N.J. CCC Standards Mathematics (Adopted 2002)

4.1.  Number and Numerical Operations: ALL STUDENTS WILL DEVELOP NUMBER SENSE AND WILL PERFORM STANDARD NUMERICAL OPERATIONS AND ESTIMATIONS ON ALL TYPES OF NUMBERS IN A VARIETY OF WAYS.   4.2.  Geometry and Measurement:   ALL STUDENTS WILL DEVELOP SPATIAL SENSE AND THE ABILITY TO USE GEOMETRIC PROPERTIES,  RELATIONSHIPS,  AND  MEASUREMENT TO MODEL, DESCRIBE AND ANALYZE PHENOMENA.   4.3.  Patterns and Algebra: ALL  STUDENTS  WILL REPRESENT AND ANALYZE RELATIONSHIPS AMONG VARIABLE QUANTITIES  AND SOLVE PROBLEMS INVOLVING PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS AND PROCESSES.   
Grade 2 (Strands A,B,C) Grade 2 (Strands A,B,C,D,E) Grade 2 (Strands A,B,C,D)
Grade 3 (Strands A,B,C) Grade 3 (Strands A,B,C,D,E) Grade 3 (Strands A,B,C,D)
Grade 4 (Strands A,B,C) Grade 4 (Strands A,B,C,D,E) Grade 4(Strands A,B,C,D)
Grade 5 (Strands A,B,C) Grade 5 (Strands A,B,C,D,E) Grade 5 (Strands A,B,C,D)
Grade 6 (Strands A,B,C) Grade 6 (Strands A,B,C,D,E) Grade 6 (Strands A,B,C,D)
Grade 7 (Strands A,B,C) Grade 7 (Strands A,B,C,D,E) Grade 7 (Strands A,B,C,D)
Grade 8 (Strands A,B,C) Grade 8 (Strands A,B,C,D,E) Grade 8 (Strands A,B,C,D)
Grade 12 (Strands A,B,C) Grade 12 (Strands A,B,C,D,E) Grade 12 (Strands A,B,C,D)

 

4.4.  Data Analysis, Probability, and Discrete Mathematics:  ALL  STUDENTS  WILL  DEVELOP  AN  UNDERSTANDING  OF  THE  CONCEPTS  AND TECHNIQUES OF DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS, AND WILL USE THEM TO MODEL SITUATIONS, SOLVE PROBLEMS, AND ANALYZE AND DRAW APPROPRIATE INFERENCES FROM DATA.   4.5.  Mathematical Processes:  ALL STUDENTS WILL USE MATHEMATICAL PROCESSES OF PROBLEM SOLVING, COMMUNICATION, CONNECTIONS, REASONING, REPRESENTATIONS, AND  TECHNOLOGY  TO SOLVE PROBLEMS AND COMMUNICATE MATHEMATICAL IDEAS.
Grade 2 (Strands A,B,C,D) Grade 2 (Strands A,B,C,D,E,F)
Grade 3 (Strands A,B,C,D) Grade 3 (Strands A,B,C,D,E,F)
Grade 4 (Strands A,B,C,D) Grade 4 (Strands A,B,C,D,E,F)
Grade 5 (Strands A,B,C,D) Grade 5 (Strands A,B,C,D,E,F)
Grade 6 (Strands A,B,C,D) Grade 6 (Strands A,B,C,D,E,F)
Grade 7 (Strands A,B,C,D) Grade 7 (Strands A,B,C,D,E,F)
Grade 8 (Strands A,B,C,D) Grade 8 (Strands A,B,C,D,E,F)
Grade 12 (Strands A,B,C,D) Grade 12 (Strands A,B,C,D,E,F)

 

STANDARD 4.1     (NUMBER AND NUMERICAL OPERATIONS)     ALL STUDENTS WILL DEVELOP NUMBER SENSE AND WILL PERFORM STANDARD NUMERICAL OPERATIONS AND ESTIMATIONS ON ALL TYPES OF NUMBERS IN A VARIETY OF WAYS.

Cumulative Progress Indicators

4.1  By the end of Grade 2, students will:

Strand A.   Number Sense

1.  Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 2 pertain to these sets of numbers as well).

·        Whole numbers through hundreds

·        Ordinals

·        Proper fractions (denominators of 2, 3, 4, 8, 10)

2.  Demonstrate an understanding of whole number place value concepts. 

3.  Understand that numbers have a variety of uses. 

4.  Count and perform simple computations with coins.

·        Amounts up to $1.00 (using cents notation)

5.  Compare and order whole numbers.

 

Strand B.   Numerical Operations

1.  Develop the meanings of addition and subtraction by concretely modeling and

discussing a large variety of problems.

·        Joining, separating, and comparing 

2.  Explore the meanings of multiplication and division by modeling and discussing problems.

3.  Develop proficiency with basic addition and subtraction number facts using a variety of fact strategies (such as .counting on. and .near doubles.) and then  commit  them  to memory.

4.  Construct,  use,  and  explain  procedures  for performing addition and subtraction calculations with:

·        Pencil-and-paper 

·        Mental math

·        Calculator

5.  Use efficient and accurate  pencil-and-paper procedures  for computation with whole numbers.

·        Addition of 2-digit numbers

·        Subtraction of 2-digit numbers

 

6.  Select pencil-and-paper, mental math, or a calculator as the appropriate computational  method in a given situation depending on the context and numbers.

7.  Check the reasonableness of results of computations.

8.  Understand and use the inverse relationship between addition and subtraction.

 

C.  Estimation

1.  Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.

2.  Determine  the  reasonableness  of  an  answer  by  estimating  the  result  of  computations (e.g., 15 + 16 is not 211).

3.  Explore  a  variety  of  strategies for estimating both quantities  (e.g.,  the  number  of marbles in a jar) and results of computation.

 

BuilB 4.1  Building upon knowledge and skills gained in preceding grades, by the end of Grade 3, students will:

 

Strand A.   Number Sense

1.  Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 3 pertain to these sets of numbers as well). 

·        Whole numbers through hundred thousands

·        Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10) as part of a whole, as a subset of a set, and as a location on a number line

2.  Demonstrate an understanding of whole number place value concepts.

3.  Identify whether any whole number is odd or even.

4.  Explore the extension of the place value system to decimals through hundredths.

5.  Understand the various uses of numbers.

·        Counting, measuring, labeling (e.g., numbers on baseball uniforms)

6.  Compare and order numbers.

 

Strand B.   Numerical Operations

1.  Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems.

·        Addition and subtraction:  joining, separating, comparing

·        Multiplication:  repeated addition, area/array

·        Division:  repeated subtraction, sharing

2.  Develop proficiency with basic multiplication and division number facts using a variety of fact strategies (such as .skip counting. and .repeated subtraction.).

3.  Construct, use, and explain procedures for performing whole number calculations with:

·        Pencil-and-paper 

·        Mental math

·        Calculator

4.  Use efficient and accurate  pencil-and-paper procedures  for computation with whole numbers.

·        Addition of 3-digit numbers

·        Subtraction of 3-digit numbers

·        Multiplication of 2-digit numbers by 1-digit numbers

5.  Count and perform simple computations with money.

·        Cents notation (¢)

6.  Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.

7.  Check the reasonableness of results of computations.

 

C.  Estimation

1.  Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.

2.  Construct and use a variety of estimation strategies (e.g., rounding and mental math) for estimating both quantities and the result of computations.

3.  Recognize  when  an  estimate  is  appropriate,  and  understand  the  usefulness  of  an estimate as distinct from an exact answer.

4.  Use estimation to determine whether the result of a computation (either by calculator or by hand) is reasonable.

 

Build  4.1  Building  upon knowledge and skills gained in preceding grades, by the end of Grade 4, students will:

 

Strand A.   Number Sense

1.  Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 4 pertain to these sets of numbers as well). 

·        Whole numbers through millions

·        Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 16) as part of a whole, as a subset of a set, and as a location on a number line

·        Decimals through hundredths

2.  Demonstrate an understanding of place value concepts. 

3.  Demonstrate a sense of the relative magnitudes of numbers.

4.  Understand the various uses of numbers.

·        Counting, measuring, labeling (e.g., numbers on baseball uniforms), locating (e.g., Room 235 is on the second floor)

5.  Use concrete and pictorial models to relate whole numbers, commonly used fractions, and decimals to each other, and to represent equivalent forms of the same number.

6.  Compare and order numbers. 

7.  Explore settings that give rise to negative numbers.

·        Temperatures below 0o, debts

·        Extension of the number line 

 

Strand B.   Numerical Operations

1.  Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems.

·        Addition and subtraction:  joining, separating, comparing

·        Multiplication:  repeated addition, area/array

·        Division: repeated subtraction, sharing

2.  Develop proficiency with basic multiplication and division number facts using a variety of fact strategies (such as .skip counting. and .repeated subtraction.) and then commit them to memory. 

3.  Construct, use, and explain procedures for performing whole number calculations and with:

·        Pencil-and-paper 

·        Mental math

·        Calculator

4.  Use  efficient  and  accurate  pencil-and-paper  procedures  for  computation  with  whole numbers.

·        Addition of 3-digit numbers

·        Subtraction of 3-digit numbers

·        Multiplication of 2-digit numbers

·        Division of 3-digit numbers by 1-digit numbers

5.  Construct and use procedures for performing decimal addition and subtraction.

6.  Count and perform simple computations with money.

·        Standard dollars and cents notation

7.  Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.

8.  Check the reasonableness of results of computations.

9.  Use concrete models to explore addition and subtraction with fractions. 

10.  Understand and use the inverse relationships between addition and subtraction and    between multiplication and division.

 

C.  Estimation

1.  Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.

2.  Construct and use a variety of estimation strategies (e.g., rounding and mental math) for estimating both quantities and the results of computations.

3.  Recognize  when  an  estimate  is  appropriate,  and  understand  the  usefulness  of  an estimate as distinct from an exact answer.

4.  Use estimation to determine whether the result of a computation (either by calculator or by hand) is reasonable.

 

    4.1  Building upon knowledge and skills gained in preceding grades, by the end of Grade 5,  students will:

 

Strand A.   Number Sense

1.  Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 5 pertain to these sets of numbers as well).

·        All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers

·        All decimals 

2.  Recognize the decimal nature of United States currency and compute with money.

3.  Demonstrate a sense of the relative magnitudes of numbers.

4.  Use whole numbers, fractions, and decimals to represent equivalent forms of the same

number. 

5.  Develop and apply number theory concepts in problem solving situations.

·        Primes, factors, multiples

6.  Compare and order numbers. 

 

Strand B.   Numerical Operations

1.  Recognize the appropriate use of each arithmetic operation in problem situations.

2.  Construct, use, and explain procedures for  performing  addition  and  subtraction  with

fractions and decimals with:

·        Pencil-and-paper 

·        Mental math

·        Calculator

         

3.  Use  an  efficient  and  accurate  pencil-and-paper  procedure  for  division  of  a  3-digit number by a 2-digit number.

4.  Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.

5.  Check the reasonableness of results of computations.

6.  Understand  and  use  the  various  relationships  among  operations and properties of operations.

 

C.  Estimation

1.  Use a variety of estimation strategies for both number and computation.

2.  Recognize  when  an  estimate  is  appropriate,  and  understand  the  usefulness  of  an estimate as distinct from an exact answer.

3.  Determine the reasonableness of an answer by estimating the result of operations.

4.  Determine whether a given estimate is an overestimate or an underestimate.

 

Bu       4.1  Building upon knowledge and skills gained in preceding grades, by the end of Grade 6, students will:

Strand A.   Number Sense

1.  Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 6 pertain to these sets of numbers as well).

·        All integers 

·        All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers

·        All decimals 

2.  Recognize the decimal nature of United States currency and compute with money.

3.  Demonstrate a sense of the relative magnitudes of numbers.

4.  Explore the use of ratios and proportions in a variety of situations.

5.  Understand  and  use  whole-number  percents between 1 and 100  in a variety of situations.

6.  Use whole numbers, fractions, and decimals to represent equivalent forms of the same number. 

7.  Develop and apply number theory concepts in problem solving situations.

·        Primes, factors, multiples

·        Common multiples, common factors

8.  Compare and order numbers. 

 

Strand B.   Numerical Operations

1.  Recognize the appropriate use of each arithmetic operation in problem situations.

2.  Construct, use, and explain procedures for  performing  calculations  with  fractions  and decimals with:

·        Pencil-and-paper 

·        Mental math

·        Calculator

3.  Use  an  efficient  and  accurate  pencil-and-paper  procedure  for  division  of  a  3-digit number by a 2-digit number.

4.  Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.

5.  Find squares and cubes of whole numbers. 

6.  Check the reasonableness of results of computations.

7.  Understand  and  use  the  various  relationships  among  operations and properties of operations.

8.  Understand  and  apply  the  standard algebraic order of operations  for  the  four  basic operations, including appropriate use of parentheses.

 

C.  Estimation

1.  Use a variety of strategies for estimating both quantities and the results of computations.

2.  Recognize  when  an  estimate  is  appropriate,  and  understand  the  usefulness  of  an estimate as distinct from an exact answer.

3.  Determine the reasonableness of an answer by estimating the result of operations.

4.  Determine whether a given estimate is an overestimate or an underestimate.

 

Buildi 4.1  Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will:

 

Strand A.   Number Sense

1.  Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 7 pertain to these sets of numbers as well): 

·        Rational numbers

·        Percents

·        Whole numbers with exponents 

2.  Demonstrate a sense of the relative magnitudes of numbers.

3.  Understand  and  use  ratios,  proportions,  and  percents  (including  percents greater than 100 and less than 1) in a variety of situations.

4.  Compare and order numbers of all named types.

5.  Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.

6.  Understand that all fractions can be represented as repeating or terminating decimals.

 

Strand B.   Numerical Operations

1.  Use  and  explain  procedures  for  performing  calculations  with  integers  and  all  number types named above with:

·        Pencil-and-paper 

·        Mental math

·        Calculator

2.  Use exponentiation to find whole number powers of numbers.

3.  Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.

         

C.  Estimation

1.  Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.

 

Buildi     4.1  Building upon knowledge and skills gained in preceding grades, by the end of Grade 8, students will:

 

Strand A.   Number Sense

1.  Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): 

·        Rational numbers

·        Percents

·        Exponents

·        Roots

·        Absolute values

·        Numbers represented in scientific notation 

2.  Demonstrate a sense of the relative magnitudes of numbers.

3.  Understand  and  use  ratios,  proportions,  and  percents  (including  percents greater than 100 and less than 1) in a variety of situations.

4.  Compare and order numbers of all named types.

5.  Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.

6.  Recognize that repeating decimals correspond to fractions and determine their fractional

equivalents.

·        5/7 = 0. 714285714285.  =  0. 714285

7.  Construct meanings for common irrational numbers, such as ð (pi) and the square root of 2.

 

Strand B.   Numerical Operations

1.  Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with:

·        Pencil-and-paper 

·        Mental math

·        Calculator

2.  Use exponentiation to find whole number powers of numbers.

3.  Find square and cube roots of numbers and understand the inverse nature of powers and roots.

4.  Solve problems involving proportions and percents.

5.  Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.

         

 

C.  Estimation

1.  Estimate square and cube roots of numbers.

2.  Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.

3.  Recognize  the  limitations  of  estimation  and  assess the amount of error resulting from estimation.

 

Build     4.1