(NO) Number and Operations Categories All categories Not categorized Prioritized Standards (AR) Algebraic Reasoning (DPS) Data, Probability, and Statistics (GM) Geometry and Measurement (NO) Number and Operations

MAT-02.NO

MAT-02.NO Domain

(NO) Number and Operations

Sub-Categories

• (CC) Counting and Cardinality
Learners will understand the relationship between numerical symbols, names, quantities, and counting sequences.
• (NBT) Number Base Ten
Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.
• (NF) Number Fractions
Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.
• (NS) Number System
Learners will expand their knowledge of the number system to create connections and solve problems within and across concepts.
• (O) Operations
Learners will expand their computational fluency to create connections and solve problems within and across concepts.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

MAT-02.NO.CC.01

 2nd Grade (MAT) Targeted Standard    (NO) Number and Operations  (CC) Counting and Cardinality Learners will understand the relationship between numerical symbols, names, quantities, and counting sequences.

Progressions

Counting Forward

• MAT-00.NO.CC.01 Count verbally in sequential order by ones and tens to 100, making accurate decuple transitions (ex.89 to 90). Count verbally forward from any given number within 100.
• MAT-01.NO.CC.01 Count forward by ones and tens from any given point within 120.
• MAT-02.NO.CC.01 Count forward from any given number within 1000.

MAT-02.NO.CC.02

 2nd Grade (MAT) Targeted Standard    (NO) Number and Operations  (CC) Counting and Cardinality Learners will understand the relationship between numerical symbols, names, quantities, and counting sequences.

Progressions

Counting Backward

• MAT-00.NO.CC.02 Count backward from 20 by ones and from a given number within 10.
• MAT-01.NO.CC.02 Count backward by ones and tens from any given number within 120.
• MAT-02.NO.CC.02 Count backward from any given number within 1000.

MAT-02.NO.CC.03

 2nd Grade (MAT) Targeted Standard    (NO) Number and Operations  (CC) Counting and Cardinality Learners will understand the relationship between numerical symbols, names, quantities, and counting sequences.

Progressions

Number Identification and Writing

• MAT-00.NO.CC.03 Identify and write any given numeral within 20.
• MAT-01.NO.CC.03 Represent several objects with a written numeral up to 120.
• MAT-02.NO.CC.03 Read and write numbers up to 1,000 using standard, word, and expanded forms.
• MAT-03.NO.CC.01 Read and write numbers up to 10,000 using objects or visual representations including standard and expanded forms.
• MAT-04.NO.CC.01 Read numbers to the millions place including word, standard and expanded form. Write numbers to the millions place including standard and expanded form.
• MAT-05.NO.CC.01 Read, write, and compare decimals to the thousandths including standard and expanded forms.

MAT-02.NO.CC.04

 2nd Grade (MAT) Targeted Standard    (NO) Number and Operations  (CC) Counting and Cardinality Learners will understand the relationship between numerical symbols, names, quantities, and counting sequences.

Progressions

Counting Patterns

• MAT-00.NO.CC.05 Count and tell how many objects up to 20 are in an arranged pattern or up to 10 objects in a scattered configuration. Represent a quantity of up to 20 with a numeral.
• MAT-01.NO.CC.05 Skip count forward and backward by 5s and 10s from multiples and recognize the patterns of up to 10 skip counts.
• MAT-02.NO.CC.04 Skip count forward and backward by 2s and 100s and recognize the patterns of skip counts.
• MAT-10.DPS.09 Determine the number of outcomes using permutations and combinations in context.
• MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.

MAT-02.NO.NBT.01

 2nd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NBT) Number Based Ten Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.

Progressions

Place Value

• MAT-00.NO.NBT.01 Compose and decompose numbers from 11 to 19 using a group of ten ones and some more ones using a model, drawing, or equation.
• MAT-01.NO.NBT.01 Demonstrate that the two digits of a two-digit number represent a composition of some tens and some ones.
• MAT-02.NO.NBT.01 Understand that the three digits of a three-digit number represent a composition of some hundreds, some tens, and some ones.
• MAT-04.NO.NBT.01 Understand that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
• MAT-05.NO.NBT.01 Understand that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
• MAT-08.NO.NS.03 Use scientific notation to represent very large or very small quantities. Interpret scientific notation generated by technology. Compare and order numbers in scientific and standard notation.

MAT-02.NO.NBT.02

 2nd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NBT) Number Based Ten Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.

Progressions

Compare Numbers and/or Expressions

• MAT-00.NO.NBT.02 Compare two numbers between 1 and 20 using words greater than, less than, or equal to.
• MAT-01.NO.NBT.02 Compare two two-digit numbers using symbols >, <, and =. Justify comparisons based on the number of tens and ones.
• MAT-02.NO.NBT.02 Compare two three-digit numbers using symbols >, <, and =. Justify comparisons based on the value of thousands, hundreds, tens, and ones.
• MAT-03.NO.NBT.01 Compare two four-digit numbers using symbols, >, <, and =. Justify comparisons based on the value of thousands, hundreds, tens, and ones.
• MAT-04.NO.NBT.02 Compare two numbers to the millions place and decimals to the hundredths place, using symbols >, <, and =. Justify comparisons based on the value of the digits.
• MAT-05.NO.NBT.02 Compare two decimals to thousandths using symbols >, <, and =. Justify comparisons based on the value of the digits.
• MAT-06.NO.NS.01 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.
• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.
• MAT-07.NO.NS.01 Describe the absolute value of a number as its distance from zero on a number line.
• MAT-08.NO.NS.01 Compare and classify real numbers within the real number system.
• MAT-08.NO.NS.02 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them on a number line diagram, and estimate the value of irrational expressions involving one operation.
• MAT-08.NO.NS.03 Use scientific notation to represent very large or very small quantities. Interpret scientific notation generated by technology. Compare and order numbers in scientific and standard notation.
• MAT-09.AR.06 Solve linear equations and inequalities (to include compound inequalities) in one variable.
• MAT-09.AR.08 Graph the solution set to a two-variable system of linear equations. Create and graph the solution set to a two-variable system of linear inequalities in context.
• MAT-09.AR.09 Solve absolute value equations and inequalities in one or two variables.
• MAT-12.AR.09 Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context.

MAT-02.NO.NBT.03

 2nd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NBT) Number Based Ten Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.

Progressions

• MAT-01.NO.NBT.03 Add within 100 using a two-digit number and a one-digit number. Use concrete models, drawings, and strategies that reflect an understanding of place value.
• MAT-02.NO.NBT.03 Add within 100 using place value strategies and/or the relationship between addition and subtraction.
• MAT-01.NO.NBT.04 Subtract multiples of 10 within 100 using concrete models, drawings, and strategies that reflect an understanding of place value.
• MAT-01.NO.NBT.05 Mentally add or subtract 10 to or from a given two-digit number and explain the reasoning used.
• MAT-02.NO.NBT.04 Subtract within 100 using place value strategies and/or the relationship between addition and subtraction.
• MAT-02.NO.NBT.05 Mentally add or subtract 10 or 100 to or from a given number between 100 and 900.
• MAT-03.NO.NBT.03 Add and subtract within 1000 using place value strategies, algorithms, and/or the relationship between addition and subtraction.
• MAT-04.NO.NBT.04 Add and subtract multi-digit whole numbers to the one million place using strategies flexibly, including the algorithm.
• MAT-05.NO.NBT.05 Use concrete models, drawings, place value strategies, properties of operations, and/or relationships to add, subtract, and multiply decimals to hundredths.
• MAT-07.NO.O.01 Add, subtract, multiply, and divide integers using visual models and properties of operations in multi-step authentic and mathematical problems, including authentic problems.
• MAT-07.NO.O.02 Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.
• MAT-07.NO.O.03 Add, subtract, multiply, and divide non-negative decimals to the hundredth place in multi-step problems using strategies or procedures, including authentic problems.
• MAT-08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.
• MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
• MAT-09.AR.11 Add, subtract, and multiply polynomials.
• MAT-12.NO.03 Demonstrate that the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.
• MAT-12.AR.13 Add, subtract, and multiply polynomials beyond quadratics. Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
• MAT-12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.
• MAT-12.NO.17 Add and subtract vectors. Represent vector subtraction graphically by connecting the tips of the appropriate order and using the components to perform vector subtraction.
• MAT-12.NO.19 Represent data in a matrix. Perform operations (i.e., addition, subtraction, multiplication) on matrices of appropriate dimensions to solve problems and in context. Know that matrix multiplication is not commutative.

MAT-02.NO.NBT.04

 2nd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NBT) Number Based Ten Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.

Progressions

• MAT-01.NO.NBT.03 Add within 100 using a two-digit number and a one-digit number. Use concrete models, drawings, and strategies that reflect an understanding of place value.
• MAT-02.NO.NBT.03 Add within 100 using place value strategies and/or the relationship between addition and subtraction.
• MAT-01.NO.NBT.04 Subtract multiples of 10 within 100 using concrete models, drawings, and strategies that reflect an understanding of place value.
• MAT-01.NO.NBT.05 Mentally add or subtract 10 to or from a given two-digit number and explain the reasoning used.
• MAT-02.NO.NBT.04 Subtract within 100 using place value strategies and/or the relationship between addition and subtraction.
• MAT-02.NO.NBT.05 Mentally add or subtract 10 or 100 to or from a given number between 100 and 900.
• MAT-03.NO.NBT.03 Add and subtract within 1000 using place value strategies, algorithms, and/or the relationship between addition and subtraction.
• MAT-04.NO.NBT.04 Add and subtract multi-digit whole numbers to the one million place using strategies flexibly, including the algorithm.
• MAT-05.NO.NBT.05 Use concrete models, drawings, place value strategies, properties of operations, and/or relationships to add, subtract, and multiply decimals to hundredths.
• MAT-07.NO.O.01 Add, subtract, multiply, and divide integers using visual models and properties of operations in multi-step authentic and mathematical problems, including authentic problems.
• MAT-07.NO.O.02 Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.
• MAT-07.NO.O.03 Add, subtract, multiply, and divide non-negative decimals to the hundredth place in multi-step problems using strategies or procedures, including authentic problems.
• MAT-08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.
• MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
• MAT-09.AR.11 Add, subtract, and multiply polynomials.
• MAT-12.NO.03 Demonstrate that the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.
• MAT-12.AR.13 Add, subtract, and multiply polynomials beyond quadratics. Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
• MAT-12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.
• MAT-12.NO.17 Add and subtract vectors. Represent vector subtraction graphically by connecting the tips of the appropriate order and using the components to perform vector subtraction.
• MAT-12.NO.19 Represent data in a matrix. Perform operations (i.e., addition, subtraction, multiplication) on matrices of appropriate dimensions to solve problems and in context. Know that matrix multiplication is not commutative.

MAT-02.NO.NBT.05

 2nd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NBT) Number Based Ten Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.

Progressions

• MAT-01.NO.NBT.03 Add within 100 using a two-digit number and a one-digit number. Use concrete models, drawings, and strategies that reflect an understanding of place value.
• MAT-02.NO.NBT.03 Add within 100 using place value strategies and/or the relationship between addition and subtraction.
• MAT-01.NO.NBT.04 Subtract multiples of 10 within 100 using concrete models, drawings, and strategies that reflect an understanding of place value.
• MAT-01.NO.NBT.05 Mentally add or subtract 10 to or from a given two-digit number and explain the reasoning used.
• MAT-02.NO.NBT.04 Subtract within 100 using place value strategies and/or the relationship between addition and subtraction.
• MAT-02.NO.NBT.05 Mentally add or subtract 10 or 100 to or from a given number between 100 and 900.
• MAT-03.NO.NBT.03 Add and subtract within 1000 using place value strategies, algorithms, and/or the relationship between addition and subtraction.
• MAT-04.NO.NBT.04 Add and subtract multi-digit whole numbers to the one million place using strategies flexibly, including the algorithm.
• MAT-05.NO.NBT.05 Use concrete models, drawings, place value strategies, properties of operations, and/or relationships to add, subtract, and multiply decimals to hundredths.
• MAT-07.NO.O.01 Add, subtract, multiply, and divide integers using visual models and properties of operations in multi-step authentic and mathematical problems, including authentic problems.
• MAT-07.NO.O.02 Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.
• MAT-07.NO.O.03 Add, subtract, multiply, and divide non-negative decimals to the hundredth place in multi-step problems using strategies or procedures, including authentic problems.
• MAT-08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.
• MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
• MAT-09.AR.11 Add, subtract, and multiply polynomials.
• MAT-12.NO.03 Demonstrate that the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.
• MAT-12.AR.13 Add, subtract, and multiply polynomials beyond quadratics. Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
• MAT-12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.
• MAT-12.NO.17 Add and subtract vectors. Represent vector subtraction graphically by connecting the tips of the appropriate order and using the components to perform vector subtraction.
• MAT-12.NO.19 Represent data in a matrix. Perform operations (i.e., addition, subtraction, multiplication) on matrices of appropriate dimensions to solve problems and in context. Know that matrix multiplication is not commutative.

MAT-02.NO.NF.01

 2nd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NF) Factions Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.

Progressions

Fractions - Partition Shapes

• MAT-01.NO.NF.01 Partition circles and rectangles into two and four equal shares using the language halves and fourths.
• MAT-02.NO.NF.01 Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the language of halves, thirds, fourths, half of, a third of, and a fourth of.
• MAT-02.NO.NF.02 Recognize that identical wholes can be equally divided in different ways.
• MAT-02.NO.NF.03 Recognize that partitioning shapes into more equal shares creates smaller shares.
• MAT-03.NO.NF.01 Partition two-dimensional figures into equal areas and express the area of each part as a unit fraction of the whole. Describe using the language of sixths, eighths, a sixth of, and an eighth of.

MAT-02.NO.NF.02

 2nd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NF) Factions Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.

Progressions

Fractions - Partition Shapes

• MAT-01.NO.NF.01 Partition circles and rectangles into two and four equal shares using the language halves and fourths.
• MAT-02.NO.NF.01 Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the language of halves, thirds, fourths, half of, a third of, and a fourth of.
• MAT-02.NO.NF.02 Recognize that identical wholes can be equally divided in different ways.
• MAT-02.NO.NF.03 Recognize that partitioning shapes into more equal shares creates smaller shares.
• MAT-03.NO.NF.01 Partition two-dimensional figures into equal areas and express the area of each part as a unit fraction of the whole. Describe using the language of sixths, eighths, a sixth of, and an eighth of.

MAT-02.NO.NF.03

 2nd Grade (MAT) Targeted Standard    (NO) Number and Operations  (NF) Factions Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.

Progressions

Fractions - Partition Shapes

• MAT-01.NO.NF.01 Partition circles and rectangles into two and four equal shares using the language halves and fourths.
• MAT-02.NO.NF.01 Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the language of halves, thirds, fourths, half of, a third of, and a fourth of.
• MAT-02.NO.NF.02 Recognize that identical wholes can be equally divided in different ways.
• MAT-02.NO.NF.03 Recognize that partitioning shapes into more equal shares creates smaller shares.
• MAT-03.NO.NF.01 Partition two-dimensional figures into equal areas and express the area of each part as a unit fraction of the whole. Describe using the language of sixths, eighths, a sixth of, and an eighth of.