21st Century Lessons

Surface Area of a Rectangular PrismDay 2 (of 2)

Mrs. ThompsonLevel 1

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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)

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Lesson Vocabulary Surface AreaFace

Materials www.online-stopwatch.com, Other website embedded in this lesson: 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)

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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).AfterIn 7th 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 lessonWhat 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.

SideFront

Top

12 in 4 in3 in

Front

Side

Top

= 3 in x 12 in

= 3 in x 4 in

= 4 in x 12 in

= 36 in2

= 12 in2

= 48 in2

OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism.

Agenda1

wait..

5 Scaffolding

Warm Up – Whole Class Review

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

+

OBJECTIVE: SWBAT describe and use the shortcut to calculate the surface area of a rectangular prism.

Agenda1

wait..

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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

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

faces on a rectangular prism…• Front and Back• Side 1 and Side 2• Top and Bottom

Scaffoldingshow the net

Agendawait..

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Warm Up – Whole Class Review

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.

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.

Agenda1

wait..

10 Scaffoldingshow 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 discussion3) Explore: Equation for Surface Area – Partner Activity and Whole Class

4) Practice5) Class work6) Review Class work

7) Exit Ticket - Individual Work to be handed in to teacher

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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

Agenda1

wait..

12MCAS

Reference Sheet

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 1Front

Length (l)Width (w)

Top

Height (h)

Don’t forget that thereare six faces on arectangular prism!

Front

Top

SideSide

Bottom

Back

Agendawait..

14Scaffolding

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 Height

Area of Side 1 =

Area of Side 2 =

Top

Width x Height

Length x Width

Width x Height

Area of Top =

Length x WidthArea of Bottom =

2 2 2

Length

LengthWidth Width

Height Height

Explore: Equation for Surface Area – Whole Class

Agenda1

wait..

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+ WH + LW

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 )

Agenda1

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Explore

Find the surface area of this rectangular prism:

6 cm3 cm

4 cm

Let’s try an example…

SA = 2LH + 2WH + 2LW

Front2 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

+

+

Practice

Agenda1

wait..

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Scaffolding

Take a shot at solving some of the problems on the class work.

I’ll time you!

Class Work

Agendawait..

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Click the answers above to see worked solutions

4) 4 mistakes and SA = 126 in2

3) Answers will vary.

2) SA = 192 in2

1) c) SA = 184 cm2

5) SA = 276 in2

Review Class Work

Internet Applet that can also be used to check answers

Grade your work. Which problems do you need help on?

Agenda21

5 cm2 cm

4 cm55

4 4

2 2

Exit TicketOn 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?

Agendawait..

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