Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 1: Addition and Subtraction with Multi-Digit Numbers – 14 Days
Maryland College and Career-Ready Standards
The focus of this unit is to provide students time to develop and practice efficient addition and subtraction of multi-digit whole
numbers, while developing place value concepts. Fourth grade is the initial grade level in which the students are expected to
be proficient at using the standard algorithm for addition and subtraction. Students may continue to use previously learned
strategies based on place value concepts and the properties of operations, as well. They will reason about the magnitude of
the digits in a whole number and apply that knowledge to compare numbers. Fourth graders will demonstrate flexibility with
the different forms that numbers can be written. Students will apply their understanding of place value and number sense to
reason and explain about rounded answers.
Research
Extending students’ conceptual understanding of numbers beyond 1,000 is sometimes difficult to do because physical models
for thousands are not commonly available. Encouraging students to extend the patterns in the place value system and to
create familiar real-world referents helps students develop a strong sense of these larger numbers. (Teaching StudentCentered Mathematics, Van de Walle and Lovin, p. 47) Rather than conduct lessons focused exclusively on place value, it is
more beneficial to create tasks that require the use of place value ideas and place value models. The goal should be to
promote “ten-structured thinking” … that is, flexibility in using the structure of tens and hundreds in the number system.
(Teaching Student-Centered Mathematics, Van de Walle and Lovin, p. 51)
To read numerals between 1,000 and 1,000,000, students need to understand the role of commas. Each sequence of three
digits made by commas is read as hundreds, tens, and ones, followed by the name of the appropriate base-thousand unit
(thousand, million, billion, etc.) Thus, 457,000 is read “four hundred fifty seven thousand.” The same methods students used for
comparing and rounding numbers in previous grades apply to these numbers, because of the uniformity of the base-ten
system. (Progressions for the Common Core State Standards in Mathematics (draft), The Common Core Standards Writing
Team, April 2012, p. 12)
The standard addition and subtraction algorithms rely on adding or subtracting like base-ten units (ones with ones, tens with
tens, hundreds with hundreds, and so on) and composing or decomposing base-ten units as needed (such as composing 10
ones to make 1 ten or decomposing 1 hundred to make 10 tens). In mathematics, an algorithm is defined by its steps and not
by the way those steps are recorded in writing. With this in mind, minor variations in methods of recording standard algorithms
are acceptable. (Progressions for the Common Core State Standards in Mathematics (draft), The Common Core Standards
Writing Team, April 2012, p. 13)
1
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 1: Addition and Subtraction with Multi-Digit Numbers – 14 Days
The chart below highlights the key understandings of Unit 1 along with important questions that teachers
should pose to promote these understandings. The chart also includes key vocabulary that should be
modeled by teachers and used by students to show precision of language when communicating
mathematically.
Enduring Understandings
Students will understand that:

Place value helps
determine relationships
between numbers.

Numbers can be
represented in many ways.

Estimation can be used to
determine the
reasonableness of an
answer.

Mathematical properties
show number relationships
and can be used to
compute flexibly.

Problems can be
represented and solved
accurately using a variety
of strategies.

Problems can be solved
using addition and
subtraction.
Essential Questions

How do we use place value
understanding to compare large
numbers?

How can patterns, strategies, and
formulas help solve problems
accurately?

When is estimation more useful than
finding a precise answer?

Why is place value understanding
important in addition and subtraction?

What is the relationship between
addition and subtraction?

How can we use mathematical
properties and/or rules to solve
problems?
Key Vocabulary
Algorithm
Commutative property
Difference
Digits
Equation
Estimate
Expanded form
Expression
Hundreds
Million
Period
Place value
Round
Sum
Thousands
Value
Variable
Background Reading
Focus in Grade 4:
Teaching with
Curriculum Focal Points
Teaching StudentCentered Mathematics
– Grades 3-5
Putting the Practices
into Action:
Implementing the
Common Core
Standards for
Mathematical Practice
K-8
2
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 1: Addition and Subtraction with Multi-Digit Numbers – 14 Days
Throughout this unit, students will develop their use of the 8 Standards for Mathematical Practices while learning the
instructional standards. The mathematical practices in the shaded boxes should be emphasized during instruction this unit
due to how well they connect with the content standards in this unit.
Standards for Mathematical
Practice
1. Make sense of problems and
persevere in solving them
2. Reason abstractly and
quantitatively
3. Construct viable arguments and
critique the reasoning of others
4. Model with mathematics
Connections to this Cluster
Solve problems in which the solution is not immediately evident.
To determine and articulate what the problem is asking:

Ask students to restate the problem in their own words.

Have students turn to a partner to state the problem.

Discuss familiar problems (When have we seen something like this before? What did we do?)
To self-monitor progress and change directions when necessary:

Have students talk or write about how they got “stuck” and then “unstuck” when solving a problem.

Think aloud to show students how to change course when needed.
To demonstrate perseverance in problem-solving and identify different ways to solve a problem:

Make a classroom list of possible strategies.

Acknowledge those who modify their thinking and persevere to get to the solution and have students show
and talk about how they solved problems.

Encourage students to show at least two ways to solve a problem.
Write an equation for a situation and be able to explain how the equation relates to the situation presented. Solve
the equation outside of the context of the problem, then connect the solution back to the situation presented.
To make sense of quantities and their relationships in problem situations:

Represent a given addition and subtraction problem situation with the equation using a variable for the
unknown.

Write a situation problem that matches a specific equation.

Students can compose and decompose numbers to1,000,000 fluently.

Students recognize that any nonzero digit in the ten thousands place is always greater than any digit in the
thousands place.
Explain why a problem with a rounded answer may have more than one solution, based on an understanding of
place value.

Provide multiple opportunities for students to explain, explore, record, and try student-invented strategies.

Model how effective labeling communicates math reasoning.

Discuss student representations and solution methods.
-Ask students to restate and try peer methods for solving problems.
-Help students make mathematical connections between different representations/solution methods.
-Evaluate the efficiency of the strategies based on the probability of an error occurring.
Write equations for various problem situations and solve problems about the situations. Represent the unknown with
a variable.
 Represent problem situations in multiple ways including numbers, words (mathematical language), drawing
pictures, using objects, and creating equations
 Connect the different representations of a number and explain the connections.
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Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 1: Addition and Subtraction with Multi-Digit Numbers – 14 Days

5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in
repeated reasoning
Evaluate their results in the context of the situation and reflect on whether the results make sense.
Use manipulatives, hundreds and thousands charts, number lines, and drawings that represent mathematical
situations.

Consider the available tools (including estimation) when solving a mathematical problem and decide when
certain tools might be helpful.

Explain how tools can assist them in seeing patterns and relationships with numbers.

Explore various place value charts and determine which helps the most for different tasks, or create a new
chart
Create accurate drawings and representations of mathematical situations.
Use specific math vocabulary to communicate mathematical ideas.
Compute accurately.

Develop and display anchor charts with precise math vocabulary.

Orally rephrase student explanations using appropriate vocabulary.

Use standard algorithm and alternative algorithms to solve one problem. If the answers are not the same
determine where a mistake was made and correct it, so that the correct solution is shown with multiple
strategies.
Look closely to discover a pattern or structure and apply the properties of operations to solve problems.

Use properties of operations to perform and explain calculations with multi-digit numbers; provide
opportunities in which students explore mathematical properties; and ask students to construct arguments
to prove mathematical properties.

Model the composing and decomposing of whole numbers greater than 1,000.

Apply concepts of place value and division
Notice repetitive actions in computation and make generalizations about rules and “short-cuts” to get to answers
more quickly.

Use models to explain calculations and understand how algorithms work.

Use models to examine patterns and generate alternative algorithms.
4
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 1: Addition and Subtraction with Multi-Digit Numbers – 14 Days
Generalize place value understanding for multi-digit whole numbers.
Maryland College and CareerReady Standards
4.NBT.A.2
Read and write multi-digit
whole numbers using
base-ten numerals,
number names, and
expanded form.
Compare two multi-digit
numbers based on
meanings of the digits in
each place, using >, =,
and < symbols to record
the results of comparisons.
Grade 4 expectations in
this domain are limited to
whole numbers less than
or equal to 1,000,000.
SMP
7. Look for and make use of
structure.
Instructional Strategies and Resource Support
This standard refers to the variety of ways that numbers can be
written. Students should be able to interpret as well as
represent numbers in a variety of forms. Traditionally, number
forms have included:
Standard form: 372
Expanded form: 300 + 70 + 2
Number Name: three hundred seventy-two
Additionally, students need to develop more flexible ways of
viewing numbers. For example, 372 can also be seen in ways
such as:



37 tens and 2 ones
2 hundreds, 17 tens, and 2 ones
12 ones, 6 tens, and 3 hundreds
Expanded form does not always have to be in order of place
value. Have students write expanded form out of order and
trade with a partner.
Write comparisons with numbers in different forms. Or, put the
comparison symbol in and have students complete the
comparison.
60 + 90,000 + 8 + 500
Eighty-two thousand, nine hundred two
743 hundreds < __________________ < 94 thousands
Formative Assessments
4.NBT.A.2a
Arrange these numbers in
decreasing order,
beginning with the
greatest.
2,380
830
823
2,038
4.NBT.A.2b
The U.S. Census Bureau conducts a
census every decade to count every
resident of the United States. The
populations of 3 cities listed in the
chart below are based on the 2010
Census.
City
Population
Baltimore
20,000 + 40 + 1,000 + 300 +
600,000 + 2
Pittsburgh
2 hundreds, 3 hundred
thousands, 11 ones, 6
thousands
Richmond
two hundred ten thousand,
three hundred nine
4.NBT.A.2c
Name a number that would
make the comparison true.
73 hundreds < ____________________ <
8 thousands, 5 hundreds, 13 ones
5
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 1: Addition and Subtraction with Multi-Digit Numbers – 14 Days
Generalize place value understanding for multi-digit whole numbers.
Maryland College and CareerReady Standards
4.NBT.A.2
Read and write multi-digit
whole numbers using
base-ten numerals,
number names, and
expanded form.
Compare two multi-digit
numbers based on
meanings of the digits in
each place, using >, =,
and < symbols to record
the results of comparisons.
Grade 4 expectations in
this domain are limited to
whole numbers less than
or equal to 1,000,000.
SMP
7. Look for and make use of
structure.
Instructional Strategies and Resource Support
Formative Assessments
Fourth graders are reading, writing, comparing, and utilizing numbers
to 1,000,000. In order to work with these greater numbers, students
need to understand the role of commas.
Each sequence of three digits made by commas is read as hundreds,
tens, and ones, followed by the name of the appropriate basethousand unit (thousand, million, billion, etc.) Thus, 457,000 is read
“four hundred fifty seven thousand.” The same methods students
used for comparing and rounding numbers in previous grades apply
to these numbers, because of the uniformity of the base-ten system.
(Progressions for the Common Core State Standards in Mathematics (draft), The
Common Core Standards Writing Team, April 2012, p. 12)
Teaching Student-Centered Mathematics – Grades 3-5
p. 45
Activity 2.5 “Who Could They Be?”
Using a number line to consider magnitude of numbers and to
compare whole numbers.
Activity 2.6 “Close, Far, and in Between”
Using larger numbers to ask a variety of questions that build number
sense and to encourage discussion of all responses.
The lesson at the following link will provide students with an
opportunity to extend their understanding of place value through one
million:
“Making Your First Million”, NCTM - Illuminations
http://illuminations.nctm.org/Lesson.aspx?id=4018
6
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 1: Addition and Subtraction with Multi-Digit Numbers – 14 Days
Generalize place value understanding for multi-digit whole
numbers.
Maryland College and Career-Ready
Standards
4.NBT.A.3
Use place value
understanding to round
multi-digit whole
numbers to any place.
Grade 4 expectations in
this domain are limited to
whole numbers less than or
equal to 1,000,000.
SMP
6. Attend to precision.
8. Look for and express
regularity in repeated
reasoning.
Instructional Strategies and Resource Support
Formative Assessments
Teaching Student-Centered Mathematics – Grades 3-5 p. 47
This standard spreads beyond a procedure or algorithm for
rounding as it encompasses place value understanding. Students
who have strong number sense and a deep understanding of
place value and number sense can reason and communicate
about the answers they get when rounding.
When rounding numbers, students traditionally substitute a number
with a multiple of 10, 100, 1,000,… that is close to the original
number. For example:
Rounded to the nearest thousand:
Rounded to the nearest hundred:
Rounded to the nearest ten:
3,629 ≈ 4,000
3,629 ≈ 3,600
3,629 ≈ 3,630
Students benefit from multiple opportunities using a number line
and a hundreds chart as tools to support their work with rounding.
Using the example above, a blank number line can be labeled in
different ways:
3,629
3,500
Brayden’s homework problem
was: Round 95,473.
Brayden wrote down 95,500.
Brayden’s father told him that he
is wrong; the answer is 100,000.
His big sister said they are both
wrong; the answer is 95,000.
4.NBT.A.3b
There are many “friendly” number substitutes. Typically, the
greater the rounding place, the easier it is to mentally manipulate
a rounded number. The lesser the rounding place, the closer a
rounded number is to the original number.
3,000
4.NBT.A.3a
4,000
3,629
Adam is an avid collector of
baseball cards. He rounded the
amount of his cards to 600.
How many cards could Adam
have if he rounded to the nearest
hundred?
4.NBT.A.3c
The distance between Boston and
Los Angeles is 3,000 miles when
rounded to the nearest thousand.
Circle the numbers that round to
3,000 when rounded to the nearest
thousand.
3,240 3,512 3,489 2,512
3,600
3,650
2,476 2,801
3,700
7
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 1: Addition and Subtraction with Multi-Digit Numbers – 14 Days
Generalize place value understanding for multi-digit whole
numbers.
Maryland College and Career-Ready
Standards
4.NBT.A.3
Use place value
understanding to round
multi-digit whole
numbers to any place.
Grade 4 expectations in
this domain are limited to
whole numbers less than or
equal to 1,000,000.
SMP
6. Attend to precision.
8. Look for and express
regularity in repeated
reasoning.
Instructional Strategies and Resource Support
Formative Assessments
Teaching Student-Centered Mathematics – Grades 3-5 p. 47
Additionally, students need to be able to reason about the range
of numbers that would round to a given number. In beginning with
smaller values, students begin to recognize boundaries for
“friendly” numbers. For example, if rounding to the nearest 10,
what whole numbers would round to 40? Using number lines,
students quickly ascertain the rounding range:
25
30
35
40
45
50
4.NBT.A.3d
The heights of several skyscrapers from
around the world are listed in the table.
City
Building
Height
New York
Empire State
1,250
Chicago
Willis Tower
1,451
Dubai
Marina 101
1,417
Hong Kong
International
1,588
Shanghai
Jin Mao Tower
1,380
Kaohsiung
Tuntex Sky Tower
1,240
55
Whole numbers 35 – 44 fall within the oval and round to 40. Keep
in mind that in this unit, decimal values are not explored.
Have students build number sense and an understanding of how
to round numbers to any place using a number line. On your
number line count by tens, hundreds or other place. Have
students mark halfway points then determine what portion of the
number line is closest to each hundred (or other place).
4.NBT.A.3e
Max used a pedometer to keep
track of how many steps he
walked yesterday. He told his
mom that when he rounds his
amount of steps to the nearest
thousand, he walked 8,000 steps.
2,849
2,700
2,750
2,800
2,850
2,900
If you are rounding to the nearest hundred, all the numbers in the
oval would round to 2,800. 2,849 is the greatest number in the
oval.
Illustrative Mathematics
“Rounding to the Nearest 1,000”
https://www.illustrativemathematics.org/contentstandards/4/NBT/A/3/tasks/1807
8
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 1: Addition and Subtraction with Multi-Digit Numbers – 14 Days
Use place value understanding and properties of operations to perform multidigit arithmetic.
Maryland College and Career-Ready
Standards
4.NBT.B.4
Fluently add and subtract
multi-digit whole
numbers using the
standard algorithm.
Grade 4 expectations in this
domain are limited to
whole numbers less than or
equal to 1,000,000.
SMP
6. Attend to precision.
8. Look for and express
regularity in repeated
reasoning.
Instructional Strategies and Resource Support
Teaching Student-Centered Mathematics – Grades 3-5
pp. 112-113
“Traditional Algorithms for Addition and Subtraction”
This standard refers to fluency, which means accuracy, efficiency
(using a reasonable amount of steps and time), and flexibility in
using a variety of strategies and in understanding number forms.
Fourth grade is the first grade level in which students are expected
to be proficient at using the standard algorithm to add and
subtract. In previous grades, students have utilized a variety of
ways to add and subtract, and these previously learned strategies
are still permissible. However, students build on their understanding
of addition and subtraction, their use of place value and their
flexibility with multiple strategies to make sense of the standard
algorithm.
Computation algorithm. A set of predefined steps applicable to a
class of problems that gives the correct result in every case when
the steps are carried out correctly.
Computation strategy. Purposeful manipulations that may be
chosen for specific problems, may not have a fixed order, and
may be aimed at converting one problem into another.
Formative Assessments
4.NBT.B.4a
Solve this addition problem.
63,874 + 29,145 =
The next problem has the same
sum as above. What is the missing
addend?
58,652 + ___________ = ____________
4.NBT.B.4b
Use each digit card once to create
an addition problem of two
5-digit numbers that have a sum
between 40,000 and 50,000.
(Progressions for the CCSSM; Number and Operation in Base Ten, CCSS
Writing Team, April 2011, page 2)
Students use the structure of the base-ten system to generalize their
strategies and to discuss reasonableness of their computations and
work towards fluency. (MP.6, MP.8)
9
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 1: Addition and Subtraction with Multi-Digit Numbers – 14 Days
Use place value understanding and properties of operations to perform multidigit arithmetic.
Maryland College and Career-Ready
Standards
4.NBT.B.4
Fluently add and subtract
multi-digit whole
numbers using the
standard algorithm.
Grade 4 expectations in this
domain are limited to
whole numbers less than or
equal to 1,000,000.
SMP
6. Attend to precision.
8. Look for and express
regularity in repeated
reasoning.
Instructional Strategies and Resource Support
In the following Illustrative Mathematics task, an incomplete
problem is presented, and students are expected to choose
numbers to subtract (subtrahends) so that the resulting problem
requires different types of regrouping. In this way students have to
recognize the pattern and not just follow a memorized algorithm. In
other words, they have to think about what happens in the
subtraction process when we regroup. This task is appropriate to
use after students have learned the standard US algorithm.
Formative Assessments
4.NBT.B.4c
Marcus and Tony both solved the same
subtraction problem but found
different answers. Which one was
correct?
Illustrative Mathematics:
“To Regroup or not to Regroup?”
http://www.illustrativemathematics.org/standards/k8
If students are having difficulty transitioning to the standard
algorithm, you may need to build understanding by connecting
the algorithm to another approach. Both place value disks and a
stacking approach help students develop this relationship when
working from right to left.
Place Value Disks Example:
326 - 52 = _____
10
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 1: Addition and Subtraction with Multi-Digit Numbers – 14 Days
Use place value understanding and properties of operations to perform multidigit arithmetic.
Maryland College and Career-Ready
Standards
4.NBT.B.4
Fluently add and subtract
multi-digit whole
numbers using the
standard algorithm.
Instructional Strategies and Resource Support
Formative Assessments
Stacking Approach
Addition Examples:
Grade 4 expectations in this
domain are limited to
whole numbers less than or
equal to 1,000,000.
247
+ 1 76
13
110
+ 300
423
SMP
6. Attend to precision.
8. Look for and express
regularity in repeated
reasoning.
Subtraction Example:
-
247 + 176 = ______
+
200
40
7
100
70
6
300 + 110 + 13 = 423
832 - 258 = ______
700
120
20
13
800
200
500
30
50
70
3
8
5
11
Carroll County Public Schools Elementary Mathematics Instructional Guide (Grade 4)
Unit 1: Addition and Subtraction with Multi-Digit Numbers – 14 Days
12