Let's Go Fly A Kite - Using the Correct Geometry Term for Diamond!

This was a comment I received from a fourth grade teacher, "Would you believe on the state 4th grade math test this year, they would not accept "diamond" as an acceptable answer for a rhombus, but they did accept "kite"!!!!!  Can you believe this? Since when is kite a shape name? Crazy."

First of all, there are NO diamonds in mathematics, but believe it or not, a kite is a geometric shape! The figure on the right is a kite. In fact, since it has four sides, it is classified as a quadrilateral. It has two pairs of adjacent sides that are congruent (the same length). The dashes on the sides of the diagram show which side is equal to which side. The sides with one dash are equal to each other, and the sides with two dashes are equal to each other.

A kite has just one pair of equal angles. These congruent angles are a light orange on the illustration on the left. A kite also has one line of symmetry which is represented by the dotted line. (A line of symmetry is an imaginary line that divides a shape in half so that both sides are exactly the same. In other words, when you fold it in half, the sides match.) It is like a reflection in a mirror.

The diagonals of the kite are perpendicular because they meet and form four right angles. In other words, one of the diagonals bisects or cuts the other diagonal exactly in half. This is shown on the diagram on the right. The diagonals are green, and one of the right angles is represented by the small square where the diagonals intersect.

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There you have it! Don't you think a geometric kite is very similar to the kites we use to fly as children? Well, maybe you didn't fly kites as a kid, but I do remember reading about Ben Franklin flying one! Anyway, as usual, the wind is blowing strong here in Kansas, so I think I will go fly that kite!

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This set of two polygon crossword puzzles features 16 geometric shapes with an emphasis on quadrilaterals and triangles. The words showcased in both puzzles are: congruent, equilateral, isosceles, parallelogram, pentagon, polygon, quadrilateral, rectangle, rhombus, right, scalene, square, trapezoid and triangle.  The purpose of these puzzles is to have students practice, review, recognize and use correct geometric vocabulary. Answer keys are included.

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Aliens and Trapezoids

I am always looking for ways to help my students remember things.  For example, when we learn about the properties of one, I sing (yes I do, and a little off key) One is the Loneliest Number.  Since there are so many quadrilaterals to learn (*7 in all), I create quadrilateral stories.  Here is one of my students' favorites.  (Keep in mind, these are college students.)

Once upon a time, I planted a broccoli garden in my backyard.  Since I love geometry, I placed triangle statues all around my garden.  Every morning I would go out to my garden to weed, hoe, fertilize, and water my precious broccoli plants.  One morning, I noticed several of my plants had been eaten.  I was one upset lady; so, I decided to stay up all night and watch to see which critters had the nerve to venture into my garden for a broccoli feast.

That night, I sat at my bedroom window watching the garden.  All of a sudden, out of the sky, came a UFO which landed in my backyard.  As I watched, the door of the UFO opened (I use my arms to imitate the opening door while I say, S-q-e-a-k!) and out came some little aliens.  As they approached my broccoli, they repeated, "Zoid, zoid, zoid".  (I use a high alien like voice.) Sure enough, they ate several of my plants!  They then proceeded back to their spaceship and flew away. 

The same thing happened the following night and the night after that; so, I knew something had to be done.  I went to my garage, and got out my trusty chain saw to cut off the top of each of my triangles.  (I imitate the noise of a chain saw.)  Inside each cut off triangle I placed a bunch of broccoli to entice my visitors.  I knew if those aliens got inside, they would never get out because of the slanting sides.  I went back into my house to wait.

Sure enough, like clockwork, the UFO returned.  Again, the door of the UFO opened (s-q-e-a-k!) and out came the same little aliens. They proceeded to my cut off triangles, and perched on the edge peering down at the broccoli, all the while saying, "Zoid, zoid, zoid".  One by one they leaped inside to eat the broccoli, and guess what.  I trapped-a-zoid!  Okay, you may not be laughing, but I swear this story does help my students to remember what a trapezoid is. 

Let's discuss a couple of important math things about trapezoids that you may not be aware of.   In my story, the trapezoid is an isosceles trapezoid or as sometimes called, a regular trapezoid.  Not only does it have one set of opposite sides parallel, but it also has one set of opposite sides equal (marked with the black line segments).  It also has one line of symmetry which cuts the trapezoid in half (the blue dotted line).  This special trapezoid is usually the one taught by most teachers, but it is really a special kind of trapezoid. 

   trapezoid                                   isosceles trapezoid

For a quadrilateral to be classified as a trapezoid, the shape only needs to have one set of opposite sides parallel as seen in figure one.  The first trapezoid is the one that sometimes appears on tests to "trick" our students.

In the second figure (the isosceles or regular trapezoid), the sides that are not parallel are equal in length and both angles coming from a parallel side are equal (shown on the right).  Lucky for me that I used the second trapezoid for my trap or my zoids would have been long gone, and with my entire crop of broccoli, too!

*square, rectangle, rhombus, parallelogram, trapezoid, kite, trapezium

Faux Diamonds

In some preschool and kindergarten classes across the country, the geometric shape formerly known as a diamond is now being called a rhombus.  Why?  Does it matter? 

To be honest, a diamond is not technically a mathematical shape whereas a rhombus is.  When someone says the word rhombus, you know they are referring to a quadrilateral that has all four sides the same length; the opposite sides are parallel, and the opposite angles are equal.  (Mathematical Warning: A rhombus is not thinner than a diamond, AND the plural form, rhombi, is not a dance performed on the program Dancing With the Stars.)  

But what comes to mind when you hear the word diamond?  If you are a woman, you might envision a large sparkling gem setting on the ring finger of your left hand.  If you are a guy, you might think of a baseball infield. (The distance between each base is the same, making the shape a diamond.)  If you play cards, the word might bring to mind a suit of playing cards, OR you might recall a line in the song, Twinkle, Twinkle, Little Star.  Calling a rhombus a diamond is similar to calling a child a "kid" (could be a baby goat), or a home your "pad" (might be a notebook).  The first is an accurate term, the second one is not. 

So how does this affect you as a teacher?  It doesn't, unless rhombus is on a local benchmark or state test.  But if you are an elementary grade teacher, please use the correct mathematical language because a middle school math teacher will thank you; a high school geometry teacher will sing your praises, (see song below) and a college math teacher, like me, will absolutely love you for it!

Rhombus, Rhombus, Rhombus

  (sung to the "Conga" tune)
(The song where everyone is in a line with their hands on each other's shoulders)

 Rhombus, rhombus, rhombus;

Rhombus, rhombus, rhombus

Once it was diamond;

Now it's called a rhombus.