SECTION 210:15-3-56. Standard One: Number and Operations

(a)   Statement of the standard. A focus on number and operations to develop fluency with an importance of understanding numbers, ways of representing numbers, relationships among numbers, relationships among number systems, and meanings of operations and how they relate to one another. Students will place an emphasis on the development of estimation to determine the reasonableness of solutions and answers and to compute efficiently and proficiently.

(b)   Standard One objectives for Pre-Kindergarten. The following objectives apply for students in Pre-Kindergarten:

(1)   Know number names and count in sequence.

(A)   Objective 1. Count aloud forward in sequence by 1s to 20.

(B)   Objective 2. Recognize and name written numerals 0-10.

(C)   Objective 3. Recognize that zero represents the count of no objects.

(2)   Count to tell the number of objects.

(A)   Objective 1. Identify the number of objects, up to 10, in a row or column.

(B)   Objective 2. Use one-to-one correspondence in counting objects and matching groups of objects.

(C)   Objective 3. Understand the last numeral spoken, when counting aloud, tells how many total objects are in a set.

(D)   Objective 4. Count up to 5 items in a scattered configuration; not in a row or column.

(3)   Compare sets using numbers.

(A)   Objective 1. Compare two sets of 1-5 objects using comparative language such as same, more, or fewer.

(c)   Standard One objectives for Kindergarten. The following objectives apply for students in Kindergarten:

(1)   Understand the relationship between quantities and whole numbers.

(A)   Objective 1. Count aloud forward in sequence to 100 by 1s and 10s.

(B)   Objective 2. Recognize that a number can be used to represent how many objects are in a set up to 10.

(C)   Objective 3. Use ordinal numbers to represent the position of an object in a sequence up to 10.

(D)   Objective 4. Recognize without counting (subitize) the quantity of a small group of objects in organized and random arrangements up to 10. Subitizing is defined as instantly recognizing the quantity of a set without having to count. "Subitizing" is not a vocabulary word and is not meant for student discussion at this age.

(E)   Objective 5. Count forward, with and without objects, from any given number up to 10.

(F)   Objective 6. Read, write, discuss, and represent whole numbers from 0 to at least 10. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives.

(G)   Objective 7. Find a number that is 1 more or 1 less than a given number up to 10.

(H)   Objective 8. Use the words more than, less than or equal to compare and order whole numbers, with and without objects, from 0 to 10.

(2)   Develop conceptual fluency with addition and subtraction (up to 10) using objects and pictures.

(A)   Objective 1. Compose and decompose numbers up to 10 with objects and pictures.

(3)   Understand the relationship between whole numbers and fractions through fair share.

(A)   Objective 1. Distribute equally a set of objects into at least two smaller equal sets.

(4)   Identify coins by name.

(A)   Objective 1. Identify pennies, nickels, dimes, and quarters by name.

(d)   Standard One objectives for Grade 1. The following objectives apply for students in Grade 1:

(1)   Count, compare, and represent whole numbers up to 100, with an emphasis on groups of tens and ones.

(A)   Objective 1. Recognize numbers to 20 without counting (subitize) the quantity of structured arrangements. Subitizing is defined as instantly recognizing the quantity of a set without having to count. "Subitizing" is not a vocabulary word and is not meant for student discussion at this age.

(B)   Objective 2. Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones.

(C)   Objective 3. Read, write, discuss, and represent whole numbers up to 100. Representations may include numbers, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks.

(D)   Objective 4. Count forward, with and without objects, from any given number up to 100 by 1s, 2s, 5s, and 10s.

(E)   Objective 5. Find a number that is 10 more or 10 less than a given number up to 100.

(F)   Objective 6. Compare and order whole numbers from 0 to 100.

(G)   Objective 7. Use knowledge of number relationships to locate the position of a given whole number on an open number line up to 20.

(H)   Objective 8. Use objects to represent and use words to describe the relative size of numbers, such as more than, less than, and equal to.

(2)   Solve addition and subtraction problems up to 10 in real-world and mathematical contexts.

(A)   Objective 1. Represent and solve real-world and mathematical problems using addition and subtraction up to 10.

(B)   Objective 2. Determine if equations involving addition and subtraction are true.

(C)   Objective 3. Demonstrate fluency with basic addition facts and related subtraction facts up to 10.

(3)   Develop foundational ideas for fractions.

(A)   Objective 1. Partition a regular polygon using physical models and recognize when those parts are equal.

(B)   Objective 2. Partition (fair share) sets of objects into equal groupings.

(4)   Identify coins and their values.

(A)   Objective 1. Identify pennies, nickels, dimes, and quarters by name and value.

(B)   Objective 2. Write a number with the cent symbol to describe the value of a coin.

(C)   Objective 3. Determine the value of a collection of pennies, nickels, or dimes up to one dollar counting by ones, fives, or tens.

(e)   Standard One objectives for Grade 2. The following objectives apply for students in Grade 2:

(1)   Compare and represent whole numbers up to 1,000 with an emphasis on place value and equality.

(A)   Objective 1. Read, write, discuss, and represent whole numbers up to 1,000. Representations may include numerals, words, pictures, tally marks, number lines, and manipulatives.

(B)   Objective 2. Use knowledge of number relationships to locate the position of a given whole number on an open number line up to 100.

(C)   Objective 3. Use place value to describe whole numbers between 10 and 1,000 in terms of hundreds, tens, and ones. Know that 100 is 10 tens, and 1,000 is 10 hundreds.

(D)   Objective 4. Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number.

(E)   Objective 5. Recognize when to round numbers to the nearest 10 and 100.

(F)   Objective 6. Use place value to compare and order whole numbers up to 1,000 using comparative language, numbers, and symbols (e.g. 425>276, 73<107, page 351 comes after page 350, 753 is between 700 and 800).

(2)   Add and subtract one- and two- digit numbers in real-world and mathematical problems.

(A)   Objective 1. Use the relationship between addition and subtraction to generate basic facts up to 20.

(B)   Objective 2. Demonstrate fluency with basic addition facts and related subtraction facts up to 20.

(C)   Objective 3. Estimate sums and differences up to 100.

(D)   Objective 4. Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers.

(E)   Objective 5. Solve real-world and mathematical addition and subtraction problems involving whole numbers up to 2 digits.

(F)   Objective 6. Use concrete models and structured arrangements, such as repeated addition, arrays and ten frames to develop understanding of multiplication.

(3)   Explore the foundational ideas of fractions.

(A)   Objective 1. Identify the parts of a set and area that represent fractions for halves, thirds, and fourths.

(B)   Objective 2. Construct equal-sized portions through fair sharing including length, set, and area models for halves, thirds, and fourths.

(4)   Determine the value of a set of coins.

(A)   Objective 1. Determine the value of a collection(s) of coins up to one dollar using the cent symbol.

(B)   Objective 2. Use a combination of coins to represent a given amount of money up to one dollar.

(f)   Standard One objectives for Grade 3. The following objectives apply for students in Grade 3:

(1)   Compare and represent whole numbers up to 10,000 with an emphasis on place value and equality.

(A)   Objective 1. Read, write, discuss, and represent whole numbers up to 10,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives..

(B)   Objective 2. Use place value to describe whole numbers between 1,000 and 10,000 in terms of ten thousands, thousands, hundreds, tens, and ones, including expanded form.

(C)   Objective 3. Find 1,000 more or 1,000 less than a given four- or five-digit number. Find 100 more or 100 less than a given four- or five-digit number.

(D)   Objective 4. Use place value to compare and order whole numbers up to 10,000, using comparative language, numbers, and symbols.

(2)   Add and subtract multi-digit whole numbers; multiply with factors up to 10; represent multiplication and division in various ways; solve real-world and mathematical problems through the representation of related operations.

(A)   Objective 1. Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting.

(B)   Objective 2. Demonstrate fluency of multiplication facts with factors up to 10.

(C)   Objective 3. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers.

(D)   Objective 4. Recognize when to round numbers and apply understanding to round numbers to the nearest ten thousand, thousand, hundred, and ten and use compatible numbers to estimate sums and differences.

(E)   Objective 5. Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results.

(F)   Objective 6. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups.

(G)   Objective 7. Recognize the relationship between multiplication and division to represent and solve real-world problems.

(H)   Objective 8. Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number.

(3)   Understand meanings and uses of fractions in real-world and mathematical situations.

(A)   Objective 1. Read and write fractions with words and symbols.

(B)   Objective 2. Construct fractions using length, set, and area models.

(C)   Objective 3. Recognize unit fractions and use them to compose and decompose fractions related to the same whole. Use the numerator to describe the number of parts and the denominator to describe the number of partitions.

(D)   Objective 4. Use models and number lines to order and compare fractions that are related to the same whole.

(4)   Determine the value of a set of coins or bills.

(A)   Objective 1. Use addition to determine the value of a collection of coins up to one dollar using the cent symbol and a collection of bills up to twenty dollars.

(B)   Objective 2. Select the fewest number of coins for a given amount of money up to one dollar.

(g)   Standard One objectives for Grade 4. The following objectives apply for students in Grade 4:

(1)   Solve real-world and mathematical problems using multiplication and division.

(A)   Objective 1. Demonstrate fluency with multiplication and division facts with factors up to 12.

(B)   Objective 2. Use an understanding of place value to multiply or divide a number by 10, 100, and 1,000.

(C)   Objective 3. Multiply 3-digit by 1-digit or a 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms.

(D)   Objective 4. Estimate products of 3-digit by 1-digit or 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns.

(E)   Objective 5. Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results.

(F)   Objective 6. Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors (e.g. mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties).

(G)   Objective 7. Determine the unknown addend or factor in equivalent and non-equivalent expressions (e.g. 5 + 6 = 4 + □, 3 × 8 < 3 × □).

(2)   Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand how decimals represent quantities.

(A)   Objective 1. Represent and rename equivalent fractions using fraction models (e.g. parts of a set, area models, fraction strips, number lines).

(B)   Objective 2. Use benchmark fractions (0, 1/4, 1/3, 1/2, 2/3, 3/4, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols.

(C)   Objective 3. Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations (e.g. 3/4 = 1/4 + 1/4 + 1/4).

(D)   Objective 4. Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations.

(E)   Objective 5. Represent tenths and hundredths with concrete models, making connections between fractions and decimals.

(F)   Objective 6. Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money.

(G)   Objective 7. Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks.

(H)   Objective 8. Compare benchmark fractions (1/4, 1/3, 1/2, 2/3, 3/4) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations.

(3)   Determine the value of coins in order to solve monetary transactions.

(A)   Objective 1. Given a total cost (whole dollars up to $20 or coins) and amount paid (whole dollars up to $20 or coins), find the change required in a variety of ways. Limited to whole dollars up to $20 or sets of coins.

(h)   Standard One objectives for Grade 5. The following objectives apply for students in Grade 5:

(1)   Divide multi-digit numbers and solve real-world and mathematical problems using arithmetic.

(A)   Objective 1. Estimate solutions to division problems in order to assess the reasonableness of results.

(B)   Objective 2. Divide multi-digit numbers, by one-and two-digit divisors, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.

(C)   Objective 3. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution.

(D)   Objective 4. Solve real-world and mathematical problems requiring addition, subtraction, multiplication, and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.

(2)   Read, write, represent, and compare fractions and decimals; recognize and write equivalent fractions; convert between fractions and decimals; use fractions and decimals in real-world and mathematical situations.

(A)   Objective 1. Represent decimal fractions (e.g. 1/10, 1/100) using a variety of models (e.g. 10 by 10 grids, rational number wheel, base-ten blocks, meter stick) and make connections between fractions and decimals.

(B)   Objective 2. Represent, read and write decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers as large as millions.

(C)   Objective 3. Compare and order fractions and decimals, including mixed numbers and fractions less than one, and locate on a number line.

(D)   Objective 4. Recognize and generate equivalent decimals, fractions, mixed numbers, and fractions less than one in various contexts.

(3)   Add and subtract fractions with like and unlike denominators, mixed numbers and decimals to solve real-world and mathematical problems.

(A)   Objective 1. Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results.

(B)   Objective 2. Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of representations (e.g. fraction strips, area models, number lines, fraction rods).

(C)   Objective 3. Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, using efficient and generalizable procedures, including but not limited to standard algorithms in order to solve real-world and mathematical problems including those involving money, measurement, geometry, and data.

(D)   Objective 4. Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.

(i)   Standard One objectives for Grade 6. The following objectives apply for students in Grade 6:

(1)   Read, write, and represent integers and rational numbers expressed as fractions, decimals, percents, and rations; write positive integers as products of factors; use these representations in real-world and mathematical situations.

(A)   Objective 1. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.

(B)   Objective 2. Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.

(C)   Objective 3. Explain that a percent represents parts "out of 100" and ratios "to 100."

(D)   Objective 4. Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.

(E)   Objective 5. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents.

(F)   Objective 6. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.

(2)   Add and subtract integers in order to solve real-world and mathematical problems.

(A)   Objective 1. Estimate solutions to addition and subtraction of integers problems in order to assess the reasonableness of results.

(B)   Objective 2. Illustrate addition and subtraction of integers using a variety of representations.

(C)   Objective 3. Add and subtract integers; use efficient and generalizable procedures including but not limited to standard algorithms.

(3)   Understand the concept of ratio and its relationship to fractions and percents and to the multiplication and division of whole numbers. Use ratios to solve real-world and mathematical problems.

(A)   Objective 1. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different.

(B)   Objective 2. Determine the unit rate for ratios.

(C)   Objective 3. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.

(D)   Objective 4. Use multiplicative reasoning and representations to solve ratio and unit rate problems.

(4)   Multiply and divide decimals, fractions, and mixed numbers; solve real-world and mathematical problems with rational numbers.

(A)   Objective 1. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.

(B)   Objective 2. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.

(C)   Objective 3. Multiply and divide fractions and decimals using efficient and generalizable procedures.

(D)   Objective 4. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.

(j)   Standard One objectives for Grade 7. The following objectives apply for students in Grade 7:

(1)   Read, write, represent, and compare rational numbers, expressed as integers, fractions, and decimals.

(A)   Objective 1. Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal.

(B)   Objective 2. Compare and order rational numbers expressed in various forms using the symbols <, >, and =.

(C)   Objective 3. Recognize and generate equivalent representations of rational numbers, including equivalent fractions.

(2)   Calculate with integers and rational numbers, with and without positive integer exponents, to solve real-world and mathematical problems; explain the relationship between absolute value of a rational number and the distance of that number from zero.

(A)   Objective 1. Estimate solutions to multiplication and division of integers in order to assess the reasonableness of results.

(B)   Objective 2. Illustrate multiplication and division of integers using a variety of representations.

(C)   Objective 3. Solve real-world and mathematical problems involving addition, subtraction, multiplication and division of rational numbers; use efficient and generalizable procedures including but not limited to standard algorithms.

(D)   Objective 4. Raise integers to positive integer exponents.

(E)   Objective 5. Solve real-world and mathematical problems involving calculations with rational numbers and positive integer exponents.

(F)   Objective 6. Explain the relationship between the absolute value of a rational number and the distance of that number from zero on a number line. Use the symbol for absolute value.

(k)   Standard One objectives for Pre-Algebra. The following objectives apply for students in Pre-Algebra:

(1)   Read, write, compare, classify, and represent real numbers and use them to solve problems in various contexts.

(A)   Objective 1. Develop and apply the properties of integer exponents, including a raised to the 0 power = 1 (with a not equal to 0), to generate equivalent numerical and algebraic expressions.

(B)   Objective 2. Express and compare approximations of very large and very small numbers using scientific notation.

(C)   Objective 3. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation.

(D)   Objective 4. Classify real numbers as rational or irrational. Explain why the rational number system is closed under addition and multiplication and why the irrational system is not. Explain why the sum of a rational number and an irrational number is irrational; and the product of a non-zero rational number and an irrational number is irrational.

(E)   Objective 5. Compare real numbers; locate real numbers on a number line. Identify the square root of a perfect square to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers.

(l)   Standard One objectives for Algebra 1. The following objectives apply for students in Algebra 1:

(1)   Extend the understanding of number and operations to include square roots and cube roots.

(A)   Objective 1. Write square roots and cube roots of monomial algebraic expressions in simplest radical form.

(B)   Objective 2. Add, subtract, multiply, and simplify roots of monomial algebraic expressions and divide square roots of whole numbers, rationalizing the denominator when necessary.

(m)   Standard One objectives for Algebra 2. The following objectives apply for students in Algebra 2:

(1)   Extend the understanding of number and operations to include square roots and cube roots.

(A)   Objective 1. Find the value of i raised to the nth power for any whole number n.

(B)   Objective 2. Simplify, add, subtract, multiply, and divide complex numbers.

(C)   Objective 3. Use matrices to organize and represent data. Identify the order (dimension) of a matrix, add and subtract matrices of appropriate dimensions, and multiply a matrix by a scalar to create a new matrix to solve problems.

(D)   Objective 4. Understand and apply the relationship of rational exponents to integer exponents and radicals to solve problems.

[Source: Added at 33 Ok Reg 1324, eff 9-11-16]