PATTY PAPER AND ORIGAMI: A TOOL FOR ALL STUDENTS
Grades 8-10

Tangrams and symmetry will be explored using patty paper. Using a basic building block in origami, polygons and three dimensional figures will be engineered.

Landscape of Geometry Program 7 - "Cracking Up"
The Riddle of the Wizard's Oak Program 4- "Shapes make shapes"
Mathematical Eye Series II Program 4- "Paper Engineering"

Tacile experience will be used to demonstrate geometry. These activities are designed to include all students and learning styles. Students will each create a tangram puzzle and use it to discuss topics of form and area. Students will create a building block that can be used to make origami.

A piece of patty paper for each student, and a pair of scissors for each pair will be needed for the tangram. For the extention a piece of centimeter graph paper for each student may be used. For the origami, each student will need thirty pieces of square paper. If origami paper is used each student may make one unit and the class complete the stellated icosahedron.

Tangram
The patty paper and scissors are passed out. Students review the vocabulary of square, isosceles right triangle, rhombus, trapezoid, and parallelogram.
Origami
Students should have their origami paper ready being sure it is square.

Tangram
To give students a specific responsibility while viewing, the students are asked to write down and be able to recall the seven figures used to make the tangram puzzle.
Origami
To give each student a specific responsibility while viewing say, "Be ready to fold your own limping seagull."

Tangram
The video from the Landscape of Geometry Program 7 "Cracking Up" is started at the point after the red grid and yellow squares (pentinoes), after the man says, "Believe it or not ... it is used on tests...your score can shoot up a few points." Start where the man is standing in front of a table with a lamp over head and says, "You know geometer's are a serious bunch.... but deep down they love games." Play to the point after he makes a triangle and stop when he states the rule about no overlapping pieces.A diagram of the puzzle can be found in the teachers guide for Wizard of the Magic Oak pages 29-30.

Students follow the following these steps to make a tangram puzzle. 1. Fold the square on the diagonal making two large isosceles right triangles. 2. Put one to the side and with the other fold in half making two smaller isosceles right triangles. These will be two of the puzzle pieces. 3. Taking the second half, the vertex with the right angle is folded to the midpoint of the opposite side. The top triangular piece is cut for a third puzzle piece. 4. The piece left is an isosceles trapezoid. When folded along a line of symmetry and cut there will be two right trapezoids. 5. Taking one of the right trapezoids the longer base fold one vertex to the other forming a square and a small right isosceles triangle. These are the fourth and fifth pieces of the puzzle. 6. This last step is the most difficult for students to follow. Using the other right trapezoid, fold the right angle vertex on the longer base to the opposite corner producing a parallelogram and an isosceles right triangle. These are the sixth and seventh pieces.

Origami
Use the Mathematical Eye Series II Program 4-"Paper Engineering". Start the video after the similar figures (the dogs) when you see the hands holding squawking seagulls. Use a remote control and play to pint where he says "Why on Earth would you want...". Pause and rewind back to where is start to fold the seagull. Using slow motion and without sound tell students to fold their square as it is done on the video. Check each student's success and rewind and play again as needed. Continue the video at regular speed until the phrase "with a little practice you can make some wonderfully complicated shapes." and stop when he says ," Here's an idea.....

Tangram
Using the seven pieces and finding the area of the square they started with, students find the area of each piece. I use dimensions of the square as 10 cm. by 10 cm. and graph paper with centimeter squares for convinence.
Origami
The thirty units are assembled as a stellated icosahedron. If time allows each student can make thirty pieces and their own. Printed directions are included at the end of this lesson plan.

Origami
Instructions on making the basic unit the "crane" are given. The story about the little girl with leukemia who was trying to make 1000 cranes and died is read. (A childrens book). Students may decide to make cranes to send to Japan or suggest some other project where they could send the cranes for good luck to a needy person.

Tangram
Students put the puzzle on graph paper and find the equation of each line used to make the puzzle, using slope-intercept.
Origami
Students make other figures from the unit shape. Gift boxes could be made. (Unit OrigamiMultidimensional Transformations, by Tomaoko Fuse', Japan Publications, Inc.,1990).

Master Teacher: Martha Tietze