South Carolina
4th GRADE MATH
2011-2012 Pacing Guide
Unit
Unit 1:
Numeration,
Place Value,
Multiplication,
and Division
Days
Standard/
Indicator*
~ 40
Days
4-1 (All)
4-2.1
4-2.2
4-2.3
4-2.4
4-2.5
Day 41
Unit 2: Fractions
and Decimals
Unit 3: Data
Analysis and
Probability
Common
Core
NBT 4
NBT 5
NBT 6
OA 1
OA 2
OA 3
OA 4
Major Topics/Concepts
Numbers can be used for different
purposes and numbers can be classified
and represented in different ways.
Division is repeated subtraction.
Multiplication is repeated addition.
1st Benchmark (cumulative to Day 41)
The fundamentally important concept of
equal partitioning (dividing a quantity
into equal-sized parts) can be done with
either countable collections (discrete
quantities) or quantities that must be
measured (continuous quantities).
~ 20
Days
~ 20
Days
4-1 (All)
4-2.6
4-2.7
4-2.8
4-2.9
4-2.10
4-2.11
4-2.12
NBT 1
NBT 2
NF 1
NF 2
NF 5
NF 6
NF 7
The parts into which the whole is
partitioned/divided must be equivalent
in area or number.
Equivalent relationships exist among
mixed numbers, decimals, and
fractions.
Each place value is ten times as great
as the place to its immediate right, and
one-tenth as great as the place to its
immediate left.
Each fraction and decimal can be
associated with a unique point on the
number line.
Some questions can be answered by
collecting and analyzing data, and the
question to be answered determines the
data that needs to be collected and how
best to collect it.
4-1 (All)
4-3.6
4-6.1
4-6.2
4-6.3
4-6.4
4-6.5
4-6.6
4-6.7
Data can be represented visually using
tables, charts, and graphs. The type of
data determines the best choice of
visual representation.
Chance has no memory. For repeated
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Unit
Days
Standard/
Indicator*
Common
Core
Major Topics/Concepts
trials of a simple experiment (i.e.,
tossing a coin), the outcomes of the
prior trials have no impact on the next.
The occurrence of a future event can be
characterized along a continuum from
impossible to certain.
The probability of an event is a number
between 0 and 1 that is a measure of
the chance that a given event will
occur.
2nd Benchmark (cumulative to Day 84)
The process of measurement is similar
for all attributes. The measurement
system and the tools used vary
according to the attribute being
measured.
Day 84
Unit 4:
Measurement
~ 20
Days
Measurements are accurate to the
extent that the appropriate unit/tool is
used properly. The measurement unit
must have the same attribute as the
attribute to be measured.
4-1 (All)
4-5.1
4-5.3
4-5.4
4-5.5
4-5.6
4-5.7
4-5.8
4-5.9
MD 2
MD 3
Unit iteration entails using a unit to
subdivide a space and count the
subdivisions.
The smaller the unit used, the more
units are needed to measure a given
attribute (Compensatory Principle).
Two objects can be compared in terms
of a measurable quantity using a third
object (Transitivity).
Unit 5: Patterns
and Algebra
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Days
The measure of an attribute is a count
of how many units are needed to fill,
cover or match the attribute of the
object being measured.
Patterns of numbers or objects can
describe relationships.
4-1 (All)
4-3.1
4-3.2
4-3.3
4-3.4
4-3.5
OA 5
Generalizations can be made when
numbers repeat in predictable ways.
Patterns follow a sequence and can be
repeated.
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Unit
Days
Day 130
Unit 6: Geometry
Days 150-160
Days 161-165
Days 166-180
~ 20
Days
Standard/
Common
Major Topics/Concepts
Indicator*
Core
3rd Benchmark (cumulative to Day 130)
Point, line, and plane are the core
attributes of space objects.
Line segments and rays are sets of
points that describe parts of lines,
shapes, and solids.
4-1 (All)
4-4.1
4-4.2
4-4.3
4-4.4
4-4.5
4-4.6
4-4.7
4-4.8
4-5.2
G1
G2
MD 5
MD 6
Geometric transformations are
movements of plane figures that affect
their orientation or position in the
geometric plane but not their size and
shape.
Objects in space can be transformed in
an infinite number of ways, and those
transformations can be described and
analyzed mathematically.
Remediation/Optional Comprehensive
Benchmark/Enrichment/Common Core Standards**
PASS Testing Dates
Remediation/Enrichment/Common Core Standards**
* Standard 4-1 should be incorporated in all units of study.
** 4th Grade Common Core standards not specifically addressed in the current South Carolina standards
could be introduced at this time: NBT 3 G 3 NF 3
NF 4
MD 1 MD 4 MD 7
*4-1: The student will understand and utilize the mathematical processes of problem
solving, reasoning and proof, communication, connections, and representation.
4-1.1 Analyze information to solve increasingly more sophisticated problems.
4-1.2 Construct arguments that lead to conclusions about general mathematical properties and
relationships.
4-1.3 Explain and justify answers to problems on the basis of mathematical properties, structures,
and relationships on mathematical properties, structures, and relationships.
4-1.4 Generate descriptions and mathematical statements about relationships between and among
classes of objects.
4-1.5 Use correct, complete, and clearly written and oral mathematical language to pose questions,
communicate ideas, and extend problem situations.
4-1.6 Generalize connections between new mathematical ideas and related concepts and subjects
that have been previously considered.
4-1.7 Use flexibility in mathematical representations
4-1.8 Recognize the limitations of various forms of mathematical representations
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Unit 1: Numeration/Place Value/Multiplication and Division
(Teachers are encouraged to pretest each unit to examine students’ needs.)
Major Concepts:
 Numbers can be used for different purposes and numbers can be classified and represented in
different ways.
 Division is repeated subtraction.
 Multiplication is repeated addition.
Pacing Guide: ~ 40 instructional days
Standard(s):
4-2 The student will demonstrate through the mathematical processes an
understanding of decimal notation as an extension of the place-value system; the
relationship between fractions and decimals; the multiplication of whole numbers;
and accurate, efficient, and generalizable methods of dividing whole numbers,
adding decimals, and subtracting decimals.
4-2.1
Recognize the period in the place-value structure of whole numbers: units, thousands,
millions, and billions. (A1)
4-2.2 Apply divisibility rules for 2, 5, and 10. (B3)
4-2.3 Apply an algorithm to multiply whole numbers fluently. (C3)
4-2.4 Explain the effect on the product when one of the factors is changed. (B2)
4-2.5 Generate strategies to divide whole numbers by single-digit divisors. (B3)
Desired Outcomes
Students should be able to:
 Recognize the consistency of place value relationships.
 Understand that multiplication and division are inverse operations.
 Understand that a number relationship can be represented with symbols, numbers, words, or
pictures.
 Understand that a number relationship represented by symbols, numbers, words or pictures
can be proved by substitution and/or reasoning.
Key Vocabulary
algebraic expression
dividend
fact family
period
array
divisor
inverse
product
billions
equal shares
millions
quotient
compose
even
multiple
remainder
decompose
factor
odd
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Unit 2: Fractions and Decimals
(Teachers are encouraged to pretest each unit to examine students’ needs.)
Major Concepts:
 The fundamentally important concept of equal partitioning (dividing a quantity into equal-sized
parts) can be done with either countable collections (discrete quantities) or quantities that must
be measured (continuous quantities).
 The parts into which the whole is partitioned/divided must be equivalent in area or number.
 Equivalent relationships exist among mixed numbers, decimals, and fractions.
 Each place value is ten times as great as the place to its immediate right, and one-tenth as
great as the place to its immediate left.
 Each fraction and decimal can be associated with a unique point on the number line.
Pacing Guide: ~ 20 instructional days
Standard(s)
4-2 The student will demonstrate through the mathematical processes an
understanding of decimal notation as an extension of the place-value system;
the relationship between fractions and decimals; the multiplication of whole
numbers; and accurate, efficient, and generalizable methods of dividing whole
numbers, adding decimals, and subtracting decimals.
4-2.6
4-2.7
4-2.8
4-2.9
4-2.10
Analyze the magnitude of digits through hundredths on the basis of their place value. (B4)
Compare decimals through hundredths by using the terms is less than, is greater than, and is
equal to and the symbols <, >, and =. (C2)
Apply strategies and procedures to find equivalent forms of fractions. (B3)
1
, and 1). (B2)
2
1
1
3
1
2
Identify the common fraction/decimal equivalents = .5,
= .25,
= .75, ≈ .33, ≈
2
4
4
3
3
1
1
.67, multiples of , and multiples of
. (A1)
10
100
Compare the relative size of fractions to benchmarks (0,
4-2.11
4-2.12
Represent improper fractions, mixed numbers, and decimals. (B2)
Generate strategies to add and subtract decimals through hundredths. (B3)
Desired Outcomes
Students should be able to:
 Recognize the consistency of place value relationships to the left and right of the decimal point.
 Use benchmark numbers such as 0, ¼, (0.25), ½, (0.5), ¾, (0.75), and 1 to judge the relative
size of numbers.
 Use a common whole when modeling fractions for comparison.
 Recognize and represent fractions and decimals in a variety of ways.
 Compare and order fractions and decimals using models and benchmark numbers.
 Use their understanding of equivalency in the relationship between and among rational
numbers.
 Distinguish between factors and multiples.
Key Vocabulary
benchmark fraction
equivalent fraction
mixed number
set model
common denominator
factors
multiples
rational numbers
decimal
fraction
numerator
tenths place
decimal equivalent
hundredths place
proper/ improper
variable
decimal point
inequality
regional or area model
whole number
denominator
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Unit 3: Data Analysis and Probability
(Teachers are encouraged to pretest each unit to examine students’ needs.)
Major Concepts:
 Some questions can be answered by collecting and analyzing data, and the question to be
answered determines the data that needs to be collected and how best to collect it.
 Data can be represented visually using tables, charts, and graphs. The type of data determines
the best choice of visual representation.
 Chance has no memory. For repeated trials of a simple experiment (i.e., tossing a coin), the
outcomes of the prior trials have no impact on the next.
 The occurrence of a future event can be characterized along a continuum from impossible to
certain.
 The probability of an event is a number between 0 and 1 that is a measure of the chance that a
given event will occur.
Pacing Guide: ~ 20 instructional days
Standard(s):
4-6 The student will demonstrate through the mathematical processes an
understanding of the impact of data-collection methods, the appropriate graph
for categorical or numerical data, and the analysis of possible outcomes for a
simple event.
4-6.1
4-6.2
4-6.3
4-6.4
4-6.5
4-6.6
4-6.7
Compare how data-collection methods impact survey results. (B2)
Interpret data in tables, line graphs, bar graphs, and double bar graphs whose scale
increments are greater than or equal to 1. (B2)
Organize data in tables, line graphs, and bar graphs whose scale increments are greater than
or equal to 1. (C4)
Distinguish between categorical and numerical data. (B4)
Match categorical and numerical data to appropriate graphs. (B2)
Predict on the basis of data whether events are likely, unlikely, certain, impossible, or equally
likely to occur. (B2)
Analyze possible outcomes of a simple event. (B4)
4-3.6
Illustrate situations that show change over time as increasing, decreasing, or varying. (B2)
Desired Outcomes
Students should be able to:
 Understand that line graphs are best used to show change over time and bar graphs are best
used to make comparisons.
 Understand the difference between numerical and categorical data.
 Choose the most appropriate graph to display a set of data.
 Use counting strategies in contexts involving simple events (e.g., tosses of coins or number
cubes; drawing objects from bag; spinners) to determine all possible outcomes and
probabilities of an event.
 Use rational numbers to represent and describe the probability of outcomes of an event.
Key Vocabulary
bar graph
equally likely
line graph
table
categorical data
frequency tables
numerical data
tally
certain
impossible
outcomes
trend
chart
increasing
prediction
unlikely
decreasing
interval
scale
varying
double bar graph
likely
survey
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Unit 4: Measurement
(Teachers are encouraged to pretest each unit to examine students’ needs.)
Major Concepts:
 The process of measurement is similar for all attributes. The measurement system and the tools
used vary according to the attribute being measured.
 Measurements are accurate to the extent that the appropriate unit/tool is used properly. The
measurement unit must have the same attribute as the attribute to be measured.
 Unit iteration entails using a unit to subdivide a space and count the subdivisions.
 The smaller the unit used, the more units are needed to measure a given attribute
(Compensatory Principle).
 Two objects can be compared in terms of a measurable quantity using a third object
(Transitivity).
 The measure of an attribute is a count of how many units are needed to fill, cover or match the
attribute of the object being measured.
Pacing Guide: ~ 20 instructional days
Standard(s):
4-5 The student will demonstrate through the mathematical processes an
understanding of elapsed time; conversions within the U.S. Customary System; and
accurate, efficient, and generalizable methods of determining area.
4-5.1
Use appropriate tools to measure objects to the nearest unit: measuring length in quarter
inches, centimeters, and millimeters; measuring liquid volume in cups, quarts, and liters;
and measuring weight and mass in pounds, milligrams, and kilograms. (C3)
4-5.3 Use equivalencies to convert units of measure within the U.S. Customary System:
converting length in inches, feet, yards, and miles; converting weight in ounces, pounds,
and tons; converting liquid volume in cups, pints, quarts, and gallons; and converting time
in years, months, weeks, days, hours, minutes, and seconds. (C3)
4-5.4 Analyze the perimeter of a polygon. (B4)
4-5.5 Generate strategies to determine the area of rectangles and triangles. (B3)
4-5.6 Apply strategies and procedures to determine the amount of elapsed time in hours and
minutes within a 12-hour period, either a.m. or p.m. (C3)
4-5.7 Use Celsius and Fahrenheit thermometers to determine temperature changes during time
intervals. (C3)
4-5.8 Recall equivalencies associated with liquid volume, time, weight, and length: 8 liquid
ounces = 1 cup, 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon; 365 days = 1
year, 52 weeks = 1 year; ounces = 1 pound, 2,000 pounds = 1 ton; 5,280 feet = 1 mile.
(A1)
4-5.9 Exemplify situations in which highly accurate measurements are required. (B2)
Desired Outcomes
Students should be able to:
 Use a variety of strategies to find area and perimeter.
 Distinguish between the application of square units of measure and linear units of measure.
 Understand that two figures with the same area may have different perimeters and that two
figures with the same perimeter may have different areas.
 Solve multi-step problems using time to the nearest minute.
 Solve problems and follow procedures using equivalent units within the same measurement
system time: seconds/minutes/hours/days/weeks/months/years
 Use appropriate tools to make measurements.
 Estimate and measure with appropriate units.
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Key Vocabulary
area
a.m.
analog
appropriate units
base
capacity
Celsius
centimeter
cup
customary
decreasing
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digital
dimensions
elapsed time
Fahrenheit
fluid ounce
gram
height
hour
inch
kilogram
kilometer
length
liter
mass
meter
metric
minute
mile
milligram
millimeter
p.m.
8
perimeter
pint
pound
quart
quarter inch
second
weight
yard
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Unit 5: Patterns and Algebra
(Teachers are encouraged to pretest each unit to examine students’ needs.)
Major Concepts:
 Patterns of numbers or objects can describe relationships.
 Generalizations can be made when numbers repeat in predictable ways.
 Patterns follow a sequence and can be repeated.
Pacing Guide: ~ 20 instructional days
Standard(s):
4-3 The student will demonstrate through the mathematical processes an
understanding of numeric and nonnumeric patterns, the representation of simple
mathematical relationships, and the application of procedures to find the value of
an unknown.
4-3.1
Analyze numeric, nonnumeric, and repeating patterns involving all operations and decimal
patterns through hundredths. (B4)
4-3.2 Generalize a rule for numeric, nonnumeric, and repeating patterns involving all operations.
(B2)
4-3.3 Use a rule to complete a sequence or a table. (C3)
4-3.4 Translate among letters, symbols, and words to represent quantities in simple mathematical
expressions or equations. (B2)
4-3.5 Apply procedures to find the value of an unknown letter or symbol in a whole-number
equation. (C3)
Desired Outcomes
Students should be able to:
 Solve multi-step problems.
 Recognize repeating and growing patterns.
 Extend a given pattern.
 Find missing terms in a pattern.
Key Vocabulary
decimal
hundredths
numeric pattern
sequence
equation
non-numeric patterns rule
tenths
expression
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Unit 6: Geometry
(Teachers are encouraged to pretest each unit to examine students’ needs.)
Major Concepts:
 Point, line, and plane are the core attributes of space objects.
 Line segments and rays are sets of points that describe parts of lines, shapes, and solids.
 Geometric transformations are movements of plane figures that affect their orientation or
position in the geometric plane but not their size and shape.
 Objects in space can be transformed in an infinite number of ways, and those transformations
can be described and analyzed mathematically.
Pacing Guide: ~ 20 instructional days
Standard(s):
4-4 The student will demonstrate through the mathematical processes an
understanding of the relationship between two- and three-dimensional shapes, the
use of transformations to determine congruency, and the representation of location
and movement within the first quadrant of a coordinate system.
4-4.1
4-4.2
4-4.3
4-4.4
4-4.5
4-4.6
4-4.7
Analyze the quadrilaterals squares, rectangles, trapezoids, rhombuses, and parallelograms
according to their properties. (A4)
Analyze the relationship between three-dimensional geometric shapes in the form of
cubes, rectangular prisms, and cylinders and their two-dimensional nets. (B4)
Predict the results of multiple transformations of the same type – translation, reflection, or
rotation – on a two-dimensional geometric shape. (B2)
Represent the two-dimensional shapes trapezoids, rhombuses, and parallelograms and the
three-dimensional shapes cubes, rectangular prisms, and cylinders. (B2)
Use transformation(s) to prove congruency. (B3)
Represent points, lines, line segments, rays, angles, and polygons. (B2)
Represent with ordered pairs of whole numbers the location of points in the first quadrant
of a coordinate grid. (B2)
4-5.2
Compare angle measures with referent angles of 45 degrees, 90 degrees, and 180 degrees
to estimate angle measures. (B2)
Desired Outcomes
Students should be able to:
 Recognize that each point in the quadrant is uniquely represented by an ordered pair.
 Understand that translations, reflections, and rotations produce a second figure (image)
congruent to the original figure (pre-image).
 Use a variety of strategies to find perimeter.
Key Vocabulary
acute angle
diagonal
line
point
slide (translation)
adjacent
endpoints
line segment
quadrilateral
square
angles
flat
net
ray
square corner/right angle
attributes
flip (reflection) obtuse angle
rectangle
trapezoid
circle
horizontal line
ordered pair
rectangular prism
turn (rotation)
congruent
intersecting
parallel lines
rhombus
vertex
cube
irregular
parallelogram
right angle
vertical line
curved/straight
perpendicular
x axis
cylinder
y axis
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