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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

Ten Black Dots

I am an avid reader, and I love books that integrate math and literature. Occasionally, my blog will feature a book that links the two.  I will summarize the book, give its overall mathematical theme, as well as list various activities you can use in your classroom.

Today's book is Ten Black Dots by Donald Crews (Greenwillow Books, 1986).  This picture book is for grades PreK-2 and deals with numbers and operations. 

The book asks the question, What can you do with ten black dots?  Then the question is answered throughout the book by using  illustrations of everyday objects beginning with one dot and continuing up to ten. Simple rhymes accompany the pictures such as:

"Two dots can make the eyes of a fox, Or the eyes of keys that open locks."

Materials Needed: 
  • Unifix cubes or Snap Cubes (multi-link cubes) as seen on the right
  • Black circles cut from construction paper or black circle stickers
  • Crayons
  • Pencils
  • Story paper
  • Calculators -simple ones like you purchase for $1.00 at Walmart

Activities:

1)  Read the book a number of times to your class.  Let the students count the dots in each picture. On about the third reading, have the children use the snap cubes to build towers that equal the number of dots in each picture.

2)  Have the children think of different ways to make combinations, such as: How could we arrange four black dots?  (e.g. 1 and 3, 4 and 0, 2 and 2)  Have the children use black dots or snap cubes to make various combinations for each numeral from 2-10.

3)  This is a perfect time to work on rhyming words since the book is written in whimsical verse. Make lists of words so that the students will have a Word Wall of Rhyming Words for activity #4.
  • How many words can we make that rhyme with:  sun?  fox?  face?  grow?  coat?  old?  rake?  rain?  rank?  tree?
  • Except for the first letter, rhyming words do not have to be spelled the same.  Give some examples (fox - locks or see - me)
4)  Have the children make their own Black Dot books  (Black circle stickers work the best although you can use black circles cut from construction paper. I'm not a big fan of glue!)  Each child makes one page at a time.  Don't try to do this all in one day.  Use story paper so that the children can illustrate how they used the dots as well as write a rhyme about what they made.  Collate each book, having each child create a cover.

5)  Have the children figure out how many black dots are needed to make each book. (The answer is 55.)  This is a good time to introduce calculators and how to add numbers using the calculator.

If you can't find Ten Black Dots in your library, it is still available on Amazon.

A Go Figure Debut for a New Yorker Who Is New!


Renee Dawn's Store
Renee has been a New York City public school teacher for over 20 years, mostly in kindergarten. She has a creative approach to teaching the whole child with the common core, music, art, dance and meditation. In her classroom you will see café-style conversations; dancing to pop, classical, world and educational music; and big dollops of laughs.

She enjoys writing and recording pop songs, sewing, long walks down city streets, the beach and forest parks....and organic dark chocolate.
Free Resource
I chose Renee's Teachers Pay Teachers store, called Renee Dawn because it incorporates many unique and engaging resources that are not readily available in other stores. Her store currently features 72 different resources (21 of them have songs), with three of the resources being free. 

The item that is closest to her heart is entitled: Free-Verse, Creative Poetry Writing for K – 5.  It includes 16 writer’s workshop lessons that are a recipe for beat-poet confections that any student can master - even an ELL kindergartner. Children will learn to think and talk through the fresh eyes of a poet. The kit includes a rubric and writing paper for display.

Only $3.00
One of her paid products that I find quite interesting is her My Counting Song MP3s. It features a soothing vocal over a relaxing instrumental with a soft beat. Besides teaching counting, skip counting, counting backwards and counting on, the songs are behavior management tools - hypnotic and calming. The songs help children to calm their minds and focus on the task at hand; whether for time out, clean up, transition, stretching or dance. All the songs count like a heartbeat, one beat per second. 

One buyer left this feedback: "I bought it for my elderly mom who has trouble sleeping, and it helps her fall asleep. If I weren't retired, I would use it in the classroom, too."

Children also love the songs for dance breaks. How about trying robotic dancing while counting backwards? Not sure this is something you could use? Then download The Counting Song 1 – 20 which is free.  

If you stop by her blog, called Teacher Ink, Renee says she will pour you a virtual cup of lemonade and then you can chat with her.  This sounds like an excellent plan to me, especially on a hot summer day! Why not join me?

Dots Lots of Fun

I am always looking for ordinary items that can be used in the classroom as manipulatives. I'm a firm believer in the Conceptual Development Model which advocates teaching the concrete (using manipulatives) prior to moving to the pictorial before even thinking about the abstract. When I was at the Dollar Tree (a great, inexpensive place to purchase school stuff) I saw sets of dominoes for $1.00 each. Since they were inexpensive and readily available, I decided to create several math activities and games to introduce, reinforce, or reteach math concepts.

The Number 52
Think about it; if you lay a domino horizontally, you have a two digit number. Put two dominoes side-by-side, and a four digit number is created. Now you can work with place value, estimation, or rounding.  How about lining up dominoes in a column, and working on addition (with or without regrouping) or subtraction (with or without renaming)? 

Another perfect domino activity is practicing addition or multiplication facts.  How about adding the two sides of the domino or multiplying the two sides together?

The Fraction 1/4
If a domino is placed vertically, you immediately have a fraction.  Placed one way it is a proper fraction, but rotated around, it is an improper fraction which can then be reduced.  A fraction can also be changed into a division problem, a ratio, a decimal, or a percent.

So think outside that box of dominoes and use them as an inexpensive math manipulative because Dots Lots of Fun!

Check out all my Domino Resources available on Teachers Pay Teachers.
The first two are absolutely FREE!
  1. Dots Fun for Everyone - FREE  Three math activities and one game for the intermediate grades.
  2. Dots Fun - FREE  Three math activities and one game for the primary grades.
  3. Dots Fun   A 24 page resource for grades 1-3 that includes 13 math activities and four games.
  4. Dots Fun for Everyone  A 29 page resource that features 15 math activities and three games for grades 3-6.
  5. Dots Lots of Fun  Seven math games that use dominoes for grades 2-5.