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

2 Lesson Objective SWBAT describe the formula (shortcut) to calculate the surface area of a rectangular prism. Lesson Description This is the second of two lessons on surface area. The focus of this lesson is to encourage students to see the efficiency of using a formula for calculation. Students are encouraged to work in pairs to explore and discover a formula or shortcut for finding surface area. However, students are not left on their own to realize full understanding of a formula. After exploring with a partner for fewer than 5 minutes the lesson guides them through the derivation of one formula they can consistently apply and use. This way students can better understand what the formula means and have an efficient means of calculating surface area of a rectangular prism in every situation. The lesson begins with a warm-up which is more fully explored in the review slide in which students use error analysis intended to guide students away from a very common mistake in calculating surface area. Students are reminded of many area formulas they have previously learned to bring to mind general algebra conventions as well as specific expressions for area calculations. After exploring and the direct instruction on one reliable and simple surface area formula students are asked to apply the formula in guided and independent practice. 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 Face Materials Other website embedded in this lesson: Applet used to check class work answers Applet used to check class work answers Scaffolding As in the previous lesson, scaffolding buttons produce an overlay of numbers indicating the values for the dimensions of each face. Students are also aided by working with a partner to find the formula, animation that deconstructs the rectangular prism into 6 faces and consistent color-coding. Struggling students should be encouraged to break the problem down and find area of each face then put them together and should gradually come to see the efficiency of the formula. Enrichment Advanced Objective- SWBAT use conventions of algebra to rewrite the surface area formula as several equivalent expressions. Students seeking enrichment can refer to the commutative property and might even be helped to understand the distributive property in writing equivalent formulas Online Resources for Absent Students StudyZone 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 After Before Surface area of rectangular prisms brings together learning about the area of two- dimensional polygons (2G2, 3G5, 3G6, 3G7) with the idea that 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 There are many ways to express the formula for surface area of a rectangular prism, including: 2LH + 2WH + 2LW (used in this lesson) 2(LH + WH + LW) and 2B + Ph (where B is the area of the base face and P is the perimeter of the base) – not used in this lesson What is most important is that students understand what surface area is (the sum of the areas of each face) and how to derive a formula that adheres to the conventions of algebra.

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 OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism. Agenda 1 wait.. 5 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 OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism. Agenda 1 wait.. 6 Scaffolding

Warm Up – Whole Class Review 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 + OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism. Agenda 1 wait.. 7

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. Warm Up – Whole Class Review 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 faces on a rectangular prism… Front and Back Side 1 and Side 2 Top and Bottom Scaffolding show the net Agenda wait.. 8

Surface Area is the sum of all the faces. Side Front Top 12 in 4 in 3 in You can easily see all the faces when you make a net. Agenda 9

Warm Up – Whole Class Review 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. 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. Agenda 1 wait.. 10 Scaffolding show the net

Agenda: OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism. Agenda 1) Warm Up – Individual Work and Whole Class Review 2) Launch – Whole class discussion 3) Explore: Equation for Surface Area – Partner Activity and Whole Class 4) Practice 5) Class work 6) Review Class work 7) Exit Ticket - Individual Work to be handed in to teacher 11

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) Area = L x W = LW Area = ½ b x h = ½bh Agenda 1 wait.. 12 MCAS Reference Sheet

Return to Lesson Agenda 13 Return

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. Side 1 Front Length (l) Width (w) Top Height (h) Don’t forget that there are six faces on a rectangular prism! Front Top Side Bottom Back Agenda wait.. 14 Scaffolding

Need a hint? Write the formulas for each face separately, then see if you can put them together. 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. Side 1 Front Length (l) Width (w) Top Height (h) Length (l) Height (h) Width (w) Don’t forget that there are six faces on a rectangular prism! Front Top Side Bottom Back Agenda wait.. 15 hh hh h h l l l l l ww w w w ww w Scaffolding

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 = 222 Length Width Height Explore: Equation for Surface Area – Whole Class Agenda 1 wait WH+ LW

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 ) Agenda 1 17 Explore

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 Practice Agenda 1 wait.. 18 Scaffolding

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 Practice Agenda 1 wait.. 19 Scaffolding

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

Click the answers above to see worked solutions 4) 4 mistakes and SA = 126 in 2 3) Answers will vary. 2) SA = 192 in 2 1) c) SA = 184 cm 2 5) SA = 276 in 2 Review Class Work Internet Applet that can also be used to check answers Grade your work. Which problems do you need help on? Agenda 21

Review 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 Agenda 22

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 Back to Solutions Agenda 23 Review Class work #2

Explain in words how to find the surface area of a rectangular prism. Answers will vary. Back to Solutions Agenda 24 Review Classwork #3

= (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 in 2 = 120 in 2 Find the mistake(s) 18 in 2 15 in in 2 6 in x 3 in Back to Solutions Agenda 25 Review Class work #4

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 in 2 ) + 2( 28 in 2 ) + 2( 40 in 2 ) SA = 140 in in in 2 SA = 276 in 2 Back to Solutions Agenda 26 Review Class work #5

5 cm 2 cm 4 cm 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? Agenda wait.. 27