Number and Operations

• understand the place- value structure of the
base-ten number system and be able to
estimate, represent, compare, & order whole
numbers (0 to1,000,000) and decimals (to
hundredths).

• develop understanding of fractions as parts of
unit wholes, as parts of a collection, as
locations on a number line, and as divisions of
whole numbers.

• describe the properties of odd and even
numbers, composite and prime numbers,
multiples, and factors .

• use models, manipulatives, benchmarks, and
equivalent forms to estimate, represent, and
determine the size of fractions.

• understand the various meanings of
multiplication and division .

• understand the effects of multiplying and
dividing whole numbers.

• understand the effects of adding and
subtracting fractions with like denominators,
using manipulatives and/or diagrams.

• add, subtract, multiply, & divide whole
numbers.

• develop and use strategies to estimate
computations and to judge the reasonableness
of those results.

• develop and use strategies to estimate
computations involving fractions and
decimals (to the hundredths) in situations
relevant to the students’ experience.

• understand the place-value structure of the
base-ten number system and be able to
represent, compare, and order whole numbers
(0 to100,000,000) and decimals (to
thousandths).

• read, write, rename, compare, and model
whole numbers, fractions (e.g., 1/2 = 3/6, 1/2
> 1/8 ) mixed numbers (e.g., 1 _ = 3/2,) and
decimals (to the thousandths.)

• recognize and generate equivalent forms of
commonly used fractions, decimals, percents,
and whole numbers.

• describe classes of numbers according to
characteristics such as factors, multiples, odd
and even numbers, prime and composite
numbers, and GCF and LCM .

• develop multiple representations of numbers
(e.g., drawings, manipulatives, and symbols.)

• develop an understanding of estimation of the
size of whole numbers and fractions.

• understand and use properties of operations,
such as the distributive property of
multiplication over addition.

• identify and use relationships between
operations to solve problems, (e.g., use
division as the inverse of multiplication to
solve problems.)

• understand the various meanings of
properties of operations such as the
commutative, associative, identity properties
of addition and multiplication, and the zero
property of multiplication.

• develop meaning for the relationships
between operations to solve problems with
fractions with unlike denominators .

• develop and use appropriate estimation
strategies with whole numbers and fractions,
and judge the reasonableness of the results.

• select appropriate methods and tools for
computing with whole numbers from among
mental computation, estimation, calculators ,
and paper and pencil computation according
to the context and nature of the computation
and the appropriate use of the selected tool.

• add and subtract simple fractions with
common denominators and decimals to the
thousandths using manipulatives or symbolic
notation.

• develop meaning for fractions, decimals,
percents (greater than 100 and less than 1) and
ratios.

• compare, order, and represent numbers in
equivalent forms through 1,000,000,000 and
ten-thousandths (e.g., models, diagrams,
symbols, and on a number line.)

• develop an understanding of place value of
large numbers (up to 1 billion) and small
numbers, decimals ( to ten-thousandths) and
integers.

• use prime, composite, prime factorization,
multiples, factors, estimation, and divisibility
rules to solve problems.

• develop meaning of ratio (describe and
compare 2 sets of data using ratios and
appropriate notations: 3:5, 3/5, 3 to 5.)

• understand the meaning and effects of
operations with whole numbers, fractions,
decimals, and with introduction to integers
(e.g., initially understand the use of integers
for noting relative changes or values .)

• use the properties of operations (associative,
commutative, and distributive) to simplify
computations with fractions, decimals, and
initial use with integers.

• develop meaning for the inverse relationship
of operations to solve problems (addition and
subtraction, multiplication and division,
squaring and finding square roots.)

• develop a variety of appropriate methods
(e.g., mental math, calculators/computers,
paper and pencil) to estimate and compute
using large and small quantities (from 1
billion to ten-thousandths) including fractions,
decimals, and initial use of integers.

• develop fluency when completing algorithms
with fractions, decimals, integers, and rational
numbers, and judge the reasonableness of the
answer.

• develop and use strategies for solving
problems which involve ratios, proportions,
and percentages (greater than 100% and
smaller than 1%.)