Science/Engineering & Technology
Instructional Design Lesson Planning Template
Grade/Course: _Geo-Ch10 Volume Lesson:2-D and 3-D Drawing Exploration
Science and Engineering Practices
engineering practice standards
2. Developing and using models
3. Planning and carrying out investigations
5. Using mathematics and computational thinking
6. Designing solutions
Mathematics practice standards
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
Cross Cutting Concepts are bolded
Core Idea
Core Idea Question
ETS1: Engineering Design
EST1: What is a design for? Why would you want to design
Mathematics – Geometry – Congruence –
something before you build it?
Experiment with transformations in the plane --A design is created to have a plan for creation of an object or
Mathematics – Geometry – Congruence –
process or system. We design before building for multiple reasons –
Understand congruence in terms of rigid
to optimize our solution, to test our solution using computer
motion
simulation before actual products (saves money), and for ease – it is
Mathematics – Geometry – Geometric
much easier to run multiple, even simultaneous, tests in a computer
Measurement and Dimension – Visualize
program than using life size materials. We want to test accuracy as
relationships between two-dimensional and
much as possible before executing the design.
three-dimensional objects
Math: What connections can be made between two-dimensional
Mathematics – Geometry – Modeling with
drawings and three-dimensional drawings?
Geometry – Apply geometric concepts in
--3D objects can be represented with 2D drawings called Nets.
modeling situations
Students will be able to explore symmetry of objects and two- and
three-dimensions. Visualization skills will be developed as students
learn to visualize and draw connections between the twodimensional net of an object and its actual three-dimensional shape.
Math: Why would you need to visualize the relationship between
two- and three-dimensional objects?
--“The development or improvement of 3-D spatial visualization
skills is often cited as one of the major goals of engineering design
graphics education,
(http://www.edgj.org/index.php/EDGJ/article/viewFile/126/122).”
“Engineers are required to have a high level of visualization skills
necessary in the design process and in the solution of engineering
problems. However, many of the freshmen engineering students have
problems in processing and understanding visual information or in
developing mental images
(http://core.ecu.edu/ITEC/chinr/59thmidyearproceedings/76.pdf).”
Component Ideas
Component Idea Questions
ETS1.B: Developing Possible Solutions
ETS1.B: Why might it be important to come up with more than one
possible solution?
--In mathematics, as in other subjects, there are always multiple
ways to approach a problem. This is part of the beauty of math that
often gets lost. Students need to see that there are, almost always,
more than one answer to a problem and the fun and excitement and
creativity of problem solving is finding your own solution!
Grade Band Endpoints (Learning Intentions)
ETS1.B: Students will use computers in representing a design in 3-D through CAD software
Success Criteria
Students will be able to visualize three dimensional objects from nets and orthographic drawings.
Students will create a two-dimensional drawing of an object.
Students will create a three-dimensional image in a CAD program of that object.
Students will apply knowledge to transition from area to volume concepts.
Formative Assessment
Summative Assessment
Two-dimensional drawing and threedimensional image created in CAD and
Chapter 10 test
journal describing understanding and
Final Unit Project
learning process.
Integration
Mathematics:
Transitions between two-dimensional and three-dimensional thinking and visualization.
Visualizing Volume from Area
ELA:
Students will journal about their experiences and their ability to visualize in three dimensions before and
after the module.
Other:
Accommodations for Differentiated Instruction *Note: individual needs will be assessed after reading
individual’s IEPs and upon meeting and working with students in the classroom.
Special Needs
English Language Learners
Gifted & Talented
Students will be provided
Students will be given translations Students will be given more challenging designs
with additional time to
for instructions
on which to work such as a bridge or kart.
complete 3-D image and 2Possibly have students work without the
D drawing.
isometric dot paper.
If needed, students will be
provided with explicit
examples of both isometric
and orthographic drawings.
Lesson Details
Lesson 1:
1. Brainstorm Journal: What is the
difference between two- and threedimensions?
2. Visualize the three-dimensional
object created by a two-dimensional
net. Students will be provided with a
2-D net and will be required to sketch
the 3-D image of the object. Students
who struggle will be given the option
of first cutting out the net and then
putting it together to see it in three
Materials Needed and Additional Notes
*8-12 blocks per student
*Investigation sheet with steps
*isometric dot paper
*computers with Autodesk inventor installed on them or
TapTapBlocks.com.
In Lesson 1, as students are introduced to two-dimensional nets, they
are engaged in discovering what the two-dimensional nets will
create. They will be able to notice patterns in nets and work with
their hands by cutting them out and gluing them together to make
connections between their existing ideas of three-dimensional
objects and the new idea that these can be represented with two-
dimensions.
3. Students will be introduced to
isometric and orthographic
definitions and types of drawings.
Students will define each and sketch
examples of each type of drawing.
Lesson 2:
1. Warm Up: Students will be given a
sheet with a mix of orthographic and
isographic drawings and be asked to
match one to the other.
2. Students will explore two- and threedimensions. They will each be given
8-12 wooden blocks to build a threedimensional figure. Once they have
decided on their figure, they will
draw three orthographic views of
their figure and an isometric drawing
of their figure.
Lesson 3:
1. Journal/Essay (to be turned informative assessment): What have
you learned about two- and threedimensional drawing? How do you
feel about your ability to draw in both
dimensions? How do you determine
each view from the other one? How
has your ability to draw and visualize
three dimensional objects changed?
Explain, in detail, how to draw
orthographically and isometrically.
Explain how a net represents its
three-dimensional object.
2. Students will be introduced to
Autodesk Inventor. They will be
given the rest of the day to learn and
play with the program.
3. Homework: To choose an object from
home (or imagination) of which they
will sketch both orthographic and
isometric drawings. This will be the
image that they will create in
Autodesk.
Lesson 4:
1. Warm-Up:
2. Students will begin creating their 2-D
sketch of their chosen (previous
lesson’s homework) object.
3. Once the 2-D sketch is completed in
Autodesk, students will work on
extruding it to make it threedimensional.
dimensional drawings.
In Lesson 2, students will begin exploring with three-dimensional
objects. They will use wooden blocks to build three-dimensional
objects and figures. They will work with each other to build new
and creative shapes. Their challenge will then be to translate their
three-dimensional design into a two-dimensional drawing.
In Lesson 3, students will journal about their experiences in the unit
thus far. They will explain what they have learned and the
connections they have made about two- and three-dimensional
objects and drawings. They will make connections between their
prior knowledge and new knowledge by answering the listed
questions for Lesson 3 Journal. They will answer the question:
What connections can be made between two-dimensional drawings
and three-dimensional drawings? This journal will be part of their
formative assessment for the unit.
In Lesson 3, students will also begin to elaborate the skills they have
been developing. They will be introduced to Autodesk Inventor.
Students will practice drawing in two dimensions in the program and
learn how to extrude their design to see it in three dimensions. They
will apply the skills developed from turning nets into threedimensional objects to the designs they will now create in this
program. They will begin to see why you would need to visualize
the relationship between two- and three-dimensional object.
In Lesson 4, will continue elaborating their two- and threedimensional design and visualization skills by working on the design
of their choice. Using their chosen object, they will design it in twodimensions first in Autodesk Inventor, then they will work to
extrude it correctly to look like the actual object they have chosen.
In Lesson 5, students will be evaluated on their design in twodimensions and the final design in three dimensions. They will be
evaluated on their reflection essay/journal about their experience,
their new skills, and how their skills have changed and evolved
through this unit. They will answer the questions: What is a design
for? Why would you want to design something before you build it?
There will also be questions on the final Chapter 10 assessment on
this unit.
**Possible extensions – continue with the different dimensional
thinking. Students could read Flatland and discuss/debate the fourth
dimension. This could also be an independent project for Gifted &
Talented students.
4. To complete their image, students
will adjust the lighting and material
aspects of the image.
Lesson 5:
1. Students will complete finishing
touches on their image and submit
both the Autodesk file and their
sketches of the object by the end of
this class.
2. Students will write a reflective
journal/essay about their experience
and their now expertise in two- and
three-dimensional visualization.
Approximate Time Needed:
5 50-minute class periods or 3 90-minute class blocks
5 e’s Instructional Design
ENGAGE
Give students a 2-Dimensional Net of a cube.
Question: Can you visualize the three-dimensional object created by this net?
If yes, draw the three-dimensional object using isometric dot paper.
If no, cut out the net and fold along the lines to make the three-dimensional
object and then draw it on the isometric dot paper.
EXPLORE
Isometric means “having equal measure.” So in our warm-up, the edges of the
cube were drawn isometrically and all have the same length. An Orthographic
drawing shows the faces of the solid as though you are looking at them head on.
(see ex pg. 555-Discovering Geometry)
Students will enhance their visualization skills and do isometric and
orthographic drawings.
Ex A: Make an orthographic drawing of the solid (provided on handout) – draw
top, front, and right side views.
Ex B: Draw the isometric view of the object shown on handout as an
orthographic drawing. The dashed lines mean that there is an invisible edge.
Exploration: Isometric and Orthographic Drawings – students will build block
models and draw their isometric and orthographic views. (Copies of activity
needed for all groups and group members)
Notes/reflection
EXPLAIN
Journal: What relationships do you see between isometric and orthographic
drawings?
How might you draw each kind of drawing if you are given the other kind?
What fields might use this type of drawing?
How is an isometric drawing different from a two-point perspective view (ask
only if we had time to do exploration in ch 3 on perspective drawings)?
What types of two dimensional shapes show up in your drawings?
ELABORATE
Students in groups will use the Autodesk Inventor program to make
orthographic drawings of their own shape. They will then extrude their
drawings (or rotate, whatever needed) to create their isometric shape. Students
will submit their two dimensional sketch of their drawing and then email me or
show me their file of their three dimensional isometric figure.
Students will later use these concepts to make connections between area and
volume.
EVALUATE
*Students will be evaluated on their final submitted two dimensional drawings and
their final three dimensional designed file as well as their journals.
*Students will be able to visualize three dimensional objects from nets and
orthographic drawings.
Additional project for advanced students: 3D Shapes for Engineering

design a functional structure, such as a bridge or a moving cart, making its
constituent parts into the simplest geometrical forms possible. Require that
students create two-dimensional diagrams of the form from at least three
different angles. This will help them to make the connection between twodimensional and three-dimensional shapes, as each diagram will show how
the 3D form intersects a different two-dimensional plane.