4th Grade Math
Dinwiddie County Public Schools
th
4 Grade
Math Curriculum
Dinwiddie County Public Schools provides each student the
opportunity to become a productive citizen, engaging the
entire community in the educational needs of our children.
1
Revised: 8/4/14
4th Grade Math
Dinwiddie County Public Schools
4th Grade
Math Curriculum

The DCPS scope and sequence/pacing guide contains key topics that must be cross referenced continuously
throughout the year with the VDOE enhanced scope and sequence and VDOE curriculum framework.
 Weekly math fact drills should start during the first nine weeks.
 Once taught, target skills should be cumulatively reviewed throughout the school year; emphasis should be placed on
covering skills that were most challenging according to assessment results.
DOE LINKS
Mathematics SOL Curriculum Framework
Mathematical Instructional Resources
2
Revised: 8/4/14
4th Grade Math
Instructor Background Knowledge
Please use the list below to guide your instruction and assessment creation.
 Use open-ended problems with students not just multiple choice.
 Use questions that have multiple answers.
Example: Mark all the numbers that would round to 45,000
 Expose students to multi-step word problems involving all operations and concepts (fractions, whole
numbers, decimals, estimation):
Example: Joey wants to buy a new iPad™ that costs $899.00. He received $150.00 for his birthday.
He earned $8.00 per hour mowing grass for 12 hours. How much money does he still need to
purchase the iPad™
 Expose students to operation words (sum, difference, product, quotient) when presenting problems
don’t stick to strictly operation symbols.
Example: Find the product of 86 and 23.
What is the difference of 500 and 32?
 Present elapsed time with digital and analog clocks. Review telling time.
 Be sure to present finding the multiples and factors of two or three numbers outside the context of
fractions.
Example: What is the greatest common factor of 12 and 16?
What is the least common multiple of 3, 5, and 6?
3
Revised: 8/4/14
4th Grade Math
Nine Weeks
Approximate # of
Days Taught
Topic
Targeted SOL
Curriculum
Framework
1
10
Whole Number Place Value Through Millions: standard, word form, comparing,
rounding, identify the value of a digit
4.1
p. 2-4
9
Adding and Subtracting
Whole Numbers: Estimation,
Word Problems (single and multistep)
4.4 a,b,d
p. 12-17
5
Line and Bar Graphs: collect, organize, display,
and interpret data
4.14
p. 34-35
1
17
Multiplication:
1-Digit Multiplier, 2-Digit Multiplier,
Estimating Product,
Word Problems(single and multistep)
*Find common multiples and common factors of two or three whole numbers.
Determine least common multiple and greatest common factor of numbers.
4.4a,b,d
4.5 a
p. 12-17
p. 18
1
3
Review
1st Nine Weeks Benchmark
See Above
Review
1
1
4
Revised: 8/4/14
4th Grade Math
Approximate # of
Days Taught
Topic
Targeted SOL
Curriculum
Framework
2
10
Division:
1-Digit Divisor
Estimating Quotient
Word Problems (Single and multistep)
4.4 a,c,d
p. 12-17
2
5
Number and Geometric Patterns
Describe, Recognize, Create, Extend
4.15
p. 37
2
5
Algebra: Equality, Associative Property
(Addition and Multiplication)
4.16
p. 38
10
Fraction Concepts:
Compare/Order(fractions/mixed numbers),
Equivalent, Identify Division Statement that represents a fraction
4.2 a,b,c
p. 5-7
2
11
Fraction Operations: Least Common Multiple, Greatest Common Factor
of two or three fractions,
Add/Subtract (like/unlike denominators), Simplify fractions,
Single and Multi-Step Word Problems
4.5 a,b,d
p. 18-19
2
3
Review
2nd Nine Weeks Benchmark
See Above
Review
Nine Weeks
2
5
Revised: 8/4/14
4th Grade Math
Nine Weeks
Approximate
# of Days
Taught
Topic
Targeted SOL
Curriculum
Framework
3
12
Decimal Concepts: Place Value (through thousandths), Compare/Order, Round,
Decimal and Fraction Equivalents for given model
4.3 a-d
p. 8-10
3
5
Decimal Operations: Add/Subtract,
Word Problems (single and multi- step)
4.5 c d
p. 18-19
3
4
Probability: Likelihood of a simple event
Probability as a number between 0 and 1
4.13
p. 32-33
7
U.S. Customary and Metric
Linear Measurement: Estimate and Measure Length(nearest 1/8 of an inch),
Identify Equivalent Measurements between units within Customary system and
between units within the Metric system
4.7 a, b
p. 22
3
4
U.S. Customary and Metric
Measurement of Mass: Estimate and Measure Weight or Mass, Identify Equivalent
Measurements between units within Customary system and between units within the metric
system
4.6 a, b
p. 21
3
4
U.S. Customary Measurement of Volume: Estimate and Measure Volume, Identify Equivalent
Measurements of Volume between units within the U.S. Customary system
4.8 a, b
p. 23
3
5
Elapsed Time: Hours and Minutes within a 12-Hour Period; Determine Elapsed Time; Solve
practical problems in relation to time that has elapsed
4.9
p. 24
3
3
Review
3rd Nine Weeks Benchmark
Above
Review
3
6
Revised: 8/4/14
4th Grade Math
Nine Weeks
Approximate
# of Days
Taught
Topic
Targeted SOL
Curriculum
Framework
4
4
Geometry: Points, Lines (intersecting, parallel, perpendicular)
Line Segments, Angles (endpoints and vertices), Rays
4.10
p. 26-27
4
5
Polygons: Define and Identify Polygons
10 or fewer sides
4.12 a,b
p. 30
4
4
Geometry: Plane Figures with Transformation (reflection, translation, rotation)
4.11
p. 28-29
4
Remainder
SOL Test Review *
ALL
Review
7
Revised: 8/4/14
SOL 4.1 – 1st Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.1 – 1st Nine Weeks
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.
Blueprint Categories
Grade 4 SOL
Number of Items
Number and Number Sense
4.1a-c, 4.2a-c, 4.3a-d
12
Prior Knowledge
4.1a
2nd read, write and identify place value in a three digit numeral
3rd read, write and identify place value of a six digit numeral
4.1b
2nd compare 2 whole numbers between 0 -999 ( greater than, less than, or equal to)
3rd compare 2 whole numbers between 0-9,999( greater than, less than or equal to)
4.1c
2nd round 2 digit numbers to nearest ten
3rd round whole numbers 9,999 or less to the nearest ten, hundred and thousand
Understanding the Standard



The structure of the Base-10 number system is based upon a
simple pattern of tens, in which the value of each place is ten
times the value of the place to its right.
Place value refers to the value of each digit and depends upon the
position of the digit in the number. For example, in the number
7,864,352, the eight is in the hundred thousands place, and the
value of the 8 is eight hundred thousand or 800,000.
Whole numbers may be written in a variety of formats:
– Standard: 1,234,567
– Written: one million, two hundred thirty-four thousand, five
Essential Understandings
All students should

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
8
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections,
and representations to

Identify and communicate, both
orally and in written form, the
placed value for each digit in
whole numbers expressed through
the one millions place.

Read whole numbers through the
Revised: 8/4/14
SOL 4.1 – 1st Nine Weeks
hundred sixty-seven
– Expanded: (1  1,000,000) + (2  100,000) + (3  10,000) + (4 
1,000) + (5  100) + (6  10) + (7  1)


Numbers are arranged into groups of three places called periods
(ones, thousands, millions, …). Places within the periods repeat
(hundreds, tens, ones). Commas are used to separate the periods.
Knowing the place value and period of a number helps students
find values of digits in any number as well as read and write
numbers.
numbers.


Understand that rounding gives a close
number to use when exact numbers are
not needed for the situation at hand.
Mathematical symbols (>, <) used to compare two unequal
numbers are called inequality symbols.

A procedure for comparing two numbers by examining place
value may include the following:
– Compare the digits in the numbers to determine which
number is greater (or which is less).
– Use a number line to identify the appropriate placement of
the numbers based on the place value of the digits.
– Use the appropriate symbol > or < or words greater than or
less than to compare the numbers in the order in which they
are presented.
– If both numbers have the same value, use the symbol = or
words equal to.

A strategy for rounding numbers to the nearest thousand, ten
thousand, and hundred thousand is as follows:
–
Use a number line to determine the rounded number (e.g.,
when rounding 4,367,925 to the nearest thousand, identify

Write whole numbers through the
one millions place in standard
format when the numbers are
presented orally or in 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.
Develop strategies for rounding.
Reading and writing large numbers should be meaningful for
students. Experiences can be provided that relate practical
situations (e.g., numbers found in the students’ environment
including population, number of school lunches sold statewide in
a day, etc.). Concrete materials such as Base-10 blocks and
bundles of sticks may be used to represent whole numbers
through thousands. Larger numbers may be represented by digit
cards and place value charts.

one millions place that are
presented in standard format, and
select the matching number in
written format.
9
Revised: 8/4/14
SOL 4.1 – 1st Nine Weeks
the ‘thousands’ the number would fall between on the
number line, then determine the thousand that the number
is closest to):
4,367,000
–
–
–
? 4,368,000
Look one place to the right of the digit to which you wish to
round.
If the digit is less than 5, leave the digit in the rounding
place as it is, and change the digits to the right of the
rounding place to zero.
If the digit is 5 or greater, add 1 to the digit in the rounding
place and change the digits to the right of the rounding
place to zero.
Additional Instructional Strategies
Students should be able to round larger numbers by locating the number on a number line.
Rounding with number lines slide resource
Additional Math Curriculum Resources
10
Revised: 8/4/14
SOL 4.1 – 1st Nine Weeks
Vocabulary
Lessons and TEI Items
Trade Books
Vocabulary Word Wall
Location, Location, Location!
How Much is a Million? By David Schwartz
Handout available: Working with Vocabulary /
Concept Development (Word)
Number and Number Sense
How Much, How Many, How Far, How Heavy, How
Long, How Tall is 1000? By Helen Nowlan and Tracy
Walker
Place Value Made Lessons
Word Wall Instructional Video
Place Value Through 999,999
Place Value - The value a digit represents
depending on its place in the number
Sir Cumference and All the King’s Tens By Cindy
Neuschwander
Who Wants to Be a Thousandaire?
Can You Count to a Googol By Robert E. Wells
Value - How much a digit is worth according to its
place in a number
Digit - There are 10 digits; any one of the symbols:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
PlaceValuable Facts
A Million Dots By Andrew Clements
Exploring Place and Space - An Out of this World
Unit on Place Value
Trade Book Lessons
Place Value/ How Much Is A Million?
Rounding – Changing a given number to the
nearest multiple of ten, hundred, thousand, etc.
that it falls between on a number line
Compare – Seeing whether two numbers are equal,
greater than, or less than each other.
Standard Form - Using digits to express a number.
Example: 123,456
Written Form - Using words to express a number.
Example: one hundred twenty-three thousand, four
hundred fifty-six.
11
Revised: 8/4/14
SOL 4.1 – 1st Nine Weeks
Expanded Form - a way to break up a number to
show how much each digit in the number
represents. Example: 100,000 + 20,000 + 3,000 +
400 + 50 + 6
Greater Than - >
Less Than - <
Equal To - =
Whole Number – 0, 1, 2, 3, …
Other Words to Consider: Ones, Tens, Hundreds,
Thousands, Ten Thousands, Hundred Thousands,
Millions, Base 10, Inequality, Periods
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
12
Revised: 8/4/14
SOL 4.4 a, b, d – 1st Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
Blueprint Categories
Grade 4 SOL
Number of
Items
Computation and Estimation
4.4a-d, 4.5a-d
13
SOL 4.4 a, b, d – 1st Nine Weeks
The student will
a) estimate sums and differences of whole numbers;
b) add, subtract whole numbers;
d) solve single-step and multistep addition and subtraction problems
with whole numbers.
Prior Knowledge
Related SOL
(3.4) estimate and solve single-step and multi -step problems involving the sum
or difference of two whole numbers each 9,999 or less with or without
regrouping.
Understanding the Standard

A sum is the result of adding two or more numbers.

A difference is the amount that remains after one quantity is
subtracted from another.

An estimate is a number close to an exact solution. An estimate
tells about how much or about how many.

Different strategies for estimating include using compatible
numbers to estimate sums and differences and using front-end
estimation for sums and differences.
– Compatible numbers are numbers that are easy to work with
mentally. Number pairs that are easy to add or subtract are
compatible. When estimating a sum, replace actual numbers
with compatible numbers (e.g., 52 + 74 can be estimated by
using the compatible numbers 50 + 75). When estimating a
Essential Understandings
All students should



Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections,
and representations to
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.
Estimate whole number sums and
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
Revised: 8/4/14
Understand how to solve single-step and
multistep problems using whole number
operations.
13
SOL 4.4 a, b, d – 1st Nine Weeks
difference, use numbers that are close to the original
numbers. Tens and hundreds are easy to subtract
(e.g., 83 – 38 is close to 80 – 40).
– The front-end strategy for estimating is computing with the
front digits. Front-end estimation for addition can be used
even when the addends have a different number of digits.
The procedure requires the addition of the values of the
digits in the greatest of the smallest number.
– For example:
2367
243
+ 1186



with or without regrouping, using
paper and pencil, and using a
calculator.

Solve single-step and multistep
problems using whole number
operations.

Verify the reasonableness of sums
and differences of whole numbers
using estimation.
2300
200
+ 1100
3600

Front-end or leading-digit estimation always gives a sum less
than the actual sum; however, the estimate can be adjusted or
refined so that it is closer to the actual sum.

Addition is the combining of quantities; it uses the following
terms:
addend  45,623
addend  + 37,846
sum  83,469

Subtraction is the inverse of addition; it yields the difference
between two numbers and uses the following terms:
minuend  45,698
subtrahend  – 32,741
difference  12,957

Before adding or subtracting with paper and pencil, addition and
subtraction problems in horizontal form should be rewritten in
vertical form by lining up the places vertically.

Using Base-10 materials to model and stimulate discussion about
a variety of problem situations helps students understand
regrouping and enables them to move from the concrete to the
pictorial, to the abstract. Regrouping is used in addition and
subtraction algorithms. In addition, when the sum in a place is 10
14
Revised: 8/4/14
SOL 4.4 a, b, d – 1st Nine Weeks
or more, is used to regroup the sums so that there is only one
digit in each place. In subtraction, when the number (minuend)
in a place is not enough from which to subtract, regrouping is
required.

A certain amount of practice is necessary to develop fluency with
computational strategies for multidigit numbers; however, the
practice must be meaningful, motivating, and systematic if
students are to develop fluency in computation, whether
mentally, with manipulative materials, or with paper and pencil.

Calculators are an appropriate tool for computing sums and
differences of large numbers, particularly when mastery of the
algorithm has been demonstrated.
Additional Instructional Strategies
Play Video
Array Model for Multiplication (grades 3-8)
Play Video
Multi-Step Problem Solving (grades 4-8) Handout available: Multi-Step Problem Solving (PPT)
Alternative Subtraction Methods
Additional Math Curriculum Resources
15
Revised: 8/4/14
SOL 4.4 a, b, d – 1st Nine Weeks
Vocabulary
Lessons and TEI Items
Trade Books
Number and Number Sense
Math Curse By Jon Scieszka and Lane Smith
Estimation Game - Computation and Estimation
Counting on Frank By Rod Clement
Modeling Addition and Subtraction - Computation and
Estimation
Great Estimations By Bruce Goldstone
Word Wall Instructional Video
Let's Do Lunch! - Computation and Estimation
Greater Estimations By Bruce Goldstone
Sum - The answer in an addition problem
Subtraction with Regrouping
Trade Book Lessons
Difference – The answer to a subtraction problem
Reasonable Estimates
Vocabulary Word Wall
Handout available: Working with Vocabulary / Concept
Development (Word)
Number Sentence – An equation 3+4=7
Rounding – Changing a given number to the
nearest multiple of ten, hundred, thousand, etc.
that it falls between on a number line
Estimation – Using mental math and/or rounding to
give an approximate sum or difference
Other words/phrases to consider:
A little more/less than, Between, Closer to,
Compatible numbers, Approximate, Equation
16
Revised: 8/4/14
SOL 4.4 a, b, d – 1st Nine Weeks
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
17
Revised: 8/4/14
SOL 4.14 – 1st Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.14 – 1st Nine Weeks
The student will collect, organize, display, and interpret data from a variety of
graphs.
Blueprint Categories
Grade 4 SOL
Number of
Items
Probability, Statistics, Patterns,
Functions and Algebra
4.13a-b, 4.14, 4.15,
4.16a-b
12
Prior Knowledge
(3.17) collect and organize data to construct a line plot, picture graph, or
bar graph, read and interpret data and write a sentence analyzing the data
Understanding the Standard

Data analysis helps describe data, recognize patterns or trends,
and make predictions.

Investigations involving practical data should occur frequently, and
data can be collected through brief class surveys or through more
extended projects taking many days.


Essential Understandings
All students should

Understand the difference
between representing
categorical data and
representing numerical data.
Students formulate questions, predict answers to questions under
investigation, collect and represent initial data, and consider
whether the data answer the questions.

Line graphs are used to show how two continuous variables are
related. Line graphs may be used to show how one variable
changes over time. If this one variable is not continuous, then a
broken line is used. By looking at a line graph, it can be
determined whether the variable is increasing, decreasing, or
staying the same over time.

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
Understand that line graphs
show change over time
(numerical data).
18
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication, mathematical
reasoning, connections, and representations to

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,
Revised: 8/4/14
SOL 4.14 – 1st Nine Weeks
– The values along the horizontal axis represent continuous data
on a given variable, usually some measure of time (e.g., time
in years, months, or days). The data presented on a line
graph is
referred to as “continuous data,” as it represents data
collected over a continuous period of time.
– The values along the vertical axis are the scale and represent
the frequency with which those values occur in the data set.
The values should represent equal increments of multiples
of whole numbers, fractions, or decimals, depending upon
the data being collected. The scale should extend one
increment above the greatest recorded piece of data.
– Each axis should be labeled, and the graph should be given a
title.
– A line graph tells whether something has increased, decreased,
or stayed the same with the passage of time. Statements
representing an analysis and interpretation of the
characteristics of the data in the graph should be included
(e.g., trends of increase and/or decrease, and least and
greatest).

interpreted so that informed
decisions can be made.

Understand that the title and
labels of the graph provide the
foundation for interpreting the
data.
Bar graphs should be used to compare counts of different
categories (categorical data). Using grid paper ensures more
accurate graphs.
– A bar graph uses parallel, horizontal or vertical bars to
represent counts for several categories. One bar is used for
each category, with the length of the bar representing the
count for that category.
– There is space before, between, and after the bars.
– The axis that displays the scale representing the count for the
categories should extend one increment above the greatest
recorded piece of data. Fourth-grade students should collect
data that are recorded in increments of whole numbers,
usually multiples of 1, 2, 5, 10, or 100.
– Each axis should be labeled, and the graph should be given a
title.
– Statements representing an analysis and interpretation of the
characteristics of the data in the graph (e.g., similarities and
19
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 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.
Revised: 8/4/14
SOL 4.14 – 1st Nine Weeks
differences, least and greatest, the categories, and total
number of responses) should be written.
Additional Instructional Strategies
Integrate data and graphing in science experiments. Students should have experiences making graphs to display and analyze data collected in science experiments
throughout the year.
Weather and Math: Data and Graphs
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Trade Books
Vocabulary Word Wall
Probability and Statistics - Probability and Statistics
Ten Minute Math – Graph Stories
Handout available: Working with Vocabulary /
Concept Development (Word)
Hot or Cold? - Probability and Statistics
Lemonade for Sale By Stuart J Murphy
Miss Pettigrew’s Unique Phone Number
The Great Graph Contest By Loreen Leedy
Football Fanatics
Tally Cat Keeps Track By Trudy Harris
Passport to the Americas
Trade Book Lessons
Word Wall Instructional Video
Data Information collected and recorded
Line graph A graph that connects points to show
how data changes over time
Carnival Craze
Bar graph A graph using bars to show data
Fast Food Discovery
Interval The number that is the difference between
Gone Graphing
20
Revised: 8/4/14
SOL 4.14 – 1st Nine Weeks
two consecutive numbers on a scale (increments)
Fall Festival
Scale Numbers that show the units used on a graph
Adventure Land
Trend Pattern (increasing or decreasing) in the data
on a line graph, can used be used to predict data
Other Words to consider: Horizontal Axis, Vertical
Axis, Interpret, Analyze, Decrease, Increase
Book Fair Fascination
Carnival Capers!!
Let's Go to the Movies!
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
21
Revised: 8/4/14
SOL 4.4 a, b, d – 1st Nine Weeks – (2)
Dinwiddie County Public Schools
Math Curriculum
Blueprint Categories
Grade 4 SOL
Number of
Items
Computation and Estimation
4.4a-d, 4.5a-d
13
SOL 4.4 a, b, d – 1st Nine Weeks – (2)
The student will
a) estimate products of whole numbers;
b) multiply whole numbers;
d) solve single-step and multistep addition, subtraction, and
multiplication problems with whole numbers.
Prior Knowledge
3.5 Recall multiplication and division fact through the nines table.
3.6 Area and set models to create and solve problems using whole numbers
Understanding the Standard

The terms associated with multiplication are
factor  376
factor   23
product  8,648

One model of multiplication is repeated addition.

Another model of multiplication is the “Partial Product” model.
24
3
12  Multiply the ones: 3  4 = 12
+ 60  Multiply the tens: 3  20 = 60
72

Essential Understandings
All students should

Understand that multiplication and
division are inverse operations.

Understand how to solve single-step
and multistep problems using whole
number operations.
Another model of multiplication is the “Area Model” (which also
represents partial products) and should be modeled first with Base-10
22
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections,
and representations to

Estimate whole number sums,
products.

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 when one
factor has two digits or fewer and
the other factor has three digits or
fewer, using paper and pencil and
Revised: 8/4/14

SOL 4.4 a, b, d – 1st Nine Weeks – (2)
blocks. (e.g., 23 x 68)
calculators.

Students should continue to develop fluency with single-digit
multiplication facts and their related division facts.

Calculators should be used to solve problems that require tedious
calculations.

Estimation should be used to check the reasonableness of the
product. Examples of estimation strategies include the following:
– The front-end method: multiply the front digits and then complete
the product by recording the number of zeros found in the
factors. It is important to develop understanding of this process
before using the step-by-step procedure.
523  500
 31   30
15,000

Solve single-step and multistep
problems using whole number
operations.

Verify the reasonableness of
products of whole numbers using
estimation.
– This is 3  5 = 15 with 3 zeros.
– Compatible numbers: replace factors with compatible numbers,
and then multiply. Opportunities for students to discover
patterns with 10 and powers of 10 should be provided.
64  64
 11   10
Additional Instructional Strategies
Lattice Method for Multiplication Video and examples
23
Revised: 8/4/14
SOL 4.4 a, b, d – 1st Nine Weeks – (2)
4.4a Students need additional practice estimating decimals and/or whole numbers and solving problems. Students should be able to choose the BEST estimate.
Additional Math Curriculum Resources
24
Revised: 8/4/14
SOL 4.4 a, b, d – 1st Nine Weeks – (2)
Vocabulary
Vocabulary Word Wall
Handout available: Working with Vocabulary / Concept
Development (Word)
Word Wall Instructional Video
Multiple The product of any two whole numbers
Product The answer to a multiplication problem
Factor The numbers multiplied together to find a
product
Lessons and TEI Items
Estimation Game - Computation and Estimation
Multiplying and Trading - Computation and Estimation
Let's Do Lunch! - Computation and Estimation
Multiplication: A Treasure Hunt to Two and Three
Digit by One Digit Multiplication
Trade Books
One Grain of Rice By Demi
Amanda Beans Amazing Dream By Cindy
Neuschwander
The Grapes of Math By Greg Tang
The Best of Times By Greg Tang
Smiling at Two Digit Multiplication
Trade Book Lessons
Multiplication Magic
Array A way of displaying objects in rows and
columns
Inverse Two operations that are the opposite of
each other (subtraction and addition are inverse
operations; multiplication and division are inverse
operations)
Multiplier The number you are multiplying by
25
Revised: 8/4/14
SOL 4.4 a, b, d – 1st Nine Weeks – (2)
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
26
Revised: 8/4/14
SOL 4.5a – 1st Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.5a – 1st Nine Weeks
The student will
a) determine common multiples and factors, including least common
multiple and greatest common factor;
Blueprint Categories
Grade 4 SOL
Number of
Items
Computation and Estimation
4.4a-d, 4.5a-d
13
Prior Knowledge
3.5 recall multiplication facts through the twelves table
Understanding the Standard

A factor of a number is an integer that divides evenly into that number with a
remainder of zero.
Essential Understandings
All students should

Understand and identify common multiples
and common factors.
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections,
and representations to

A factor of a number is a divisor of the number.

A multiple of a number is the product of the number and any natural
number.

Find common multiples and
common factors of numbers.

A common factor of two or more numbers is a divisor that all of the numbers
share.


The least common multiple of two or more numbers is the smallest common
multiple of the given numbers.
Determine the least common
multiple and greatest common
factor of numbers..

The greatest common factor of two or more numbers is the largest of the
common factors that all of the numbers share.
27
Revised: 8/4/14
SOL 4.5a – 1st Nine Weeks
Additional Instructional Strategies
Students need additional practice determining common multiples and factors, including least common multiple and greatest common factor.
Additional Math Curriculum Resources
Vocabulary
Vocabulary Word Wall
Handout available: Working with Vocabulary / Concept
Development (Word)
Lessons and TEI Items
Trade Books
Factor Frenzy - Computation and Estimation, Number
and Number Sense
Multiple Madness - Computation and Estimation,
Number and Number Sense
28
Revised: 8/4/14
SOL 4.5a – 1st Nine Weeks
Word Wall Instructional Video
Number Ray Investigators - Computation and
Estimation, Number and Number Sense
Common Factors factors that are shared between
two or more numbers
Finding Factors, Making Multiples - Computation and
Estimation, Number and Number Sense
Common multiples multiples that are shared by two
or more numbers
Smart Cookie Factors
Greatest common factor the factor with the
greatest value that is shared between two or more
numbers
Least common multiple the multiple with the least
value that is shared between two or more numbers
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
29
Revised: 8/4/14
SOL 4.4a,c,d – 2nd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
Blueprint Categories
Grade 4 SOL
Number of
Items
Computation and Estimation
4.4a-d, 4.5a-d
13
SOL 4.4 a, c, d –2nd Nine Weeks
The student will
a) estimate quotients of whole numbers;
c) divide whole numbers, finding quotients with and without
remainders; and
d) solve single-step and multistep addition, subtraction, and
multiplication problems with whole numbers.
Understanding the Standard

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. Both situations may be modeled with Base-10
manipulatives.

Multiplication and division are inverse operations.

Terms used in division are dividend, divisor, and quotient.
dividend  divisor = quotient
quotient
divisor ) dividend

Opportunities to invent division algorithms help students make
sense of the algorithm. Teachers should teach division by various
methods such as repeated multiplication and subtraction (partial
quotients) before teaching the traditional long division
algorithm.
Prior Knowledge
3.5 Recall multiplication and division fact through the nines table.
3.6 Area and set models to create and solve problems using whole numbers.
Essential Understandings
All students should

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
30
dividend
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication, mathematical
reasoning, connections, and representations
to

Estimate whole number quotients.

Refine estimates by adjusting the final
amount, using terms such as closer to,
between, and a little more than.

Estimate and find the quotient of two
whole numbers, given a one-digit divisor
and a two- or three-digit dividend.

Solve single-step and multistep problems
using whole number operations.

Verify the reasonableness of quotients of
whole numbers using estimation.
Revised: 8/4/14
SOL 4.4a,c,d – 2nd Nine Weeks

Understand how to solve single-step and multistep
problems using whole number operations.
Additional Instructional Strategies
Partial Products Video
SOL 4.4a includes estimation of products of whole numbers. In particular, students need additional practice with problems presented in context for which an
estimated product is the solution, as in the examples provided.
For SOL 4.4d, students need additional practice solving single-step and multistep addition, subtraction, and multiplication problems with whole numbers. In
particular, student performance was inconsistent when one or more of the steps involved multiplication.
The first example is a single-step multiplication problem, and the second is a multistep problem involving both addition and multiplication. It should be noted that
students could choose to use addition to find the correct answers to both problems, although using multiplication is more efficient.
31
Revised: 8/4/14
SOL 4.4a,c,d – 2nd Nine Weeks
Vocabulary
Vocabulary Word Wall
Handout available: Working with Vocabulary / Concept
Development (Word)
Word Wall Instructional Video
Dividend The number to be divided
Divisor The number by which another number is
divided
Lessons and TEI Items
Estimation Game - Computation and Estimation
Pears in a Basket - Computation and Estimation
Defining Division
Trade Books
The Doorbell Rang By Pat Hutchins
A Remainder of One By Elinor Pinczes
Divide and Ride By Stuart J Murphy
March of the Dividing Ant
The School Store
The Multiplying Menace Divides By Pam Calvert
Trade Book Lessons
Fraction Action
Quotient The answer to a division problem
Remainder The number that remains or is leftover
after the division is complete
32
Revised: 8/4/14
SOL 4.4a,c,d – 2nd Nine Weeks
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
iPad™ Resources
33
Revised: 8/4/14
SOL 4.4a,c,d – 2nd Nine Weeks
Manipulatives
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Super Teacher Worksheets
Worksheet Fun
34
Revised: 8/4/14
SOL 4. 15 – 2nd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.15 – 2nd Nine Weeks
The student will recognize, create, and extend numerical and geometric
patterns.
Blueprint Categories
Grade 4 SOL
Number of
Items
Probability, Statistics, Patterns,
Functions and Algebra
4.13a-b, 4.14, 4.15,
4.16a-b
12
Prior Knowledge
3.24 Recognize and describe a variety of patterns formed using concrete
objects, pictures, tables, and extend the pattern using the same or different
forms.
Understanding the Standard



Most patterning activities should involve some form of concrete
materials to make up a pattern.
– Students will identify and extend a wide variety of patterns,
including rhythmic, geometric, graphic, numerical, and
algebraic. The patterns will include both growing and repeating
patterns.
Essential Understandings
All students should

Understand that patterns and
functions can be represented in many
ways and described using words,
tables, graphs, and symbols.
Reproduction of a given pattern in a different representation, using
symbols and objects, lays the foundation for writing the relationship
symbolically or algebraically.
Tables of values should be analyzed for a pattern to determine the
next value.
35
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections,
and representations to

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.
Revised: 8/4/14
SOL 4. 15 – 2nd Nine Weeks
Additional Instructional Activities
Teachers are encouraged to provide practice with patterns presented in a variety of formats. The examples provided include a number pattern presented in a
list, as shown in number one, and a number pattern presented within a horizontal table, as shown in number two.
36
Revised: 8/4/14
SOL 4. 15 – 2nd Nine Weeks
Students also need additional practice with geometric patterns. Students could find the solution to the example shown by drawing triangles to create the next
figure or by recognizing the pattern that exists in the number of triangles used to create each figure. The sixth figure will have six rows of triangles, with six
triangles in each row, for a total of 36 triangles.
Additional Math Curriculum Resources
37
Revised: 8/4/14
SOL 4. 15 – 2nd Nine Weeks
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
Toothpick and Staircase Patterns - Patterns,
Functions, and Algebra
Handout available: Working with Vocabulary / Concept
Development (Word)
Patterning Through the Rainforest
Word Wall Instructional Video
Pepe's Problematic Pizzeria
Extend Continue a pattern using a growing or
repeating rule
Fun Functions
Trade Books
Roller Functions!
Geometric pattern Pattern using geometric figures
Building Patterns with Polygons
Growing pattern Pattern using a rule that increases
as the pattern continues (the rule changes the same Describing, Extending and Generating, Growing
way in a predictable way)
Patterns and Numeric Patterns
Numerical pattern Pattern using numbers
Repeating pattern Pattern using a repeating rule
(numbers change the same way each time)
Out of This World Multiplication
Exploring Growing Patterns
Function Fun
Patterns/Algebraic Thinking (More lessons)
38
Revised: 8/4/14
SOL 4. 15 – 2nd Nine Weeks
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
39
Revised: 8/4/14
SOL 4.16 – 2nd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.16 – 2nd Nine Weeks
Blueprint Categories
Grade 4 SOL
Number of
Items
Probability, Statistics, Patterns,
4.13a-b, 4.14, 4.15,
4.16a-b
12
Functions and Algebra
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
3.25
multiplication.
Prior Knowledge
a) investigate and create patterns involving numbers, operations + X, and
relationships
b) understanding equality =
Understanding the Standard



Investigating arithmetic operations with whole
numbers helps students learn about several different
properties of arithmetic relationships. These
relationships remain true regardless of the numbers.
The commutative property for addition states that
changing the order of the addends does not affect the
sum (e.g., 4 + 3 = 3 + 4). Similarly, the commutative
property for multiplication states that changing the
order of the factors does not affect the product (e.g.,
2  3 = 3  2).
The associative property for addition states that the
sum stays the same when the grouping of addends is
changed [e.g., 15 + (35 + 16) = (15 + 35) + 16]. The
Essential Understandings
All students should




Essential Knowledge and Skills
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Understand that mathematical
relationships can be expressed using
equations.

Understand that quantities on both
sides of an equation must be equal.
Recognize and demonstrate that the equals sign
(=) relates equivalent quantities in an equation.

Write an equation to represent 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
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
40
Revised: 8/4/14
SOL 4.16 – 2nd Nine Weeks
associative property for multiplication states that the
product stays the same when the grouping of factors
is changed [e.g., 6  (3  5) = (6  3)  5].
more factors without changing the
product.
for multiplication as (3 x 2) x 4 = 3 x (2 x 4).
Additional Instructional Activities
Play Video
Properties (grades 3-8)
Play Video
Associative Property for Addition (grades 4-8)
Additional Math Curriculum Resources
41
Revised: 8/4/14
SOL 4.16 – 2nd Nine Weeks
Vocabulary
Vocabulary Word Wall
Handout available: Working with Vocabulary /
Concept Development (Word)
Lessons and TEI Items
Trade Books
What's It Worth? - Patterns, Functions, and
Algebra
Outside Algebra
Word Wall Instructional Video
Associative property Addends/factors can be
regrouped and the sum/product remains the same
Commutative property Addends/factors can be
added/multiplied in any order and the sum/product
remains the same
Equation A balanced number sentence using
computation symbols
Equivalent Equal
42
Revised: 8/4/14
SOL 4.16 – 2nd Nine Weeks
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
43
Revised: 8/4/14
SOL 4.2 a,b,c – 2nd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
Blueprint Categories
Grade 4 SOL
Number of
Items
Number and Number Sense
4.1a-c, 4.2a-c, 4.3a-d
12
SOL 4.2 a,b,c – 2nd Nine Weeks
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.
Prior Knowledge
K-2 identify and write fractions for halves, thirds, fourths, sixths, eighths, and tenths
(3.3) identify, write, fractions using a model that include mixed numbers, model
fractions including mixed numbers, and write the fraction names; compare like and
unlike denominators
Understanding the Standard
Essential Understandings
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections,
and representations to

A fraction is a way of representing part of a whole (as in a
region/area model or a measurement model) or part of a group
(as in a set model). A fraction is used to name a part of one
thing or a part of a collection of things.
All students should
 Develop an understanding of fractions as
parts of unit wholes, as parts of a collection,
and as locations on a number line.

In the area/region and length/measurement fraction models,
the parts must be equal. In the set model, the elements of the
set do not have to be equal (i.e., “What fraction of the class is
wearing the color red?”).

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.

The denominator tells how many equal parts are in the whole or
set. The numerator tells how many of those parts are being
counted or described.

Use models, benchmarks, and equivalent
forms to judge the size of fractions.

When fractions have the same denominator, they are said to
have “common denominators” or “like denominators.”
Comparing fractions with like denominators involves comparing

Recognize that a whole divided into nine
equal parts has smaller parts than if the
whole had been divided into five equal
parts.
44

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 parts (numerators) (e.g.,
1 3
5 < 5 ).

Compare and order fractions with
Revised: 8/4/14
SOL 4.2 a,b,c – 2nd Nine Weeks
only the numerators.



Strategies for comparing fractions having unlike denominators
may include
1
– comparing fractions to familiar benchmarks (e.g., 0, , 1);
2
– finding equivalent fractions, using manipulative models such
as fraction strips, number lines, fraction circles, rods,
pattern blocks, cubes, Base-10 blocks, tangrams, graph
paper, or a multiplication chart and patterns; and
– finding a common denominator by finding the least
common multiple (LCM) of both denominators and then
rewriting each fraction as an equivalent fraction, using
the LCM as the denominator.

size of the parts (e.g.,


Understand the division statement that
represents a fraction.
Equivalent fractions name the same amount. Students should
use a variety of models to identify different names for
equivalent fractions.

Students should focus on finding equivalent fractions of familiar
fractions such as halves, thirds, fourths, sixths, eighths, tenths,
and twelfths.
Decimals and fractions represent the same relationships;
however, they are presented in two different formats. The

Understand that the more parts the whole
is divided into, the smaller the parts (e.g.,
1 1
5 < 3 ).
A variety of fraction models should be used to expand students’
understanding of fractions and mixed numbers:
– Region/area models: a surface or area is subdivided into
smaller equal parts, and each part is compared with the
whole (e.g., fraction circles, pattern blocks, geoboards,
grid paper, color tiles).
– Set models: the whole is understood to be a set of objects,
and subsets of the whole make up fractional parts (e.g.,
counters, chips).
– Measurement models: similar to area models but lengths
instead of areas are compared (e.g., fraction strips, rods,
cubes, number lines, rulers).
A mixed number has two parts: a whole number and a fraction.

like numerators and unlike
denominators by comparing the
Recognize and generate equivalent forms
of commonly used fractions and decimals.
45
3 3
< ).
9 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).
Revised: 8/4/14
SOL 4.2 a,b,c – 2nd Nine Weeks
1
decimal 0.25 is written as 4 . When presented with the
3
fraction 5 , the division expression representing a fraction is
written as 3 divided by 5.
Additional Instructional Activities
Play Video
Models for Teaching Fractions (grades 3-8)
Play Video
Fraction Concepts (grades 4-8)
For SOL 4.2a, students need additional practice ordering fractions and mixed numbers. Teachers are encouraged to provide experiences that promote the use of a
variety of strategies when comparing and ordering fractions. In the first example provided, using ½ as a benchmark is a helpful strategy. Recognizing that 3/8 and
4/9 are both less than one-half, while 2/3 and 7/12 are both greater than one-half, enables the student to strategically order two sets of two fractions rather than
one set of four fractions. Opportunities that allow students to consider and apply a variety of methods for comparing and ordering fractions are encouraged.
To extend the second question, a teacher could ask students to write a number less than one that could be placed in the blank, or write a number greater than one
that could be placed in the blank.
46
Revised: 8/4/14
SOL 4.2 a,b,c – 2nd Nine Weeks
For this 4.2b, students also need additional practice identifying models that represent equivalent fractions and mixed numbers. Teachers are encouraged to
provide experiences in which students are asked to represent equivalent fractions and mixed numbers using more than one type of model. In the example
provided, students are given a number line model, but the options include a set model as well as area or region models. The fraction represented on the number
line at point A is 6/8. Each model that is a correct answer has been shaded to represent a fraction that is equivalent to 6/8.
Teachers are also encouraged to help students make connections between fractions and decimals whenever possible.
This ten-by-ten grid serves as both a fraction and a decimal model for 75/100. While the denominator of 100 is greater than the denominators included in SOL 4.2,
this extension provides a connection to the content included in SOL 4.3.
Students also have difficulty demonstrating an understanding of equivalent mixed numbers. In this example, students are given a model of a fraction greater than
one and asked to represent an equivalent number on a number line. The given model has been divided into tenths, while the number line has been divided into
fifths. One extension for this example is also provided, as well as connections to other SOL. To extend the concept further, teachers could require that the models
students generate in the extension activity be of a different type than the ones provided- for example, a set model.
47
Revised: 8/4/14
SOL 4.2 a,b,c – 2nd Nine Weeks
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Trade Books
Vocabulary Word Wall
Circle Fractions - Number and Number Sense
The Hershey’s Milk Chocolate Fractions Book By
Jerry Pallotta
Handout available: Working with Vocabulary /
Concept Development (Word)
Pattern Block Fractions - Number and Number Sense
The Wishing Club By Donna Jo Napoli
Pattern Blocks Fraction Game - Number and Number
Sense
Pizza Counting By Christina Dobson
Word Wall Instructional Video
Fraction Action By Loreen Leedy
Numerator the top number in a fraction that
represents the number of parts
Comparing Fractions - Number and Number Sense
Trade Book Lessons
Fraction Strips - Number and Number Sense
Denominator the bottom number in a fraction that
represents the number of equal that makes a whole
Candy Bar Fractions - Number and Number Sense
48
Revised: 8/4/14
SOL 4.2 a,b,c – 2nd Nine Weeks
Equivalent Equal
Number and Number Sense
Mixed numbers A number that has a whole number
and a fraction
Exploring Equivalent Fractions
Fractions In Action
Region/area model A fraction represented by parts
of a solid figure
Set model A fraction represented by parts of a set
Linear model A fraction represented by a number
line
Fractions on a Number Line
Marathon Markers (Comparing and Ordering
Fractions)
What Fraction Am I?
Wacky Weather
Improper Fraction A fraction in which the
numerator is equal or greater than the denominator
Flying Through Fractions!
A Do Something Day
Design a Flag
A Fraction of the Rain Forest
Fractions (See for additional lessons)
49
Revised: 8/4/14
SOL 4.2 a,b,c – 2nd Nine Weeks
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
50
Revised: 8/4/14
SOL 4.5 a, b, d – 2nd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.5 a, b, d – 2nd Nine Weeks
The student will
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; (the common denominator may
be larger than 12 when computing two or more fractions)
d) solve single-step and multistep practical problems involving addition
and subtraction with fractions.
Blueprint Categories
Grade 4 SOL
Number of
Items
Computation and Estimation
4.4a-d, 4.5a-d
13
Prior Knowledge
4.5a Determine common multiples and factors, including least common
multiple and greatest common factor (1st Nine Weeks)
3.5 Divide region and sets to represent a fraction. Name and write fractions.
3.11 Add and subtract fractions with like denominators.
Understanding the Standard

A factor of a number is an integer that divides evenly into that
number with a remainder of zero.

A factor of a number is a divisor of the number.

A multiple of a number is the product of the number and any
natural number.

A common factor of two or more numbers is a divisor that all of
the numbers share.

The least common multiple of two or more numbers is the
smallest common multiple of the given numbers.

The greatest common factor of two or more numbers is the
largest of the common factors that all of the numbers share.
Essential Understandings
All students should

Understand and use common
multiples and common factors for
simplifying fractions.

Develop and use strategies to estimate
addition and subtraction involving
fractions and decimals.

Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections, and
representations to

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.
Use visual models to add and subtract
with fractions and decimals.
51
Revised: 8/4/14
SOL 4.5 a, b, d – 2nd Nine Weeks

Students should investigate addition and subtraction with
fractions, using a variety of models (e.g., fraction circles, fraction
strips, rulers, linking cubes, pattern blocks).

When adding or subtracting with fractions having like
denominators, add or subtract the numerators and use the same
denominator. Write the answer in simplest form using common
multiples and factors.

When adding or subtracting with fractions having unlike
denominators, rewrite them as fractions with a common
denominator. The least common multiple (LCM) of the unlike
denominators is a common denominator (LCD). Write the answer
in simplest form using common multiples and factors.

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.

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.

Solve single-step and multistep
problems that involve adding and
subtracting with fractions.
Please note when computing fractions with unlike denominators the
common denominator may be larger than 12. See below.
Additional Instructional Strategies
Play Video
Fraction Computation (grades 4-8)
52
Revised: 8/4/14
SOL 4.5 a, b, d – 2nd Nine Weeks
The Butterfly Method is an alternative method to adding and
Subtracting fractions with unlike denominators.
Butterfly Method
SOL 4.5a, students need additional practice determining the least common multiple and the greatest common factor for a given set of numbers, as in the examples
provided.
53
Revised: 8/4/14
SOL 4.5 a, b, d – 2nd Nine Weeks
SOL 4.5d reads: The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and with decimals. Students
would benefit from additional practice solving multistep practical problems that require the addition and/or subtraction of fractions.
54
Revised: 8/4/14
SOL 4.5 a, b, d – 2nd Nine Weeks
Additional Math Curriculum Resources
Vocabulary
Vocabulary Word Wall
Handout available: Working with Vocabulary /
Concept Development (Word)
Lessons and TEI Items
Trade Books
Fraction Strip Subtraction - Computation and
Estimation
Fraction Strip Addition - Computation and
Estimation
Word Wall Instructional Video
Four in a Row - Computation and Estimation
Common factors Factors that are shared between
two or more numbers
Common multiples Multiples that are shared by
two or more numbers
Fraction Riddles - Computation and Estimation
Which Is Closer? - Computation and Estimation
Fraction Fever
55
Revised: 8/4/14
SOL 4.5 a, b, d – 2nd Nine Weeks
Greatest common factor The factor with the
greatest value that is shared between two or more
numbers
Fractions In Action
Harvey's Pencil Box
Least common multiple The multiple with the least
value that is shared between two or more numbers
Simplest form A fraction in which the numerator
and denominator have no common factors other
than 1
Simplify (Reduce, Lowest Terms) Using GCF to put a
fraction into simplest form
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
56
Revised: 8/4/14
SOL 4.3 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.3 – 3rd Nine Weeks
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.



Grade 4 SOL
Number of Items
Number and Number Sense
4.1a-c, 4.2a-c, 4.3a-d
12
Prior Knowledge
1st year decimals are introduced
Understanding the Standard

Blueprint Categories
Essential Understandings
The structure of the Base-10 number system is based upon a simple
pattern of tens, where each place is ten times the value of the place
to its right. This is known as a ten-to-one place value relationship.

Understanding the system of tens means that ten tenths represents
one whole, ten hundredths represents one tenth, ten thousandths
represents one hundredth.
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
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.
57
A decimal point separates the whole number places from the places
that are less than one. Place values extend infinitely in two
directions from a decimal point. A number containing a decimal
point is called a decimal number or simply a decimal.
To read decimals,
– read the whole number to the left of the decimal point, if there
is one;
– read the decimal point as “and”;
– read the digits to the right of the decimal point just as you
All students should
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

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
Revised: 8/4/14
SOL 4.3 – 3rd Nine Weeks
would read a whole number; and
– say the name of the place value of the digit in the smallest
place.
 Any decimal less than 1 will include a leading zero (e.g., 0.125).

Decimals may be written in a variety of forms:
– Standard: 26.537
– Written: twenty-six and five hundred thirty-seven thousandths
– Expanded: (2  10) + (6  1) + (5  0.1) +
(3  0.01) + (7 
0.001).

Decimals and fractions represent the same relationships; however,
they are presented in two different formats. The decimal 0.25 is
1
written as 4 . Decimal numbers are another way of writing
3
fractions. When presented with the fraction 5 , the division
expression representing a fraction is written as 3 divided by 5. The
Base-10 models concretely relate fractions to decimals (e.g., 10-by10 grids, meter sticks, number lines, decimal squares, money).

numerical symbols (e.g., relate
the appropriate drawing to
0.05).
Understand that models are used to show
decimal and fraction equivalents.

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 manipulatives,
drawings, and numerical
symbols.

Round decimals to the nearest
whole number, tenth, and
hundredth.

The procedure for rounding decimal numbers is similar to the
procedure for rounding whole numbers.

Compare decimals, using the
symbols >, <, =.

A strategy for rounding decimal numbers to the nearest tenth and
hundredth is as follows:
– Look one place to the right of the digit you want to round to.
– If the digit is 5 or greater, add 1 to the digit in the rounding
place, and drop the digits to the right of the rounding place.
– If the digit is less than 5, leave the digit in the rounding place as
it is, and drop the digits to the right of the rounding place.

Order a set of decimals from
least to greatest or greatest to
least.

Represent fractions for halves,
fourths, fifths, and tenths as
decimals through hundredths,
using concrete objects (e.g.,
demonstrate the relationship
1
between the fraction 4 and its
decimal equivalent 0.25).

Relate fractions to decimals,
using concrete objects (e.g., 10by-10 grids, meter sticks,
 Different strategies for rounding decimals include:
– Use a number line to locate a decimal between two numbers.
For example, 18.83 is closer to 18.8 than to 18.9.
– Compare the digits in the numbers to determine which number
is greater (or which is less).
– Compare the value of decimals, using the symbols >, <, = (e.g.,
0.83 > 0.8 or 0.19 < 0.2).
– Order the value of decimals, from least to greatest and greatest
58
Revised: 8/4/14
SOL 4.3 – 3rd Nine Weeks
to least (e.g., 0.83, 0.821, 0.8 ).


number lines, decimal squares,
decimal circles, money [coins]).
Decimal numbers are another way of writing fractions (halves,
fourths, fifths, and tenths). The Base-10 models concretely relate
fractions to decimals (e.g., 10-by-10 grids, meter sticks, number
lines, decimal squares, decimal circles money).

Provide a fraction model (halves, fourths, fifths, and tenths) and ask
students for its decimal equivalent.
– Provide a decimal model and ask students for its fraction
equivalent .
Write the decimal and fraction
equivalent for a given model
1
1
(e.g., 4 = 0.25 or 0.25 = 4 ).
Additional Instructional Strategies
SOL 4.3b requires students to round decimals to the nearest whole number, tenth, and hundredth. This continues to be an area in which students would benefit
from additional practice. Students perform better on questions in which they round a number to a given place value, but they have more difficulty when
determining which numbers, when rounded, would result in a given number, as shown in example one.
The answers to the first example are shown on the screen.
Questions like example two are also more challenging to students. This example requires students to apply the skill of rounding to more than one place value.
Look at the answer in the second row, second column. When rounding 1,498.954 to the nearest tenth, students must change not only the digit in the tenths place
but also the digit in the ones place in order to round the number correctly. It is also important to recognize that some students may answer 1,499 rather than
1,499.0 . While both of these numbers are equivalent, it is impossible to know from the answer 1,499, without discussion, whether the student rounded to the
nearest ones place, rather than the tenths place, or rounded to the nearest tenths place and answered an equivalent. For this reason, 1,499.0 is shown, as this
definitely indicates that the number 1,498.954 was rounded to the tenths place.
59
Revised: 8/4/14
SOL 4.3 – 3rd Nine Weeks
SOL 4.3c Students need additional practice comparing and ordering decimals of different ending place values.
SOL 4.3d Students need additional practice identifying equivalent fractions and decimals when presented with a model. Experience with decimal models that have
been shaded in a variety of ways is important.
60
Revised: 8/4/14
SOL 4.3 – 3rd Nine Weeks
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Trade Books
Fractions, Decimals, and Percents By David Adler
Vocabulary Word Wall
Handout available: Working with Vocabulary /
Concept Development (Word)
Reading and Writing Decimals - Number and
Number Sense
Piece = Part = Portion By Scott Gifford
Rounding Decimals - Number and Number Sense
Trade Book Lessons
Word Wall Instructional Video
Comparing Decimals - Number and Number Sense
Decimal Number A number that contains a whole
number and a number representing a fractional
part separated by a decimal point ex. 0.57, 15.2
Fraction Grids - Number and Number Sense
Number and Number Sense
Decimal Point a dot used to separate dollars from
cents or whole numbers from tenths (numbers less
than one)
Don't Be Bugged By Decimals Lessons
PlaceValuable Facts (whole # and decimal lessons)
Tenth 1/10 = 0.1
61
Revised: 8/4/14
SOL 4.3 – 3rd Nine Weeks
Decimals Decide Olympic Champions!
Hundredth 1/100 = 0.01
Decimals in the Dugout (Place Value) Pt. I | Pt. II |
Pt. III
Thousandth 1/1000=0.001
Go One.On.One With Decimals
Place Value of Decimals to Hundredths: Diving For
Decimals
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
StarrMatica
New York State Assessments
*Multiple Languages
Math Study Jams
NCTM Illuminations
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
62
Revised: 8/4/14
SOL 4.5 c, d – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.5 c, d – 3rd Nine Weeks
The student will
c) add and subtract with decimals; and
d) solve single-step and multistep practical problems involving addition
and subtraction with decimals.
Blueprint Categories
Grade 4 SOL
Number of
Items
Computation and Estimation
4.4a-d, 4.5a-d
13
Prior Knowledge
4.3 read, write, identify decimals; round and compare decimals
Understanding the Standard



Addition and subtraction of decimals may be explored, using a variety
of models (e.g., 10-by-10 grids, number lines, money).
For decimal computation, the same ideas developed for whole
number computation may be used, and these ideas may be applied to
decimals, giving careful attention to the placement of the decimal
point in the solution. Lining up tenths to tenths, hundredths to
hundredths, etc. helps to establish the correct placement of the
decimal.
Essential Understandings
All students should

Develop and use strategies to estimate
addition and subtraction involving
decimals.

Use visual models to add and subtract
with decimals.
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

Add and subtract with decimals
through thousandths, using
concrete materials, pictorial
representations, and paper and
pencil.

Solve single-step and multistep
problems that involve adding
and subtracting with decimals
through thousandths.
Fractions may be related to decimals by using models (e.g., 10-by-10
grids, decimal squares, money).
63
Revised: 8/4/14
SOL 4.5 c, d – 3rd Nine Weeks
Additional Instructional Strategies
Students should be expected to estimate all decimals to check reasonableness of their answers using mental math.
Example: 12.45 + 8.4 = 13 + 8 = 21
If students line up the decimals incorrectly, the mistake will quickly be realized if the estimate is determined first.
12.45
+8.4
13.29 or 1.329 Neither answer can be correct because the answer should be close to 21. Students should recognize the mistake of not lining up the place values
correctly.
SOL 4.5c includes adding and subtracting decimals. Students performed better on items involving addition than on items involving subtraction. In particular,
performance indicates that students would benefit from additional practice finding the difference when given decimals represented by models, as in the example
provided.
Additional Math Curriculum Resources
64
Revised: 8/4/14
SOL 4.5 c, d – 3rd Nine Weeks
Vocabulary
Lessons and TEI Items
Word Wall Instructional Video
Handout available: Working with Vocabulary /
Concept Development (Word)
Trade Books
Decimal Sums and Differences - Computation
and Estimation
Problem Solving - Computation and Estimation
Vocabulary Word Wall
I'll Have an Order of Subtraction, Please!
Review Sum, Difference
When Life Serves You Lemons!
Kids 'R Kings Katering
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
65
Revised: 8/4/14
SOL 4.5 c, d – 3rd Nine Weeks
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
66
Revised: 8/4/14
SOL 4.13 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.13 - 3rd Nine Weeks
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.
Blueprint Categories
Grade 4 SOL
Number of
Items
Probability, Statistics, Patterns,
Functions and Algebra
4.13a-b, 4.14, 4.15,
4.16a-b
12
Prior Knowledge
3.18 investigate and describe the concept of probability as chance and list
possible results of a given situation
Understanding the Standard

Essential Understandings
A spirit of investigation and experimentation should permeate
probability instruction, where students are actively engaged in
explorations and have opportunities to use manipulatives.

Understand and apply basic concepts of
probability.

Probability is the chance of an event occurring.


The probability of an event occurring is the ratio of desired outcomes
to the total number of possible outcomes. If all the outcomes of an
event are equally likely to occur,
the probability of the event = number of favorable outcomes
total number of possible outcomes.
Describe events as likely or unlikely and
discuss the degree of likelihood, using
the terms certain, likely, equally likely,
unlikely, and impossible.


The probability of an event occurring is represented by a ratio
between 0 and 1. An event is “impossible” if it has a probability of 0
(e.g., the probability that the month of April will have 31 days). An
event is “certain” if it has a probability of 1 (e.g., the probability that
the sun will rise tomorrow morning).
All students should

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.
When a probability experiment has very few trials, the results can be
67
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

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
Revised: 8/4/14
SOL 4.13 – 3rd Nine Weeks
misleading. The more times an experiment is done, the closer the
experimental probability comes to the theoretical probability (e.g., a
coin lands heads up half of the time).

Conduct experiments to determine the probability of an event
occurring for a given number of trials (no more than 25 trials), using
manipulatives (e.g., the number of times “heads” occurs when flipping
a coin 10 times; the chance that when the names of 12 classmates are
put in a shoebox, a name that begins with D will be drawn).

Students should have opportunities to describe in informal terms (i.e.,
impossible, unlikely, as likely as unlikely, equally likely, likely, and
certain) the degree of likelihood of an event occurring.

Activities should include practical examples.

For an event such as flipping a coin, the equally likely things that can
happen are called outcomes. For example, there are two equally likely
outcomes when flipping a coin: the coin can land heads up, or the coin
can land tails up.

For another event such as spinning a spinner that is one-third red and
two-thirds blue, the two outcomes, red and blue, are not equally
likely. This is an unfair spinner (since it is not divided equally),
therefore, the outcomes are not equally likely.
fewer.

Identify the likelihood of an
event occurring and relate it to
its fractional representation
(e.g., impossible/0; equally
1
likely/2 ; certain/1).

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.
Additional Instructional Strategies
For SOL 4.13b, students need additional practice representing the probability of a given situation on a number line. Examples are provided. In this first example,
students represent two different probabilities that are related to the same situation.
In the following two examples for SOL 4.13b, students must analyze a spinner to determine the probability of different outcomes. In the first question, students
must determine the probability of landing on a section that is NOT blue and then represent that probability on a number line. In question two, students determine
the probability of landing on a red section.
68
Revised: 8/4/14
SOL 4.13 – 3rd Nine Weeks
69
Revised: 8/4/14
SOL 4.13 – 3rd Nine Weeks
Additional Math Curriculum Resources
Vocabulary
Word Wall Instructional Video
Handout available: Working with Vocabulary /
Concept Development (Word)
Lessons and TEI Items
How Certain Are You? - Probability and
Statistics
Trade Books
Probably Pistachio By Stuart J Murphy
It’s Probably Penny By Loreen Leedy
Lucky Sums? - Probability and Statistics
Probability (likelihood)The chance that something
will happen, how likely it is that some event will
happen
Spinning Color - Probability and Statistics
Likely An event that probably will happen (greater
½)
Passionate About Probability
Unlikely An event that will probably not happen
(less than ½)
Certain An event that is sure to occur (1 on a
number line, 100%)
Looking for a Pet - Probability and Statistics
Pigs at Odds By Amy Axelrod and Sharon Nally
Trade Book Lessons
Let's Get Physical
Something's Fishy - Probability
Sweet Prediction Factory
Equally likely or As Likely As Unlikely An event that
is just as likely to happen as not to happen (1/2,
0.5, 50%)
Probability CHEX©plorations
Impossible An event that cannot occur (0 on a
number line, 0%)
Spin To Win
Outcomes possible results of a game, experiment
A Very Improbably Story By Edward Einhorn
Probability: How Much Can I Earn?
"The Unfair Fair"
Games Galore
70
Revised: 8/4/14
SOL 4.13 – 3rd Nine Weeks
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
StarrMatica
New York State Assessments
*Multiple Languages
Math Study Jams
NCTM Illuminations
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
71
Revised: 8/4/14
SOL 4.7 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
Blueprint Categories
Grade 4 SOL
Number of
Items
Measurement and Geography
4.6a-b, 4.7a-b, 4.8a-b,
4.9, 4.10a-b, 4.11a-b,
4.12a-b
13
SOL 4.7 – 3rd Nine Weeks
The student will
a) estimate and measure length, and describe the result in both
metric and U.S. Customary units; and
b) identify equivalent measurements between units within the U.S.
Customary system (inches and feet; feet and yards; inches and
yards; yards and miles) and between units within the metric
system (millimeters and centimeters; centimeters and meters;
and millimeters and meters).
Understanding the Standard

Length is the distance along a line or figure from one point to
another.

U.S. Customary units for measurement of length include
inches, feet, yards, and miles. Appropriate measuring devices
include rulers, yardsticks, and tape measures. Metric units for
measurement of length include millimeters, centimeters,
meters, and kilometers. Appropriate measuring devices
include centimeter ruler, meter stick, and tape measure.


Practical experience measuring the length of familiar objects
helps to establish benchmarks and facilitates the student’s
ability to estimate length.
Prior Knowledge
2.11 estimate and measure length to the nearest centimeter and inch
3.9 estimate and use customary and metric units to measure length to the
nearest half inch, inch, foot, yard, cm, meter
Essential Understandings
All students should

Use benchmarks to estimate and measure
length.

Understand how to convert units of length
between the U.S. Customary and metric
systems, using ballpark comparisons.

Understand the relationship between U.S.
Customary units and the relationship
between metric units.
Students should estimate the length of everyday objects (e.g.,
72
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections,
and representations to

Determine an appropriate unit of
measure (e.g., inch, foot, yard, mile,
millimeter, centimeter, and meter) to
use when measuring everyday objects
in both metric and U.S. Customary
units.

Estimate the length of everyday
objects (e.g., books, windows, tables)
in both metric and U.S. Customary
Revised: 8/4/14
SOL 4.7 – 3rd Nine Weeks
books, windows, tables) in both metric and U.S. Customary
units of measure.

units of measure.

Measure the length of objects in both
metric and U.S. Customary units,
1 1
measuring to the nearest inch (2 , 4 ,
1
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.
When measuring with U.S. Customary units, students should
1 1 1
be able to measure to the nearest part of an inch (2 , 4 , 8 ),
inch, foot, or yard.
Additional Instructional Strategies
Play Video
Converting Units (grades 3-8)
Dena McElligott, Virginia Middle School Mathematics Teacher Corps member in Virginia Beach Public Schools, shares a problem-solving strategy for converting units.
Handout available: Converting Units (Word)
There are several helpful strategies that students can use to help them convert. One strategy is “King Henry Died Unexpectantly By Drinking Chocolate Milk”.
(There are several versions of this phrase.)
73
Revised: 8/4/14
SOL 4.7 – 3rd Nine Weeks
King Henry Drinks Ucky Dark Chocolate Milk
Additional Math Curriculum Resources
74
Revised: 8/4/14
SOL 4.7 – 3rd Nine Weeks
Vocabulary
Lessons and TEI Items
Trade Books
Vocabulary Word Wall
Handout available: Working with Vocabulary /
Concept Development (Word)
Stick-Figure Measurements - Measurement
How Tall, How Short, How Far Away By David Adler
Measurement Conversion
Is A Blue Whale The Biggest Thing There Is? By Robert
Wells
Word Wall Instructional Video
Inching Along
US Customary System a system of measuring
commonly used in the United States (US Standard
System)
Measurement: Using a Ruler to Measure Sea
Creatures to the Nearest Eighth Inch
Measuring Penny By Loreen Leedy
Inch a standard unit of US Customary measure of
length
Counting on Converting Metric Measurements |
Part II | Part III | Part IV | Part V
Millions to Measure By David Schwartz
Counting On Frank By Rod Clement
How Long or How Wide: A Measuring Guide By Brian
Cleary
Feet/foot a standard unit of US Customary
measure of length (12 in. = 1 ft)
Trade Book Lessons
Yard a standard unit of US Customary measure of
length (36 in. = 1 yd; 3 ft = 1 yd)
Mile a standard unit of US Customary measure of
distance (1,760 yd = 1 mi)
Metric System a system of measuring based on ten
Millimeter a metric unit of length
Centimeter a metric unit of length (10 mm = 1 cm)
Meter a metric unit of length (1000 mm = 1 m; 100
cm = 1 m)
75
Revised: 8/4/14
SOL 4.7 – 3rd Nine Weeks
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
76
Revised: 8/4/14
SOL 4.6 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.6 – 3rd Nine Weeks
The student will
a) estimate and measure weight/mass and describe the results
in U.S. Customary and metric units as appropriate; and
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).
Weight and mass are different. Mass is the amount of matter in an
object. Weight is determined by the pull of gravity on the mass of an
object. The mass of an object remains the same regardless of its
location. The weight of an object changes depending on the
gravitational pull at its location. In everyday life, most people are
actually interested in determining an object’s mass, although they use
the term weight (e.g., “How much does it weigh?” versus “What is its
mass?”).

Balances are appropriate measuring devices to measure weight in U.S.
Customary units (ounces, pounds) and mass in metric units (grams,
kilograms).

Practical experience measuring the mass of familiar objects helps to
establish benchmarks and facilitates the student’s ability to estimate
Grade 4 SOL
Number of
Items
Measurement and Geography
4.6a-b, 4.7a-b, 4.8a-b,
4.9, 4.10a-b, 4.11a-b,
4.12a-b
13
Prior Knowledge
2.11 estimate and measure objects in pounds, ounces, and kilograms, grams using a
scale
3.9 estimate and use US customary and metric units to measure weight/mass in
ounces, pounds, grams, and kilograms
Understanding the Standard

Blueprint Categories
Essential Understandings
All students should

Use benchmarks to estimate
and measure weight/mass.

Identify equivalent measures
between units within the U.S.
Customary and between units
within the metric
measurements.
77
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication, mathematical
reasoning, connections, and representations
to

Determine an appropriate unit of measure
(e.g., ounce, pound, ton, gram, kilogram)
to use when measuring 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.
Revised: 8/4/14
SOL 4.6 – 3rd Nine Weeks
weight/mass.

– Students should estimate the mass/weight of everyday objects
(e.g., foods, pencils, book bags, shoes), using appropriate
metric or U.S. Customary units.
Record the mass of an object including the
appropriate unit of measure (e.g., 24
grams).
Additional Instructional Strategies
Play Video
Converting Units (grades 3-8)
Dena McElligott, Virginia Middle School Mathematics Teacher Corps member in Virginia Beach Public Schools, shares a problem-solving strategy for converting units.
Handout available: Converting Units (Word)
SOL 4.6a requires students to estimate and measure weight/mass and describe the estimate using the appropriate U.S. Customary or metric units. Students need
additional practice with estimation when metric units are involved. Students had difficulty with estimation items involving mass rather than weight.
In the first example provided, students have to use their understanding of the mass of 1 kilogram to determine which of several items would have a mass closest to
1 kg.
In the second example, students apply knowledge of the metric units of mass and their estimation skills to sort several items according to the most appropriate
metric unit to use when determining the mass of each item.
78
Revised: 8/4/14
SOL 4.6 – 3rd Nine Weeks
For SOL 4.6b, students had particular difficulty determining equivalent measurements within the U.S. Customary system. Students must be able to apply their
knowledge of equivalent measurements within the U.S. Customary system, as shown in these examples. Note that all students have access to a four-function
calculator when responding to questions of this nature.
There are several helpful strategies that students can use to help them convert. One strategy is “King Henry Died Unexpectantly By Drinking Chocolate Milk”.
(There are several versions of this phrase.)
79
Revised: 8/4/14
SOL 4.6 – 3rd Nine Weeks
King Henry Drinks Ucky Dark Chocolate Milk
80
Revised: 8/4/14
SOL 4.6 – 3rd Nine Weeks
Vocabulary
Vocabulary Word Wall
Lessons and TEI Items
This Fruit Is a Mass! - Measurement
Trade Books
On the Scale, A Weighty Tale By Brian Cleary
Hershey’s Milk Chocolate Weights and Measures By
Jerry Pallotta
Handout available: Working with Vocabulary / Concept
Development (Word)
Word Wall Instructional Video
Trade Book Lessons
US Customary
Weight the downward force caused by gravity on
an object
Ounces a standard unit of weight measure
Pounds a standard unit of weight measure (16 oz. =
1 lb)
Tons a standard unit of weight measure (2000 lb =
1 T)
Metric
Mass a measure of how much matter is in an object
Grams a metric unit of mass measure
Kilograms a metric unit of mass measure (1000 g =
1 kg)
81
Revised: 8/4/14
SOL 4.6 – 3rd Nine Weeks
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
82
Revised: 8/4/14
SOL 4.8 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.8 – 3rd Nine Weeks
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).
Understanding the Standard

U.S. Customary units for measurement of liquid volume
include cups, pints, quarts, and gallons.

The measurement of the object must include the unit of
measure along with the number of iterations.



Students should measure the liquid volume of everyday
objects in U.S. Customary units, including cups, pints,
quarts, gallons, and record the volume including the
appropriate unit of measure (e.g., 24 gallons).
Blueprint Categories
Grade 4 SOL
Number of
Items
Measurement and Geography
4.6a-b, 4.7a-b, 4.8a-b,
4.9, 4.10a-b, 4.11a-b,
4.12a-b
13
Prior Knowledge
2.11 estimate and measure liquid volume in cups, pints, quarts, gallons, and
liters
3.9 estimate and use customary and metric units to measure liquid volume in
cups, pints, quarts, gallons, and liters
Essential Understandings
All students should

Use benchmarks to estimate and
measure volume.

Identify equivalent measurements
between units within the U.S.
Customary system.
Practical experience measuring liquid volume of familiar
objects helps to establish benchmarks and facilitates
the student’s ability to estimate liquid volume.
Students should estimate the liquid volume of
containers in U.S. Customary units to the nearest cup,
83
Essential Knowledge and Skills
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to

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 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
Revised: 8/4/14
SOL 4.8 – 3rd Nine Weeks
pint, quart, and gallon.
gallons).

Identify equivalent measures of volume between
units within the U.S. Customary system.
Additional Instructional Strategies
Play Video
Liquid Measure (grades 4-8)
A fun strategy to help students remember and convert Customary measures of capacity is taught with the story “Gallon Land”. See the Promethean lesson on the
Additional Resources page.
Additional Math Curriculum Resources
84
Revised: 8/4/14
SOL 4.8 – 3rd Nine Weeks
Vocabulary
Lessons and TEI Items
Trade Books
Vocabulary Word Wall
Kiddy Pool - Measurement
Pastry School in Paris By Cindy Neuschwander
Handout available: Working with Vocabulary /
Concept Development (Word)
Go for the Gallon
Room for Ripley By Stuart J Murphy
Capacity Counts
Lulu’s Lemonade By Barbara deRubertis
What's Your Capacity?
Measuring Penny By Loreen Leedy
Word Wall Instructional Video
Capacity the amount that something can hold
(liquid volume)
Trade Book Lessons
Cup a standard unit of liquid measure
Pint a standard unit of liquid measure (2 c = 1 pt)
Quart a standard unit of liquid measure
(4 c = 1 qt, 2 pt = 1 qt)
Gallon a standard unit of liquid measure
(16 c = 1 g, 8 pt = 1 g, 4 qt = 1 g)
85
Revised: 8/4/14
SOL 4.8 – 3rd Nine Weeks
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
86
Revised: 8/4/14
SOL 4.9 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.9 – 3rd Nine Weeks
The student will determine elapsed time in hours and minutes within a 12hour period.
Blueprint Categories
Grade 4 SOL
Number of
Items
Measurement and Geography
4.6a-b, 4.7a-b,
4.8a-b, 4.9, 4.10a-b,
4.11a-b, 4.12a-b
13
Prior Knowledge
3.11 tell time to nearest minute; determine elapsed time in 1‐hr increments
over 12‐hour period
Understanding the Standard

Elapsed time is the amount of time that has passed between two
given times.

Elapsed time should be modeled and demonstrated using analog
clocks and timelines.

Elapsed time can be found by counting on from the beginning time to
the finishing time.
– Count the number of whole hours between the beginning time
and the finishing time.
– Count the remaining minutes.
– Add the hours and minutes.
For example, to find the elapsed time between 10:15 a.m. and 1:25
p.m., count 10 minutes; and then, add 3 hours to 10 minutes to find
the total elapsed time of 3 hours and 10 minutes.
Essential Understandings
All students should

Understanding the “counting on”
strategy for determining elapsed time in
hour and minute increments over a 12hour period from a.m. to a.m. or p.m. to
p.m.
87
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 12hour period (times can cross
between a.m. and p.m.).

Solve practical problems in
relation to time that has
elapsed.
Revised: 8/4/14
SOL 4.9 – 3rd Nine Weeks
Additional Instructional Strategies
There are 2 strategies that help students with this skill. The elapsed number line and the T Chart can be shown to you by your Math Resource Teacher.
88
Revised: 8/4/14
SOL 4.9 – 3rd Nine Weeks
For SOL 4.9, students need additional practice determining elapsed time. Teachers are encouraged to include elapsed time problems within the context of word
problems, as shown in both question one and question two on this slide. Additionally, question two requires students to use the prior knowledge of reading an
analog clock (from grade three) in order to select the correct answer.
89
Revised: 8/4/14
SOL 4.9 – 3rd Nine Weeks
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Trade Books
Vocabulary Word Wall
Handout available: Working with Vocabulary /
Concept Development (Word)
It’s About Time
It’s About Time By Stuart J Murphy
How Much Longer? - Measurement
A Second is a Hiccup By Hazel Hutchins
Word Wall Instructional Video
Elapsed Time in the Real World
Trade Book Lessons
Elapsed Time The time that goes by while an event
is occurring
Elapsed Time
A Day in Elapsed Time
Jock O’Clock’s Time Sports Complex
90
Revised: 8/4/14
SOL 4.9 – 3rd Nine Weeks
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
91
Revised: 8/4/14
SOL 4.10 – 4th Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.10 – 4th Nine Weeks
The student will
a) identify and describe representations of points, lines, line
segments, rays, and angles, including endpoints and vertices;
b) identify representations of lines that illustrate intersection,
parallelism, and perpendicularity.
Blueprint Categories
Grade 4 SOL
Number of
Items
Measurement and Geography
4.6a-b, 4.7a-b, 4.8a-b,
4.9, 4.10a-b, 4.11a-b,
4.12a-b
13
Prior Knowledge
3.19 Identify and draw representations of line segments and angles.
Understanding the Standard





A point is a location in space. It has no length, width, or height. A
point is usually named with a capital letter.
Essential Understandings
All students should

Understand that points, lines, line
segments, rays, and angles, including
endpoints and vertices are fundamental
components of noncircular geometric
figures.
A line is a collection of points going on and on infinitely in both
directions. It has no endpoints. When a line is drawn, at least two
points on it can be marked and given capital letter names. Arrows
must be drawn to show that the line goes on in both directions

infinitely (e.g., AB , read as “the line AB”).

A line segment is part of a line. It has two endpoints and includes all
the points between those endpoints. To name a line segment, name
the endpoints (e.g., AB , read as “the line segment AB”).
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.
A ray is part of a line. It has one endpoint and continues infinitely in
one direction. To name a ray, say the name of its endpoint first and

then say the name of one other point on the ray (e.g., AB , read as
“the ray AB”).
Two rays that have the same endpoint form an angle. This endpoint is
92
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

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.

Identify practical situations that
illustrate parallel, intersecting,
and perpendicular lines.
Revised: 8/4/14
SOL 4.10 – 4th Nine Weeks
called the vertex. Angles are found wherever lines and line segments
intersect. An angle can be named in three different ways by using
– three letters to name, in this order, a point on one ray, the vertex,
and a point on the other ray;
– one letter at the vertex; or
– a number written inside the rays of the angle.

Intersecting lines have one point in common.

Perpendicular lines are special intersecting lines that form right angles
where they intersect.

Parallel lines are lines that lie in the same place and do not intersect.
Parallel lines are always the same distance apart and do not share any
points.

Students should explore intersection, parallelism, and
perpendicularity in both two and three dimensions. For example,
students should analyze the relationships between the edges of a
cube. Which edges are parallel? Which are perpendicular? What plane
contains the upper left edge and the lower right edge of the cube?
Students can visualize this by using the classroom itself to notice the
lines formed by the intersection of the ceiling and walls, of the floor
and wall, and of two walls.
Additional Instructional Strategies
Play Video
Angles (grades 3-8)
Math-a-rama Geometry Song: See your Math Resource Teacher
Additional Math Curriculum Resources
93
Revised: 8/4/14
SOL 4.10 – 4th Nine Weeks
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
Handout available: Working with Vocabulary /
Concept Development (Word)
Simple Drawings - Geometry
Word Wall Instructional Video
Amusement Angles
Point an exact location in space
Angling for Fitness
Trade Books
Sir Cumference and the Great Knight of Angleland, By
Cindy Neuschwander
Geometric Line Relationships
Trade Book Lessons
Line a straight path of points that goes on and on in
two directions
End point point indicating where a ray of line ends
Line segment a part of a line that has two
endpoints
Ray a part of a line that has one endpoint and
continues endlessly in one direction
Angle a figure formed by two rays that share a
single endpoint
Vertex the point where two rays, two sides, or two
edges meet (plural, vertices)
Intersecting lines that cross at one point
Parallel lines that never intersect
Perpendicular two intersecting lines that form one
or more right angles
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SOL 4.10 – 4th Nine Weeks
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
95
Revised: 8/4/14
SOL 4.12 – 4th Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
Blueprint Categories
Grade 4 SOL
Number of
Items
Measurement and Geography
4.6a-b, 4.7a-b, 4.8a-b,
4.9, 4.10a-b, 4.11a-b, 4.12a-b
13
SOL 4.12 – 4th Nine Weeks
The student will
a) define polygon; and
b) identify polygons with 10 or fewer sides.
Prior Knowledge
3.18 analyze 2 dimensional figures (square, circle, rectangle, triangle)
Understanding the Standard

A polygon is a closed plane geometric figure composed of at least three
line segments that do not cross. None of the sides are curved.

A triangle is a polygon with three angles and three sides.

A quadrilateral is a polygon with four sides.

A rectangle is a quadrilateral with four right angles.

A square is a rectangle with four sides of equal length.

A trapezoid is a quadrilateral with exactly one pair of parallel sides.

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

A rhombus is a quadrilateral with 4 congruent sides.

A pentagon is a 5-sided polygon.

A hexagon is a 6-sided polygon.

A heptagon is a 7-sided polygon.

An octagon is an 8-sided polygon.
Essential Understandings
All students should
96

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).
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections and
representation to

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).
Revised: 8/4/14
SOL 4.12 – 4th Nine Weeks

A nonagon is a 9-sided polygon

A decagon is a 10-sided polygon.
Additional Instructional Strategies
Play Video
Properties of Polygons (grades 4-8)
For SOL 4.12a, students continue to have difficulty differentiating between figures that are polygons and figures that are not polygons.
For SOL 4.12b, students need additional practice naming polygons with no more than 10 sides.
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SOL 4.12 – 4th Nine Weeks
Student performance with this content continues to be inconsistent, especially when concave figures must be named. As a follow-up activity, students could use
straightedges to draw examples of the figures whose names were not used in this example.
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SOL 4.12 – 4th Nine Weeks
Additional Math Curriculum Resources
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SOL 4.12 – 4th Nine Weeks
Vocabulary
Lessons and TEI Items
Trade Books
Geometric Figures - Geometry
Vocabulary Word Wall
Handout available: Working with Vocabulary /
Concept Development (Word)
Shape Up! By David Adler
Polygons Galore! - Geometry
The Greedy Triangle By Marilyn Burns
Capturing Polygons
Word Wall Instructional Video
Does Poly Want a Polygon
Sir Cumference and the First Round Table By Cindy
Neuschwander
Polygon Power
Trade Book Lessons
Ponder the Polygon
Shaping Up- Exploring the Attributes of Shapes all
Around Us
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
100
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SOL 4.12 – 4th Nine Weeks
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
101
Revised: 8/4/14
SOL 4.11 – 4th Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 4.11 – 4th Nine Weeks
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.
Understanding the Standard

The van Hiele theory of geometric understanding describes how
students learn geometry and provides a framework for structuring
student experiences that should lead to conceptual growth and
understanding.
– Level 0: Pre-recognition. Geometric figures are not recognized.
For example, students cannot differentiate between threesided and four-sided polygons.
– Level 1: Visualization. Geometric figures are recognized as
entities, without any awareness of parts of figures or
relationships between components of a figure. Students should
recognize and name figures and distinguish a given figure from
others that look somewhat the same. (This is the expected level
of student performance during grades K and 1.)
– Level 2: Analysis. Properties are perceived but are isolated and
unrelated. Students should recognize and name properties of
geometric figures. (Students are expected to transition to this
Blueprint Categories
Grade 4 SOL
Number of
Items
Measurement and Geography
4.6a-b, 4.7a-b, 4.8a-b,
4.9, 4.10a-b, 4.11a-b,
4.12a-b
13
Prior Knowledge
3.20 Identify and describe congruent and symmetrical using tracing.
Essential Understandings
All students should

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.
102
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

Recognize the congruence of
plane figures resulting from
geometric transformations such
as translation, reflection, and
rotation, using mirrors, paper
folding and tracing.
Revised: 8/4/14
SOL 4.11 – 4th Nine Weeks
level during grades 2 and 3.)
– Level 3: Abstraction. Definitions are meaningful, with
relationships being perceived between properties and between
figures. Logical implications and class inclusion are understood,
but the role and significance of deduction is not understood.
(Students should transition to this level during grades 5 and 6
and fully attain it before taking algebra.)

Congruent figures are figures having exactly the same size and shape.
Opportunities for exploring figures that are congruent and/or
noncongruent can best be accomplished by using physical models.

A translation is a transformation in which an image is formed by
moving every point on a figure the same distance in the same
direction.

A reflection is a transformation in which a figure is flipped over a line
called the line of reflection. All corresponding points in the image and
preimage are equidistant from the line of reflection.

A rotation is a transformation in which an image is formed by turning
its preimage about a point.

The resulting figure of a translation, reflection, or rotation is
congruent to the original figure.
Additional Instructional Strategies
Tricks to remember the Transformations:
Reflection (Flip)
Rotation (Turn) Translation (Slide)
Additional Math Curriculum Resources
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SOL 4.11 – 4th Nine Weeks
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
Handout available: Working with Vocabulary /
Concept Development (Word)
Congruent Figures - Geometry
Word Wall Instructional Video
Mathematical Movements
Trade Books
Slides, Flips, and Turns -- Tessellation ...
Congruent figures that have same shape and size
Non congruent not congruent
Plane figure a figure with only 2 dimensions (length
and width)
Transformation moving a shape so that it is in a
different position but still has the same area, size,
angles, and line segments
Reflection (flip) to flip a plane figure over (as seen
in a mirror)
Rotation (turn) moving a figure about on a fixed
point
Translation (slide) moving a shape in any direction
without rotating or flipping
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Revised: 8/4/14
SOL 4.11 – 4th Nine Weeks
Additional Links and Resources – 4th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Fun 4 the Brain
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Recess Room
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
Sheppard Software
Jefferson Lab
Math Study Jams
NCTM Illuminations
StarrMatica
New York State Assessments
*Multiple Languages
Pearson Success Net
Turtle Diary
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
105
Revised: 8/4/14