Surface Area of 3-D Composite Objects
Grade 9 Unit Plan
Surface Area of 3-D Composite Objects
By Mark Johnston & Kaylyn Wallen
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Surface Area of 3-D Composite Objects
Table of Contents:
1. Title Page
2. Table of Contents
3. Broad Areas of Learning
4. Cross Curricular Competencies
5. Outcomes
5. Indicators
5. I Can… Statements
6. Big Idea (Essential Questions, Students Will Understand, and Students Will
Know)
7. Differentiation
8. Record of Adaptation
8. Tier 1 Intervention
9. Lesson 1
16. Lesson 2
21. Lesson 3
25. Lesson 4
32. Assessment
33. Grading Plan
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Surface Area of 3-D Composite Objects
Broad Areas of Learning
Developing Lifelong Learners: One of the areas of our unit plan that focuses on this
broad area of learning is the fact that it enables the student to learn through inquiry.
They are learning through doing and making connections. Students are discovering
answers for themselves instead of the teacher providing them with these answers. The
unit also gets students to think about the 3D composite objects that surround them in
everyday life as well as realizing how the calculation of surface area can be useful in
everyday life.
Developing a Sense of Self and Community: Throughout our unit plan we did our
best to have students working together as much as possible. This helps students
interact not only with the mathematical content that is being taught, but also encourages
interaction amongst one another. This allows them to share ideas as well as value and
respect the contribution of others.
Developing Engaged Citizens: Mathematics can be considered as a “vehicle to
develop the mind”. This unit and more so math in general encourages students to try
and understand what the content that is being taught can be used for. The goal is that
students will think beyond the mathematical equations used to calculate surface area
and focus more on how this might be useful to them in the real world.
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Surface Area of 3-D Composite Objects
Cross Curricular Competencies
Developing Thinking: The unit and more so the inquiry section pushes students to
think critically and become stronger problem solvers. Students experience both real
world problems and problems that deal with mathematical context that have to do
surface area of 3D composite objects. The students are asked specifically in lesson 4
“How can we determine how much tin is needed to re-tin the storage shed?”
Developing Identity and Interdependence: The unit involves a lot of group work
which allows students to become more confident in their abilities and see that their
opinion is value as well as learning to value the opinion of others. (Ask if we need to say
where this happens!!)
Developing Literacies: Students communicate the learning of mathematical
knowledge through the assessment strategies. These strategies are numerical and
written and use a variety of representation such as manipulatives, visuals, and symbols.
(i.e. Entrance slips, exits slips, journal entries etc.)
Developing Social Responsibility: Throughout the unit students will experience the
opportunity to share ideas, and solve problems by working together. It will help students
consider the perspective of others and empower them to help others in the development
of their understanding, as well as find ways to respectfully seek the help of others.
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Surface Area of 3-D Composite Objects
Outcome
Shape and Space 9.2: Extend understanding of area to surface area of right
rectangular prisms, right cylinders, right triangular prisms, to composite 3-D objects.
Indicators
A) Describe 3-D composite objects from the natural and constructed world, including
objects relevant to First Nations and Métis people (e.g., Mesoamerican pyramids).
B) Analyze a composite 3-D object to identify areas of overlap and explain the impact of
these areas on determining the surface area of the composite 3-D object.
C) Critique the statement “To find the surface area of a composite 3-D object, add
together the surface areas of the individual 3-D objects from which the composite 3-D
object is comprised”.
D) Determine the surface area of composite 3-D objects.
E) Solve situational questions involving the surface area of composite 3-D objects.
“I Can Statements”
A) I can…talk about 3D compound objects from the natural and man-made world
including objects that have to do with First Nations and Metis people.
B) I can…look at compound 3D objects to find areas of overlap and how those areas
affect how we find the surface area of a compound object.
C) I can…critique the statement “To find the surface area of a composite 3D object, add
together the surface areas of the individual 3D objects that make up the composite
object.”
D) I can...find the surface area of a compound 3D object.
E) I can…solve situational questions that have to do with surface area of compound
objects.
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Surface Area of 3-D Composite Objects
Big Idea
It explores the relationship between measurement and 3-D composite objects, and
applies this understanding to real life world problems. It develops an understanding of
the uses of surface area in everyday life.
Essential Questions:
1) What is the difference between a 3-D object and a 3-D composite object?
2) What relationship can be generalized for find surface area of the following
(formulating formulas):
 Rectangular prisms?
 Triangular prisms?
 Right cylinders?
3) How does the process of calculating surface area differ when we are looking at a
3-D composite object compared to a 3-D object?
4) What is the importance of knowing how to calculate surface area? Why is it used
in the real world?
Students Will Understand:




How to determine the difference between 3-D objects and 3-D composite objects.
How calculating surface area of 3-D composite objects is essential to the real
world.
That there exists a general relationship when it comes to finding the surface area
of a rectangular prism, triangular prism, and right cylinder.
How overlap can affect how surface area of a 3-D composite object is calculated.
Students Will Know:




The difference between 3-D objects and 3-D composite objects.
How to calculate the surface area of a 3-D composite object that is made up of
rectangular prisms, triangular prisms, and right cylinders.
How to identify composite objects in the world around them.
How to make connections between mathematics and the real world.
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Surface Area of 3-D Composite Objects
Differentiation
Differentiation of Instruction:
The time has come where it is unacceptable for teachers to simply enter the classroom and
expect for their students to adjust to the content that is being taught. Educators need to
become aware of the diversity that surrounds their classrooms, and they themselves need
to be able to adjust to the learning needs of the students. It is important for educators to
remember that not all students learn in the same way. Throughout this unit a wide
variety of instructional methods are used in an attempt to meet the needs of every
student in the classroom. Here are the instructional methods that are used:

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Direct instruction (tradition lecture where students are expected to take notes).
Visual representation (pictures of 3-D objects and 3-D composite objects, and
stop motion videos).
Manipulatives (3-D prisms and cylinders).
Inquiry based learning (student-centered learning).
Group/partner and individualized work.
Class discussions for auditory learners.
Differentiation of Assessment:
Traditionally mathematics has been assessed through written exams; however, this
does accurately measure progress and overall knowledge as many students become
anxious when it comes to written tests. Although sometimes difficult, there are
alternative ways to assess mathematics. Throughout this unit a wide variety of
assessment strategies have been implemented. They are:

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Entrance slips.
Exits slips.
Class, group, and partner discussions.
Journal Entries.
Checklist
Quiz
Interviews
Oral Presentation
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Surface Area of 3-D Composite Objects
Record of Adaptation
A Record of Adaptations provides documentation for students who follow approved
Saskatchewan curricula but require extensive and continuing use of the Adaptive
Dimension.
For students having Difficulty:








Students can use a calculator to help with mathematical operations such as
addition, subtraction, multiplication, and division which will allow them to focus
more on the concept of surface area.
Formula sheet can be supplied to those who need it.
Before moving to 3-D composite objects, be sure students are successful with 3D objects.
Frequent use of manipulatives.
Use of interviews instead of written tests/quiz and journal entries.
Group student(s) with strong, organized peers willing to help.
Permit extended time for problem solving
Use simpler problems of the same type to model methods.
For students needing a challenge:


Introduce more complex 3-D composite objects that use rectangular prisms,
triangular prims, and right cylinders.
Introduce pyramids, cones, and other objects and have them think about how the
surface area would be determined.
Tier 1 Interventions
There are many forms of Tier 1 Interventions that are used throughout this unit. They
are represented throughout the unit plan.
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Core Curriculum – Outcomes and Indicators
Universal Screening/ Value-Added Assessment
Differentiated and Adaptation
Frequent Progress Monitoring
Learning Environment
Inclusive and Culturally Responsive Practices
Metacognition and Self- Regulation
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Surface Area of 3-D Composite Objects


Fostering Independence and Assistive Technology
Collaborative Problem Solving
Lesson 1: 3-D Objects
Topic:
 Review of Surface Area
 Introduction to composite objects
Targets for Professional Growth:
 Classroom Management
Big Idea:
EQ: What is the difference between a 3-D object and a 3-D composite object?
What relationship can be generalized for find surface area of the following
(formulating formulas):



Rectangular prisms?
Triangular prisms?
Right cylinders?
SWU: How to determine the difference between 3-D objects and 3-D composite objects.
SWK: The difference between 3-D objects and 3-D composite objects.
Outcome:
SS9.2
Extend understanding of area to surface
area of right rectangular prisms, right
cylinders, right triangular prisms, to
composite 3-D objects.
Indicators/ I Can Statements:
a. Describe 3-D composite objects from
the natural and constructed world,
including objects relevant to First Nations
and Métis people (e.g., Mesoamerican
pyramids).

Prerequisite Learning:
 How to calculate area of rectangles,
circles, and triangles
 How to calculate surface area of
rectangular prisms, triangular prisms,
and right cylinders
I can…talk about 3D compound objects
from the natural and man-made world
including objects that have to do with
First Nations and Metis people.
Considerations:
 Students may already know what
composite objects are
 Students may have other ideas
about composite objects that they
have seen in the world other than
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Surface Area of 3-D Composite Objects

What a 3D object is
the examples
Students may have different objects
that are composite objects that
have cultural significance to them
Advanced Preparation:
-Make the Pecha Kucha
-Photocopy entrance and exit slips
-Have examples ready to do with students
-Photocopy formula sheets
-Have nets prepared
-Organize manipulatives and have them
ready for students use

Materials:
-Square blocks (or other manipulatives)
-Smartboard
-Nets (if students need)
Presentation
Set (Estimated time- 10 min):


Give students an entrance slip with the gift wrapping problem [TN 2]
Have students work on problem on their own
Development (Estimated time- 45 min):
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
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
Engage in a class discussion regarding the entrance slip
o Have students explain how they solved the problem.
o Get several students answers in order to gain an understanding of what
students know about calculating surface area.
Give examples to formulate formulas:
o Formulate formula for right rectangular prism, triangular prism, and right
cylinder
Give examples with dimensions to find surface area: 1 of a right rectangular prism, 1
of a triangular prism, 1 right cylinder. [TN 3]
Present students with a slideshow showing them different 3D objects and 3D
composite objects that exist in the real world.
o Ask the class if they noticed a difference between the two.
o Continue through pictures until the class sees the difference
o Ask students how these may differ in calculating the surface area of the
objects [TN 1]
o
Explain what a 3D composite object is.
o A composite object is an object made of more than one 3D object
Closure (Estimated time- 5 min):

Students will be given an exit slip with a picture of a 3D composite object. They will
be asked to explain how they think the surface area of this object would be
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Surface Area of 3-D Composite Objects
calculated and to bring their idea to the next class. [TN 4]
Differentiation:
Adaptive Dimension

Students can use nets for
manipulatives to help them better
understand calculating surface area
(linking cubes, wooden blocks)

Entrance slip- allows us to see where the students are at when we begin the unit.
We can tell if they remember the topic and what areas we need to review before we
can begin to move on to the new outcomes
Class Discussion- assesses for students learning. This allows for teachers to
question students and make them think about the topic being discussed. Can lead to
students arriving at and answer without being told (take anecdotal notes during
discussion)
Exit Slip- gives teachers and idea of what the students have learned in the lesson. It
also gives the students an idea of what they will be learning about in the next lesson
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
For Struggling Students:
 Give students a formula sheet to help
them remember the formulas and allow
them to focus on the topic of surface
area and how it works [TN 4]
 Allow students to use calculators for
calculations to allow them to focus on
the content
 Students could record how they would
solve the problem instead of writing it in
the exit slip
For Students who need a challenge:
 Give students other examples of
pyramids, cones, and spheres
Assessment
Lesson 1 Teacher Notes
1. Pictures for slideshow
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Surface Area of 3-D Composite Objects
2. Entrance Slip
Name: __________________
Nathan is wrapping his parents Christmas gifts. He wants to know how much paper he needs to
buy to wrap both of them. If the paper costs $0.01 per centimeter squared and the gifts have the
dimensions below, how much will it cost him to wrap the gifts? (Rounded to the nearest cent)
2 cm
19 cm
10 cm
45 cm
10 cm
Answer:
Tool Box
SA= 2(lw) + 2(lh) + 2(hw)
SA= 2(45cm)(10cm) + 2(45cm)(19cm) + 2(10cm)(19cm)
SA= 2(450cm^2) + 2(855cm^2) + 2(190cm^2)
SA= 900cm^2 + 1710cm^2 + 380cm^2
SA= 2990cm^2
Candle
SA= 2πrh + 2πr^2
Total= 2990cm^2 + 150.7964474cm^2
SA= 2π(2cm)(10cm) + 2π(2cm)^2
= 3140.796447 cm^2
SA= 40π cm^2 + 8π cm^2
(3140.796447 cm^2) ($0.01/cm^2)
SA= 150.7964474cm^2
=$31.41
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Surface Area of 3-D Composite Objects
Therefore Nathan would need to spend $31.41 on paper to wrap his parents’ Christmas gifts
3.
a)
6 cm
10 cm
17 cm
b)
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Surface Area of 3-D Composite Objects
c)
4. Exit Slip
Name: ________________________
Describe how you would calculate the surface area of the whole object below if the side length
of each square is 5 cm.
5 cm
5 cm
5 cm
4.
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Surface Area of 3-D Composite Objects
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Surface Area of 3-D Composite Objects
Lesson 2: Introduction to 3-D Composite Objects With an Inquiry Approach
Topic:
 Introduction to surface area of
composite objects through inquiry
Targets for Professional Growth:

Organizing group work
Big Idea:
EQ: How does the process of calculating surface area differ when we are looking at a 3D composite object compared to a 3-D object?
SWU: How overlap can affect how surface area of a 3-D composite object is calculated
SWK: How to calculate the surface area of a 3-D composite object that is made up of
rectangular prisms, triangular prisms, and right cylinders
Outcome:
SS9.2
Indicators/ I Can Statements:
b. Analyze a composite 3-D object to
identify areas of overlap and explain
the impact of these areas on
determining the surface area of the
composite 3-D object.
Extend understanding of area to surface
area of right rectangular prisms, right
cylinders, right triangular prisms, to
composite 3-D objects.
c. Critique the statement “To find the
surface area of a composite 3-D
object, add together the surface
areas of the individual 3-D objects
from which the composite 3-D
object is comprised”.
Prerequisite Learning:

I can…look at composite 3D objects to
find areas of overlap and how those
areas affect how we find the surface
area of a compound object.

I can…critique the statement “ To find
the surface area of a composite 3D
object, add together the surface areas
of the individual 3D objects that make
up the composite object.”
Considerations:
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Surface Area of 3-D Composite Objects




How to calculate area of rectangles,
circles, and triangles
How to calculate surface area of
rectangular prisms, triangular prisms,
and right cylinders
What a 3D object is
What a 3D composite object is
Materials:
-Paper
-Rulers
-Scissors
-Rectangular prisms
-Triangular prism [TN 1]
-Right cylinders
-Presentation materials (poster paper,
computers, smartboard, etc.)

Advanced Preparation:
 Put students into groups ahead of time
 Have materials set out so they are
ready for students to use
 Have checklists made and photocopied
to hand out to students before they
make their presentation and to mark
students presentations
Presentation
Set (Estimated time- 10 min):
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
Have students discuss with a pair what a composite object is and how they would
calculate the surface area of a composite object
Get each pair to write their ideas on the board
Development (Estimated time- 1 hr 30 min):
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Split students up into groups of three
Give each group paper, rulers, scissors and three blocks which will include:
o Rectangular prisms
o Triangular prism and/or
o Right cylinders
Have students work on their own with the questions given [TN 2]
o Have students’ trace all the sides of their objects individually and then cut
them out.
o Then have students use the ruler to find the dimensions of each piece and
use them to calculate the surface area of the whole object.
o Then tell the students to place the objects on top of one another and trace
the sides while the objects are together and find the surface area using
the same method as before.
 While doing the activity ask students what they notice about the
difference between the two calculations
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Surface Area of 3-D Composite Objects
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 Asks students why there may be a difference
Question groups about what they found for the surface area of their 3D
composite object during their group work.
o Ask students whether they predicted the results they achieved
o If not ask why their results might be different then what they predict
o Ask students what this tells us about how we calculate surface area of
composite objects
Have students present their findings to the class. (Can choose any method of
presentation. Must include visuals and everyone in the group must be involved)
Discuss with students how the overlap effects the surface area on the composite
objects (You can’t just add the surface area of the individual objects because
they overlap. You must subtract the overlap from the addition of the surface area
of the individual objects to get the surface area of the composite object) [TN 3]
As a class come to a conclusion about what you need to do to account for the
overlap when calculating surface area of composite objects
Have students hand in assignment sheet at the end of the lesson
Closure (Estimated time- 20 min):

Write a journal entry on what is wrong with this sentence. “To find the surface
area of a composite 3-D object, add together the surface areas of the individual
3-D objects that makes up the composite object”. In this journal entry, explain
how you came to this conclusion and how you would apply it to calculating
surface area.
Differentiation:
 Students can present their information
in a variety of ways to best suit the
group as learners
 Journal entry could be recorded, hand
written, blogged, etc.
Adaptive Dimension
For Struggling Students:
 Students can use formula sheet
provided in previous lesson to help
them focus on the activity
 Students can use calculators to
help them with the process
 Students could do only the
rectangular prism and/or triangular
prism if having difficulty
For Students who need a challenge:
 Students could go on to calculating
the surface area of composite
objects without the use of the paper
 Students can work on finding the
surface area of composite function
that include more complex objects
such as cones and pyramids
Assessment
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Surface Area of 3-D Composite Objects
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Pair Share- students share the knowledge and opinions they have with a partner
Assignment- Students will hand in their work so the teacher can assess what the
students have understood and where they are still confused
Presentation- Students will be assessed on having the required information, having
whole group involvement and the mathematical content and reasoning involved.
Journal Entry- assessment will focus on students thoughts, connections made, and
supportive evidence
Lesson 2 Teacher Notes
1.
2. Assignment
1) -Trace each side of the rectangular prism onto your piece of paper.
- Cut out the pieces and calculate the area of each piece.
- Add together the area of the pieces to get the surface area of the rectangular
prism.
- Repeat the process for the triangular prism and right cylinder
- Add the surface area of all 3 objects together
2) – Put all three objects together to create a composite object
-Trace each side of the composite object onto your paper
- Cut out the pieces and calculate the area of each piece.
- Add together the area of the pieces to get the surface area of the composite
object
3) – Compare your results from questions 1) and 2).
- What do you notice about your results?
- What conclusions can you draw from these results about surface area
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Surface Area of 3-D Composite Objects
4) Present your findings to the class
3. Rubric
Rubric for Assignment
Established
Meeting
Progressing
Beginning
Mathematics
Involved
Always shows
evidence of
mathematics.
Frequently shows
evidence of
mathematics.
Presentation
of Data
Highly effective.
Generally effective.
Somewhat
effective.
Ineffective.
Evidence of
Argument
Argument is
clearly stated and
exceptionally
clear.
Argument is stated and
generally clear.
Argument
lacks clarity.
Argument is
unclear.
Overall
Presentation
Presentation
Presentation shows
Presentation Presentation
shows creativity
some
shows lack
shows no
and organization, creativity, organization, of creativity,
creativity,
and is engaging and engagement and is organization, organization,
and informative.
informative.
and
or
Contributions are Contributions are made engagement engagement
made by all group
by most group
and is not
and is not
members.
members.
informative.
informative.
Contributions Contributions
are made by are made by
few group
only one
members.
group
member
Sometimes
Rarely or
shows
never shows
evidence of
evidence of
mathematics. mathematics.
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Surface Area of 3-D Composite Objects
Lesson 3: Finding Surface Area of 3-D Composite Objects
Topic:
Finding the surface area of 3-D composite
objects.
Targets for Professional Growth:


Good classroom management.
Clear instruction so that students
have a good understanding of how
to find the surface area of 3-D
composite objects.
Big Idea:
EQ: How does the process of calculating surface area differ when we are looking at a 3D composite object compared to a 3-D object?
SWU: How overlap can affect how surface area of a 3-D composite object is calculated.
SWK: How to identify composite objects in the world around them.
How to make connections between mathematics and the real world.
Outcome:
Shape and Space 9.2: Extend
understanding of area to surface area of
right rectangular prisms, right cylinders,
right triangular prisms, to composite 3-D
objects.
Indicators/ I Can Statements:
Indicators:
b) Analyze a composite 3-D object to
identify areas of overlap and explain the
impact of these areas on determining the
surface area of the composite 3-D object.
d) Determine the surface area of
composite 3-D objects.
I Can Statement:
b) I can look at compound 3D objects to
find areas of overlap and how those areas
affect how we find the surface area of a
compound object.
d) I can find the surface area of composite
3-D objects.
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Surface Area of 3-D Composite Objects
Prerequisite Learning:



Considerations:

Estimate the surface area of a 3-D
composite object.
Calculate the surface area of a 3-D
object.
Understand how overlap influences
the surface area of a 3-D composite
object.
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Materials:
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

Students may try to determine the
surface area of 3-D composite
objects that include more than
rectangular prisms, triangular
prisms, and right cylinders.
May be limited composite objects
(that are formed of prisms and
cylinders) around the classroom
and school for students to analyze
and calculate the surface.
Students who are struggling with 3D composite objects may have
difficulty with this activity. What can
be done to help them out?
Advanced Preparation:
SmartBoard
Measuring devices (rulers or meter
sticks)
Paper
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
Have examples ready to go over
with students on the SmartBoard.
Have students grouped into
partners that will best work
together.
Prepare the “3-2-1” activity for
students to complete for the closure
of the lesson.
Presentation
Set (Estimated time-10 minutes):

Number students off 1-5 to form groups where they will engage in a discussion
regarding the overlap of 3-D composite objects. Encourage students to ask
themselves questions such as:
o How does overlap influence surface area?
o 3-D composite objects include overlap. What is the best way to account
for it?
Development (Estimated time-40 minutes):

Start with examples of 3-D composite object that deal with overlap when finding
surface area (3-5 examples). Students should be well engaged in these
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Surface Area of 3-D Composite Objects
examples.

Divide students up into partners and have them browse around the classroom
and school looking around for at least three 3D composite objects. State these
composite objects can only include rectangular prisms, triangular prisms, and
right cylinders. Have the students sketch these objects and measure their sides .

Once students have returned to the classroom, have them calculate the surface
area of the composite objects they have found. Have the students hand these in
for assessment.
Closure (Estimated time-10 minutes):


Have students complete a “3-2-1” which consists of the following three questions:
o What are 3 things you found out?
o What are 2 things you find interesting?
o What is 1 thing you still have questions about?
Have the students had this in so the teacher has an idea where the students are
before they begin the next lesson.
Differentiation:
 Students could look objects up
online or in magazines
 Students could work in larger
groups or individually
Adaptive Dimension
For Struggling Students:


Group these students with a partner
who understands the content and
will be willing to help.
Have set 3-D composite objects in
place for these students to analyze,
find dimensions, and calculate
surface area.
For Students who need a challenge:


Have these students work
individually.
Encourage them to find 3-D
composite objects that include more
than rectangular prisms, triangular
prisms, and right cylinders. Have
them figure out for themselves how
they can determine the surface area
of these objects.
Assessment:
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Surface Area of 3-D Composite Objects


Observe the group discussions that are going on at the beginning of class.
o Are all students of each group engaged in the discussion?
o Are students building off the ideas of others?
o Is there teamwork going on to determine how overlap influences surface
area and how it can be accounted for?
The “3-2-1” activity that students will be handing in. Educators should pay close
attention to these as they can be very beneficial in learning what students are
thinking as well as what else they might be interested in learning.
Lesson 3 Teacher notes
Examples that will be used during the development of the lesson.
1) Two rectangular prisms that are different in size are stacked on top of each other
 What are the shapes of the faces that make up this 3-D composite object?
 Does it matter in which way the prisms are stacked?
2) Two triangular prisms that are attached at the base.
3) Right cylinder stacked on top of a rectangular prisms (the cylinder is stacked with
the base facing down)
Are the students making the connection of how to account for the overlap?
Here is the “3-2-1” slip you will have students complete for the closure.
1) What are 3 things you found out?
2) What are 2 things you find interesting?
3) What is 1 thing you still have questions about?
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Surface Area of 3-D Composite Objects
Lesson 4: Re-tinning the Ol’ Storage Shed
Topic:
How calculating surface area of 3-D
composite objects can be beneficial in real
world situations.
Targets for Professional Growth:


Proximity- walk around the room
and scan student behavior and
make sure they are staying on task.
Proper wait time when it comes to
student answers. Give them time to
think about the problems before
giving them answers.
Big Idea:
EQ: How does the process of calculating surface area differ when we are looking at a 3D composite object compared to a 3-D object?
What is the importance of knowing how to calculate surface area? Why is it used in
the real world?
SWU: That there exists a general relationship when it comes to finding the surface area
of a rectangular prism, triangular prism, and right cylinder.
How overlap can affect how surface area of a 3-D composite object is calculated
SWK: How to identify composite objects in the world around them.
How to make connections between mathematics and the real world
Outcome:
Shape and Space 9.2: Extend
understanding of area to surface area of
right rectangular prisms, right cylinders,
right triangular prisms, to composite 3-D
objects.
Indicators/ I Can Statements:
Indicators:
b) Analyze a composite 3-D object to
identify areas of overlap and explain the
impact of these areas on determining the
surface area of the composite 3-D object.
c) Critique the statement “To find the
surface area of a composite 3-D object,
add together the surface areas of the
individual 3-D objects from which the
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Surface Area of 3-D Composite Objects
composite 3-D object is comprised”.
d) Determine the surface area of
composite 3-D objects.
e) Solve situational questions involving the
surface area of composite 3-D objects.
I Can Statement:
b) I can look at compound 3D objects to
find areas of overlap and how those areas
affect how we find the surface area of a
compound object.
c) I can critique the statement “ To find the
surface area of a composite 3D object,
add together the surface areas of the
individual 3D objects that make up the
composite object.”
d) I can find the surface area of composite
3-D objects.
e) I can solve situational questions that
have to do with surface area of compound
objects.
Prerequisite Learning:



Estimate the surface area of a 3-D
composite object.
Calculate the surface area of a 3-D
object.
Understand how overlap influences
the surface area of a 3-D composite
object.
Considerations:


Some students may already know
the general relationship for finding
surface area of a rectangular
prisms, triangular prisms, and right
cylinders.
o What are you going to do for
these students who have
already know how to
formulate the necessary
formulas?
Some students may really struggle
understanding why these formulas
work for all rectangular prisms,
triangular prisms, and right
cylinders.
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Surface Area of 3-D Composite Objects
o What will you do in this
situation?
Materials:

Advanced Preparation:

SmartBoard



Have stop motion videos prepared
that will be shown in the set.
PowerPoint that is put together for
this lesson that encourages
students to break objects up into
faces.
Have extension question made up
on papers.
Have adaptive dimension strategies
in place if they are necessary.
Presentation
Set (Estimated time-10 minutes):


Begin by showing a picture of the shed. Ask the question:
o How much tin would it take to re-tin this shed?
o How can we solve this problem?
Show the videos and re-state the question:
o How much tin would it take to re-tin this shed?
o What other information do you need to solve the problem? (ex.
Dimensions)
Development (Estimated time-40 minutes):





Consider mentioning to students that they need to consider the shed as we move
through the lesson.
Begin with a rectangular prism (dimensions included). Ask:
o How would I tin this rectangular prism?
o Can I generalize this? Is there a relationship?
Repeat the above process with a triangular prism (dimensions included)
o How would I tin this triangular prism?
o Can I generalize this? Is there a relationship?
Go back to the shed: Ask the question, “What 3d figures make up this composite
object?”
Restate the question:
o How can we tin the shed?
o Can we just add the surface areas together of the rectangular prism and
the triangular prism?
o Why does this method not work?
Closure (Estimated time-10 minutes):
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Surface Area of 3-D Composite Objects

Extension:
o What if I added a door which is 1 m x 2 m and two windows measuring 1
m x 1 m, how much tin would you need?
o Intuitively, do you need more or less tin?
o Does it matter where the door and windows are?
Differentiation:


Traditional lecture
Visualization through stop motion
videos. Students are able to see
what a composite object looks like
when it is broken down.
o How would this help
students?
Adaptive Dimension
For Struggling Students:




Use simpler problems of the same
type to model methods.
One to one instruction for students
still struggling.
Bring in manipulatives for more
visual learners.
Utilize dimensions that are easy to
calculate in order to be sure
students understand the process of
finding the surface area of the
storage shed.
For Students who need a challenge:


After these students have finished
the extension included in the
closure of the lesson, have them
think even further.
o What else might change the
amount of tin needed to retin the shed?
o How might the process
change if a sliding door was
installed in the shed (garage
type door)?
Have students sketch their own
house.
o What is the surface area
excluding the doors and
windows?
o What is the surface area with
the doors and windows?
Assessment:
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Surface Area of 3-D Composite Objects



Ongoing assessment throughout the PowerPoint to get an idea who has an
understanding of the material.
o Circulate the room to see if students are making effective notes. Are there
any students jumping ahead and experimenting with ideas in advance?
(these could be students needing more of a challenge).
o Do some students need more time to take notes? Why might they be
behind? Are these students who may possibly be struggling?
Who are the students that are engaging themselves into the lesson?
Have them hand in their work of determining the surface area of the shed, both
before and after the extension.
o Are they aware of the shapes that make up the shed?
o Are they aware of the overlap?
o Most importantly, do they understand the process of finding the surface
area of the shed? If not, perhaps something needs to change with
teaching method of the lesson. Did you progress through the unit to
quickly?
Lesson 4 Teacher notes
The stop motion videos included in the set for this lesson can be found by visiting the
following links:
http://www.youtube.com/watch?v=jZnoz3GJ7og
http://www.youtube.com/watch?v=FkmZAXbK6Ms
Here are the formulas that should be formulated throughout the lesson (the general
relationship for finding surface area of a rectangular prisms and triangular prism).
Rectangular prism formula:
SA= 2(wl) + 2(hl) + 2(hw); w=width, l=length, and h=height
SA= 2(wl + hl + hw)
Triangular Prism formula
SA= 2(area of triangle) + 2(area of side rectangle) + area of base rectangle
Area of Triangle = ½(bh); b=base of triangle, h=height of triangle
Area of Rectangle = wl + hl + hw; w=width, l=length, and h=height
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Surface Area of 3-D Composite Objects
Here is the quiz that will be given at the beginning of the next class to evaluate
the unit.
1) The base of the lamp is a triangular prism with an equilateral triangle base. The surface of the
stand is to be painted. What is the area that will be painted? Give the answer to the nearest
whole number.
2) Rory will paint this birdhouse he built for his backyard. The perch is a cylinder with length 7
cm and diameter 1 cm. The diameter of the entrance is 3 cm. What is the area that needs to
be painted? Give the answer to the nearest whole number.
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Surface Area of 3-D Composite Objects
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Surface Area of 3-D Composite Objects
Assessment
Diagnostic Assessment:
This form of assessment provides teachers with information regarding student prior
knowledge and misconceptions before beginning learning activity. Here are the
diagnostic assessment methods used in the unit and their purpose.


Entrance slip- used at the beginning of the unit to learn about what students
know about calculating surface area of 3-D objects before advancing to 3-D
composite objects.
Group/class discussions- allows for students to share ideas, make connections,
and build off the knowledge of others. Informs the teachers of what the students
took out of the last lesson and where they might be struggling.
Formative Assessment:
This form of assessment takes place during the learning of an activity and provides
teachers with information on how well the learning objectives are being met. Here are
the formative assessment methods used in the unit and their purpose.




Journal Entry- Used in order to get every students perspective on the topic. This
helps students explain their understandings and gives the teacher an idea of how
the students are progressing.
Checklist- Used in lesson 2 to assess their presentations on what conclusions
have been drawn from the inquiry activity. This gives students feedback on what
they have considered and what they need to consider in the future.
Interviews- Speak to students about how they feel they are progressing through
the unit. This is used in all lessons when the teacher is circulating the room and
observing and talking to students. Allows for students to inform the teacher of
how they feel they might learn better. This helps with differentiation and adaptive
dimension
Exit Slip- Used in the closure of a lesson in order to determine how much the
students learned throughout the lesson. Useful for teachers to self-assess their
teaching and helps with the process of giving feedback.
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Surface Area of 3-D Composite Objects
Summative Assessment:
This form of assessment takes place at the end of a lesson or unit and is used to
measure the level of success or proficiency that has been obtained. Here are the
summative assessment methods used in the unit and their purpose.

Quiz- Used after the last lesson to determine how much progress the students
have made throughout the unit. Did the students reach the intended outcome?
Grading Plan
Presentation regarding inquiry lesson – graded according to the rubric provided in
lesson 2 teacher notes. Students will be provided with the rubric ahead of time so they
know what is expected. 25%
Journal Entry- graded according to the criteria for journal entries that was given in the
syllabus at the beginning of the year. (Focuses on students thoughts, connections
made, and supportive evidence) 25%
Calculation of Surface Area for 3-D Composite objects located around the schoolgraded according to whether or not students distinguish 3-D composite objects and the
process they used to calculate the surface area. Was the overlap taken into
consideration? 25%
Quiz- Students will be graded on both the process used and whether or not they
received the correct answer. 25%
*** Each component is worth 25% of the unit. It has been divided this way to assess
students in a variety of ways which allows a better opportunity for all students showcase
their knowledge.*****
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