Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 32087
Using Nets to Find the Surface Area of Pyramids
In this lesson, students will explore and apply the use of nets to find the surface area of pyramids.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Suggested Technology: Document Camera,
Computer for Presenter, Basic Calculators, LCD
Projector
Instructional Time: 1 Hour(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: pyramid, lateral area, base area, surface area, slant height
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Square Pyramid.docx
Surface Area Pyramids.docx
Answers to Surface Area Worksheet Irwin.docx
Square Pyramids and Surface area (revised).docx
SAP Lesson Assessment.docx
SAP Lesson Assessment Key.docx
SAP Extension.docx
SAP Extension Key.docx
SAP Row by Row A.docx
SAP Row by Row B.docx
SAP Row by Row Key.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:
be able to identify parts of a three-dimensional pyramid and use proper terminology when describing a pyramid.
find the surface area of a pyramid using the net of the pyramid.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be familiar with the Standard MAFS.6.G.1.1 - Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into
rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Guiding Questions: What are the guiding questions for this lesson?
How can a net help find the surface area of a pyramid?
What shapes do you recognize in a pyramid?
page 1 of 4 What area formulas can help find the surface area of a pyramid?
How might you check your work after you have computed the surface area of a pyramid?
Teaching Phase: How will the teacher present the concept or skill to students?
Before beginning the lesson, the teacher should lead a discussion reviewing prior knowledge. Ask the students to think about what is required before finding the
surface area of a three-dimensional object, such as the need to be able to find the area of a two-dimensional figure.
"With what figures have we already had practice in finding area?"
Possible answers: square, rectangle, triangle, parallelogram, trapezoid
Ask the students what is needed to find the area of a quadrilateral.
Possible answer: multiplying the base and height to find how many square units will cover the figure
Ask the students what is needed to find the area of a triangle.
Possible answer: multiplying half the base and height; multiplying base and height then taking half, essentially taking half of a quadrilateral
Tell students that when we find the surface area of a figure, we are taking the area of each surface of the figure, then adding all the individual areas together.
Making a comparison to prisms as a segue to pyramids.
Elicit from students that prisms are three-dimensional figures that have two congruent and parallel bases, and rectangular lateral faces (sides).
Ask students what makes a pyramid a pyramid.
Answer: pyramids are three-dimensional figures that only have one base and triangular lateral faces.
Ask students, "What do prisms and pyramids have in common?"
Possible answers: they are three-dimensional; they are named by their base shape.
Ask students, "What are the main differences between prisms and pyramids?"
Possible answers: one has 2 bases, one has 1 base; one has rectangular lateral faces, one has triangular lateral faces
Elicit from students that when they find the surface area of pyramids, it is much the same as they find the surface area of prisms. They can use a net of a pyramid
to find the individual face areas, then add them together.
Display a square pyramid for the students. Identify the parts of the pyramid so they are familiar with the term slant height.
Explain the difference between the height of the pyramid (from the vertex of the pyramid, perpendicular to the base of the pyramid) and the slant height of the lateral
face (the height from the vertex of the pyramid, perpendicular to the edge of the base of the pyramid.)
Explain that the height of the pyramid is used in finding the volume (filling up the inside) of the pyramid, whereas the slant height is used in finding the surface area
(covering the faces) of the pyramid.
The most concrete demonstration of finding the surface area is to show a net of the pyramid.
You can show the students the dimensions and demonstrate how to find the areas of the individual figures.
page 2 of 4 Area of base:
Area of sides:
Total surface area: The sum of the five parts of the pyramid is 56 in2.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
The teacher will display the Guided Practice sheet with several examples providing students with an opportunity to practice finding surface areas of pyramids with both
triangular bases and rectangular (includes square) bases.
The teacher will circulate while the students work the problems on their dry erase boards. The teacher will look for common misconceptions, such as not using the
triangle area formula correctly or not summing all faces of the pyramid. This should take no more than 10 minutes.
After practicing at their seats, students should be given a shoulder partner and proceed to complete the Row by Row activity. The students will be paired as one high,
one medium ability student, or one medium, one low ability student. Each student will be given 4 pyramids and asked to find the surface area, however, each partner
will have one of two forms, A form or B form. The A form is for students who are more proficient at solving problems; the B form is for struggling students. The
answer for both numbered problems is the same. The partners work independently, then compare their answers to see if they both found the same surface area. If
the partners do not have the same answers, they need to explain how they arrived at their answers and find the correct answers.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
The students will be given the Pyramid Practice sheet to complete as independent practice. This can be given as a homework assignment, or after the Row by Row
activity has been completed.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will bring the class back together as a whole group and review the concepts learned in the lesson by asking students for answers to the following
questions:
What is the same when finding the surface area of a prism and pyramid?
You have to find the area of each surface then add them together.
What is different when finding the surface area of a prism and pyramid?
A prism will have rectangular lateral faces and a pyramid has triangular lateral faces; a prism has 2 bases, a pyramid has only 1 base.
What is always true about the number of faces for a pyramid?
It will have as many lateral faces as its base has sides.
What formula will you need to use when finding the surface area of a pyramid?
Area of a triangle
What operations will you perform when finding the surface area of a pyramid?
Multiply when finding areas; adding when totaling all the faces
Summative Assessment
Students will be given a lesson assessment to show mastery of finding the surface area of a pyramid and answer questions that elicit the understanding of a pyramid
being comprised of a base figure and as many triangular lateral faces as are sides of the base.
Formative Assessment
The teacher will administer the SAP Formative Assessment for prior knowledge a day or more before teaching the lesson. The teacher will use the responses to
determine the level of support individual students will require during the lesson and adjust instruction accordingly.
Throughout the lesson, the teacher will formatively assess by observing students' work, listening and being mindful of misconceptions. The teacher will ask questions
to probe students' thinking and provide guidance. Students will be encouraged to revise their work.
The teacher's observations related to these and other questions will yield information about what the students appear to know and are able to do and will provide
guidance in making instructional decisions.
page 3 of 4 Feedback to Students
The teacher will provide immediate verbal feedback during the teaching phase as the students practice with nets of pyramids.
Students will receive verbal feedback from their peers in the partner activity as the students will hear what their peers perceive their directions to be.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Students experiencing difficulty in remembering all the steps may be provided with a skeleton assessment that provides all the steps to finding the surface area,
however, blanks replace the numeric values so the students are required to calculate the surface areas.
The teacher should provide support for English Language Learners with translations, dictionaries, and/or examples of unfamiliar vocabulary words.
Extensions:
Students who show advanced ability in finding the surface area of pyramids should be offered opportunities to generalize their knowledge and skills by finding the
surface areas of composite figures. Two suggested problems are included as attachments.
Suggested Technology: Document Camera, Computer for Presenter, Basic Calculators, LCD Projector
Special Materials Needed:
Sufficient copies of the following worksheets:
Row by Row A
Row by Row B
Independent Practice
Lesson Assessment
Extension (optional)
SOURCE AND ACCESS INFORMATION
Name of Author/Source: Anonymously Submitted
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional
objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
MAFS.7.G.2.6:
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
Work toward meeting this standard draws together grades 3–6 work with geometric measurement.
page 4 of 4