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 RectangleRectangular 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 SquareCube Rectangle Rectangular Prism B D

Side 2 Bottom Back Top Side 1 Front Length (L) Width (W) Height (H) A rectangular prism always has ____ sides, or faces. 6 Extension 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 cubeNetFaces Internet AppletVocabulary 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 Prism Rectangular Prism BackBack to lesson

Vocabulary Each side of a rectangular prism is called a face. A rectangular prism has six faces. BackBack to lesson

So, how do we find the surface area of this rectangular prism? 4 cm 2 cm 3 cm Answer Internet Applet Front Side Top Front = 4 cm x 3 cm= 12 cm 2 = 4 cm x 3 cm= 12 cm 2 = 2 cm x 3 cm= 6 cm 2 = 2 cm x 3 cm= 6 cm 2 = 4 cm x 2 cm= 8 cm 2 = 4 cm x 2 cm= 8 cm 2 52 cm 2 + Scaffolding Back Side 2 Bottom Example Back Side 1 Side 2 Top Bottom

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 Front = 6 in x 12 in= 72 in 2 Back = 6 in x 12 in = 72 in 2 Side= 4 in x 6 in= 24 in 2 Side= 4 in x 6 in= 24 in 2 Top= 6 in x 4 in = 24 in 2 Bottom= 6 in x 4 in= 24 in in 2 + The side is not 4 x 6, it’s 4 x 12!! = 4 cm x 12 cm = 48 in 2 = 288 in 2 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. Side Front Top 12 in 4 in 3 in Front Side Top = 3 in x 12 in = 3 in x 4 in = 4 in x 12 in = 36 in 2 = 12 in 2 = 48 in 2 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 = πr 2 = 3.14 x 5 cm x 5 cm = 78.5 cm 2

Summarize – Whole Class Discussion OBJECTIVE: SWBAT find the surface area of a rectangular prism 1. Find the area of the front, side, and top of this rectangular prism. Side Front Top 12 in 4 in 3 in Front Side Top = 36 in 2 = 12 in 2 = 48 in 2 96 in 2 …right?Surface Area = 96 in 2 +

1. Find the area of the front, side, and top of this rectangular prism. Summarize – Whole Class Discussion OBJECTIVE: SWBAT find the surface area of a rectangular prism Side Front Top 12 in 4 in 3 in Front Side Top = 36 in 2 = 12 in 2 = 48 in 2 96 in 2 + …right?Surface Area = 96 in 2 No! Remember, there are six sides to a rectangular prism… Front and Back Side 1 and Side 2 Top and Bottom

Summarize – Whole Class Discussion OBJECTIVE: SWBAT find the surface area of a rectangular prism Side Front Top 12 in 4 in 3 in Front Side Top = 36 in 2 = 12 in 2 = 48 in 2 Back = 36 in 2 Side = 12 in 2 Bottom = 48 in 2 96 in 2 + Surface Area = 192 in 2 1. Find the area of the front, side, and top of this rectangular prism.

Agenda: 1) Warm Up – Individual Work 2) Launch – Whole class discussion 3) Explore: Making the Equation for Surface Area – Partner Activity 4) Class work 5) Review Class work 6) Summary 7) 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 = πr 2

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. Explore With your partner, try to write a formula to find the surface area using l for length, w for width, and h for height. Back Side 2 Bottom Side 1 Front Length (l) Width (w) Top Height (h) Length (l) Height (h) Width (w) Don’t forget that there are six sides on a rectangular prism!

Back Side 2 Bottom Side 1 Front Length (l) Width (w) Height (h) Area of the Front = SA = Length x Height LH Area of the Back = Length x Height Area of Side 1 = Area of Side 2 = Top Width x Height Length x Width Width x Height Area of Top = Length x Width Area of Bottom = 2+ WH2+ LW2 Length Width Height Scaffolding Formula for Surface Area – Whole Class

SA = LH WH + 2 LW 2+ 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 cm 3 cm 4 cm Let’s try an example… SA = 2LH + 2WH + 2LW Front 2 x 6 cm x 4 cm = 48 cm 2 2 x 3 cm x 4 cm Side = 24 cm 2 2 x 3 cm x 6 cm Top = 36 cm cm 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 cm 2 ) + 2( 20 cm 2 ) + 2( 32 cm 2 ) SA = 80 cm cm cm 2 SA = 184 cm 2

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 in 2 ) + 2( 12 in 2 ) + 2( 36 in 2 ) SA = 96 in in in 2 SA = 192 in 2

5 cm 2 cm 4 cm 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 about surface area?

Surface Area of a Prism Prism Surface Area Formula Top: lw Bottom: lw Front: hl Back: hl Left: hw Right: hw Total : lw + lw + hl + hl + hw + hw : 2lw + 2hl + 2hw : 2(lw + hl + hw)

21 st Century Lessons Thanks to Sarita Thomas Shane Ulrich Surface Area of a Rectangular Prism Lesson