Math3 2NDQ

Saint Vincent Ferrer Academy (SVFA), Inc.
MATH 3, 2ND QUARTER
Visualizing Multiplication of
Lesson 1
Numbers 1 to 10 by 6, 7, 8, and 9
In this lesson you will be able to multiply the numbers 1

to 10 by 6, 7, 8, and 9. You will also know that multiplication
is a repeated addition, and that the Multiplier tells the number
of times a number is to be added or the number of sets/groups,
while the Multiplicand is the number to be added or the
number of elements in a set.
0
Saint Vincent Ferrer Academy (SVFA), Inc. MATH 3, 2ND QUARTER
In your previous grade level, you already have

knowledge on using the multiplication table from 1, 2, 3, 4
and 5. To test your prior knowledge answer the following
questions. Match the correct multiplication sentence from
column A to the pictures on column B and write the product.
0
❖ How many groups of stars are there?

❖ How many stars are there in each group?
❖ How many stars are there in all?
Let us answer the questions above. There are 6 groups of stars

and there are 2 stars in each group. 2 + 2 + 2 + 2 + 2 + 2 = 12
When we add merely repeating a number several times, then
we are doing multiplication. So, 2 + 2 + 2 + 2 + 2 + 2 = 12 can
be written in 2 x 6 = 12.
Multiplication – is one of the four elementary mathematical
operations. The multiplication of whole numbers may be
thought as a repeated addition.
Multiplier – tells the number of times a number is to be added
or the number of groups
Multiplicand – is the number to be added or the number of
elements in a set.
Product – is the result of multiplication.
0
Repeated addition sentence:
3 + 3 + 3 + 3 + 3 + 3 + 3 = 21
Multiplication sentence: 3 x 7 = 21
Here’s another example:
There are 4 boxes of pumpkins and in each box, there are 6

pumpkins so all in all there are 24 pumpkins. Repeated addition
sentence: 4 + 4 + 4 + 4 + 4 + 4 = 24 Multiplication sentence: 6 x
4 = 24
0
There are 9 groups of buses and in each group, there are 6

buses.
There are 54 buses altogether.
Repeated addition sentence:
6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 54
Multiplication sentence:
6 x 9 = 54
0
Do the multiplication process by visualizing the repeated

addition using objects like sticks or disc by answering the
activity below. Complete the multiplication sentences in the box
by visualizing using sticks and disc. Box the sticks or discs
below to visualize the multiplication sentence in the box and
write the product in the blank.
0
1. Multiplication is a repeated addition

2. To get the product in multiplication, visualize the
multiplicand and the multiplier. 8
3. Multiplier tells the number of groups while the
Multiplicand is the number of elements in a group.
4. After visualizing the multiplier and the multiplicand,
apply the repeated addition by adding the number of
elements according to the number of groups.
5. The sum of the repeated addition is the product of the
multiplication sentence.
0
0
NAME:___________________________________
_
ACTIVITY
Find the product by writing the corresponding repeated
addition sentence.
Repeated Addition Sentence
1. 6 x 4 = ____ _____________________
2. 7 x 4 = ____ _____________________
3. 8 x 6 = ____ _____________________
4. 9 x 5 = ____ _____________________
5. 7 x 7 = ____ _____________________
ASSESSMENT
Visualize multiplication of numbers using sticks or discs then
write the product in the blank.
1. 5 x 7 =____
2. 3 x 8 = ____
3. 7 x 2 = ____
4. 2 x 9 = ____
5. 5 x 6 = ____ 0
1
Visualizing and Stating Basic

Lesson 2
Multiplication Facts
Children like you are fond of reading and writing

numbers using the four fundamental operations that could be
very useful in daily life. In this module, you will learn how to
visualize and state basic multiplication facts for numbers up to
10.
LET’S WARM UP!

Give the multiplication sentence for the given phrases.
1. 3 rows of 2 ____________________
2. 2 rows of 6 ____________________
3. 4 sets of 5 ____________________
4. 6 sets of 7 ____________________
5. 9 groups of 4 ____________________
1
Answer the basic facts in multiplication. Use the multiplication

table as your guide.
1. 6 x 2 = ______ 6. 4 x 7 = ______
2. 4 x 5 = ______ 7. 3 x 3 = ______
3. 9 x 9 = ______ 8. 2 x 5 = ______
4. 4 x 4 = ______ 9. 6 x 7 = ______
5. 8 x 8 = ______ 10. 10 x 4 = ____
1
In the previous lesson we already learned the following:

Multiplication is one of the four elementary mathematical
operations. The multiplication of whole numbers may be thought
as a repeated addition.
Multiplier tells the number of times a number is to be added or
the number of groups.
Multiplicand is the number to be added or the number of
elements in a set.
Product is the result of multiplication. Multiplication sentence:
3 × 6 = 18 is also called a multiplication fact.

This process 3 x 6 = 18 is the multiplication process.
The symbol or sign ‘x’ is the sign of multiplication.
In this module, you will learn the basic multiplication facts:
1
A. Zero Property of Multiplication. Any number multiplied

by zero is zero.
Example: 3 x 0 = 0 10 x 0 = 0 0 x 1 = 0
B. Identity Property of Multiplication. Any number multiplied
by one is the number itself.
Example: 5 x 1 = 5 1 x 1 = 1 10 x 1 = 10
C. Multiplication is a repeated addition.
Example: 6 x 4 =?
To get the product of 6 x 4, follow the steps:
Step 1. Interpret the phrase 6 x 4 into groupings. 6 x 4 means “4
groups of 6”.
Step 2. Visualize the groupings.
Step 3. Interpret the visualization into a repeated addition. 6 + 6

+ 6 + 6 = 24
Step 4. State the multiplication fact. 6 x 4 = 24
D. Commutative Property of Multiplication states that when
multiplicand and multiplier is interchanged, there will be the
same product.
1
Example:
➢ 6 x 7 = 42 can also be written as 7 x 6 = 42
➢ 5 x 9 = 9 x 5 = 45
➢ “3 groups of 8” is equal to “8 groups of 3”
E. When a number is multiplied by 10, the product is found by

writing a zero after the number.
Example:
➢ 2 x 10 = 20
➢ 10 x 7 = 70
➢ 10 x 10 = 100
Give the product using the basic multiplication facts.
A. Zero Property of Multiplication
B. Identity Property of Multiplication
1
C. Multiplication is a repeated addition
5. Visualize 5 x 6 using sticks and give the product.

5 x 6 = ____
6. Visualize 2 x 9 using discs and give the product.
Repeated Addition Sentence: _________________

2 x 9 = ____
D. Commutative Property of Multiplication
7. 6 x 9 = 54, 9 x 6 = ____
8. 8 x 7 = ___, 7 x 8 = 56
E. When a number is multiplied by 10, the product is found by
9. 5 x 10 = ____
10. 10 x 9 = ____
1
The basic multiplication facts:

1. Any number multiplied by zero is zero.
2. Any number multiplied by one is the number itself.
3. When a number is multiplied by 10, the product is found by
4. When multiplicand and multiplier is interchanged, the
product is the same.
5. Multiplication is a repeated addition.
How to multiply numbers?

Step 1. Interpret the multiplication phrase into groupings.
Step 2. Visualize the groupings.
Step 3. Interpret the visualization into a repeated addition.
Step 4. State the multiplication fact.
1
1
NAME:______________________________________
ACTIVITY
A. Give the product.
1. 1 x 6 = ___
2. 0 x 9 = ___
3. 3 x 10 = ___
B. Visualize and use repeated addition to find the product.
4. 6 x 6 = _____
Visualize here:
Addition Equation: _________________________________
5. 4 x 8 = _____
Visualize here:
Addition Equation: __________________________________
ASSESSMENT
Visualize using sticks and complete the basic multiplication fact.
1. 8 x 5 = ____
2. 4 x 9 = ____
3. 2 x 7 = ____
4. 10 x 3 = ____
5. 9 x 1 = ____
1
2
Illustrates the Properties of

Lesson 3
Multiplication in Relevant Situations
In the previous lesson you learn how to multiply

numbers by visualizing multiplication sentence into groups or
sets of objects.
You also learn the basic multiplication facts in multiplying
numbers through 0 to 10.
In this module, you will learn the properties of
multiplication; commutative, distributive and associative.
Read the problem below.
Andy and Loida work in a bakery shop. Andy has to prepare

an order from a customer of 6 trays with 5 cupcakes per tray.
On the other hand, Loida has accepted an order from another
customer of 5 trays with 6 cupcakes per tray. Who has more
cupcakes to prepare?
2
1. What order does Andy have to prepare?

Answer: ___ trays of ___ cupcakes per tray.
2. What order does Loida have to prepare?

Answer: ___ trays of ___ cupcakes per tray.
3. What is the multiplication sentence for Andy’s work?

Answer: ____ x ____ = n
4. What is the multiplication sentence for Loida’s work?
5. Answer: ____ x ____ = n

What is the product?
Andy: (multiplication sentence) ____ x ____ = ____ (repeated
addition)___+___+___+___+___ +___ = _____
Loida: (multiplication sentence) ____ x ____ = ____ (repeated
addition)____+____+____+____+____ = _____
Answer to the problem question:

_____________________________________________________
_____________________________________________________
2 __
In our problem in Activity 1, if you answered that Andy and

Loida have the same number of cupcakes to prepare then you are
correct!
The multiplication phrases “5 x 6” and “6 x 5” are both equal to
30. This illustrates the Commutative Property of Multiplication.
In this lesson we will discuss the three Properties of
Multiplication:
A. Commutative Property
This property indicates that changing the order of factors does not
change or affect the product.
Example: 5 x 6 = 6 x 5
B. Distributive Property
Multiplying the sum of two or more addends by a number will
give the same result as multiplying each addend individually by
the number and then adding the products together.
Distributive property is helpful in multiplying numbers especially
if one of the factors is a 2-digit number.
Example: 13 x 2 =?
2
C. Associative Property
This property states that when three numbers are multiplied, the
product is the same regardless of the grouping of the factors.
Example: (2 x 4) x 6 = 2 x (4 x 6)
To multiply three 1-digit numbers using associative property.
a. Multiply first the factors enclosed in parentheses.
b. Multiply the remaining factors.
2
Example: Apply the associative property to multiply 2 x 4 x 6.

Solution:
Step 1. Enclose the two factors to be multiplied first.
(2 x 4) x 6 or 2 x (4 x 6)
Step 2. Multiply first the factors enclosed in parentheses.
(2 x 4) x 6 = 8 x 6 2 x (4 x 6) = 2 x 24
Step 3. Multiply the remaining factors.
8 x 6 = 48 2 x 24 = 48
2
Three Properties of Multiplication:

1. Commutative Property: a x b = b x a
This property indicates that changing the order of factors does not
change or affect the product.
2. Distributive Property: (a + b) x c = (a x c) + (b x c)
Multiplying the sum of two or more addends by a number will give
the same result as multiplying each addend individually by the
number and then adding the products together.
3. Associative Property: a x (b x c) = (a x b) x c
This property states that when three numbers are multiplied, the
product is the same regardless of the grouping of the factors.
2
NAME: ____________________________________________
ACTIVITY
Complete each multiplication sentence to illustrate the given
Property of Multiplication.
1. 8 x 9 = _____________ (commutative)
2. ____________ = 3 x (4 x 9) (associative)
3. (7 + 8) x 9 = _____________ (distributive)
4. (4 x 5) x 8 = _____________ (associative)
5. ____________ = (3 x 6) + (3 x 2) (distributive)
ASSESSMENT
Choose the letter of the correct answer. Write your answers on a
separate sheet of paper.
6. Using Commutative Property, complete the equation: 9 x 10
= ______?
a. 10 + 9 b. 9 + 10
c. 9 x (9 + 1) d. 10 x 9
7. What property of multiplication is illustrated in 9 x 7 = 7 x
9?
a. Identity Property
b. Commutative Property
c. Distributive Property
d. Associative Property
2
3. Using Distributive Property, which of the following completes

the multiplication sentence: 2 x (10 + 8) = _____________?
a. (2 x 10) + (10 x 8)
b. (2 x 10) + (10 x 2)
c. (2 x 10) + (2 x 8)
d. (2 + 10) x (2 + 8)
4. What property of multiplication is being illustrated:

3 x (9 x 2) = (3 x 9) x 2?
a. Identity Property
c. Distributive Property
b. Commutative Property
d. Associative Property
5. Which of the following illustrates Distributive Property?

a. 6 x (7 + 8) = (6 x 7) + (6 x 8)
b. 2 x 4 = 4 x 2
c. (5 x 4) x 7 = 5 x (4 x 7)
d. 3 x (4 + 7) = 3 + (4 x 7)
2
Multiply 2-3 Digit Numbers by 1-

Lesson 4 Digit Numbers without or with
Regrouping
The children like you are fond of counting and

multiplying numbers that could help you in day to day
activities in your home or in school. In this module, you will
learn how to Multiply 2-3 Digit Numbers with 1-Digit
Numbers without or with Regrouping.
Activity 1
Applying the associative property of multiplication find the
product.
1. (3 x 2) x 4 = 3 x (2 x 4) ______ x 4 = 3 x _____ ____ =
____
2. (4 x 6) x 3 = 4 x (6 x 3) ______ x 3 = 4 x ______ ____ =
____
Which of the items above you find it easy to solve?
Why? Which item you find it difficult? Why?
2
In Activity 1, we are given two items on multiplication. As

you go through the solution applying associative property of
multiplication, observe that item no. 1 is easier to solve than item
no. 2 because the first item only includes multiplying 1-digit
number by 1-digit number while second item involves 2-digit
number multiplied to 1-digit numbers. Let us take a look at their
solution: 1. (3 x 2) x 4 = 3 x (2 x 4) 6 x 4 = 3 x 8 multiplying 1-
digit numbers 24 = 24 2. (4 x 6) x 3 = 4 x (6 x 3) 24 x 3 = 4 x 18 In
here, we multiply 2-digit number by 1-digit number. How to
multiply 2-digit number by 1-digit number? Remember that
multiplication is a repeated addition. This process is still useful in
multiplying larger numbers but takes a long process. However, it
would be easy to visualize repeated addition of 2-digit numbers if it
is in multiple of ten. Therefore, our goal is to convert the 2-digit
number into multiples of 10 as shown below.
Going back to our solution we need to multiply; 24 x 3 and 4 x 18.

Step 1. Expand the 2-digit number into its addition form with
multiples of 10. 24 = 20 + 4, 18 = 10 + 8
3
Step 2. Apply Distributive Property of Multiplication (20 + 4) x

3 = 4 x (10 + 8) expanded form (20 x 3) + (4 x 3) = (4 x 10) + (4
x 8) distributive property 60 + 12 = 40 + 32 by repeated addition
72 = 72
As mentioned, the process of multiplying numbers using

Distributive Property and repeated addition is considered as
long method especially if large numbers are involved like 3-
digit numbers. This time, you will learn the basic rules of
multiplying 2- to 3-digit numbers by 1-digit number without or
with regrouping. Recall this!
Multiplicand – the number that is to be multiplied by another
Multiplier – one that multiplies
Product – the answer or result of multiplication process
3
Multiplying Without Regrouping

Just like addition and subtraction, it would be easy to
multiply large numbers by aligning them in vertical column.
When you observe that as you multiply the 1-digit number to
each digit on the right of the leftmost digit of the multiplicand
and its result is less than 10 then the process of multiplication
needs no regrouping.
Here are the steps in multiplying 2- to 3-digit numbers by 1-
digit number without regrouping:
Example: 341 x 2 = ?
Step 1. Arrange the two numbers vertically with the multiplicand
place above the multiplier. 341 x 2
Step 2. Multiply the 1-digit multiplier to each digit of the
multiplicand from right to left starting from ones place then to the
tens place and extend up to the hundreds place if exist.
3
3
3
3
How do we multiply 2-to 3-digit numbers by 1-digit numbers

without or with regrouping?
In multiplying 2- to 3-digit numbers by 1-digit number
without or with regrouping:
Step 1. Arrange the two numbers vertically with the multiplicand

place above the multiplier.
Step 2. Multiply the 1-digit multiplier to each digit of the

multiplicand from right to left starting from ones place then to the
tens place and extend up to the hundreds place if exist. When the
product upon multiplying each pair of digits is a 2-digit number,
apply regrouping. To regroup follow these steps,
a. bring down the digit in the ones place of the product and
carry over its digit in the tens place
b. multiply again the multiplier to the next digit of the
multiplicand then add the regrouped digit
3
NAME: ______________________________________
ASSESSMENT
Multiply
4. 4 x 123 5. 5 x 678
3
3
Multiplies 2-digit Numbers by 2-

Lesson 5 digit Numbers without or with
Regrouping
3
You are tasked to do the activity below.
4
4
4
Method 2: Distributive Property of Multiplication Over Addition
4
Method 3: Multiplication using the short method.
4
4
The following are the steps in multiplying 2-digit numbers by 2-

digit numbers:
• First, multiply the 2-digit multiplicand by the ones of the

multiplier. Regroup if necessary. Write the first partial product
with its rightmost digit aligned in the ones column.
• Second, multiply the multiplicand by tens of the multiplier.

Regroup if necessary. Write the second partial product with
its rightmost digit aligned in the tens column.Third, add the
partial products to get the final product.
4
NAME: ____________________________________________________
ASSESSMENT
Multiple Choice. Choose the letter of the correct answer.
1. What is the product of 18 and 22?

a. 306 b. 396 c. 420 d. 329
2. Mika makes 30 packs of lemon. If each pack contains 13 pieces of
lemon, how many pieces of lemon does Mika need in all?
a. 390 b. 380 c. 340 d. 320
3. In Mati City, 12 mango seedlings are packed in a box for delivery to
Davao City. How many seedlings are in 44 boxes?
a. 528 b. 628 c. 728 d. 428
4. If 93 is multiplied by 72 we get __.
a. 6 969 b. 6 796 c. 6 876 d. 6 696
5. Find the product using Short Cut Method. Show your solution.
4
4
4
Estimates the Product of 2- to 3-Digit

Lesson 6
Numbers and 1- to 2-Digit Numbers
About 125 passenger jeepneys pass by a particular house in one hour.

About how many passenger jeepneys would have passed by in 12 hours?
In answering this problem, you need to estimate the product by rounding
off first the factor to its highest place value. (Remember not to round off 1-
digit factor). Then multiply the resulting factors to get the estimated
products.
Solve the problem.

Every day, 594 food packages are delivered to the Typhon Pablo Operation
Tulong Center. About how many food packages are being received by the
Operation Tulong Center in 7 days? When estimating products, round off
each factor to its highest place value, then multiply.
Remember: Do not round off 1-digit factors
➢ Round off the factors to their highest place value.
➢ Multiply the resulting factors.
5
Set of Examples:
5
How do we estimate the product of 2-to-3- digit numbers

multiplied by 1-to-2-digit numbers?
To estimate the product:
1. Round off either the multiplicand or multiplier or both to its

greatest place value.
2. Multiply the rounded factors.

Remember: Do not round off 1-digit factor.
5
NAME: ________________________________________
Assessment
A. Estimate each product.

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What are the steps in visualizing multiplication?

What are the steps in visualizing multiplication?

What are the properties of multiplication?

What are the properties of multiplication?

Saint Vincent Ferrer Academy (SVFA), Inc.

MATH 3, 2ND QUARTER

In this lesson you will be able to multiply the numbers 1

In your previous grade level, you already have

❖ How many groups of stars are there?

Let us answer the questions above. There are 6 groups of stars

Repeated addition sentence:

Here’s another example:

There are 4 boxes of pumpkins and in each box, there are 6

There are 9 groups of buses and in each group, there are 6

Do the multiplication process by visualizing the repeated

1. Multiplication is a repeated addition

Visualizing and Stating Basic

Children like you are fond of reading and writing

LET’S WARM UP!

Answer the basic facts in multiplication. Use the multiplication

5. 8 x 8 = ______ 10. 10 x 4 = ____

In the previous lesson we already learned the following:

3 × 6 = 18 is also called a multiplication fact.

A. Zero Property of Multiplication. Any number multiplied

Step 3. Interpret the visualization into a repeated addition. 6 + 6

E. When a number is multiplied by 10, the product is found by

B. Identity Property of Multiplication

C. Multiplication is a repeated addition

5. Visualize 5 x 6 using sticks and give the product.

6. Visualize 2 x 9 using discs and give the product.

Repeated Addition Sentence: _________________

D. Commutative Property of Multiplication

The basic multiplication facts:

How to multiply numbers?

Illustrates the Properties of

In the previous lesson you learn how to multiply

Read the problem below.

Andy and Loida work in a bakery shop. Andy has to prepare

1. What order does Andy have to prepare?

2. What order does Loida have to prepare?

3. What is the multiplication sentence for Andy’s work?

4. What is the multiplication sentence for Loida’s work?

5. Answer: ____ x ____ = n

Answer to the problem question:

In our problem in Activity 1, if you answered that Andy and

Example: Apply the associative property to multiply 2 x 4 x 6.

Three Properties of Multiplication:

3. Using Distributive Property, which of the following completes

4. What property of multiplication is being illustrated:

5. Which of the following illustrates Distributive Property?

Multiply 2-3 Digit Numbers by 1-

The children like you are fond of counting and

Why? Which item you find it difficult? Why?

In Activity 1, we are given two items on multiplication. As

Going back to our solution we need to multiply; 24 x 3 and 4 x 18.

Step 2. Apply Distributive Property of Multiplication (20 + 4) x

As mentioned, the process of multiplying numbers using

Multiplying Without Regrouping

5. 8 x 8 = __ 10. 10 x 4 =

5. Answer: x = n