Math News!
Grade 3, Module 1, Topic A
3rd Grade Math
Focus Area– Topic A
Module 1: Properties of Multiplication and Division and Solving Problems
with Units of 2-5 and 10
Multiplication and the Meaning of Factors
Math Parent Letter
This document is created to give parents and students a better
understanding of the math concepts found in Eureka Math (©
2013 Common Core, Inc.) that is also posted as the Engage
New York material which is taught in the classroom. Module 1
of Eureka Math (Engage New York) covers Properties of
Multiplication and Division and Solving Problems with Units of
2-5 and 10. This newsletter will discuss Module 1, Topic A.
Topic A. Multiplication and the Meaning of the Factors
Vocabulary Words
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
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
Multiply/Divide
Repeated Addition
Equal Groups
Number of Groups
Equation
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Array
Row
Column
Size of Groups
Factor
Things to Remember!!!
Array – repeated rows of numbers or objects
Multiply - an operation showing how many times a number is
added to itself
Equal groups – same number of objects in each group
Factor – number of groups and the number in each group
Equation – a statement that two expressions are equal, for
example 5 x 4 = 20
Divide – separate into equal groups
Students will be introduced to multiplication with the
concept of repeated addition.
Draw a picture to show 3 + 3 + 3 + 3 = 12. Then write a
multiplication sentence to represent the picture.
The size of each group is 3,
because there are 3 circles in
each group. (In the repeated
addition sentence 3 is the
number repeated)
The number of groups needed is 4, because there are 4
equal groups of three. (In the repeated addition problem we
see 3 four times) Think: 4 times I see 3; 4 x 3 = 12.
Students will be introduced to arrays as a visual tool to
help solve word problems.
Tommy collects baseball cards.
He arranges them in 4 rows of 5.
Draw Tommy’s array to show
how many baseball cards he has all
together. Then write a
multiplication sentence to describe
the array.
Lesson 3, will check their understanding of the concepts
taught in the previous two lessons.
There are 3 balloons in each circle. How many balloons
are in three circles?
OBJECTIVE OF TOPIC A
1
Understand equal groups of as multiplication.
2
Relate multiplication to the array model.
3
Interpret the meaning of factors—the size of the group or the
number of groups.
Number of groups: 3 Size of group: 3
3x 3 =
9 .
There are 9 balloons all together.
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 3, Module 1, Topic B
Focus Area– Topic B
3rd Grade Math
Module 1: Properties of Multiplication and Division and Solving Problems
with Units of 2-5 and 10
Math Parent Letter
This document is created to give parents and students a better
understanding of the math concepts found in Eureka Math (©
2013 Common Core, Inc.) that is also posted as the Engage
New York material which is taught in the classroom. Module 1
of Eureka Math (Engage New York) covers Properties of
Multiplication and Division and Solving Problems with Units of
2-5 and 10. This newsletter will discuss Module 1, Topic B.
Topic B. Division as an Unknown Factor Problem
Vocabulary Words
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Multiplication
Quotient
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
Unknown
Division
Division as an Unknown Factor Problem
Students will be introduced to division. They will see
multiplication as a way to find the total and division as a
way to find out how many groups or the size of each group.
Tony puts 20 baseballs into bags. He divided them equally
between 5 tables. Draw the baseballs on each table. (Students
will need to draw what is stated in the word problem)
There are 4 baseballs on each table.
20
5 = 4 .
Tracy puts 20 baseballs into bags. Each bag holds 5 balls.
Circle the groups of 5 to show the balls in each bag.
Things to Remember!!!
When we multiply we want to find the total. When we divide
we start with the total and want to find either the number of
groups or the size of the group.
There are 20 marbles and 5 children sharing the marbles. The
total number of marbles and the number of children that is
sharing the marbles is what you know. The unknown in this
situation is how many marbles per child.
You can think 20 5 or 5 x ? = 20.
Tracy needs 4 bags.
4 x 5 = 20
=4
The numbers in the blank represent the number of groups.
Tracy uses 20 baseballs to make 4 equal groups. Draw to
show how many baseballs are in each group.
20 5 = 4
4 is the quotient in this problem.
5 x 4 = 20
4 is the unknown factor in this problem.
There are 5 baseballs in each group.
4 x 5 = 20
=5
The numbers in the blank represent the number in each group.
Use an array to model.
OBJECTIVE OF TOPIC B
1
Understand the meaning of the unknown as the size of the
group in division.
2
Understand the meaning of the unknown as the number of
groups in division.
3
Interpret the unknown in division using the array model.
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 3, Module 1, Topic C
3rd Grade Math
Focus Area– Topic C
Module 1: Properties of Multiplication and Division and Solving Problems
Analyzing Arrays to Multiply Using Units of 2 and 3
with Units of 2-5 and 10
Math Parent Letter
This document is created to give parents and students a better
understanding of the math concepts found in Eureka Math (©
2013 Common Core, Inc.) that is also posted as the Engage
New York material which is taught in the classroom. Module 1
of Eureka Math (Engage New York) covers Properties of
Multiplication and Division and Solving Problems with Units of
2-5 and 10. This newsletter will discuss Module 1, Topic C.
Topic C. Analyzing Arrays to Multiply Using Units of 2 and 3
Vocabulary Words
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Commutative Property

Becky organizes her stickers on a page in her sticker book.
She arranges them in 2 rows and 4 columns. Draw an array
to show Becky’s stickers. (Label the array to show how you
skip-count to solve the multiplication sentence)
Use your array to write a multiplication sentence to find the
total number of stickers.
2x4=8
Use what you know about the commutative property to
write a different multiplication sentence for your array.
Parenthesis
Things to Remember!!!
Students are introduced to the commutative property. They will
gain an understanding that the commutative property means
that when multiplying, the factors can change places, but the
total does not change.
4x2=8
Tracy is making a sticker album. She puts 3 pictures in
each row.
a.
Use the multiplication sentence on the right.
Draw arrays to show the stickers on the upper and
lower part of Tracy’s album page.
b.
Tracy calculates the total number of pictures as
shown below. Use the array you drew to help
explain.
6 x 4 = 24 and 4 x 6 = 24
6x4=4x6
They will distinguish rows from columns, noticing that the
meaning of the factors change according to the orientation of
the array.
Rotate – turn, used with reference turn 90ᴼ.
Students will also begin to learn about parenthesis ( ).
5 x 3 = 6 + 9 = 15
OBJECTIVE OF TOPIC C
1
Demonstrate the commutativity of multiplication and practice
related facts by skip-counting objects in array models.
2
Find related multiplication facts by adding and subtracting
equal groups in array models.
3
Model the distributive property with arrays to decompose
units as a strategy to multiply.
The whole array shows 5 rows times 3 in each
row. (5 rows times 3 columns which is 5 x 3).
Then maybe Tracy did not know the answer to 5
x 3 so she broke it into 2 smaller facts. 2 x 3,
which is 6 and 3 x 3, which is 9. So she did 6 +
9 because 5 x 3 = 6 + 9. Then if you multiply 5 x
3 it is 15, and if you add 6 + 9 it is 15.
So 5 x 3 = 6 + 9 = 15
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 3, Module 1, Topic D
Focus Area– Topic D
3rd Grade Math
Module 1: Properties of Multiplication and Division and Solving Problems
with Units of 2-5 and 10
Math Parent Letter
This document is created to give parents and students a better
understanding of the math concepts found in Eureka Math (©
2013 Common Core, Inc.) that is also posted as the Engage
New York material which is taught in the classroom. Module 1
of Eureka Math (Engage New York) covers Properties of
Multiplication and Division and Solving Problems with Units of
2-5 and 10. This newsletter will discuss Module 1, Topic D.
Topic D Division Using Units of 2 and 3
Vocabulary Words
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
Equation
Tape Diagram
Quotients
Students will begin to use tape diagrams to solve word
problems. A tape diagram is a model that students draw in
order to help visualize the relationships between quantities. The
first lesson on Topic D will compare an array to a tape diagram.
Things to Remember!!!
An equation is a statement that says two expressions are equal.
4 x 3 = 12
or
12
4=3
The quotient is the results of a division problem
12
4=3
3 is the quotient.
Division Using Units of 2 and 3
Ms. Cara has 12 apples. She puts 3 apples in each bag. How
many bags does she have?
In previous lessons, students solved
word problems with an array.
Now they will relate an array to
a tape diagram. Students will draw
the array and place a box around it.
Ms. Cara puts 3 apples in each bag.
Students will separate the array to
show 3 apples in each bag.
The next step is to label the known
and unknown parts of the word
problem. The word problem states
there are 12 apples. The entire tape
diagram is equal to 12 apples. The
diagram is labeled 12 apples. For
every 1 bag there are 3 apples. The
first rectangle represents 3 apples or
1 bag of apples. The information
that is unknown is the number of
bags Ms. Cara has, which is labeled with a question mark.
Ms Rose has 12 boxes of crayons. Each class gets 4 boxes.
How many classes get boxes of crayons?
The word problem states each class
will get 4 boxes of crayons. Start by
drawing and labeling the 4 boxes.
Next estimate what 12 boxes would
look like and draw a dotted line to
represent the total.
OBJECTIVE OF TOPIC D
1
Model division as the unknown factor in multiplication using
arrays and tape diagrams.
2
Interpret the quotient as the number of groups or the number
of objects in each group using units of 2.
3
Interpret the quotient as the number of groups or the number
of objects in each group using units of 3.
Label the total and the unknown.
There are 12 boxes but we do not
know how many classrooms. (?)
Skip-count and solve. We have to
count by 4’s until we have 12.
4, 8, 12. We counted 3 times to get
12. So we know 3 classrooms will
get 4 boxes of crayons.
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 3, Module 1, Topic E
3rd Grade Math
Focus Area– Topic E
Module 1: Properties of Multiplication and Division and Solving Problems
Multiplication and Division Using Units of 4
with Units of 2-5 and 10
Find the number of sides on 6 squares.
Math Parent Letter
This document is created to give parents and students a better
understanding of the math concepts found in Eureka Math (©
2013 Common Core, Inc.) that is also posted as the Engage
New York material which is taught in the classroom. Module 1
of Eureka Math (Engage New York) covers Properties of
Multiplication and Division and Solving Problems with Units of
2-5 and 10. This newsletter will discuss Module 1, Topic E.
Topic E Multiplication and Division Using Units of 4
We know there are 4 sides on a square and we have 6 squares.
The tape diagram is labeled with all of the information given in
the word problem. We are looking for the total number of
sides in 6 squares, so we will multiply to find the answer.
Vocabulary Words
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Array

Tape Diagram
Things to Remember!!!
A number bond
Students will also begin to explore the
use of smaller facts to solve a larger
fact by using arrays.
This array shows how dividing the
problem into two smaller factors
can make it easier to solve.
Students already know 5 x 4 and
2 x 4. So they know 7 x 4.
7 x 4 is (5 x 4) + (2 x 4) or 20 + 8.
Craig arranges 24 baseball cards into 4 equal rows. How many
cards are in each row?
OBJECTIVE OF TOPIC E
1
Skip-count objects in models to build fluency with
multiplication facts using units of 4.
2
Relate arrays to tape diagrams to model the commutative
property of multiplication.
3
Use the distributive property as a strategy to find related
multiplication facts.
4
Model the relationship between multiplication and division.
I can find the unknown by skip-counting by 4’s.
4, 8, 12, 16, 20, 24 – there are 6 groups of 4
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 3, Module 1, Topic F
3rd Grade Math
Focus Area– Topic F
Module 1: Properties of Multiplication and Division and Solving Problems
Distributive Property and Problem Solving Using
Units of 2-5 and 10
with Units of 2-5 and 10
Math Parent Letter
This document is created to give parents and students a better
understanding of the math concepts found in Eureka Math (©
2013 Common Core, Inc.) that is also posted as the Engage
New York material which is taught in the classroom. Module 1
of Eureka Math (Engage New York) covers Properties of
Multiplication and Division and Solving Problems with Units of
2-5 and 10. This newsletter will discuss Module 1, Topic F.
Topic F Distributive Property and Problem Solving Using
Units of 2 – 5 and 10
Davie used the distributive property to solve a multiplication
problem. Look at his work below, write the multiplication
problem Davie solved and complete the number bond.
(5 x 4) + (3 x 4) =
Davie adds 5 fours and
3 fours to get his answer.
5 fours + 3 fours = 8 fours
(5 + 3) x 4 = 8 x 4 = 32
Vocabulary Words
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Distributive Property

Unit
Things to Remember!!!
A unit is a group of the same items.
If you have 7 apples, the unit is apples because it is a group of
the same thing. In math we can use numbers as units.
3 + 3 + 3 + 3 + 3 + 3 + 3 is the same as 7 threes. There are 7
of the same number (3).
The distributive property says that multiplying a number by a
group of numbers added together is the same as doing each
multiplication separately.
Complete the equation below to solve 24
2 = _______.
Students will see the same concepts
when dividing as they did when
multiplying. Students will use smaller
facts to solve the larger fact. 24 can
be seen as (20 + 4). They will divide
the array to show 20 blocks and 4
blocks. 20 divided by 2 is 10, 4
divided by 2 is 2. 10 plus 2 is 12.
Students will begin to solve two step word problems using tape
diagrams.
Lacey eats 6 cookies each day at school. On Friday, she drops
2 cookies and only eats 4. Write and solve an equation to
show the total number of cookies Lacey eats this week.
OBJECTIVE OF TOPIC F
1
Apply the distributive property to decompose units.
2
Solve two-step word problems involving multiplication and
division and assess the reasonableness of answers.
3
Solve two-step word problems involving all four operations
and assess the reasonableness of answers.
We go to school for 5 days a week. Lacey has 6 cookies to eat
each day, but on Friday she drops some. So for 4 out of the 5
days she ate 6 cookies. 4 x 6 = 24. On Friday she only ate 4
cookies, 24 + 4 = 28.
This information was generously shared by LPSS, Lafayette, LA