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-concreteOrganizational 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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