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