Materials Needed:

Squares of origami or tissue paper

Scissors

Pencil, if desired

Children become aware of two repeat symmetry with this exercise. Cutting paper dolls or animal chains is a variation of this exercise, as is the intricate Portugese lace tree shown. To make this tree, multiple layers are cut at once and then stitched together.

Exercises

Activity 1: Two Repeats

Show the children to fold a square of paper in half forming a rectangle, or folding along the diagonal forming a triangle. If the paper is colored on one side and white on the other, fold it with the color to the inside. The children may either begin cutting freehand with scissors, or sketch half a design with pencil.  It is important to show them that part of the fold can be removed, but some of it must remain intact. After the design is cut, show them to open the design and press it flat. If desired, the paper cut may be mounted on contrasting paper.

Activity 2: Four Repeats

Using a square of paper, show the child to fold it once, from one corner to opposite corner, diagonally, to form a triangle. Fold it again at right angles to the first fold, forming a smaller triangle. Show them that two sides of the triangle have folded sides. They can begin cutting free hand, or sketch their plan onto the paper. It's important, once again to leave some of the folded sides intact

When they have finished cutting, show them to open one fold at a time, pressing out each fold carefully.

Activity 3: Six Repeats

To fold the paper for a six repeat design, begin by folding the paper in half diagonally.

Then show the child to find the midpoint of the folded side by bringing the opposite corners of the folded side together and pinching the center of the fold slightly.

Place the thumb of one hand along the fold and bring up the right corner of the folded side up to about the ten o'clock position. Crease firmly.

Bring the left corner of the folded edge up to about the two o'clock position. The edges of the fold should be lined up.

Continue as before, cutting from the folds into the center.

When they have finished cutting, show them to open one fold at a time, pressing out each fold carefully.

Activity 5: Eight Repeats

To fold in order to get the most accurate result from eight layers of paper, fold the square twice, diagonally, as you did for the four repeats.

Then open the last fold and bring the folded edge to the center crease and press down firmly on the edge.

Do the same on the other side.

Then fold the two sides back together as they were before along the center crease, forming a small triangle.

Cut as before. When finished cutting, open each fold carefully and smooth, before opening the next fold.

Activity 6: Sixteen Repeats

Activity 4: Twelve Repeats

To make a twelve repeat design (which could result in a six pointed star) simply follow the steps above as for a six repeat pattern and then fold it in half one more time forming the shape to the left.

They can then cut any way  they want, making sure to leave a part of the fold.  Then open up and see the design you have created.

To fold for a sixteen repeat the same pattern as for the eight repeat, but simply fold the final triangle in half again, from the center point. Proceed as before.