Grade 4
School Year 2012-13
GRADE 4 MATHEMATICS CURRICULUM GUIDE
2012-2013
Loudoun County Public Schools
Page 1 of 26
Grade 4
School Year 2012-13
INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE
This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun
County Public Schools. The CURRICULUM GUIDE includes excerpts from documents published by the Virginia Department of Education. Other
statements, such as suggestions on the incorporation of technology and essential questions, represent the professional consensus of Loudoun’s
teachers concerning the implementation of these standards. In many instances the local expectations for achievement exceed state
requirements. The GUIDE is the lead document for planning, assessment and curriculum work. It is a summarized reference to the entire
program. Other documents, called RESOURCES, are updated more frequently. These are published separately but teachers can combine them
with the GUIDE for ease in lesson planning.
Mathematics Internet Safety Procedures
1. Teachers should review all Internet sites and links prior to using it in the classroom.
During this review, teachers need to ensure the appropriateness of the content on the site,
checking for broken links, and paying attention to any
inappropriate pop-ups or solicitation of information.
2. Teachers should circulate throughout the classroom while students are on the
internet checking to make sure the students are on the appropriate site and
are not minimizing other inappropriate sites.
3. Teachers should periodically check and update any web addresses that they have on their
LCPS web pages.
4. Teachers should assure that the use of websites correlate with the objectives of
lesson and provide students with the appropriate challenge.
Page 2 of 26
Grade 4
School Year 2012-13
Grade 4 Mathematics Nine Weeks Overview
1st Quarter
2nd Quarter
3rd Quarter
4th Quarter
48 days
42 days
43 days
47 days
Place value
4.1
Multiplication and division
of whole numbers
4.4
Fractions
4.5 a, b, d
4.2
Add and subtract
whole numbers
4.4 a, b, d
Probability
Decimals
4.3
4.5 c
Functions
4.15
Equality
4.16
Graphing
4.13
Measurement
4.6
4.7
4.8
Geometry
4.10
4.11
4.12
Elapsed time
4.9
4.14
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and
representations as they engage in mathematics activities throughout the year.
Page 3 of 26
Grade 4 Quarter 1
Topics, Essential Questions, and
Essential Understandings
(Students should be able to answer
essential questions.)
Number
of Days
Working with Whole Numbers
25 days
4.1 Essential Questions
 Demonstrate and explain the
relationship between each place in a
number.
 Demonstrate and explain how the place
value system can be used to name and
compare large numbers.
 Compare and contrast the
appropriateness of using estimation and
finding the exact value.
4.1 Essential Understandings
 Understand the relationships in the
place value system in which the value of
each place is ten times the value of the
place to its right.
 Use the patterns in the place value
system to read and write numbers.
 Understand that reading place value
correctly is essential when comparing
numbers.
 Understand that rounding gives a close
Page 4 of 26
REQUIRED
Critical Thinking
Lessons
INV: Mathematical
Thinking at Grade 4
Investigation 1: “How
Many Hundreds,”
Sessions 1-4
Investigation 3:
“Using Number
Patterns,”
Sessions 1-5
INV: Landmarks in
the Thousands
Investigation 1:
“Working with 100,”
Sessions 1-3
Investigation 2:
“Exploring Multiples
of 100,”
Sessions 1-5
Standards of Learning
Essential Knowledge and Skills
SOL 4.1 The student will
a) identify orally and in writing the place
value for each digit in a whole number
expressed through millions;
b) compare two whole numbers expressed
through millions using symbols (>, <, or =);
and
c) round whole numbers expressed through
millions to the nearest thousand, ten
thousand, and hundred thousand.
4.1 Essential Knowledge and Skills
 Identify and communicate, both orally
and in written form, the place value for
each digit in whole numbers expressed
through the one millions place.
 Read whole numbers through the one
millions place that are presented in
standard format, and select the
matching number in written format.
 Write whole numbers through the one
millions place in standard format when
the numbers are presented orally or in
Additional
Instructional
Resources
ESS: VDOE
Enhanced Scope
and Sequence
Lessons
Math vocabulary
word wall cards
Http://www.doe
.virginia.gov/inst
ruction/mathem
atics/resources/
vocab_cards/ind
ex.shtml
Grade 4 Quarter 1

number to use when exact numbers are
not needed for the situation at hand.
Develop strategies for rounding.
Investigation 3: “How
Much is 1000,”

Sessions 1-5
Investigation 4:
“Making a 10,000
Chart,” Sessions 1-3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.4 Essential Questions
 Demonstrate and explain finding a sum,
a difference.
 Demonstrate and explain inverse
operations.
4.4 Essential Understandings
 Develop and use strategies to estimate
whole number sums and differences
and to judge the reasonableness of such
results.
 Understand that addition and
subtraction are inverse operations.
 Understand how to solve single-step
and multistep problems using whole
number operations.
Page 5 of 26
written format.
Identify and use the symbols for greater
than, less than, and equal to.
 Compare two whole numbers expressed
through the one millions, using symbols
>, <, or =.
 Round whole numbers expressed
through the one millions place to the
nearest thousand, ten thousand, and
hundred-thousand place.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.4 The student will
a) estimate sums, differences, …;
b) add, subtract, and multiply whole
numbers;
d) solve single-step and multistep addition,
subtractions, …problems with whole
numbers.
4.4 Essential Knowledge and Skills
 Estimate whole number sums,
differences.
 Refine estimates by adjusting the final
amount, using terms such as closer to,
between, and a little more than.
 Determine the sum or difference of two
whole numbers, each 999,999 or less, in
vertical and horizontal form with or
without regrouping, using paper and
pencil, and using a calculator.
 Solve single-step and multistep problems
using whole number operations.
Grade 4 Quarter 1

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.15 Essential Questions
 Create and justify numerical patterns
using words, tables, graphs, and/or
symbols.
 Analyze and extend numerical patterns
using various methods.
4.15 Essential Understandings
Understand that patterns and functions can
be represented in many ways and described
using words, tables, graphs, and symbols.
~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.16 Essential Questions
 What is an equation?
 Demonstrate and explain the associative
property.
 How are the associative properties for
20 days
addition and multiplication alike?
 Demonstrate and explain the
commutative property.
 How are the commutative properties for
addition and multiplication alike?
Page 6 of 26
Verify the reasonableness of sums,
differences … of whole numbers using
estimation.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.15 The student will recognize, create,
and extend numerical and geometric
patterns.
4.15 Essential Knowledge and Skills
 Describe geometric and numerical
patterns, using tables, symbols, or
words.
 Create geometric and numerical
patterns, using concrete materials,
number lines, tables, and words.
 Extend geometric and numerical
patterns, using concrete materials,
number lines, tables, and words.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.16 The student will
a) recognize and demonstrate the meaning
of equality in an equation; and
b) investigate and describe the associative
property for addition and multiplication.
4.16 Essential Knowledge and Skills
 Recognize and demonstrate that the
equals sign (=) relates equivalent
quantities in an equation.
 Write an equation to represent
~~~~~~~~~~~~~~
Exploration of
a Balance
(Lesson 2)
Grade 4 Quarter 1

Compare and contrast the associative
properties for addition and
multiplication.
4.16 Essential Understandings
 Understand that mathematical
relationships can be expressed using
equations.
 Understand that quantities on both
sides of an equation must be equal.
 Understand that the associative
property for addition means you can
change the groupings of three or more
addends without changing the sum.
 Understand that the associative
property for multiplication means you
can change the groupings of three or
more factors without changing the
product.
3 days
Page 7 of 26
Enrichment, Assessment, and Remediation



equivalent mathematical relationships
(e.g., 4  3 = 2  6).
Recognize and demonstrate appropriate
use of the equals sign in an equation.
Investigate and describe the associative
property for addition as (6 + 2) + 3= 6 +
(2 + 3).
Investigate and describe the associative
property for multiplication as (3 x 2) x 4 =
3 x (2 x 4).
Grade 4 Quarter 2
Topics, Essential Questions, and
Essential Understandings
(Students should be able to answer
essential questions.)
Number
of Days
Working with Whole Numbers
4.4 Essential Questions

20 days







There are many methods for
determining a product. What are the
criteria considered when choosing a
strategy?
What are inverse relationships?
What does it mean to divide?
What does multiplication mean?
What effect does multiplication have on
a number?
What does the divisor represent in a real
life application? Dividend? Quotient?
How are each of these represented using
the three division models?
What is the similarity between
multiplication and addition?
What is the similarity between division
and subtraction?
REQUIRED
Critical Thinking
Lessons
INV: Packages and
Groups
Investigation 2:
Double Digit
Multiplication,
Sessions 1 – 3
Investigation 3:
Multiplication and
Division Choices,
Sessions 1 - 10
Standards of Learning
Essential Knowledge and Skills
SOL 4.4 The student will
a) estimate … products, and quotients of
whole numbers;
b) …multiply whole numbers;
c) divide whole numbers, finding quotients
with and without remainders; and
d) solve single-step and multistep …
multiplication problems with whole numbers.
4.4 Essential Knowledge and Skills





Page 8 of 26
Estimate whole number … products, and
quotients.
Refine estimates by adjusting the final
amount, using terms such as closer to,
between, and a little more than.
Estimate and find the products of two
whole numbers ….
Estimate and find the quotient of two
whole numbers….
Solve single-step and multipstep
problems using whole number
operations.
Additional
Instructional
Resources
ESS: VDOE
Enhanced Scope
and Sequence
Lessons
Grade 4 Quarter 2
4.4 Essential Understandings





Develop and use strategies to estimate
whole number sums and differences
and to judge the reasonableness of such
results.
Understand that addition and
subtraction are inverse operations.
Understand that division is the
operation of making equal groups or
equal shares. When the original amount
and the number of shares are known,
divide to find the size of each share.
When the original amount and the size
of each share are known, divide to find
the number of shares.
Understand that multiplication and
division are inverse operations.
Understand various representations of
division and the terms used in division
are dividend, divisor, and quotient.
dividend  divisor = quotient
quotient
divisor

dividend
Understand how to solve single-step
and multistep problems using whole
number operations.
Page 9 of 26

Verify the reasonableness of sums,
differences, products, and quotients of
whole numbers using estimation.
Grade 4 Quarter 2
Outcomes and Data
4.13 Essential Questions

6 days




Between what 2 numbers do probability
values lie? Why?
Explain how the outcome of a simple
event relates to the numbers of 0 and 1.
Identify the likelihood of an event
occurring and relate it to its rational
representation.
Provide a real life example of something
1
that has a probability of 1, 0, and
2
others in between.
Represent the probability of an event as
a common fraction.
SOL 4.13 The student will
a) predict the likelihood of an outcome of a
simple event; and
b) represent probability as a number
between 0 and 1, inclusive.
4.13 Essential Knowledge and Skills


4.13 Essential Understandings




Understand and apply basic concepts of
probability.
Describe events as likely or unlikely and
discuss the degree of likelihood, using
the terms certain, likely, equally likely,
unlikely, and impossible.
Predict the likelihood of an outcome of
a simple event and test the prediction.
Understand that the measure of the
probability of an event can be
represented by a number between 0
and 1, inclusive.
Page 10 of 26



Model and determine all possible
outcomes of a given simple event where
there are no more than 24 possible
outcomes, using a variety of
manipulatives, such as coins, number
cubes, and spinners.
Write the probability of a given simple
event as a fraction, where the total
number of possible outcomes is 24 or
fewer.
Identify the likelihood of an event
occurring and relate it to its fractional
representation (e.g., impossible/0;
1
equally likely/ ; certain/1).
2
Determine the outcome of an event that
is least likely to occur (less than half) or
most likely to occur (greater than half)
when the number of possible outcomes
is 24 or less.
Represent probability as a point between
0 and 1, inclusively, on a number line.
Grade 4 Quarter 2
4.14 Essential Questions

11 days

Collect, organize, display, and interpret
data from a variety of graphs.
Compare and contrast line, bar,
picture, circle graphs, and line plots.
4.14 Essential Understandings





Understand the difference between
representing categorical data and
representing numerical data.
Understand that line graphs show
change over time (numerical data).
Understand that bar graphs should be
used to compare counts of different
categories (categorical data).
Understand how data displayed in bar
and line graphs can be interpreted so
that informed decisions can be made.
Understand that the title and labels of
the graph provide the foundation for
interpreting the data.
Page 11 of 26
INV: The Shape of
Data
Investigation 1:
Introduction to Data
Analysis,
Sessions 1 – 3
Investigation 2:
Landmarks in the
Data,
Sessions 1 – 7
SOL 4.14 The student will collect, organize,
display, and interpret data from a variety of
graphs.
4.14 Essential Knowledge and Skills




Collect data, using, for example,
observations, measurement, surveys,
scientific experiments, polls, or
questionnaires.
Organize data into a chart or table.
Construct and display data in bar graphs,
labeling one axis with equal whole
number increments of 1 or more
(numerical data) (e.g., 2, 5, 10, or 100)
and the other axis with categories
related to the title of the graph
(categorical data) (e.g., swimming,
fishing, boating, and water skiing as the
categories of “Favorite Summer Sports”).
Construct and display data in line graphs,
labeling the vertical axis with equal
whole number increments of 1 or more
and the horizontal axis with continuous
data commonly related to time (e.g.,
hours, days, months, years, and age).
Line graphs will have no more than 10
identified points along a continuum for
continuous data. For example, growth
charts showing age versus height place
Grade 4 Quarter 2




5 days
Assessment, Enrichment, and Remediation
Page 12 of 26
age on the horizontal axis (e.g., 1 month,
2 months, 3 months, and 4 months).
Title or identify the title in a given graph
and label or identify the axes.
Interpret data from simple line and bar
graphs by describing the characteristics
of the data and the data as a whole (e.g.,
the category with the greatest/least,
categories with the same number of
responses, similarities and differences,
the total number). Data points will be
limited to 30 and categories to 8.
Interpret the data to answer the
question posed, and compare the
answer to the prediction (e.g., “The
summer sport preferred by most is
swimming, which is what I predicted
before collecting the data.”).
Write at least one sentence to describe
the analysis and interpretation of the
data, identifying parts of the data that
have special characteristics, including
categories with the greatest, the least, or
the same.
Grade 4 Quarter 3
Number
of Days
Topics, Essential Questions, and
Essential Understandings
(Students should be able to answer
essential questions.)
Working with Rational Numbers
20 days
F
R
A
C
T
I
O
N
S
Fractions
4.5 a, b, d Essential Questions
 Compare and contrast whole number
operations with fraction operations.
 Explain why least common multiples
and least common denominators are
used when computing the sums and
differences of fractions.
 Give an example of a practical problem
using fractions.
 Give an example of a practical problem
using decimals.
4.5 a, b, d Essential Understandings
 Understand and use common multiples
and common factors for simplifying
fractions.
 Develop and use strategies to estimate
addition and subtraction involving
fractions ….
Page 13 of 26
REQUIRED
Critical Thinking
Lessons
INV: Different
Shapes, Equal Pieces
Investigation 3:
Ordering Fractions,
Sessions 1 – 9
INV: Three Out of
Four Like Spaghetti
Investigation 1:
Using Fractions to
Describe Data,
Sessions 1 – 4
Standards of Learning
Essential Knowledge and Skills
Additional
Instructional
Resources
ESS: VDOE
Enhanced Scope
and Sequence
Lessons
SOL 4.5 a, b, d The student will
a) determine common multiples and
factors, including least common multiple and
greatest common factor;
b) add and subtract fractions having like and
unlike denominators that are limited to 2, 3,
4, 5, 6, 8, 10, and 12, and simplify the
resulting fractions, using common multiples
and factors;
INV: Different
Shapes, Equal
Pieces
Investigation 1:
Parts of
Squares:
Halves, Fourths,
and Eighths,
Sessions 1 – 5
4.5 a, b, d Essential Knowledge and Skills
 Find common multiples and common
factors of numbers.
 Determine the least common multiple
and greatest common factor of numbers.
 Use least common multiple and/or
greatest common factor to find a
common denominator for fractions.
 Add and subtract with fractions having
like denominators whose denominators
are limited to 2, 3, 4, 5, 6, 8, 10, and 12,
and simplify the resulting fraction using
common multiples and factors.
Investigation 2:
Parts of
Rectangles:
Thirds, Sixths,
and Twelfths,
Sessions 1 – 4
Grade 4 Quarter 3

Use visual models to add and subtract
with fractions and decimals.


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.2 a, b, c Essential Questions
 Demonstrate and explain patterns within
equivalent fractions.
 Given more than one fraction, how do
you determine which fraction is
smallest?
 Identify the division statement that
represents a fraction.
 Explain the strategy of using the
landmarks 1 , 1 , 3 to help you in
4

2
4
comparing and ordering fractions.
Explain how a fraction can represent a
relationship as well as a division
operation.
Page 14 of 26
Add and subtract with fractions having
unlike denominators whose
denominators are limited to 2, 3, 4, 5, 6,
8, 10, and 12, and simplify the resulting
fraction using common multiples and
factors.
Solve problems that involve adding and
subtracting with fractions having like and
unlike denominators whose
denominators are limited to 2, 3, 4, 5, 6,
8, 10, and 12, and simplify the resulting
fraction using common multiples and
factors.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.2 a, b, c The student will
a) compare and order fractions and mixed
numbers;
b) represent equivalent fractions; and
c) identify the division statement that
represents a fraction.
4.2 Essential Knowledge and Skills
Compare and order fractions having
denominators of 12 or less, using
manipulative models and drawings, such
as region/area models.
 Compare and order fractions with like
denominators by comparing number of
1 3
parts (numerators) (e.g., 5 < 5 ).
Grade 4 Quarter 3



Justify how a fractional number
describes part of a set.
Explain how to determine a fraction is in
simplest form.
Demonstrate and explain that multiple
representations of answers are

(e.g.,

equivalent. (For example, 1 and 2
2

4
are the same.)
Explain equivalent fractions through
multiple representations.

4.2 a, b, c Essential Understandings
 Two fractions are equivalent (represent
the same number) when both fractions
correspond to the same point on the
number line.
 Recognize and generate equivalent
fractions with denominators of 2, 3, 4,
and 6 (e.g., 1 = 2 ,
2

4
4 2
= ), and explain the
6 3
reasoning.
Fractions apply to situations where a
whole is decomposed into equal parts;
use fractions to describe parts of wholes.
For example, to show 1 of a length,
3
decompose the length into 3 equal parts
and show one of the parts.
 Develop an understanding of fractions
Page 15 of 26
Compare and order fractions with like
numerators and unlike denominators by
comparing the size of the parts



3
9
<
3
5
).
Compare and order fractions having
unlike denominators of 12 or less by
comparing the fractions to benchmarks
1
(e.g., 0, 2 or 1) to determine their
relationships to the benchmarks or by
finding a common denominator.
Compare and order mixed numbers
having denominators of 12 or less.
Use the symbols >, <, and = to compare
the numerical value of fractions and
mixed numbers having denominators of
12 or less.
Represent equivalent fractions through
twelfths, using region/area models, set
models, and measurement models.
Identify the division statement that
3
represents a fraction (e.g., 5 means the
same as 3 divided by 5).
Grade 4 Quarter 3
as parts of unit wholes, as parts of a
collection, and as locations on a number
line.
 Understand that a mixed number is a
fraction that has two parts: a whole
number and a proper fraction. The
mixed number is the sum of these two
parts.





Use models, benchmarks, and
equivalent forms to judge the size of
fractions.
Recognize that a whole divided into
nine equal parts has smaller parts than
if the whole had been divided into five
equal parts.
Recognize and generate equivalent
forms of commonly used fractions and
decimals.
Understand the division statement that
represents a fraction.
Understand that the more parts the
whole is divided into, the smaller the
parts (e.g.,
1 1
5 < 3 ).
Decimals
Page 16 of 26
Grade 4 Quarter 3
20 days
D
E
C
I
M
A
L
S
4.3 a, b, c, d Essential Questions
 Prove how a fraction and a decimal can
represent the same value.
 Explain the difference between reading a
number with a decimal compared to
reading a number without a decimal.
 Describe the differences between
saying, reading, and/or writing one
hundred and one hundredths? (also do
tens vs. tenths. . . and thousands vs.
thousandths)
 Explain how the place value system is
used to name and compare decimal
numbers smaller than 1.
 Justify how the magnitude of a base-10
model represents decimals.
 Demonstrate and prove fraction and
decimal equivalents.
 Compare and prove decimal values using
>, <. =.
 Explain when it would be appropriate to
round a number to a whole number,
tenths, or hundredths.
4.3 a, b, c, d Essential Understandings
 Understand the place value structure of
decimals and use this structure to read,
write, and compare decimals.
 Understand that decimal numbers can
be rounded to an estimate when exact
Page 17 of 26
SOL 4.3 The student will
a) read, write, represent, and identify
decimals expressed through thousandths;
b) round decimals to the nearest whole
number, tenth, and hundredth;
c) compare and order decimals; and
d) given a model, write the decimal and
fraction equivalents.
4.3 Essential Knowledge and Skills
 Investigate the ten-to-one place value
relationship for decimals through
thousandths, using Base-10
manipulatives (e.g., place value
mats/charts, decimal squares, Base-10
blocks, money).
 Represent and identify decimals
expressed through thousandths, using
Base-10 manipulatives, pictorial
representations, and numerical symbols
(e.g., relate the appropriate drawing to
0.05).
 Identify and communicate, both orally
and in written form, the position and
value of a decimal through thousandths.
For example, in 0.385, the 8 is in the
hundredths place and has a value of
0.08.
 Read and write decimals expressed
through thousandths, using Base-10
Grade 4 Quarter 3



numbers are not needed for the
situation at hand.
Understand that decimals are rounded
in a way that is similar to the way whole
numbers are rounded.
Understand that decimals and fractions
represent the same relationship;
however, they are presented in two
different formats.
Understand that models are used to
show decimal and fraction equivalents.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.5 c Essential Questions
 Compare and contrast adding and
subtracting fractions and decimals.
 Compare and contrast whole number
operations with decimal operations.
4.5 c Essential Understandings
 Develop and use strategies to estimate
addition and subtraction involving
fractions ….
 Use visual models to add and subtract
with …decimals.
Page 18 of 26



manipulatives, drawings, and numerical
symbols.
Round decimals to the nearest whole
number, tenth, and hundredth.
Compare decimals, using the symbols >,
<, =.
Order a set of decimals from least to
greatest or greatest to least.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.5 c The student will
c) add and subtract with decimals; and….
4.5 c Essential Knowledge and Skills
 Find common multiples and common
factors of numbers.
 Determine the least common multiple
and greatest common factor of numbers.
 Use least common multiple and/or
greatest common factor to find a
common denominator for fractions.
 Add and subtract with fractions having
like denominators whose denominators
are limited to 2, 3, 4, 5, 6, 8, 10, and 12,
and simplify the resulting fraction using
common multiples and factors.
Grade 4 Quarter 3


3 days
Add and subtract with fractions having
unlike denominators whose
denominators are limited to 2, 3, 4, 5, 6,
8, 10, and 12, and simplify the resulting
fraction using common multiples and
factors.
Solve problems that involve adding and
subtracting with fractions having like and
unlike denominators whose
denominators are limited to 2, 3, 4, 5, 6,
8, 10, and 12, and simplify the resulting
fraction using common multiples and
factors.
Enrichment, Assessment, and Remediation
***Adjustment to pacing may be necessary due to the timing of the SOL testing window.
Page 19 of 26
Grade 4 Quarter 4
Topics, Essential Questions, and
Essential Understandings
(Students should be able to answer
essential questions.)
Number
of Days
Measurement
15 days
REQUIRED
Critical Thinking
Lessons
INV: Measurement
Benchmarks
(from 5th grade
Investigations)
Standards of Learning
Essential Knowledge and Skills
SOL 4.7 The student will
a) estimate and measure length, and
4.7 Essential Questions
describe the result in both metric and
Length/Distance
U.S. Customary units; and
 Give a real life example of what you
b) identify equivalent measurements
Investigation 1:
would measure in inches, feet, yards,
between units within the U.S. Customary
Measures of Length
miles, millimeters, centimeters, meters,
system (inches and feet; feet and yards;
and Distance,
and kilometers.
inches and yards; yards and miles) and
Sessions 1 – 6
 Why are there two different units of
between units within the metric system
measurement?
(millimeters and centimeters;
 What is an appropriate tool to measure in Investigation 2:
centimeters and meters; and millimeters
Measures of
inches, feet, yards, millimeters,
and meters).
Weight and Liquid
centimeters, meters, and kilometers?
Volume,
4.7 Essential Knowledge and Skills
Sessions 1 - 6
4.7 Essential Understandings
 Determine an appropriate unit of
 Use benchmarks to estimate and
measure (e.g., inch, foot, yard, mile,
measure length.
millimeter, centimeter, and meter) to
 Understand how to convert units of
use when measuring everyday objects
length between the U.S. Customary and
in both metric and U.S. Customary
metric systems, using ballpark
units.
comparisons.
 Estimate the length of everyday objects
 Understand the relationship between
(e.g., books, windows, tables) in both
U.S. Customary units and the
metric and U.S. Customary units of
relationship between metric units.
measure.
Page 20 of 26
Additional
Instructional
Resources
ESS: VDOE
Enhanced Scope
and Sequence
Lessons
http://illuminations
.nctm.org/LessonD
etail.aspx?id=L184
Smart
Measurement Site
http://smartmeasu
rement.wikispaces.
com/
How Long? How
Tall? How Wide?
How Deep?
http://illuminations
.nctm.org/LessonD
etail.aspx?id=L635
Grade 4 Quarter 4

Investigate the relationship between
decimal numbers and the metric system.



~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.6 Essential Questions
Weight/Mass


What is the difference between weight
and mass?
Give a real life example of what you
would measure in ounces, pounds, tons,
grams, and kilograms.
4.6 Essential Understandings

Page 21 of 26
Use benchmarks to estimate and
measure weight/mass.
Measure the length of objects in both
metric and U.S. Customary units,
1 1 1
measuring to the nearest inch (2 , 4 , 8 ),
foot, yard, mile, millimeter, centimeter,
or meter, and record the length
including the appropriate unit of
measure (e.g., 24 inches).
Compare estimates of the length of
objects with the actual measurement of
the length of objects.
Identify equivalent measures of length
between units within the U.S.
Customary measurements and between
units within the metric measurements.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.6 The student will
a) a) estimate and measure weight/mass and
describe the results in U.S. Customary and
metric units as appropriate; and
b) b) identify equivalent measurements
between units within the U.S. Customary
system (ounces, pounds, and tons) and
between units within the metric system
(grams and kilograms).
4.6 Essential Knowledge and Skills

Determine an appropriate unit of
measure (e.g., ounce, pound, ton, gram,
kilogram) to use when measuring
Grade 4 Quarter 4

Identify equivalent measures between
units within the U.S. Customary and
between units within the metric
measurements.


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.8 Essential Questions
Liquid Volume
 Give a real life example of what you
would measure in cups, pints, quarts,
and gallons.
4.8 Essential Understandings


Use benchmarks to estimate and
measure volume.
Identify equivalent measurements
between units within the U.S. Customary
system.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.8 The student will
a) estimate and measure liquid volume and
describe the results in U.S. Customary units;
and
b) identify equivalent measurements
between units within the U.S. Customary
system (cups, pints, quarts, and gallons).
4.8 Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections, and
representations to


Page 22 of 26
everyday objects in both metric and
U.S. Customary units.
Measure objects in both metric and U.S.
Customary units (e.g., ounce, pound,
ton, gram, or kilogram) to the nearest
appropriate measure, using a variety of
measuring instruments.
Record the mass of an object including
the appropriate unit of measure (e.g.,
24 grams).
Determine an appropriate unit of
measure (cups, pints, quarts, gallons) to
use when measuring liquid volume in
U.S. Customary units.
Estimate the liquid volume of
containers in U.S. Customary units of
Grade 4 Quarter 4


measure to the nearest cup, pint, quart,
and gallon.
Measure the liquid volume of everyday
objects in U.S. Customary units,
including cups, pints, quarts, and
gallons, and record the volume
including the appropriate unit of
measure (e.g., 24 gallons).
Identify equivalent measures of volume
between units within the U.S.
Customary system.
Geometry
20 days
Plane Figures
4.10 Essential Questions
 Compare and contrast a line, line
segment, angle and ray.
 Create and identify a line, line segment,
angle, and ray.
 What is the relationship between a line
segment and an angle?
 Explain the relationship between a ray
and an angle.
 Identify and justify real life examples of
parallel lines.
 Identify and justify real life examples
perpendicular lines.
 Compare and contrast characteristics of
intersecting lines and perpendicular lines.
Page 23 of 26
SOL 4.10 The student will
a) identify and describe representations of
points, lines, line segments, rays, and angles,
including endpoints and vertices; and
b) identify representations of lines that
INV:
illustrate intersection, parallelism,
Mathematical
perpendicularity
Thinking in Grade 4
Investigation 4:
“Making Geometric
Patterns”,
4.10 Essential Knowledge and Skills
Sessions 1 – 6
 Identify and describe representations of
points, lines, line segments, rays, and
angles, including endpoints and
vertices.
 Understand that lines in a plane can
intersect or are parallel.
Perpendicularity is a special case of
intersection.
Grade 4 Quarter 4
4.10 Essential Understandings
 Understand that points, lines, line
segments, rays, and angles, including
endpoints and vertices are fundamental
components of noncircular geometric
figures.
 Understand that the shortest distance
between two points on a flat surface is a
line segment.
 Understand that lines in a plane either
intersect or are parallel. Perpendicularity
is a special case of intersection.
 Identify practical situations that illustrate
parallel, intersecting, and perpendicular
lines.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

4.11 Essential Questions
 Compare and contrast geometric
transformations.
 Demonstrate and explain congruency of a
plane figure after a reflection, translation,
and/or rotation.
 Demonstrate and justify various
strategies for rotation, reflection, and
translation of an image.
 What are real life models of reflection,
translation, and rotation?
 Prove the image of a plane figure is
congruent to the original image after a
transformation.
SOL 4.11 The student will
a) investigate congruence of plane figures
after geometric transformations, such as
reflection, translation, and rotation, using
mirrors, paper folding, and tracing; and
b) recognize the images of figures resulting
from geometric transformations, such as
translation, reflection, and rotation.
Page 24 of 26
Identify practical situations that
illustrate parallel, intersecting, and
perpendicular lines.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.11 Essential Knowledge and Skills
Recognize the congruence of plane figures
resulting from geometric transformations
such as translation, reflection, and rotation,
using mirrors, paper folding and tracing.
Grade 4 Quarter 4

Explain what understandings are
important when determining if two
figures are congruent.
4.11 Essential Understandings
 Understand the meaning of the term
congruent.
 Understand how to identify congruent
figures.
 Understand that the orientation of
figures does not affect congruency or
noncongruency.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.12 Essential Questions
 What is a polygon?
 Create and identify polygons with ten or
fewer sides.
4.12 Essential Understandings
 Identify polygons with 10 or fewer sides
in everyday situations.
 Identify polygons with 10 or fewer sides
in multiple orientations (rotations,
reflections, and translations of the
polygons)
~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Page 25 of 26
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.12 The student will
a) define polygon; and
b) identify polygons with ten or fewer sides.
4.12 Essential Knowledge and Skills
 Define and identify properties of
polygons with 10 or fewer sides.
 Identify polygons by name with 10 or
fewer sides in multiple orientations
(rotations, reflections, and translations
of the polygons).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Grade 4 Quarter 4
Elapsed Time
5 days
4.9 Essential Questions
 What is elapsed time?
 How do you determine elapsed time?
 Determine elapsed time given between 2
given hours and additional minutes.
 Given a beginning and ending time of an
event, use at least two different
strategies to calculate elapsed time.
 Provided an ending time and an elapsed
time, determine the start time of the
event.
4.9 Essential Understandings
 Understand the “counting on” strategy
for determining elapsed time in hour and
minute increments over a 12-hour
period from a.m. to a.m. or p.m. to p.m.
7 days
SOL 4.9 The student will determine elapsed
time in hours and minutes within a 12-hour
period.
4.9 Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections, and
representations to


Determine the elapsed time in hours
and minutes within a 12-hour period
(times can cross between a.m. and
p.m.).
Solve practical problems in relation to
time that has elapsed.
Enrichment, Assessment, and Remediation
***Adjustment to pacing may be necessary due to the timing of the SOL testing window.
Page 26 of 26