21st Century Lessons

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21st Century Lessons
Surface Area of a Rectangular Prism Day 1 (of 2)
Mrs. Thompson Level 1
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Lesson Overview (1 of 3)
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 Godzillas 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 Godzillas Problem so you can informally asses their learning. The homework provides students the opportunity to practice, and reinforces, the key concepts from class.
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Lesson Overview (2 of 3)
Lesson Vocabulary Surface Area Faces
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
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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.
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Warm Up
OBJECTIVE SWBAT find the surface area of a
rectangular prism
Find the area of these 2-dimensional figures
1
2
6 cm
36 cm2
8 in
88 in2
6 cm
11 in
Scaffolding
1
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Warm Up
OBJECTIVE SWBAT find the surface area of a
rectangular prism
Find the area of these 2-dimensional figures
1
2
6 cm
36 cm2
8 in
88 in2
Square Area side x side Rectangle Area length
x width
6 cm
11 in
Scaffolding
1
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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
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Getting Ready Calling Stick Activity
What is the name of shape A?
What is the name of shape B?
What is the name of shape C?
What is the name of shape D?
Square
Cube
Rectangle
Rectangular Prism
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Getting Ready Think Pair Share
What similarities and differences do you see
between these shapes?
Square
Cube
Rectangular Prism
Rectangle
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Launch - Problem
, Godzilla
For Valentines Day
would like to pick up this building,
wrap it,
and give it to Mrs. Godzilla.
wait..
1
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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
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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
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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
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Launch - Vocabulary
A rectangular prism always has ____ faces, or
sides.
6

Height (H)
Width (W)
Length (L)
More About Faces
wait..
1
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Extension Vocabulary
Each side of a rectangular prism is called a face.
A rectangular prismhas six faces.
Back to lesson
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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
Net of a cube
Internet applet
wait..
1
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Practice Independent Example
Lets try an example
So, how do we find the surface area of this
rectangular prism?
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.
Front Back Side 1 Side 2 Top Bottom
Scaffolding
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Practice Independent Example
Lets try an example
So, how do we find the surface area of this
rectangular prism?
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.
Front Back Side 1 Side 2 Top Bottom
Top
Front
Side
Scaffolding
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Practice Guided Example
Surface area of the rectangular prism
Remember
4 cm x 3 cm
12 cm2
Front
4 cm x 3 cm
12 cm2
Back
Top
2 cm x 3 cm
6 cm2
Side 1
Front
Side
2 cm x 3 cm
6 cm2
Side 2
4 cm x 2 cm
8 cm2
Top
4 cm x 2 cm
8 cm2
Bottom
52 cm2
wait..
1
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Explore - Class Work
Take a shot at solving some of the problems on
the class work. Ill time you!
wait..
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Summary - Review Answers from Class Work Click
on the answers below to see worked solutions
4) SA 294 in2 (cube)
1) b) push for answers
5) SA 166.8 cm2
2) 2 mistakes and SA 112 in2
6) SA 20 ½ in2
3) SA 248 cm2
Internet Applet that can also be used to check
answers
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Class work 1
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
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Class work 2
S I D E
4 in x 2 in
Find the mistake(s)
(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
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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
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Class work 4
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
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Class work 5
S I D E
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
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Class work 6
F R O N T
S I D E
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
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Summary Question Think Pair Share
Find the mistake(s) in the problem below.
Top
Front
12 in
4 cm x 12 cm 48 in2 4 cm x 12 cm 48 in2
4 in
288 in2
240 in2
6 in
The side is not 4 x 6, its 4 x 12!!
Scaffolding
wait..
1
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Summary Question Think Pair Share
Find the mistake(s) in the problem below.
Top
Front
12 in
4 cm x 12 cm 48 in2 4 cm x 12 cm 48 in2
4 in
288 in2
240 in2
6 in
The side is not 4 x 6, its 4 x 12!!
Scaffolding
wait..
1
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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?
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
Thats a lot of paper! Thanks Honey!
wait..
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