SYMMETRICAL ORIGAMI
TAY LO R R U M S E Y
ESSENTIAL QUESTION
How can we use origami to model
different types of symmetry?
OBJECTIVES
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Students will learn the 3 different types of symmetry
(Reflection, Rotation and Translation), and then demonstrate
their knowledge by creating a “Symmetrical Origami Art Project”
Students will become familiar with Origami as a Japanese art
form; and they will master some of the folding techniques
(turning a rectangular paper into a square paper without a ruler,
and making sure a fold is lined up perfectly)used in this
Japanese form of art, which will also be demonstrated in their
Origami art project
Students will use the 4 explicitly taught Origami folds (kite,
skinny kite, triangular 1 and triangular 2) to create an artwork
that reflects the different types of symmetry (more specifically
reflection and rotation symmetry)
VOCABULARY
Symmetry- when one shape becomes
exactly like another if you flip it around,
slide it, or turn it.
Reflection Symmetry —when you fold a 2-D
figure in half, the two parts will match
up perfectly; also known as mirror
symmetry
Rotation Symmetry- the image/figure can be
turned a certain amount and look exactly
the same; also known as radial symmetry
Translation Symmetry- moving an object to
the right, left, up, down or diagonally
Line of symmetry- divides a figure into two
equal halves (can be horizontal,
vertical or diagonal)
Origami- the Japanese art of folding
paper into decorative shapes and
figures
Fold- to bend something over on itself
so that one part of it covers
another
Kite Fold- a fold that looks like a kite
Skinny Kite Fold- a fold that looks like
a skinny kite
Triangular Fold- a fold that looks like a
triangle
REFLECTION SYMMETRY
Example:
• Also known as
“Mirror Symmetry”
• When you fold a 2-D
figure in half and the
two parts will match
up perfectly
Non-example:
LINE OF SYMMETRY
Divides a figure into
two equal halves (can
be horizontal, vertical
or diagonal)
A shape can have
more than one line
of symmetry
HOW MANY LINES OF SYMMETRY? WHERE
ARE THEY?
ROTATION SYMMETRY
• Also known as
“Radial symmetry”
• The image can be
turned/rotated a
certain degree and
look exactly the
same as it originally
did
WHICH SHAPE IS NOT AN EXAMPLE OF
ROTATION SYMMETRY?
TRANSLATION SYMMETRY
Moving an object to the
right, left, up, down or
diagonally
 Your initial shape does
not move
 The translated shape is
the one that is moved
The translated figure
may not be rotated or
flipped!
Correct:
Incorrect:
WHICH OPTION SHOWS TRANSLATION
SYMMETRY?
HISTORY OF ORIGAMI
Origami- The Japanese art of folding paper
into decorative shapes and figures
 The word “Origami” comes from the
Japanese words oru (to fold) and kami
(paper)
 Paper folding in ancient Japan was used
only for religious purposes
 Early 1600’s-paper folding became a
recreational activity as well
 Late 1700’s- first written instructions for
paper folding appeared
 Origami was/is a huge part of
Japanese culture
 It is now an art form used all over the
world!
Examples
ORIGAMI FOLDS
1. Kite Fold
3. Triangle Fold
2. Skinny Kite Fold
4. Triangle Fold #2
THE KITE FOLD
Step 1: Fold the square
paper in half to make a
triangle
Step 2: Take outside corners and
line them up with the crease that
you made in the middle
The Skinny Kite Fold
Step 1: Make regular Kite
fold
Step 2: Take outside edges
and fold them towards the
center once more
TRIANGULAR FOLD 1
Step 1: Fold Square in half
(hotdog style)
Step 2: Fold paper
in half again to
create a small
square
Step 3: Open fold once; Take
the bottom corners and line the
edges up with the fold line you
created
TRIANGULAR FOLD 2
Step 1: Fold the square in half
diagonally to make a large triangle.
Open it, and fold it the opposite way.
Open again.
Step 2: Push two opposite
triangles together and pinch the
top
Step 3: Squish flat!
SYMMETRICAL ORIGAMI
You will create a symmetrical design using the origami folds you make!