GRADE 4 MATHEMATICS
CURRICULUM GUIDE
Loudoun County Public Schools
2010-2011
Complete scope, sequence, pacing and resources are available on the CD and will be available on the LCPS Intranet.
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 that remains relatively
unchanged over several student generations. 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.
Teachers should periodically check and update any web addresses that they have on their
LCPS web pages.
3. Teachers should assure that the use of websites correlate with the objectives of
lesson and provide students with the appropriate challenge.
4. Teachers should assure that the use of websites correlate with the objectives
of the lesson and provide students with the appropriate challenge.
Grade 4 Mathematics Nine Weeks Overview
1st Quarter
2nd Quarter
3rd Quarter
4th Quarter
4.10 a, b
4.11
4.12
4.15
4.1
4.4
4.15
4.16 a, b
4.1
4.4
4.15
4.16 a, b, c
4.6
4.7
4.8
4.9
4.2 a, b, c
4.3 a, b, c
4.5 a, b, c, d
4.13 a, b
4.14
38 days
48 days
47 days
48 days
Quarter 1: Academic Year 2010-2011
Number of
Days
Grade 4 Mathematics
Topic and Essential Questions
(refer to 2009 SOL only)
Standard(s) of Learning
Essential Knowledge and Skills
Essential Understandings
REQUIRED Critical
Indicators for 2009 SOLs
Thinking Lessons
*Deleted or moved to a different grade level
‡
Quarter 1: Plane Figures
38 days 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.
15 days Identify and justify real life examples of parallel
Continued lines.
on next Identify and justify real life examples
perpendicular lines.
page
Compare and contrast characteristics of
intersecting lines and perpendicular lines.
What is a polygon?
Create and identify polygons with ten or fewer
sides.
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.
Additional
Instructional
Resources
Remains the same
New content to this grade
2009: 4.10 a, b;, 4.11, 4.12, 4.15
ESS (Enhanced Scope
and Sequence)
TSWBAT (The Students Will Be http://www.doe.virginia.
Able To):
gov/testing/sol/standards
Draw points, lines, line segments, _docs/mathematics/inde
rays, angles, endpoints, vertices,
x.shtml
and intersecting, perpendicular and Simple Pictures p.
parallel lines. Identify these in
Geometry Review p.
plane figures.
Geometric Figures p.
Classify shapes based on the
Congruent Figures p.
presence or absence of parallel or Coordinate Points p.
perpendicular lines, or the
Toothpick, Door and
presences of angles of specified
Staircase Patterns p.
size.
Understand an angle is formed by INV: Mathematical
two rays with a common endpoint. Thinking in Grade 4
Define polygons and identify
Investigation 4: Making
polygons with 10 or fewer sides.
Geometric Patterns,
Investigate congruence of plane
Sessions 1 – 6
figures after geometric
transformations, such as
translation, reflection, and rotation.
Quarter 1: Academic Year 2010-2011
Grade 4 Mathematics
Number of
Days
Topic and Essential Questions
(refer to 2009 SOL only)
Standard(s) of Learning
Essential Knowledge and Skills
Essential Understandings
REQUIRED Critical
Indicators for 2009 SOLs
Thinking Lessons
*Deleted or moved to a different grade level
‡
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.
Explain what understandings are important when
15 days determining if two figures are congruent.
concluded Compare and contrast numerical and geometric
patterns.
Compare and contrast a growing pattern and a
repeating pattern.
Demonstrate and explain geometric and numerical
patterns using words, tables, graphs, and symbols.
Working with Whole Numbers
How can the place value system be used to name
and compare large numbers?
What is the relationship between each digit?
When is it appropriate to estimate a calculation,
and when is it necessary to find an exact value?
20 days There are many methods for determining a sum
Continued and difference. What are the criteria considered
for next 2 when choosing a strategy?
What are inverse relationships?
pages
What is a numerical pattern?
Provide an example of a numerical pattern using
words, tables, graphs, and symbols.
Additional
Instructional
Resources
Remains the same
New content to this grade
Recognize the images of figures
resulting from geometric
transformations, such as
translation, reflection, and rotation.
Recognize, create, and extend
numerical and geometric patterns.
INV Mathematical 2009: 4.1, 4.5, 4.15, 4.16
Thinking at Grade 4
Understand the relationships in the
Investigation 1: How
place value system in which the
Many Hundreds,
value of each place is ten times the
value of the place to its right.
Sessions 1 - 4
Investigation 3: Using
Use the patterns in the place value
Number Patterns,
system to read and write numbers.
Sessions 1 – 5
Understand that reading place value
correctly is essential when
comparing numbers.
Understand that rounding gives a
close number to use when exact
numbers are not needed for the
situation at hand.
Develop strategies for rounding.
ESS
http://www.doe.virginia.
gov/testing/sol/standards
_docs/mathematics/inde
x.shtml
Location, Location,
Location p.
Estimation Game p.
Modeling Addition and
Subtraction p.
Multiplying and Trading
Balance Beams p.
Weighty Problems p.
Quarter 1: Academic Year 2010-2011
Number
of Days
Topic and Essential Questions
(refer to 2009 SOL only)
Extend numerical patterns using concrete materials,
number lines, tables, and words.
Create and describe numerical patterns, using
concrete materials, number lines, tables, and words.
What is an equation?
Use the Associative Property to demonstrate the
equality in an equation.
Use the Commutative Property to demonstrate the
equality in an equation.
20 days
cont
Grade 4 Mathematics
Standard(s) of Learning
Essential
Knowledge and Skills
REQUIRED Critical
Essential Understandings
Thinking Lessons
INV Landmarks in
the Thousands
Investigation 1:
Working with 100,
Sessions 1 - 3
Investigation 2:
Exploring Multiples
of 100,
Sessions 1 – 5
Investigation 3: How
Much is 1000,
Sessions 1 – 5
Understand and use common
multiples and common factors for
simplifying fractions.
Develop and use strategies to
estimate addition and subtraction
involving fractions and decimals.
Use visual models to add and
subtract with fractions and decimals.
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.
Additional
Instructional
Resources
Quarter 1: Academic Year 2010-2011
Number of
Days
Topic and Essential Questions
(refer to 2009 SOL only)
Grade 4 Mathematics
Standard(s) of Learning
REQUIRED Critical
Essential Knowledge and Skills
Thinking Lessons
Essential Understandings
Additional
Instructional
Resources
Investigation 4: Making
a 10,000 Chart, Sessions
1–3
INV Arrays and Shares
Investigation 1:
Multiples on the 100
Chart, Sessions 1 – 3
Understand how to solve single-step
and multistep problems using whole Investigation 2: Arrays,
Sessions 1 – 8
number operations.
Investigation 3:
Understand that patterns and
functions can be represented in many Multiplication and
ways and described using words,
Division with Two-Digit
tables, graphs, and symbols.
Numbers, Sessions 1 – 5
Understand various representations
of division and the terms used in
division are dividend, divisor, and
quotient.
dividend divisor = quotient
quotient
divisor dividend
20 days
concluded
3 days
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.
Assessment, Enrichment, and Remediation
All About Multiplication
http://illuminations.nctm
.org/LessonDetail.aspx?i
d=U109
Order, Please (adapt for
millions place)
http://www.learnnc.org/l
p/pages/2961?ref=search
Quarter 2: Academic Year 2010-2011
Number
of Days
Grade 4 Mathematics
Topic and Essential Questions
(refer to 2009 SOL only)
Quarter Working with Whole Numbers
There are many methods for determining a product.
2:
47 days What are the criteria considered when choosing a
strategy?
What are inverse relationships?
What does it mean to divide?
In a problem situation, what does a remainder
describe?
Is there a difference in calculating the sum of
numbers which are written horizontally rather than
vertically?
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
25 days these represented using the three division models?
What is the similarity between multiplication and
addition?
What is the similarity between division and
subtraction?
What is a numerical pattern?
Provide an example of a numerical pattern using
words, tables, graphs, and symbols.
Extend numerical patterns using concrete materials,
number lines, tables, and words.
Standard(s) of Learning
REQUIRED Critical Essential Knowledge and Skills
Thinking Lessons
Essential Understandings
INV Packages and
Groups
Investigation 2:
Double Digit
Multiplication,
Sessions 1 – 3
Investigation 3:
Multiplication and
Division Choices,
Sessions 1 - 10
INV Measurement
Benchmarks
Investigation 1:
Measures of Length
and Distance,
Sessions 1 – 6
Investigation 2:
Measures of Weight
and Liquid Volume,
Sessions 1 - 6
2009:
4.1, 4.4, 4.15, 4.16 a, b‡, 4.6, 4.7,
4.8, 4.9‡
Additional
Instructional
Resources
Quarter 2: Academic Year 2010-2011
Number
of Days
Grade 4 Mathematics
Topic and Essential Questions
(refer to 2009 SOL only)
Equivalent Measurements
What is the difference between weight and mass?
Why are there two different units of measurement?
Give a real life example of what you would measure
in ounces, pounds, tons, grams, and kilograms.
Give a real life example of what you would measure
in inches, feet, yards, miles, millimeters,
centimeters, meters, and kilometers.
Why are there two different units of measurement?
When is it appropriate to estimate a measurement?
Provide real life examples between U.S. and metric
20 days
systems.
cont
What is an appropriate tool to measure in inches,
feet, yards, millimeters, centimeters, meters, and
kilometers?
Give a real life example of what you would measure
in cups, pints, quarts, and gallons.
Why are there two different units of measurement?
What is elapsed time?
How do you determine elapsed time?
Determine elapsed time given between 2 given
hours and additional minutes.
Standard(s) of Learning
REQUIRED Critical Essential Knowledge and Skills
Thinking Lessons
Essential Understandings
INV Measurement
Benchmarks (from
Grade 5)
Investigation 1:
Measures of Length
and Distance,
Sessions 1 – 6
Investigation 2:
Measures of Weight
and Liquid Volume,
Sessions 1 - 6
Additional
Instructional
Resources
ESS Grade 4
http://www.doe.virginia.
gov/testing/sol/standards
_docs/mathematics/inde
x.shtml
This Fruit is a Mass! p.
Kiddy Pool p.
ESS Grade 5
Measurement Mania p.
Smart Measurement Site
http://smartmeasurement
.wikispaces.com/
How Long? How Tall?
How Wide? How
Deep?
http://illuminations.nctm
.org/LessonDetail.aspx?i
d=L635
Quarter 2: Academic Year 2010-2011
Number
of Days
Grade 4 Mathematics
Topic and Essential Questions
(refer to 2009 SOL only)
Given a beginning and ending time of an event, use
at least two different strategies to calculate elapsed
20 days time.
concluded Provided an ending time and an elapsed time,
determine the start time of the event.
2 days
Assessment, Enrichment, and Remediation
Standard(s) of Learning
REQUIRED Critical Essential Knowledge and Skills
Thinking Lessons
Essential Understandings
Additional
Instructional
Resources
Exploration of a Balance
(Lesson 2)
http://illuminations.nctm
.org/LessonDetail.aspx?i
d=L184
Quarter 3: Academic Year 2010-2011
Number
of Days
Grade 4 Mathematics
Standard(s) of Learning
Essential
Knowledge and Skills
REQUIRED Critical
Essential Understandings
Thinking Lessons
Topic and Essential Questions
(refer to 2009 SOL only)
Quarter Working with Rational Numbers
Demonstrate and explain patterns within equivalent
3:
48 days 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 landmark ¼, ½, ¾ help
you in comparing and ordering fractions.
Prove how a fraction and a decimal can represent the
40 days same value.
Continue Explain how a fraction can represent a relationship
d for next as well as a division operation.
2 pages Justify how a fractional number describes part of a
set.
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.
Quarter 3: Academic Year 2010-2011
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
Grade 4 Mathematics
2009: 4.2 a, b, c‡, 4.3 a, b, c, d‡,
4.5 a, b, c, d‡
Additional
Instructional
Resources
ESS
http://www.doe.virginia.
gov/testing/sol/standards
_docs/mathematics/inde
x.shtml
Decimal Rings
Fraction Grids
Register Tape Fractions
Circle Fractions
Fraction Strips
Egg Carton Fractions
Pattern Block Fractions
Build the Whole
Pattern Block Fraction
Game
Comparing Fractions
Which is Closer?
Fraction Strip Addition
Fraction Riddles
Reading and Writing
Decimals
Comparing Decimals
Rounding Decimals
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., ½ =2/4, 4/6=2/3),
and explain the reasoning.
Fractions apply to situations where
a whole is decomposed into equal
parts; use fractions to describe
parts of wholes. For example, to
show 1/3 of a length, decompose
the length into 3 equal parts and
show one of the parts.
Compare and order fractional
quantities with equal numerators,
or equal denominators, using the
fractions themselves, tape
diagrams, number line
representations, and area models.
Use >, <, to record the results of
Fraction Bar Kit
the comparisons.
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.
Compare and contrast adding and subtracting
fractions and decimals.
Compare and contrast whole number operations with
fraction operations.
40 days
Compare and contrast whole number operations with
cont
decimal operations.
Give an example of a practical problem using
fractions.
Give an example of a practical problem using
decimals.
Explain why least common multiples and least
common denominators are used when computing the
sums and differences of fractions.
Explain how to determine a fraction is in simplest
form.
Identify the division statement that
represents a fraction.
Read, write, represent, and identify
decimals expressed through
thousandths.
Round decimals to the nearest
whole number, tenth, and
hundredth.
Compare and order decimals.
Given a model, write the decimal
and fraction equivalents.
Determine common multiples and
factors, including least common
multiple and greatest common
factor of up to two fractions.
Add and subtract fractions having
both like and unlike denominators
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
Investigation 2: Parts of
Rectangles: Thirds,
Sixths, and Twelfths,
Sessions 1 – 4
Quarter 3: Academic Year 2010-2011
Number
of Days
Topic and Essential Questions
(refer to 2009 SOL only)
Demonstrate and explain that multiple
representations of answers are equivalent. (For
40 days example, ½ and 2/4 are the same.)
concluded Explain equivalent fractions through multiple
representations.
8 days
Assessment, Enrichment, and Remediation
Grade 4 Mathematics
Standard(s) of Learning
Essential
Knowledge and Skills
REQUIRED Critical
Essential Understandings
Thinking Lessons
Add and subtract with decimals.
Solve single-step and multistep
practical problems involving
addition and subtraction with
fractions and decimals.
Additional
Instructional
Resources
Quarter 4: Academic Year 2010-2011
Number
of Days
Grade 4 Mathematics
Topic and Essential Questions
(refer to 2009 SOL only)
Quarter Outcomes and Data
Probability values lie between what two numbers?
4:
47 days Explain how the outcome of a simple event relates
to the numbers of 0 and 1.
20 days Identify the likelihood of an event occurring and
relate it to its rational representation.
Provide a real life example of something that has a
probability of 1. 0. ½ and others in between.
Represent the probability of an event as a common
fraction.
Collect, organize, display, and interpret data from a
variety of graphs.
Compare and contrast line, bar, picture, circle
graphs, and line plots.
10 days Review and Assessment
17 days Enrichment
Standard(s) of Learning
Essential
Knowledge and Skills
REQUIRED Critical
Essential Understandings
Thinking Lessons
INV: The Shape of
Data
Investigation 1:
Introduction to Data
Analysis, Sessions 1 –
3
Investigation 2:
Landmarks in the
Data, Sessions 1 – 7
2009: 4.13 a, b‡, 4.14
Additional
Instructional
Resources
ESS
http://www.doe.virginia.
Predict the likelihood of an
gov/testing/sol/standards
outcome of a simple event
_docs/mathematics/inde
Represent probability as a number x.shtml
between 0 and 1, inclusive.
Lucky Sums?
Collect, organize, display, and
Looking for a Pet!
interpret data from a variety of
How Certain Are You?
graphs.
Sandwich Data
Say, “Here!”
Spinning Colors