surface area of a rectangular prism. getting ready – calling stick activity what is the name of...
TRANSCRIPT
Surface Area of a Rectangular Prism
Getting Ready – Calling Stick Activity
What is the name of shape A?
A
What is the name of shape B?
C
Square Cube
Rectangle Rectangular Prism
What is the name of shape C?What is the name of shape D?
B
D
Getting Ready – Think – Pair – Share
What similarities and differences do you see between any of these shapes?
A
C
Square Cube
Rectangle Rectangular Prism
B
D
Side 2
Bottom
BackTop
Side 1Front
Length (L)Width (W)
Height (H)
A rectangular prism always has____ sides, or faces.6
Extension
Calculating Surface Area
Calculating Surface Area
To help us see all six faces of a rectangular prism, mathematicians sometimes unfold the
box to see a drawing called a net.
Net of a cube Net FacesInternet Applet Vocabulary
Back to lesson
Vocabulary
When a box is unfolded so you can see all the sides as a flat pattern, this is called it’s net.
Net of a Rectangular PrismRectangular Prism
BackBack to lesson
Vocabulary
Each side of a rectangular prism is called a face.
A rectangular prismhas six faces.
BackBack to lesson
So, how do we find the surface area of this rectangular prism?
4 cm2 cm
3 cm
Answer
Internet Applet
FrontSide
Top
Front = 4 cm x 3 cm = 12 cm2
= 4 cm x 3 cm = 12 cm2
= 2 cm x 3 cm = 6 cm2
= 2 cm x 3 cm = 6 cm2
= 4 cm x 2 cm = 8 cm2
= 4 cm x 2 cm = 8 cm2
52 cm2+
Scaffolding
3 34
422
BackSide 2
Bottom
Example
BackSide 1Side 2
TopBottom
Find the surface area
Calculate the area of your rectangular prism
Find the mistake(s) in the problem below.
Front
Top
Side
6 in
12 in
4 in
Scaffolding
6
12
46
4
12
Front = 6 in x 12 in = 72 in2
Back = 6 in x 12 in = 72 in2
Side = 4 in x 6 in = 24 in2
Side = 4 in x 6 in = 24 in2
Top = 6 in x 4 in = 24 in2
Bottom = 6 in x 4 in = 24 in2
240 in2+
The side is not 4 x 6, it’s 4 x 12!!
= 4 cm x 12 cm = 48 in2
= 4 cm x 12 cm = 48 in2
= 288 in2
Summary Question – Think – Pair – Share
OBJECTIVE: SWBAT find the surface area of a rectangular prism
Scaffolding
Warm Up
1. Find the area of the front, side, and top of this rectangular prism.
SideFront
Top
12 in 4 in3 in
3 3 4
4 12
12 Front
Side
Top
= 3 in x 12 in
= 3 in x 4 in
= 4 in x 12 in
= 36 in2
= 12 in2
= 48 in2
2) Find the circumference and area of a circle with radius 5 cm.
Radius = 5 cm
C = 2πr = 2 x 3.14 x 5 cm = 31.4 cm
A = πr2 = 3.14 x 5 cm x 5 cm = 78.5 cm2
Summarize – Whole Class DiscussionOBJECTIVE: SWBAT find the surface area of a rectangular prism
1. Find the area of the front, side, and top of this rectangular prism.
SideFront
Top
12 in 4 in3 in
FrontSideTop
= 36 in2
= 12 in2
= 48 in2
96 in2
…right?Surface Area = 96 in2
+
1. Find the area of the front, side, and top of this rectangular prism.
Summarize – Whole Class DiscussionOBJECTIVE: SWBAT find the surface area of a rectangular prism
SideFront
Top
12 in 4 in3 in
FrontSideTop
= 36 in2
= 12 in2
= 48 in2
96 in2
+
…right?Surface Area = 96 in2
No! No!
No! No!No!No!
No!No!No! No!
No!No!
Remember, there are six sides to a rectangular prism…• Front and Back• Side 1 and Side 2• Top and Bottom
Summarize – Whole Class DiscussionOBJECTIVE: SWBAT find the surface area of a rectangular prism
SideFront
Top
12 in 4 in3 in
FrontSideTop
= 36 in2
= 12 in2
= 48 in2
Back = 36 in2
Side = 12 in2
Bottom = 48 in2
96 in2 96 in2+
Surface Area = 192 in2
1. Find the area of the front, side, and top of this rectangular prism.
Agenda:
1) Warm Up – Individual Work 2) Launch – Whole class discussion3) Explore: Making the Equation for Surface Area –
Partner Activity4) Class work5) Review Class work6) Summary7) Exit Ticket – Individual Work to be
handed in to teacher
OBJECTIVE: SWBAT find the surface area of a rectangular prism
Launch – Whole Class Discussion
Are you ready for some algebra?!
A formula uses only letters, numbers, and symbols to find a mathematical value.You already know area formulas for some shapes:
Length (L)
Width (W)Rectangle
Triangle
base (b)
Height (h)
Circle radius (r)
Area = L x W
Area = ½ b x h
Area = 3.14 x r x r = πr2
Scaffolding
Need a hint? Write the formulas for the front, side 1, and the top.Then write the formulas for the back, side 2, and the bottom.
ExploreWith your partner, try to write a formula to find the surface area using l for length, w for width, and h for height.
BackSide 2
Bottom
Side 1Front
Length (l)Width (w)
Top
Height (h) Length (l)
Length (l)
Height (h) Height (h)
Width (w) Width (w)
Don’t forget that thereare six sides on arectangular prism!
BackSide 2
Bottom
Side 1Front
Length (l)Width (w)
Height (h)
Area of the Front =
SA = Length x Height
LH
Area of the Back = Length x HeightArea of Side 1 =Area of Side 2 =
Top
Width x Height
Length x WidthWidth x Height
Area of Top =
Length x WidthArea of Bottom =
2 + WH2 + LW2
Length
LengthWidth Width
Height Height
Scaffolding
Formula for Surface Area – Whole Class
SA = LH WH+ 2 LW2 + 2
One cool thing about this equation is that it doesn’t matter in what order you find the area of the faces.
SA = 2 WH +2 LW + 2 LH
This is an example of the Commutative Property of Addition ( a + b = b + a )
Find the surface area of this rectangular prism:
6 cm3 cm
4 cm
Let’s try an example…
SA = 2LH + 2WH + 2LW
Front 2 x 6 cm x 4 cm = 48 cm2
2 x 3 cm x 4 cm
Side
= 24 cm2
2 x 3 cm x 6 cm
Top
= 36 cm2
108 cm2
+
+
4 46
633
Scaffolding
Practice
Take a shot at solving some of the problems on the class
work.
I’ll time you!
Class Work
Class work #1
Back to Solutions
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 cm2 + 40 cm2 + 64 cm2
SA = 184 cm2
Class work #2
Back to Solutions
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 in2 + 24 in2 + 72 in2
SA = 192 in2
5 cm2 cm
4 cm55
4 4
2 2
Scaffolding
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 aboutsurface area?
Surface Area of a Prism
Prism Surface Area FormulaTop : lw
Bottom : lwFront : hlBack : hlLeft : hw
Right : hw
Total : lw + lw + hl + hl + hw + hw
: 2lw + 2hl + 2hw
: 2(lw + hl + hw)
21st Century Lessons
Thanks to Sarita ThomasShane Ulrich
Surface Area of a Rectangular PrismLesson