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A Perfect Ten

Don't you love tests where you ask a question which you believe everyone will get correct, and then find out it just isn't so?  I gave my PreAlgebra college students a pretest to see what they knew and didn't know.  One of the first questions was:  Why is our number system called Base Ten?  This is an extremely important concept as it reveals what they know about place value.  Below are some of the answers I received.

1)  It is called Base Ten because we have ten fingers.  (Yikes! If that is so, should we include our toes as well?)

2)  It is called Base Ten because I think you multiply by ten when you move past the decimal sign.  (Well, sort of.  You do multiply by ten when you move to the left of the decimal sign, going from the ones place, to the tens place, to the hundreds place, etc.)

3)  I think it is called Base Ten because it's something we use everyday.  (Really????)

Enough!  It is called Base Ten because we use ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to write all of the other numbers.  Each digit can have one of ten values: any number from 0 through 9. When the value reaches 9, just before 10, it starts over at zero again.  (Notice the pattern below.)

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, etc.

In addition, each place is worth ten times more than the last. Ten is worth ten times more than 1, and 1,000 is ten times more than 100. The pattern continues infinitely both ways on a number line.

The decimal point allows for the place value to continue in a consistent pattern with numbers smaller than one. As we move to the right of the decimal point, each place is divided by ten to get to the next place value.  One hundredth is one tenth divided by ten, and one thousandth is one hundredth divided by ten.  The pattern goes on infinitely. 
          100's, 10's, 1's . 0.1, 0.01, 0.001, 0.0001, 0.00001, etc.
Since all mathematics is based on patterns, this shouldn’t be a new revelation. Perhaps on the posttest, my students will omit the fingers and instead rely on patterns to answer the questions!

For more information about teaching place value, refer to the September 7th posting entitled: There’s A Place for Us.

Trash to Treasure

FlapJack Educational Resources
While searching teacher blogs, I came across Flap Jack Educational Resources.  Sra. Corra, also known as Mrs. Green, creates clever and useful things for her classroom from what might be considered trash.  I think she might be better named "The Trash to Treasure Lady".  She also has quality products at her Teachers Pay Teachers store:  FlapJack Products

Her blog caused me to think about: "What sort of extraordinary things could I create from ordinary things which might otherwise be thrown away?"  Here is one of my Trash to Treasure ideas.

Go to any Quick Trip or a store similar to that and ask if you could have some plastic cup lids, two for each child.  (Stores are usually happy to help out teachers.)  I like the sturdy 4" red ones.  Instead of placing a straw in the designated spot, place a brad to connect two of the lids.  These should be touching each other top to top or flat side to flat side.  After the lids are together, place a few stickers on the outside of the lids.  What do you have?  A card holder!  Just slide the game cards in between the two lids, and they will actually stay there!  These are great for little hands which have difficulty holding several cards, or for older hands which aren't functioning like they use to, or for disabled or crippled hands.  My granddaughters love them because they can now play Go Fish without dropping and showing everyone all of their cards.

Do you have a Trash to Treasure idea?  Share it with us by leaving a comment.

Free Resource

Check out a free resource entitled Trash to Treasure.  It is an eight page handoutthat features clever ideas, fun and engaging mini-lessons in addition to cute and easy to construct crafts made from recycled or common, everyday items.  In this resource, discover how to take old, discarded materials and make them into new, useful, inexpensive products or tools for your classroom.

Just click on the link below the resource cover.