Straw polygons are a simple and effective "low-tech" way for students to have hands-on experience with the properties of the polygons. The teacher can make large ones for display, and the students can make their own smaller ones to own and to experiment with. The only materials needed are drinking straws (either clear or colored ones) and elastic string. The students can create a square, rhombus, rectangle and parallelogram, by threading elastic string through pairs of straws as shown below. For all 4 quadrilaterals, students can add the diagonals by tying additional strings from each vertex to the opposite vertex. All four straws should be congruent to create a square or rhombus. To create the rectangle and parallelogram, students should use one pair of equal straws for the top and bottom, and second pair of equal straws, which are longer than the first pair, for the left and right sides. They can then "play with" and have their own hand-held models with which to investigate the definitions and properties of these quadrilaterals.

The parallelogram becomes a rectangle once you make one of the angles a right angle. What properties does the parallelogram retain? What new properties does it gain? For example, the students will discover that the diagonals of the rectangle appear to be congruent, but this does not seem to be true for the diagonals of the parallelogram. The diagonals of the square seem to be always congruent, but this does not seem to be true for the diagonals of the rhombus. All angles of the square appear to be congruent but this does not appear to be true for the rhombus, etc. The students can then derive their own proof of these properties, as verification.

It is important that a discussion follows these experiments and observations, in which either the teacher or the students prove those things that appear to be true from these "experiments". The teacher might ask "Do these properties appear to be true? Are you sure? Can we prove it beyond a doubt? Is measurement proof? Can you think of something that was thought to be true, based on observation but turned out to be false?" Some good examples to give the students are: "The world was once thought to be flat, because it looks like that when we see out over the ocean." The teacher might offer an "extra credit" project, for students to find other examples of beliefs that people used to have but which turned out to be incorrect.

Students will find these models inexpensive, quick and easy to make, as well as very helpful in investigating most if not all of the properties of the quadrilaterals. Once they have experimented with them, they will more readily understand the proofs when they are presented and discussed, and remember the properties as well. Whenever students are unsure if a quadrilateral has a particular property, they can recall and visualize what they discovered when working with their "toys!

The straw polygons are equally valuable when investigating other polygons. Students can create a pentagon, with 5 equal straws, and then experiment with this model. If a pentagon is equilateral, is it equiangular? If a hexagon is equiangular, is it equilateral? Students will find it much easier to understand and remember the properties of all polygons with these convenient, hands-on teaching aids.

Here are some examples of straw polyons.

First, two positions of a polygon with all 4 sides congruent:

. . . and second, 2 positions of a quadrilateral with 2 pairs of congruent sides (but not all 4 sides congruent)/

 

Students will enjoy making these, and by manipulating them they will be able to easily observe certain properties of the polygons. For example, if the rectangle above is pushed sideways to form a parallelogram, the previously congruent diagonals are no longer congruent. Congruent tiagonals is one of the properties of a rectangle but not a parallogram. When the square in the second pair of diagrams becomes a rhombus, we see that the diagonals of a rhombus are not necessarily congruent.

These straw polygons can be used to make conjectures about all of the properties of the quadrilaterals, which can then be verified by mathematical proof.Students can also make straw trapezoids (isosceles and non-isoscleles), pentagons and hexagons, etc.The polygons become a bit unwieldy as the nuber of sides increase, but they are easily manipulated if placed horizontally on the table.

The teacher can can create and use these models to display and discuss the properties, but models work best when created and manipulated by the students them selves. It does take a bit of classtime and require materials, but the effort is well worth the results, both in student participation and in learning.