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

2. Lesson Overview (1 of 3) Lesson Objective Lesson Description
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.

3. Lesson Overview (2 of 3) Lesson Vocabulary Materials Scaffolding
Surface Area
Faces
Materials
* Calling Sticks
* Class Work Handouts
* Homework Handouts
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

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 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.

5. Warm Up Find the area of these 2-dimensional figures: 6 cm 8 in 6 cm
OBJECTIVE: SWBAT find the surface area of a rectangular prism
Find the area of these 2-dimensional figures: #1 #2
36 cm2
6 cm
88 in2
8 in
6 cm
11 in
Have students work independently at first to answer warm-up questions. If many students are struggling, use the “scaffolding” button to show formulas.
All students are not expected to be able to answer the challenge question. As such, it is advisable not to spend a lot of class time explaining the challenge question solution. If students are close to answering the challenge question but just need a little bit of help, break the problem down for them into smaller parts by having them find the areas of the square and the circle.
Scaffolding 1

6. 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
Take a moment to quickly highlight that students will be working in pairs as well as participating in whole class activities.
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 C?
What is the name of shape D?
What is the name of shape B?
What is the name of shape A? B A
Square
Cube C D
Present this activity as a way to recall shapes students have previously learned. Tell students its important to answer the question in their heads before you select a calling stick. Using the calling sticks allows all students the wait time (around 3 seconds) to answer the questions for themselves before the teacher selects a student to answer.
Few students will know the vocabulary rectangular prism. Many students will say “box” instead of rectangular prism.
Rectangle
Rectangular Prism

8. Getting Ready – Think – Pair – Share
What similarities and differences do you see between these shapes? A B
Square
Cube C D
In a Think-Pair-Share activity, have students think for a half minute on their own, turn to their partner for a one minute conversation, and then give students the opportunity to answer in a whole class setting.
Students are likely to point out the differences among 2-dimensional vs. 3-dimensional shapes. They may even note that 3D shapes are made up of 2D shapes. This is a good opportunity to explain that we will be working with rectangular prisms today.
Rectangle
Rectangular Prism

9. would like to pick up this building,…
Launch - Problem
For Valentine’s Day
, Godzilla…
would like to pick up this building,…
wrap it,…
and give it to Mrs. Godzilla.
wait.. 1

10. 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?
Through whole class conversation try to elicit various strategies from students about how to find the total area around the outside of the building (rectangular prism).
If students are struggling, use the scaffolding button to pose the question a different way and help steer students’ conversations.
Scaffolding
wait.. 1

11. 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.
To help give students a visual context for a rectangular prism, it may help to bring in an empty cardboard cereal or other box to show a real-life example of a rectangular prism. 1

12. A rectangular prism always has
Launch - Vocabulary
A rectangular prism always has
____ faces, or sides. 6
Side 2
Bottom
Back
Top
Side 1
Front
Height (H)
Width (W)
Length (L)
More About
Faces
wait.. 1

13. 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
This slide is designed to be a teacher-led discussion of the important vocabulary for rectangular prisms. The internet applet shows students how a rectangular prism opens up to form the net (sometimes called a flat pattern). Before showing students what a “face” is you can ask them what they think the face of a rectangular prism is or how many faces they think a rectangular prism has.
You can easily see all three pairs of faces in a net.
Back
Internet applet:
Net of a cube
wait.. 1

14. Practice – Independent Example
Let’s try an example…
So, how do we find the surface area of this rectangular prism?
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.
4 cm
2 cm
3 cm
Even though students have not yet solved a surface area problem, many will be prepared to attempt solving this independently, particularly with the cue of “Front, Back, Side 1, Side 2, Top, and Bottom” Give students 2-3 minutes to try and solve this problem on their own so that they feel more invested in the learning experience.
Students often struggle with which dimensions go with which faces. Use the scaffolding button to bring up an overlay to help students see which dimensions go with which faces.
Scaffolding

15. Practice – Guided Example
Front
Top
Side
Bottom
Back
Surface area of the rectangular prism
Remember:
= 4 cm x 3 cm
= 12 cm2
Back
Front
Side 2 3 4 2
= 4 cm x 3 cm
= 12 cm2
Back
Top
4 cm
2 cm
3 cm
Side 1
= 2 cm x 3 cm
= 6 cm2
Front
Side
Side 2
= 2 cm x 3 cm
= 6 cm2
Top
= 4 cm x 2 cm
= 8 cm2
Bottom
= 4 cm x 2 cm
= 8 cm2
Bottom +
52 cm2
wait.. 1

16. Explore - Class Work
Take a shot at solving some of the problems on the class work.
I’ll time you!
Students should work in pairs or small groups (depending on the structure of your classroom). As groups are working, move between the groups to check for understanding and guide students through misconceptions. This is a good opportunity to notice if some problems are more challenging than others so that you can discuss in depth only the problems most students struggled with during the review portion later in class.
wait..

17. 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)
5) SA = cm2
2) 2 mistakes and
SA = 112 in2
6) SA = 20 ½ in2
3) SA = 248 cm2
Give students minutes to work in pairs or small groups on the class work assignment. Then, this slide can be used to prompt students to grade their own work. Using your observations from watching students solve the problems you can choose which questions to explore in depth. Each answer can be clicked on directly to link to a slide with the solution already written out.
Internet Applet that can also be used to check answers

18. Summary Question – Think – Pair – Share
Find the mistake(s) in the problem below.
Top
Side
Front
= 6 in x 12 in
= 72 in2
Back
Front
12 in
Side
= 4 in x 6 in
= 24 in2
= 4 cm x 12 cm = 48 in2
Top
= 6 in x 4 in
= 24 in2
Bottom
This is a think-pair-share activity. Give students 1-2 minutes to look over the problem individually and try to find the mistake. Then, partners can turn to each other and discuss what mistake they found. Finally, one student can share with the class what the mistake in the problem is.
4 in +
= 288 in2
6 in
240 in2
The side is not 4 x 6, it’s 4 x 12!!
Scaffolding
wait.. 1

19. Exit Question 80 ft 40 ft 200 ft Front Back Side 1 Side 2 Top Bottom
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
40 ft
80 ft
200 ft
Front
Side
Top
= 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
Have your students work on this problem independently or with partners.
= 40 ft x 80 ft
= 3,200 ft2
54,400 ft2
That’s a lot of paper! Thanks Honey!
wait.. 1