N.J. CCC Standards Mathematics (Adopted 2002)
| 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 DAT |
4.5.
Mathematical Processes: |
| 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) |
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