CCGPS Mathematics Unit Outline
Subject(s)
Grade / Course
Unit of Study
Pacing
Math
4th Grade
Unit 1B – Multiplication and Division
30 days
STAGE 1 – Identify Desired Results
Standards
Related Standards
MCC4.NBT.5 Multiply a whole number of up to four digits by a onedigit whole number, and multiply two two-digit numbers, using
strategies based on place value and the properties of operations.
Illustrate and explain the calculation by using equations, rectangular
arrays, and/or area models.
MCC4.NBT.6 Find whole-number quotients and remainders with up
to four-digit dividends and one-digit divisors, using strategies based
on place value, the properties of operations, and/or the relationship
between multiplication and division. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or area
models.
MCC4.OA.1 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. Represent verbal statements of
multiplicative comparisons as multiplication equations.
MCC4.OA.2 Multiply or divide to solve word problems involving
multiplicative comparison, e.g., by using drawings and equations
with a symbol for the unknown number to represent the problem,
distinguishing multiplicative comparison from additive comparison.
MCC4.OA.3 Solve multistep word problems posed 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 letter
standing for the unknown quantity. Assess the reasonableness of
answers using mental computation and estimation strategies
including rounding.
MCC4.OA.4 Find all factor pairs for a whole number in the range 1–
100. Recognize that a whole number is a multiple of each of its
factors. Determine whether a given whole number in the range 1–
MCC4.MD.3. Apply the area and perimeter formulas for rectangles
in real world and mathematical problems. For example, find the
width of 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.
SMP1 Make sense of problems and persevere in solving them.
SMP2 Reason abstractly and quantitatively.
SMP3 Construct viable arguments and critique the reasoning of
others.
SMP7 Look for and make use of structure.
SMP8 Look for and express regularity in repeated reasoning.
100 is a multiple of a given one-digit number. Determine whether a
given whole number in the range 1–100 is prime or composite.
MCC4.OA.5 Generate a number or shape pattern that follows a
given rule. Identify apparent features of the pattern that were not
explicit in the rule itself
Key Knowledge
Key Skills
Students will know:
Students will be able to:
 Multiplication may be used to find the total number of objects
 Represent multiplication and division using a rectangular area
when objects are arranged in equal groups.
model.
 One of the factors in multiplication indicates the number of
 Understand that multiplication may be used in problem
objects in a group and the other factor indicates the number of
contexts involving equal groups, rectangular arrays/area
groups.
models, or rate.
 The properties of multiplication and division help us solve
 Multiply up to a 4-digit number by a 1- or 2-digit number using
computation problems easily and provide reasoning for
strategies.
choices we make in problem solving.
 Solve division problems using strategies.
 Unfamiliar multiplication problems may be solved by using
 Divide whole-numbers quotients and remainders with up to
known multiplication facts and properties of multiplication and
four-digit dividends and remainders with up to four-digit
division. For example, 8 x 7 = (8 x 2) + (8 x 5) and 18 x 7 = (10
dividends and one-digit divisors.
x 7) + (8 x 7).
 Interpret a remainder and its effect on the quotient.
 Division interprets the quotient as “how many groups” OR
“how many are in each group”.
 The dividend, divisor, quotient, and remainder are related in
the following manner: dividend = divisor x quotient +
remainder, and are also related to the factors and product of
multiplication.
Big Ideas / Enduring Understandings
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Products may be calculated using invented strategies.
Multiplication may be represented by rectangular arrays/area
models.
There are two common situations where division may be
used: fair sharing (given the total amount and the number of
equal groups, determine how many/much in each group) and
measurement (given the total amount and the amount in a
group, determine how many groups of the same size can be
created).
Some division situations will produce a remainder
Adapted from Understanding by Design
Essential Questions
EQ 1: How are multiplication and division related to each other?
EQ 2: How do multiplication, division, and estimation help us solve
real world problems?
EQ 3: What are strategies for solving multiplication and division
problems?
EQ 4: What patterns do I notice when I am multiplying whole
numbers that can help me multiply more efficiently?
EQ 5: How is understanding the role or the remainder in the context
of a word problem important to solving for the quotient?
EQ 6: How do I determine the factors of a number?
EQ 7: How do you identify prime and composite numbers and what
is the difference between the two?
STAGE 2 – Determining Acceptable Evidence
Assessments
Pre-Assessment
Pre-assessment is posted in Common Core Central https://aspen.marietta-city.org/aspen/logon.do
Checks for Understanding
Bi-weekly assessments are posted in Common Core Central –
http://aspen.marietta-city.org/aspen/logon.do
Post-Assessment
Unit Assessment – multiple choice and constructed response
STAGE 3 – Plan Learning Experiences
Engaging Learning Experiences
Hook: Engaging Student Learning: Number Talks: Numbers talks should be used within a lesson at least 3-5 times a week, however it
may precede or follow the “Engage/mini-lesson”
Georgia DOE Number
Talks Unit 1B.docx
Other examples of great “activating strategies” – think active – students thinking, problem solving, discussing ideas and questions
 Graph of the Day
 Weather Data
 Literature – Hook with a Book
 Real – World connection including a picture/photo/newspaper headline
 Problem of the Day or Puzzle
 Incredible Equations – Number of the Day
 Error Analysis – unraveling misconceptions – of an anonymous piece of student work
The Outstanding Math Guide (OMG) is packed with creative folded graphic organizers which contain steps and examples for each key
concepts encountered throughout the year. These graphic organizers are kept in a folder, standard 3-prong pocket folder. The OMG
serves as a visual reference that students keep in their notebooks and use in class or at home when completing homework, studying, or
reviewing spiraling material. These activities can be used as an additional resource for each of the units and can be used as a
supplement. They are not required.
OMG Foldable for Unit 1B:
Adapted from Understanding by Design
OMG 4th Grade Unit
OMG 4th Grade Unit
1B-Factors and MultiplesDoc29.docx
1B-Finding Primes.docx
OMG 4th grade Unit
OMG 4th Grade Unit
1B-Prime and Composite NumbersOperations
1B-RoundingDoc13.docx
and Algebraic Thinking.docx
EQ 1: How are multiplication and division related to each other?
Multiplication Bump x 100 - This activity can be changed to incorporate both multiplication and division and can be differentiated by using
10’s instead of 100’s
Multiplication Bump x
100.pdf
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Pass out a white board to each student
Ask a student to call out a 2 digit number. Write that number on the board.
Next write a division problem that includes that number.
Ask the students to write down a multiplication problem that can help prove that the division problem on the board is correct.
Call on several students to discuss and note responses on the board.
Advise students that for every division problem there is an equivalent multiplication problem or a multiplication problem that
includes the same numbers.
Read Aloud: Grapes of Math by Greg Tang and Divide and Run by Stuart Murphy
EQ 2: How do multiplication, division, and estimation help us solve real world problems?
Estimate the Quotient activity from K-5 Math Teacher Resources
Estimate-the-Quotie
nt.pdf
Read aloud: The Best of Times by Greg Tang
Adapted from Understanding by Design
Explain the following scenario to students and ask for responses
 Mrs. White and Mr. Taylor took their students are preparing to take their students on a field trip to the park. There is a total of 48
students. Students will be broken into groups of 2 and given 1 entry card per group. How many entry cards should the teacher
ask the park to give them?
 Ask the following questions: What other ways could we have solved this problem? (such as multiplication, estimation – HOW?)
EQ 3: What are strategies for solving multiplication and division problems?
Hook 1: Simply ask: What are some different ways to solve multiplication and division problems? (area model, partial product, partial
quotient, halving and doubling, drawing a model, acting it out…) Chart some of the examples on the board or chart paper to refer back to.
Read aloud: How Big is a Million by Anna Milbourne
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Pass out small white board to each student or student pair.
Write 1 multiplication and 1 division problem on the board.
Ask the students to solve the multiplication problem first using their best strategy to solve it.
Ask a student to come up and show how they solved the problem.
Inquire if someone solved it a different way. Have the student come up and show how he or she solved the problem.
Do the same for the division problem and discuss with the class.
Be sure to provide students with examples of any remaining ways the problems can be solved.
EQ 4: What patterns do I notice when I am multiplying whole numbers that can help me multiply more efficiently?
Square Numbers.pdf
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Pass out a hundred squares sheet to students. Ask them count by two’s and circle those numbers. Ask the students what do they
notice about the patterns? What numbers would you multiply together to get the answers when counting by 2’s? What pattern do
you see with the numbers you used to multiply?
Count by three’s and place a triangle around those numbers. Ask the same questions as above for the 3’s.
Have students skip count by 4’s and ask students to place another shape around those numbers. Again, ask the same questions
as above.
Additional questions at this time could be if there are any numbers that have several shapes around them. Also, what do they
notice about those numbers used when multiplying (specifically the factors)?
EQ 5: How is understanding the role of the remainder in the context of a word problem important to solving for the quotient?
Adapted from Understanding by Design
Remainder of One/One Hundred Hungry Ant by Elinor J. Pinczes
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Place any word problem on the board that when solved will have a remainder.
Below the word problem show the problem solved showing the remainder.
Ask the class what the remainder tells them about the problem/solution.
Write responses on the board.
Explain that remainders tell us several things: The quotient wasn’t enough and if we can do something else with the remainder in
the real world.
EQ 6: How do I determine the factors of a number?
Find the Factor: This activity could be placed on the board and the class can talk about the different solutions.
Find the Factor 4.pdf
Place the word “factor” on the board. Have students come up with what they think is the definition for this word. Place the student’s
answers on the board around the word. Then have student place all of the definitions into an order from what they think is the correct
definition down to what they think is incorrect. Define the word factor.
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Write the number 24 on the board as big as you can and draw a circle around it.
Ask a student to come up and write 2 numbers they can multiply together to give them 24 on the outside of the circle.
Ask several students to come up and do the same until all possible factors have been discovered.
Introduce that term factor and have a student come up and put a square around a factor they see. Continue until all numbers
(factors) have a square around them.
EQ 7: How do you identify prime and composite numbers and what is the difference between the two?
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Make life-size flash cards using a black marker and 8 ½ x 11 paper. Place the number 3 on one card and the number 12 on the
other.
Next, make additional cards using the same size paper using a red marker placing the number 1 on one card and the number 3 on
another card. Do the same writing the number 1 on another card, 12 on another card, 3 on another card, 4 on another card, 2 on
another, and 6 on the final card.
Ask a student to stand on one side of the room with the black 3 flash card and another to stand on the other side of the room with
the black 12 flash card.
Pick students to choose a red flash card and go to either side of the room to show that the number on their card is a factor of the
black flash card.
Adapted from Understanding by Design
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Once all of the numbers have been chosen ask the class how many factors do we see on the “3” side and how many on the “12”
side.
Introduce the definition of prime and composite and then ask students which of the numbers 3 and 12 or prime and composite.
Write additional prime and composite numbers on the board with students and include factors for extra practice.
Prime Number
Hunt.pdf
Least Common
Multiples.pdf
These games can give more practice in prime and composite numbers.
Learning Activities/Authentic Performance Tasks
Aligned Instructional Resources
(Physical and Digital)

www.georgiastandards.org – Georgia Department of
Education website for all Framework tasks and related math
resources

http://www.engageny.org/mathematics - Engage New York
includes modules for 3rd – 5th with lessons/ assessments/
tasks

www.K-5mathteachingresources.com – a site for a variety of
games, tasks, and math journal strategies

www.insidemathematics.org – the Common Core Math
website for performance tasks and assessments for all math
standards

http://illuminations.nctm.org - lessons and activities by
grade and domain

http://highered.mcgrawhill.com/sites/dl/free/0072533072/78543/CentimeterGrid.pd Printable centimeter grid paper

http://www.gameclassroom.com - Additional standard base
activities and interactive games.

http://www.k-5mathteachingresources.com/4th-grade-
Task 1:
Framework Task: (Please Note that this task will take more than a
day of work. This task could last a week or more.) In this task,
students will make diagrams to discover and demonstrate the
answers to 2-digit to 2-digit or 4-digit to 1-digit multiplication story
problems.
Implantation: This task provides opportunities for students to work
with arrays in real world situations as they work with larger
numbers. The recording sheet also asks students to develop a story
problem of their own. The idea of moving beyond building arrays
with base-ten blocks to drawing rectangles on paper or grid paper is
critical. At this point students must begin to visualize the
multiplication process without the blocks. As students begin to work,
they may realize that modeling problems such as these can require
a large number of base-ten blocks. Ask them to think of ways to do
the same problem without having to utilize base-ten blocks.
Adapted from Understanding by Design
Additional Resources:
From K-5 Teacher Resources:
multiplication-strateg
Breaking a Part a
y-doubling-and-halving.pdf Factor 5.pdf
OnCore:
Lesson 2: Students are solving problems to make sense of the
reasonableness of their answers as they model with subtraction.
Lesson 26: Students will use expanded form to find the product of a
multiplication problem.
Lesson 27: Students will use partial products to find the product of a
multiplication problem.
Lesson 33: Students will use the area model and partial products
for multiplication.
Lesson 34: Students will be working with partial products for
multiplication.
Task 2:
Framework Task: Students explore their understanding of
multiplication and how it applies to multiplying 2 digit numbers by 2digit numbers and 1-digit up to 4-digit whole numbers.
Implantation: This is an opportunity for students to use what they
know about multiplication to find the product of 1-digit and 2-digits
by up to 4-digit whole numbers. This task should be completed
before students have any experiences with the standard algorithm
for multiplying two digit numbers.
Additional Resources:
Adapted from Understanding by Design
number-activities.html - Additional activities and read aloud
activities.
http://illuminations.nctm.org/LessonDetail.aspx?ID=U109
This resource is in eight lesson unit which takes students through
the developmental understanding of multiplication. Portions of this
unit can be used for remediation or additional practice.
FORMATIVE ASSESSMENT
CHECKPOINT ONE
Use this checkpoint to see student progress.
4th Grade - Math Unit 1B - Checkpoint 1.pdf
Task 3:
Framework Task: This task provides several contexts in which
students will have to determine the best estimation for the situation.
Implantation: For students to be able to round accurately,
“rounding should be flexible and well understood conceptually” (Van
de Walle, 246). In order for students to conceptually understand
rounding, they must be engaged in context to allow them to make
sense of this concept. This task provides several contexts in which
students will have to determine the best estimation for the situation.
With these estimations, students will use the most familiar form of
estimation, rounding (Van de Walle, 241).
Adapted from Understanding by Design
Additional Resources:
From K-5 Teaching Resources
Multiplication Number
Story.pdf
The Baker.pdf
OnCore
Lesson 23: Multiply tens, hundreds, and thousands by whole
numbers through 10.
Lesson 24: Estimate products by rounding and determine if exact
answers to multiplication problems are reasonable.
Lesson 32: Estimate products by rounding or by using compatible
numbers.
Task 4:
Framework Task: This task deals with using friendly numbers to
divide.
Implantation: Ask students how they could estimate the number of
small prizes each of Mr. Wong’s 9 students would receive if he had
exactly 893 prizes to give away. If no one mentions compatible
numbers, remind the class that they can estimate the answer to a
problem by replacing the numbers in the problem with numbers that
are easier to calculate with. Such easier numbers are called
compatible numbers. You might show these two examples of
compatible numbers:
● To estimate 3,456 ÷ 7, students might recognize 3,456 is close to
3,500 and choose compatible numbers 3,500 and 7. So, 3,456 ÷ 7
is about 3,500 ÷ 7, or 500.
Additional Resources:
OnCore
Adapted from Understanding by Design
Lesson 37: Use multiples to estimate quotients.
Lesson 39: Divide tens, hundreds, and thousands by whole
numbers through 10.
Task 5:
Framework Task: In this task, students analyze multiplication and
division expressions to find patterns and make connections among
division and multiplication problems.
Implantation: It is critical for students to understand the
relationship that exists between multiplication and division as well
as the strong relationship between the dividend, divisor, and
quotient. This task is designed to allow students to further explore
these relationships.
Additional Resources:
OnCore:
Lesson 25: Students will use the distributive property to be used to
find the product.
In this lesson, students generate products using a number line
model. It can be used as remediation, additional practice or in an
independent center.
RunRaces-AS-FactM
astery.pdf
http://www.mathcats.com/grownupcats/ideabankmultiplication.html This resource provides additional ideas for approaching
multiplication instruction. This could be used in small group review
or additional practice.
http://illuminations.nctm.org/ActivityDetail.aspx?ID=224 - This game
Adapted from Understanding by Design
requires the use of division skills to figure dining situations. It can be
used to practice the concept.
Task 6:
Framework Task: Generating Patterns (Developed by MariettaCity to address OA.5)
Implementation: Place the multiples of different numbers on the
board, i.e. 5, 10, 15… students recognize the multiples results in a
5, 0; do the same for 10, 20, 30….and 9, 18, 27…
- Have students find the patterns for a variety of numbers; including
finding the missing numbers in a pattern.
Additional Resources:
The task challenges a student to demonstrate understanding of the
concepts involved in generating and analyzing a pattern.
Piles of Oranges.pdf
Triangular
Numbers.pdf
Buttons - Growing
Patterns.pdf
Growing Stair
Steps.pdf
Task 7:
Framework Task: Students explore why dividing by zero is
undefined.
Adapted from Understanding by Design
Implantation: Students determine whether a child’s work is
mathematically sound and give evidence for their conclusions.
Please review the background information before starting the task.
Background
Information for What is 2500 by 300.docx
Additional Resources:
Diminishing Return: Problem of the month that could be used with
the lesson or as an extension in a small group.
Diminishing
Return.pdf
http://www.homeschoolmath.net/operation-game.php - This
resources uses a variety of operations to solve problems. This can
be used as practice.
http://www.toonuniversity.com/flash.asp?err=517&engine=13 - This
is an activity students can complete to practice solving multiplication
problems with multiples of ten. It can be used as an introduction to
this task or for additional practice.
FORMATIVE ASSESSMENT
CHECKPOINT TWO
Use this checkpoint to see student progress.
4th Grade - Math Unit 1B - Checkpoint 2.pdf
Task 8:
Adapted from Understanding by Design
Framework Task: Students will discover the difference between
prime and composite numbers through the making of arrays using
color tiles or counters.
Investigating
Prime.pdf
Implantation: Have students create a T-chart and label one side
only two ways and the other more than two ways.
Additional Resources:
Background Information: This standard requires students to
demonstrate understanding of factors and multiples of whole
numbers. This standard also refers to prime and composite
numbers. Prime numbers have exactly two factors, the number one
and their own number. For example, the number 17 has the factors
of 1 and 17. Composite numbers have more than two factors. For
example, 8 has the factors 1, 2, 4, and 8. A common misconception
is that the number 1 is prime, when in fact; it is neither prime nor
composite. Another common misconception is that all prime
numbers are odd numbers. This is not true, since the number 2 has
only 2 factors, 1 and 2, and is also an even number.
A prime number is a number greater than 1 that has only 2 factors,
1 and itself. Composite numbers have more than 2 factors.
Students investigate whether numbers are prime or composite by
building rectangles (arrays) with the given area and finding which
numbers have more than two rectangles (e.g. 7 can be made into
only 2 rectangles, 1 x 7 and 7 x 1, therefore it is a prime number) or
by finding factors of the number.
http://www.sheppardsoftware.com/mathgames/numbers/fruit_shoot
_prime.htm - This resource has games dealing with prime and
composite. It can be used to for additional practice.
Adapted from Understanding by Design
(Additional Resource for Task 8)
Framework Task: This task refers to prime and composite
numbers. Adapted from Yummymath.com Cicadas
Cicadas Brood X
Student Sheet.docx
Implantation: Students will work through the student sheet.
Task 9:
Framework Task: This task refers to prime and composite
numbers.
Prime vs Composite
Recording Sheet.docx
Implantation: Students will follow the directions from the “Prime vs.
Composite” recording sheet. List the factors and draw lines to
connect factor pairs. Write P for prime, C for composite, or N for
neither. What is the only even prime number? Use a diagram to
explain how you know the number is prime. How can you determine
if a number is prime, composite, or neither by looking at the factors
of the number?
Additional Resources:
http://wonderopolis.org/wonder/what-is-a-prime-number/ - Have
students investigate larger prime numbers
Task 10:
Framework Task: This task requires students to demonstrate
Adapted from Understanding by Design
understanding of factors and multiples of whole numbers.
THE FACTOR GAME
Recording Sheet.docx
Implantation: One way to introduce this task is to model the first
one or two steps on the overhead. Discuss the patterns students
see. Write these on the board or chart paper as students share
them. Each group will complete a game board, however students
need to answer questions separately. Let students share their
observations. Record these on a chart or the board.
Additional Resources:
Factor
Game-AS-Problems.pdf
http://learnzillion.com/lessons/786-determine-if-a-number-is-primeor-composite-using-area-models - In this lesson you have learned
how to determine if a number is prime or composite by using area
models.
http://learnzillion.com/lessons/799-find-multiples-by-using-anumber-line - In this lesson you are going to figure out multiples of a
number by using a number line.
https://www.khanacademy.org/math/arithmetic/factorsmultiples/divisibility_and_factors/v/finding-factors-of-a-number from Khan Academy for students to have extra practice at home
FORMATIVE ASSESSMENT
CHECKPOINT THREE
At this point the unit 1B should be complete. Use this
checkpoint to see student progress.
Adapted from Understanding by Design
4th Grade - Math Unit 1B - Checkpoint 3.pdf
Formative Constructed Response for 1B
4th Grade - Math Unit 1B - Constructed Response.pdf
Unit Vocabulary Terms
Common Core State Standards Glossary
http://www.corestandards.org/Math/Content/
mathematics-glossary/glossary
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•
algorithm
composite
digits
dividend
divisor
division (repeated subtraction)
estimate
expanded form
factors
multiplicand
multiplier
multiples
numbers
numerals
partition division (fair-sharing)
period
place value
prime
product
properties
quotient
Adapted from Understanding by Design
Interdisciplinary Connections:
SCIENCE
S4E3. Students will differentiate between
the states of water and how they relate to
the water cycle and weather.
S4E4. Students will analyze weather
charts/maps and collect weather data to
predict weather events and infer patterns
and seasonal changes.
https://www.georgiastandards.org/Framewor
ks/GSO%20Frameworks/4%20Science%20
Framework%20Weather.pdf
S4L1. Students will describe the roles of
organisms and the flow of energy within an
ecosystem.
S4L2. Students will identify factors that
affect the survival or extinction of organisms
such as adaptation, variation of behaviors
(hibernation), and external features
(camouflage and protection).
https://www.georgiastandards.org/Frameworks/G
SO%20Frameworks/4%20Science%20Framewo
rk%20Ecosystems.pdf
MCC4.MD.2 Use the four operations to
solve word problems involving distances,
Differentiation
Differentiation strategies for extension/
intervention may be found in each
performance task listed.
•
•
remainder
rounding
intervals of time, liquid volumes, masses of
objects, and money, including problems
involving simple fractions or decimals, and
problems that require expressing
measurements given in a larger unit in
terms of a smaller unit. Represent
measurement quantities using diagrams
such as number line diagrams that feature a
measurement scale.
MCC4.MD.4. Make a line plot to display a
data set of measurements in fractions of a
unit (1/2, 1/4, 1/8). Solve problems involving
addition and subtraction of fractions by
using information presented in line plots.
Designer Notes:
Adapted from Understanding by Design