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Comparison of 1998 Core Curriculum and 2005 Core Curriculum for Grades PreK8
May 2005
The following chart lists the concepts and skills in Number Sense and Operations and indicates the grade level that includes that topic in both the 1998 Core Curriculum and the 2005 Core Curriculum.
NUMBER SENSE AND OPERATIONS 

Concept/Skill 
1998 Core Curriculum 
2005 Core Curriculum 
Counting (Cardinality)  PrekindergartenKindergarten and 12 (forward and backward using a number line) 
PrekindergartenKindergarten (1 to 10) Grade 1 (1 to 100) and backwards from 20 by 1’s Grade 2 (backwards from 100 by 1’s) 
Skip Counting 
Grades 12 and 34 
Grade 1 (skip count by10’s to 100, by 5’s to 50, and by 2’s to 20) Grade 2 (skip count to 2’s, 5’s,10’s to 100, count back from 100 by 5’s and 10’s using a number chart, skip count by 3’s to 36 and 4’s to 48) Grade 3 (skip count by 25’s, 50’s, and 100’s to 1,000) Grade 4 (skip count by 1,000’s) 
Types of Numbers  Grades 12 (even and odd)
Grades 34 (prime, role of zero) Grades 56 (prime and composite numbers) Grades 78 (integers, and rational and irrational numbers) 
Grade 2 (use concrete
materials to justify a number as odd or even, recognize the meaning of zero
in the place value system (0100)) Grade 3 (identify odd and even numbers, develop an understanding of the properties of odd/even numbers as a result of addition or subtraction) Grade 4 (properties of odd/even numbers as a result of multiplication) Grade 5 (prime and composite numbers) Grade 7 (integers, rational and irrational numbers, including π) 
Reading, Writing, and Speaking Numbers  Grades 12 (number names
orally through 100) Grades 34 (extend to hundred millions) 
Prekindergartenkindergarten (1 to 10) Grade 1 (read the number words one, two, three…ten, count to 100) Grade 3 (whole numbers to 1,000) Grade 4 (read and write whole numbers to 10,000) Grade 5 (read and write whole numbers to millions) Grade 6 (read and write whole numbers to trillions) 
Ordinal 
PrekindergartenKindergarten (first
to tenth) Grades 12 (first to 31^{st}, words such as first, last, before, and after) Grades 34 (first through 500^{th}) 
Prekindergarten (first and
last) Kindergarten (first to tenth) Grade 1 (first to twentieth) Grade 2 (use and understand verbal ordinal terms, read written ordinal terms (first through ninth) and use them to represent ordinal relations) 
OnetoOne Correspondence 
PrekindergartenKindergarten Grades 12 (onetoone and manytoone, readiness for ratio) 
PrekindergartenKindergarten
(count objects in a collection to 10) Grade 1 (count objects in a collection of a specified size (10 to 100), using groups of 10) 
Place Value 
PrekindergartenKindergarten (relate
counting to grouping and place value) Grades 12 (concrete models for numbers up to 999, regrouping ones and tens, meaning of zero in the place value system) Grades 34 (extend to millions and hundredths) 
Grade 1 (explore and use
place value, develop an initial understanding of the base ten system:
Grade 2 (extend to 10 hundreds = 1 thousand) Grade 3 (understand the place value structure of the base ten number system:
Grade 4 (expand place value structure to include
Grade 5 (expand to include:

Composition of Numbers  Not directly addressed in core curriculum 
Grades 12 (compose and
decompose onedigit numbers) Grade 2 (extend to twodigit numbers) Grade 3 (extend to threedigit numbers) Grade 4 (extend to fourdigit numbers) 
Expanded Notation  Grades 12  See "Composition of Numbers" above 
Comparing and Ordering Whole Numbers 
Prekindergarten (concept of
first, last, and middle) Grades 12 (whole numbers, small sets of numbers) Grade 34 (whole numbers to millions) Grades 56 
Grades 12 (compare and
order whole numbers up to 100) Grades 12 (before, after, and between with whole numbers to 100) Grade 3 (compare and order whole numbers up to 1,000) Grade 4 (extend to 10,000) Grade 5 (extend to millions) 
Meaning of Fractions 
PrekindergartenKindergarten (awareness in
daily life, use of words "whole" and "half," concept that a whole can be
divided into any number of equal parts) Grades 34 (use in daily life, meaning of numerator and denominator) Grades 78 
Grade 3 (part of whole or
part of set, meaning of numerator and denominator in the symbolic form of a
fraction, as equal parts of a whole) Grade 4 (locations on number lines and as divisions of whole numbers) 
Comparing and Ordering
Fractions

Grades 34 (unit fractions)
Grades 56 Grades 78 
Grade 3 (compare and order
unit fractions and find their approximate location on a number line) Grade 4 (unit fractions or fractions with the same denominator with and without the use of a number line) Grade 5 (fractions including unlike denominators, compare using <, >, or =) 
Estimation  Grades Prekindergarten8 as appropriate 
Grade 1 (number quantity up
to 50) Grade 2 (extend to 100) Grade 3 (extend to 500) Grade 5 (sums and differences of fractions with like denominators, sums, differences, products, and quotients of decimals) Grade 6 (estimate a percent of quantity 0% to 100%) Grade 8 (estimate a percent of quantity given an application) 
Rounding 
Grades 56 (round numbers to
the nearest hundredth and up to 10,000, relate to estimation, fractions and
decimals for estimates in computation) Grades 78 (whole numbers, decimals, and fractions) 
Grade 4 (round numbers less
than 1,000 to the nearest tens and hundreds) Grade 5 (round numbers to the nearest hundredth and up to 10,000) 
Basic Facts 
PrekindergartenKindergarten (readiness
activities for addition and subtraction facts, counting on) Grades 12 (master addition facts with sums 018 and subtraction with differences 09) Grades 34 (inverse relationships of operations) Grades 56 
Prekindergarten (develop addition
and subtraction readiness with sums up to 4 and subtraction involving one to
four items, using manipulatives) Kindergarten (determine sums and differences by various means) Grade 1 (demonstrate fluency and apply addition and subtraction facts to and including 10) Grade 2 (demonstrate fluency and apply addition and subtraction facts up to and including 18, develop readiness for multiplication by using repeated addition, develop readiness for division by using repeated subtraction, dividing objects into groups (fair share)) Grade 3 (develop fluency with singledigit multiplication facts, demonstrate fluency and apply singledigit division facts) 
Addition and Subtraction of Whole Numbers 
PrekindergartenKindergarten (readiness
activities) Grades 12 (understanding meaning of addition and subtraction, develop addition strategies) Grades 12 (up to three digits without regrouping and up to two digits with regrouping) Grades 34 (less than 1 million, subtraction with zeros in the minuend) 
Grade 1 (use a variety of
strategies to solve addition and subtraction problems with one and
twodigit numbers without regrouping) Grade 2 (use a variety of strategies to solve addition and subtraction problems using one and twodigit numbers with and without regrouping, use doubling to add 2digit numbers, use compensation to add 2digit numbers) Grade 3 (use a variety of strategies to add and subtract 3digit numbers with and without regrouping) Grade 4 (use a variety of strategies to add and subtract numbers up to 10,000) 
Factors and Multiples  Grades 56 
Grade 5 (calculate multiples
of a whole number and the least common multiple of two numbers, identify the
factors of a given number, find the common factors and the greatest common
factor of two numbers) Grade 7 (find the common factors and greatest common factor of two or more numbers, determine multiples and least common multiple of two or more numbers, determine prime factorization of a given number and written in exponential form) 
Divisibility Rules  Grades 78  Not directly addressed in the core curriculum 
Multiplication and Division of Whole Numbers 
Grades 12 (explore the
meaning of multiplication and division) Grades 34 (multiplication of threedigit number by twodigit number, division of threedigit dividends by one and twodigit divisors (quotient and remainder)) 
Grade 3 (use the area model,
tables, patterns, arrays, and doubling to provide meaning for
multiplication, use tables, patterns, halving, and manipulatives to provide
meaning for division) Grade 4 (understand various meanings of multiplication and division, use multiplication and division as inverse operations, use a variety of strategies to multiply twodigit numbers by one and twodigit numbers (with and without regrouping), use a variety of strategies to divide twodigit dividends by onedigit divisors (with and without remainders), interpret the meaning of remainders) Grade 5 (use a variety of strategies to multiply threedigit by threedigit numbers and to divide threedigit numbers by one and twodigit numbers 
Multiplication and Division by Powers of 10  Grades 34 (multiplication and division through 144)  Grade 4 (develop fluency in multiplying and dividing multiples of 10 and 100 up to 1,000) 
Properties, Inverse, and Identify Elements  Grades PrekindergartenKindergarten, 12, 34, 56, and 78 
Grade 2 (understand and use
the commutative property of addition, use zero as the identity element for
addition) Grade 3 (commutative property of addition and multiplication, use 1 as the identity element for multiplication, use the zero property of multiplication, understand and use the associative property of addition) Grade 4 (understand, use, and explain the associative property of multiplication) Grade 6 (define and identify the commutative and associative properties of addition and multiplication and the distributive property of multiplication over addition, define and identify the identity and inverse properties of addition and multiplication, define and identify the zero property of multiplication) 
Order of Operations (Arithmetic Expressions) 
Grades 56 and 78 
Grade 5 (addition,
subtraction, multiplication, division, and parentheses) Grade 6 (exponents of two or three) Grade 7 (absolute value and/or integral exponents > 0) Grade 8 (integral exponents) 
Equivalence Fractions  Grades 34, 56, and 78 
Grade 3 (informally)
Grade 4 (halves, fourths, thirds, fifths, sixths, and tenths) Grade 5 (create equivalent fractions given a fraction) 
Least Common Denominator  Grades 56  Not directly addressed in core curriculum 
Operations with Fractions  Grades 56 and 78 
Grade 4 (add and subtract
proper fractions with common denominators) Grade 5 (Use a variety of strategies to add and subtract fractions with like denominators, simplify fractions to lowest terms) Grade 6 (add and subtract fractions with unlike denominators, multiply and divide fractions with unlike denominators) 
Mixed Numbers  Grades 56 (change improper fractions to mixed numbers and vice versa)  Grade 5 (convert improper fractions to mixed numbers, and vice versa) 
Operations with Mixed Numbers  Grades 56 
Grade 5 (add and subtract
mixed numbers with like denominators) Grade 6 (add, subtract, multiply, and divide mixed numbers with unlike denominators) 
Meaning of Decimals 
Grades 12 (money) Grades 34 
Grade 4 (develop an
understanding of decimals as part of a whole, read and write decimals to
hundredths, using money as a context) Grade 5 (read and write decimals to thousandths) 
Terminating and Repeating Decimals  Grades 78  Grade 6 
Mixed Decimals  Grades 56  Not directly addressed in core curriculum 
Equivalent Decimals  Grades 34  Not directly addressed in core curriculum 
Rounding Decimals  Grades 34 (using concrete materials and symbols)  Grade 5 (round decimals to the nearest hundredth) 
Comparing and Ordering Decimals 
Grades 34 (to hundredths) Grades 56 
Grade 4 (to the hundredths
place using concrete materials and visual models in the context of money) Grade 5 (order decimals to thousandths, compare decimals using <, >, or =) 
Operations with Decimals  Grades 56 and 78 
Grade 4 (add and subtract
decimals to tenths and hundredths using a hundreds chart) Grade 5 (use a variety of strategies to add, subtract, multiply, and divide decimals to thousandths) 
Meaning of Percent 
Grades 34 (percents that
are multiples of 5) Grades 56 (percent as part of 100) 
Grade 5 (part of 100) Grade 6 (read, write, and identify percents of a whole (0% to 100%)) Grade 8 (read, write, and identify percents less than 1% and greater than 100%) 
Fraction, Decimal, Percent Equivalence  Grades 78 
Grade 4 (express decimals as
an equivalent form of fractions to tenths and hundredths) Grade 5 (write percents as fractions and decimals) Grade 6 (find multiple representations of rational numbers (fractions, decimals, and percents 0 to100)) 
Percent Problems  Grades 78 
Grade 6 (involving percent,
rate, and base) Grade 8 (apply percents to tax, increase/decrease, simple interest, sale price, commission, interest rates, gratuities) 
Absolute Value  Grade 6 (determine absolute value of rational numbers)  
Rational and Irrational Numbers  Grades 78 
Grade 6 (order rational
numbers) Grade 7 (place rational and irrational numbers (approximations) on a number line) 
Scientific Notation  Grades 78  Grade 7 (write numbers in scientific notation, compare numbers written in scientific notation and translate numbers from scientific notation into standard form) 
Ratio 
Grades 34 (basic concept) Grades 56 (problem solving) Grades 78 (solving) 
Grade 5 (concept of ratio, express ratios in different forms) 
Rate  Grades 78 (problem solving)  Grade 6 
Proportions  Grades 56  Grade 6 
Right Triangle Trigonometry  Grades 78  Algebra (high school course) 
Operations with Integers  Grades 78  Grade 7 (add, subtract, multiply, and divide) 
Squares and Square Roots  Grades78 (identify perfect squares, find two consecutive whole numbers between which the square root lies)  Grade 7 (square root of a perfect square up to 225, identify the two consecutive integers between which the square root of a nonperfect square number less than 225 lies) 
Roots and Powers of Integers  Grades 78 
Grade 6 (exponents where the
power is an exponent of one, two, or three) Grade 7 (laws of exponents for multiplication and division, conceptual understanding of negative and zero exponents with a base of 10) Grade 8 (develop and apply laws of exponents for multiplication and division) 