Math News!
Grade 3, Module 3, Topic A
Focus Area– Topic A
3rd Grade Math
Module 3: Multiplication and Division with Units of 0, 1, 6-9,
and Multiples of 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 3 of Eureka Math (Engage New York)
covers Multiplication and Division with Units of 0, 1, 6-9
and Multiples of 10. This newsletter will discuss Module 3,
Topic A.
Topic A. Properties of Multiplication and Division
Vocabulary Words
 Commutative Property
 Product
 Unknown
 Factors
Properties of Multiplication and Division
The commutative property of multiplication means
that changing the order of factors does not change the
answer or product. This means that 7 x 4 = 4 x 7.
By understanding this property students also learn that
a majority of their multiplication facts are already
known.
Learning how to solve multiplication problems by
using the commutative property and n+1 is also taught
in this topic. Solve


Tape Diagram
n+1
Things to Remember!!!
What is a tape diagram?
A tape diagram uses a rectangle(s) with numbers to
represent the number in a word problem. Now that
numbers are getting bigger a rectangle is used to represent
the number instead of drawing dots or pictures. A tape
diagram allows the student to visualize the problem.
OBJECTIVE OF TOPIC A
1
Study commutatively to find known facts of 6, 7, 8 and 9.
2
Apply the distributive and commutative properties to
relate multiplication facts of 5 x n + n to 6 x n and n x 6
where n is the size of the unit.
3
Multiply and divide with familiar facts using a letter to
represent the unknown.
The commutative property states that factors can
change order and still have the same product. 6 x 8 can
also be written as 5 x 8 + 1 x 8. By using a
multiplication fact that is already known, solving 6 x 8
can be easy. The n+1 rule is simply saying to add one
more group. In this case we know 5 x 8 is 40 and if 1
more group of 8 is added (repeated addition), then 6
groups of 8 = 6 x 8 = 42.
In previous lessons a question mark (?) was used to
represent an unknown number. In this topic using a
letter to represent the unknown is also introduced.
Mrs. James has 48 pencils for her library. Mrs. James
placed a pack of 6 pencils on each desk. How many
packs of pencils does Mrs. James have?
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 3, Module 3, Topic B
3rd Grade Math
Focus Area– Topic B
Module 3: Multiplication and Division with Units of 0, 1, 6-9,
and Multiples of 10
Multiplication and Division Using Units of 6 & 7
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 3 of Eureka Math (Engage New York)
covers Multiplication and Division with Units of 0, 1, 6-9
and Multiples of 10. This newsletter will discuss Module 3,
Topic B.
Topic B Multiplication and Division Using Units of 6 & 7
Vocabulary Words
 Commutative Property
 Distributive Property

Decompose
Things to Remember!!!
What is decomposing?
Decompose it to break a number apart. When the numbers
are not as big it is easier for students to multiply or divide
problems. The number 25 can be decomposed into 20 + 5,
or 10 + 10 + 5.
Using number bonds to decompose and to skip count
When adding two numbers together it is easier to add
to a ten. Students will decompose numbers to make 10
so it is easier to add and find the answer. In the
problem above the student will decompose one of the
7’s in order to combine 7 and another number to make
a 10. 7 + 3 = 10, so if we decompose 7 into 3 and 4 we
can add the 7 and 3 together to make 10 then add the
remaining 4 to 10 and the answer is 14. Students will
gain a better understanding that multiplying is actually
repeated addition.
Distributive Property of Multiplication – When one of
the factors of a product is a sum, multiplying each
addend before adding does not change the product.
9x7=?
We can decompose the number 9 to create two smaller
multiplication problems. Below is a tape diagram that
decomposes 9 into 5 and 4. The problem could be
written (5 + 4) x 7. If we use the distributive property
the problem is written (5 x 7) + (4 x 7) = ? We
distributed the 7 to both the 5 and the 4. Now we can
multiply two smaller problems and add them together
to get the answer.
OBJECTIVE OF TOPIC B
1
Count by units of 6 to multiply and divide using number
bonds to decompose
2
Count by units of 7 to multiply and divide using number
bonds to decompose
3
Use the distributive property as a strategy to multiply and
divide units of 6 & 7
4
Interpret the unknown in multiplication and division to
model and solve problems using units of 6 & 7
Using number bonds to apply the distributive
property.
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 3, Module 3, Topic C
3rd Grade Math
Focus Area– Topic C
Module 3: Multiplication and Division with Units of 0, 1, 6-9,
and Multiples of 10
Multiplication and Division Using Units up to 8
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 3 of Eureka Math (Engage New York)
covers Multiplication and Division with Units of 0, 1, 6-9
and Multiples of 10. This newsletter will discuss Module 3,
Topic C.
Topic C Multiplication and Division Using Units up to 8
Vocabulary Words
 Associative Property
 Distributive Property
 Product



Mental Math
Parentheses
Unknown
Solve 16 x 3
This is a difficult problem to solve. Let’s simplify the
problem. Begin by listing the factors of 16. 2, 4 and 8 are
factors of 16. Knowing that 8 x 2 are factors we can rewrite
the problem as (8 x 2) x 3. In math the parentheses are used
to group important things together, so you always do them
first. (8 x 2) is in parentheses so you would multiply them
first to get 16. This problem is still hard to solve because we
are still trying to multiply 16 x 3. We can use the associative
property to help solve the problem. The associative
property says that when we are multiplying all numbers
together we can multiply the numbers in any order and still
get the same answer. So we can move the parentheses to
make the problem easier to solve. 8 x (2 x 3). Drawing an
array to solve the problem is a simple solution to the
problem. Draw 8 groups of 2 x 3.
Division Word Problem
The store sells 1 meter of fabric for $7. Tonya buys some
fabric that costs a total of $56. She uses 3 meters to sew a
dress. How many meters of fabric does she have left?
Students may also realize that the problem can also be
written as 8 x 6 or they may use the distributive property
to solve the problem. The
distributive property says that when
one of the factors of a product is a
sum, multiplying each addend before
adding will not change the product or answer.
Moving Parentheses
OBJECTIVE OF TOPIC C
1
Understand the function of parentheses and apply to
solving problems.
2
Model the associative property as a strategy to multiply.
3
Use the distributive property as a strategy to multiply and
divide.
4
Interpret the unknown in multiplication and division to
model and solve.
The first time we solved this problem the parentheses was
around the addition problem. Now the parentheses are
around the multiplication problem. The parentheses tell us
what problems to solve first. First multiply the problem in
the parentheses, 8 x 3 = 24. Next we add 8 to that answer.
24 + 8 = 32. It is very important to solve the problems in
parentheses first because the answer will not be the same.
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 3, Module 3, Topic D
3rd Grade Math
Focus Area– Topic D
Module 3: Multiplication and Division with Units of 0, 1, 6-9,
and Multiples of 10
Multiplication and Division Using Units of 9
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 3 of Eureka Math (Engage New York)
covers Multiplication and Division with Units of 0, 1, 6-9
and Multiples of 10. This newsletter will discuss Module 3,
Topic D.
Topic D Multiplication and Division Using Units of 9
Students will use the distributive property to establish
the 9 = 10 – 1 pattern for multiplication.
Understanding this pattern will enable students to see
this method of multiplication as a tool, rather than a
trick.
What is easier to solve, 9 x 6 or 10 x 6? 10 x 6
How many sixes are in 10 x 6? 10 sixes
6

Unit
6
6
6
6
6
6
6
6
How many sixes are in 9 x 6? 9 sixes
6
Vocabulary Words
 9 = 10 – 1 Strategy
6
6
6
6
6
6
6
6
6
9 x 6 = (10 x 6) – (1 x 6)
9 x 6 = 60 – 6
Division Word Problem
What is 60 – 6? 54
Joey has 54 trading cards and shares them with 7 of his
friends. He is so excited he drops his box of cards and
looses 14 trading cards. How many trading cards will Joey
and each of his friends get?
First find out how many trading cards Joey has left.
54 – 14 = c
c = 40
They will also learn to break up 9 into 5 and 4.
9 x 6 = (5 + 4) x 6
Now use the distributive property to distribute the 6
9 x 6 = (5 x 6) + (4 x 6)
9 x 6 = 30 + 24
Next divide the trading cards that are left into 8 people.
9 x 6 = 54
d=5
Joey and each of his 7 friends get 5 trading cards.
OBJECTIVE OF TOPIC D
1
Apply the distributive property and the fact 9 = 10 – 1 as
a strategy to multiply.
2
Identify and use arithmetic patterns to multiply.
3
Interpret the unknown multiplication and division to
model and solve problems.
Kim has 9 packs of cookies with 5 in each pack. After
giving1 to each classmate she has 15 left. How many
cookies did Kim give away?
First find out how many cookies Kim has.
9x5=h
h = 45
Next subtract 15 from the total to see how many she
gives away.
45 – 15 = g
g = 30
How many classmates does Kim have? 30
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 3, Module 3, Topic E
3rd Grade Math
Focus Area– Topic E
Module 3: Multiplication and Division with Units of 0, 1, 6-9,
and Multiples of 10
Analysis of Patterns and Problem Solving Including Units
of 0 and 1
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 3 of Eureka Math (Engage New York)
covers Multiplication and Division with Units of 0, 1, 6-9
and Multiples of 10. This newsletter will discuss Module 3,
Topic E.
In Lesson 16, students use patterns to understand:
Topic E Analysis of Patterns and Problem Solving
Including Units of 0 and 1
In Lesson 18, students apply the tools, representation,
and concepts they have learned to solve two-step word
problems using all four operations. (+, -, x, )
Multiplication Table
They will also use the rounding skills learned in prior
lessons to assess the reasonableness of the answers.
nx0=0
and
nx1=n
they will also understand that when dividing 0 by
another number results in 0 but when dividing a
number by 0 the answer is undefined.
In Lesson 17, students use a multiplication table to
explore patterns of multiplication. They will recognize
the patterns of particular factors and make connections
to multiplication and division.
Troy has $105 in the bank. He earns the same amount of
money each week for 7 weeks and puts this in money in the
bank also. Now Troy has $273 in the bank. How much
does Troy earn each week?
How much money did Troy put in the bank in 7
weeks?
273 – 105 = m
m = 168
w = the number of dollars earned each week
w = $24
Troy earns $24 a week,
OBJECTIVE OF TOPIC E
1
Reason about and explain arithmetic patterns using units
of 0 and 1 as they relate to multiplication and division.
2
Identify patterns in multiplication and division facts using
the multiplication table.
3
Solve two-step word problems involving all four
operations and assess the reasonableness of solutions.
Tammy does homework for 43 minutes. She then does 7
chores. Each chore took 4 minutes. How many minutes
does it take for Tammy to finish all of her chores and her
homework?
How long does it take to complete chores?
7x4=c
c = 28
How many minutes total?
43 + 28 = t
t = 71 minutes
This information was generously shared by LPSS, Lafayette, LA
Math News!
Grade 3, Module 3, Topic F
Focus Area– Topic F
3rd Grade Math
Module 3: Multiplication and Division with Units of 0, 1, 6-9,
and Multiples of 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 3 of Eureka Math (Engage New York)
covers Multiplication and Division with Units of 0, 1, 6-9,
and Multiples of 10. This newsletter will discuss Module 3,
Topic F.
Multiplication of Single-Digit Factors and Multiples of 10
In Lessons 19-21 students will use the place value chart to
multiply multiples of 10. For example, to solve 2 x 40, they
begin modeling 2 x 4 in the ones place. Students relate this
to multiplying 2 x 4 tens, locating the basic fact in the tens
column. They see that when multiplied by 10, the product
shifts one place value to the left.
In Lesson 19, students will multiply by multiples of 10
using a place value chart.
Topic F: Multiplication of Single-Digit Factors and
Multiples of 10
Vocabulary Words
 array
 tape diagram

associative property
Things to Remember!!!
In Lesson 20, students will use the associative property to
multiply multiples of 10.
2 x 20 = 2 (2 x 10)
= (2 x 2) x 10
= 4 x 10
=
40
There are 60 seconds in 1 minute. Use a tape diagram to find
the total number of seconds in 5 minutes and 45 seconds.
OBJECTIVE OF TOPIC F
1
Multiply by multiples of 10 using the place value chart.
2
Use place value strategies and the associative property n x
(m x 10)= (n x m) x 10 (where n and m are less than 10) to
multiply by multiples of 10.
3
Solve two-step word problems involving multiplying
single-digit factors and multiples of 10.
In Lesson 21, students will solve two-step word problems
involving multiplying single-digit factors and multiples of
10.
This information was generously shared by LPSS, Lafayette, LA