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 GradeLevel
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 4^{th} 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
alphabetical order; and 2) A table of contents for each section in alphabetical
order. In
addition, if there is a word or phrase that you are unclear about within a
definition, check
the overall table of contents to determine if the word or phrase is defined in
another
location in this document.
Section # 
GradeLevel 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.
Please send comments, corrections.
* GradeLevel Expectations are called Grade Expectations (GEs) in Vermont.
Table of Contents
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 