21st Century Lessons
Surface Area of a Rectangular Prism
Day 1 (of 2)
Mrs. Thompson
Level 1
Lesson Overview (1 of 3)
Lesson
Objective
Lesson
Description
2
SWBAT find the surface area of a rectangular prism.
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 (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 twodimensional 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.
StudyZone Lesson
Online Resources
for Absent Students
3
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 realworld 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 realworld situations (7G6) and in high school these understandings will be
applied to taking two-dimensional cross-sections of 3D shapes (GGMD4), 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.
4
Warm Up
OBJECTIVE: SWBAT find the surface area of a rectangular prism
Find the area of these 2-dimensional figures:
#1
36
cm2
6 cm
6 cm
5
#2
88 in2
8 in
11 in
Scaffolding
1
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
What
Whatis
is
isthe
the
thename
name
nameof
of
ofshape
shape
shapeC?
D?
A?
B?
Square
8
A
B
C
D
Rectangle
Rectangular Prism
Cube
Getting Ready – Think – Pair – Share
What similarities and differences do you see
between these shapes?
Square
A
C
Rectangle
9
B
Cube
D
Rectangular Prism
Launch - Problem
For Valentine’s Day
, Godzilla…
would like to pick up this building,…
wrap it,…
and give it to Mrs. Godzilla.
10
wait..
1
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?
11
Scaffolding
wait..
1
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.
13
1
Launch - Vocabulary
A rectangular prism always has
6 faces, or sides.
____
Top
Back
Side 2
Front
Side 1
Height (H)
Bottom
Width (W)
Length (L)
14
More About
Faces
wait..
1
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
Side
Side Front
Side
Bottom
You can easily see all three
pairs of faces in a net.
Internet applet:
16
Back
Net of a cube
wait..
1
Practice – Independent Example
Let’s
try do
an example…
So, how
we find the surface area of this
rectangular prism?
3 cm
4 cm
17
2 cm
Front
Back
Side 1
Side 2
Top
Bottom
Scaffolding
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.
Top
Practice – Guided Example
Surface area of the rectangular prism
Side
Front
Side
Remember:
Bottom
Back
Front = 4 cm x 3 cm
= 12 cm2
Back = 4 cm x 3 cm
2
Top
2
4
Side 1 = 2 cm x 3 cm
Side3 cm
3 Front 3
Side 2 = 2 cm x 3 cm
Top = 4 cm x 2 cm
2 cm
4 cm
Bottom = 4 cm x 2 cm
= 12 cm2
= 6 cm2
= 6 cm2
= 8 cm2
= 8 cm2
Back
Side 2
4
Bottom
+
52 cm2
19
wait..
1
Explore - Class Work
Take a shot at solving some of
the problems on the class work.
I’ll time you!
20
wait..
Summary - Review Answers from
Class Work –
Click on the answers below to see worked solutions
1) b) push for answers
4) SA = 294 in2 (cube)
2) 2 mistakes and
SA = 112 in2
5) SA = 166.8 cm2
6) SA = 20 ½ in2
3) SA = 248 cm2
Internet Applet that can also be used to check answers
21
Summary Question – Think – Pair – Share
Find the mistake(s) in the problem below.
Top
Side
Front
Front = 6 in x 12 in
= 72 in2
Back = 6 in x 12 in
= 72 in2
22
in x 6
==44cm
12incm = =4824inin
22
12incm = =4824inin
Side ==44cm
in x 6
12 in Side
Top
4 in Bottom
= 6 in x 4 in
= 24 in2
= 6 in x 4 in
2
=
24
in
+
22
240
in
=
288
in
The side is not 4 x 6, it’s 4 x
6 in
12!!
28
Scaffolding
wait..
1
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?
Top
40 ft
Side
80 ft
Front = 80 ft x 200 ft
= 16,000 ft2
Back = 80 ft x 200 ft
= 16,000 ft2
Side 1 = 40 ft x 200 ft
= 8,000 ft2
Side 2 = 40 ft x 200 ft
= 8,000 ft2
Top = 40 ft x 80 ft
= 3,200 ft2
Bottom = 40 ft x 80 ft
= 3,200 ft2
Front 200 ft
54,400 ft2
30
That’s a lot of paper!
Thanks Honey!
wait..
1