Fourth Grade Unit 1 Whole Numbers, Place Value and Rounding In Computation & Multiplication
9 weeks
In this unit students will:
● Read and write multi-digit whole numbers.
● Recognize numbers in standard, expanded, and word form.
● Round multi-digit numbers to any place.
● Compare rounded multi-digit numbers and express their relationship using >, <, or =.
● Estimate sum and/or difference of numbers apply estimation to solve problems and determine when it is necessary or appropriate to apply
estimation strategies.
● Discuss and demonstrate the relationship between area and multiplication.
● Understand the decomposition of an area model through multiplication.
● Decompose rectilinear figures into non-overlapping squares and rectangles to find the total area of the rectilinear figure.
Unit 1 Overview video
Prerequisite Skills Assessment
Parent Letter
Number Talks Calendar
Vocabulary Cards
(All documents in the outline file)
Whole Numbers, Place Value, and Rounding
Big Ideas/Enduring Understandings:
● The value of a number is determined by the place of its digits.
● Using rounding is an appropriate estimation strategy for solving problems and estimating.
● Rounded numbers are approximate and not exact. Exact answers can be rounded to different place values.
● A number can be written using digits in standard form, word, or expanded form.
● Larger numbers can be compared using the place value of the digits within the numbers. The relationship between the two numbers can be
expressed using the symbols >, <, or =.
Essential Questions:
● How does our base ten number system work?
● How does understanding the base ten number system help us add and subtract?
● How does the value of a digit change if its location is changed in a large number?
● What determines the value of a digit?
● How does estimation help us understand large numbers?
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Content Standards
Content standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to
emphasize the natural connections that exist among mathematical topics.
Generalize place value understanding for multi-digit whole numbers.

MGSE4.NBT.1 Recognize that in a multi-digit whole number, a digit in any one place represents ten times what it represents in the place to
its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division

MGSE4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MGSE4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.
Use place value understanding and properties of operations to perform multi-digit arithmetic.

MGSE4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Use the four operations with whole numbers to solve problems.
 MGSE4.OA.3 Solve multistep word problems with whole numbers and having whole-number answers using the four operations, including
problems in which remainders must be interpreted. Represent these problems using equations with a symbol or letter standing for the
unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Second Grade Place Value Standard
Understand Place Value.
MGSE2.NBT.1 Understand that the three digits
of a three-digit number represent amounts of
hundreds, tens, and ones; e.g., 706 equals 7
hundreds, 0 tens, and 6 ones.
a. Understand the following as special
cases: 100 can be thought of as a bundle
of ten tens — called a “hundred.”
b. The numbers 100, 200, 300, 400, 500,
4th Grade Quarter 1
Vertical Articulation of Place Value
Third Grade Place Value Standard
Use place value understanding and properties
of operations to perform multi-digit
arithmetic.
MGSE3.NBT.1 Use place value understanding to
round whole numbers to the nearest 10 or 100.
2
Fifth Grade Place Value Standard
Understand the place value system.
MGSE5.NBT.1 Recognize that in a multi-digit
number, a digit in one place represents 10 times
as much as it represents in the place to its right
and 1/10 of what it represents in the place to its
left.
2015-2016
600, 700, 800, 900 refer to one, two,
three, four, five, six, seven, eight, or nine
hundreds (and 0 tens and 0 ones).
Instructional Strategies
In second and third grade students only worked with numbers to one thousand. It is important to provide multiple opportunities in the classroom
setting and use real-world context for students to read and write multi-digit whole numbers.
Students need to have opportunities to compare numbers with the same number of digits, e.g., compare 5,478 and 4,892; numbers that have the
same number in the leading digit position, e.g., compare 35,126 and 38,087, e.g., and numbers that have different numbers of digits, e.g., 549, 86,
1,246, and 12,199.
Students also need to create numbers that meet specific criteria. For example, provide students with digit cards numbered 0 through 9. Ask
students to select 4-6 cards; then, using all cards make the largest number possible number with the cards, the smallest number possible and then
the closest number to 5000 that is greater than 5000 or less than 5000.
Rounding is not new in grade 4. Students need to build on the Grade 3 skill of rounding to the nearest 10 or 100 to include larger numbers and place
value. What is new for Grade 4 is rounding to digits other than the leading digit, e.g., rounding 32,580 to the nearest hundred. This requires a
deeper understanding than rounding to the nearest ten thousand. Using an open number line is crucial for developing this deep understanding.
In terms of adding and subtracting multi-digit whole numbers using the standard algorithm, it is crucial that students understand, can think about,
and explain the standard algorithm instead of following a sequence of directions that they don’t understand. Both Grade 2 and Grade 3 spent time
working on developing strategies for addition and subtraction so students should be ready to bridge the gap to the standard algorithm with
understanding. The goal for Grade 4 students is for them to understand all the steps in the algorithm, and be able to explain the meaning of each
digit. For example, a 1 can represent one, ten, one hundred, and so on. Holding students accountable to correct vocabulary using the Standards for
Mathematical Practices is also very important as they move to the standard algorithm. It is not appropriate for students to say, “I carried the one”
when it is actually a ten.
Common Misconceptions
NBT.2 - There are several misconceptions students may have about writing numerals from verbal descriptions. Numbers like one thousand two
causes problems for students. Many students will understand the 1000 and the 2 but instead of placing the 2 in the ones place, students will write
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the numbers as they can hear them, 10002 (ten thousand two). There are multiple strategies that can be used to assist with this concept, including
place-value boxes and vertical-addition methods.
Students often assume that the first digit of a multi-digit number indicates the “greatness” of a number. The assumption is made the 954 is greater
than 1002 because students are focusing on the first digit instead of the number as a whole.
Students need to be aware of the greatest place value. In this example, there is one number with the lead digit in the thousands and another
numbers with its lead digit in the hundreds.
Development of a clear understanding of the value of the digits in a number is critical for the understanding of and using numbers in computations.
Helping students build the understanding that 12345 means one ten thousand or 10,000, two thousands or 2000, three hundreds or 300, four tens or
40, and 5 ones or 5. Additionally, the answer is the sum of each of these values 10,000 + 2000 + 300 + 40 + 5.
NBT.4 - Often students mix up when to “carry” and when to “borrow”. Also students often do not notice the need of borrowing and just take the
smaller digit from the larger one. Emphasize place value and the meaning of the digits.
If students are having difficulty with linking up similar place values in numbers as they are adding and subtracting, it is sometimes helpful to have
them write their calculations on the grid paper. This assists the student with lining up the numbers more accurately.
If students are having a difficult time with a standard addition algorithm, a possible modification to the algorithm might be helpful. Instead of the
“shorthand” of “carrying,” students could add by place value, moving left to right placing the answers down below the “equals” line. For example:
249
+ 372
500
110
11
621
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(Start with 200 + 300 to get the 500
then 40 + 70 to get 110
and 9 + 2 to get 11.)
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Evidence of Learning
●
●
●
●
●
●
Read multi-digit whole numbers.
Write multi-digit-numbers.
Recognize numbers in standard, expanded, and word form.
Round multi-digit numbers to any place.
Compare rounded multi-digit numbers and express their relationship using >, <, or =.
Estimate sum and/or difference of numbers apply estimation to solve problems and determine when it is necessary or appropriate to
apply estimation strategies.
Adopted Resources
Adopted Online Resources
Think Math:
My Math:
Chapter 1: Place Value
1.1 Place Value
1.2 Read and Write Multi-Digit Numbers
1.3 Compare Numbers
1.4 Order Numbers
1.5 Use Place Value to Round
1.6 Problem-Solving Investigation
Chapter 2: Add and Subtract Whole Numbers
2.2 Addition and Subtraction Patterns
2.3 Add and Subtract Mentally
2.4 Estimate Sums and Differences
2.5 Add Whole Numbers
2.6 Subtract Whole Numbers
2.7 Subtract Across Zeros
2.8 Problem-Solving Investigation
2.9 Multi-Step Word Problems
http://connected.mcgraw-hill.com/connected/login.do
Chapter 3: The Eraser Store
3.5 Packaging Erasers In Tens
Chapter 8: Decimals
8.1 Using Place Value
Teacher User ID: ccsde0(enumber)
Password: cobbmath1
Student User ID: ccsd(student ID)
Password: cobbmath1
http://www.exemplarslibrary.com/
User: Cobb Email
Password: First Name
*These lessons are not to be completed in
consecutive days as it is too much material. They
are designed to help support you as you teach
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your standards.
Additional Resources
K-5 Math Teaching Resources
http://www.k-5mathteachingresources.com/4th-grade-number-activities.html
Illustrative Mathematics
https://www.illustrativemathematics.org/content-standards/4/NBT/A
Estimation 180
http://www.estimation180.com/days.html
Greg Tang
http://www.gregtang.com
For additional assistance with this unit, please watch the unit webinar
https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx
Suggested Manipulatives
Vocabulary
Suggested Literature
Base ten blocks
Place value chart
Number line
Expanda-numbers
Hundreds chart
digit
place value
Count to a Million
A Million Fish…More or Less
The Grapes of Math
How Much, How Many, How Far, How Heavy,
How Long, How Tall is 1000?
Task Descriptions
Scaffolding Task
Constructing Task
Practice Task
Culminating Task
Formative
Assessment Lesson
(FAL)
3-Act Task
4th Grade Quarter 1
Task that build up to the learning task.
Task in which students are constructing understanding through deep/rich contextualized problem solving
Task that provide students opportunities to practice skills and concepts.
Task designed to require students to use several concepts learned during the unit to answer a new or unique situation.
Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key
mathematical ideas and applications.
Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and
solution seeking Act Two, and a solution discussion and solution revealing Act Three.
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Task Name
What Comes Next?
Task Type/Grouping
Strategy
Content Addressed
Standard(s)
Scaffolding Task
Partner/Small Group Task
Relative size of
numbers
MGSE4.NBT. 1
Description of Task
Students work with base ten materials to
experience that a place value in a number is ten
times more than the digit to its right.
Relative Value of
Places
Constructing Task
Partner/ Small Group Task
Relative size of
numbers
MGSE4.NBT.2
MGSE4.NBT. 1
Students work with dotty array pieces to
understand patterns within the base ten
number system. Students solve place value
problems to show understanding of the
patterns learned.
Number Scramble
Practice Task
Individual/Partner Task
Making and Naming
Large Numbers
MGSE4.NBT.2
Students create numbers given specific
directions and write those numbers in
standard, word and expanded form.
3 Act Task
Individual/Partner Task
Comparing Multi-digit
Numbers, Adding
Multi-digit Numbers
MGSE4.NBT.2
MGSE4.NBT.4
Students make connections between the base
ten number system and the Roman Numeral
number system.
Super Bowl Numbers
Ordering and
Comparing Numbers
Practice Task
Individual/Partner Task
Ordering Larger
Numbers
NFL Salaries
3 Act Task
Individual/Partner Task
Comparing Multi-digit
Numbers, Adding
Multi-digit Numbers
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MGSE4.NBT.2
MGSE4.OA.3
MGSE4.NBT.4
Students order and compare numbers through
a dice game played with a partner.
Students compare salaries of football players to
discuss why certain players are paid a particular
amount of money.
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Nice Numbers
Estimation as a Check
Making Sense of the
Algorithm
Reality Checking
It’s in the Number
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Constructing Task
Partner/Small group Task
Rounding, Four
Operations
Constructing Task
Individual/ Partner Task
Rounding, Adding,
Subtracting multi-digit
numbers
MGSE4.OA.3
MGSE4.NBT.4
MGSE4.NBT.3
MGSE4.MD.2
Students apply rounding concepts to find
estimated solutions to word problems.
Students find estimated solutions to problems.
MGSE4.NBT.4
MGSE4.NBT.3
Students write about strategies that are used
for given problems in the task, leading to a
discussion of procedures within the subtraction
standard algorithm.
Constructing Task
Individual/Partner Task
Fluently subtracting
multi-digit numbers
MGSE4.NBT.4
Constructing Task
Individual/ Partner Task
Ordering, Adding,
Subtracting and
Rounding multi-digit
numbers
MGSE4.NBT.2
MGSE4.NBT.4
MGSE4.NBT.3
MGSE4.MD.2
Students apply knowledge of the addition and
subtraction standard algorithm in order to
balance a mock check registry.
Culminating Task
Individual Task
Calculation and
Estimation with Whole
Numbers
MGSE4.OA.3
MGSE4.NBT.2
MGSE4.NBT.3
MGSE4.MD.2
Students gather data about populations in the
U.S. to draw conclusions about why people
choose to live in certain regions of the country.
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Fourth Grade Unit 1 Whole Numbers, Place Value and Rounding In Computation & Multiplication
Relating Area and Multiplication
Big Ideas/Enduring Understandings:
 Arrays and area models are ways to illustrate multiplication. Multiplication using area models shows the distributive property and partial
products. Multiplication should begin with models and move to the written record.
 Division with
 In multiplicative comparison, the underlying question is what factor would multiply one quantity in order to result in the other.
 Perimeter is the linear measurement of a boundary.
 Area is the measurement of square units within a figure (l x w) which also relates to the area model of multiplication.
 Rectilinear figures can be decomposed into smaller rectangles and squares. The area of the smaller rectangles and squares can be determined
using the formula a = l x w. The areas of the smaller rectangles and squares can be added together to find the total area of the rectilinear figure.
Essential Questions:
 How can I use the area model to multiply?
 How are multiplication and area related?
● How are area perimeter related?
● How can I decompose a rectilinear figure to find its area?
Content Standards
Content standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to
emphasize the natural connections that exist among mathematical topics.
Use the four operations with whole numbers to solve problems

MGSE4.OA.1 Understand that a multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get
another quantity.
a. Interpret a multiplication equation as a comparison e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7
times as many as 5.
b. Represent verbal statements of multiplicative comparisons as multiplication equations.
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

MGSE4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of
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a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown
factor.
Geometric Measurement: understand concepts of angle and measure angles.

MGSE4.MD.8 Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and
adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
Vertical Articulation
Third Grade Standard
Fifth Grade Standard
Sixth Grade Standard
Geometric Measurement: understand
concepts of area and relate area to
multiplication and to addition.
MGSE3.MD.7 Relate area to the operations
of multiplication and addition.
a. Find the area of a rectangle with
whole-number side lengths by tiling
it, and show that the area is the
same as would be found by
multiplying the side lengths.
b. Multiply side lengths to find areas of
rectangles with whole number side
lengths in the context of solving real
world and mathematical problems,
and represent whole-number
products as rectangular areas in
mathematical reasoning.
c. Use tiling to show in a concrete case
that the area of a rectangle with
whole-number side lengths a and b +
c is the sum of a × b and a × c. Use
area models to represent the
distributive property in
mathematical reasoning.
4th Grade Quarter 1
Solve problems involving the four operations,
and identify and explain patterns in arithmetic.
MGSE5.MD.3 Recognize volume as an attribute
of solid figures and understand concepts of
volume measurement.
a. A cube with side length 1 unit, called a
“unit cube,” is said to have “one cubic
unit” of volume, and can be used to
measure volume.
b. A solid figure which can be packed
without gaps or overlaps using n unit
cubes is said to have a volume of n cubic
units.
10
Solve real-world and mathematical problems
involving area, surface area, and volume.
Find area of right triangles, other triangles,
special quadrilaterals, and polygons by
composing into rectangles or decomposing into
triangles and other shapes; apply these
techniques in the context of solving real-world
and mathematical problems.
2015-2016
Instructional Strategies
Grade 3 students began to understand the meaning of area in relation to rectangles by using concrete and pictorial models such as square tiles,
geoboards and graph paper. Grade 4 students should apply their knowledge of squares and rectangles to decompose rectilinear figures into smaller
rectangles and squares. Then, using the formula developed through their work in fourth grade with area, students can find the area of each smaller
rectangle or square and find the area of the rectilinear figure by finding the sum of the areas calculated in the smaller rectangles or squares.
Students need to be given the opportunity to solve many real life problems that involve decomposing two dimensional figures into rectangles. For
example, design an “L-shaped” bathroom within a house and find the area 12 inch square tiles that will be needed to cover the room.
Common Misconceptions
Students may confuse perimeter and area when they measure the sides of a rectangle and then multiply. They think the attribute they find is
length, which is perimeter. Pose problems situations that require students to explain whether they are to find the perimeter or area.
Students may also think that different shapes made with the same units have different areas as well. This is due to lack of experience in developing
conservation on area. (Math Misconceptions: From Misunderstanding to Deep Understanding (2010), Bamberger, Oberdorf, and Shultz-Ferrel.
Using activities such as Piles of Tiles with tangrams and arrays will provide the needed spatial experience for students to develop this
understanding.
Evidence of Learning
●
●
●
●
Understand that area means to cover a certain amount of space without gaps.
Discuss and demonstrate the relationship between area and multiplication.
Understand the decomposition of an area model through multiplication.
Decompose rectilinear figures into non-overlapping squares and rectangles to find the total area of the rectilinear figure
Adopted Resources
Adopted Online Resources
Suggested Manipulatives
My Math:
http://connected.mcgrawhill.com/connected/login.do
base ten blocks
area model mats
grid paper
geo-boards
Chapter 13
13.1 Measure Perimeter
4th Grade Quarter 1
Teacher User ID: ccsde0(enumber)
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13.2 Problem Solving
13.3 Hands On: Model Area
13.4 Measure Area
13.5 Relate Area and Perimeter
Password: cobbmath1
Student User ID: ccsd(student ID)
Password: cobbmath1
pentominos
square unit items (centimeter cubes, one inch
tiles)
grid paper
http://www.exemplarslibrary.com/
User: Cobb Email
Password: First Name
Additional Resources
K-5 Math Teaching Resources
http://www.k-5mathteachingresources.com/4th-grade-number-activities.html
LearnZillion
https://learnzillion.com/lesson_plans/rectilinearfigures
Think Math
4th Grade Quarter 1
Vocabulary
Suggested Literature
area
area model
distributive property
dividend
divisor
equation
expression
rectangular array
rectilinear
polygons
quotient
Bigger, Better, Best!
Racing Around
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Task Descriptions
Scaffolding Task
Constructing Task
Practice Task
Culminating Task
Formative Assessment
Lesson (FAL)
3-Act Task
Task Name
Task that build up to the learning task.
Task in which students are constructing understanding through deep/rich contextualized problem solving
Task that provide students opportunities to practice skills and concepts.
Task designed to require students to use several concepts learned during the unit to answer a new or unique situation.
Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key
mathematical ideas and applications.
Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and
solution seeking Act Two, and a solution discussion and solution revealing Act Three.
Task Type/Grouping
Strategy
Content Addressed
Chocolate Covered
Candies
3 Act Task
Individual/Partner Task
Finding approximate
area
MGSE4.MD.3
Students will calculate the area of chocolate
candies using centimeter grid paper.
Perimeter and Area
Constructing Task
Individual/Partner
Determine area and
perimeter
MGSE4.MD.2
MGSE4.MD.3
Students will create rectangles with different
areas, but the same perimeter. Students will
create formulas that help find the perimeters
and areas of any given rectangle or square.
Parking Lot
3 Act Task
Individual/Partner
Determine area
MGSE4.MD.2
MGSE4.MD.3
Students will create a question to investigate
and answer about a vacant lot.
Indoor Playground
3 Act Task
Individual/Partner
Determine area when
given the perimeter
MGSE4.MD.2
MGSE4.MD.3
Students will determine the area and
perimeter of a playground that is being
moved indoors.
Scaffolding Task
Comparing area and
MGSE4.MD.3
Students will find the area and perimeter of
The Fence or the
4th Grade Quarter 1
13
Standard(s)
Task Description
2015-2016
Yard?
Piles of Tiles
4th Grade Quarter 1
Individual/ Partner
perimeter and finding
the area of rectilinear
figures
MGSE4.MD.8
rectangles and rectilinear figures using
concrete materials.
3-Act Task
Whole Group
Finding the area of a
rectilinear figure
MGSE4.MD.3
MGSE4.MD.8
Students will determine the area of a
rectilinear table using color tiles and if there
are enough color tiles in the bag to cover the
area of the table.
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4th Grade Quarter 1
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