Surface Area of 3-D Composite Objects - Web viewStudents may try to determine the surface area of 3-D composite objects that include more than rectangular prisms, triangular prisms,

Surface Area of 3-D Composite Objects

Grade 9 Unit Plan


By Mark Johnston & Kaylyn Wallen

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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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Broad Areas of LearningDeveloping 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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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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OutcomeShape 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.

IndicatorsA) 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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Big IdeaIt 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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DifferentiationDifferentiation 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:

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:

Entrance slips. Exits slips. Class, group, and partner discussions. Journal Entries. Checklist Quiz Interviews Oral Presentation

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Record of AdaptationA 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 3-

D 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 InterventionsThere are many forms of Tier 1 Interventions that are used throughout this unit. They are represented throughout the unit plan.

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 Fostering Independence and Assistive Technology

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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).

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.

Prerequisite Learning: 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

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 the examples

Students may have different objects

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that are composite objects that have cultural significance to them

Materials:-Square blocks (or other manipulatives)-Smartboard-Nets (if students need)

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

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):

Engage in a class discussion regarding the entrance slipo 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 differenceo 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 calculated and to bring their idea to the next class. [TN 4]

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Differentiation:

Students can use nets for manipulatives to help them better understand calculating surface area (linking cubes, wooden blocks)

Adaptive Dimension

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 spheresAssessment

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

Lesson 1 Teacher Notes

1. Pictures for slideshow

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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)

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

Therefore Nathan would need to spend $31.41 on paper to wrap his parents’ Christmas gifts

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2 cm

19 cm10 cm

45 cm

10 cm


3.

a)

b)

c)

13

6 cm

10 cm

17 cm


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.

4.

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5 cm

5 cm

5 cm


Lesson 2: Introduction to 3-D Composite Objects With an Inquiry Approach

Topic: Targets for Professional Growth:

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Introduction to surface area of composite objects through inquiry Organizing group work

Big Idea:

EQ: 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?

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

Extend understanding of area to surface area of right rectangular prisms, right cylinders, right triangular prisms, to composite 3-D objects.


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”.

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.”

Prerequisite Learning: 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

Considerations:

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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):

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):

Split students up into groups of three Give each group paper, rulers, scissors and three blocks which will include:

o Rectangular prismso 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

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 achievedo If not ask why their results might be different then what they predicto Ask students what this tells us about how we calculate surface area of

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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 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

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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

4) Present your findings to the class

3. Rubric

Rubric for Assignment

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Established Meeting Progressing Beginning

Mathematics Involved

Always shows evidence of

mathematics.

Frequently shows evidence of mathematics.

Sometimes shows evidence of

mathematics.

Rarely or never 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 shows creativity

and organization, and is engaging and informative. Contributions are made by all group

members.

Presentation shows some

creativity, organization,

and engagement

and is informative.

Contributions are made by most group members.

Presentation shows lack of

creativity, organization, and engagement and is not informative. Contributions are

made by few group members.

Presentation shows no creativity,

organization, or

engagement and is not

informative. Contributions are made by

only one group

member

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

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have a good understanding of how to find the surface area of 3-D composite objects.

Big Idea:


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:

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.

Prerequisite Learning:

Estimate the surface area of a 3-D composite object.

Calculate the surface area of a 3-D object.

Considerations:

Students may try to determine the surface area of 3-D composite objects that include more than rectangular prisms, triangular

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Understand how overlap influences the surface area of a 3-D composite object.

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 3-D composite objects may have difficulty with this activity. What can be done to help them out?

Materials:

SmartBoard Measuring devices (rulers or meter

sticks) Paper

Advanced Preparation:

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 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

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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:

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.

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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?

Lesson 4: Re-tinning the Ol’ Storage Shed

Topic:

How calculating surface area of 3-D

Targets for Professional Growth:

Proximity- walk around the room

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composite objects can be beneficial in real world situations.

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:


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:

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.

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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.

o What will you do in this situation?

Materials:

SmartBoard

Advanced Preparation:

Have stop motion videos prepared that will be shown in the set.

PowerPoint that is put together for

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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):

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?

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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 re-tin 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:

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?

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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

Here is the quiz that will be given at the beginning of the next class to evaluate the unit.

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http://www.youtube.com/watch?v=FkmZAXbK6Ms

http://www.youtube.com/watch?v=jZnoz3GJ7og


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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AssessmentDiagnostic 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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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 PlanPresentation 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 school- graded 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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Documents

Surface Area of 3-D Composite Objects - Web viewStudents may try to determine the surface area of 3-D composite objects that include more than rectangular prisms, triangular prisms,