cm16 cm

2.6 cm 3 cm

4 c

m

3 cm

9 cm

6 in

1

1. Find the total surface area of the net below. 2. The block of cheese shown below is wrapped in shrink wrap. How many square inches of shrink wrap are needed to cover the cheese?

3. Find the lateral surface area of the figure below.

4. The net of a triangular prism is shown below. Find the total surface area of the triangular prism.

Solve the problems below. Be sure to show your work. Figures are not drawn to scale.


Name _____________________________________Date ____________________________Pd ______


9 m

3 m

2.6 m

6 in

2 in

10 ft

9 ft

4 ft

8 ft

4.6 cm

15 cm

4 c

m5 c

m

SURFACE AREA OF TRIANGULAR PRISMS

Match the following three dimensional figures to the appropriate nets below.

1. 2. 3.

A. B. C.

D. E. F.

Name _____________________________________Date ____________________________Pd ______

Unit: Surface Area Quiz 1


Answers

1. ______________

2. ______________

3. ______________

4. ______________

5. ______________

6. ______________

7. ______________

8. ______________

9. ______________

10. _____________

4. The base of the rectangular prism is shaded. What is the lateral surface area?

5. A mini game cube is covered in different colors and has a side length of 1.8 inches. Which of the following would represent the amount of space covered in various colors?

A. 116.64 in2

B. 3.24 in2

C. 19.44 in2

D. 10.8 in2

Answer the questions below. Be sure to show your work.

QUIZ: SURFACE AREA OF PRISMS

16 cm

6 c

m

9.5 cm

10 c

m

2.5 cm

10 in

2.5 cm

9 in

2.5 cm

12 in

6 m

9.5

m

16 m

10 in

9 in

12 in

10 in9 in

12 in

12 in

16 cm

6 c

m

9.5 cm

8 c

m

11 ft3 ft

4.5 ft

©M

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6. The rectangular prism below has a total surface area of 198 in2. Use the net below to determine the missing dimension, x.

7. A net of a building block is shown below. What is the total surface area of the building block?

A. 120 cm2

B. 108 cm2

C. 96 cm2

D. 84 cm2

8. If the total surface area of a cube is 302.46 in2, which best describes the length of the side of the cube?

A. less than 5 in.B. between 5 in. and 6 in.C. between 6 in. and 7 in.D. greater than 7 in.

9. Find the total surface area of the net below.

10. A triangular prism is covered with a foil label. The label does not cover the two ends. How much foil is necessary to cover the prism?

A. 346.5 ft2

B. 336 ft2

C. 495 ft2

D. 247.5 ft2 16.5 ft

13 ft

5 ft

12 ft

45 in2 30 in2

24 in2

45 in2 30 in2

24 in2

6 in

4 in

4 cm

2 c

m

7.2

cm

x

4 c

m

3 cm

5 cm

9 cm

SURFACE AREA OF PYRAMIDS

• A pyramid is composed of a _________ and ___________________ faces.

The pyramid is named by the ___________ of the base.

• The ____________________________ , also called the slant height, is the

height of the triangular faces.

Which shapes make up the pyramids above? What is the key characteristic of a pyramid?

________________________________________________________________________________________

________________________________________________________________________________________

________________________________________________________________________________________

Name _____________________________________Date ______________________________Pd______



SHAPE 1 SHAPE 2

FORMULA

PLUG IN VALUES

AREA

TOTAL SURFACE AREA

7 mm

6 m

m

7 m

m

1. Decompose each net into different figures. Then, find the area of each figure.


Label the various parts of each pyramid below: base, faces, lateral height. Then, name the shape.

PYRAMID LATERAL SURFACE AREA TOTAL SURFACE AREA

2.

3.

4.

98 ft2

33 ft2

54 ft2

44 ft2

81 ft2

72 ft2

108 ft2

124 ft2

68 ft2

54 ft2

96 ft2

160 ft2


Draw a line connecting each pyramid to the appropriate lateral and total surface area.

Answer the questions below using your knowledge of surface area.

5. A triangular pyramid has four congruent faces. The triangular face measures 11 inches high and 8 inches across the base. What is the total surface area of the pyramid?

6. A pyramid has a square base with an area of 64 square centimeters. The triangular faces have a base of 8 centimeters and a height of 14 centimeters. What is the total surface area of the square pyramid?

4 f

t

6 ft

6 ft

9 ft

3 f

t

3 f

t

7 ft


4 ft

5 ft

4 ft

Name _____________________________________Date ____________________________Pd ______


Use your understanding of surface area of pyramids to answer the questions below.


1. Determine the lateral and total surface area of the pyramid.

Lateral Surface Area _____________________

Total Surface Area _____________________










5. Explain the difference between lateral and surface area below. If you are given the total surface area, then how could you determine the lateral surface area.

______________________________________________________________________________________

______________________________________________________________________________________

______________________________________________________________________________________


5 cm

8 cm

4 cm

8.2 cm

16 cm

6 cm6 cm

5.8 cm

3.5

cm

4.2 cm

6 c

m


Name _____________________________________Date ____________________________Pd ______


2. A square pyramid and a cube have the same total surface area. The length of each side of the base of the square pyramid is 12 meters. The width of the cube is 6 meters. What is the lateral height of the square pyramid?

Surface area can be used to solve __________________problems.

I KNOW: I NEED TO KNOW:

PLAN AND WORK: MY SOLUTION:



1. The cereal box shown at the right is cut from a piece of cardboard that measures 600 square inches. How many cereal boxes can be cut from this piece of cardboard?

8 in

12 in

2 in

PROBLEM SOLVING WITH SURFACE AREA

4. Decompose the shape below into two rectangular prisms. Then, determine the total surface area.

3. A shoe box is covered with packing paper before being shipped. The paper costs $0.01 per square inch. How much will it cost to cover three pairs of shoes?

16 in

8 in





10 in

3 cm

8 c

m


1. What is the total surface area of the package in plan A? Plan B?

2. What is the lateral surface area of the package in plan A? Plan B?

3. If it costs $0.15 per square inch for the wood, then what is the cost for plan A? Plan B?

4. If it costs $0.05 per square inch for the cardboard label, then what is the cost for plan A? Plan B?

5. Which plan will be more cost effective? By how much?

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

Name _____________________________________Date ____________________________Pd ______


A jewelry company is considering two different packages for their new bracelet. Both options are constructed as a wooden box with a cardboard label that covers the lateral surfaces. Use the information to answer the questions.


PLAN A PLAN B

3 in

2 in1 in

5 in2 in

5 in

2.8 in

PROBLEM SOLVING WITH SURFACE AREA

Name _____________________________________Date ______________________________Pd______

Unit: Surface AreaReview - CCSS

Solve each of the problems below. These represent the types of questions on your test. Be sure to ask questions if you need more help with a topic.

I CAN SOLVE PROBLEMS INVOLVING LATERAL AND TOTAL SURFACE AREA. 7.G6

1. A large game cube is wrapped with shrink wrap. How many square inches of shrink wrap will be used to wrap five game cubes?

2. What is the total surface area of the figure below?

3. What is the lateral surface area of the equilateral triangular pyramid below?

4. What is the total surface area of the square pyramid in square inches?

5. What is the total surface area of the rectangular prism?

6. Sketch a net that will not result in a cube.


8 m

15 m

6 m

8 in9 in

9 c

m

5.2 cm

SURFACE AREA UNIT STUDY GUIDE

I CAN SOLVE PROBLEMS INVOLVING LATERAL AND TOTAL SURFACE AREA. 7.G6

7. A square pyramid and a cube have the same surface area. The length of each side of the base of the square pyramid is 10 feet. The width of the cube is 6 feet. What is the slant height of the square pyramid?

A. 2.9 feetB. 5.8 feetC. 8.7 feetD. 11.6 feet

8. The pyramid pictured below has a total surface area of 336 inches squared. Find the missing lateral height, x.

9. Which of the rectangular prisms below has the greatest total surface area?

10. If the surface area of a cube is 390 cm2,then which best describes the length of the side of the cube?

A. less than 7 cmB. between 7 cm and 8 cmC. between 8 cm and 9 cmD. greater than 9 cm




I’VE GOT IT!What concepts can I ace on the test?

HELP!What concepts do I need to study?

14 in

4 in

8 in 40 in2 24 in2

15 in2

x

40 in2 24 in2

15 in2

5 in

3 in

6 in

12 in6 in

3 in

15 in6 in

12 in

x

12 in

A B

Name _____________________________________Date ______________________________Pd______

Unit: Surface AreaReview

Solve each of the problems below. These represent the types of questions on your test. Be sure to ask questions if you need more help with a topic.

I CAN SOLVE PROBLEMS INVOLVING LATERAL AND TOTAL SURFACE AREA.

1. A large game cube is wrapped with shrink wrap. How many square inches of shrink wrap will be used to wrap five game cubes?


3. What is the lateral surface area of the equilateral triangular pyramid below?


5. What is the total surface area of the rectangular prism?

6. Sketch a net that will not result in a cube.


8 m

15 m

6 m

8 in9 in

9 c

m

5.2 cm

SURFACE AREA UNIT STUDY GUIDE

I CAN SOLVE PROBLEMS INVOLVING LATERAL AND TOTAL SURFACE AREA.

7. A square pyramid and a cube have the same surface area. The length of each side of the base of the square pyramid is 10 feet. The width of the cube is 6 feet. What is the slant height of the square pyramid?

A. 2.9 feetB. 5.8 feetC. 8.7 feetD. 11.6 feet

8. The pyramid pictured below has a total surface area of 336 inches squared. Find the missing lateral height, x.

9. Which of the rectangular prisms below has the greatest total surface area?

10. If the surface area of a cube is 390 cm2,then which best describes the length of the side of the cube?

A. less than 7 cmB. between 7 cm and 8 cmC. between 8 cm and 9 cmD. greater than 9 cm




I’VE GOT IT!What concepts can I ace on the test?

HELP!What concepts do I need to study?

14 in

4 in

8 in 40 in2 24 in2

15 in2

x

40 in2 24 in2

15 in2

5 in

3 in

6 in

12 in6 in

3 in

15 in6 in

12 in

x

12 in

A B

1. A large game cube with a three inch side length is wrapped with shrink wrap. How many square inches of shrink wrap will be used to wrap ten game cubes?

A. 450 in2 B. 540 in2

C. 270 in2 D. 720 in2

2. The net below represents which 3D figure?

A. rectangular pyramidB. cubeC. rectangular prismD. square pyramid


4. A rectangular prism is shown below. What is the lateral surface area?

5. If the surface area of a cube is 390 cm2, then which best describes the length of the side of the cube?

A. less than 7 inB. between 7 in and 8 inC. between 8 in and 9 inD. greater than 9 in

6. The net below shows four equilateral triangles. What is the total surface area of the triangular pyramid in square feet?


Name _____________________________________Date ____________________________Pd ______

Solve the problems below. Be sure to show your thinking.


Unit: Surface AreaTest

13.1

cm

6 c

m

7 in

11

in

11 c

m

5 cm2 cm

A. 359.1 cm2

B. 275.1 cm2

C. 400cm2

D. 317.1 cm2

SURFACE AREA UNIT TEST

8. The pyramid pictured below has a total surface area of 156 feet squared. Find the missing measurement, x.

9. Anna has purchased three gifts for her closest friends. She decides to wrap them in holiday paper. How many square inches of wrapping paper will she need if the boxes are cubes with a side length of 7 inches?

A. 294 in2 B. 49 in2

C. 588 in2 D. 882 in2

10. A juice box is constructed from a cardboard net. How many inches of cardboard are needed for each juice box?

11. What is the lateral surface area of the rectangular pyramid below?

12. What is the surface area of the jewelry box that would need to be wrapped with wrapping paper?

A. 146 cm2

B. 292 cm2

C. 336 cm2

D. 672 cm2

13. What is the lateral surface area of the figure below?

14. What is the combined surface area of the two rectangular prisms?

A. 314 in2

B. 376 in2

C. 690 in2

D. 724 in2

Solve the problems below. Be sure to show your thinking.


7 cm

8 cm6 cm

6 ft

6 ft

x

9 f

t

18 f

t

20 ft

10 in

8 in

10 in6 in

8 in

9 in

5 in

8 ft4 in

2 in

1.5 in

THANK YOU FOR YOUR PURCHASE!mrscloughmath.weebly.com/.../113277025/surface_area...21-22 Surface Area...

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