Okla. Admin. Code § 210:15-3-62

Current through Vol. 42, No. 8, January 2, 2025

Section 210:15-3-62 - Standard One: Numbers and Operations

(a)Statement of the standard. A focus on numbers 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 0 (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 up to 10.

(C)Objective 3. Understand the last numeral spoken, when counting aloud, tells how many total objects are in a set up to 10.

(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 0-5 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.

(E)Objective 5. Count forward, with and without objects, from any given number up to 20.

(F)Objective 6. Read, write, discuss, and represent whole numbers from 0 to at least 20. Representations may include numerals, pictures, real objects and pictographs, 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. Compare and order whole numbers from 0 to 10 with and without objects, using the vocabulary "more than," "less than," or "equal to."

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

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

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

(A)Objective 1. Distribute 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 grouping in terms of tens and ones.

(A)Objective 1. Recognize numbers to 20 without counting (subitize) the quantity of structured arrangements.

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

(C)Objective 3. Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, words, addition and subtraction, pictures, tally marks, number lines and manipulatives.

(D)Objective 4. Count forward, with objects, from any given number up to 100 by 1s, 2s, 5s, and 10s.

(E)Objective 5. Count forward, without objects, by multiples of 1s, 2s, 5s, and 10s, up to 100.

(F)Objective 6. Find a number that is 10 more or 10 less than a given number up to 100.

(G)Objective 7. Compare and order whole numbers from 0 to 100.

(H)Objective 8. Use knowledge of number relationships to locate the position of a given whole number, up to 20, on an open number line.

(I)Objective 9. Use words such as "more than", "less than", and "equal to" to describe the relative value of numbers.

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

(A)Objective 1. Represent and solve problems using addition and subtraction with sums and minuends of up to 10.

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

(C)Objective 3. Demonstrate fluency with basic facts of addition and subtraction with sums and minuends of 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 two and three equal groups.

(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 1s, 5s, and 10s.

(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 should include, but are not limited to, 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, up to 100, on an open number line.

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

(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. Use objects to determine whether a number is even or odd.

(F)Objective 6. Use place value understanding to round numbers to the nearest ten and nearest hundred (up to 1,000). Recognize when to round in real-world situations.

(G)Objective 7. 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 with sums and minuends of up to 20.

(B)Objective 2. Demonstrate fluency with basic facts of addition and subtraction with sums and minuends of 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 addition and subtraction problems involving whole numbers up to two 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 (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 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 100,000 with an emphasis on place value and equality.

(A)Objective 1. Read, write, discuss, and represent whole numbers up to 100,000. Representations should include but are not limited to numerals, words, pictures, number lines, and manipulatives (ex: 350 = 3 hundreds, 5 tens = 35 tens = 3 hundreds, 4 tens, 10 ones).

(B)Objective 2. Use place value to describe whole numbers between 1,000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones, including written, standard, and expanded forms.

(C)Objective 3. Applying knowledge of place values, use mental strategies (no written computations) to find 100 more or 100 less than a given number, 1,000 more or 1,000 less than a given number, and 10,000 more or 10,000 less than a given number, up to a five digit number.

(D)Objective 4. Use place value to compare and order whole numbers up to 100,000, using comparative language, numbers, and symbols.

(E)Objective 5. Use place value understanding to round numbers to the nearest thousand, ten-thousand and hundred-thousand.

(2) Solve real-world and mathematical problems using addition, subtraction, multiplication, and division.

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

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

(C)Objective 3. Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract up to five digit numbers (answer not to exceed 100,000).

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

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

(F)Objective 6. Represent division facts and divisibility by modeling a variety of approaches (e.g., repeated subtraction, equal sharing, forming equal groups) to show the relationship between multiplication and division.

(G)Objective 7. Apply the relationship between multiplication and division to represent and solve problems.

(H)Objective 8. Use various strategies (e.g., base ten blocks, area models, arrays, repeated addition, algorithms) based on knowledge of place value, equality, and properties of addition and multiplication to multiply a two-digit factor by a one-digit factor.

(3) Use and justify fractional representations in real-world and mathematical problems.

(A)Objective 1. Read and write fractions with words and symbols using appropriate terminology (i.e., numerator and denominator).

(B)Objective 2. Model fractions using length, set, and area for halves, thirds, fourths, sixths, and eighths.

(C)Objective 3. Apply understanding of unit fractions and use this understanding to compose and decompose fractions related to the same whole.

(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 and determine the value of a set of bills in monetary transactions.

(A)Objective 1. Use addition and subtraction to determine the value of a collection of coins up to one dollar using the cent symbol and in monetary transactions.

(B)Objective 2. Add and subtract a collection of bills up to twenty dollars using whole dollars in monetary transactions.

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

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

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

(B)Objective 2. Use place value to describe whole numbers between 1,000 and 1,000,000 in terms of millions, hundred thousands, ten thousands, thousands, hundreds, tens and ones, with written, standard, and expanded forms.

(C)Objective 3. Applying knowledge of place value, use mental strategies (no written computations) to multiply or divide a number by 10, 100 and 1,000.

(D)Objective 4. Use place value to compare and order whole numbers up to 1,000,000, using comparative language, numbers, and symbols.

(2) 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. Multiply 3-digit by 1-digit and 2-digit by 2-digit whole numbers, using various strategies, including but not limited to standard algorithms.

(C)Objective 3. Estimate products of 3-digit by 1-digit and 2-digit by 2-digit whole number factors using a variety of strategies (e.g., rounding, front end estimation, adjusting, compatible numbers) to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns.

(D)Objective 4. Apply and analyze models to solve multi-step 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.

(E)Objective 5. Use strategies and algorithms (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties) based on knowledge of place value, equality, and properties of operations to divide a 3-digit dividend by a 1-digit whole number divisor, with and without remainders.

(3) Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand decimal 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 with denominators up to twelfths on a number line.

(C)Objective 3. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols.

(D)Objective 4. Decompose a fraction into a sum of fractions with the same denominator in more than one way, using concrete and pictorial models and recording results with numerical representations (e.g., 3/4 = 1/4 + 1/4 + 1/4, 3/4 = 2/4 + 1/4).

(E)Objective 5. Use models to add and subtract fractions with like denominators.

(F)Objective 6. Represent tenths and hundredths with concrete and pictorial models, making connections between fractions and decimals.

(G)Objective 7. Read and write decimals in standard, word, and expanded form up to at least the hundredths place in a variety of contexts, including money.

(H)Objective 8. Compare and order decimals and whole numbers using place value and various models including but not limited to grids, number lines, and base 10 blocks.

(I)Objective 9. Compare and order benchmark fractions (0, 1/4, 1/3, 1/2, 2/3, 3/4, 1) and decimals (0, 0.25, 0.50, 0.75, 1.00) in a variety of representations.

(4) Determine the value of bills and coins in order to solve monetary transactions.

(A)Objective 1. Select the fewest number of coins for a given amount of money up to one dollar.

(B)Objective 2. Given a total cost (dollars and coins up to twenty dollars) and amount paid (dollars and coins up to twenty dollars), find the change required in a variety of ways.

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

(1) 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, base-ten blocks, meter stick) and show the rational number relationship among fractions, decimals and whole numbers.

(B)Objective 2. Read, write, and represent decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers up to seven digits.

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

(D)Objective 4. Recognize and generate equivalent terminating decimals, fractions, mixed numbers, and fractions in various models.

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

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

(B)Objective 2. Divide multi-digit numbers, by one- and two-digit divisors, based on knowledge of place value, including but not limited to standard algorithms.

(C)Objective 3. Recognize that remainders can be represented in a variety of ways, including a whole number, fraction, or decimal. Determine the most meaningful form of a remainder based on the context of the problem.

(D)Objective 4. Construct models to solve multi-digit whole number problems requiring addition, subtraction, multiplication, and division using various representations, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.

(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 mathematical models (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, involving money, measurement, geometry, and data. Use various models and efficient strategies, including but not limited to standard algorithms.

(D)Objective 4. Apply mental math and knowledge of place value (no written computations) to find 0.1 more or 0.1 less than a number, 0.01 more or 0.01 less than a number, and 0.001 more or 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 rational numbers expressed as integers, fractions, decimals, percents, and ratios; use these representations in real-world and mathematical situations.

(A)Objective 1. Use manipulatives and models (e.g., number lines) to determine positive and negative numbers and their contexts, identify opposites, and explain the meaning of 0 (zero) in a variety of situations.

(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, mixed numbers, decimals, and percents.

(2) Read, write, and model whole-number and integer operations to solve problems.

(A)Objective 1. Estimate solutions for integer addition and subtraction 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 in a variety of situations; use efficient and generalizable procedures including but not limited to standard algorithms.

(D)Objective 4. Identify and represent patterns with whole-number exponents and perfect squares. Evaluate powers with whole-number bases and exponents.

(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.

(3) Explain and use the concept of ratio and its relationship to other rational numbers and to the multiplication and division of whole numbers. Use ratios to solve problems.

(A)Objective 1. Identify and use ratios to compare and relate quantities in multiple ways. 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, unit rates, and percents to solve problems in various contexts.

(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. Use mathematical modeling to solve and interpret problems including 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. Explain and apply the concept of absolute value.

(A)Objective 1. Compare and order rational numbers expressed in various forms using the symbols "<",">", and "=".

(B)Objective 2. Recognize and generate equivalent representations of rational numbers, including equivalent fractions.

(C)Objective 3. 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. Apply the concept of absolute value to model and solve problems.

(2) Calculate with rational numbers, with and without positive integer exponents, to model and solve mathematical problems.

(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. Multiply and divide integers in a variety of situations; use efficient and generalizable procedures, including standard algorithms.

(D)Objective 4. Raise rational numbers (integers, fractions, and decimals) to positive integer exponents.

(E)Objective 5. Model and solve problems using rational numbers involving addition, subtraction, multiplication, division, and positive integer exponents.

(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 aº = 1 (with a [NOT EQUAL] 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 and express the answer in scientific notation.

(D)Objective 4. Compare and order real numbers; locate real numbers on a number line. Identify the square roots of perfect squares 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 exponents to include square roots and cube roots.

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

(B)Objective 2. Add, subtract, multiply, divide, and simplify square roots of constants, 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 numbers and operations to include complex numbers, radical expressions, and expressions written with rational exponents.

(A)Objective 1. Find the value iⁿ of for any whole number n.

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

(C)Objective 3. Understand and apply the relationship between rational exponents to integer exponents and radicals to solve problems.

(2) Extend the understanding of numbers and operations to matrices.

(A)Objective 1. Use matrices to organize and represent data. Identify the order (dimension) of a matrix.

(B)Objective 2. Use addition, subtraction, and scalar multiplication of matrices to solve problems.

(n)Standard One objectives for Pre Calculus and Trigonometry. The following objectives apply for students in Pre Calculus and Trigonometry:

(1) Explore complex numbers.

(A)Objective 1. Use the relation i² = -1 and the mathematical properties to add, subtract, and multiply complex numbers.

(B)Objective 2. Find the conjugate of a complex number in rectangular forms and quotients of complex numbers.

(C)Objective 3. Solve quadratic equations in one variable that have complex solutions.

Okla. Admin. Code § 210:15-3-62

Adopted by Oklahoma Register, Volume 40, Issue 5, November 15, 2022, eff. 12/11/2022