KINDERGARTEN Use ordinals first through fifth. [1.06] Use ...

KINDERGARTEN 2003 revision
1998 revision Whole numbers through 30
Eliminated
1. Number and Operations Use ordinals (1st –10th) [1.01 e]
… and backward from 10. [1.02] Eliminated
Use ordinals first through fifth. [1.06]
Combine and remove objects from sets, Estimate quantities fewer than or equal to
describe results. [1.08] 10. [1.01 f]
Estimate quantities less than 20. [1.09]
Moved to grade 1 [2.01a]
2. Measurement
Use non-standard measurement of length, Recognize concepts of calendar time using
weight…[2.05] appropriate vocabulary (days of the week,
Name the days of the week. [2.06] months of the year, seasons). [2.02]

3. Geometry Moved to grade 1 [3.01]
Recognize basic two-
dimensional…square… [2.01] Added:
Not mentioned: Identify, build, draw and name triangles,
Spheres and cubes rectangles and circles; identify, build, and
name spheres and cubes. [3.01]
4. Data Analysis and Probability
No changes in content

5. Algebra
No changes in content.

NCSCOS Mathematics
Comparison of 1998 document and 2003 revision

Prepared by NCDPI
July 31, 2003
Page 1

GRADE 1 2003 revision
Whole numbers through 99
1998 revision Moved to Kindergarten [1.01 e]

1. Number and Operations Eliminated

Use ordinal numbers first through tenth. Estimate quantities fewer than or equal to
[1.07] 100. [1.01 f]

Identify one more/less/before/after/between. Build understanding of place value (ones,
[1.09] tens). [1.01 e]
Create, model, and solve problems that use
Estimate quantities up to 30. Recognize addition, subtraction, and fair shares
when solutions to problems are reasonable. (between two or three). [1.04]
[1.12] Move to Grade 2 [5.02]

Group objects into tens and ones, recognize Eliminated
models; record. [1.13] Eliminated

Model the division of sets into two, three or
four equal parts; explain solution. [1.16],
[2.08]

Relate addition and subtraction to symbolic
notation and write equations. [1.17]

Model 10 more/less to 100. [1.20]

Model 2-digit addition/subtraction with
multiples of 10 to 100. [1.21]

2. Measurement Moved to Kindergarten [2.02]

Use calendar language…seasons and Develop an understanding of the concept of
months of the year, today, time.
yesterday…month. [2.10] a) Tell time at the hour and half-hour.
b) Solve problems involving applications of
Tell time to nearest hour…clocks. [2.11] time (clock and calendar). [2.02]

NCSCOS Mathematics
Comparison of 1998 document and 2003 revision

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GRADE 1 (continued) Moved to Kindergarten [3.01]
3. Geometry
Recognize, identify…circle…triangle, Eliminated
rectangle. [2.01] Moved to Kindergarten [3.03]
Identify open and closed figures. [2.04]
Use directional and positional words. Added:
[2.05] Identify, build, and name cylinders, cones
Not mentioned: and rectangular prisms. [3.02]
Rectangular prisms
Describe events as certain, impossible, more
4. Data Analysis and Probability likely, less likely to occur. [4.02]
Make predictions based on experiences. Added:
[4.03] Collect, organize, describe and display data
Not mentioned: using line plots and tallies. [4.01]
Line plots and tallies
Added:
5. Algebra Use Venn diagrams to illustrate similarities
Not mentioned: and differences in two sets. [5.02]
Venn diagrams

NCSCOS Mathematics
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Page 3

GRADE 2 2003 revision
1998 revision
1. Number and Operations Whole numbers through 999
Identify and use 10 more and 10 less.
[1.02] Eliminated
Read word names for numbers to 100.
[1.04] Develop number sense for whole numbers
through 999
Group objects into…[1.07] b) Read and write numbers. [1.01]

Model 2-digit…subtraction…[1.15] Develop number sense for whole numbers
through 999
Not mentioned: f) Use a variety of models to build
Fractions understanding of place value (ones, tens,
hundreds). [1.01]

Develop fluency with multi-digit addition
and subtraction through 999 using multiple
strategies. [1.04]

Added:

Use area or region models and set models of
fractions to explore part-whole relationships
in contexts.
a) Represent fractions (halves, thirds,
fourths) concretely and symbolically.
b) Compare fractions (halves, thirds,
fourths) using models.
c) Make different representations of the
same fraction.
d) Combine fractions to describe parts of a
whole.[1.02]

2. Measurement Moved to Grade 3 [2.02]
Measure capacity…[2.07]
Weigh objects…[2.08] Moved to Grade 1 [2.02 b]
Sequence months; use the calendar… [2.10] Moved to Grade 1 [2.02]
Tell time to the nearest half-hour…[2.11] Eliminated
Money
[2.12, 2.13, 2.14, 2.15] Added:
Not mentioned: Tell time at the five-minute intervals. [2.02]
Time at the five-minute intervals

NCSCOS Mathematics
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GRADE 2 (continued) Moved to Kindergarten [3.01],
3. Geometry Grade 1 [3.01]
Describe and make plane figures…[2.01]
Moved to Kindergarten [3.01],
Describe and make solid figures…cones Grade 1 [3.02]
[2.02]
…and pyramids. [2.02] Eliminated
Use spatial visualization…[2.05] Combine simple figures to create a given
shape. [3.01]
4. Data Analysis and Probability Describe the change in attributes as two-
Collect, sort, organize…[4.01] and three-dimensional figures are cut and
rearranged. [3.02]
Locate points…[4.04]
Collect, organize, describe and display data
5. Algebra using Venn diagrams (three sets) and
Sort by one or more attributes…[3.01] pictographs where symbols represent
Solve simple logic problems. [3.06] multiple units (2’s, 5’s, 10’s). [4.01]
Not mentioned: Moved to Grade 3 [3.02 a]
Number sentences; symbols to represent
unknown quantities Moved to Grade 1 [5.01]
Eliminated
Added:
Write addition and subtraction number
sentences to represent a problem; use
symbols to represent unknown quantities.
[5.02]

NCSCOS Mathematics
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Page 5

GRADE 3 2003 revision
1998 revision
1. Number and Operations Whole numbers through 9,999
Read and write word names for numbers to
1,000 [1.01] Develop number sense for whole numbers
Identify odd and even… [1.05] through 9,999.
Fractions [1.06, 1.07, 1.08] a) Connect model, number word, and
number using a variety of representations.
Subtract 2- and 3-digit numbers. [1.09] [1.01]
Multiplication and division [1.10, 1.12,
1.13] Moved to Grade 2 [1.06]

Model and use…properties…[1.11] Use area or region models and set models of
fractions to explore part-whole
relationships.
a) Represent fractions concretely and
symbolically (halves, fourths, thirds,
sixths, eighths).
b) Compare and order fractions (halves,
fourths, thirds, sixths, eighths) using
models and benchmark numbers (zero, one-
half, one); describe comparisons.
c) Model and describe common equivalents,
especially relationships among halves,
fourths, and eighths, and thirds and sixths.
d) Understand that the fractional
relationships that occur between zero and
one also occur between every two
consecutive whole numbers.
e) Understand and use mixed numbers and
their equivalent fraction forms. [1.05]

Moved to Grade 2 [1.04]

Develop fluency with multiplication from
1 x 1 to 12 x 12 and division up to two-digit
by one-digit numbers using:
a) Strategies for multiplying and dividing
numbers.
b) Estimation of products and quotients in
appropriate situations.
c) Relationships between operations. [1.03]

Use basic properties (identity, commutative,
associative, order of operations) for
addition, subtraction, multiplication, and
division. [1.04]

NCSCOS Mathematics
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Page 6

GRADE 3 (continued) Moved to Grade 2 [2.01 a]
2. Measurement Moved to Grade 4 [2.01]
Estimate and measure length. [2.06]
Model the concepts of area and Eliminated
perimeter…[2.08]
Money [2.09, 2.10] Added:
Time to the nearest minute [2.11] Estimate and measure…miles, kilometers,
Not mentioned: kilograms…[2.02]
Miles, kilometers, kilograms

3. Geometry Moved to Grade 2 [3.03].
Identify and model symmetry and
congruence…[2.02] Moved to Grade 1 [3.02]
Construct with cubes a solid…[2.03] Moved to Grade 7 [3.01 a]
Recognize a three-dimensional object from
different perspectives. [2.04] Added:
Not mentioned: Use a rectangular system to solve problems.
b) Describe the path between given points
Coordinate system problems on the plane. [3.02]

4. Data Analysis and Probability Moved to Grade 1 [4.01]
…line plots…[4.02] Moved to Grade 4 [4.01]
…bar graphs…[4.02] Moved to Grade 4 [4.02]
…mode…[4.02] Moved to Grade 2 [4.01]
Construct graphs…multiple units. [4.03] Eliminated
Time lines [4.06] Moved to Grade 1 [4.02]
Describe the probability…[4.07] Added:
Not mentioned: Solve probability problems using
Probability problems permutations and combinations. [4.03]

5. Algebra Moved to Grade 1 [5.01, 5.02]
Organize object or ideas…rules for sorting.
[3.01] Moved to Grade 2 [5.01]
…translate…patterns. [3.04] Moved to Grade 1 [5.02]
Use Venn diagrams…[3.06] Added:
Not mentioned: Use symbols to represent unknown
Use of symbols quantities in number sentences. [5.03]
Find the value of the unknown in a number
Find the value of an unknown sentence. [5.04]

NCSCOS Mathematics
Comparison of 1998 document and 2003 revision

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July 31, 2003
Page 7

GRADE 4 2003 revision
1998 revision
1. Number and Operations Rational numbers 0.01 through
99,999
Read and write numbers less than one
million…[1.01] Develop number sense for rational numbers
Multiplication and division [1.11, 1.12] 0..01 through 99,999. [1.01]
Not mentioned:
Problems with unlike denominators Moved to Grade 3 [1.03]

Added:

Solve problems using models, diagrams,
and reasoning about fractions and
relationships among fractions involving
halves, fourths, eights, thirds, sixths,
twelfths, fifths, tenths, hundredths, and
mixed numbers. [1.03]

2. Measurement Moved to Grade 5 [2.02]
Identify…angles [2.01]
Estimate and measure…[2.07] Moved to Grade 2 [2.01] and
Grade 3 [2.02]
Tons and milliliters [2.07]
Not mentioned: Eliminated
Problems involving perimeter and area
Added:

Solve problems involving perimeter of plane
figures and areas of rectangles. [2.02]

3. Geometry Moved to Grade 3 [3.01]

…appropriate vocabulary… plane figures…
[2.02]
…appropriate vocabulary… solid figures…
[2.03]

4. Data Analysis and Probability

Stem-and-leaf plots [4.01] Moved to Grade 5 [4.01]

Not mentioned: Added:

Line graphs and bar graphs Collect, organize, analyze and display data
(including line graphs and bar graphs) to
solve problems. [4.01]

Sets of related data Solve problems by comparing two sets of
related data. [4.03]

5. Algebra

…determine solutions to open sentences. Moved to Grade 3 [5.04]
[3.04]

Not mentioned: Added:

Proportionality Identify, describe, and generalize
relationships in which:
Quantities change proportionally
Change in one quantity relates to change in a

NCSCOS Mathematics
Comparison of 1998 document and 2003 revision

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July 31, 2003
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second quantity. [5.01]

NCSCOS Mathematics
Comparison of 1998 document and 2003 revision

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July 31, 2003
Page 9

GRADE 5 2003 revision
1998 revision
1. Number and Operations Rational numbers 0.001 through
Use place value…[1.01] 999,999

Rules for divisibility…[3.02] Develop number sense for rational numbers
Estimate products…[1.02] 0.001 through 999,999
Relate exponential notation…[1.03] a) Connect model, number word, and
Estimate and solve division…[1.04] number using a variety of representations.
Use the order of operations…[1.05] b) Build understanding of place value
Multiples, factors, primes…[1.06, 1.07, (thousandths through hundred thousands).
1.08] c) Compare and order rational numbers.
Add and subtract fractions and d) Make estimates of rational numbers in
decimals…[1.12, 1.14, 1.15] appropriate situations. [1.01]

Multiply fractions, whole numbers, Moved to Grade 3 [1.03 a]
decimals…[1.13, 1.16]
Moved to Grade 4 [1.02 a, d]

Moved to Grade 6 [1.05]

Moved to Grade 4 [1.02 b, d]

Moved to Grade 4 [5.03 b]

Moved to Grade 6 [1.05]

Develop fluency in adding and subtracting
non-negative rational numbers (halves,
fourths, eighths; thirds, sixths, twelfths;
fifths, tenths, hundredths, thousandths;
mixed numbers).
a) Develop and analyze strategies for adding
and subtracting numbers.
b) Estimate sums and differences.
c) Judge the reasonableness of solutions.
[1.02 ]

Moved to Grade 6 [1.04]

2. Measurement Moved to Grade 4 [2.01, 2.02]
Calculate area and perimeter…[2.01, 2.02]
Model proportions…[2.07] Moved to Grade 7 [2.01]
Not mentioned:
Comparison (by estimation) of measures in Added:
two different systems.
Estimate the measure of an object in one
system given the measure of that object in
another system. [2.01]

NCSCOS Mathematics
Comparison of 1998 document and 2003 revision

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July 31, 2003
Page 10

GRADE 5 (continued) Moved to Grade 1 [3.02]
3. Geometry Eliminated
…model polyhedra…[2.03]
…pyramids. [2.03] Moved to Grade 6 [3.02]
Circles [2.04]
Investigate similar figures…[2.08] Moved to Grade 7 [3.02]
Not mentioned:
Classification of plane figures according to Added:
symmetry
Classify plane figures according to types of
symmetry (line, rotational). [3.03]

4. Data Analysis and Probability Moved to Grade 4 [4.01]
…line graphs. [4.01] Moved to Grade 7 [4.02]
…mean [4.05, 4.06] Moved to Grade 4 [4.04]
…permutations and combinations. [4.07] Moved to Grade 6 [4.04]
Compare experimental and theoretical
probabilities…[4.08] Added:
Not mentioned: Collect, organize, analyze, and display data
Stem-and-leaf plots (including stem-and-leaf plots) to solve
problems. [4.01]

5. Algebra Added:
Not mentioned:
Use of equations to solve problems Use algebraic expressions, patterns, and
one-step equations and inequalities to solve
Rates of change problems. [5.02]

Identify, describe, and analyze situations
with constant or varying rates of change.
[5.03]

NCSCOS Mathematics
Comparison of 1998 document and 2003 revision

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July 31, 2003
Page 11

GRADE 6 2003 revision
1998 revision All rational numbers
1. Number and Operations Moved to Grade 7 [1.01]
…concepts of ratio, proportion, and
percent...[1.09] Moved to Grade 4 [5.02], Grade 5 [5.02]
Translate word problems…[1.13] Added:
Not mentioned:
Use exponential, scientific, and calculator
Exponential and scientific notation notation to write very large and very small
numbers. [1.06]

2. Measurement Moved to Grade 7 [2.02]
…concept of volume…[2.10] Moved to Grade 3 [2.01 b]
Convert measures of length…[2.11]

3. Geometry Eliminated
Constructions [2.01] Eliminated
Define and identify…including skew lines.
[2.02] Eliminated
Define and identify…vertical angles. [2.03] Moved to Grade 7 [3.02]
Identify and distinguish among…[2.04] Transform figures in the coordinate plane
Locate, give the coordinates…[2.05] and describe the transformation. [3.03]
Added:
Not mentioned: Identify and describe the intersection of
Intersection of figures in a plane figures in a plane. [3.01]
Solve problems involving geometric figures
Problem solving in the coordinate plane in the coordinate plane. [3.04]

NCSCOS Mathematics
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Page 12

GRADE 6 (continued) Moved to Grade 5 [4.01, 4.02]
4. Data Analysis and Probability
Create and evaluate graphic…[4.01] Eliminated
Spreadsheets [4.02]
Use measures of central tendency…[4.04] Moved to Grade 4 [4.03], Grade 5 [4.03]
Construct convincing arguments…[4.05] Mean taught in Grade 7 [4.02]
Not mentioned:
Fluency with counting strategies Moved to Grade 5 [4.01]

Use of sample space Added:
Simple and compound events
Experimental and theoretical probabilities Develop fluency with counting strategies to
determine the sample space for an event.
Independent and dependent events Include lists, tree diagrams, frequency
distribution tables, permutations,
combinations, and the Fundamental
Counting Principle. [4.01]

Use a sample space to determine the
probability of an event. [4.02]

Conduct experiments involving simple and
compound events. [4.03]

Determine and compare experimental and
theoretical probabilities for simple and
compound events. [4.04]

Determine and compare experimental and
theoretical probabilities for independent and
dependent events. [4.05]

5. Algebra Moved to Grade 5 [5.01]
Describe, extend and write rules…[3.01]
Generate a set of ordered pairs…[3.02] Moved to Grade 5 [5.01]
Use variables to describe…[3.04]
Use graphs and tables to represent…[3.05] Moved to Grade 4 [5.02], Grade 5 [5.02]
Not mentioned:
Simplify algebraic expressions. Moved to Grade 7 [5.01] and
Grade 8 [5.01 a, b, d]
Use algebraic expressions.
Solve equations or inequalities. Added:
Rates of change and ratios
Simplify algebraic expressions and verify
the results using the basic properties of
rational numbers.
a) Identity.
b) Commutative.
c) Associative.
d) Distributive.
e) Order of operations. [5.01]

Use and evaluate algebraic expressions.
[5.02]

Solve simple (one- and two-step) equations
or inequalities. [5.03]

Use graphs, tables, and symbols to model
and solve problems involving rates of
change and ratios. [5.04]

NCSCOS Mathematics
Comparison of 1998 document and 2003 revision

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July 31, 2003
Page 13

GRADE 7 2003 revision
1998 revision All rational numbers
1. Number and Operations Moved to Grade 6 [1.06]
…scientific notation [1.01] Moved to Grade 6 [1.01 b]
Compare and order…[1.02] Moved to Grade 8 [1.01, 5.04]
…square root…[1.07]

2. Measurement Moved to Grade 6 [2.02], Grade 8 [2.01]
Recognize the effect…[2.10]
Not mentioned: Added:
Scale drawings
Draw objects to scale and use scale
drawings to solve problems. [2.01]

3. Geometry Eliminated
Construct perpendicular…[2.01] Eliminated
Identify the congruent and
supplementary…[2.02] Moved to Grade 6 [3.03]
Locate and give the coordinates of…[2.03] Moved to Grade 8 [3.02]
…Pythagorean Theorem. [2.04] Added:
Not mentioned: Using three-dimensional figures:
Cross-sectional views c) Describe cross-sectional views. [3.01]
Identify, define, and describe similar and
Similar and congruent polygons congruent polygons with respect to angle
measures, length of sides and
Scaling and proportional reasoning proportionality of sides. [3.02]
Use scaling and proportional reasoning to
solve problems related to similar and
congruent polygons. [3.03]

NCSCOS Mathematics
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GRADE 7 (continued) Moved to Grade 5 [4.02]
4. Data Analysis and Probability Moved to Grade 8 [4.03]
Create, compare, contrast…[4.04] Moved to Grade 6 [4.01]
…misuses of…data [4.06] Moved to Grade 4 [4.04] and
Find all possible outcomes…[4.07]
Compute and apply…permutations…[4.08] Grade 6 [4.01, 4.02]
Moved to Grade 6 [4.05]
…independent events. [4.09] Moved to Grade 6 [4.04, 4.05]
…experimental results and theoretical
probability. [4.10] Added:
Not mentioned: Collect, organize and display data…box
Box plots plots…to solve problems. [4.01]
Calculate, use, and interpret the
Mean, frequency distribution and mean…frequency distribution, and
interquartile range interquartile range for a set of data. [4.02]
Describe how the mean…frequency
Outliers distribution and interquartile range of a set
of data affect its graph. [4.03]
Identify outliers and determine their effect
on the mean, median, mode and range of a
set of data. [4.04]

5. Algebra Moved to Grade 6 [5.02]
Evaluate algebraic expressions. [3.01]
Equations and inequalities [3.02] Moved to Grade 5 [5.02], Grade 6 [5.03]
Not mentioned:
Linear relations and functions Added:

Formulas Identify, analyze, and create linear relations,
sequences, and functions using symbols,
graphs, tables, diagrams, and written
descriptions. [5.01]

Develop fluency in the use of formulas to
solve problems. [5.04]

NCSCOS Mathematics
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Page 15

GRADE 8 2003 revision
1998 revision Real numbers
1. Number and Operations Eliminated
Identify subsets of the real number system.
[1.01] Moved to Grade 7 [1.02]
Estimate and compute…[1.02] Moved to Grade 6 [1.03]
Compare, order and convert…[1.03] Moved to Grade 7 [1.01]
…percent of increase…[1.04] Moved to Grade 6 [1.06]
Use scientific notation…[1.05] Moved to Grade 6 [1.05]
Use rules of exponents. [1.06] Moved to Grade 6 [1.05, 1.06, 1.07]
Solve problems involving exponents and
scientific notation. [1.08] Eliminated
…absolute value…[1.09] Moved to Grade 6 [5.01]
Identify…properties…[1.10] Moved to Grade 6 [5.01]
Simplify algebraic expressions. [1.11] Added:
Not mentioned: Develop number sense for the real numbers.
Irrational numbers a) Define and use irrational numbers.
b) Compare and order.
c) Use estimates of irrational numbers in
appropriate situations. [1.01]

2. Measurement Moved to Grade 7 [2.01]

Calculate distances…[2.02] Moved to Grade 7 [2.02]

…surface area…[2.03] Moved to Grade 7 [2.02]
Eliminated
Use models…volume…[2.04]
…pyramid…[2.04] Moved to Grade 7 [2.02]
Eliminated
Find the volume…[2.05]
…pyramid…[2.05] Moved to Grade 6 [2.01]

Select appropriate units and tools…[2.12]

3. Geometry Moved to Grade 7 [3.03]
Solve problems related to similar…[2.08] Moved to Grade 6 [3.03]
Locate…rotations…[2.09] Moved to Grade 7 [3.01 a]
Identify and draw 3-d figures…[2.10] Moved to Grade 7 [3.01 b]
Build 3-d figures…[2.11]

NCSCOS Mathematics
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July 31, 2003
Page 16

GRADE 8 (continued) Moved to Grade 7 [4.01]
4. Data Analysis and Probability
…box plots. [4.01] Moved to Grade 7 [4.02, 4.03, 4.04]
Interpret the mean, explain…[4.03]
…random vs. biased sampling. [4.04] Eliminated
…probability of independent…[4.05]
…theoretical probabilities…[4.06] Moved to Grade 6 [4.05]
Not mentioned:
Line of best fit Moved to Grade 6 [4.04]

Misuses of data Added:

Approximate a line of best fit for a given
scatterplot; explain the meaning of the line
as it relates to the problem and make
predictions. [4.02]

Identify misuses of statistical and numerical
data. [4.03]

5. Algebra Moved to Grade 7 [5.04]
Use formulas…[3.01]
Solve one- and two-step…[3.02] Moved to Grade 6 [5.03]
…geometric and numerical patterns…[3.05]
Not mentioned: Moved to Grade 5 [5.01, 5.02, 5.03]
Function
Added:
Write an equation of a line.
Develop an understanding of function.
Solve problems using linear equations and a) Translate among verbal, tabular, graphic,
inequalities. and algebraic representations of functions.
Solve equations. b) Identify relations and functions as linear
or nonlinear.
c) Find, identify, and interpret the slope
(rate of change) and intercepts of a linear
relation.
d) Interpret and compare properties of linear
functions from tables, graphs, or equations.
[5.01]

Write an equation of a linear relationship
given: two points, the slope and one point
on the line, or the slope and y-intercept.
[5.02]

Solve problems using linear equations and
inequalities; justify symbolically and
graphically. [5.03]

Solve equations using the inverse
relationships of addition and subtraction,
multiplication and division, squares and
square roots, and cubes and cube roots.
[5.04]

NCSCOS Mathematics
Comparison of 1998 document and 2003 revision

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July 31, 2003
Page 17