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```					                       Math-in-CTE Lesson Plan Template
Lesson Title: Into to 3D Solid Computer Modeling Using
Lesson #
Soma Cubes
Susan Fitzwilliam             720-423-6688           Susan_fitzwilliam@dpsk12.org
Craig Magtutu                               720-423- 6612            Craig_magtutu@dpsk12.org
Occupational Area: Architectural Technology
CTE Concept(s): Use of technology to model solid objects
Math Concepts: Standard 4.2c (solids geometry) – Use properties of geometric solids to
find volumes and surface areas of regular and irregular geometric solids.
Lesson Objective:        Draw and manipulate 3-dimensional parts and join them to form
an assembly. Calculate volume and surface area of geometric
solids.
Supplies Needed:         Wooden or foam cubes, Solid Works ® software program,
internet

THE "7 ELEMENTS"                                           TEACHER NOTES
1. Introduce the CTE lesson.                                   This can be an introductory lesson for
SolidWorks® or Inventor® or any other 3D
Today we are going to be working with cubes.
solid modeling computer program.
We are going to calculate the volume and
surface areas of cubes and groups of cubes. We
are going to talk about a special group of cubes
called Soma Cubes. We will be using SolidWorks
computer program to model Soma Cubes.

2. Assess students’ math awareness as it                       Pre test –Students will calculate volume and
relates to the CTE lesson.                                  surface area of rectangular, irregular solids.
Please complete this pre test so I can see what
surface area of cubes and groups of cubes.
3. Work through the math example embedded
in the CTE lesson.
The Soma cube is a solid geometric puzzle
invented by Piet Hein, a Danish mathematician.
Seven pieces made out of cubes must be
assembled into a 3x3x3 cube. The pieces can
also be used to make a variety of other
interesting shapes.
The pieces of the Soma cube consist of all
possible combinations of four or fewer cubes,
excluding all convex shapes. The seven Soma
pieces are all polycubes of order three (tricube)

National Research Center for Career and Technical Education
or four (tetracube).
How may cubes are in a 3x3x3 cube?
What is a convex shape?
What is a polycube?
What is a tricube?
What is a tetracube?
Has anyone ever played the computer game
called Tetris®? Why is it named “tetris”                      A 3x3x3 cube contains 27 cubes:
Let’s go to http://www.tetrical.com/                          3*3*3=27 (volume)
and spend a few minutes playing 3D Tetris.                    A polygon is convex if the segment
The goal of 3D Tetris is to arrange the shapes so             connecting any two points in the interior of
they all fit together and there are no gaps. In a             the polygon is in the interior of the polygon.
Soma cube, we arrange the polycubes in a                      Polygons that are not convex are concave.
similar way, so there are no gaps and the                     The same rule applies to 3D shapes.
finished form is a cube.                                      A polycube is an assembly of more than one
cube attached to the other.
A tricube is an assembly 3 cubes
A tetracube is an assembly 4 cubes

4. Work through related, contextual math-in-
CTE examples.
The "L" tricube
Let’s get out the wooden cubes and, working in
groups, see if you can figure out the seven Soma
cubes using the definition we just talked about.                              T tetracube: a row of three
blocks with one added below the center

DO NOT cheat and look this up on the internet.
We are going to use our BRAINS to try and figure                               L tetracube: a row of three
this out.                                                        blocks with one added below the left side

When we have figured out the shapes, we will                                   S tetracube: bent with block
assign descriptive names to them.                                placed on outside of clockwise side

Left screw tetracube: unit cube
placed on top of anticlockwise side.

Right screw tetracube: unit
cube placed on top of clockwise side..
When you have them figured out, tape them
together and see if you can fit them together into
one large 3x3x3 cube.                                                       Branch tetracube: unit cube

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placed on bend..

5. Work through traditional math examples.                    Volume:
Let’s talk about the volume and surface area of               2” cubes: 2*2*2=8 in³ (27 cubes) =216 in³
you assembled cube.
Surface area:
How would you figure out the total volume?
2” cubes: 2*2=4 in²
How would you figure out the surface area?
9 cube faces exposed on 6 sides = 54 faces
Is the volume equal to the surface area?
4 in² (54) = 216 in²
Even though the numbers are the same, the
units are different.
6. Students demonstrate their understanding.                  In Solid Works ®, go through method to draw
a 2”x2” square and extrude it 2” to form a
Let’s open a Solid Works® part file and draw a
cube.
cube. First we draw a rectangle and then assign
dimensions to it and then we extrude it 2”.                   Students will mate unit cubes to form the
seven Soma shapes.
Now that you know how to make a single cube,
make each of your seven Soma cubes and save                   Mating and assembling objects in Solid
them as seven different parts, labeling them L                Works ®.
tricube, T tetracube, L tetracube, S tetracube,
Left screw tetracube, right screw tetracube,
branch tetracube.
Open a Solid Works® assembly file and insert
your seven parts and mate them to form the
3x3x3 cube.
7. Formal assessment.                                         Students will retake pre test to see what they
have learned.
Please re take the pre test so I can see what you
have learned about calculating volume and
surface area of cubes and groups of cubes.

National Research Center for Career and Technical Education

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