Number Sense, Concepts, Operations, and Estimation Standards

Standard 1: The student understands the different ways numbers are represented and used in the real world.

associates verbal names, written word names, and standard numerals with the whole numbers less than 1000.
understands the relative size of whole numbers between 0 and 1000.
uses objects to represent whole numbers or commonly used fractions and relates these numbers to real-world situations.
understands that whole numbers can be represented in a variety of equivalent forms.

names whole numbers combining 3-digit numeration (hundreds, tens, ones) and the use of number periods, such as ones, thousands, and millions and associates verbal names, written word names, and standard numerals with whole numbers, commonly used fractions, decimals, and percents.
understands the relative size of whole numbers, commonly used fractions, decimals, and percents.
understands concrete and symbolic representations of whole numbers, fractions, decimals, and percents in real-world situations.
understands that numbers can be represented in a variety of equivalent forms using whole numbers, decimals, fractions, and percents

associates verbal names, written word names, and standard numerals with integers, fractions, decimals; numbers expressed as percents; numbers with exponents; numbers in scientific notation; radicals; absolute value; and ratios.
understands the relative size of integers, fractions, and decimals; numbers expressed as percents; numbers with exponents; numbers in scientific notation; radicals; absolute value; and ratios.
understands concrete and symbolic representations of rational numbers and irrational numbers in real-world situations.
understands that numbers can be represented in a variety of equivalent forms, including integers, fractions, decimals, percents, scientific notation, exponents, radicals, and absolute value.

understands and applies the concepts of counting (by 2s, 3s, 5s, 10s, 25s, 50s), grouping, and place value with whole numbers between 0 and 100.
uses number patterns and the relationships among counting, grouping, and place value strategies to demonstrate an understanding of the whole number system.

uses place-value concepts of grouping based upon powers of ten (thousandths, hundredths, tenths, ones, tens, hundreds, thousands) within the decimal number system.
recognizes and compares the decimal number system to the structure of other number systems such as the Roman numeral system or bases other than ten.

understands and uses exponential and scientific notation.
understands the structure of number systems other than the decimal number system.

understands and explains the effects of addition and subtraction on whole numbers, including the inverse (opposite) relationship of the two operations.
selects the appropriate operation to solve specific problems involving addition and subtraction of whole numbers.
adds and subtracts whole numbers to solve real-world problems using appropriate methods of computing, such as objects, mental mathematics, paper and pencil, calculator.

understands and explains the effects of addition, subtraction, and multiplication on whole numbers, decimals, and fractions, including mixed numbers, and the effects of division on whole numbers, including the inverse relationship of multiplication and division.
selects the appropriate operation to solve specific problems involving addition, subtraction, and multiplication of whole numbers, decimals, and fractions, and division of whole numbers.
adds, subtracts, and multiplies whole numbers, decimals, and fractions, including mixed numbers, and divides whole numbers to solve real-world problems, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator.

understands and explains the effects of addition, subtraction, multiplication, and division on whole numbers, fractions, including mixed numbers, and decimals, including the inverse relationships of positive and negative numbers.
selects the appropriate operation to solve problems involving addition, subtraction, multiplication, and division of rational numbers, ratios, proportions, and percents, including the appropriate application of the algebraic order of operations.
adds, subtracts, multiplies, and divides whole numbers, decimals, and fractions, including mixed numbers, to solve real-world problems, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator.

uses and justifies different estimation strategies in a real-world problem situation and determines the reasonableness of results of calculations in a given problem situation.

uses estimation strategies to predict results and to check the reasonableness of results.

understands and applies basic number theory concepts, including primes, composites, factors, and multiples.

uses concepts about numbers, including primes, factors, and multiples, to build number sequences.