Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 70911
Cone Formula
Students are asked to write the formula for the volume of a cone, explain what each variable represents, and label the variables on a diagram.
Subject(s): Mathematics
Grade Level(s): 8
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, cone, volume, radius, height, dimensions, variable
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ConeFormula_Worksheet.docx
MFAS_ConeFormula_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Cone Formula worksheet.
2. The teacher asks follow-up questions, as needed.
Note: This task assesses students’ knowledge of the volume of a cone formula. Reference sheets should not be used.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not know the formula for the volume of a cone.
Examples of Student Work at this Level
The student cannot correctly identify a formula for finding the volume of a cone. The student writes an incorrect expression and imprecisely describes the meaning of the
variables.
page 1 of 4 Questions Eliciting Thinking
What are the parts of a cone? If you were to create a net of a cone, what two-dimensional shapes would you draw?
What is a variable? Is
a variable? Why or why not?
What terms describe the dimensions of the cone?
Instructional Implications
Ensure that the student is familiar with cylinders and cones as well as terms used to describe their parts and dimensions such as base, lateral surface, height, slant height,
and radius. If necessary, review the formula for finding the area of a circle and be sure the student understands how to apply it. Remind the student that the volumes of
prisms and cylinders can be found by multiplying the area of their bases by their heights. Similarly, the volume of a pyramid or cone can be found by multiplying the product
of the base area and height by one-third. Explain (or use a demonstration to show) why the volume of a cone is one-third the volume of a cylinder with the same base
radius and height. Emphasize the general formulas for finding the volumes of prism and pyramids. Explain to the student that the general formulas along with some basic area
formulas is all that is needed to calculate volumes of prisms, cylinders, pyramids, and cones.
Provide the student with the general formula for finding the volume of a cone, V=
Bh, and show how the specific formula, V=
, can be easily derived from it.
Clearly identify the meaning of the variables in each formula and explain why the two formulas are equivalent. Address any misconceptions about the meaning of
(or how
pi is spelled). Be sure the student can locate the base, base radius or diameter, and height on a model and in a drawing of a cone.
Provide specific examples of cones and ask the student to identify a relevant formula and calculate the volume. Provide feedback.
Making Progress
Misconception/Error
The student does not understand the variables in the formula.
Examples of Student Work at this Level
The student correctly identifies a formula for finding the volume of a cone but:
Does not specifically explain the meaning of each variable and does not correctly label the diagram.
page 2 of 4 Describes h as “height” rather than specifically as the “height of the cone” and refers to the base of the cone as the “bottom circle.”
Questions Eliciting Thinking
Can you identify any parts of a cone? How does the formula you wrote correspond to the diagram?
Can you label where the volume would be located in the diagram?
What is the difference between the base and the area of the base?
How do you measure the height of a cylinder? Is the height on the three-dimensional figure? Where is the height?
What is a variable? Is
a variable? Why or why not?
Instructional Implications
Review the terms used to describe the parts and dimensions of cylinders and cones such as base, lateral surface, height, slant height, and radius. Provide the student with
both the general formula for finding the volume of a cone, V=
Bh, and the specific formula, V=
and explain why the two formulas are equivalent. Address any misconceptions about the meaning of
, and clearly identify the meaning of the variables in each formula
(or how pi is spelled). The student should understand that
is a
specific value and is not a variable. Be sure the student can locate the base, base radius or diameter, and height on a model and in a drawing of a cone.
Provide specific examples of cones and ask the student to calculate the volume. Provide feedback.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student writes:
V=
Bh or V=
.
V is volume, B is the area of the base, r is the radius of the base, and h is the height of the cone.
The student correctly labels the dimensions on the diagram.
Questions Eliciting Thinking
Can you explain how the two different volume formulas, V=
Can you explain why there is a factor of
Bh and V=
, are related? Why do they result in the same answer?
in the formula for finding the volume of a cone?
Instructional Implications
Provide opportunities to solve mathematical and real-world problems by calculating volumes of cylinders, cones, and spheres. Include some figures that are composites of
these solids.
page 3 of 4 Consider implementing other MFAS tasks for this standard (8.G.3.9).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Cone Formula worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and
mathematical problems.
Remarks/Examples:
Fluency Expectations or Examples of Culminating Standards
MAFS.8.G.3.9:
When students learn to solve problems involving volumes of cones, cylinders, and spheres — together with their
previous grade 7 work in angle measure, area, surface area and volume (7.G.2.4–2.6) — they will have acquired a
well-developed set of geometric measurement skills. These skills, along with proportional reasoning (7.RP) and
multistep numerical problem solving (7.EE.2.3), can be combined and used in flexible ways as part of modeling
during high school — not to mention after high school for college and careers.
page 4 of 4