1. Surface Area of a Rectangular Prism
Day 1

2. Warm Up Find the area of these 2-dimensional figures: 6 cm 8 in 6 cm
OBJECTIVE: SWBAT find the surface area of a rectangular prism
Find the area of these 2-dimensional figures: #1 #2
36 cm2
6 cm
88 in2
8 in
6 cm
11 in
Square
20 x 20 = 400 cm2
Circle
3.14 x 10 x 10 = 314 cm2
Square - Circle
400 cm2– 314 cm2
#3 Challenge Question
86 cm2
Radius =
10 cm
Side =
20 cm
Find the area of the red region in the square to the right.
Scaffolding 1

3. Warm Up Find the area of these 2-dimensional figures: 6 cm 8 in 6 cm
OBJECTIVE: SWBAT find the surface area of a rectangular prism
Find the area of these 2-dimensional figures: #1 #2
36 cm2
6 cm
88 in2
8 in
Square Area = side x side
Rectangle Area = length x width
6 cm
11 in
Square
20 x 20 = 400 cm2
Circle
3.14 x 10 x 10 = 314 cm2
Square - Circle
400 cm2– 314 cm2
#3 Challenge Question
86 cm2
Radius =
10 cm
Side =
20 cm
Find the area of the red region in the square to the right.
Area of a circle =
3.14 x radius x radius
Scaffolding 1

4. would like to pick up this building,…
Launch - Problem
For Valentine’s Day
, Godzilla…
would like to pick up this building,…
wrap it,…
and give it to Mrs. Godzilla.
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5. Launch - Problem
Wrapping paper is expensive! I want to use as little as possible. How could I calculate how much wrapping paper I would need to exactly cover the building without any paper overlapping?
Scaffolding
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6. Launch - Problem
Wrapping paper is expensive! I want to use as little as possible. How could I calculate how much wrapping paper I would need to exactly cover the building without any paper overlapping?
How might knowing the area of each side (or face) help you to find the amount of wrapping paper needed to cover the building?
Scaffolding
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7. Launch - Vocabulary
The exact amount of paper needed to cover a rectangular prism (or box) is called the Surface Area.
To help us discover how to calculate the surface area, we need to know how many faces a rectangular prism has. 1

8. A rectangular prism always has
Launch - Vocabulary
A rectangular prism always has
____ faces, or sides. 6
Side 2
Bottom
Back
Top
Side 1
Front
Height (H)
Width (W)
Length (L)
More About
Faces
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9. A rectangular prism has six faces.
Extension Vocabulary
Each side of a rectangular prism is called a face.
A rectangular prism has six faces.
Back to lesson

10. Launch - Vocabulary
To help us see all six faces of a rectangular prism, mathematicians sometimes unfold the rectangular prism to see a drawing called a net.
Top
Top
Front
Front
Side
Side
Side
Bottom
You can easily see all three pairs of faces in a net.
Back
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11. Practice – Independent Example
Let’s try an example…
So, how do we find the surface area of this rectangular prism?
Front
Back
Side 1
Side 2
Top
Bottom
Take a couple minutes to see how many faces you can find the area of. If you can, also try to find the total surface area.
4 cm
2 cm
3 cm
Scaffolding

12. Practice – Independent Example
Let’s try an example…
So, how do we find the surface area of this rectangular prism?
Back
Side 2
Front
Back
Side 1
Side 2
Top
Bottom
Take a couple minutes to see how many faces you can find the area of. If you can, also try to find the total surface area. 3 4 2
4 cm
2 cm
3 cm
Top
Front
Side
Bottom
Scaffolding

13. Practice – Guided Example
Front
Top
Side
Bottom
Back
Surface area of the rectangular prism
Remember:
= 4 cm x 3 cm
= 12 cm2
Back
Front
Side 2 3 4 2
= 4 cm x 3 cm
= 12 cm2
Back
Top
4 cm
2 cm
3 cm
Side 1
= 2 cm x 3 cm
= 6 cm2
Front
Side
Side 2
= 2 cm x 3 cm
= 6 cm2
Top
= 4 cm x 2 cm
= 8 cm2
Bottom
= 4 cm x 2 cm
= 8 cm2
Bottom +
52 cm2
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14. Explore - Class Work
Take a shot at solving some of the problems on the class work.
I’ll time you!
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15. Class work #1 Area of Front: 6 cm x 4 cm = 24 cm2
S I D E
Area of Front: 6 cm x 4 cm = 24 cm2 
Area of Back: 6 cm x 4 cm = 24 cm2
 Area of Top: 6 cm x 2 cm = 12 cm2
 Area of Bottom: 6 cm x 2 cm = 12 cm2
 Area of Side 1: 2 cm x 4 cm = 8 cm2
 Area of Side 2: 2 cm x 4 cm = 8 cm2
Back to Solutions

16. Class work #2 112 in2 Find the mistake(s) = 120 in2 S I D E
4 in x 2 in
= (8 in x 4 in) + (8 in x 4 in) + (8 in x 2 in) + (8 in x 2 in) + (8 in x 2 in) + (4 in x 2 in)
= 32 in in in in in in2
= 120 in2
112 in2
Back to Solutions

17. Class work #3 SA = AFront + ABack + ASide1 + ASide2 + ATop + ABottom
SA = 10 x x x x x x 4
SA = 60 cm cm cm cm cm cm2
SA = 248 cm2
Back to Solutions

18. Class work #4 This 3-D shape with all equal sides is called a Cube
SA = AFront + ABack + ASide1 + ASide2 + ATop + ABottom
SA = 7 x x x x x x 7
SA = 49 in in in in in in2
SA = 294 in2
This 3-D shape with all equal sides is called a Cube
Back to Solutions

19. Class work #5 SA = AFront + ABack + ASide1 + ASide2 + ATop + ABottom
SA = 5.4 x x 8+ 3 x x x x 3
SA = 43.2 cm cm cm cm cm cm2
SA = cm2
Back to Solutions

20. Class work #6 SA = AFront + ABack + ASide1 + ASide2 + ATop + ABottom
SA = 10 x ½ + 10 x ½ + 10 x ½ + 10 x ½ + ½ x ½ + ½ x ½
SA = 5 in in in in2 + ¼ in2 + ¼ in2
SA = 20 2/4 in2 = 20 ½ in2
Back to Solutions

21. Summary Question – Think – Pair – Share
Find the mistake(s) in the problem below. 6 12 4
Top
Side
Front
= 6 in x 12 in
= 72 in2
Back
Front
12 in
Side
= 4 in x 6 in
= 24 in2
= 4 cm x 12 cm = 48 in2
Top
= 6 in x 4 in
= 24 in2
Bottom
4 in +
= 288 in2
6 in
240 in2
The side is not 4 x 6, it’s 4 x 12!!
Scaffolding
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22. Exit Question 80 ft 40 ft 200 ft Front Back Side 1 Side 2 Top Bottom
Wrapping paper is expensive! I want to use as little as possible. How much wrapping paper would I need to exactly cover the building without any paper overlapping?
Front
Back
Side 1
Side 2
Top
Bottom
= 80 ft x 200 ft
= 16,000 ft2
40 ft
80 ft
200 ft
Front
Side
Top
= 80 ft x 200 ft
= 16,000 ft2
= 40 ft x 200 ft
= 8,000 ft2
= 40 ft x 200 ft
= 8,000 ft2
= 40 ft x 80 ft
= 3,200 ft2
= 40 ft x 80 ft
= 3,200 ft2
54,400 ft2
That’s a lot of paper! Thanks Honey!
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23. Surface Area of a Rectangular Prism
Day 2

24. Warm Up – Whole Class Review
OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism.
1. Find the area of the front, side, and top of this rectangular prism.
Front
= 36 in2
Side
= 12 in2
Side
Front
Top
12 in
4 in
3 in
Top
= 48 in2 +
96 in2
Surface Area = 96 in2
…right?
Agenda
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25. Warm Up – Whole Class Review
No!
No!
OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism.
No!
No!
No!
No!
Remember, there are six faces on a rectangular prism…
Front and Back
Side 1 and Side 2
Top and Bottom
No!
1. Find the area of the front, side, and top of this rectangular prism.
No!
Front
= 36 in2
No!
Side
= 12 in2
No!
No!
Side
Front
Top
12 in
4 in
3 in
No!
Top
= 48 in2 +
96 in2
Surface Area = 96 in2
…right?
Agenda
Scaffolding
show the net
wait..

26. Surface Area is the sum of all the faces.12
Top 4 4
You can easily see all
the faces when you
make a net. 4 12 4
Side
Side
Front 3 3 3 3 12 4 4
Side
Front
Top
12 in
4 in
3 in
Bottom 4 4 12
Back 3 3 12
Agenda

27. Warm Up – Whole Class Review
OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism.
For surface area, we need to find the sum the areas of all 6 faces.
1. Find the area of the front, side, and top of this rectangular prism.
Front
= 36 in2
Back
= 36 in2
Side
= 12 in2
Side
= 12 in2
Side
Front
Top
12 in
4 in
3 in
Top
= 48 in2
Bottom
= 48 in2
96 in2 +
Surface Area = 192 in2
Agenda
Scaffolding
show the net
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28. Launch – Whole Class Discussion
A formula uses only letters, numbers, and symbols to find a mathematical value.
You already know area formulas for some shapes:
Are you ready for some algebra?!
Length (L)
Width (W)
Rectangle
Area =
L x W = LW
Area =
½ b x h = ½bh
Triangle
base (b)
Height (h)
Circle
radius (r)
Area =
3.14 x r x r = πr2
MCAS
Reference Sheet
Agenda
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29. Explore: Equation for Surface Area – Partner Activity
With your partner, try to write a formula to find the surface area using L for length, W for width, and H for height. h l w
Length (l)
Height (h)
Width (w)
Top
Top
Side 1
Front
Height (h)
Front
Side
Side
Width (w)
Length (l)
Bottom
Don’t forget that there are six faces on a rectangular prism!
Back
Need a hint? Write the formulas for each face separately, then see if you can put them together.
Agenda
Scaffolding
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30. Explore: Equation for Surface Area – Whole Class
SA = 2 LH
+ WH 2
+ LW 2
Area of the Front =
Length x Height
Area of the Back =
Length x Height
Area of Side 1 =
Width x Height
Area of Side 2 =
Width x Height
Area of Top =
Length x Width
Area of Bottom =
Length x Width
Length
Width
Height
Top
Back
Side 2
Side 1
Front
Height (h)
Bottom
Width (w)
Length (l)
Agenda
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31. Explore SA = SA = 2 WH +2 LW + 2 LH 2 LH + 2 WH + 2 LW
One cool thing about this equation is that it doesn’t matter in what order you find the area of the faces.
SA =
SA = 2 WH +2 LW + 2 LH 2 LH
+ 2 WH
+ 2 LW
This is an example of the Commutative Property of Addition ( a + b = b + a )
Agenda 1

32. Find the surface area of this rectangular prism:
Practice
Find the surface area of this rectangular prism:
Let’s try an example…
SA = 2LH + 2WH + 2LW
Top
6 cm
3 cm
4 cm
Front
2 x 6 cm x 4 cm
= 48 cm2
Side +
2 x 3 cm x 4 cm
= 24 cm2 +
2 x 3 cm x 6 cm
= 36 cm2
108 cm2
Agenda
Scaffolding
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33. Find the surface area of this rectangular prism:
Practice
Find the surface area of this rectangular prism:
Let’s try an example…
SA = 2LH + 2WH + 2LW 4 6 3
6 cm
3 cm
4 cm
Top
Front
2 x 6 cm x 4 cm
= 48 cm2
Side +
2 x 3 cm x 4 cm
= 24 cm2 +
2 x 3 cm x 6 cm
= 36 cm2
108 cm2
Agenda
Scaffolding
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34. Class Work
Take a shot at solving some of the problems on the class work.
I’ll time you!
Agenda
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35. Review Class work #1 SA = 2(L x H) + 2(W x H) + 2(L x W)
SA = 2( 8 x 5 ) + 2( 4 x 5 ) + 2( 8 x 4 )
SA = 2 (40 cm2) + 2( 20 cm2) + 2( 32 cm2)
SA = 80 cm cm cm2
SA = 184 cm2
Back to Solutions
Agenda

36. Review Class work #2 SA = 2(L x H) + 2(W x H) + 2(L x W)
SA = 2( 12 x 4 ) + 2( 3 x 4 ) + 2( 12 x 3 )
SA = 2 (48 in2) +2( 12 in2) + 2( 36 in2)
SA = 96 in in in2
SA = 192 in2
Back to Solutions
Agenda

37. Review Classwork #3
Explain in words how to find the surface area of a rectangular prism.
Answers will vary.
Back to Solutions
Agenda

38. 126 in2 Review Class work #4 Find the mistake(s) = 120 in2 6 in x 3 in
= (6 in x 5 in) + (6 in x 5 in) + (3 in x 5 in) + (3 in x 5 in) + (6 in x 3 in) + (6 in x 6 in)
= 30 in in in in in in2
= 120 in2
15 in2
18 in2
126 in2
Back to Solutions
Agenda

39. Review Class work #5 SA = 2(L x H) + 2(W x H) + 2(L x W)
SA = 2( 10 x 7 ) + 2( 4 x 7 ) + 2( 10 x 4 )
SA = 2 (70 in2) + 2( 28 in2) + 2( 40 in2)
SA = 140 in in in2
SA = 276 in2
Back to Solutions
Agenda

40. Exit Ticket
On a separate piece of notebook paper to be handed in to your teacher:
Choose one of the following and answer on your paper:
1. Explain how to find surface area.
2. Find the surface area of this rectangular prism.
3. If you aren’t sure about #1 or #2, what is confusing to you about surface area? 5 4 2
5 cm
2 cm
4 cm
Agenda
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