21 st Century Lessons Surface Area of a Rectangular Prism Day 1 (of 2) Mrs. Thompson Level 1

2 Lesson Objective SWBAT find the surface area of a rectangular prism. Lesson Description This lesson is bookended with a comical context designed to engage students and provide a reason for the direct instruction. Animation and color coding are used to highlight the structure of a rectangular prism – there are three identical pairs of faces, one of each is visible from a traditional perspective drawing. The lesson begins with a warm-up that establishes students can already find the area of rectangles. Vocabulary is reviewed after the warm-up and students are asked to distinguish between 2D and 3D shapes in a Think-Pair-Share. The lesson is launched with Godzilla’s Problem which is revisited in the exit question. Animation is used to show the structure of a rectangular prism then students are encouraged to attempt to calculate surface area before a formal definition and procedure are established. Students are then guided through the steps of calculating each of three pairs of faces and finding the sum of all 6 faces for the same problem. There is a link to a website with an animation showing all 6 faces as a net. Students then apply this understanding and procedure by attempting several class work problems in pairs or small groups. To review, teachers may select which problems to highlight from the answer slide based on feedback from students or observation of student work in class. The summary question asks students to work in a Think-Pair-Share format to find a calculation error. Finally, students will answer the exit question which revisits Godzilla’s Problem so you can informally asses their learning. The homework provides students the opportunity to practice, and reinforces, the key concepts from class. Lesson Overview (1 of 3)

3 Lesson Vocabulary Surface Area Faces Materials * Calling Sticks * Class Work Handouts * Homework Handouts Links to applets embedded in lesson: Net of a CubeNet of a Cube, Net for Class Example, Applet for Class Work Answers, Extra PracticeNet for Class ExampleApplet for Class Work AnswersExtra Practice Scaffolding Students may have trouble determining which dimensions are used for each face of the prism. Scaffolding buttons are provided that will place an overlay on each image showing the dimensions for each face. Some students may “see” the problem better if the prism is redrawn as a net. Use the “extension” buttons and “applet” buttons to show nets for the given examples. Additionally students are encouraged to work in pairs or small groups for all class work problems in this lesson since it is the first day with this topic. Enrichment Advanced Objective: Students will be able to visualize rectangular prisms as two- dimensional nets. Students can be shown the extension slides and applets that transform prisms to nets. Students can also solve surface area problems on this website. website Online Resources for Absent Students StudyZone Lesson Lesson Overview (2 of 3)

4 Lesson Overview (3 of 3) Common Core State Standard 6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real- world and mathematical problems. Before and AfterBefore: Surface area of rectangular prisms brings together learning about the area of two-dimensional polygons (2G2, 3G5, 3G6, 3G7) with the idea that the surface area of three-dimensional shapes are a composite of a set number of two-dimensional shapes (1G2). After: In 7 th grade students will apply this understanding to real- world situations (7G6) and in high school these understandings will be applied to taking two-dimensional cross-sections of 3D shapes (G- GMD4), using geometric shapes to describe and model real-life objects (G-MG1) and applying geometric methods to solve design problems (G-MG3). Topic Background Surface area Surface area is equal to the sum of the areas of the faces.

Warm Up OBJECTIVE: SWBAT find the surface area of a rectangular prism Find the area of these 2-dimensional figures: 6 cm #1 11 in 8 in #2 88 in 2 36 cm Scaffolding

Warm Up OBJECTIVE: SWBAT find the surface area of a rectangular prism Find the area of these 2-dimensional figures: 6 cm #1 11 in 8 in #2 88 in 2 Square Area = side x side Rectangle Area = length x width 36 cm Scaffolding

Agenda: OBJECTIVE: SWBAT find the surface area of a rectangular prism 1) Warm Up 2) Getting Ready - Calling Stick Activity and Think-pair-share 3) Launch - Problem, Vocabulary 4) Practice - Class Example (Independent and Guided) 5) Explore - Class work with partners 6) Summary – Whole class review of class work, Think-Pair-Share, Exit Question 7

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 8

Getting Ready – Think – Pair – Share What similarities and differences do you see between these shapes? A C SquareCube Rectangle Rectangular Prism B D 9

Launch - Problem For Valentine’s Day would like to pick up this building,… wrap it,… and give it to Mrs. Godzilla., Godzilla… 1 wait.. 10

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? Launch - Problem 1 wait.. 11 Scaffolding

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? Launch - Problem 1 wait.. 12 Scaffolding

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 13

Side 2 Bottom Back Top Side 1 Front Length (L) Width (W) Height (H) A rectangular prism always has ____ faces, or sides. 6 Launch - Vocabulary 1 wait.. 14 More About Faces

Extension Vocabulary Each side of a rectangular prism is called a face. A rectangular prism has six faces. Back to lesson 15

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. Front Side Top Front Top Side Bottom Back Net of a cube You can easily see all three pairs of faces in a net. Internet applet: 1 wait.. 16

4 cm 2 cm 3 cm 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. Practice – Independent Example So, how do we find the surface area of this rectangular prism? Let’s try an example… 17 Scaffolding

4 cm 2 cm 3 cm Front Side Top Front Back Side 1 Side 2 Top Bottom Back Side 2 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. Practice – Independent Example So, how do we find the surface area of this rectangular prism? Let’s try an example… 18 Scaffolding

Surface area of the rectangular prism 4 cm 2 cm 3 cm 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 Back Side 2 Bottom Practice – Guided Example Back Side 1 Side 2 Top Bottom Front Top Side Bottom Back Remember: 1 wait.. 19

Take a shot at solving some of the problems on the class work. I’ll time you! Explore - Class Work wait.. 20

4) SA = 294 in 2 (cube) 3) SA = 248 cm 2 2) 2 mistakes and SA = 112 in 2 1) b) push for answers 5) SA = cm 2 Summary - Review Answers from Class Work – Click on the answers below to see worked solutions Internet Applet that can also be used to check answers 6) SA = 20 ½ in 2 21

Class work #1 Back to Solutions Area of Front: 6 cm x 4 cm = 24 cm 2 Area of Back: 6 cm x 4 cm = 24 cm 2 Area of Top: 6 cm x 2 cm = 12 cm 2 Area of Bottom: 6 cm x 2 cm = 12 cm 2 Area of Side 1: 2 cm x 4 cm = 8 cm 2 Area of Side 2: 2 cm x 4 cm = 8 cm 2 S I D E 22

Class work #2 Back to Solutions = (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 in 2 = 120 in 2 Find the mistake(s) 4 in x 2 in 112 in 2 S I D E 23

Class work #3 Back to Solutions SA = A Front + A Back + A Side1 + A Side2 + A Top + A Bottom SA = 10 x x x x x x 4 SA = 60 cm cm cm cm cm cm 2 SA = 248 cm 2 24

Class work #4 Back to Solutions SA = A Front + A Back + A Side1 + A Side2 + A Top + A Bottom SA = 7 x x x x x x 7 SA = 49 in in in in in in 2 SA = 294 in 2 This 3-D shape with all equal sides is called a Cube 25

SA = A Front + A Back + A Side1 + A Side2 + A Top + A Bottom SA = 5.4 x x 8+ 3 x x x x 3 SA = 43.2 cm cm cm cm cm cm 2 SA = cm 2 Class work #5 Back to Solutions S I D E 26

Class work #6 Back to Solutions SA = A Front + A Back + A Side1 + A Side2 + A Top + A Bottom SA = 10 x ½ + 10 x ½ + 10 x ½ + 10 x ½ + ½ x ½ + ½ x ½ SA = 5 in in in in 2 + ¼ in 2 + ¼ in 2 SA = 20 2/4 in 2 = 20 ½ in 2 F R O N T S I D E 27

Find the mistake(s) in the problem below. Front Top Side 6 in 12 in 4 in 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 1 wait.. 28 Scaffolding

Find the mistake(s) in the problem below. Front Top Side 6 in 12 in 4 in 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 1 wait.. 29 Scaffolding

Exit Question 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? 40 ft 80 ft 200 ft Front Side Top That’s a lot of paper! Thanks Honey! Front Back Side 1 Side 2 Top Bottom = 80 ft x 200 ft= 16,000 ft 2 = 80 ft x 200 ft= 16,000 ft 2 = 40 ft x 200 ft= 8,000 ft 2 = 40 ft x 200 ft= 8,000 ft 2 = 40 ft x 80 ft= 3,200 ft 2 = 40 ft x 80 ft= 3,200 ft 2 54,400 ft 2 1 wait.. 30