# Number and Operations

Overview

The purpose of these resource materials is to provide K – 8 educators with explanations
and examples that facilitate understanding of the mathematics in the Grade-Level
Expectations (GLEs)*. These resource materials are organized by content strand and by
GLE “stems.” The definitions and explanations within each section are not alphabetized,
but are organized to parallel the introduction of new concepts and skills within each GLE
stem” across grades. The materials contained in this document focus on the Number
and Ope ration strand and only address the NECAP GLEs that are common to all three
states.

 Grade 3 Grade 4 M(N&O)–3–3 Demonstrates conceptual understanding of mathematical operations by describing or illustrating the inverse relationship between addition and subtraction of whole numbers; and the relationship between repeated addition and multiplication using models , number lines , and explanations. M(N&O)–4–3 Demonstrates conceptual understanding of mathematical operations by describing or illustrating the relationship between repeated subtraction and division (no remainders); the inverse relationship between multiplication and division of whole numbers; or the addition and subtraction of positive fractional numbers with like denominators using models , number lines, or explanations.

To facilitate access, each definition is coded (e.g., N&O – 4, the 4th definition for the
Number and Operations strand ). There are multiple tables of contents: 1) An overall table
of contents on page 3 contains all the terms or phrases defined for the content strand in
addition, if there is a word or phrase that you are unclear about within a definition, check
location in this document.

 Section # Grade-Level Expectation “Stem” NECAP GLE Stem Codes (Vermont codes) X re presents grades K– 8 Page Numbers Section 1 Demonstrates understanding of rational numbers… NECAP: M(N&O) – X – 1 (Vermont GE MX: 1) 4 – 18 Section 2 Demonstrates conceptual understanding of the magnitude of numbers… NECAP: M(N&O) – X – 2 (Vermont GE MX: 2) 19 – 25 Section 3 Demonstrates understandings of mathematical operations… NECAP: M(N&O) – X – 3 (Vermont GE MX: 3) 26 – 29 Section 4 Accurately solves problems involving… NECAP: M(N&O) – X – 4 (Vermont GE MX: 4) 30 – 36

Note: Examples are provided throughout this document to illustrate definitions or phrases
used in the mathematics GLEs. However, the kinds of questions students might be asked
in instruction or on the NECAP assessment about the mathematics being illustrated are
NOT necessarily limited to the specific examples given. It is the intent, over time, to add
released NECAP items to expand the set of examples.

 Definition Section Number Page Number Definition Number Absolute value 2 21 N&O – 23 Accurately solves problems 4 31 N&O – 35 Across number formats 2 21 N&O – 22 Area model to represent part to whole relationshipx 1 13 N&O – 17 Comparing 2 24 N&O – 27 Composite number 4 35 N&O – 41 Composition of numbers 1 12 N&O – 15 Concept of multiplication 4 33 N&O – 37 Decimal 1 7 N&O – 7 Decomposition of numbers 1 12 N&O – 16 Describing or illustrating the meaning of a power 3 28 N&O – 33 Effect on magnitude of a whole number when multiplying or dividing by a whole number, fraction, or decimal 3 29 N&O – 34 Equivalent numbers 1 12 N&O – 14 Expanded notation 1 12 N&O – 13 Factor 4 33 N&O – 38 Fraction 1 5 N&O – 3 Greatest common factor ( GCF ) 4 35 N&O – 42 Improper fraction 1 7 N&O – 5 In and out of context 4 32 N&O – 36 Integer 1 8 N&O – 9 Inverse relationships in operations 3 27 N&O – 29 Irrational number 1 8 N&O – 10 Least common multiple ( LCM ) 4 36 N&O – 43 Linear model 1 18 N&O – 19 Meaning of remainders with respect to division of whole numbers 3 28 N&O – 32 Mixed number 1 7 N&O – 6 Multiples 4 34 N&O – 39 Number line 2 24 N&O – 28 Ordering 2 23 N&O – 26 Percent 1 7 N&O – 8 Prime numbers 4 35 N&O – 40 Proper fraction 1 6 N&O – 4 Proportional reasoning 4 36 N&O – 44 Ratio 1 10 N&O – 12 Rational number 1 5 N&O – 1 Real numbers 1 9 N&O –11 Relationship between repeated addition and multiplication of whole numbers 3 27 N&O – 30 Relationship between repeated subtraction and division of whole numbers 3 27 N&O – 31 Relative magnitude 2 20 N&O – 20 Scientific notation 2 23 N&O – 25 Set model 1 17 N&O – 18 Whole number 1 5 N&O – 2 Whole number bases and whole number exponents , and fractional bases with whole number exponents 2 22 N&O – 24 Within number formats 2 21 N&O – 21
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