Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 45410
Volumes about Volume
This lesson explores the formulas for calculating the volume of cylinders, cones, pyramids, and spheres.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Computer for Presenter,
Internet Connection, Basic Calculators, LCD Projector,
Microsoft Office
Instructional Time: 50 Minute(s)
Freely Available: Yes
Keywords: volume, cylinders, cones, pyramids, spheres
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
VolumesaboutVolumeAnswerKey.pdf
VolumesaboutVolumeChallengeQuestion.docx
VolumesaboutVolumeExitTicket.docx
VolumesaboutVolumeWarmUp.docx
VolumesaboutVolumeWorksheet.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:
Understand differences between area and perimeter of 2D figures and relate concepts to the volume of 3D figures
Calculate the volume of spheres, pyramids, cones and cylinders
Apply volume formulas correctly
Prior Knowledge: What prior knowledge should students have for this lesson?
Be able to properly calculate the perimeter of a variety of 2D shapes.
Be able to properly calculate the area of a variety of 2D shapes.
Guiding Questions: What are the guiding questions for this lesson?
How can you determine the specific volume of a sphere, pyramid, cone and cylinder?
Given the volume and one other dimension of a 3D figure, how do you identify the missing dimension?
Teaching Phase: How will the teacher present the concept or skill to students?
Share the guiding questions for the basis of introduction:
1. How can you determine the specific volume of a sphere, pyramid, cone and cylinder? (Use the correct formula for the specific figure and complete calculations)
2. Given the volume and one other dimension of a 3-D figure, how do you identify the missing dimension? (Using the correct formula for the figure, substitute in the
dimensions and volume given, then solve for the missing variable.)
page 1 of 3 Ask students to explain volume in their own words. (Most answers will be along the lines of "how much something holds" or "how much you can put into something.")
Let this interaction build upon positive classroom engagement.
Now bring students together and focus on the primary formula for volume: Volume equals Area of the base, B, multiplied by the height (V=Bh). Now show students
the formula for the volume of a cylinder, V=∏r2h. Ask students how that ties back into the primary formula (the ∏r2 is the actual area of the base).
Next move to the formula for the volume of a cone, V=
develop, but how do they work the
Bh or
into their answer? (The
Next, move to the volume of a pyramid, V=
∏r2h. Pose same question: how does that relate to the primary formula? Similar answers should
relates to the fact that this shape comes to a point at the top.)
Bh. Once again, the
shows up for the same reason. Ask students why do they only give one formula for this. See
what conversation develops. (They are only given "B" because of the number of different types of bases you can have on a pyramid.)
Finally, introduce the formula for volume of a sphere, V=
∏r3. Develop this formula once you work on the example in the guided practice section. Move onto guided
practice and distribute the worksheet.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Distribute the worksheet and call on students to help you solve the problems. Odd-numbered problems are essentially "fill in formula and solve." Even-numbered
problems are for students to solve for the missing variable. Call on students to work out some of the problems on the board or whatever technology you have within
the classroom. After working through these problems, students should be able to complete the homework assignment with ease. Finally, have students complete the
remainder of the problems in class.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Students will work through the remaining problems located on the worksheet for independent practice. If needed, you can assign additional problems from the
textbook.
The teacher will circulate around room, checking for student understanding and correctness
The teacher assigns homework as necessary.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Students will complete exit ticket, consisting of several figures with a specified volume. Student will have to solve for the missing variable.
Summative Assessment
The teacher will provide students with an exit ticket. Students will be required to calculate the volume of a number of 3D figures as well as calculate the missing
dimension of 3D figures with a given volume.
Formative Assessment
1. Students will calculate volume of a variety of shapes, given all of the dimensions. The teacher will circulate to ensure students correctly use the dimensions within
the formulas.
2. Students will determine the missing lengths within various figures, utilizing ratio, proportion and algebraic methods. The teacher will ask students to explain their
method of solving.
The warm-up activity will consist of several area-type problems to activate students' prior knowledge.
Feedback to Students
Checking to ensure students are using the correct formulas for volume.
Provide additional instruction and/or examples when needed.
Routinely check student work to ensure accuracy.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Students may need to work with partners.
Special needs students may need larger printed worksheets or assistance.
Extensions:
A challenge question is attached, involving an architectural situation.
This lesson could very easily be extended to teach surface area and lateral area.
Suggested Technology: Computer for Presenter, Internet Connection, Basic Calculators, LCD Projector, Microsoft Office
Further Recommendations:
Have all materials prepared and organized ahead of time.
Prepare worked out examples for students who may need additional assistance.
Additional Information/Instructions
By Author/Submitter
This lesson supports the following Standards for Mathematical Practice:
MAFS.K12.MP.1.1 - Make sense of problems and persevere in solving them.
MAFS.K12.MP.6.1 - Attend to precision.
page 2 of 3 SOURCE AND ACCESS INFORMATION
Contributed by: Joe Whitfield
Name of Author/Source: Joe Whitfield
District/Organization of Contributor(s): Jackson
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-GMD.1.3:
Description
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. ★
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