Surface Area of a Rectangular Prism Day 1

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

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

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. wait.. 1

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 wait.. 1

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 wait.. 1

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

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 wait.. 1

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

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 wait.. 1

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

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

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 wait.. 1

Explore - Class Work Take a shot at solving some of the problems on the class work. I’ll time you! wait..

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

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 in2 + 32 in2 + 16 in2 + 16 in2 + 8 in2 + 8 in2 = 120 in2 112 in2 Back to Solutions

Class work #3 SA = AFront + ABack + ASide1 + ASide2 + ATop + ABottom SA = 10 x 6 + 10 x 6 + 4 x 6 + 4 x 6 + 10 x 4 + 10 x 4 SA = 60 cm2 + 60 cm2 + 24 cm2 + 24 cm2 + 40 cm2 + 40 cm2 SA = 248 cm2 Back to Solutions

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 7 + 7 x 7 + 7 x 7 + 7 x 7 + 7 x 7 + 7 x 7 SA = 49 in2 + 49 in2 + 49 in2 + 49 in2 + 49 in2 + 49 in2 SA = 294 in2 This 3-D shape with all equal sides is called a Cube Back to Solutions

Class work #5 SA = AFront + ABack + ASide1 + ASide2 + ATop + ABottom SA = 5.4 x 8 + 5.4 x 8+ 3 x 8 + 3 x 8 + 5.4 x 3 + 5.4 x 3 SA = 43.2 cm2 +43.2 cm2 + 24 cm2 + 24 cm2 + 16.2 cm2 + 16.2 cm2 SA = 166.8 cm2 Back to Solutions

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 in2 + 5 in2 + 5 in2 + 5 in2 + ¼ in2 + ¼ in2 SA = 20 2/4 in2 = 20 ½ in2 Back to Solutions

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 wait.. 1

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! wait.. 1

Surface Area of a Rectangular Prism Day 2

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 wait.. 1

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..

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

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 wait.. 1

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 wait.. 1

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 wait..

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 wait.. 1

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

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 wait.. 1

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 wait.. 1

Class Work Take a shot at solving some of the problems on the class work. I’ll time you! Agenda wait..

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 cm2 + 40 cm2 + 64 cm2 SA = 184 cm2 Back to Solutions Agenda

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 in2 + 24 in2 + 72 in2 SA = 192 in2 Back to Solutions Agenda

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

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 in2 + 30 in2 + 15 in2 + 8 in2 + 18 in2 + 36 in2 = 120 in2 15 in2 18 in2 126 in2 Back to Solutions Agenda

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 in2 + 56 in2 + 80 in2 SA = 276 in2 Back to Solutions Agenda

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 wait..