A Perfect Square to a Cube; Utilizing a Cube
Subject: Math, Art, Language Arts
Grade Level: 4
Standards Alignment:
Mathematics
Standard: Geometry and Spatial Sense
Benchmark: Characteristics and Properties
Indicator: 1.Identify, describe and model
intersecting, parallel and perpendicular lines
and line segments.
Indicator: 2.Describe, classify, compare and
model two- and three-dimensional objects
using their attributes.
Standard: Measurement
Benchmark: Measurement Units
Indicator: 3.Identify and select appropriate units
to measure: a. perimeter, b. area, c. volume.
Art
Standard: 2. Creative Expression and Communication
Benchmark: 2-A. Demonstrate knowledge of visual art materials,
tools, techniques and processes by using them
expressively and skillfully.
Indicator: 2-3 Initiate and use strategies to solve visual
problems (e.g., construct three-dimensional art
objects that have structural integrity and a sense of
completeness).
Standard: 5. Connections, Relationships and Applications
Benchmark: 5-B Use the visual arts as a means to understand
concepts and topics studied in disciplines outside the
arts.
Indicator: 5-4 Demonstrate technical skill by creating an art
product that uses common materials and tool from
different subject areas (e.g., ruler, compass, graph
paper and computer).
(Variation) Language Arts
Standard: 5.Reading Applications: Literary Text
Benchmark: 5-E: Organize presentations to provide a beginning,
middle and ending and include concrete details.
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5-G: Deliver a variety of presentations, using visual
materials where appropriate.
Indicator: 5-1 Describe the thoughts, words and interactions
of characters.
5-2 Identify the influence of setting on a selection.
5-3 Identify the main incidents of a plot sequence,
identifying the major conflict and its resolution.
Description:
Students will be able to construct and describe a square using a compass
and straight edge and then proceed to make a full net for a cube in any desired
measurement. Then, make use of the cube as a box or other learning tool, (i.e.
Language Arts literary applications, brainstorming ideas, or math fact practice.)
Taken from The Geo-Art Workbook: Conceptualizing in Three Dimensions;
Chapter 4, pgs. 55-67.
Duration: Two one-hour class sessions
Vocabulary:
Perimeter
Area
Volume
Horizontal
Perpendicular
Vertical
Shape
Form
Net
Face
Edge
Design
Illustrate
Objective: To model perpendicular lines, and use the appropriate units to
construct a square and cube, then use the form to practice other skills.
Procedure:
1. Define a square and have the students point out examples.
2. Following the directions explained in The Geo-Art Workbook:
Conceptualizing in Three Dimensions, Chapter 4, pgs. 55-59
demonstrate on the board or overhead, how to use a compass to
make a perfect square.
3. Pick any point on horizontal line AB, call it O. Set the compass point to
O, and sweep out arc CDE. Arc CDE should be at least a half circle.
4. Set the compass point at D, and sweep out another arc, which crosses
line AB at O, and meets arc CDE at the top and bottom. A straight line
drawn from C to E crossing line AB at point F is perfect perpendicular
to line AB.
5. This perpendicular on the horizontal line now gives two of the four
sides of the square. Determine how long a side is to be and set the
compass to that dimension. Sweep out that length along line AB and
perpendicular FE with the arc GH.
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6. To complete the other two sides of the square, set the compass at G
and sweep a small arc just above H at I. Do the same at H, crossing
the arc just made from G, at the same point I. A line drawn from G to I
and from H to I will complete the square.
7. To make a net for a cube, start with a straight line and erect a
perpendicular (explained above) at point O. Decide how large of a
cube you want to make (ex. 4 inches on a side) measure off this
dimension both on the perpendicular line OA, and also on
the horizontal line at OB. With the compass set on B, strike off an arc
from O to F. Lines drawn from A to F and from B to F will provide a
true corner to the firs square. With the compass at B, mark off C, D,
and E. Arcs from F and C will give the second complete square at G;
G and D will give H, etc. Lines connecting all of these points will give
the four of the six squares required for the net. By simply extending
two vertical lines of any one square, say BF and CG above and below
the line using the correct dimension will give the full net for a cube.
8. Have the students make their own constructions on heavy
poster board. (Pictured are pre-cut squares, from the Canton Museum
of Art, being assembled with clear tape to create the net and cube.)
9. Before cutting out the completed net, go over all the lines
between the connecting squares with the point of the
compass guided by the straight-edge, and gently press in to
“score” the board. This will facilitate folding along these
lines. Hold the compass point at a steep angle—45 degrees
or so, not upright—to score. Otherwise, the board will
shred or ripple. Don’t press so hard that it cuts through
the poster-board. A light groove is all that is needed. Cut
out the cube, fold it up and tape it together.
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10. Once a cube is constructed, it can serve many purposes in the
classroom. Shown here, are cubes constructed as gift boxes.
11. Cubes can also be used to practice literary skills (such as explained in
the lesson “Making the Perfect Triangle for Story Telling”. Students
use each face of the cube to draw/write the different parts of a literary
piece, such as characters, plot, setting etc.
12. Another variation might be to use the cubes for math practice games.
Placing common math facts on each face, to “roll and answer” played
in small groups. Math vocabulary practice (one term on each face to
practice) and probability skills are all useful variations for the cubes.
Below Basic: Have a pattern of the square and the net for the cube for the
student to trace around to make the shapes. Make sure the fold marks are on the
pattern.
Gifted and Talented: These students can extend this activity to make a box and
a house. (See The GeoArt Workbook for detailed instructions, Chapter 4, pgs.
68-72.)
Assignments: Have the students carefully unglue a cubic or rectangular box to
see what the net looks like.
Supplies: Plain paper, straight edge, compass for each student, heavy poster
board, clear tape
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Assessments:
Rubric: Art Standards
1
Creative
Incomplete
Expression &
project/work
communication
Connections
Relationships
& Applications
Author:
2
Minimal use
of design.
Unrelated
patterns/ideas
Unable to
Form
complete the constructed
square or net with some
misalignment
or mismeasurement
3
Use of
elements of
design,
general
design
concept, few
mistakes
Form built has
good
alignment, but
is loose or
wobbly. With
minimal mismeasurement.
4
Cohesive
design. Good
use of artistic
qualities,
creativity and
use of media.
Very well
constructed,
good
alignment and
measurement
Sharon M. McConnell - Plain Local Schools, Warstler Elementary,
Terri Bradshaw - Canton Local Schools, Walker Elementary
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