PATTY PAPER AND ORIGAMI: A TOOL FOR ALL STUDENTS
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
The patty paper and scissors are passed out. Students review the vocabulary
of square, isosceles right triangle, rhombus, trapezoid, and parallelogram.
Students should have their origami paper ready being sure it is square.
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.
To give each student a specific responsibility while viewing say, "Be
ready to fold your own limping seagull."
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.
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.....
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.
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.
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.
Students put the puzzle on graph paper and find the equation of each line
used to make the puzzle, using slope-intercept.
Students make other figures from the unit shape. Gift boxes could be made.
(Unit OrigamiMultidimensional Transformations, by Tomaoko Fuse', Japan Publications,
Master Teacher: Martha Tietze
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