Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 43137
Surface Area of Prisms and Pyramids
In this lesson students will find the surface area of three-dimensional figures. Students will use nets made up of rectangles and triangles to calculate
the surface area of rectangular prisms, triangular prisms, and square pyramids.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Suggested Technology: Document Camera,
Computer for Presenter, Internet Connection, LCD
Projector, Adobe Acrobat Reader, Microsoft Office
Instructional Time: 2 Hour(s)
Freely Available: Yes
Keywords: area, surface area, rectangular prism, triangular prism, square pyramid, nets, dimensions
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
FIND THE ERROR_surface area.docx
MAFS.6.G.1.4 scale.docx
Prism Nets.pdf
PSP.SAdynamic.docx
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will represent three-dimensional figures using nets made up of rectangles and triangles. They will use the nets to find the surface area of these figures.
Prior Knowledge: What prior knowledge should students have for this lesson?
Before beginning this lesson students should be able to recall and apply formulas for areas of triangles, rectangles, parallelograms, and composite plane figures.
Guiding Questions: What are the guiding questions for this lesson?
How do you find the Surface Area of a rectangular prism?
How do you find the Surface Area of a triangular prism?
How do you find the Surface Area of a square pyramid?
Teaching Phase: How will the teacher present the concept or skill to students?
The "Hook" and Activation of Prior Knowledge
1. The pre-requisite skills needed for this lesson are: mastery in use of area formulas for triangles, rectangles, parallelograms, and composite plane figures.
2. Cut out and assemble three-dimensional figures from Nets. Prism and Pyramid Nets.pdf
3. Identify each face as a two-dimensional figure (i.e. rectangle or triangle).
Introduce the Concept or Skill
1. Do the "Formative Assessment" here.
page 1 of 3 2. To begin the lesson, show students a box (i.e. a shoebox, tissue box, or cereal box.) Ask students to describe the name of each face (rectangle).
3. Ask, "What shapes make up the faces of this ___ (name of the figure)?" "How do you find the area of that (rectangle or triangle)?" Demonstrate how to measure
the length and width of the front face of the box (in inches or cm). Have students tell you the area. Repeat for the back (a student may comment that the front and
back faces are the same).
4. Continue measuring the dimensions of each face of the box and having the students tell you the area of each face. (Again, students may conclude that you only
have to find the area of one face--just multiply it by 2 to account for the face opposite.)
5. Elicit from the students that the total surface area of the box is the sum of all the faces. This could be listed as front + back + right + left + top + bottom. Or, 2 x
front + 2 x right + 2 x top.
6. Record the "formula" from the formative assessment on the board.
7. Ask "Is there a more efficient way to find the surface area without calculating the area of the faces separately?" ( SA = 2bh + 2bw + 2hw)
8. Discuss what changes in the calculations need to be made if the top of the box (or any other face) is removed. The next part of the lesson addresses this where
only 5 faces of the box comprise the surface area.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Introduce the activity
1. Students will find the surface area of boxes with the "top" removed.
2. At first, they may find the total area of all five faces, one face at a time.
3. Then, lead them to see which face was removed and how to recalculate the surface area. For example, SA = bottom + right + left + front + back.
4. Additional figures can be introduced, such as pyramids and triangular prisms.
Student Actions during the activity
Students will find the surface area of boxes in one of two ways: (1) finding the area of one face at a time, then summing to find the total; or (2) using the formula,
modified to reflect the appropriate missing face.
Students will find the surface area of pyramids by finding the area of the triangular faces and square base first, then summing to find the total area.
Students will find the surface area of triangular prisms by finding the area of the two triangular faces, the three rectangular faces, then summing to find the total
area.
(Students may create their own formulas for triangular pyramids: 4 x area of triangle + area of square = total surface area)
(Students may create their own formulas for triangular prisms: 3 x area of rectangle + 2 x area of triangle = total surface area)
Teacher Actions during the activity
Feedback to Students: The teacher will check on each pair of students and ask which way they calculated the surface area of the given object (either the total of
each face, or using the formula)
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Introduce the activity
1. In this last activity before closure, students will solve problems involving surface area.
2. Students will work alone, but will compare answers with a partner when both have finished. You can give the students the answer key after they have reviewed
their work.
3. Use the attached worksheet, "Problem Solving Practice" PSP.SAdynamic.docx
Expected Student Products and/or Performance
Students should show their method for finding the surface area in each problem (which may include using the formula and showing the substitution in their work).
Answer key provided.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Lesson Review Activity (Teacher Guidance Required)
1. Exit Ticket: Students will answer the given question on an index card. (Teacher should project on the screen "Find the Error" ). FIND THE ERROR_surface area.docx
2. The teacher can collect the index cards and sort them by response.
3. The teacher will revisit the guiding question, "How do find the surface area of a rectangular prism, triangular prism, or pyramid?"
Summative Assessment
1. At the conclusion of the lesson, students will be asked to derive a strategy for calculating the surface area of a rectangular prism, triangular prism and pyramid (the
sum of the areas of the faces)
2. The teacher should write these conclusions on the board or chart paper as the students verbalize them.
Formative Assessment
1. Pre-requisite skills needed for this lesson are: mastery in use of area formulas for triangles, rectangles, parallelograms, and composite plane figures.
2. After the concepts have been introduced, transition to the middle part of the lesson where students will create rectangular prisms and triangular prisms from nets.
3. Students will first find the area of each face, then sum to find the total surface area.
4. Then students can cut out and fold the nets into rectangular and triangular prisms.
Feedback to Students
1. The teacher will give students verbal feedback about their performance and understanding throughout the lesson as the teacher circulates.
2. Use the following questions to clarify any misconceptions that students may have: "How can you convince me that you have found the surface area for the entire
prism?"; "What is the shape of that face?"; How do you find the area of that shape?"
3. Additionally, students will be provided a scale delineating mastery level for the associated standards (see attached MAFS.6.G.14 scale.docx)
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
To accommodate struggling students, use figures whose dimensions are smaller whole number values (less than 10)
Struggling students may be overwhelmed by working with the three different figures. Instead, focus on one figure-and spend the lesson just on rectangular prisms.
page 2 of 3 There are two attached worksheets: one for rectangular prisms, and one for triangular prisms.
When pairing students, consider doing so by ability. (Higher level with higher level; lower level with lower level; that way, you can focus on a few pairs of students
and let the higher level students work independently
Another option for pairing students is to put a strong student with a weaker one. Sometimes a student can explain something to a friend that just couldn"t get it
from the teacher. This also hones the skills of the stronger student.
Students respond to tasks when they take ownership. Students could calculate surface areas of their own boxes (cereal, oatmeal, etc) that they bring in from home.
Support Materials List
The attached worksheet has drill practice on rectangular prisms. (It includes volume practice, but you can disregard that piece). http://www.mathdrills.com/measurement/geom_rectangular_prism_a.html
The attached worksheet has drill practice on triangular prisms. (It includes volume practice, but you can disregard that piece). http://www.mathdrills.com/measurement/geom_triangular_prism_001.html
Extensions:
For advanced students, numerical values in the dimensions do not need to be limited to whole numbers. Include decimal and fractional values.
Problem solving activities can include solving for a missing dimension and don"t need to include an accompanying figure.
The Great Pyramid of Giza was originally covered in bright white casing stones, which made it appear much smoother and more brilliant than today. Ask, "How
could the Egyptians figure out the number of casing stones needed to cover the Great Pyramid thousands of years ago?" This is not focused on the exact number,
but the method.
The attached worksheet has additional practice (the second page is on cylinders and can be disregarded.) http://www.education.com/study-help/article/surfacearea-word-problems_answer/
Suggested Technology: Document Camera, Computer for Presenter, Internet Connection, LCD Projector, Adobe Acrobat Reader, Microsoft Office
Special Materials Needed:
• Scissors • Tape or glue • Rulers • Empty boxes (cereal, oatmeal, etc)
Further Recommendations:
Start collecting cereal and other boxes several days before the lesson.
SOURCE AND ACCESS INFORMATION
Contributed by: Crystal Varnadore
Name of Author/Source: Crystal Varnadore
District/Organization of Contributor(s): Palm Beach
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.6.G.1.4:
Description
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.
page 3 of 3