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```					Excerpts of Expectations from
the Number and Operations

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

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

   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

   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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