Okay, let me summarize:- Changing the order of factors in multiplication does not change the product. - 4 x 3 is the same as 3 x 4. Both give an answer of 12.- Grouping or regrouping objects in different ways but with the same total gives the same result

Lesson Guide
In
Elementary Mathematics
Grade 3
Reformatted for distribution via
DepEd LEARNING RESOURCE MANAGEMENT and DEVELOPMENT SYSTEM PORTAL
DEPARTMENT OF EDUCATION
BUREAU OF ELEMENTARY EDUCATION
in coordination with
ATENEO DE MANILA UNIVERSITY
2010
Chapter I
Whole Numbers
Multiplication
INSTRUCTIONAL MATERIALS COUNCIL SECRETARIAT, 2011

Lesson Guides in Elementary Mathematics
Grade III
Copyright © 2003
All rights reserved. No part of these lesson guides shall be reproduced in any form without a written
permission from the Bureau of Elementary Education, Department of Education.
The Mathematics Writing Committee
GRADE 3
Region 3
Agnes V. Canilao – Pampanga
Josefina S. Abo – Tarlac City
Alma Flores – Bataan
Region 4 - A
Cesar Mojica – Regional Office
Marissa J. de Alday – Quezon
Henry P. Contemplacion – San Pablo City
Region 4 – B
Felicima Murcia – Palawan
National Capital Region (NCR)
Laura N. Gonzaga – Quezon City
Dionicia Paguirigan – Pasig/San Juan
Yolita Sangalang – Pasig/San Juan
Bureau of Elementary Education (BEE)
Elizabeth J. Escaño
Galileo L. Go
Nerisa M. Beltran
Ateneo de Manila University
Pacita E. Hosaka
Support Staff
Ferdinand S. Bergado
Ma. Cristina C. Capellan
Emilene Judith S. Sison
Julius Peter M. Samulde
Roy L. Concepcion
Marcelino C. Bataller
Myrna D. Latoza
Eric S. de Guia - Illustrator
Consultants
Fr. Bienvenido F. Nebres, SJ – President,
Ms. Carmela C. Oracion – Principal,
High School
Ms. Pacita E. Hosaka – Ateneo de Manila
University
Project Management
Yolanda S. Quijano – Director IV
Angelita M. Esdicul – Director III
Simeona T. Ebol – Chief, Curriculum Development Division
Irene C. Robles – OIC - Asst. Chief, Curriculum Development Division
Virginia T. Fernandez – Project Coordinator
EXECUTIVE COMMITTEE
Jesli A. Lapus – Secretary, Department of Education
Teodosio C. Sangil, Jr. – Undersecretary for Finance and Administration
Jesus G. Galvan – OIC - Undersecretary for Programs and Projects
Teresita G. Inciong – Assistant Secretary for Programs and Projects
Printed By:
ISBN – 971-92775-2-1

iii
TABLE OF CONTENTS
Introduction ..................................................................................................................................iv
Matrix ........................................................................................................................................v
I. WHOLE NUMBERS
A. Multiplication
Changing the Order or Regrouping in Multiplication ...................................................... 1
Multiplying 2- to 4- digit numbers by 1- to 2- digit numbers
 Without regrouping............................................................................................. 6
 With grouping..................................................................................................... 11
Multiplying 2- digit numbers by 1- digit number with zero in the multiplicand..... 16
Multiplying 3- to 4- digit numbers by 1- digit numbers with zero in the
multiplicand. ..................................................................................................... 20
Multiplying 2- to 4- digit numbers by multiples of 10......................................... 25
Multiplying 2- to 4- digit numbers by multiples of 100....................................... 30
Estimating the product of 2- to 3- digit numbers by 1- to 2- digit numbers........ 35
Estimating the product of 4- digit numbers by 1- to 2- digit numbers................ 39
Multiplying mentally 2- digit numbers with products up to 100 without
regrouping............................................................................................ 43
Solving word problems involving multiplication of whole numbers including
money.................................................................................................. 47
Solving 2- to 3- step word problems involving multiplication and any one of
addition/subtraction......................................................................................... 50

iv
I N T R O D U C T I O N
The Lesson Guides in Elementary Mathematics were developed by the
Department of Education through the Bureau of Elementary Education in
coordination with the Ateneo de Manila University. These resource materials
have been purposely prepared to help improve the mathematics instruction in
the elementary grades. These provide integration of values and life skills using
different teaching strategies for an interactive teaching/learning process.
Multiple intelligences techniques like games, puzzles, songs, etc. are also
integrated in each lesson; hence, learning Mathematics becomes fun and
enjoyable. Furthermore, Higher Order Thinking Skills (HOTS) activities are
incorporated in the lessons.
The skills are consistent with the Basic Education Curriculum
(BEC)/Philippine Elementary Learning Competencies (PELC). These should be
used by the teachers as a guide in their day-to-day teaching plans.

v
MATRIX IN ELEMENTARY MATHEMATICS
Grade III
COMPETENCIES VALUES INTEGRATED STRATEGIES USED
MULTIPLE INTELLIGENCES
TECHNIQUES
With HOTS
I. Whole Numbers
A. Multiplication of Whole Numbers
1. Comprehension of Multiplication
1.1 Multiply 2 to 4 digit numbers by 1 to 2
digit numbers without and with
regrouping in all places
1.1.1 Multiply 2 to 4 digit numbers
without and with regrouping
1.1.1.1 Show that changing the order
and/or regrouping in
multiplication makes
computation easy
Industry Concept development
Simplifying the problem
Singing (Musical) Climbing the
ladder (Bodily Kinesthetic)
Game
Drawing (Spatial)

1.1.1.2 Multiply 2 to 4 digit numbers
by 1 to 2 digit numbers without
regrouping
Accuracy/carefulness Simplifying the problem Game "Giant Step" (Bodily
kinesthetic)

by 1 to 2 digit numbers with
regrouping
Speed and accuracy Simplifying the problem "Solve and Deliver"
Game(Bodily kinesthetic)

1.1.1.4 Multiply 2 digit numbers by 1
digit number with zero in the
multiplicand
Care and concern for the
Environment
Drawing pictures Movements (Bodily Kinesthetic 
by 1 digit numbers with zero in the
multiplicand
Following rules and
regulations
Simplifying the problem Song (Musical)
Game "Flaglet Race"(Bodily
kinesthetic)

by multiples of 10
Develop the habit of being
independent
Looking for patterns "Skip" movement (Bodily
kinesthetic)

by multiples of 100
Cooperation Looking for patterns Cooperative
groups(Interpersonal)

1.1.2 Estimate the product of 2 to 3 digit
numbers by1 to 2 digit numbers
Neatness Simplifying the problem Cooperative

1.1.3 Estimate the product of 4 digit
numbers by 1 to2 digit numbers
Active participation Simplifying the problem Listening to music while doing
the game (Musical)

1.1.4 Multiply mentally 2 digit numbers
by 1 digit numbers without
regrouping with products up to 100
Cooperation and
Independence
Drawing pictures Puzzle (Logical mathematics)
Coloring (Spatial)
Manipulation (Bodily
kinesthetic)

2. Application of Multiplication

vi
2.1 Solve word problems involving
multiplication of whole numbers
including money following the steps in
problem solving
Thriftiness/Cooperation Polya's steps in problem
solving Drawing table
Cooperative

3. Application of Multiplication and any one of
Addition/Subtraction
3.1 Solve 2-3 step word problems involving
multiplication and any one of
addition/subtraction following the steps
in problem solving
Honesty Acting out the problem
Polya's steps in problem
solving
Diagram (Spatial) Cooperative


1
Changing the Order or Regrouping in Multiplication
I. Learning Objectives
Cognitive: Show that changing the order and/or regrouping in multiplication makes
computation easy
Psychomotor: Illustrate multiplication in different orders of factors
Affective: Show sportsmanship when working in the activities
II. Learning Content
Skill: Changing the order or regrouping in multiplication
Reference: BEC PELC I.D1.1.1.1
Materials: counters, flash cards, cut-outs of a rabbit and a frog, cut-outs of
rectangular arrangements, drawings
Value: Sportsmanship
III. Learning Experiences
A. Preparatory Activities
1. Drill “Climbing the Ladder”
Call two pupils to answer the multiplication facts as fast as they can. The one who makes
a mistake will fall from the ladder.
6 x 6
4 x 8
3 x 5
8 x 3
6 x 4
2. Review
In 3 x 4 = 12, what are 3 and 4?
Give the factors of: 10, 16
3. Motivation
What game/sport do you enjoy playing?
If you do not win in a game, how would you feel?
What will you do to show that you are a good sport?
Is it good to engage in sports? Why?
18
21 32
24
16

2
 Let all the pupils stand and form
- two lines
- three lines
- four lines
Ask: Did the number of pupils change as they change their position/groupings?
B. Developmental Activities
1. Presentation
a. In a race, Lady rabbit takes 4 hops of 3. Mr. Frog takes 3 hops of 4. Who is ahead?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Discuss:
- How many hops did Lady Rabbit take?
- How about Mr. Frog? Who won the race?
- Why did you say it’s a tie?
- Compare the number of hops done.
- Ask some pupils to hop as what Lady Rabbit and Mr. Frog did.
Lady Rabbit 4 hops of 3
Mr. Frog 3 hops of 4
Transform 4 hops of 3 into addition and multiplication sentence.
3 + 3 + 3 + 3 = 12 4 x 3 = 12
Transform 3 hops of 4 into addition and multiplication sentence.
4 + 4 + 4 = 12 3 x 4 = 12
Is 4 x 3 the same as 3 x 4? Why?
b. Present another activity.
● Have the pupils get 8 counters. Let them group the counters by 4s
● Ask: How many groups of 4 did you get?
Give the multiplication sentence.
● This time, have the pupils group the counters by 2s
● Ask: How many groups of 2s did you get?
What is the multiplication sentence for this?
● Guide the pupils to analyze the number sentence on the board.
a.) 2 x 4 = 8 b.) 4 x 2 = 8
● What are the factors of 8? Which factor comes first in sentence a, 2 or 4? How
about in sentence b? What did we do to the order of the factors? Did the product
change?
c. Mang Tony prepared 2 groups of sugarcane seedlings for his plantation. Each group had
seedlings. He cut each seedling into 3 pieces. How many pieces were there in all?
Lady rabbit
Mr. Frog

3
Sometimes a number pattern can help when we multiply three or more numbers.
(2 x 8) x 3 = 48 thirds of sugar cane seedlings
2 x (8 x 3) = 48 thirds of sugar cane seedlings
Give more examples:
(4 x 2) x 3 = 24 4 x (2 x 3) = 24
(6 x 3) x 2 = 36 6 x (3 x 2) = 36
(5 x 3) x 3 = 45 5 x (3 x 3) = 45
2. Guided Practice
a. Write two multiplication sentences for the following.
4 sets of 3 3 sets of 4
16 16 x 3 = 48
24 24 x 2 = 48
______ x _____
______ x _____
______ x _____ ______ x _____

4
3. Generalization:
Does the product change when we change the order of the factors?
Can you have product if you don’t have factors?
Changing the order of the factors does not affect the product. Regrouping of
the factors makes computation easy.
C. Application
1. Fill in the blanks to complete each equation.
1) 5 x 3 = __ x 5
3) 6 x 2 = __ x 6
5) __ x 5 = 5 x 7
2) 6 x 8 = 8 x __
4) __ x 5 = 5 x 7
6) Write the multiplication sentence:
2. Activity
The learners are asked to examine a set of rectangular arrangements and explore the
situation.
Activity Card
Directions:
Examine the following figures. How many squares does each figure have? _______ Hold
it in vertical and horizontal positions and take note how the number of rows and column
change.
NOTE: Do these in all rectangles.
Rectangle cut outs
______ x _____
______ x _____
______ x _____ ______ x _____

5
a. Write all the possible multiplication sentences.
Rectangle A 3 x 6= 18 6 x 3 = 18
Rectangle B ___________ ___________
Rectangle C ___________ ___________
Rectangle D ___________ ___________
Rectangle E ___________ ___________
b. How many multiplication sentences did you form in each rectangle? _____
c. Complete the table
Rectangle Write the multiplication
sentences based on the
rectangle.
What are the
factors in each
multiplication
sentence?
What is their
product?
A
B
C
D
E
d. Compare the two multiplication sentences for each rectangle. What do you observe
about their factors?
3. Draw a if the number sentence is correct and a  if it is wrong.
____ 1) (3 x 4) x 2 = 3 x (4 x 2)
____ 2) 2 x (8 x 3) = (3 x 7) x 2
____ 3) 4 x (5 x 2) = 4 x (7 x 3)
____ 4) 8 x (6 x 2) = (8 x 6) x 2
____ 5) 10 x (2 x 3) = (10 x 2) x 4
4. Find the missing numbers.
1) 2 x (3 x 9) = (2 x _) x 9
2) (5 x 4) x _ = 5 x (4 x 8)
3) (7 x 8) x 3 = _ x (8 x 3)
4) (6 x 2) x 9 = 6 x (_ x 9)
5) 8 x (3 x 1) = (_ x 3) x 1
Rectangle A
Rectangle B
Rectangle C
Rectangle D
Rectangle E

6
IV. Evaluation
A. Complete the following.
1) (4 x 2) x 3 = 4 x (__ x 3)
2) 2 x (2 x 4) = (2 x 2) x __
3) 8 x (3 x 5) = (8 x __) x 5
4) (6 x 7) x 4 = __ x (7 x 4)
5) 9 x (6 x __) = (9 x 6) x 3
B. Group the following in two ways. Find the product.
1) 2 x 5 x 8 = ______
2) 3 x 3 x 10 = ______
3) 3 x 4 x 2 = ______
4) 6 x 2 x 5 = ______
5) 7 x 2 x 10 = ______
V. Assignment
A. Perform the operations. Multiply the numbers inside the parenthesis first.
1) (4 x 5) x 7
3) (6 x 5) x 4
5) (7 x 3) x 8
2) (9 x 4) x 2
4) (3 x 2) x 6
B. Let N represent the missing number in each sentence. Find N.
1) 9 x 8 = N x 9 2) (2 x 3) x 5 = N x (3 x 5)
3) N x 3 = 3 x 7 4) 5 x 6 = N x 6
5) (5 x 8) x 2 = 5 x (N x 2)
Multiplying 2- to 4- Digit Numbers by 1- to 2- Digit Numbers without Regrouping
Cognitive: Multiply 2- to 4- digit numbers by 1- to 2- digit number without regrouping
Psychomotor: Compute the product of 2 numbers with accuracy
Affective: Show accuracy/carefulness in solving number problems
Skill: Multiplying 2- to 4- digit numbers by 1- to 2- digit numbers without regrouping
Reference: BEC PELC I.D.1.1.1.2
Materials: flash cards, problem written on manila paper
Value: Accuracy/Carefulness

7
1. Drill: Basic multiplication facts
8 3 4 9 5 10
x 1 x 7 x 0 x 2 x 6 x 4
2. Review
Recall the importance of accuracy and carefulness in doing things.
In 8 x 3 = 24. What do you call 8? 3? 24?
Put the factors and the products in the correct box.
4 x 2 = 8 12 x 3 = 36 9 x 5 = 45
6 x 7 = 42 5 x 5 = 25 10 x 6 = 60
11 x 3 = 33 9 x 8 = 72 13 x 3 = 39
FACTORS PRODUCTS
3. Motivation
Message in Boxes
Multiply. Write the letter that is next to each answer in the correct box below. Read the
secret message.
9 4 3 9 5
x 2 x 9 x 4 x 7 x 2
A E H O R
9 5 9 9 6
x 8 x 9 x 9 x 3 x 9
S T U W Y
27 63 27 45 12 18 45 72 81 10 36
W O W T H A T S U R E
27 18 72 36 18 72 54
W A S E A S Y

8
1. Presentation
a. Present this problem
Andres Bonifacio Elementary School received 12 boxes of toys from the
governor of the province. Each box had 24 assorted toys. How many toys were there in
all?
Let us analyze the problem
■ Understand the problem
What is asked in the problem? Number of toys in all.
What are given? 12 boxes of toys, 24 assorted toys.
What process will you use? Multiplication.
■ Plan
What is the number sentence? What is your answer?
Did you do it this way?
12 x 24 = N 24= 20 + 4
x 12= 10 + 2
■ Carry out the plan
Tell the pupils that the following solutions used expanded notation.
Step 1: Step 2: Step 3:
20 + 4 20 + 4 24 = 20 + 4
x 10 + 2 x 10 + 2 x 12 = 10 + 2
40 + 8 200 + 40 40 + 8
2 x 4 = 8 10 x 4 = 40 + 200 + 40
2 x 20 = 40 10 x 20 = 200 240 + 48
= 288 toy planes
Introduce now the short method.
Multiply the multiplicand by the ones in the multiplier. Write the product (48) beginning
from the ones place.
Multiply the multiplicand by the tens in the multiplier. Write the product (240)
Multiply by ones Multiply by tens
24 24 24
x 12 x 2 x 10
48 48 240
240
Add the two partial products
24
x 12
48 partial products
+ 240
288 product
■ Look back
Did you answer correctly the given problem? Check your answer.

9
Let the class do these on the board.
1) 22 2) 322 3) 31 4) 1 243
x 11 x 3 x 33 x 21
Let the pupils do these exercises on their seats.
1) 23 2) 23 3) 223 4) 312
x 22 x 12 x 23 x 12
2. Guided Practice
a. Game (GIANT STEP)
Teacher will call on 5 pupils. Provide each pupil illustration board and chalk. They
will stand and start from the back. The teacher will flash the multiplication. The first one
who will give the correct answer will step forward, the one who reaches first the front
desk wins the contest.
1) 232 2) 24 3) 231 4) 321 5) 4 321
x 2 x 22 x 32 x 33 x 2
6) 1 431 7) 324 8) 33
x 12 x 22 x 22
b. Group Activity: (4 groups)
Give each group an activity card. Each group will present their work after 3
minutes. After working, ask questions that will emphasize the value of accuracy and
carefulness.
Group I = 124 6321 21
x 2 x 12 x 21
Group II = 221 32 412 13
x 4 x 12 x 12
Group III = 212 4 213 14
x 13 x 12 x 2
Group IV = 212 2 134 23
x 3 x 12 x 13
c. Problem Solving
1. Miss Cruz arranges 142 books in every shelf in the library. If there are 12 shelves,
how many books are there in all?
2. Gerry spent his vacation working in a supermarket. He worked 8 hours a day for 11
days. How many hours did he work in all?
3. Marnelyn counted 24 small chocolate bars in a package. If there were 21 packages in
the shelf, how many chocolate bars were there?
4. Marlon delivers 50 letters each day. How many letters does Marlon deliver in 3 days?
5. Tony has 4 packs of pencils. There are 20 pencils in each pack. How many pencils
does Tony have?

10
3. Generalization
How do you multiply 2- to 4- digit numbers by 1- to 2- digit number without regrouping?
In multiplying 2- to 4- digit numbers by 1- to 2- digit numbers without regrouping,
start with the ones, then the tens, then the hundreds, and lastly the thousands.
C. Application
1. What is the greatest product you can get using the digits 3, 2, 1, 4 as factors?
Write in the boxes the factors that will give the largest product.
Product = _______
2. Pick a number from box X. Multiply it by a number from box Y to find the given answers.
Box X Box Y
42 22 123 21 12 32
23 31 431 24 33 20
1) 483 2) 8620 3) 3936
X = _______ X = _______ X = _______
Y = _______ Y = _______ Y = _______
4) 504 5) 528 6) 1023
X = _______ X = _______ X = _______
Y = _______ Y = _______ Y = _______
IV. Evaluation
A. Find the missing digits.
1) 2 3 4 2) 4 3 2 1 3) 2 4
2 2 x 2 3 x 1 1
+4 _ 8 1 2 9 _ _ 2 _
_ 6 8 _ 8 _ 4 2 _ _ _ _
5 _ 4 8 9 9 _ 8 3 _ 6 4
4) 3 2 5) 1 2 3
x 1 2 x 1 3
_ _ _ 6 9
_ 2 _ 1 2 _ _
3 8 4 1 _ 9 9
__ __
x __ __

11
B. Find the product:
1) 234 2) 143 3) 322
x 2 x 21 x 13
4) 2 233 5) 6 321
x 32 x 3
V. Assignment
A. Find the product.
1) 452 2) 313 3) 23
x 11 x 13 x 21
4) 2 431 5) 421
x 22 x 21
B. Solve the following problems.
1. Ellen has 23 pages of stamps. Each page has 112 pieces. How many stamps does she have
in all?
2. Mang Mario needs 4 poles for his vegetable garden. Each pole should be 122 centimetres
long. What will be the total length of 4 poles?
3. The bookstore received a shipment of 13 boxes of books. Each box contained 112 books.
How many books were in the shipment?
4. Puring and Linda are going home after visiting their grandmother. The trip takes 3 hours. If
the bus travels 122 kilometres an hour, how far away is their house?
5. Edith bought 231 pieces of linen paper at P3 each. How much did she spend for the linen
paper?
Multiplying 2- to 4- Digit Numbers by 1- to 2- Digit Numbers with Regrouping
Cognitive: Multiply 2- to 4- digit numbers by 1- to 2- digit numbers with regrouping
Psychomotor: Write the product of 2- to 4- digit numbers by 1- to 2- digit numbers
Affective: Compute the product of two numbers with speed and accuracy
Skill: Multiplying 2- to 4- digit numbers by 1- to 2- digit numbers with
regrouping
Materials: chalkboard, flash cards, activity cards
Value: Speed and accuracy

12
1. Drill : (Multiplying by 1-digit number)
2. Review
Give the factors of the given number.
72 = (9 x 8) 24 = ? 36 = ? 81 = ?
64 = ? 18 = ? 45 = ? 90 = ?
3. Motivation (Song) Be alert in answering the multiplication sentence while singing. (Tune:
Skip to My Love)
Teacher: I’m Mathematics how do you do?
Children: I’m Mathematics how do you do?
Teacher: Who are you? Tell me too?
Children: I’m just a child but I know you.
Teacher: Speak, speak, 7 x 7
Children: _____ (The pupils will answer)
Teacher: Speak, speak, 5 x 8
Children: _____
All: It’s so easy I tell you.
1. Presentation
a. There are 36 newspapers in a bundle. How many newspapers are in 125 bundles?
Analyze the problem with the pupils to determine the solution. To find the answer, we
multiply 125 by 36.
Multiply 125 by 6 ones Multiply 125 by 3 tens
125 125
x 36 x 6
750 750
125
x 30
3750
Add the partial products.
125
x 36
750
+ 3 750 There are 4 500 newspapers.
4 500
- Emphasize that the multiplier 36 in the example means multiplying the multiplicand
by 6 ones and by 3 tens. (30)
25
x 2
20
x 4
43
x 2
32
x 4
11
x 6

13
b. Copy then complete.
2 4 0
x 2 5
12 0 0
4 8 0 0
_ _ _ _
2 5 6
x 2 4
1 0 2 4
5 1 2 _
_ _ _ _
2. Guided Practice
a. Write the missing numbers.
22
x 39
198
_ _ _
_ _ _
232
x 16
1392
_ _ _ _
_ _ _ _
8721
x 24
34884
_ _ _ _ _
_ _ _ _ _
32
x 15
160
_ _ _
_ _ _
128
x 22
256
_ _ _ _
_ _ _ _
b. Show a chart “How many Fruits Are There in All.” Group the pupils into 4. Each group will
work on one fruit. Ask each group to present their work on the board.
Number of
Baskets
Fruits and Number per Basket
Mangoes
24
Avocados
146
Atis
36
Melon
18
25 baskets
30 baskets
12 baskets
36 baskets
24 x 25 = 600
e. Game (SOLVE AND DELIVER). Be fast and accurate while answering the multiplication
sentences.
Why is it necessary to be accurate in solving any problem?
1. Get a partner.
2. Pretend you are cousins who live in the same house. Your grandmother is sick. You
are asked to bring food to her. Just like Little Red Riding Hood, you will meet lots of
danger and obstacles along the way. These obstacles are in the form of multiplication
exercises like the ones below.
3. Cut and place them on the table upside down. Take turns with your partner in picking
up a card.
4. Answer the problem in the card. If you get the correct answer, you will move one step
forward towards grandma’s house.
5. If your answer is wrong, you will move one step backward. Use a marker to indicate
your position. Let us see who can deliver the food to grandma.
45
x 23
18
x 46
29
x 51
84
x 70
92
x 12
15
x 65
24
x 62
77
x 14
32
x 56
40
x 63

14
3. Generalization:
How do we multiply 2- to 4- digit numbers by 2- digit numbers with regrouping?
 Multiply the 2- to 4- digit multiplicand by the ones of the multiplier. Regroup if
needed.
 Multiply the multiplicand by the tens of the multiplier. Regroup if needed.
 Add the partial products to get the final product.
C. Application
a. Find the product:
1) 32
x 15
2) 42
x 52
3) 25
x 35
4) 821
x 52
5) 1503
x 22
b. Follow the arrows. Fill in the missing numbers.
1) 73 x ___  365 - ___  305 x 9 = ___
2) ___ x 8  200 + ___  449 x 6 = ___
3) 39 x ___  78 + 294  ___ x 7 = ___
4) ___ x 4  256 – 178  ___ x 5 = ___
5) The sum of all four numbers is ____.

15
IV. Evaluation
A. Multiply
1) 179 x 12 2) 643 x 12
3) 370 x 16 4) 145 x 18
5) 224 x 10
B. Find the missing digits
1)
33_
x 16
2_22
33_ _
5_9_
2)
60_
x _8
4_32
1_08_
169_ _
3)
_48
x 36
2 6 _ _
1 _4
_6 12 8
4)
_8
x 1_
_34
78_
10_ _
5)
4_0
x 3_
_52_
_260_
15_ _0
V. Assignment
A. Find the missing digits.
1)
3 9
x 1 4
1 5 6
_ 9_
_ _ 6
2)
25
x 31
_5
75_
775
3)
2 4 7
x 3 6
1 4 8 2
7 4 1_
_ _ _ _
4)
261
x 13
_83
261_
339_
5)
1 8 3
x 2 5
9 _ _
_ 6 6_
_ 5 _ 5
B. Find the products.
1) 137
x 12
2) 4500
x 38
3) 538
x 26
4) 763
x 46
5) 1256
x 49

16
Multiplying 2-Digit Numbers by 1-Digit Number with Zero in the Multiplicand
Cognitive: Multiply 2-digit numbers by 1-digit number with zero in the multiplicand
Psychomotor: Apply basic skills in multiplying numbers
Affective: Show care and concern for the environment
Skills: a. Multiplying 2-digit numbers by 1-digit number with zero in the
multiplicand
b. Applying basic skills in multiplying numbers
Materials: number wheel, flash card, strips, drawing
Value: Care and concern for the environment
1. Drill : Conduct a contest by spinning the wheels and giving the product.
2. Review
If (4 x 3) x 2 = 24, then 4 x (3 x 2) = N
If (6 x 1) x 7 = 42, then 6 x (1 x 7) = N
If 4 x (2 x 5) = 40, then (4 x 2) x 5 = N
If 3 x (2 x 4) = 24, then (3 x 2) x 4 = N
Name the missing factors.
8 x 3 = 3 x ___ 8 x 4 = ___ x 8
5 x 4 = ___ x 5 6 x 8 = ___ x 6
12 x 2 = ___ x 12 15 x 7 = ___ x 15
3. Motivation
Present a problem opener.
Mang Ato harvested 5 crates of mangoes. If each crate has 50 mangoes, how many
mangoes were there in all?
What trees do you have in your backyard?
Why are trees important?
What do you think will happen if there are no trees around us?
1
2
3
45
6
7
8
x 7
1
2
3
45
6
7
8
x 8
1
2
3
45
6
7
8
x 9

17
1. Presentation
a. Analyze the problem.
How many crates of mangoes did Mang Ato harvest?
How many mangoes were there in each crate?
What is asked in the problem?
What facts are given?
What process is to be used?
(Steps in solving the problem)
Step 1 50
x 5
0
Step 2 50
x 5
250
- Remind the pupils about the zero property of multiplication.
 Any number multiplied by zero, the product is zero.
b. Present another problem.
Mr. de Alday gave 90 santol seedlings to each of the 8 classes, how many seedlings
were given out?
What seedlings did Mr. de Alday give to each of the 8 classes?
How many santol seedlings did each class receive?
What are the given facts?
What process will you use?
How will you solve the problem?
90 90
x 8 8
0 720 santol seedlings
More examples:
1) 70 70
x 7 7
0 490
2) 60 60
x 5 5
0 300
3) 20 20
x 8 8
0 160
4) 40 40
x 9 9
0 360
5) 90 90
x 6 6
0 540
2. Guided Practice
a. Let the pupils study the coding of numbers.
Let them do it afterwards.
Multiply the ones on the multiplicand by the
multiplier.
Now multiply the tens on the multiplicand by the
multiplier.

18
Digit Movement
0
1
2
3
4
5
6
7
8
9
- - Forefinger and thumb together forming zero
- - Right arm forward closed fist
- - Left arm forward closed fist
- - Left and right arm folded vertically
- - Hands on waist
- - Right hand on the chest
- - Bend forward to pick something
- - Stand straight
- - Arms obliquely upward
- - Do the McDonald sign
Work in Dyads
Direction: Find the missing number in the product. Use the number coding in answering.
1) 50
x 4
20_
2) 90
x 3
_70
3) 70
x 6
4_0
4) 20
x 8
_ _0
5) 60
x 6
36_
6) 30
x 9
_70
7) 80
x 5
4_0
8) 10
x 7
_0
9) 40
x 6
_40
b. Group Activity - Draw Lots
The teacher will prepare a box with word problems inside. Any member of the
group will draw 1 strip inside the box, then the group will answer it afterwards. The group
will be given 2 minutes to answer the problem. The group with the highest points wins.
Sample problems:
1. There are 50 passengers in one provincial bus. How many passengers are there in 8
buses?
2. Jean saves 90 a month. How much will she save in 5 months?
3. Celia can sell 50 sampaguita garlands a day. How many garlands can she sell in 9
days?
4. Mang Dianong has 9 rows of corn plants in his farm. There are 20 plants in each row.
How many corn plants are there?
5. Aldy planted 30 pechay seedlings in each plot. How many seedlings did he plant in 8
plots?
What should you remember in multiplying a number with zero?
c. (Little Brother Approach)
Let the fast learners develop their own simple word problems, They’ll answer
these together with the slow learners.
1. Mang Andy saves __ a day. How much will he save in __ days?
2. Jojo has __ piles of tanzan. Each pile has ___ tanzans. How many tanzans are there
in all?
3. There were __ students in the library. Each student borrowed ___ books. How may
books were borrowed by the students?
4. Maris has __ boxes of chalk. Each box contains __ pieces of halk. How many pieces
of chalk does Maris have?
5. Edith earned __ a day in selling newspaper. How much will she earn in __ days?
3. Generalization:
How do we multiply 2-digit numbers by 1-digit number with zero in the multiplicand?

19
a. Multiply the ones in the multiplicand by the multiplier.
b. Multiply the tens in the multiplicand by the multiplier.
 Any number multiplied by zero is equal to zero.
C. Application
Solve the following problems.
1. A baker bakes 60 pieces of bread in one day. How many pieces of bread will he bake in 7
days?
2. Aling Marta has 8 baskets of tomatoes. If each basket contains 90 tomatoes, how many
tomatoes will she have in all?
3. Mang Ading harvested 20 mangoes from each of the 9 mango trees. How many mangoes did
he harvest in all?
4. There are 30 cans of milk in a box. If there are 9 boxes, how many cans of milk will there be
in all?
5. A Mathematics Dictionary cost 80.00. How much will 6 Mathematics Dictionary cost?
IV. Evaluation
A. Give the product.
1) 80 x 5 = 2) 60 x 4 =
3) 50 4) 70 5) 90
x 6 x 5 x 6
B. SECRET MESSAGE
1. Find the product. Write the answer on the boxes.
A.
70
x 4
10
x 9
50
x 8
90
x 4
90
x 7
A C E H I
40
x 4
20
x 9
35
x 2
30
x 2
40
x 7
L M N O P
20
x 4
30
X 8
60
x 5
70
x 7
80
x 9
60
x 7
R T U W Y Z
2. Write the letter that matches with the numbers.
720 60 300 280 80 400 280
Y O U A R E A
180 300 160 240 630 280 160 630 90 280 240 630 60 70
M U L T I P L I C A T I O N
490 360 630 420
W H I Z

20
3. What is the secret message?
V. Assignment
A. Fill in the box with correct answer.
1) 90
x 7
6_0
2) 60
x 6
36_
3) 40
x 7
2_0
4) 80
x 8
_40
5) 50
x 8
4_ _
B. Write >, < or = in the box.
1) 80 x 6 ___ 60 x 8 2) 40 x 5 ___ 20 x 9
3) 50 x 7 ___ 70 x 4 4) 30 x 6 ___ 40 x 6
5) 70 x 5 ___ 90 x 2
Multiplying 3- to 4-Digit Number by 1-Digit Number with Zero in the Multiplicand
Cognitive: Multiply 3- to 4-digit numbers by 1-digit number with zero in the
multiplicand
Psychomotor: Apply basic skills in multiplying numbers
Affective: Follow the rules and regulations in every activity
Skills: Multiplying 3- to 4-digit number by 1-digit number with zero in the
multiplicand
Applying basic skills in multiplying numbers
Materials: pictures, flaglets, box
Value: Following rules and regulations
1. Drill (Song)
Multiply (Tune: Mary Had a Little Lamb)
Let us learn to multiply
Multiply, multiply
Let us learn to multiply

21
Table 2 and 3 (Pupils will recite table 2 and 3)
2 x 1 3 x 1
2 x 10 3 x 10
We had learn to multiply
Multiply, multiply
Table 2 and 3.
Pupils recite the other multiplication tables.
2. Review
Spin any of the roulettes. Then multiply the number at the center with the number where
the arrow points.
3. Motivation
Show a picture of a boy in a library. Talk about the picture.
Ask: Have you been to a library?
How should you behave when you’re in a library?
What should you do in the library?
What are some of the rules to be followed while you are in the library?
Do you always follow them? Why?
1. Presentation
a. Present the problem.
Manolito is a student assistant in the school library. He is counting the
Mathematics books in the shelf. There are 120 books in each shelf. How many
Mathematics books are there in the 6 shelves?
b. Ask the following questions to the pupils.
 Who is the student assistant?
 How many books are there in each shelf?
 What is asked in the problem?
 What facts are given?
 What process is to be used?
 How will you solve the problem?
- To find the number of Mathematics books, multiply 6 by 120

22
Step 1 – Multiply the ones by 6
120
x 6
0
Step 2 – Multiply the tens by 6. Regroup the product.
120
x 6
20
Step 3 – Multiply the hundreds by 6. Add the regrouped hundreds. 6 hundreds +
1 hundred = 7 hundreds.
120
x 6
720 Mathematics books
Ask: How many Mathematics books are there in all?
c. Present another problem.
A bookstore sold 2 105 greeting cards each month for three successive months.
How many cards were sold altogether?
Ask the following:
- Have you received any greeting card? What kind of greeting card was it?
- How many greeting cards did the bookstore sell in one month?
- How many successive months did the bookstore sell greeting cards?
- How will you find the answer?
(Guide the pupils in answering the problem.)
Step 1 2 105
x 3
5
Step 2 – Multiply the tens by 3. Add the regrouped ten. Zero ten + 1 ten = 1 ten
2 105
x 3
15
Step 3 – Multiply the hundreds by 3.
2 105
x 3
315
Step 3 – Multiply the thousands by 3.
2 105
x 3
6 315
The bookstore sold 6 315 greeting cards in 3 successive months.
2. Guided Practice
a. Game: (Flaglet Race) Divide the class into 4 teams. A representative from each group
will get a flaglet which has multiplication sentence written on it. The first one who can answer
it can claim that flag. Do these with the other members of the group. The group who will earn
more flaglets wins the game.
b. Another activity
(Find a Partner)
Multiply the ones by 3. Regroup the product.
15 ones is 1 ten and 5 ones.

23
Let the individual pupil get one number from the box. The numbers in the box are the
multiplicands and the multipliers written separately on a strip of paper. The 1- digit
number represents the multiplier, while the 2-3-digit numbers represent as the
multiplicand. Every pupil will find a partner as – Multiplicand to multiplier and vice versa.
Partners will solve it together.
Multiplicand Multiplier
450 , 205 , 4501
1009 , 2380 , 8026
8 9 4
7 6 5
c. RIDDLE
“What is the term used when giraffes going in one direction get mixed-up with giraffes
going in another direction?
Here’s how to get the answer.
1. Find the products of the exercises given below.
2. Then cross out the letters that show the same products in the boxes found on the
next page.
3. The remaining letters spell the answer to our riddle.
1) 405
x 3
2) 360
x 8
3) 1204
x 5
4) 830
x 2
5) 310
x 8
6) 2035
x 6
7) 4510
x 4
8) 7068
x 9
9) 3205
x 5
4 305 1 660 18 040 1 215 8 550 7 065 16 025
A I T S G I U
15 270 2 480 4 501 7 782 8 900 2 880 4 320
R R A F F A I
2 670 12 210 7 028 6 020 4 950 63 612 3 201
C B J E A T M
Answer:
A G I R A F F I C J A M
3. Generalization:
How do we multiply 3- to 4-digit numbers by 1-digit number with zero in the multiplicand?
 Multiply the ones, tens, hundreds and thousands in the multiplicand by the
multiplier.
 Regroup when necessary.
 Zero times any number is zero and zero plus any number equals the same number.

24
C. Application
1. A baker bakes 1 052 pieces of bread in one day. How many pieces of bread will he bake in
7 days?
2. Aling Marta has 8 baskets of tomatoes. If each basket contains 405 tomatoes, how many
tomatoes will she have in all?
3. Mang Ading harvested 105 mangoes from each tree in his orchard. How many mangoes
did he harvest from 7 trees? from 9 trees?
4. Pinky can read 260 words in 1 minute. If she spends 4 minutes reading, how many words
can she read?
IV. Evaluation
Seatwork
A. Fill in the blanks with the missing number.
1) 302
x 4
1 2_8
2) 4 510
x 6
2_ 0_0
3) 820
x 3
2 46_
4) 905
x 7
6 _ _5
5) 1 075
x 8
8 _00
B. Check the multiplication problems and encircle any incorrect solution.
1) 408
x 5
2 040
2) 3 450
x 7
20 157
3) 6 071
x 8
48 568
4) 4 095
x 3
12 126
5) 5 708
x 4
22 832
C. Solve the following problems.
1. Miss de Alday arranges 140 books in every shelf in the library. There are 9 shelves. How
many books are there in all?
2. Brylle collects 8 pages of stamps. Each page has 306 pieces. How many stamps are there in
all?
3. Gloria helps her mother sell calamansi in the market. She puts 150 calamansi in each bag.
How many calamansi are there in 7 bags?
4. Mrs. Pantoja bought 3 kilos of meat at 130 per kilo. How much did she pay the vendor?
5. There are 250 apples in a box. If an apple cost 5, how much will the apples cost?
V. Assignment
A. Multiply the following
1) 360
x 5
2) 4 008
x 2
3) 7 005
x 3

25
4) 6 041
x 4
5) 5 730
x 6
B. Cross number puzzle
Multiply the following number to solve the puzzle.
a b
c
d g e f
h
i
Across
a. 170 x 5
b. 160 x 3
d. 320 x 8
h. 8 702 x 4
i. 108 x 2
Down
a. 406 x 2
c. 3 520 x 2
e. 506 x 8
f. 1 620 x 3
g. 908 x 7
Multiplying 2- to 4-Digit Numbers by Multiples of 10
Cognitive: Multiply 2 to 4 digit numbers by multiples of 10
Psychomotor: Solve multiplication sentence accurately
Affective: Show the value of doing work independently
Skills: Multiplying 2 to 4 digit numbers by multiples of 10
Solving multiplication sentence accurately
Reference: BEC PELC I. D.1.1.1.6
Materials: flash cards, activity cards
Value: Independence
1. Drill: Have a drill on multiplication basic facts using flashcards.
4 3 1 4 8 9
x 5 x 6 x 5 x 9 x 7 x 3

26
5 2 5 3 2 3
x 7 x 9 x 0 x 8 x 7 x 5
2. Review
Find the product.
a) 21 b) 122 c) 3 012 d) 4 024 e) 313
x 5 x 6 x 4 x 2 x 3
3. Motivation
Let all the pupils stand and do the skip movement on the floor.
As they skip, let them count by 10s.
(Say “10, 20, 30, 40, 50, 60, 70…)
Ask: What do you observe about these numbers?
(Possible answers are: “These numbers end in zero; or, These numbers can be divided
by 10.”)
Can you give other numbers that end in zero or that can be divided by 10? (Accept
possible answers.)
Say, “These numbers are called multiples of 10.”
1. Presentation
a. Present this problem.
1) In a toy factory, a group of workers filled the 21 boxes with 50 toy cars each How
many toy cars were filled in all the boxes?
2) Analyze the problem.
Ask: What is asked? (The total number of toy cars that were filled in all the boxes)
What are the given facts? (21 boxes and 50 toy cars)
What shall we do to find the answer? (multiply)
What is the number sentence for the problem? (21 x 50 = N)
3) Discuss with the pupils the three steps of multiplication.
Step 1 Ask, “What shall we do first?
21 (Multiply 21 by 0)
x 50
00
Step 2 “What shall we do next?
21 (Multiply 21 by 5)
x 50
00
105_

27
Step 3
21
x 50 “What shall we do with the partial
00 products?”
+ 105_ (Add the partial products to get the
1 050 final product.)
“So, what’s the answer to the problem?” (1050 toy cars were filled in all the boxes.)
b. Now, let them study other examples. This time, help them discover a pattern that will help
them multiply by multiples of 10 easily.
25 22 210 3140
x 10 x 30 x 40 x 40
250 660 8400 125 600
Ask,” How many zeros are there in the factors in the first and second examples? (1
zero) in the product? (1 zero)
How about in the 3
rd
and 4
th
examples, how many zeros are there in the factors?
(2 zeros each) in the product? (2 zeros)
Point out that the number of zeros in the factors is equal to the number of zeros in the
product.
Say, “Multiply the non-zero digits and then annex zeros in the product.
The number of zeros in both factors is equal to the number of zeros in the
product.
c. Now look at the number line.
0 | | | | | | | | | | | | |
10 20 30 40 50 60 70 80 90 100110120130
How many zeros are there in 12 tens? 12 x 10 = 120
How many zeros are there in 10? (1)
What did you do with zero?
12
x 10 or 12 x 10 = 120
120
(Do the same process/procedure in the remaining numbers in the number line?)
d. Error Analysis – For some exercises, some pupils might do this:
20 x 5 = 10
Have pupils who made this error look first at the product to see if it made sense.
Ask: “Can 5 twenties be equal to 10? (No)
Then have the pupils concentrate first on the product of 5 and 2 (10), then on writing the
correct number of zeros after the product.
2. Guided Practice
a. Divide the class into 3 groups. Let each group do the following:
Look for the hidden message by solving each problem. Find the letter in the code that
matches each answer. Write the correct letters in the boxes. (Each group will work
independently.)

28
1) 10 2) 80 3) 10 4) 560 5) 10
x 7 x 10 x 37 x 10 x 20
6) 70 7) 80 8) 90 9) 70 10) 80
x 5 x 70 x 30 x 80 x 50
11) 90 12) 300 13) 630 14) 72 o.) 640
x 70 x 70 x 10 x 30 x 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
ayou are Math Whiz
Code
A – 5 600 I – 2 160 T – 4 000
K – 700 V – 40 Z – 12 800
H – 6 300 X – 210 M – 2 700
L – 560 R – 200 P – 240
W – 21 000 E – 350 U – 370
Y – 70 O – 800 S – 720
b. Investigation
Divide the class into 2 groups. Give them activity card.
ACTIVITY CARD # 1
Investigate, then write your investigation afterwards.
6 x 10 = 60
3 x 30 = 90
7 x 20 = 140
4 x 40 = 160
Questions:
1. How many zeros are there in each factor? ______
2. How about the zeros in the products? ______
3. Do they have the same number of zeros?
4. What is your investigation about it?
ACTIVITY CARD # 2
Investigate, then write your investigation afterwards.
5 x 20 = 100
2 x 50 = 100
5 x 40 = 200
8 x 50 = 400
Questions:
1. How many zeros are there in each factor? ______
2. How about the zeros in each product? ______
3. Are the number of zeros in the factors the same with the number of zeros in the
product? ________
4. What is your investigation about it? __________
How did you answer your activity?

29
Did you copy from the other group? Why? Stress the value of doing ones work
independently.
3. Generalization
How do we multiply 2- to 4-digit numbers by multiples of 10?
a. To multiply by a multiple of 10, multiply the non-zero digits first, and then annex zeros
in the product.
b. The number of zero in the factors is equal to the number of zeros in the product.
Is there a short cut for this?
C. Application
1. There are 165 trays of oranges. Each tray has 20 oranges. How many oranges are there in
all?
2. Grade Three SPED A class has 43 pupils. Each pupil has 10 books each. How many books
did they have altogether?
3. If there are 24 bottles in a case, how many bottles will there be in 30 cases?
IV. Evaluation
A. Encircle the letter of the correct product.
1) 36 a. 36 b. 360 c. 3 610
x 10
2) 25 a. 2 520 b. 2 500 c. 500
x 20
3) 45 a. 1 350 b. 1 530 c. 1 340
x 30
4) 232 a. 2 320 b. 6 420 c. 4 640
x 20
5) 9 201 a. 276 030 b. 270 603 c. 273 060
x 30
B. Write >, <, or = in the blank.
1) 55 x 10 _____ 25 x 20 2) 500 x 70 _____ 50 x 70
3) 315 x 30 _____ 154 x 50 4) 750 x 20 _____ 20 x 750
5) 81 x 10 _____ 75 x 10
C. Solve the following problems.
1. A vendor sold 15 boxes of soap. Each box has 20 bars of soap. How many bars of soap did
he sell?
2. Mang Ben gathered 213 baskets of mangoes. Each basket has 30 mangoes. How many
mangoes did he gather?

30
V. Assignment
A. Answer the following:
1) 73 x 10 =
2) 25 x 30 =
3) 15 x 10 =
4) 62 x 10 (<, >, =) 60 x 10
5) 43 x 20 (<, >, =) 53 x 10
B. Find the product.
1) 77 x 10 =
2) 250 x 20 =
3) 2 248 x 20 =
4) 1 623 x 30 =
5) 4 132 x 40 =
Multiplying 2- to 4- Digit Numbers by Multiples of 100
Cognitive: Multiply 2- to 4- digit numbers by multiples of 100
Psychomotor: Annex the same number of zeros in the factors to the product
Affective: Show cooperation in doing the activities
Skill: Multiplying 2- to 4- digit numbers by multiples of 100
Reference: BEC PELC D.I.1.2.3
Materials: flash cards, picture, bean bags
Value: Cooperation
1. Drill
Present the TIC-TAC-TOE GAME. Divide the class into 2 groups. Show flash cards on
multiplication by tens. To determine which group will play first, show a card to the
representative of each group and the first one to answer correctly after a go signal will have
his/her turn first. The group will choose another representative to answer the first card. If
he/she gets it rig -Tac-Toe board: if not, the group will get an
X.
2. Review
Show cards 1 to 10 for the pupils to multiply mentally by 10s. Tell them that they will just
add 1 zero after the number.
40
x 6
20
x 2
60
x 3
40
x 3
40
x 8
50
x 5
40
x 5
50
x 7

31
3. Motivation
Show a picture of an Indian.
Ask: Have you seen an Indian?
Say: Long ago a man in India decided to write a small dot to mean “zero”. Later the small dot
became a circle. The circle is now called zero
Working Together: Each member should cooperate.
● Work in a small group. Pretend zero does not exist. Try to write the numbers below
without using zero. Talk about what you do.
 one hundred twenty
 one thousand, and two
 one thousand, two hundred
 one hundred two
What if the man in India had never invented zero?
What symbol would you use to stand for nothing?
Say: Now we are going to work with zeros.
1. Presentation
A pharmacy ordered 100 packs of surgical gloves. Each pack contained 15 pairs
of surgical gloves. How many pairs were delivered to the pharmacy?
Show number card again and now multiply with 100.
100 x 15 = ____
To find the answer, we count by 100s.
Long Method
Step 1 100
x 15 (Multiply 100 by 5)
500
Step 2 100
x 15 (Multiply 100 by 1)
500
100_
Step 3 100
x 15 (Add the partial products to get
500 the final product)
+ 100_
1 500
1 500 pairs of surgical gloves were delivered
Short method
100
x 15 (Multiply the non-zero digits 15 by 1)
15__
100

32
x 15 (Affix the number of zeros to the product)
1 500
b. Present this number sentence.
1 100 x 100 = N
How many zeros are there in 11 hundreds? 100?
What are the non-zero digits in 11 x 100?
After multiplying the non-zero digits, what did you do with zeros?
2. Guided Practice
a. Give this activity sheet to the group.
The Bean Bag Game
Materials: 2 bean bags (x 100)
Have the children play a toss game to practice multiplying by hundreds.
Tape the numbered squares of paper to the floor as shown below.
2 324 175 231 3 561
25 38 74
15
Divide the class into 2 teams. Provide each team with 1 bean bag. The bean bags
represent the factor 100.
The teacher calls out a product 17 500. Since the factors of 17 500 are 175 and 100,
a player from each team tosses the bean bag to the correct number on the grid (175)
and earns one point for his/her team. For the product 1 500, the bean bag should be
tossed to the number 15 on the grid.
The first team to score 10 points wins the game.
b. Divide the class into 4 groups. Let each representative of the group do the “Jack en Poy”
game. The first one to win can choose the problem which he think is easier to solve.
This will be done respectively by all the representatives of the group.
Problems:
1. Cheryl bought 400 boxes of cough syrup from the drugstore. Each box contained 18
bottles. How many bottles of cough syrup did she buy?
2. Eva needs 300 packs of lozenges. Each pack contains 26 tablets. How many
lozenges does she need in all?
3. Mary ordered 200 bags of syringes. Each bag has 114 syringes. How many
syringes did she order?
4. Glenda will distribute 18 bedsheets in every room in the hospital. How many
bedsheets will she need in all if there are 100 rooms?

33
Solutions
Problem No. 1 Problem No. 2
400 300
x 18 x 26
7 200 7 800
Problem No. 3 Problem No. 4
114 100
x 200 x 18
22 800 1 800
c. Problem solving using a table
The table shows how some of the fastest vehicle in the world.
Vehicle Speed (k/h)
(rounded to the nearest hundreds)
Hayaba Motorcycle 300
SSC Ultimate Aero Car 400
Spirit of Australia Water Vessel 500
French TGV Train 600
(Source: www.bukisa.com/47080)
1. If Hayaba Motorcycle run for 3 hours without stopping how far could it go?
2. If SSC Ultimate Aero Car travel for 2 hours, how far could it go?
3. If French TGV Train travel for 5 hours, how many kilometres could it reach?
4. If Spirit of Australia Water Vessel take a trip for 3 hours, how many kilometres could it
travel?
3. Generalization:
How do we multiply 2- to 4- digit numbers by multiples of 100?
 Multiply the non-zero digits.
 Then affix to the product the number of zeros from both the factors.
C. Application
Solve each problem.
1. There are 500 bags of peanuts. If each bag of peanuts contains 125 peanuts, how many
peanuts will there be in all?
2. Jack delivers 25 magazine to 400 customers. How many magazines does he deliver in all?
3. One volume of encyclopedia has 400 pages. How many pages are there in 3 volumes?
4. When one-digit number is multiplied by 100, the product is 720 more than the product of the
number and 10. What is the number?
Answer:
8 x 100 = 800 720 more
8 x 10 = 80
The number is 8.

34
IV. Evaluation
A. Write the missing number.
1) 13 x 3 hundreds = ___ hundreds
13 x 300 = ___
24 x 200 = ___
16 x 700 = ___
14 x 800 = ___
15 x 600 = ___
B. Encircle the letter of the correct answer.
1) 219 multiplied by 100 gives the product of ___
a. 21 900 b. 25 c. 2 500 d. 2 600
2) 25 times 100 equals ___
a. 250 b. 25 c. 2 500 d. 2 600
3) 24 times 200 = ___ what number should be placed in the box.
a. 2 400 b. 4 800 c. 2 242 d. 24 000
4) What number when multiplied by 100 gives the product of 2800?
a. 28 b. 2 807 c. 280 000 d. 2 888
5) What is the missing number in this sentence? 36 x ___ = 3 600
a. 10 b. 100 c. 1 000 d. 120
C. Supply with the multiples of 100.
1) 5 x ___ = 3 500
2) 8 x ___ = 7 200
3) 4 x ___ = 2 400
4) 12 x ___ = 6 000
5) 23 x ___ = 13 800
V. Assignment
A. Multiply mentally. Write the product.
1) 800
x 24
2) 600
x 17
3) 900
x 25
4) 300
x 18
5) 700
x 24
B. Write >, < or = in the blank.
1) 9 x 900 ___ 9 x 8000
2) 600 x 7 ___ 70 x 600
3) 70 x 500 ___ 50 x 70

35
4) 500 x 81 ___ 50 x 800
5) 800 x 21 ___ 31 x 900
Estimating the Product of 2- to 3-Digit Numbers by 1- to 2-Digit Numbers
Cognitive: Estimate the product of 2- to 3-digit numbers by 1- to 2-digit numbers
Psychomotor: Follow the steps in estimating the product
Affective: Show neatness in one’s computation
Skill: Estimating the product of 2- to 3-digit numbers by 1- to 2-digit numbers
Reference: BEC PELC I.D.1.1.2
Materials: chart, activity sheets, flash cards, roulette
Value: Neatness
1. Drill
Give a drill on multiplication using flashcard. Present the Give-Me-The-Card Game to the
class.
Arrange the cards on the chalk ledge. The teacher will give the product and the pupils from
each team will find the card of its factors. The first one to get the correct card wins a point.
2. Review
Let the pupils spin the roulette then round off the numbers to the nearest tens, hundreds
and thousands.
9
x 6
8
x 7
9
x 6
3
x 7
9
x 9
7
x 4
5
x 8
2
x 8
8
x 3
9
x 10
Nearest
Tens
75
46
23
68 84
32
Nearest
Hundreds
372
296
734
524 850
415

36
3. Motivation
(Show a picture of a school garden.)
What vegetables grow in the school garden? How many okra plants are there? Estimate
the numbers of each kind of plants. What should you do to make your plants healthy and
robust?
1. Presentation
a. Let us read this problem.
A farmer prepares 15 plots for vegetables. About how many seedlings will be needed if
each plot could be planted with 9 seedlings?
How many plots are being prepared by the farmer?
How many seedlings could be planted in one plot?
What is the mathematical sentence?
Multiply: 9 x 15 = N
Think:
15
x 9 rounded to
20
x 9
180 estimated product
15
x 9 rounded to
15
x 10
150 estimated product
therefore
15
x 10
150 nearest estimated product
b. Let’s have another problem.
Mang Delfin harvested 263 sacks of rice in one hectare. About how many sacks of rice
will be harvested in 12 hectares?
Multiply: 263 x 12 = N
Estimate the product.
Think:
263
x 12
rounded to 300
x 10
600
3 000
3 600
263
x 12 rounded to
263
x 10
2 630
263
x 12
rounded to
rounded to
300
x 10
3 000 nearest estimated product

37
c. Here are some examples.
491
x 4
is rounded off to 500
x 4
2 000 estimated product
Remember that we do not round off a 1-digit number.
98
x 23
x 20
832
x 67
x 70
2. Guided Practice
a. Estimate each product. Please avoid too many erasures.
1) 73 2) 87 3) 74 4) 473 5) 664
x 5 x 6 x 4 x 6 x 8
6) 38 7) 76 8) 526 9) 89 10) 479
x 23 x 44 x 48 x 23 x 29
b. Group pupils into pairs then have them perform the activity shown below.
MANIPULATIVE ACTIVITY CARD 19
Activity: Estimating Products
Materials: number cards (1-10)
Group Size: Pairs
Procedure:
 Distribute number cards to each pair, face down, in pile.
 Write on board: 374, 438, 152, 297.
 Partner 1 draws number card (e.g. 6).
 Partners write multiplication example using the number on the board and number
card. (374 x 6)
 Partner 1 rounds up 374 and finds the product (400 x 6); Partner 2 rounds down and
finds the product. (300 x 6)
 Continue the activity with the remaining numbers on the board. (5-10 min.)
c. Perfect Score
Pamela Perfect would like you to check her Math problems so she can get a perfect
score. Estimate to check the product. Encircle any incorrect solution.
Ex.:
325  300
X 12  x 10
3000
1) 22 2) 163 3) 573
x 16 x 5 x 45

38
4) 465 5) 727 6) 26
x 15 x 36 x 14
7) 982 8) 230 9) 318
x 43 x 75 x 48
3. Generalization
How do we estimate the product of 2- to 3-digit numbers multiplied by 1- to 2-digit
numbers?
To estimate the product:
 Round either the multiplicand or multiplier or both to its greatest place value.
 Multiply the rounded factors.
Why is estimation useful?
C. Application
Estimate and solve each problem.
1. There are 5 cages. Each cage has 38 birds. About how many birds are there?
2. There are 35 pupils in a class. Each pupil collected 125 copies of old newspapers. About
how many copies of newspapers did the class collect?
3. Mang Celso gathered 285 eggs from his poultry farm in one day. About how many eggs
would he gather in one week?
4. Simon spends 645 for his transportation per month. About how much would his total
transportation expenses be for 18 months?
5. A movie theater can accommodate 375 people in each show. About how many people can
the theater accommodate in 24 shows?
IV. Evaluation
A. Estimate the products.
1) 83 2) 67 3) 365
x 12 x 41 x 77
4) 622 5) 776 6) 634
x 56 x 52 x 59
B. Multiply then estimate to check the product.
1) 183 x 6 =
___ x ___ = _____
2) 698 x 7 =
___ x ___ = _____
3) 68 x 71 =
___ x ___ = _____
4) 236 x 18 =
___ x ___ = _____
5) 732 x 5 =
___ x ___ = _____

39
V. Assignment
A. Find the factors that when multiplied will give each estimated product on the left.
1) 60 6 x 14 5 x 18 5 x 13
2) 150 4 x 34 4 x 36 5 x 28
3) 270 9 x 24 9 x 26 8 x 31
4) 360 6 x 53 7 x 47 6 x 58
5) 4500 8 x 542 7 x 684 9 x 487
B. Estimate the products then compare using <, > or =.
1) 321 x 6  119 x 23
2) 506 x 12  605 x 9
3) 159 x 4  591 x 18
4) 679 x 4  663 x 4
5) 872 x 37  834 x 27
Estimating the Product of 4-Digit Numbers by 1- to 2- Digit Numbers
Cognitive: Estimate the product of 4-digit numbers by 1- to 2- digit numbers
Psychomotor: Follow the steps in estimating the product
Affective: Participate actively in the discussion
Skills: a. Estimating the product of 4-digit numbers by 1- to 2- digit
numbers
b. Following the steps in estimating the product
Reference: BEC PELC I D 1.1.3
Materials: roulette, word problems written on manila paper
Value: Active participation
1. Drill : Spin a roulette. Multiply the numbers by 10.

40
2. Review
Round off the following numbers.
Number Nearest tens Nearest hundreds Nearest thousands
9 375 9 380 9 400 9 000
12 478
13 265
24 563
46 814
3. Motivation (Problem Opener)
A bookstore sold 2 165 greeting cards each month for 3 successive months. About how
many cards were sold in these months?
1. Presentation
a. How many successive months did the bookstore sell greeting cards?
How many greeting cards were sold in each month?
To find out, estimate the product. Circle the thousands digit in the multiplicand. Round off
the multiplicand to the place value of that digit. Then multiply to estimate the product.
2165
x 3
2 000
x 3
6 000
Round off to the nearest thousand.
About 6 000 cards were sold in 3 months. We can also use estimation to check the
answer.
- How many digits does the multiplicand have?
Into what place are you going to round off 2 165?
Do we need to round off 3? Why?
b. Let’s try another example.
Aling Cora sells big watermelons in the market every summer. If she can sell 1
023 watermelons in a month, about how many watermelons can she sell in 12 months?
 Step 1: Round the multiplicand and the multiplier to the highest place value.
1 025
x 12
watermelons
months
1 000
x 10
 Step 2: Multiply to find the product.
1 000
x 10
10 000 Estimated number of watermelons.
c. Examine carefully how the estimated products of these examples are found.
4 735
x 28
5 000
x 30
150 000
6 423
x 6
6 000
x 6
36 000
In example A, did you round off both the multiplicand and the multiplier? Into what
places were they rounded off?
In example B did you round off the multiplier? Why?

41
2. Guided Practice
a. Let all the pupils chant with the “Pass it On” music
Let the pupils form a big circle. They are going to pass a rolled strip of cartolina. When
the music stops, the one who holds the strip will answer what is written on it through
estimation.
b. Estimate to solve each problem.
1) A bus travels 1 263 kilometres in a week. About how many kilometres does it travel in
6 weeks?
2) Mang Simon spends 2 645 for his transportation per month. About how much will
be spend for 3 months?
3) A movie theater can accommodate 3 405 people in each show. About how many
people will it be able to accommodate in 24 shows?
4) The Sport Club ordered 1 171 boxes of basketball. Each box contains 4 balls. About
how many balls did they order?
5) Sta. Catalina Central School received 35 boxes of pencils from a rich balikbayan.
Each box contains 2 356 pencils. About how many pencils did the school receive?
c. Round the multiplicands to their highest place, then find the estimated products. Write the
answers on your paper.
1) 1 208 2) 3 946 3) 6 854 4) 8 309
x 8 x 5 x 3 x 7
5) 9 287
x 9
d. Try harder. Find the actual and the estimated products. Write the answers on your paper.
1) 5 456 2) 7 812 3) 8 743 4) 1 090 5) 6 731
x 2 x 16 x 41 x 7 x 8
3. Generalization:
How do we estimate the product of a 4-digit number by 1- to 2- digit numbers?
 When we estimate a product, we round off the factor to its highest place value,
then multiply. We do not need to round off a one-digit factor.
3 882
x 26
1 392
x 38
7 056
x 2
4 481
x 12
6 970
x 78

42
C. Application
Solve each problem.
1. Mang Mario can harvest 1 252 ears of corn from his farm a day. About how many ears of
corn can he harvest in 3 days?
2. Mang Delfin harvested 2 637 sacks of rice in one hectare. About how many sacks of rice will
be harvested in 12 hectares?
3. Last year, a car manufacturer shipped 3 705 cards to each of his 14 dealers. About how
many cars were shipped in all?
4. There are 1 203 subdivisions in Cavite. Each subdivision has 85 houses. About how many
houses are there in Cavite?
5. Chris delivers 1 710 letters each month. About how many letters will Chris deliver in 9
months?
IV. Evaluation
A. Find the factors that when multiplied will give each estimated product on the left.
1) 12 000 6 x 1 561 5 x 1 842 5 x 3 423
2) 15 000 7 x 2 165 3 x 4 583 6 x 1 252
3) 24 000 4 x 5 983 3 x 9 754 5 x 8 392
4) 45 000 8 x 5 425 7 x 6 846 9 x 4 873
5) 200 000 42 x 4 868 49 x 4 869 34 x 4 863
B. Estimate each product.
1) 8 025 2) 3 676 3) 4 236 4) 7 632 5) 6 423
x 4 x 12 x 23 x 35 x 82
V. Assignment
A. Estimate the products.
1) 6 620
x 8
2) 7 676
x 28
3) 3 812
x 28
4) 8 905
x 34
5) 9 135
x 36

43
Multiplying Mentally 2-Digit Numbers with Products up to 100 without Regrouping
Cognitive: Multiply mentally 2-digit numbers by 1-digit number with product up to 100
without regrouping
Psychomotor: Solve mentally word problems involving multiplication
Affective: Work well with classmates
Skill: Multiplying mentally 2-digit numbers with product up to 100 without regrouping
Reference: BEC PELC I.D.1.1.4
Materials: flash cards, drawing, crayon
Value: Cooperation and independence
1. Drill
Game: Salute
Materials: set of number cards (1 digit-number)
1. Each group is composed of three members.
2. Two members will get each card and put it on their head (two members facing each other)
as the remaining member of the group says “salute”.
3. The one who says salute will give the product of the two numbers written on the cards.
4. The first to give the number on his/her head gets the point.
5. The team with the highest point wins.
2. Review
GAME: Color the Mailbox – 2 Groups
Teacher will call out 2 pupils, one from each group. She will flash combination of
numbers. Then the pupils will give the estimated product. The first one who can give the
correct answer will have the chance to color the first figure in the mailbox. The teacher
will repeat the process until the group had completed coloring the figures in the mailbox.
The first group to complete coloring the mailbox wins the game.
Flashcards:
1 212
x 2
326
x 5
4 213
x 12
3 214
x 25
1 432
x 32

44
Group I Group II
3. Motivation
Astronomers sometimes need calculators and computers in their study of space.
When do you need a calculator?
When is mental Math a faster way to find an answer?
Find these products as quickly as you can.
9 x 3 8 x 9 6 x 8 7 x 7
1. Presentation
Four boys helped their teacher return some workbooks to the library. Each boy
carried 12 workbooks. How many workbooks did they carry altogether?
Multiply 12 by 4. Do it mentally.
Think:
Multiply the ones by ones. Multiply the tens by ones. Give the product.
1 2 12
X 4 x 4
8 48 The product is 48.
So, 48 workbooks were carried by the boys.
Marlon picked avocados from their farm. He put them in 3 bags. If there are 13
avocados in each bag, how many avocados did Marlon pick?
Think:
1 3 13
X 3 x 3
9 39
1
4
3
5
7
8
6
2
1
4
3
5
7
8
6
2

45
b. The teacher will give more examples.
11 1 1 11
X 5 x 5 x 5
5 55
22 2 2 22
X 3 x 3 x 3
6 66
13 1 3 13
X 2 x 2 x 2
6 26
12 1 2 12
X 2 x 2 x 2
4 24
2. Guided Practice
a. Divide the class into four groups then assign a leader in each group.
 Each group will be given an activity sheet with word problems to be answered
mentally. The first group to finish shall post their work on the board. What should
you do when you work in groups?
 Will it give better results? Why?
ACTIVITY SHEET
Find the answer as fast as you can by multiplying mentally.
 There are 22 eggs in a tray. How many eggs are there in 4 trays?
 Tina has 3 pencil cases. If there are 12 pencils in each case, how many pencils
does she have?
 Fifteen pupils are seated in a row. If there are 4 rows in the classroom, how
many pupils are there?
 Thirty two guavas were placed in a basket. If there are 4 baskets, how many
guavas are there in all?
After 5 minutes, post your work on the board.
 Which group got the highest score?
 What does it mean?
b. Work in Pairs
Answer mentally.
13 12 20 23 13 12
x 3 x 4 x 1 x 2 x 2 x 3
c. Treasure Hunting
Have you experienced hunting treasures? Do you want to experience it? Well, trace the
path by passing the obstacles. Look for a card in the box and tape the answer in the
correct tree from the START. Follow the arrow until you reach the finish line.
55
66
26
24

46
3. Generalization
How do you multiply mentally 2-digit numbers by 1-digit number without regrouping?
To multiply mentally 2-digit numbers without regrouping
● Multiply the ones by ones.
● Multiply the tens by ones.
● Then give the product.
C. Application
What did the boy say when he met his teacher? Look at the hidden message by solving the
exercises. Find the letter in the code that matches each answer. Write the letter inside the
circles.
12 13 23 11 12 13 13 26 20 22 23
x 5 x 2 x 2 x 4 x 3 x 2 x 3 x 1 x 3 x 2 x 3
A – 36
B – 28
C – 59
D – 54
E – 69
F – 66
G – 53
H – 39
I – 60
J – 77
K – 61
L – 30
M – 44
N – 48
O – 34
P – 38
Q – 41
R – 42
S – 46
T – 26
U – 72 Z – 2
V – 94
W – 76
X – 89
Y – 57

47
IV. Evaluation
A. Listen to these multiplication sentences. Find their products without using paper and pencil.
Answer as fast as you can.
1) 34 2) 23 3) 44 4) 20 5) 13
x 2 x 3 x 2 x 3 x 3
B. Solve each problem.
1. Elvie planted 3 rows of sampaguita. Each row had 12 sampaguita plants. How many
sampaguita plants did she plant in all?
2. Francis planted 11 plots with eggplant seedlings. Each plot has 8 eggplant seedlings. How
many eggplant seedlings did he plant?
3. A jeepney driver charges each passenger 20 for a sight-seeing trip. How much will he
earn if he has 5 passengers?
4. A farmer prepares 11 plots for vegetables. How many seedlings will be needed if each plot is
planted with 9 seedlings?
5. You need 2 oranges to make a glass of orange juice. How many oranges do you need to
make 13 glasses of orange juice?
V. Assignment
A. Solve mentally.
1) 11 2) 12 3) 23 4) 24 5) 13
x 7 x 2 x 3 x 2 x 3
B. Cut out colorful pictures from magazines and paste them on 2
1
index card. Write a word problem
involving multiplication of 2-digit by 1-digit without regrouping. Answer each problem mentally.
Write the answer at the back of the card.
Solving Word Problems Involving Multiplication of Whole Numbers Including
Money
Cognitive: Solve word problems involving multiplication of whole numbers including money
Psychomotor: Write the solution to the problem correctly
Affective: Practice being thrifty
Skills: Solving word problems involving multiplication of whole numbers including
money
Giving solution to the problems correctly
Reference: BEC PELC I D 2.1
Materials: textbook, flash cards, roulette, chart, activity cards, pictures of plants
Value: Thrift

48
1. Drill: Basic multiplication facts using this double roulette.
2. Review:
Transform this problem into number sentence.
Ask: Who helped father in the garden?
What did they plant?
How many tomato seedlings did they plant in a row?
How many rows were planted with tomatoes?
What are you going to look for in this problem?
What are the given data?
What is the number sentence?
3. Motivation
Present this story problem.
Cheena saves 15.00 a day. How much will she save in 5 days?
Ask: How much does Cheena save in a day?
For how many days will Cheena save?
Who among you are like Cheena?
How much do you save in a day?
Is it good to save? Why?
1. Presentation
a. Group the children into four. Using the problem, let each group illustrate the problem.
Present this guide to the children in analyzing and illustrating the problem.
Problem:
What is asked for?
What are the given
information?
Draw/illustrate the
problem.
What is the process or
operation to be used?
What word/s help you
determine the
operation to use.
Write the number
sentence.
Jobette helped his father in the garden. They planted 63 tomato
seedlings in a row. How many tomato seedlings did they plant in 7 rows?

49
Let the pupils show their work and explain it. Involve the class in checking to see
whether what the group did is correct or not.
If you were to solve the problem, what process would you use?
Is there a word or words in the problem that tell what process or operation to use?
b. Present problems that used different keywords or word clues to determine the operation
to be used. Let them analyze.
1. A vendor buys 85 boxes of candies. Each box has 100 candies. How many candies
are there in all?
2. Nena bought 12 sets of baby dresses. Each set costs 185. How much did she pay
for all the dresses?
3. Mr. Santos is a postman. He has to deliver 178 letters in a day. How many letters will
he deliver in 25 days?
Problem 1 Problem 2 Problem 3
How many candies; in
all
How much; for all How many
What operations will you use if you see these words?
c. Assign the problems to three group. Let them solve the problem showing the correct
solution and operation.
Ex.
What is asked? Total number of candies
What data/facts are given?
85 boxes of candies
100 candies in each box
What is the operation/process to be used? Multiplication
85 x 100 = n
Solve the number sentence.
85 x 100 = 8 500
What is the complete answer?
There are 8 500 candies in all.
2. Guided Practice
Using the strategy – multiplication concentration.
Materials: 12 cards with multiplication problems
12 cards with their products
Procedures:
 Shuffle all 24 cards and place them face down in four rows of six cards each.
 Players take turns turning over two cards. If one shows a problem and the other card
shows its product, the player keeps those cards. If the cards do not match, the player
will read the problem in the cards and solve it showing the correct solution and
operations.
- The player with the most cards or who solve the most number of problems will be
declared winner.
3. Generalization
What did you do to solve/get the correct answer?
What are the steps that we should follow in solving problems.

50
C. Application
Read and understand each problem. Solve using Polya’s method.
1. Mang Berto picked 25 small baskets of atis. If each basket contained 45
atis, how many atis were there in all?
2. If each basket of atis costs 120.00, how much will Mang Berto
receive for 25 small basket of atis?
3. Mr. Lee sells mangoes by baskets. Each basket contains 26 mangoes.
How many mangoes does 34 baskets have?
4. Alma saves 25.00 a day in her piggy bank. How much money will she
save in twelve days?
5. Pet could read 75 pages of his favorite pocket book in a day. If he would
read for 12 days, how many pages would he finish?
IV. Evaluation
A. Read and solve the following.
1. Grandma gave her 6 grandsons 100 each last Christmas. How much did she give-away in
all?
2. Mr. Cruz deposits 2 500 every month. How much will be his deposit in 8 months?
3. A tray contains 30 eggs. How many eggs will there be in 115 trays?
4. A one-way plane ticket to Cebu costs 1 540. If there were 100 passengers with one-way
tickets, how much did all their tickets cost?
5. A dictionary costs 1 345.00 pesos each. A teacher needs a dictionary for her class. How
much will it costs her to buy the dictionary?
V. Assignment
Read and solve.
1. A bus can accommodate 72 passengers. How many passengers can be accommodated in 15
buses?
2. Three vendors sold small flags at 3.00 at Luneta during the Independence Day
celebration. These vendors were able to sell 320 flags. How much was the total sale of the three
vendors?
3. The Grade III class of 45 pupils used bottle caps for their project. Each child used 25 pieces
of bottle caps. How many bottle caps did the children use?
4. Simon spends 645 for his transportation per month. How much is his total transportation
expenses for 9 months?
5. Nancy can type 32 words per minute. How many words can she type in 400 minutes?
Solving 2- to 3-Step Word Problems involving Multiplication and any one of
Addition/Subtraction
Cognitive: Solve 2- to 3-step word problems involving multiplication and any one of
addition/subtraction
Psychomotor: Follow the steps in problem solving
Affective: Practice the habit of being honest

51
Skill: Solving 2-3 step word problems involving multiplication and any one of
addition/subtraction
Reference: BEC-PELC I.D.3.1
Materials: Textbooks, charts, flash cards, “Show Me Card”, real objects
Value: Honesty
1. Drill
The teacher flashes the flashcards and the children write their answers on their “Show Me”
board.
32 20 83 42 21
x2 x4 x3 x2 x2
2. Review
a. Present the problem written on Manila paper.
Laura made 56 sampaguita garlands. Each garlands has
13 pieces of sampaguita. How many pieces of sampaguita did she use in all?
Ask:
Who made sampaguita garlands?
How many sampaguita garlands did she make?
What are given?
What is the operation to be used to solve the problem?
Let the children solve the problem and show the answer in their “Show Me Board.”
b. Add in the review multiplication of numbers with decimal point (including money).
3. Motivation
Present the word problem.
Gally bought 5 shirts for 94.50 each. If he had 475.00,
how much change would he get?
Ask:
Who bought 5 shirts?
How much did each shirt cost?
How much money had he?
How much would he spend for his five shirts?
The salesgirl happened to give a change more than what Gally should receive? If you
were Gally, what would you do? Why?

52
Is it good to return the money that does not belong to you? Why?
1. Presentation
a. Using the problems in the motivation, ask the pupils to act out through “Play Store”
wherein pictures or objects like shirts, play money, etc are used. A pupil will go to the
store and buy shirts.
b. Present the problem using a diagram.
■ Read How many shirts were bought?
How much did a shirt cost?
How much money did Gally have?
■ Plan What is the hidden question?
the cost of 4 shirts
What is asked?
change Gally would get
What operation should be used?
475 - ( 94.50 x 5) = N
■ Solve
STEP 1 - Look for the cost of 5 shirts.
94.50 cost of 1 shirt
X 5 number of shirts bought
472.50 cost of 4 shirts
STEP 2
475.00 money of Gally
-472.50 costs of 4 shirts
2.50 change
■ Check Go over the solution.
Is it correct?
Is your answer reasonable?
Is it complete?
2. Guided Practice
Learning Barkadas
LBs will be given 5 two-step word problems to solve. The first LBs who will get the most
points wins.
Solve each problem.

53
1. Allan and Andy have one garden plot each, Allan has 4 rows of 12 pechays in each row.
Andy has 5 rows of 10 pechay in each row. How many pechay plants do they have
altogether?
2. Rafael is saving money for a new pair of pants worth 386.00. He has been saving
20.00 a day for ten days. How much more has he to save to buy new pants?
3. Mr. Rey went on a vacation. He bought 35 pasalubong items for his relatives and
friends. If each item costs 50.00 and he gave the seller 2 000, how much change
would he get?
4. In the canteen’s refrigerator, there were four trays of eggs. Each tray had 12 eggs. The
cook got 15 eggs. How many eggs were left in the refrigerator?
3. Generalization
What are the important points to consider in solving 2-step word problems?
In solving 2-step word problems, first answer the hidden question
then the given question. The operation inside the parenthesis
is done first.
C. Application
1. A “litson manok” vendor uses 2 sacks of charcoal a day. How much will be paid for charcoal
in 30 days, if each sack costs 80.00?
2. Cherry has 500.00. She bought 3 books at 150.00 each. How much did she pay for
the books? How much money was left ?
IV. Evaluation
Read and solve the following problems.
1. Joseph earned 35.00 each day for 5 days. He spent 55.00 for his snacks. How much
money was left?
2. Alyssa bought three kilograms of sugar at 26.00 per kilogram and a bottle of chocolate for
25.00. How much did she spend in all?
Using the table below, answer the questions that follow.
sandwich 25.00
pineapple juice 15.00
cookies 10.00
3. Alma bought 2 sandwiches and a can of pineapple juice. How much did she spend in all?
4. If Josie bought 3 cookies, how much change would she get from her 50.00?
5. If Marlon bought two packs of pineapple juice and gave the vendor 100.00, how much change
would he get?

54
V. Assignment
Solve these problems.
1. Fely packed bottles of honey in 8 boxes. Each box had 3 layers of 12 bottles. How many bottles
did Fely pack?
2. Jun bought 18 baskets of mabolo. Each basket costs 90.00. How much change would he get
from his 2,000.00?

Okay, let me summarize:- Changing the order of factors in multiplication does not change the product. - 4 x 3 is the same as 3 x 4. Both give an answer of 12.- Grouping or regrouping objects in different ways but with the same total gives the same result

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Similaire à Okay, let me summarize:- Changing the order of factors in multiplication does not change the product. - 4 x 3 is the same as 3 x 4. Both give an answer of 12.- Grouping or regrouping objects in different ways but with the same total gives the same result

Similaire à Okay, let me summarize:- Changing the order of factors in multiplication does not change the product. - 4 x 3 is the same as 3 x 4. Both give an answer of 12.- Grouping or regrouping objects in different ways but with the same total gives the same result (20)

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Okay, let me summarize:- Changing the order of factors in multiplication does not change the product. - 4 x 3 is the same as 3 x 4. Both give an answer of 12.- Grouping or regrouping objects in different ways but with the same total gives the same result