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					Excerpts of Expectations from
the Number and Operations
Standard Grades Pre-K-8

  Principles and Standards for School
   Mathematics National Council of
      Teachers of Mathematics
                 2000
      Understand numbers, ways of representing
     numbers, relationships among numbers, and
                   number systems


                  Grades Pre-K-2
       Use multiple models to develop initial
     understandings of place value and the base-ten
                   number system.

                     Grades 3-5
   Understand the place-value structure of the base-
    ten number system and be able to represent and
        compare whole numbers and decimals.
 Understand numbers, ways of representing
numbers, relationships among numbers, and
              number systems



               Grades 6-8
   Develop an understanding of large
       numbers and recognize and
      appropriately use exponential,
    scientific, and calculator notation.
Place Value Models                 (for base ten)

1.   Proportional-The material for 10 is ten times
     the size of 1; 100 is ten times the size of 10.
     Ex. base ten blocks, bean sticks, bundled
     sticks
                              Tens   Ones

                               2      3
Place Value Models               (for base ten)

   Non-proportional-The material does not
    maintain any size relationships. Ex. money,
    abacus, color tiles or chips

                   Tens   Ones
Place Value Models
Concrete Physical Models =>

   Semi-concrete
Organizational Models
    Tens | Ones          Symbolic
     2 | 5            Representation
                          Models
                           25
Interviewer, "Circle in your drawing what the six means.
      Circle what this part (points to one) means."
          Abbie: Fifth Month of Second Grade
Interviewer, "I'm going to say a number and I want you
     to write it... thirteen...sixty-seven...one hundred
  twenty...three hundred twenty-four... four hundred
   eight...three thousand, five hundred twenty-three.“
            Abbie: Fifth Month of Second Grade
Interviewer, "Circle in your drawing what the 4 means.
     Circle what this part (points to one) means."
         Clay: Fifth Month of Fourth Grade
Interviewer, "I'm going to say a number and I want you
to write it... fifty-six...three hundred forty-eight...four
  hundred five... two thousand, seven hundred thirty
         one...thirty-five thousand, forty-eight.“
           Clay: Fifth Month of Fourth Grade
Interviewer, "Circle in your drawing what the 4 means.
  Circle in your drawing what this part (points to one)
                        means."
           Elsa: Fifth Month of Fourth Grade
 Interviewer, "I'm going to say a number and I want you
   to write it... three hundred forty-eight...four hundred
five... two thousand, seven hundred thirty-one...thirty-five
                     thousand, forty-eight."
             Elsa: Fifth Month of Fourth Grade

				
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