Lesson Title – Calculating Mass Properties when Designing Course – Technical Drawing
Grade Level – 9-12
Author – Paul Clinton
School – Cherokee Trail High School
Length of Lesson – 100 minutes
CTE Academic Integration Lesson Planner
What do I want students to learn?
Standards and Benchmarks
NBEA Standards…or MarkEd Standards…
or … ITEA Standards
ITEA Standards:
 Students will develop the abilities to
apply the design process.
 Students will develop an understanding
of the attributes of design.
 Students will understand that expressing
ideas to others verbally and through
sketches and models is an important part
of the design process
Standards and Benchmarks
ACT College Readiness Standards


Compute the area and circumference
of circles after identifying necessary
information (Math 24-27)
Use relationships involving area,
perimeter, and volume of geometric
figures to compute another measure
(Math 28-32)
Students will:
Students will:
•Know: (Content and Vocabulary)
•Do: (Skills, Strategies, Processes and Literacy)



Students will know how to calculate the
volume, mass, and surface area of a cylinder.
Students will know equations for cirlces and
cylinders.
Students will know how to calculate the
surface area of a 3D part.




Students will be able to calculate the surface
area, mass, and volume of a cylinder using
Solidworks.
Students will be able to calculate the surface
area of a cylinder using mathematical
formulas
Students will be able to calculate the cost of a
mold base
Students will be able to calculate break even
cost of a manufactured part
Enduring Understandings (Big Ideas)
For example… principles, themes, generalizations or macro-concepts
Students will understand how the differences in material affect the density, mass, and volume of a part.
Students will understand how material choice and size affect the break even cost of a part.
Students will understand how considering mathematical concepts when designing is important to manufacture
and profitability.
Essential Questions
Guiding, driving questions which lead to enduring understandings
How does choice of material affect the density and mass of a manufactured part?
Why do mass properties differ when one applies the fillet feature?
How am I going to assess student learning?
Assessments: Formative assessments and/or Summative assessments
Students will be provided with a tutorial packet to guide them through the lesson.
Worksheet questions included in packet (See attached)
Short answer quiz
Multi-view drawing of bracelet
Lesson Title – Calculating Mass Properties when Designing Course – Technical Drawing
Grade Level – 9-12
Author – Paul Clinton
School – Cherokee Trail High School
Length of Lesson – 100 minutes
Instructional Plan
Prerequisite Skills: Preparation
What prior knowledge, skills and understanding do the students need? How will you assess their background
knowledge and readiness?
Students should have prior knowledge of using a calculator to calculate basic equations. Example problems will
be used as a warm up to refresh & assess student knowledge.
Volume (V) = (π2h)mm3
Sample: d = 75mm, h = 10mm
r  75 / 2  37.5mm
V  (r 2 h)mm3
V   (37.5mm) 2 (10mm)
V   (37.52 mm2 )(10mm)
V   (1406.25)mm2 (10)mm
V  3.14(14062.5)mm3
V  44156.3mm3
Mass (m)
Know:
V  44156.3mm3
  .001g / mm3 for rubber
m  V
g
(44156.3mm3 )
3
mm
m  44.16 g
m  .001
Surface Area, S(mm2)
Know:
r  75 / 2  37.5mm
h  10mm
S  2rh  2r 2
S  2 (rh  r 2 )
S  2 ((37.5mm)(10mm)  (37.5mm) 2 )
S  2 (375mm2  1406.3mm2 )
S  2 (1781.3mm2 )
S  11186.3mm2
Lesson Title – Calculating Mass Properties when Designing Course – Technical Drawing
Grade Level – 9-12
Author – Paul Clinton
School – Cherokee Trail High School
Length of Lesson – 100 minutes
Instruction and Activities:
What procedure (sequence), teaching strategies, and student activities are used in this lesson? State the student
roles, teacher roles, and grouping for this lesson.
See attached tutorial and quiz.
Academic Integration
What core academic topics are integrated? What terminology is common? What terminology is different?
Include specific examples to be used to introduce, teach, or review the topics.
Core academic topics integrated:
Calculating for:



Mass
Volume
Surface Area
Terminology:
Radius: r
Diameter: d
Area: A
Circumference: C
Height: h
Volume: V
Total Surface Area: S
Lateral Surface Area: SLAT
Density: ρ
Mass: m
Mold Base
Break Even Cost
Specific Examples:
Using the following diagram, calculate for:
Volume:___________________
Mass:_____________________
Surface Area:______________
Lesson Title – Calculating Mass Properties when Designing Course – Technical Drawing
Grade Level – 9-12
Author – Paul Clinton
School – Cherokee Trail High School
Length of Lesson – 100 minutes
ACT Problem From p. 459
The end-on view of a cylindrical milk tank on its support is shown in the figure below. The interior radius of the
tank’s end is 4 feet. The length of the tank is 25 feet.
39. Which of the following is closest to the tank’s volume, in cubic feet?
A.
B.
C.
D.
E.
310
630
1,300
2,500
5,000
40. The tank currently holds 5,000 gallons of milk. Each gallon of milk weighs about 8 pounds. About how
many pounds does the milk weigh?
A.
B.
C.
D.
E.
625
4,000
4,992
5,008
40,000
Resources
What materials and resources are needed for this lesson? Describe the learning environment where this lesson
will take place.
Math teacher to help with example problems and resources for calculating surface area, mass, and volume.
Materials Needed:
Students will need a computer with the SolidWorks software installed. Additionally, students will need a
calculator, or the student can use the calculator tool that installed on the computer. Scratch paper and pencil are
also suggested.
Ideally, instructors would have access to a projector to demonstrate procedures and/or show calculation methods.
A whiteboard could also be utilized for calculations.
Learning Environment:
The classroom is a computer lab & work table combination
Specific Teacher Web Resources:
http://www.onlinemathlearning.com/volume-formula.html
http://math.about.com/library/blmeasurement.htm