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Comparison of 1998 Core Curriculum and 2005 Core Curriculum for Grades PreK-8
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) Prekindergarten-Kindergarten and 1-2 (forward and backward using a number line)

Prekindergarten-Kindergarten (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 1-2 and 3-4

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 1-2 (even and odd)

Grades 3-4 (prime, role of zero)

Grades 5-6 (prime and composite numbers)

Grades 7-8 (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 (0-100))

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 1-2 (number names orally through 100)

Grades 3-4 (extend to hundred millions)

 Prekindergarten-kindergarten (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 Prekindergarten-Kindergarten (first to tenth)
Grades 1-2 (first to 31st, words such as first, last, before, and after)

Grades 3-4 (first through 500th)

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)
One-to-One Correspondence Prekindergarten-Kindergarten

Grades 1-2 (one-to-one and many-to-one, readiness for ratio)

 Prekindergarten-Kindergarten (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 Prekindergarten-Kindergarten (relate counting to grouping and place value)

Grades 1-2 (concrete models for numbers up to 999, regrouping ones and tens, meaning of zero in the place value system)

Grades 3-4 (extend to millions and hundredths)

 Grade 1 (explore and use place value, develop an initial understanding of the base ten system:

10 ones = 1 ten
10 tens = 1 hundred)

Grade 2 (extend to 10 hundreds = 1 thousand)

Grade 3 (understand the place value structure of the base ten number system:

10 ones = 1 ten
10 tens = 1 hundred
10 hundreds = 1 thousand)

Grade 4 (expand place value structure to include

10 thousands = 1 ten thousand)

Grade 5 (expand to include:

10 ten thousands = 1 hundred thousand
10 hundred thousands = 1 million)
Composition of Numbers Not directly addressed in core curriculum Grades 1-2 (compose and decompose one-digit numbers)

Grade 2 (extend to two-digit numbers)

Grade 3 (extend to three-digit numbers)

Grade 4 (extend to four-digit numbers)
Expanded Notation Grades 1-2 See "Composition of Numbers" above
Comparing and Ordering Whole Numbers Prekindergarten (concept of first, last, and middle)

Grades 1-2 (whole numbers, small sets of numbers)

Grade 3-4 (whole numbers to millions)

Grades 5-6

 Grades 1-2 (compare and order whole numbers up to 100)

Grades 1-2 (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 Prekindergarten-Kindergarten (awareness in daily life, use of words "whole" and "half," concept that a whole can be divided into any number of equal parts)

Grades 3-4 (use in daily life, meaning of numerator and denominator)

Grades 7-8

 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 3-4 (unit fractions)

Grades 5-6

Grades 7-8

 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 Prekindergarten-8 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 5-6 (round numbers to the nearest hundredth and up to 10,000, relate to estimation, fractions and decimals for estimates in computation)

Grades 7-8 (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 Prekindergarten-Kindergarten (readiness activities for addition and subtraction facts, counting on)

Grades 1-2 (master addition facts with sums 0-18 and subtraction with differences 0-9)

Grades 3-4 (inverse relationships of operations)

Grades 5-6

 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 single-digit multiplication facts, demonstrate fluency and apply single-digit division facts)
Addition and Subtraction of Whole Numbers Prekindergarten-Kindergarten (readiness activities)

Grades 1-2 (understanding meaning of addition and subtraction, develop addition strategies)

Grades 1-2 (up to three digits without regrouping and up to two digits with regrouping)

Grades 3-4 (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 two-digit numbers without regrouping)

Grade 2 (use a variety of strategies to solve addition and subtraction problems using one- and two-digit numbers with and without regrouping, use doubling to add 2-digit numbers, use compensation to add 2-digit numbers)

Grade 3 (use a variety of strategies to add and subtract 3-digit 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 5-6 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 7-8 Not directly addressed in the core curriculum
Multiplication and Division of Whole Numbers Grades 1-2 (explore the meaning of multiplication and division)

Grades 3-4 (multiplication of three-digit number by two-digit number, division of three-digit dividends by one- and two-digit 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 two-digit numbers by one- and two-digit numbers (with and without regrouping), use a variety of

strategies to divide two-digit dividends by one-digit divisors (with and without remainders), interpret the meaning of remainders)

Grade 5 (use a variety of strategies to multiply three-digit by three-digit numbers and to divide three-digit numbers by one- and two-digit numbers
Multiplication and Division by Powers of 10 Grades 3-4 (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 Prekindergarten-Kindergarten, 1-2, 3-4, 5-6, and 7-8 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 5-6 and 7-8 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 3-4, 5-6, and 7-8 Grade 3 (informally)

Grade 4 (halves, fourths, thirds, fifths, sixths, and tenths)

Grade 5 (create equivalent fractions given a fraction)
Least Common Denominator Grades 5-6 Not directly addressed in core curriculum
Operations with Fractions Grades 5-6 and 7-8 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 5-6 (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 5-6 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 1-2 (money)

Grades 3-4

 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 7-8 Grade 6
Mixed Decimals Grades 5-6 Not directly addressed in core curriculum
Equivalent Decimals Grades 3-4 Not directly addressed in core curriculum
Rounding Decimals Grades 3-4 (using concrete materials and symbols) Grade 5 (round decimals to the nearest hundredth)
Comparing and Ordering Decimals Grades 3-4 (to hundredths)

Grades 5-6

 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 5-6 and 7-8 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 3-4 (percents that are multiples of 5)

Grades 5-6 (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 7-8 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 7-8 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 7-8 Grade 6 (order rational numbers)

Grade 7 (place rational and irrational numbers (approximations) on a number line)
Scientific Notation Grades 7-8 Grade 7 (write numbers in scientific notation, compare numbers written in scientific notation and translate numbers from scientific notation into standard form)
Ratio Grades 3-4 (basic concept)

Grades 5-6 (problem solving)

Grades 7-8 (solving)

 Grade 5 (concept of ratio, express ratios in different forms)
Rate Grades 7-8 (problem solving) Grade 6
Proportions Grades 5-6 Grade 6
Right Triangle Trigonometry Grades 7-8 Algebra (high school course)
Operations with Integers Grades 7-8 Grade 7 (add, subtract, multiply, and divide)
Squares and Square Roots Grades7-8 (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 non-perfect square number less than 225 lies)
Roots and Powers of Integers Grades 7-8 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)