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Let's Go Fly A Kite!

One of the comments on the posting Faux Diamonds was quite intriguing. One teacher wrote, "Would you believe on the NY 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."

Well, 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 one dashed sides are equal to each other, and the two dashed sides are equal to each other.



A kite has just one pair of equal angles. These congruent angles are a light orange on the illustration at 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 of yourself 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.

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

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, 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.