• Happy Long Weekend

   

  September 6, 2009

  Here we are starting a new year with lots of possibilities.  After sitting in on a textbook presentation recently, I was reminded how important it is to have a balanced math program.  Five to nine minutes each day should include drill and practice of basic facts using a sequential approach to the computational strategies.  I talk so much about this at my workshops but it continues to be important not for fact sake alone but as tools for application into more complex mathematics.

  There are three steps on the road to fluency with basic facts:

  •  Teach for understanding

  •  Teach the strategies sequentially

  •  Practice, practice, practice!

  There are two models for each of the four operations.  Addition has two picture models that need to be developed with students.  Additions means to combine quantity.  That is the part/part/whole model.  This will be so important for fractions later on.  The other model is number line growth and that will be important for integers.  Subtraction has two models.  One is to “take away.”  That is the inverse of part/ part/ whole.  The other model is the inverse of number line growth, the difference between model.  

  The two models for multiplication are critical for connections to be made with proportional relationships and measurement.  One model is repeated addition of like quantity.  This is the “groups of” model.  I always talk at my workshops about having that “groups of” statement as one of your five important visuals in the elementary classroom.  The other model is the area/array model.  Division is the inverse of multiplication so one model is repeated subtraction of like quantity.  The other would be the inverse of the area/array relationship.  This would be if given the area and one side, what is the length of the missing side?

  I do not see the understandings developed adequately in math textbooks.  I also think that the computational strategies are “hit and miss” in the textbooks.  I like to think about the computational strategies as the bridge connecting the understanding and fluency.  In my next blog, I will write about the ten “power” strategies!

  Remember that the tenth day of school is a day to celebrate how powerful ten is in developing number sense.  Don’t forget to use page 13 in my book, Math Drills to Thrill with the Random Number CD.  The ladybugs are arranged in a ten-frame.  While students circle the number they hear, they are also seeing what remains.  Later on, they can write the equation to the right of the frame.  Also, play my game “Take Two for 10″ with a deck of playing cards.  Have students place 10 cards face up in two rows of five.  Ace is worth one and every face card is a zero.  Jokers are worth 10.  The player picks up two cards with a sum of ten.  If there are no pairs showing equaling 10, two more cards are turned over.  A player is not cheating.  The check is only face cards are left at the end of the game.  

  Understanding base ten is generated when cutting out the digit cards for the place value pocket.  There are only ten symbols to express quantity or measure.  Read Stuart Murphy’s book, Earth Day Hooray! to help students understand that we recycle the digits because we only have ten.  

  These are just a few quick ideas for celebrating ten in your classroom!  The payoff will come throughout the year!

  Hope you are relaxing this Labor Day weekend.  I am enjoying the mountain air with my family before our daughter goes back to UC Santa Cruz on Monday to begin a new season of golf and get ready for her senior year.  Ah, empty nest!

  Mathematically yours,

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