Title of Book:
The Warlord’s Puzzle
Author:
Virginia Walton Pilegard
Publisher/Date: Pelican Publishing Company/ 2000
ISBN:
1-56554-495-1
Grade Levels for Recommended Use: 3-8
T.E.K.S.(6.6) Geometry and spatial reasoning. The student uses
geometric vocabulary to describe angles, polygons, and circles.
The student is expected to:
(A) use angle measurements to classify angles as acute, obtuse, or
right.
(7.6) Geometry and spatial reasoning. The student compares and
classifies two- and three-dimensional figures using geometric vocabulary
and properties.
The student is expected to:
(B) use properties to classify triangles and quadrilaterals.
Brief Summary: Hoping to avoid punishment for breaking a beautiful
tile that was his gift to a Chinese warlord, an artist suggests that the
warlord hold a contest to see if anyone can put it back together.
Materials: colored paper, scissors
Suggested Activity: The directions for constructing a tangram can be
found at http://mathforum.org/trscavo/tangrams/construct.html
1. Start by asking students what they know about a square: it has 4
congruent sides and angles, the angles are 90 degrees, it is a
rectangle (is a rectangle a square? No) it is a parallelogram, a
polygon (regular), a quadrilateral, a rhombus (a rhombus is a
quadrilateral with 4 congruent sides).
2. While folding from one corner to the other, discuss the difference
between adjacency and opposites.

Adjacent corners or sides are next-door neighbors to each
other

Opposite corners or sides are across the street from each
other
3. Once the fold has been made, discuss what the fold creates: a
diagonal line or a line of symmetry.
4. After the cut has been made, discuss what you have created: 2
congruent, isosceles, right triangles.
5. After the second set of triangles have been cut, discuss what type
of triangles you have made. Again they are 2 congruent, isosceles,
right triangles. We can test whether they are right or not by
comparing the corners to the one large triangle we have left.
6. Take one of the triangles and point out the names of the sides: 2
legs and one hypotenuse. Ask what the midpoint of a line is.
Create a crease at the midpoint of the hypotenuse.
7. After cutting off the top of the triangle, discuss the shape we have
created. (It is a trapezoid). What do you know about this
trapezoid? (It is a quadrilateral with exactly 1 set of parallel sides.
Also this trapezoid is a polygon with 2 sets of congruent angles).
8. Cut the trapezoid in half. What do the two halves create? Two
more trapezoids. What is the difference between these two and the
original trapezoid that we had? The original had two sets of
congruent angles; these two have no congruent angles.
9. Take one of the halves and fold it to create a triangle and a square.
Make the cuts.
10.
This is the hardest step. Now take the last trapezoid and
fold the right angle down and cut the triangle off. Besides a
triangle, what did we create? A parallelogram. What is the
definition of a parallelogram? A quadrilateral with opposite sides
which are parallel.
11.
Point out that we have made a Chinese Tangram Puzzle.
Close by saying that we have four different sizes of isosceles, right
triangles. Do you think they are proportional? Why or why not?
If time permits, use rulers to measure the sides to confirm that
they are proportional.
Adapted by Dr. Faye Bruun (2012)