21st Century Lessons

Surface Area of a Rectangular PrismDay 1 (of 2)

Mrs. ThompsonLevel 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)

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Lesson Vocabulary Surface AreaFaces

Materials * Calling Sticks

* Class Work Handouts

* Homework Handouts•www.online-stopwatch.com

Links to applets embedded in lesson:

Net of a Cube, Net for Class Example, Applet for Class Work Answers, Extra 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.

Online Resources for Absent Students

StudyZone Lesson

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 the surface area of three-dimensional shapes are a composite of a set number of two-dimensional shapes (1G2).After: In 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 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

6 cm

#1

11 in

8 in#2

88 in236 cm2

1

5 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

Rectangle Rectangular 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

Square Cube

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…

1wait..

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

1wait..

11Scaffolding

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 1Front

Length (L)Width (W)

Height (H)

A rectangular prism always has____ faces, or sides.6

Launch - Vocabulary

1wait..

14 More About Faces

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.

FrontSide

Top

Front

Top

SideSide

Bottom

Back

Net of a cube

You can easily see all three pairs of faces in a net.

Internet applet:

1wait..

16

4 cm2 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…

17Scaffolding

Surface area of the rectangular prism

4 cm2 cm

3 cmFront

Side

Top

Front = 4 cm x 3 cm = 12 cm2

= 4 cm x 3 cm = 12 cm2

= 2 cm x 3 cm = 6 cm2

= 2 cm x 3 cm = 6 cm2

= 4 cm x 2 cm = 8 cm2

= 4 cm x 2 cm = 8 cm2

52 cm2

+

3 34

422

BackSide 2

Bottom

Practice – Guided Example

Back

Side 1

Side 2Top

Bottom

Front

Top

SideSide

Bottom

Back

Remember:

1wait..

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 in2 (cube)

3) SA = 248 cm2

2) 2 mistakes and SA = 112 in2

1) b) push for answers

5) SA = 166.8 cm2

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 in2

21

Find the mistake(s) in the problem below.

Front

Top

Side

6 in

12 in

4 in

Front = 6 in x 12 in = 72 in2

Back = 6 in x 12 in = 72 in2

Side = 4 in x 6 in = 24 in2

Side = 4 in x 6 in = 24 in2

Top = 6 in x 4 in = 24 in2

Bottom = 6 in x 4 in = 24 in2

240 in2

+

The side is not 4 x 6, it’s 4 x 12!!

= 4 cm x 12 cm = 48 in2

= 4 cm x 12 cm = 48 in2

= 288 in2

Summary Question – Think – Pair – Share

1wait..

28 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 ftFrontSide

Top

That’s a lot of paper! Thanks Honey!

Front

Back

Side 1

Side 2

Top

Bottom

= 80 ft x 200 ft = 16,000 ft2

= 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

1wait..

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