Career Academy Integrated Unit Plan
Academy Name: Engineering Academy
School: Deland High School
Integrated Unit Plan Title: Geometry Applications
Courses to integrate: Geometry Honors, Engineering Technology I
Grade Level: 9
Timeline & Duration: 3 weeks
Unit Summary: In order to enrich curriculum being learned in geometry, students will use CAD skills to reinforce their
understanding of the subject matter, such as changes in perimeter and area, changes in parameters, surface area, and
volume.
Overview of Activities/Lessons per Course
Course
Activity/Lesson
Activity/Lesson
Geometry Honors
Students will find the surface area and
volume of prisms, pyramids, cones,
spheres and cylinders.
Students will compare and find the areas
and volumes of similar solids. Students will
analyze what effects occur to surface area
and volumes by changing parameters of
the dimensions of various solids.
Engineering Tech I
Students will learn and apply parametric and
geometric constraints.
Students will learn and apply 3D modeling
skills using AutoCAD along with solid modeling
skills using Inventor.
Lesson Instructions for Geometry Honors, Activity 1:
Standards (Performance Tasks or Course Frameworks or Sunshine State Standards): MA.912.G.7.5,
MA.912.G.7.4, MA.912.G.7.6, MA.912.G.7.7, MA.912.G.2.7, LA.912.1.6.1, MA.912.G.8.2
Rigor & Relevance (quadrant): B (Application)
Instructions to Teacher: Instruct students using wooden/plastic solids models to identify polyhedrons and determine the
number of faces, edges and vertices. Instruct students on finding surface area and volumes of various solids. Demonstrate
using isometric dot paper transparencies how to draw 3-D figures. Demonstrate using isometric dot paper and unit cubes
how to draw a set of plans for an existing building to illustrate the base, front and right views so that the set of plans can be
read correctly to recreate the building formed by the unit blocks. Prepare copies of handouts for students.
Instructions to Students: Complete all textbook and handouts assignments related to surface area and volume. Work
cooperatively in group activities. Participation in all class room discussions. Complete all isometric drawings.
Instructions for Student Accommodations: Hands on activity, group and individual activities. Subject matter expertise
according to their activity project.
Assessment for Activity: Completion of all textbook and handout assignments. Participation in discussions. Completion
of isometric drawing activity.
Approximate Length of Time for Activity: 2-3 weeks (50 minute class periods) Suggest doing the isometric drawings
after the EOC exam.
Materials Needed: Geometry textbook, appropriate handouts for surface area and volume. Handouts for isometric
drawings, ruler for straight edge for drawings, and interlocking unit cubes.
Resources Needed: “Middle Grades Mathematics Project: Spatial Visualization”: use pages 65-89 and pages 37-48
“Pre-Algebra with Pizzazz Series” pages CC-42 – CC-46
Attachments: Real-World Volume Applications handout.
Real-World Volume Applications
Show all work.
1. The rectangular lead sleeve shown in illustration has a cored hole 2.0 in. by 3.0 in. How
many cubic inches of lead are in this sleeve?
Answer: ________________
2. Find the diameter of a cylindrical tank 23.8 ft. high with a capacity of 136,000 gallons
(1 ft3 = 7.48 gal.) Hint: first find the volume of the cylinder in ft 3 and then plug the data into
the volume formula. Answer: ______________
3. A loading chute in a flour mill goes directly into a feeding bin. The feeding bin is in the
shape of an inverted right circular cone, as show in the illustration. How many bushels of
wheat can be place in the feeding bin? (0.804 bu. = 1 ft3)
Answer: _______________
4. Find the volume of the cylindrical-shaped silo with a hemispherical top shown in the
illustration. Answer: _____________
Lesson Instructions for Geometry Honors, Activity 2:
Standards (Performance Tasks or Course Frameworks or Sunshine State Standards): MA.912.G.7.7, MA.912.G.2.7
Rigor & Relevance (quadrant): B (Application)
Instructions to Teacher: Instruct students to compare and find the areas and volumes of similar solids. Instruct students
with examples on how to analyze what effects occur to surface area and volumes by changing parameters of the
dimensions of various solids. Apply similar solids to real-world applications.
Instructions to Students: Complete all textbook and handouts assignments related to similar solids. Work cooperatively
in group activities. Participation in all class room discussions.
Instructions for Student Accommodations: Group and individual activities. Subject matter expertise according to their
activity project.
Assessment for Activity: Completion of all textbook and handout assignments. Participation in discussions.
Approximate Length of Time for Activity: 2-3 days (50 minute class periods).
Materials Needed: Geometry textbook, appropriate handouts for surface area and volume similarity problems.
Resources Needed: Same as materials needed.
Attachments: Surface Area and Volume handout.
Surface Area and Volume
Similar figures
1. If the radius and height of a cylinder are both doubled, then the surface area is
_____________________
h
2h
d
2d
2. The dimensions of the right rectangular prism shown are doubled. How many times larger is
the volume of the new prism? ________________
7 ft.
2 ft.
12 ft.
3. Two similar cylinders have surface areas of 96π square feet and 150π square feet. The
height of each cylinder is equal to its diameter. Find the dimensions of one cylinder and use
their scale factor to find the dimensions of the other cylinder. ________________
4. The scale factor of the model car at the right to the actual car is 1:16. Use the scale factor to
complete the exercises.
a) The model has a height of 5.5 inches. What is the height of the actual car? _____________
b) Each tire of the model has a surface area of 12.9 square inches. What is the surface area of
each tire of the actual car? ________________
c) The model’s engine has a volume of 2 cubic inches. Find
the volume of the actual car’s engine. ______________
Lesson Instructions for Engineering Technology I:
Standards (Performance Tasks or Course Frameworks or Sunshine State Standards): 11.04, 17.06, 25.01, 25.05,
25.06
Rigor & Relevance (quadrant): B (Application)
Instructions to Teacher: AutoCAD will be used to reinforce concepts and applications being learned in geometry, such
as perimeter, area, changes in parameters affecting the figure, surface area, and volume. Students will learn how to use
constraints (parametric and geometric) commands that would enrich the geometry curriculum. Students will also learn
how to develop 3D models using AutoCAD, and solid modeling using Inventor. Surface area and volume will be studied as
part of this learning. Use geometry text and assignments as a resource.
NOTE: Expand with CNC programming of a part using these concepts and commands.
Instructions to Students: Using AutoCAD, show how to use constraints to change the parameters of a figure. Explain
the function formula of this relationship. Using the AutoCAD 3D modeling and Inventor platforms, show how to create
three-dimensional figures and how to adjust for side lengths, radius, diameter, height, etc. Calculate the surface area and
volume of these figures.
Instructions for Student Accommodations: Hands-on learning, follow along.
Assessment for Activity: CAD drawings and explanation with regards to the geometry curriculum.
Approximate Length of Time for Activity: 3 weeks.
Materials Needed: Computer, AutoCAD, Inventor, geometry text.
Resources Needed: Geometry text, notes, and class assignments.
Attachments: None.