Symmetrical Origami

1. Symmetrical Origami Taylor Rumsey

2. Essential Question • How can we use origami to model different types of symmetry?

3. Objectives • 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)

4. 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

5. 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:

6. 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

7. How many lines of symmetry? Where are they?

8. 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

9. Which shape is not an example of rotation symmetry?

10. Translation Symmetry Correct: • 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! Incorrect:

11. Which option shows translation symmetry?

12. 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!

13. Examples

14. Origami Folds 2. Skinny Kite Fold • Kite Fold 4. Triangle Fold #2 3. Triangle Fold

15. The Kite Fold Step 2: Take outside corners and line them up with the crease that you made in the middle Step 1: Fold the square paper in half to make a triangle

16. The Skinny Kite Fold Step 2: Take outside edges and fold them towards the center once more Step 1: Make regular Kite fold

17. Triangular Fold 1 Step 3: Open fold once; Take the bottom corners and line the edges up with the fold line you created Step 1: Fold Square in half (hotdog style) Step 2: Fold paper in half again to create a small square

18. 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!

19. Symmetrical Origami You will create a symmetrical design using the origami folds you make!