1. 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
Subtraction
INSTRUCTIONAL MATERIALS COUNCIL SECRETARIAT, 2011
3. iii
TABLE OF CONTENTS
Introduction ..................................................................................................................................iv
Matrix ........................................................................................................................................v
I. WHOLE NUMBERS
A. Subtraction
Subtracting Numbers without Regrouping
3-Digit Numbers from 4- to 5-Digit Numbers .................................................... 1
4-Digit Numbers from 4- to 5-Digit Numbers .................................................... 7
Subtracting Numbers with Regrouping in the:
Tens Place ........................................................................................................ 15
Hundreds Place ................................................................................................. 21
Thousands Place .............................................................................................. 27
Ten Thousands Place ....................................................................................... 32
Subtracting Numbers with Zero Difficulty ....................................................................... 38
Estimating Differences ................................................................................................... 45
Subtracting Mentally without Regrouping ...................................................................... 49
Solving Word Problems .................................................................................................. 55
Solving Word Problems Mentally ................................................................................... 61
Solving 2-Step Word Problems involving Addition and Subtraction
including Money ................................................................................................ 65
4. 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.
5. v
MATRIX IN ELEMENTARY MATHEMATICS
Grade III
COMPETENCIES VALUES INTEGRATED STRATEGIES USED
MULTIPLE INTELLIGENCES
TECHNIQUES
With HOTS
I. Whole Numbers
A. Subtraction of Whole Numbers
1. Comprehension of Subtraction
1.1 Subtract 3 to 4 digit numbers from
4 to 5 digit numbers with minuends
up to 100 000 without and with
regrouping and with zero difficulty
1.1.1 Subtract 3 digit numbers
from 4 to 5 digit numbers with
minuends up to100 000 without
regrouping
Cooperation Modeling
Simplifying the problem
Diagrams and chart (Spatial)
Cooperative groups
(Interpersonal)
1.1.2 Subtract 4 digit number from
4 to 5 digit numbers with minuends
up to 100 000 without regrouping
Cooperation Draw pictures Simplifying
the problem
Puzzle (Logical mathematics)
Diagrams and chart (Spatial)
Cooperative
groups(Interpersonal
1.1.3 Subtract 3 to 4 digit numbers
from 4 to 5 digit numbers with
regrouping
1.1.3.1 in the tens place Helpfulness and following
rules
Draw pictures Body movements (Bodily
kinesthetic)
Manipulative (Bodily
kinesthetic)
Diagram (Spatial)
1.1.3.2 in the hundreds place Cooperation Simplifying the problem Song (Musical) Manipulative
(Bodily kinesthetic)
1.1.3.3 in the thousands place Helpfulness Draw pictures Simplifying
the problem
Cooperative
groups(Interpersonal) Puzzle
(Logical mathematics)
1.1.3.4 in the ten thousand place Cooperation Draw pictures Simplifying
the problem
Cooperative
groups(Interpersonal)
Manipulative (Bodily
kinesthetic)
1.1.3.5 with zero difficulty in either
tens or hundreds place
Helpfulness Polya's steps in problem
solving
Acting out the problems
Body movements (Bodily
kinesthetic)
6. vi
1.1.4 Estimate the difference of two
numbers with 3 to 4 digits
Following simple
directions
Simplifying the problem Puzzle (Logical mathematics)
1.2 Subtracts mentally 2 digit numbers
with minuends up to 99 without
regrouping
Speed and accuracy Simplifying the problem Number Puzzle (Logical
mathematics)
Illustrations (Spatial)
Body movements (Bodily
kinesthetic)
2. Application of Subtraction
2.1 Solve 1 step word problems involving
subtraction of whole numbers
including money with minuends up
to100 000 without and with
regrouping following the steps in
problem solving
Cooperation/Helpfulness Drawing pictures/figures
Polya's steps in problem
solving
Song (Musical)
Body movements (Bodily
kinesthetic)
2.2 Solve mentally 1 step word problems
involving subtraction without
regrouping
Speed and accuracy Draw the problem Body movements (Bodily
kinesthetic)
Illustrations (Spatial)
1. Application of Addition and Subtraction
3.1 Solve 2 step word problems involving
addition and subtraction of whole
numbers including money following the
steps in problem solving
Active participation Polya's steps in problem
solving
Cooperative groups
(Interpersonal)
7. 1
Subtracting Numbers without Regrouping
I. Learning Objectives
Cognitive: Subtract 3-digit numbers from 4- to 5-digit numbers with minuends up to 99
999 without regrouping.
Psychomotor: Write correctly the numeral in vertical column according to their place value.
Affective: Work cooperatively during the class and group activities
II. Learning Content
Skill: Subtracting numbers without regrouping
Reference: BEC PELC I.C.1.1.1
Materials: 0-9 number cards, place value pocket chart, flash cards of basic subtraction
Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill: (flashcards of basic subtraction)
2. Review – Game
Divide the children into 5 groups. Distribute place value pocket charts and number cards.
The teacher will give instructions on what number they will form. The group who answers first
will have the point and the group with the highest points will be the winner.
Tell the pupils to do the following:
Ask: Form the largest 3-digit number without repetition
Form the smallest 3-digit number without repetition
Form the largest 4-digit number without repetition
Form the smallest 4-digit number without repetition.
Using the digits 4, 7, 3 and 0, what is the largest number you can form? the smallest number
you can form?
3. Motivation:
Who among you has a bank account? What are you doing with your savings? What
happens to your money if you deposit and withdraw? Is it okay to withdraw money from your
savings account? Why?
8
- 5
3
- 2
9
- 7
6
- 2
5
- 3
7
- 4
2
- 1
4
- 0
10
- 6
1
- 1
8. 2
B. Developmental Activities
Present the table:
Number of Trees Planted in Barangay Malinis
Trees Number of Trees
Acacia 3 875
Narra 2 554
Molave 432
How many more acacia trees are there than molave trees?
1. Presentation
a. Compare the number of acacia trees to the number of molave trees. Which has more
trees, acacia or molave? How many trees more?
What process are we going to use to find the answer?
What is the number sentence?
Ask a pupil to write the number sentence on the board.
(3 875 – 432 = N)
Which is the minuend? the subtrahend?
b. Let the pupils work in pairs.
Ask them to represent the minuend through their cubes, flats, longs and ones.
cube long flat
1 flat = (100 cubes) 1 block = (1000 cubes)
Activity 1 – Using Manipulatives – Working by pairs
9. 3
Let us solve the problem by using manipulative. Let us do it by pairs.
How many acacia trees are there? What about molave trees?
How many more acacia trees are there than molave trees?
Ask: How will you represent 3 875 using the cubes, flats, longs and ones?
How many cubes, flats, longs and ones will you use?
(3 blocks, 8 flats, 7 longs and 5 cubes)
Thousands Hundreds Tens Ones
What about our subtrahend, 432? How many flats, longs and cubes will there be? (4 flats,
3 longs and 2 cubes)
Since 432 is the number to be taken away, let’s get it from 3 875. (Let the pupil get 4
flats, 3 longs and 2 cubes from 3 blocks, 8 flats, 7 longs and 5 cubes.)
How many blocks, flats, longs and cubes were left?
(3 blocks, 4 flats, 4 longs and 5 cubes)
How will you read blocks, flats, longs and ones in numeral?
How will you write it in figure? 3 443
So, what is 3 875 – 432? 3 443
Activity 2 – Using the expanded form
Here is another way of subtracting numbers by Expanded Form.
3 875 3 000 + 800 + 70 + 5
- 432 400 + 30 + 2
3 000 + 400 + 40 + 3 = 3 443
What is the difference? 3 443
X X
X
XX
X
X
X
X
10. 4
Activity 3 – Short Cut Method
Let us represent the same number through the place value chart.
How will you write the numerals in the place value chart.
Short Form:
3 875 minuend
- 432 subtrahend
N
Thousands Hundreds Tens Ones
3 8 7 5
- 4 3 2
3 4 4 3
1. Subtract the ones. (5 – 2 = 3)
2. Subtract the tens. (7 tens – 3 tens = 4 tens)
3. Subtract the hundreds. (8 hundreds – 4 hundreds = 4 hundreds)
4. Subtract the thousands. (3 thousands – 0 thousands = 3 thousands)
So, 3 875 – 432 is 3 443.
c. Give again another problem. Group the class into three.
Let the 1
st
group solve it by manipulative (blocks, flats, long and cubes);
the 2
nd
group by expanded form (value form) and,
the 3
rd
group by short-cut form (short form-place value chart).
Expected Answer:
1
st
Group: 4 blocks, 1 flat, 1 long and 3 cubes = 4,113
2
nd
Group: 4 356 4 000 + 300 + 50 + 6
- 243 200 + 40 + 3
4 000 + 100 + 10 + 3 = 4 113
3
rd
Group: Th H T O
4 3 5 6
– 2 4 3
4 1 1 3
Did you get the same difference?
2. Guided Practice
a. Group Work – (4 members per group)
Let the pupils group themselves with 4 members each. Ask them to answer the following
numbers using only their blocks, flats, long and cubes. Then they will put their answers in
the place value pocket chart with the use of their number cards.
What is 4 356 minus 243?
Number Cards
0 1 2 3 4
5 6 7 8 9
Place Value Pocket Chart
Th H T O
11. 5
1) 3 674 2) 4 356 3) 5 243 4) 6 532 5) 8 547
- 532 - 143 - 112 - 321 - 217
Did you get all the answers right? Why?
b. Work by pairs
Use the expanded form method in solving the number problem. You will work now in
pairs.
1) 19 236 2) 24 379 3) 17 874 4) 26 728 5) 36 745
- 220 - 234 - 762 - 312 - 233
Did you get all the answers right? Why?
c. Individual Work
Let us use the short-cut method.
1) 7 419 2) 7 923 3) 8 465 4) 24 936 5) 35 985
- 306 - 412 - 254 - 224 - 865
Did you get all the answers correctly?
Which of the three methods do you prefer or like? Why?
Why do you think you got the right answer easily?
Which group got all correct answers first?
Why do you think they got it easily?
What did the group do to make their work easy?
3. Generalization:
How do we subtract numbers without regrouping?
How do we write the numeral when subtracting?
Where do we start subtracting?
Why do you think subtracting is very important?
Remember:
In subtracting 3-digit numbers from 4-digit numbers, the digits must be aligned according
to their place value. Then, subtract the ones first, then the tens, the hundreds and the
thousands.
C. Application
Individual work (Use of show-me-board, chalk and flashcards)
Subtract the numbers I’m going to show you. Then write the difference on your show-me-
board.
1) 8 537 2) 3 489 3) 7 642
- 315 - 158 - 132
(Note to the teacher: Make the materials
ready before the activity)
12. 6
4) 5 783 5) 9 857 6) 16 476
- 241 - 315 - 324
7) 22 879 8) 34 364 9) 21 976
- 524 - 134 - 235
10) 19 752
- 421
IV. Evaluation
A. Work by pairs.
Find the missing numbers.
1) 8 362 2) 2 514 3) 4 _ _2 4) 3 2_5
- _50 - 1_ _ - 261 - _3_
8 21_ 2 _11 4 63_ 3 063
5) 7 384 6) 12 _ _ _ 7) 4 _ _2 8) 3 2_5
- _ _ _ - 315 - 261 -_3_
7 120 2 _11 4 63_ 3 063
9) 8 362 10) 2 514
- _50 - 1_ _
8 21_ 2 _11
B. Individual Work
Find what number is being asked.
1. What is the difference between 8 753 and 213?
2. What number is 320 less than 1 975?
3. Subtract 514 from 2 758.
4. What is 6 788 less 351?
5. What number is 502 less than 4 735?
6. Take away 485 from 13 596.
7. What is 24 359 minus 134?
8. What is the difference between 523 and 21 785?
V. Assignment
Do as indicated.
1. What is the difference between the largest 4-digit number without repetition and the smallest 3-
digit number without repetition?
2. What is the difference between the largest 4-digit number with repetition and the smallest 3-digit
number without repetition?
3. What is the difference between the largest 4-digit number with repetition and the largest 3-digit
number with repetition?
13. 7
Subtracting Numbers without Regrouping
I. Learning Objectives
Cognitive: Subtract 4-digit numbers from 4-5 digit numbers with minuends up to 100
000 without regrouping.
Psychomotor: Write correctly the numeral in vertical column according to their place value.
Affective: Work cooperatively during the class and group activities
II. Learning Content
Skill: Subtracting numbers without regrouping
Reference: BEC PELC I.C.1.1.2
Materials: maze, play money (money kit)
Value: Cooperation, Helpfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill – Maze
Procedure:
a. The teacher will post the maze on the board. There will be 2 teams with 10 members
each.
b. Each member will unblock the path on the maze by answering the subtraction sentence
written inside the box.
c. Each member will answer one at a time. A member goes to the board only upon the
return of the member before him/her.
d. The first group to finish and unblock the path wins the game.
(Note to the teacher: Each box should have basic subtraction fact written inside)
14. 8
2. Review
a. Find the difference
7 436 3 853 8 789 2 432 5 859
- 215 - 701 - 237 - 102 - 325
b. Checking of Assignment
3. Motivation: Present a problem opener.
The Boy and Girl Scouts Drama Group presented a play. On the first day, they earned
4,865. On the second day, they earned 5,985. How much more did they earn on the
second day than on the first day?
B. Developmental Activities
1. Presentation
a. Let us analyze and solve the problem.
- Who presented the play in the problem?
(The Boy and Girl Scout Drama Group)
- How much did they earn on the 1
st
day? 2
nd
day?
(1
st
day- 4,865; 2
nd
day- 5,985)
- What operation are we going to use to solve the problem? (subtraction)
- What will be our number sentence? ( 5,985 – 4,865 = N)
- How much more did they earn on the second day than on the first day?
( 1,120)
15. 9
Activity 1. Using Play Money/Drawing Pictures – Work in pairs
Ask the pupils to work in pairs. Let them get their money kit and represent the money
earned on the first day and on the second day.
1
st
Day 2
nd
Day
4,865 5,985
1,000
1,000
1,000
1,000
500
100
100
100
50
10
5
1,000
1,000
1,000
1,000
1,000
500
100
100
100
100
50
10 10
10 5
16. 10
From the money kit can you tell how much more they earned on the second day than on
the 1
st
day? Why/Why not?
Let them pair the money earned on the 1
st
day to the money earned on the second day.
1
st
Day 2
nd
Day
4,865 5,985
Do all the money earned on the first day have pairs on the 2
nd
day?
1,000
1,000
1,000
1,000
500
100
100
100
50
10
5
1,000
1,000
1,000
1,000
5
1,000
500
100
100
100
100
50
10
1
0
1
0
has no pair
has no pair
has no pair
has no pair
17. 11
What about the other way around? Do all the money earned on the 2
nd
day have pairs on
the first day?
How much money do not have pairs?
1,000 + 100 + 10 + 10 = 1,120
Therefore, how much more money did they earn on the 2
nd
day? 1,120
Does our answer make sense?
Activity 2 – Expanded Form:
Let’s recall the problem, “How much more did they earn on the second day than on the
first day?”
What process are we going to use? Subtraction
Why did you say subtraction? Let’s write the number sentence.
(Ask the pupil to write the number sentence on their drill board and show it to the
teacher.)
Ask the pupils to write the given numerals in expanded form.
5 985 5 000 + 900 + 80 + 5
- 4 865 4 000 + 800 + 60 + 5
1 000 + 100 + 20 + 0 = 1 120
partial differences
Subtract each number vertically, then add the partial differences horizontally.
Activity 3 – Short Form:
Let us use the short cut method. Place the minuend and subtrahend in the place value
chart.
Short Form
5 985
- 4 865
1 120
1
st
– Subtract the ones (5 – 5 = 0)
2
nd
– Subtract the tens (8 tens – 6 tens = 2 tens)
3
rd
– Subtract the hundreds (9 hundreds – 8 hundreds = 1 hundreds)
4
th
– Subtract the thousands (5 thousands – 4 thousands = 1 thousands)
Did we get the same answer from the 3 activities?
a. Group Work
Group 1 will answer no. 1, Group 2, no. 2 and Group 3, no. 3
Group 1 will use the drawing method either by one to one pairing or crossing-out just like
what we did yesterday.
Use _______ for 1000, for 100, for 10 and __ for 1
Group 2 will use the expanded form method.
Group 3 will use the short-cut method
1. What is the difference between 2 532 and 8 975?
2. Subtract 3 526 from 64 729
3. From 78 324, take away 5 302
Expected Answers:
4
th
3
rd
2
nd
1
st
Th H T O
5 9 8 5
4 8 6 5
1 1 2 0
18. 12
1.
Drawing (Pairing) Drawing (crossing-out)
8975
2 532 8 975
2.
64 729 60 000 + 4 000 + 700 + 20 + 9
- 3 526 - 3 000 + 500 + 20 + 6
= 60 000 + 1 000 + 200 + 0 + 3
= 61 203
3.
78 324 Ten Thousands Hundreds Tens Ones
- 5 302 Thousands
7 8 3 2 4
- 5 3 0 2
7 3 0 2 2
Which group finished first?
Why do you think they have done the activity easily?
What did each member do to make their work easy?
no pair
How many
have no pairs?
1 000
1 000
1 000
1 000
1 000
1 000
100
100
100
100
100
10
10
10
10
1
6 000
400
40
3
6 443
Take away 2 532
How many were left?
1 000 + 1 000 + 1 000 + 1 000
+ 1 000 + 1 000 + 100 + 100 +
100 + 100 + 10 + 10 + 10 + 10
+ 1 + 1 + 1 = 6 443
19. 13
2. Guided Practice
a. Work in pairs
Subtract the following. Use the short-cut method
1) 7 635 2) 2 304 3) 6 287 4) 6 789 5) 4 236
- 3 413 - 1 203 - 6 152 - 3 436 - 2 225
6) 98 325 7) 88 766 8) 83 293 9) 72 844 10)54 678
- 3 103 - 2 513 - 1 021 - 1 342 - 1 325
a. Group Work – (with 3 members)
Number Puzzle – (Provide each group with number puzzle to work on.)
Subtract the following numbers and write your answer on the number puzzle. You have 5
minutes to complete it.
a b c
d e
f
g h
i j
k
Across
a. 6 898 – 4 353
d. 1 215 less than 4 885
f. 6 548 minus 1 240
g. 5 487 less 4 035
i. 1 270 – 1 230
j. What is the difference between 4 562 and 4 510?
k. Subtract 1 231 from 2 477
Down
b. What number is 1 000 less than 6 755?
c. From 5 244, subtract 1 212
d. 5 346 – 2 132
e. 3 866 minus 2 014
h. The difference between 2 726 and 1 325
Did you get the answers right?
Did your team work together to finish the puzzle fast?
How did you subtract easily? Which method did you use?
3. Generalization
How do we subtract 4-digit numbers from 4 to 5-digit numbers?
Where do we start subtracting?
Do you think there is a technique in doing this? How?
20. 14
Remember
In subtracting 4-digit numbers, the numbers must be aligned properly according
to their place value. Then start subtracting from ones first, then tens,
hundreds and thousands.
C. Application
a. Find the missing numbers
1) 4 921_ 2) 69 4_ _ 3) 32 9_8
- _ 112 - 3 _12 - 2 _0_
45 _ _1 6_ 220 3_ 135
b. Do as indicated
1. What number is 2 541 less than 87 876?
2. Subtract 3 487 from 56 899.
IV. Evaluation
(To be done individually) Paper and pencil
Write in column then subtract
1) 4 732 – 2 301 = N
3) 7 857 – 3 412 = N
5) 8 576 – 4 253 = N
7) 5 436 – 1 034 = N
9) 6 258 – 2 153 = N
2) 73 259 – 1 143 = N
4) 62 987 – 2 543 = N
6) 25 737 – 3 705 = N
8) 48 635 – 2 125 = N
10) 75 557 – 5 423 = N
V. Assignment
Write in expanded form then subtract.
1) 59 875 = _____ + _____ + _____ + _____ + _____
- 4 362 = _____ + _____ + _____ + _____ + _____
2) 37 589 = _____ + _____ + _____ + _____ + _____
- 3 251 = _____ + _____ + _____ + _____ + _____
3) 87 639 = _____ + _____ + _____ + _____ + _____
- 3 318 = _____ + _____ + _____ + _____ + _____
21. 15
Subtracting Numbers with Regrouping in the Tens Place
I. Learning Objectives
Cognitive: Subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the
tens place.
State the rules in subtracting numbers with regrouping
Psychomotor: Follow the rules in subtracting numbers with regrouping in the tens place and use
the body-number coding (kinesthetic math) properly.
Affective: Follow simple rules correctly. Practice helpfulness at all times.
II. Learning Content
Skill: Subtracting numbers with regrouping in the tens place
Reference: BEC PELC I-C 1.1.3.1
Materials: chart of the body number coding, problem chart, flash cards of basic subtraction,
Popsicle sticks or straws
Value: Following simple rules correctly/Helpfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill – Body Number Coding
Let the pupils do the coding of numbers through their hands and body. (Write the code on
a manila paper)
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 arms bend forward close to the body
- Hands on waist
- Right hand on the chest
- Bend forward to pick something
- Stand straight
- Arms obliquely upward
- Do McDonald sign
The teacher will show some flashcards about basic subtraction and the pupils will give
the answer through their body action without giving the answer.
Example: 7 – 3 = 4 (They have to act the code for number 4 which is hands on waist)
2. Motivation – Present a problem opener.
Mang Pedro brought 2 752 eggs to sell in the public market. Danny, his eldest son,
helped him sell 1 345 eggs. How many eggs were left?
8
- 7
5
- 1
3
- 0
5
- 5
6
- 4
10
- 5
9
- 2
8
- 2
9
- 1
10
- 1
22. 16
B. Developmental Activities
1. Presentation
a. What do you think is the work of Mang Pedro?
What did he sell in the public market?
Who is his eldest son?
What kind of son is he? Are you also helpful? In what ways are you helpful?
How many eggs did Mang Pedro bring?
How many eggs were sold by his eldest son?
What is asked in the problem?
How are we going to solve it? What process are we going to use?
What will be our number sentence?
b. Let a pupil write the number sentence on the board.
2 752 – 1 345 = N
(Pre-Activities)
Note to the Teacher:
(The pupils should have their Math Kit where they can place their Popsicle
sticks/straws, rubber bands, counters, etc. A place value containers should always be
inside their classroom. If possible, the place value containers should be made as a
project of the pupil.)
Place Value Containers
Guide the pupils to bundle 10 straws which should be placed in the tens place of the
place value container.
Let them bundle 10 groups of 10 straws each which will be placed in the hundreds
place of the place value container.
Lastly, let them bundle 10 groups of 100 straws to be placed in the thousands place
of the place value container.
Let them see and observe how many is 1 ten, 1 hundred and 1 thousand.
Activity 1 – Using Manipulatives and Drawings/Diagram
Tell the pupils to work in groups with 5 members each.
Let them represent the number of eggs brought by Mang Pedro through their
straws/Popsicle sticks and place value containers.
Ask: How will you represent 2 752?
2 bundles of 1 000 straws
7 bundles of 100 straws
5 bundles of 10 straws
2 pieces of straws
23. 17
Thousands Hundreds Tens Ones
A
B
C
1 4 0 7
So, 2 752 therefore, 1 407 eggs were left.
- 1 345
1 407
Now, let us take away the number of eggs sold by Danny.
How many eggs were sold by Danny? 1 345 eggs
How will you represent 1 345 in bundled straws?
1 bundle of 1 000 straws, 3 bundles of 100 straws each, 4 bundles of 10 straws
each and 5 pieces of straws)
Ask the pupils to take away 1 345 from 2 752.
Did you get all the straws in each place value containers?
In what place value container did you find it difficult to get the straws?
Can you get 5 straws from 2 straws? You cannot subtract 5 from 2;
Therefore, we will regroup 1 group of ten straws from the tens cup and place it in the
ones cup.
But we cannot still get 5 straws because the straws are still in bundle.
So, what should we do? (Unbundle the tens straws)
So, how many straws are there in the ones container now? 12
How many group of tens straws were left at the tens container?
Can you get 4 bundles of 10 straws from it? What about 3 bundles of 100 straws
each, can you get it from the hundreds container?
What about a bundle of 1 000 straws, can you get it from the thousands container?
So, how many straws were left in each container?
How will you read it in numeral?
So, how many eggs were left? Does our answer make sense?
24. 18
Activity 2 – Using Expanded Form
1) Let us try solving the same problem using the Expanded Form. Let us see if we can
get the same difference.
1. Subtract the ones.
2 752 2 000 + 700 + 50 + 2
- 1 345 1 000 + 300 + 40 + 5
2. Regroup the tens.
2 000 + 700 + (50 – 10) + (10 + 2)
- 1 000 + 300 + 40 + 5 _
2 000 + 700 + 40 + 12
- 1 000 + 300 + 40 + 5
7
3. Subtract the tens.
2 000 + 700 + 40 + 12
- 1 000 + 300 + 40 + 5
0 + 7
4. Subtract the hundreds.
2 000 + 700 + 40 + 12
- 1 000 + 300 + 40 + 5
400 + 0 + 7
5. Subtract the thousands.
2 000 + 700 + 40 + 12
- 1 000 + 300 + 40 + 5
1 000 + 400 + 0 + 7 = 1407
Did we get the same difference? 1407 eggs were left.
2) Let us try using the short cut method or the short form.
Th H T O
2 7
4
5
1
2
- 1 3 4 5
1 4 0 7
1. Subtract the ones. But since you cannot subtract 5 ones from
2 ones; we will regroup the tens place.
5 tens becomes 4 tens and 1 ten; then 1 ten becomes 10 ones
then, we will rename the ones place.
10 ones + 2 ones equals 12 ones
Then subtract the ones place. (12 ones – 5 ones = 7 ones)
2. Subtract the tens. (4 tens – 4 tens = 0 ten)
3. Subtract the hundreds. (7 hundreds – 3 hundreds = 4 hundreds)
4. Subtract the thousands. (2 thousands – 1 thousand = 1 thousand)
Did we get the same difference? 1 407 eggs were left.
You cannot subtract 5
from 2; therefore,
regroup one 10 from the
tens column and add it
to 2.
Subtract 5 from 12
Subtract 40 from 40
Subtract 300 from 700
Subtract 1000 from
2000. Add all the
partial differences.
2 752
- 1 345
N
2 7
4
5
12
2
- 1 3 4 5
1 4 0 7
25. 19
2. Guided Practice
Group work with 5 members each
a. Solve by using the place value containers and straws/Popsicle sticks.
1) 1 343 – 236 = N
2) 2 491 – 1 358 = N
3) 2 635 – 1 217 = N
Work in Triads
b. Solve the following by Expanded Form Method.
1) 3 942 – 719 = N
2) 7 363 – 247 = N
3) 6 475 – 2 136 = N
4) 32 635 – 2 217 = N
5) 25 136 – 4 018 = N
Work in Dyads
b. Subtract the following using the Short Form Method.
1) 5 785 – 349 = N 2) 15 324 – 2 106 = N
3) 3 642 – 235 = N 4) 26 483 – 3 248 = N
5) 4 384 – 248 = N 6) 56 587 – 2 359 = N
7) 8 252 – 4 036 = N 8) 43 462 – 1 357 = N
9) 7 461 – 3 237 = N 10) 34 677 – 2 338 = N
Were you able to finish all the exercises? Why?
How did each of your member work to come up with the correct answer?
Did you help each other during the activities?
Which method do you like best? Why?
3. Generalization:
How do we subtract numbers with regrouping in the tens place?
To subtract whole numbers, start with the ones column. If the digit in the minuend is
smaller than the digit in the subtrahend, regroup from the next column to the left. To check
the difference, add it to the subtrahend to get the minuend.
C. Application
a. Work in Dyads – (Use flash cards and show me board.)
The teacher will flash some cards and the pupils will give the answer using their show me
board.
1) 2) 3) 4) 5)
3 521
- 417
8 463
- 237
7 482
- 158
5 366
- 139
6 834
- 318
26. 20
IV. Evaluation
A. Group work (with 4 members each) – Body Number Coding and flash cards
Form groups with 4 members each. Let the pupils answer on a piece of paper the exercise on the
flash card. They will give the answer orally using the body-number coding. One pupil will act out
the ones digit, the other one on the tens digit, the next one will act out the hundreds digit and the
4
th
member will act out the thousands digit.
1) 2) 3) 4) 5)
B. Individual Work – (Paper and Pencil)
Subtract the following.
1) 67 893 2) 25 876 3) 37 735 4) 49 852 5) 57 651
- 5 376 - 2 138 - 1 317 - 5 214 - 3 425
V. Assignment
A. Find the missing minuend, subtrahend or difference.
1) 3 462 2) 5 463 3) _____ 4) 8 364 5) _____
- 345 - _____ - 134 - _____ - 418
_____ 5 227 7 228 8 227 6 124
6) _____ 7) 9 594 8) _____ 9) 5 866 10) 3 425
- 3 158 - _____ - 2 136 - 1 437 - 1 207
3 224 6 358 2 559 _____ _____
B. Write the missing numerals.
1) 2) 3)
8 5
- 3 2 6
8 4 0
4 7 5 2
- 2
4 4 7
6 7 3
- 2 3 1
6 5 3 9
4) 5)
3 4 5
- 1 7 6
3 3 1 5
7 5 8 2
- 3 1 2
7 3 5
7 853
-3 614
2 746
-1 327
3 745
-1 316
4 853
-1 315
8 597
-4 319
27. 21
Subtracting Numbers with Regrouping in the Hundreds Place
I. Learning Objectives
Cognitive: Subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the
hundreds place
Psychomotor: State the rule in subtracting whole number with regrouping
Affective: Work cooperatively with others in finding the difference of the given number with
accuracy
II. Learning Content
Skill: Subtracting numbers with regrouping in the hundreds place
Reference: BEC PELC I.C.1.1.3.2
Materials: flash cards of subtraction (2-digit by 1), Math kit (cubes, flats, longs and ones),
Show Me Board, place value pocket chart, chart of exercises
Value: Cooperation
III. Learning Experiences
A. Preparatory Activities
1. Drill – Mental Computation
2. Review
Checking of assignment.
3. Motivation
Song: Math Time
(Tune: It’s a Small World)
Chorus: Oh, it’s Math time after all (3x)
Come together and come all.
There is just one class
We enjoy so much
Where our mind think hard
And compute a lot
Though the drills are so fast
And the problem so tough
We enjoy our class in Math
(Repeat Chorus)
Do you really enjoy our Math class? Why?
What are the things we do in Math?
12
- 5
17
- 8
15
- 6
11
- 7
13
- 4
19
- 9
14
- 7
16
- 9
18
- 5
15
- 8
28. 22
B. Developmental Activities
1. Presentation
a. Let us read and analyze this number sentence.
Subtract 275 from 1 359 = N
b. Ask the pupils which is the minuend and the subtrahend in the number sentence. Let
them write the numerals in column and analyze it.
1 359
- 275
Ask:
Can we subtract the ones place?
What is the answer?
What about the tens place?
Can we subtract 7 from 5?
1. Activity 1 – Manipulatives (cubes, longs, flats and blocks)
c. Now, ask the pupils to get their Math kit and get their cubes, longs, flats and blocks. Let
them do it by pairs. Let them represent first the minuend. Ask: How many blocks, flats,
longs and cubes can make 1 359?
d. Ask the pupils to take away 275 from the blocks, flats, longs and cubes.
Ask: How many flats, longs and cubes will make 275?
Do I have enough cubes to take away 5 from it?
How many cubes will be left?
What about the longs, do I have enough to take away 7 from it?
What shall we do then?
= 1,359
(blocks) (flats) (longs) (cubes)
29. 23
Thousands Hundreds Tens Ones
X X
X X X
X X
X X X
30. 24
1 0 8 4
So, we will regroup 1 flat and rename it as longs.
How many longs will there be in 1 flat? (10)
So, how many longs do we have now? Can we not get 7 longs from it?
How many longs were left?
e. Now, ask the pupils to focus on flats. Let them take away 2 flats from it. Ask how many
flats remain in the flats column. Then, ask if they are going to take away anything from
the blocks column and then ask why. Let the pupils express their answers.
f. Let them now count the number of blocks, flats, longs and cubes that were left in each
column. How do you read the numeral?
Let’s solve the same problem using the expanded form method.
2. Activity 2 – Expanded Form Method
1 359
- 275
1 000 + 300 + 50 + 9
- 200 + 70 + 5
a. Subtract 5 from 9.
b. Subtract 70 from 50. Is it
possible? (No)
? + 4
Rename 1 000 + 200 + 100 + 50 + 9 c. Rename 300 into 200 and 100.
Regroup 100 with 50.
Regroup 1 000 + 200 + 150 + 9
- 200 + 70 + 5
d. Subtract 70 from 150.
80 + 4
1 000 + 200 + 150 + 9
- 200 + 70 + 5
e. Then, subtract 200 from 200
and bring down 1 000.
1 000 + 0 + 80 + 4
= 1 084 f. Lastly, add the partial
differences.
Let’s solve it again using the short form. Write the numeral in the place value chart.
31. 25
Th H T O 1) Subtract the ones (9 – 5 = 4)
1 3 5 9
- 2 7 5 2) Subtract the tens. Can you take away 7 tens from 5
tens? Why not?
4
Th H T O Regroup 3 hundreds into 2 hundreds and 10 tens. Then
rename the tens. How many tens are there now? Can we
subtract 7 tens from it? Then subtract. How many
hundreds were left?
1 2(3) 15(5) 9
- 2 7 5
1 0 8 4
3) Subtract the hundreds.
(2 hundreds – 2 hundreds = 0 hundreds)
4) Then bring down the digit in the thousands place
because you will not subtract anything from it.
Did we get the same difference?
Which of the three methods do you like best? Why?
2. Guided Practice
a. Group Work
1. Divide the class into 3 groups and the members of the groups will work in pairs.
2. The first group will use the manipulative method to find the difference.
3. The 2
nd
group will use the expanded method.
4. The 3
rd
group will use the short form method.
5. Then they are going to report to the class the answer they got.
Write in column then subtract.
Group 1 Group 2 Group 3
3 735 – 562 8 628 – 4 253 56 816 – 3 745
b. Work in Pairs
The teacher will show some numbers to be subtracted. The pupils will write their answer
on their Show Me Board. They will use the short form method.
8 237
- 162
5 648
- 353
7 525
- 281
4 419
- 345
9 456 5 645 8 266 7 538
- 7 271 - 2 183 - 1 173 - 3 252
25 325 15 815 32 546 47 679
- 4 151 - 2 732 - 1 476 - 2 385
1. Which pairs got the most number of correct answers?
2. What do you think they did to get all the correct answers?
32. 26
3. Did they work cooperatively?
4. Did they get the correct answer fast by working in pairs?
Do you think regrouping is important? Why? Why not?
3. Generalization
How do we subtract 3- to 4-digit numbers with regrouping?
Where do we start?
Remember this:
Regroup the numeral in the hundreds place of the minuend when necessary
Rename the numeral in the tens place
Then, start subtracting from the right going to the left. (Start with ones place, then tens
place, etc.)
C. Application
Subtract the following:
1) th h t o 2) th h T o
7 4 2 5 8 5 3 6
- 3 5 3 - 1 6 2
3) tth th h t o 4) tth th h T o
2 8 6 1 4 4 5 6 4 6
- 4 2 4 2 - 3 2 7 1
5) hth tth th h t o
3 2 6 3 4 8
- 4 1 5 3
IV. Evaluation
A. Write in column then subtract.
1) 4 537 – 352 2) 2 913 – 771
3) 6 435 – 2 152 4) 2 854 – 1 692
5) 13 429 – 2 275
B. Write the missing minuend, subtrahend or difference.
1) 7 325 2) . 3) 8 526 4) 53 436 5) .
- _ . - 2 391 - _ . - _ . - 3 145
7 172 1 072 4 153 52 074 24 171
33. 27
V. Assignment
A. Fill in the blanks with the correct numerals then subtract.
1) 3 538 = ____ + ____ + ____ + ____ ____ + ____ + (____ + ____) + ____
- 253 = 200 + 50 + 3___
-____ + ____ __ ____ + ____
_____________
_____ +____ + ____ __ ____ + ____
= ___________________
2) 5 627 = ____ + ____ + ____ + ____ ____ + ____ + (____ + ____) + ____
- 4 353 = 4000 + 300 + 50 + 3___
-_____ + ____ + ____ _ ____ + ____
_______________________________
____ + ____ + ____ _ ____ + ____
= ___________________
3) 47 859 = ____ +___ + ___+ ____ +___ ____ + ____ + ____ + (___ + ___) + ____
- 5 383 = 5 000 + 300 + 80 + 3__
- ____ + ____ + ________ + ____
___________________________________
_____ +_ ____ + ____+ ________ + ____
= ___________________
B. Fill in the box with the missing numeral.
1) 3 9 2) 7 5 2 6 3) 5 8 5 3
- 1 2 7 3 - 4 3 4 - 2 3 2
2 4 7 2 1 3 8 4
C. Complete the table. Subtract the numerals in the first column from the numerals in the first row.
9 537 9 835 87 563
273 9 562
3 181 6 356
7 393 80 170
Subtracting 3- to 4-Digit Numbers from 4- to 5-Digit Numbers with Regrouping in
the Thousands Place
I. Learning Objectives
Cognitive: Subtract 3- to 4-digit numbers from 4- to 5-digit numbers with
regrouping in the thousands place
Psychomotor: Write numbers neatly and correctly
Affective: Practice helpfulness
34. 28
II. Learning Content
Skills: Subtracting 3- to 4-digit numbers from 4- to 5-digit numbers with
regrouping in the thousands place
Reference: BEC PELC I C 1.1.3.3
Materials: flash cards, show me board, leaf cut-outs, puzzle board
Value: Helpfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill (Basic Subtraction Facts)
Using the flashcards, ask the children to give the answer orally.
10 7 12 16 11 15 8 14
- 2 - 4 - 6 - 9 - 3 - 9 - 3 - 7
Check the assignment.
2. Review
Subtraction with regrouping in the hundreds place
Have a group game, boys against girls. Ask each group to answer number problems
written on a chart. Ask them to write their answers on show me board.
1) 349 2) 765 3) 734 4) 649 5) 6 734
- 76 - 194 - 282 - 82 - 291
____ ____ ____ ____ ____
3. Motivation
Present a problem through storytelling. Ask children to listen to the story problem.
Edgar is a vendor. He received 25 855 newspapers. At the end of the day, 3 935
newspapers were left. How many newspapers were sold?
B. Developmental Activities
1. Presentation
a. Have a comprehension check-up about the story problem presented in the motivation.
Ask:
Who’s the newspaper boy?
Have you seen a boy like Edgar? Why do you think he is selling newspapers?
Do you think he can help his parents by doing this kind of work? How?
b. Let’s try solving the problem using these steps.
Step 1:
■ Understand the problem
a. How many newspapers did Edgar receive?
b. How many were left?
c. What is asked in the problem?
35. 29
Step 2:
■ Plan
a. What process is involved in the problem?
b. What helps you decide to use this process?
Step 3:
■ Carry out the plan
Ask a pupil to write the number sentence. (25 855 – 3 935 = N)
Activity 1:
Let’s solve the problem using the indicated method.
Expanded form:
4 000 1 800 .
25 855 = 20 000 + 5 000 + 800 + 50 + 5
- 3 935 = 3 000 + 900 + 30 + 5
= 20 000 + 1 000 + 900 + 20 + 0
= 21 920 newspapers sold
In what place did we have the regrouping?
Why?
Step 4:
■ Looking back
a. Have we answered the problem?
b. Is our answer sensible?
c. Did we place the correct label?
Activity 2:
Now, let’s use the short method. Compare the digits in the minuend and subtrahend
in each place where regrouping is needed.
1. Start from the ones.
Subtract 5 ones
from 5 ones.
25 855
- 3 935
0
2. Subtract 3 tens from
5 tens.
25 855
- 3 935
20
3. Regroup 1 thousand
from 5 thousands as 1
thousand. Rename 8
as 18 hundreds.
4 18
25 855
- 3 935
920
4. Subtract 3
thousands from 4
thousands.
4 18
25 855
- 3 935
1 920
5. Bring down the last
digit 2.
4 18
25 855
- 3 935
21 920
Answer: There were
21 920 newspapers sold.
21 920 difference
+ 3 935 subtrahend
25 855 minuend
To check: Add the difference and the subtrahend to get the minuend.
Give more examples. Ask pupils to explain how the difference was obtained.
36. 30
9 736 8 245 9 364 75 864 8 369
- 924 - 813 - 2 721 - 2 942 - 1 925
8 812 7 432 6 643 72 922 6 444
2. Guided Practice
a. Work in pairs.
Give each pair a leaf cut-out with a number problem. Ask them to write their answers
on a piece of paper.
3 486 7 645 26 598 5 345 54 394
- 924 - 813 - 1 732 - 1 824 - 2 653
b. Work in groups of 4.
Each group will be given a puzzle board. Ask them to complete the puzzle using
subtraction. The first group to finish wins.
1) 9 7 6 2) 8 4 3) 5 3 4
9 2 8 1 3 2 2
8 4 2 4 2 6 4 3
4) 7 8 4 5) 6 3 3 9
2 9 4 1 2
7 2 2 2 6 5 2 4
Is regrouping important? Why?
3. Generalization:
How do we subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in
the thousands place?
Remember:
To subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in
the thousands place, we do the following:
Compare the digits in the minuend and subtrahend.
Start subtracting from the ones, then the tens.
If the subtrahend in the hundreds place is greater than the minuend,
regroup 1 thousand.
Rename the hundreds place and the thousands place, then subtract up to
the last digit.
To check: add the difference and the subtrahend.
C. Application
Match the number problem with the correct answer on the right.
1) 3 695
- 934
2) 78 478
- 59 264
3) 5 633
- 811
a. 4822
b. 74 322
c. 6961
37. 31
4) 76 146
- 1 824
5) 7 686
- 725
IV. Evaluation
Solve these problems:
1) The pupils in Tucop Elementary School need to collect 7 345 instant noodles wrappers for their
school project. They had collected 4 531 wrappers. How many more wrappers do they need to
collect?
Answer: ________________
2) Lyn bought 1 355 eggs. She sold 822 eggs. How many eggs were left?
Answer: ________________
3) 76 895
- 7 443
4) 98 674
- 9 432
5) 86 738
- 7 424
V. Assignment
A. Do as indicated. Write the answer on the blank.
1. The difference between 9 349 and 825 ___________
2. Subtract 8911 from 29 834 __________
3. From 36 384 take away 4 962 _________
4. 9 369 minus 3 924 _________
5. Take away 5 925 from 38 567 ___________
B. Fill in the box with the correct difference.
1. 7 349 – 826
2. 9 298 – 3 436
3. 24 364 – 2 952
4. 59 462 – 7 621
5. 73 398 – 964
d. 2761
e. 19 214
= _
_
_
_
_
= _
_
_
_
_
= _
_
_
_
_
= _
_
_
_
_
= _
_
_
_
_
38. 32
Subtracting Numbers with Regrouping in the Ten Thousands Place
I. Learning Objectives
Cognitive: Subtract 4-digit numbers from 5-digit numbers with regrouping in the ten
thousands place.
Psychomotor: Write the numbers vertically according to their place value.
Affective: Work cooperatively in the class during the activities and discussion.
Choose the leader wisely.
II. Learning Content
Skill: Subtracting numbers with regrouping in the ten thousands place
Reference: BEC PELC IC 1.1.3.4
Materials: problem chart, exercises chart, colored chalk, picture chart for coloring
activity, regrouping game chart.
Value: Wise choice of leader
III. Learning Experiences
A. Preparatory Activities
1. Drill – Regrouping Game
Divide the class into 5 groups. Choose a leader for each group. Give each group a
regrouping activity sheet. Ask them to match the numeral in column A with the renamed
numerals in column B by drawing a line that will connect them. The first group who will post
their work on the board with all answers correct will be the winner.
A B
1. 41 325 • a. 4 ten thousands + 16 thousands + 3
hundreds + 85 ones
2. 32 853 • b. 3 ten thousands + 13 thousands + 584
ones
3. 56 385 • c. 1 ten thousands + 17 thousands + 26
tens + 7 ones
4. 27 267 • d. 3 ten thousands + 11 thousands + 325
ones
5. 43 584 • e. 2 ten thousands + 12 thousands + 85
tens + 3 ones
2. Review – Checking of assignment
3. Motivation:
Are you familiar with the word “election?”
When do we hold election here in our country?
If you are going to elect a candidate, what good qualities of a leader/candidate would earn
your vote? Why?
39. 33
B. Developmental Activities
1. Presentation
In an election, Mr. Santos received 21 785 votes. His opponent, Mr. Gomez, received 9
465 votes. How many more votes did Mr. Santos receive than Mr. Gomez?
a. Ask:
Who were the candidates in the story problem?
How many votes did Mr. Santos receive?
How many votes did Mr. Gomez receive?
Who won in the election?
How many more votes did Mr. Santos receive than Mr. Gomez?
What process are we going to use to get the answer?
What will be our number sentence?
b. Let a pupil write the number sentence on the board.
21 785 – 9 465 = N
Activity 1 – Drawing/Pictorial
Let us draw the problem to see how many more votes Mr. Santos received than Mr.
Gomez.
Mr. Santos
Mr. Gomez
Now ask the pupil to draw again the diagram vertically starting with Mr. Santos. Then let
them do the pairing.
10 000 1000
10 000
1000
1000
1000
1000
1000
1000
1000
1000
1000
100
100
100
100
100
100
100
100 100 100 100
10
10
10
10
10
10
10
10
10
10
10
10
10
10
1 1
1 1
1
1 1
1 1
1
10 000
1000
10 000
100
100
100
100
100
100
100
1000 1000 1000 1000 1000
1000 1000 1000 1000
100
100
100
100
40. 34
What have you observed with the thousands drawing? Does Mr. Santos have enough
thousands to compare or pair with Mr. Gomez? What shall we do?
10
10
1010
10 10
10
10
1 1 11 1
10
10
10
10
10
10
1 1 11 1
10 000
10 000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
Regroup 1 ten thousand from the ten
thousands drawing and rename it as
thousands.
How many thousands are there in 1 ten
thousand? 10
How many thousands do we have now?
Can we now pair it with Mr. Gomez’s
thousands?
How many ten thousands drawing were
left?
10 000
1000
100
100
100
100
100
100
100
10
10
1010
10 10
10
10
100
100
100
100
10
10
10
10
10
10
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
41. 35
Which of the candidates has drawings with no pairs at all?
Let us count how many of each was left with Mr. Santos.
How many were left? 1 = 10 000
How many were left? 2 = 2 000
How many were left? 3 = 300
How many were left? 2 = 20
How many were left? 0 = 0
How many in all were left? 12 320
How many more votes did Mr. Santos receive than Mr. Gomez? 12 320 votes
Does our answer make sense?
c. Let us use the Expanded Method
21 785 20 000 + 1000 + 700 + 80 + 5
- 9 465 9000 + 400 + 60 + 5
N
20 000 + 1000 + 700 + 80 + 5
Regroup : 10 000 + (10 000 + 1000) + 700 + 80 + 5
Rename : 10 000 + 11 000 + 700 + 80 + 5
Subtract : 9000 + 400 + 60 + 5
Difference : 10 000 + 2 000 + 300 + 20 + 0 = 12 320
Did we get the same difference?
Activity 3 – Short Form Method
d. Let us use the Short form method.
TTh Th H T O
21 785 2 1 7 8 5 21 785
- 9 465 9 4 6 5 - 9 465
N ? 3 2 0 ? 320
Steps:
1. Subtract the ones. (5 ones – 5 ones = 0 ones)
2. Subtract the tens. (8 tens – 6 tens = 2 tens)
3. Subtract the hundreds. (7 hundreds – 4 hundreds = 3 hundreds)
4. Subtract the thousands. Can you subtract them? Why not?
1 1 11 1 1 1 11 1
1 1
10 10
100 100
1000 1000
10 000 10 000
42. 36
TTh Th H T O
1 +
1
10 +
1
2 1 7 8 5
9 4 6 5
3 2 0
Rename the ten thousands.
2 ten thousands becomes 1 ten thousands + 1 ten thousands
How many thousands are there in 1 ten thousands? 10 thousands?
Regroup 1 ten thousands to the thousands place.
Rename the thousands.
10 thousands + 1 thousands becomes 11 thousands or
10 000 + 1000 = 11 000
Can we now subtract 9 thousands from it?
TTh Th H T O 1 11
21 785 2
1
1
11
7 8 5 21 785
- 9 465 9 4 6 5 - 9 465
? 3 2 0 12 320
Then, subtract the thousands place.
(11 thousands – 9 thousands = 2 thousands)
5. Bring down the digit that was left in the ten thousands.
How many more votes did Mr. Santos receive than Mr. Gomez?
Did we also get the same difference?
2. Guided Practice
a. The pupils will work in groups with 4 members each. They are going to solve the
following numbers using the three methods.
1) 34 659 – 9 327
2) 51 485 – 2 135
3) 23 764 – 5 321
Ask: Which method do you like best? Why?
Were you able to finish the activity faster when you used that method? Why?
Work in pairs – Written
b. Write the following in column then subtract. Use the short method.
1) 73 864 – 7 321
2) 65 492 – 8 252
3) 51 276 – 3 214
4) 83 472 – 7 122
5) 31 597 – 4 132
6) 24 856 – 6 313
7) 32 583 – 6 321
8) 53 642 – 7 120
9) 81 731 – 7 401
10) 44 367 – 6 135
Ask: Were you able to finish all the exercises? Why?
How did you work as a pair so that you will come up with the correct answer?
Did you help each other during the activities?
43. 37
3. Generalization:
How do we subtract numbers with regrouping in the ten thousands place?
Remember:
To subtract numbers with regrouping in the ten thousands place:
1. Write the numbers vertically to align the digits in each place value.
2. Regroup the ten thousands place and rename the thousands place.
3. Subtract from right to left, starting with the ones.
C. Application
The table below shows the accumulated points of NCR, Region 4 and Region 3 during
the Palarong Pambansa.
Palarong Pambansa
Team Scores
Team Points
NCR 12 535
Region 4 8 302
Region 3 9 421
1. Which team scored the highest points? the lowest points?
2. How many more points does Region 3 have than Region 4?
3. How many more points does NCR have than Region 3?
4. Knowing the differences, can you tell the winner?
IV. Evaluation
A. Do what is asked.
1. Subtract 4 312 from 73 852.
2. What is 26 321 – 9120?
3. Take away 7313 from 42 763.
4. What is 5 235 less than 51 659?
5. How much more is 36 859 than 8 312?
6. What is 25 867 minus 8 314?
7. From 72 859, subtract 9 424.
8. What is the differences between 13 598 and 4 323?
B. Complete the table. Find each output
Rule: Subtract 7 537 from each input. Rule: Subtract 8 231 from each input.
Input Output Input Output
a. 41 215
b. 35 136
c. 24 523
d. 73 213
e. 56 105
a. 92 587
b. 34 346
c. 75 973
d. 23 832
e. 16 763
44. 38
V. Assignment
Find the difference then compare. Write >, < or = in the Box
1) 72 859 – 9 424 _____ 68 633
2) 27 613 _____ 32 789 – 6 413
3) 21 473 – 7 152 _____ 14 321
4) 75 272 _____ 82 659 – 7 417
5) 24 593 – 5 321 _____ 19 275
Subtracting Numbers with Zero Difficulty in Either Tens or Hundreds Place
I. Learning Objectives
Cognitive: Subtract 3– to 4-digit numbers from 4– to 5-digit numbers with zero
difficulty in either tens or hundreds place.
Psychomotor: State the rule in subtracting whole numbers with zero difficulty in the
tens or hundreds place
Affective: Help others in doing group activities
II. Learning Content
Skill: Subtracting numbers with zero difficulty in either tens or hundreds place
Reference: BEC PELC I C 1.1.3.5
Materials: flash cards of basic subtraction, chart of body-number coding, cut-outs
of different geometrical shape with number value, secret message
activity sheets, strips of cartolina with subtraction sentences
Value: Helpfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill : Kinesthetic Math
Review the body symbols for digits 0 – 9. Then the teacher will show some basic subtraction
facts (flash cards) and the pupils will act out the answer.
Digit Movement
0 - Forefinger and thumb together forming zero
1 - Right arm forward closed fist
2 - Left arm forward closed fist
3 - Left and right arms folded vertically closed to the body
4 - Hands on waist
5 - Right hand on the chest
6 - Bend forward to pick something
7 - Stand straight
8 - Arms obliquely upward
9 - Do the McDonald sign
7
- 3
9
- 7
10
- 1
8
- 3
5
- 2
6
- 5
5
- 5
10
- 3
10
- 4
10
- 2
45. 39
2. Motivation : Present a problem opener
The Grade Three class collected bottle caps for their doormat project. The boys collected 3
234 caps while the girls collected 5 405 caps. How many more caps did the girls collect than
the boys?
B. Developmental Activities
1. Presentation
a. Ask: What was the project of the grade three class?
Do you know what a doormat is?
Is the project of the grade three pupils a good project? Why?
What benefit can we get from it?
Is it an expensive project?
Is it helpful and useful in our lives?
b. Let us solve the problem using Polya’s 4 steps in problem solving.
■ Understand the problem
a. How many bottle caps did the grade three boys collect?
b. How many caps did the grade three girls collect?
c. Who collected more caps?
d. How many more caps did the girls collect than the boys?
e. What process are we going to use?
■ Make a plan
What operation will be used to solve the problem?
■ Carry out the plan
Ask a pupil to write the number sentence on the board.
5 405 – 3 234 = N
Activity 1 – Acting Out the problem
The class forms 5 groups. Each group chooses a leader.
Give each group a set of different geometric shapes with different number
value written on it. Let them illustrate the number of caps collected by the
grade three boys and the number of caps collected by the grade three girls
through acting out.
Girls
Boys
1000
100
10 1
1000
1000
1000
1000
100
100
100
100
1000
1
1
1
1
1
1000
1000
1000
100 100
1
1
1
1
10 10
10
46. 40
10
10
100
10
100
100
Let them use pairing technique wherein the number of caps collected by the
grade three boys will be paired to the number of caps collected by the grade
three girls. Starting with the s place, how many s were left with no pair?
Girls
Boys
Pair the s. Did you find it easy to do so? Why not? Since the girls’
number of caps do not have s, what shall we do?
Borrow one in the s place. Rename it as .
How many s are there in 1 ? 10 s
Girls
Boys
How many s were left with no pair?
Pair the s and s. How many s and
s were left with no pairs?
Girls
11
1000 100 10 1
1000
1000
1000
1000
100
100
100
100
1000
1
1
1
1
1
1000
1000
1000
100 100
1
1
1
1
10 10
10
XX
XX
XX
XX
10 10
1000 100
10 1
1000
1000
1000
1000
100
100
100
100
1000
1
1
1
1
1
1000
1000
1000
100 100
1
1
1
1
10 10
10
XX
XX
XX
XX
10 10 10
10 10 10
10 10
10 10
10
100 1000
1000
1000 100
10 1
1000
1000
1000
1000
100
100
100
1000
1
1
1
1
1
XX
XX
10 10 10
10 10 10
10 10
10 10X
X X
X
X X
X X
100
47. 41
1
Boys
No pair
Answer 2 1 7 1
Count how many s, s, s and s
were left with no pair at all?
How will you read it in numerals?
So, how many more caps did the girls collect than the boys?
■ Look back
Is your answer sensible?
What is the correct label?
Did all the groups get the same difference?
Activity 2: Expanded Form Method
Let the children solve the same problem using the expanded form. Will you get
the same difference?
a. Subtract the ones.
5 405 5 000 + 400 + 0 + 5
- 3 234 3 000 + 200 + 30 + 4
1
b. Subtract the tens.
5 000 + 400 + 0 + 5
- 3 000 + 200 + 30 + 4
? + 1
5 000 + (400 – 100) + (100 + 0) + 5
- 3 000 + 200 + 30 + 4
? + 1
5 000 + 300 + 100 + 5
- 3 000 + 200 + 30 + 4
70 + 1
c. Subtract the hundreds.
5 000 + 300 + 100 + 5
- 3 000 + 200 + 30 + 4
100 + 70 + 1
d. Subtract the thousands.
5 000 + 300 + 100 + 5
- 3 000 + 200 + 30 + 4
2 000 + 100 + 70 + 1
1000
1000
1000
100 100
1
1
1
1
10 10
10
XX
XXX
X X X X X X
X
1000 1000
100
110 10
10
10
10
1010
1000 100 10
Subtract 4 from 5.
You cannot subtract 30
from 0; therefore borrow 100
from the hundreds column and
put it in the tens column
Subtract 30 from 100.
Subtract 200 from 300.
Subtract 3 000 from 5 000. Add
all the partial differences.
48. 42
So, we get the same difference.
Activity 3 – Short form method
Solve the same problem using the short cut method.
Th H T O
5 405 5 4 0 5 5 405
- 3 234 3 2 3 4 - 3 234
N 1 1
Steps:
a. Put the numerals in the place value chart or align them according to their place
value.
b. Subtract the ones. (5 ones – 4 ones = 1 ones)
c. Subtract the tens. Is it possible to subtract 3 tens from 0 tens?
Th H T O Checking :
3 + 1 10 + 0 310
5 405 5 4 0 5 5 405 3 234
- 3 234 3 2 3 4 - 3 234 + 2 171
N 1 2 171 5 405
Regroup the hundreds.
4 hundreds = 3 hundreds + 1 hundreds.
Transfer 1 hundreds to the tens place.
How many tens are there in 1 hundred?
Rename the tens.
10 tens + 0 tens = 10 tens
Can we now subtract 3 tens from it?
(10 tens – 3 tens = 7 tens)
d. Subtract the hundreds.
(3 hundreds – 2 hundreds = 1 hundreds)
e. Subtract the thousands.
(5 thousands – 3 thousands = 2 thousands)
Did we get the same difference?
4. Solve the number sentence.
What is 37 067 – 2 532?
Divide the class into 3 groups. Each group will work by partners.
The first group will solve it using the geometric cutouts with numbers written
on it.
The 2
nd
group will solve it using the expanded form.
The 3
rd
group will solve it using the short cut method.
Ask:
Did we get the same difference?
Which of the three methods do you like best? Why?
49. 43
2. Guided Practice
a. SECRET MESSAGE – To be done by groups with 4 members each. The teacher will
provide each group with the secret message activity.
Directions: Find the secret message. Find the difference of the number sentences in the
box of Activity A. The difference will give the letters. Then use them in Activity B to
decode the message.
Activity A
4 305 8 607 5 906 5 037
- 142 - 473 - 283 - 516
A B C E
2 086 7 049 3 608 4 509 6 907 23 075
- 423 - 635 - 1 273 - 1 393 - 2 273 - 2 532
H I N O R S
32 095 47 032 54 308 38 053 12 507
- 1 731 - 3 412 - 135 - 4 531 - 1 242
T U W Y Z
Activity B
SECRET MESSAGE:
33 522 3 116 43 620 4 163 4 634 4 521 4 163
Y O U A R E A
20 543 43 620 8 134 30 364 4 634 4 163 5 623 30 364 6 414 3 116 2 335
54 173 1 663 6 414 11 265
W H I Z
b. Math kinesthetic – (Body Number Coding)
Group work with 5 members in each group.
The teacher shows some subtraction sentences written in strips of cartolina. Each group
will solve the number sentence on their paper. When they get the correct difference, each
member acts out the answer using the body number coding.
(To be written in strips of cartolina)
1. What is 3 050 minus 1 322?
2. Subtract 3 435 from 28 078?
3. Find the difference of 735 and 8 809.
4. Take away 1 345 from 8 907?
5. What is 3 253 less than 8 094?
SS U B OR A C T IT N
50. 44
c. Dyads
Ask the pupils to write some subtraction sentences in a piece of paper. The pair
exchanges their work with the other pair. Both pairs answer the problem they are holding.
Let them show their answers for the class to check.
What makes you enjoy the activities we had?
What happens to your work when you help one another?
3. Generalization:
How do we subtract numbers with zero difficulty in tens or hundreds?
What do you always bear in mind when a digit in the minuend is zero and the corresponding
digit in the subtrahend is a non-zero number?
Remember:
To subtract numbers with zero difficulty in tens or hundreds:
1. Align the numerals according to their place value.
2. Subtract starting with the ones place.
3. If the tens digit in the minuend is smaller than the subtrahend, regroup the
hundreds then rename the tens.
4. To check: Add the difference and the subtrahend. The sum should be equal
to the minuend.
C. Application
Individual work – Written
Find the difference using the short cut method.
1) 3 059
- 432
2) 7 306
- 132
3) 6 059
- 1 325
4) 15 025
- 4 321
5) 27 309
- 4 132
IV. Evaluation
Work by pairs
Find the missing minuend, subtrahend or difference.
1) 3 059
- 432
____
2) 4 603
- ____
2 471
3) ____
- 2 823
622
4) 13 087
- ______
11 355
5) 24 809
- 1 372
______
V. Assignment
A. Write in column then subtract.
1) 3 405 – 393 2) 7 049 – 1 323
3) 25 306 – 2 134 4) 16 087 – 3 053
5) 73 059 – 2 124
B. Fill in the box with missing numeral
1) 5 _05
- 79_
5 1_2
2) _ 087
- 1 _43
4 7_4
3) 8 _ _3
- 132
7 27_
4) 1_ 03_
- 2 _34
15 9_3
C. Read and solve.
1. What should your minuend be if you have 45 453 as difference and 2 173 as subtrahend?
51. 45
2. Patrick was able to save P5,430 from his monthly allowance. He wants to buy a cabinet that
costs P9,050. How much more does he need to save so that he can buy the cabinet?
3. Bicycles are popular all over the world. The first bicycle was invented about 1790. How many
years ago was the first bicycle invented?
Estimating Differences
I. Learning Objectives
Cognitive: Estimate the difference of two numbers with 3- to 4-digits
Psychomotor: State the rules in estimating differences
Affective: Follow the rules in estimating differences correctly
II. Learning Content
Skill: Estimating differences
Reference: BEC PELC I.C.1.1.4
Materials: flash cards, Show Me Board, word problem chart, cards with subtraction
sentences and estimated difference, puzzle, table chart
Value: Following simple directions correctly
III. Learning Experiences
A. Preparatory Activities
1. Drill (flash cards)
Flashcards with numerals written on it. The pupils will read the numeral and tell the place
value of the underlined digit.
2. Review
a. Checking of assignment.
b. Rounding Numbers
Round the following numbers to the nearest:
Hundreds Thousands
1) 253 _____________ 2) 3 437 _____________
3) 125 _____________ 4) 6 053 _____________
5) 478 _____________ 6) 4 857 _____________
7) 659 _____________ 8) 8 210 _____________
9) 304 _____________ 10) 7 489 _____________
3. Motivation
a. Guessing Game
1. Present a bottle filled with multicolored buttons.
Ask: How many buttons do you think are there in this bottle?
4 753 1 543 84 387 47 259 547 203 3 575 4 385
59 367 38 732
52. 46
2. Give 10 seconds for the pupils to give their guesses. Let them write their answers
on the show-me-board.
3. Call 1 or 2 pupils to count the number of buttons in the bottle. The one who can give
the closest guess will be the winner.
Ask: How did you come up with the correct/nearest answer?
Why is it not possible to get the exact answer immediately?
There are times that we do not need the exact answer to a problem. All we need is just
the closest possible answer.
b. Present a Problem Opener
Mr. Cruz has 782 square metres of land planted with corn and 575 square metres planted
with palay. About how many square metres more of land were planted with palay than
with corn?
B. Developmental Activities
1. Presentation
a. Let us understand the problem.
1. How many square metres of land was planted corn?
2. How many square metres of land was planted palay?
3. What is asked in the problem?
4. Do we need an exact answer?
5. What word clues tell that we do not need an exact answer?
The phrase “about how many” tell us that we should estimate the answer.
6. What operation are we going to use?
b. Let us plan on how we can solve the problem.
1. What will be the number sentence for the problem?
2. Ask a pupil to write the number sentence on the board.
c. Let us execute our plan.
1. To find the estimated difference, round each
number to the greatest place value
782
- 575
800
- 600
2. Then subtract. 800
- 600
3. Around 200 square metres of land were planted
to palay than corn.
d. Check your work.
Exact Difference Estimated
Difference
1. Did I answer the question?
2. Compare the estimated difference
with the exact difference.
782
- 575
207
800
- 600
200
3. Is my answer sensible? 207 is close to 200
e. The teacher will give more exercises for the pupils to solve.
Round each number then estimate the difference.
53. 47
845
- 458
____?____
____?____
7 541
- 1 825
____?____
____?____
Is the estimate difference close to the exact one?
2. Guided Practice
a. Individual Work (flashcards and show me board)
1. Teacher shows some flashcards with subtraction sentences.
2. The pupils give the numerals rounded to the highest place value and then find their
difference. Let them write the answer on their show me board.
B. Game: Finding Patterns
1. Divide the class into 2. Give sets of cards with subtraction sentence in one group
and cards with estimated difference in another group.
2. The first pair who matched the correct sentence with the correct estimated difference
wins.
Subtraction Sentence Cards
Estimated Difference Cards:
Did you find your partner easily?
How did you do it?
Did you follow the rules in estimating difference?
Did you get the correct answer?
483
- 124
536
- 275
296
- 154
748
- 334
882
- 416
4 615
- 3 243
6 427
- 3 281
7 086
- 2 540
8 937
- 4 352
6 836
- 2 595
534-357 919-422 856-580 8 545-7 903
7 581-2 614 842-221 667-308 5 049-2 836
858-139 425-186 893-754 7 145-3 780
7 943-3 607 8 605-2 807 9 145-1 863 9 045-1405
100 200 300 400 500
600 700 800 1 000 2 000
3 000 4 000 5 000 6 000 7 000
8 000 900 9 000Joker cards:
54. 48
3. Generalization
a. What are the steps in estimating the difference?
b. Why do we need to estimate?
c. In what situation in life is estimation important?
Remember:
To estimate the difference:
a. Round the minuend and the subtrahend to their greatest place value.
b. Subtract the rounded numbers.
C. Application
Individual Work (Written)
1. Write the puzzle on the board.
2. Complete the puzzle boxes by estimating. The answer in the bottom right
corner of each box will be the same when subtracting across or down.
1 287 891
888 641
IV. Evaluation
Work by Pairs (Written)
Estimate the difference by rounding the numbers to its highest place value then subtract. Write the
answer in your notebook.
1) 673 _______ 2) 846 _______ 3) 558 _______
- 448 _______ - 551 _______ - 98 _______
_______ _______ _______
4) 452 _______ 5) 758 _______ 6) 8 435 _______
- 125 _______ - 174 _______ - 2 526 _______
_______ _______ _______
7) 9 071 _______ 8) 4 892 _______ 9) 8 465 _______
- 2 052 _______ - 1 261 _______ - 3 259 _______
_______ _______ _______
10) 4 936 _______
- 2 143 _______
_______
V. Assignment
A. Answer the following questions based on the table below.
55. 49
LAND AREAS OF SOME PROVINCES
Province Area (sq. km)
Oriental Mindoro 4 365
Leyte 6 268
Bohol 4 117
Marinduque 959
Tawi-Tawi 1 087
1. About how much bigger is Oriental Mindoro than Leyte?
2. Estimate the difference between the areas of Tawi-Tawi and Marinduque.
3. About how much smaller is Marinduque than Leyte?
B. Write a good estimate after each problem, then solve.
1. Mr. Reyes wanted to sell 302 tickets for a cultural show. He sold 191 tickets. About how
many more tickets should he sell?
Estimate by rounding to the nearest hundreds: ___________
Answer: ___________
2. There are 8 936 books in Manuel L. Quezon Elementary School. Manuel Roxas Elementary
School has 7 642 books in its library. How many more books does Manuel L. Quezon
Elementary School have than Manuel Roxas Elementary School?
Estimate by rounding to the nearest thousands: ___________
Answer: ___________
Subtracting Mentally 2-Digit Numbers without Regrouping
I. Learning Objectives
Cognitive: Subtract mentally 2-digit numbers with minuends up to 99 without regrouping
Psychomotor: Tell the difference without using paper and pencil
Affective: Show speed and accuracy when working in the activities
II. Learning Content
Skill: Subtracting mentally 2-digit numbers without regrouping
Reference: BEC PELC I.C.1.2
Materials: spinner numbered 0 to 9 and 10 to 18, drill boards, flash cards, number coding
chart
Value: Speed and accuracy
III. Learning Experiences
A. Preparatory Activities
1. Drill
Conduct a drill on basic subtraction facts using spinners. Provide a pair of spinners as shown
below.
56. 50
a. First, use the 0 to 9 spinner to generate two single-digit subtraction facts.
b. Then call two pupils.
c. Let pupil A spin Spinner 1 and pupil B spin Spinner 2 to generate 2-digit minuends such
as 18-4 and other subtraction facts. (15-6, 12-2)
d. The rest of the class answer them on their drill boards.
e. At a given signal they show their answer to the teacher and to their seatmates.
2. Review
Distribute 2 sets of strips of cartolina with numbers written on it. Then ask the pupils to
find the expanded form of the number on their strips. The first partner to find each other wins.
(The teacher may add more to the given strips)
3. Motivation
Present a problem opener.
Dick gathered 56 shells at the beach. He gave 24 shells to his friend. How many shells
were left?
B. Developmental Activities
1. Presentation
a. Have you been to a beach? What are the things you saw there? In our story problem,
who gathered shells? What did he do after gathering some shells? What kind of friend is
he? Are you also kind to your friends? In what ways?
How many shells did Dick gather?
How many shells did he give to his friends?
How many shells were left? What operation are we going to use?
What will be our number sentence?
b. Let a pupil write the number sentence on the board.
56 – 24 = N
Ask somebody to write the number in vertical column.
56
- 24
N
Say: Today, we will not use paper and pencil to find the difference but instead we will try
to compute it mentally.
Think of how we subtract numbers. In what direction do we follow when we subtract
numbers?
Subtract mentally the ones, then the tens
59 87 68 76 95 74
50 + 9 80 + 7 60 + 8 70 + 6 90 + 5 70 + 4
57. 51
Think: 5 6 5 6
- 2 4 2 4
2 3 2
c. The teacher will give more example.
8 4 8 4 8 4
- 2 1 2 1 2 1 63
3 6 3
7 8 7 8 7 8
- 3 5 - 3 5 - 3 5 43
3 4 3
2. Guided Practices
a. Let the pupils study the coding of numbers. Let them do it afterwards and memorize if
possible
(To be written in manila paper)
Digit Movement
0 - Say “Yo!”
1 - Clap once
2 - Clap twice
3 - Clap thrice
4 - Raise your left hand
5 - Raise your right hand
6 - Say “Ole”
7 - Do the yes clap
8 - Say “Mabuhay!”
9 - Say “Be Happy!”
(To be done by pairs)
Direction: Find the missing number in the difference. Use the number coding.
(Use flashcards)
1. 46 2. 88 3. 96 4. 78 5. 98
- 21 - 25 - 24 - 35 - 35
2_ _3 7_ _3 6_
Then give
the
difference
32
So, 32 shells were left to Dick. Is
this the correct answer? Is it
sensible?
58. 52
6. 95 7. 29 8. 59 9. 62 10. 39
- 25 - 19 - 20 - 51 - 11
_0 1_ 3_ _1 2_
b. Cross number puzzle – (Individual work)
Subtract mentally the following numbers to solve the puzzle.
(Make 1 copy of the puzzle for every pupil.)
a b
c d
e f
g h
I j
k
Across Down
a. 95 – 63 a. 42 – 12
b. 72 – 20 b. 68 – 11
c. 89 – 29 c. 84 – 21
d. 68 – 21 d. 79 – 34
e. 98 – 33 e. 99 – 32
g. 49 – 12 f. 68 – 43
h. 35 – 20 h. 25 – 21
j. 28 – 14 i. 92 – 20
k. 56 – 33 j. 49 – 33
d. Telephone Game – (By Group)
Directions: Group the pupils by column with 10 members each. The teacher gives
subtraction sentence written on a piece of paper to the last pupil in every
59. 53
column. On cue, the pupils who received the piece of paper simultaneously
solve the subtraction sentence mentally. Then he/she whispers the answer to
the next pupil until it reaches the pupils in front. The pupils in front will then
write the answer on the board. The group with the correct answer gets a
point. The first group to get 5 points wins.
Illustration:
The following subtraction sentences should be written on a strip of paper as many as the
number of groups formed.
1) 85 2) 79 3) 67 4) 59 5) 89
- 24 - 34 - 35 - 32 - 25
6) 79 7) 94 8) 83 9) 99 10) 68
- 45 - 72 - 23 - 26 - 34
Did you do it fast? Were all your answers correct?
3. Generalization
How do we subtract mentally? How did you do it?
Where do we start subtracting?
Remember:
To subtract mentally 2-digit numbers mentally without regrouping, subtract the ones first,
then the tens. Then give the difference.
C. Application
Subtract mentally. (Use drill board and flash cards)
Chalk Board
60. 54
1) 35 2) 56 3) 94 4) 48 5) 68
- 12 - 32 - 72 - 25 - 34
IV. Evaluation
A. Subtract the following mentally.
1) 74 2) 86 3) 97 4) 94 5) 79
- 12 - 35 - 84 - 72 - 45
B. Game – Rally Robin
Pupils will make their own subtraction sentence. Then they will pass it to their right and the
pupils on the right answer the question. Then, they will do the reverse way. The one who
answered correctly will also make a subtraction sentence and pass it to her/his right.
V. Assignment
A. Subtract mentally. Write only the answer.
1) 36 2) 89 3) 56 4) 67 5) 83
- 12 - 36 - 34 - 45 - 51
B. Find the difference of the numbers on the fruits by subtracting them mentally.
76 89 86 68 95
- 24 - 36 - 41 - 43 - 62
___ ___ ___ ___ ___
C. Have the pupils subtract each number from 86 using mental arithmetic and write their
answers in the triangles.
86
43 34
22 57
61. 55
Solving Word Problems involving Subtraction
I. Learning Objectives
Cognitive: Solve 1-step word problems involving subtraction of whole numbers including
money with minuends up to 100 000 without and with regrouping
Psychomotor: Write the number sentence correctly
Affective: Work cooperatively by helping one another in the group activities
II. Learning Content
Skill: Solving word problems involving subtraction
Reference: BEC PELC I.C.2.1
Materials: flash cards of basic subtraction facts, chart of the song, problems written on
manila papers, activity answer sheet, activity cards, play money, geometric
cutouts with value written on it
Value: Cooperation and helpfulness
III. Learning Experiences
A. Preparatory Activities
1. Drill: Kinesthetic Math
The teacher will show flashcards (butterfly design) of basic subtraction facts and the pupils
will act out the answer through body number coding.
Digit Movement
0 Forefinger and thumb together forming zero
1 Right arm forward, closed fist
2 Left arm forward, closed fist
3 Both fists folded vertically close to the body
4 Hands on waist
5 Right hand on the chest
6 Bend forward to pick something
7 Stand straight
8 Arms obliquely upward
9 Do Mcdonald sign
4 8 10 9 7 5
- 2 - 3 - 4 - 1 6 2
6 9 10 8
- 2 - 2 - 1 - 8
2. Review
Checking of assignment.
62. 56
3. Motivation
A. Song: This is the Time
(Tune: This is the Day)
This is the time (2x)
That we’re waiting for (2x)
We’ll learn our Math (2x)
And apply them all (2x)
So this is the time
That we solve problems
We’ll learn them all
And apply them well.
This is the time (2x)
That we’re waiting for
1) Did you like the song?
2) What is the song all about?
3) What are we going to do with the problems?
B. Present a problem opener.
Two of the highest mountains in the Philippines are Mt. Apo in Mindanao which is 2
954 metres high and Mt. Pulog in Luzon which is 2 928 metres high. How many metres
higher is Mt. Apo than Mt. Pulog?
B. Developmental Activities
1. Presentation
a. Let a pupil read the problem aloud to the class while the rest follow silently.
b. Ask: Have you seen a mountain? Where?
What happened to some of our mountains?
What can we do to preserve our natural resources especially mountains?
c. Let us analyze and solve the word problem using Polya’s 4 steps.
■ Understand the problem
a. What are the two highest mountains in the Philippines?
b. Where can you find Mt. Apo? What about Mt. Pulog?
c. What are given? How high is Mt. Apo? How high is Mt. Pulog?
d. What is being asked?
e. What operation is needed to solve the problem?
f. Why did you say so? What keywords/word clues were used?
■ Plan
What equation will solve the problem?
■ Solve
Ask a pupil to write the equation on the board.
2 954 – 2 928 = N
d. Let the pupils draw the given height of the 2 mountains using the following geometric
shapes and their equivalent values.
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Shape Value
1000
500
100
10
1
Mt. Apo =
Mt. Pulog =
Cross out the drawings that will make a pair.
What were left? How many are there? I I I = 10 + 10 + 3 = 23
How many metres higher is Mt. Apo than Mt. Pulog? 23 metres
■ Look Back
a. Did you use the correct operation?
b. Does the answer make sense?
c. Did you label the answer correctly?
d. Mt. Apo is 23 metres higher than Mt. Pulog.
e. Present another word problem for the pupils to analyze and solve.
There were 2 995 people who went to see the basketball game. Nine hundred
eighty-six were in the front rows and the rest were in the back rows. How many were left
in the back rows?
■ Understand
a. What are given? What do we already know?
b. What is being asked?
c. What operation is needed to solve the problem?
d. Why did you say so? What keywords/word clues were used in the problem?
■ Plan
What equation will represent the problem?
■ Solve
a. Ask a pupil to write the equation on the board.
2 995 – 986 = N
b. Write the number sentence in vertical column.
The numerals must be aligned according to their place value.
Subtract starting from ones column. If the minuend is smaller than the
subtrahend, borrow 1 from the next column on the left.
8 15
2 995 2 995
- 986 - 986
2 009
■ Look Back
a. Did you use the correct operation?
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b. Does the answer make sense?
c. Did you label the answer correctly?
2 009 people were left in the back rows
2. Guided Practice
Group Work
Divide the class into small groups, around 3-4 members in a group. Have them answer
the following problems cooperatively using the different strategies suggested. Then,
discuss the solutions to the problems with the whole class.
To be written in an index card:
1. The baker baked 3948 cupcakes. He sold 2437 of them. How many cupcakes were left?
Instructions: Solve the problem through illustration. Use the following geometric shapes
as representation.
Shape Value
- 1 000
- 500
- 100
- 10
- 1
2. Aling Maria earned 4,976 from selling meat. She spent 3,365 for the family’s food.
How much money were left?
Instructions: Solve the problem by acting it out. Use play money as your materials.
3. Cora sold 5 485 raffle tickets. Four thousand three hundred seventy-three of them were
paid. How many raffle tickets were not paid?
Instructions: Solve the problem by acting it out. Use geometric cutouts with value written
on it.
Ex.:
1 000 10
100 1
65. 59
4. Mang Rexon harvested 6 884 ears of corn. He sold 4 693. How many ears of corn were
unsold?
Instruction: Solve the problem using the 4 steps of Polya.
5. Fely picked 3 953 flowers for the festival. She used 1 842. How many flowers were
unused?
Instruction: Use the 4-step in solving problems by Polya.
6. Ask the pupils about their feelings during the group activity.
How did you work with your group?
Did you help one another? Did you cooperate with the group?
What happened to your work when everybody is cooperative and helpful?
Were you able to arrive at the correct answer?
3. Generalization
How do we analyze and solve word problems involving subtraction?
What are the 4 steps in solving problems?
What are the questions under each step?
C. Application
Group Work (5 members in each group)
The teacher will give each group an activity card where a problem is written, and an activity
answer sheet where they are going to write their answer.
The group will report to the class about their work/solution for the class to check.
Example of an activity answer sheet:
Answer Sheet for Problem #1
■ Understand
a. What are the given facts?
b. What is being asked?
c. What are the necessary information or facts?
d. What words tell what operation to use?
e. What operation will you use?
Polya’s 4 steps in solving problems are:
a. UNDERSTAND – Understand the problem.
What do I know?
What do I need to find?
b. PLAN – Make a plan.
What shall I do?
c. SOLVE – Carry out the plan.
I will put my plan to work.
d. LOOK BACK – Look back.
Have I answered the question?
Is my answer sensible?
66. 60
■ Plan
What equation will solve the problem?
■ Solve
Solve the equation.
■ Look Back
a. Did you use the correct operation?
b. Does the answer make sense?
c. Did you label the answer correctly?
IV. Evaluation
A. Read, analyze and solve the following problems.
1. Mrs. Castro wants to buy a washing machine for 5,795. She saved 3,273. How much
more does she need?
2. In a basketball game, 1 735 people watched the game. After the first half of the game 214
left. How many people stayed to watch the game?
3. Rhona wanted to sell 1 876 tickets for a dance exhibition. She has sold 934 tickets. How
many more tickets should she sell?
4. During the local elections. Mr. Gonzales received 7 859 votes while Mr. Manzano
received 6 347 votes. How many more votes did Mr. Gonzales receive than Mr. Manzano?
5. A morning newspaper has 29 347 subscribers. An afternoon newspaper has only 8 732
subscribers. How many more subscribers do the morning newspaper has than the afternoon
newspaper?
B. Written – Triads
The problems below have no numbers. Decide how you would solve each one. If it will help you,
fill in reasonable numbers.
1. Mario saved some money by buying a book of movie passes rather than individual
tickets. How can he figure out how much money he had saved?
2. John knows the weight and price of two different sizes of boxes for dog food. How can he
figure out which of the two is a better buy?
3. Anna bought a pair of rubber shoes. She went to the cashier to pay for it. How will she know
how much change she had received?
4. Rebecca wanted to buy a refrigerator. She only save a certain amount. How can she figure
out how much more does she need to save?
5. Laura made some circles. She colored some of them red and the rest blue. How will she
know how many circles were colored blue?
(The group will publish their work on the board for the class to check.)
C. Work in Pairs
Ask the pupils to create their own problem, then let her/his partner answer it. Then they are going
to publish their work for the class to check.
V. Assignment
Read, analyze and solve. Use the 4 steps of Polya.
1. A total of 1750 tourists went to Baguio City in April and 639 in May. How many more tourists
went to Baguio in April than in May?
2. Mother had 1,590. She bought groceries worth 1,587. How much was her change?
67. 61
3. Robert harvested 1 659 cavans of palay from his farm. He sold 735 cavans. How many
cavans of palay were left?
Solving Word Problem Mentally
I. Learning Objectives
Cognitive: Solve mentally 1-step word problems involving subtraction without regrouping
Psychomotor: State the complete answer
Affective: Show speed and accuracy in solving word problems
II. Learning Content
Skill: Solving word problem mentally
Reference: BEC PELC I.C.2.2
Materials: problem chart, flash cards, body number coding chart
Value: Speed and accuracy
III. Learning Experiences
A. Preparatory Activities
1. Drill: Mental Computation
Use flashcards.
2. Review
Name the place value of the underlined digit.
3. Motivation
Ask the pupils to subtract each number in the outer circle from the number in the inner circle.
8
- 5
4
- 2
10
- 7
18
- 7
12
- 5
29
- 8
17
- 8
485 376 109 362 785
87
32 41
2556
43
11 21
1233
75
32 20
5314
96
37 52
5634
68. 62
B. Developmental Activities
1. Presentation
Fely helped her mother sold pineapples in the market. She had 48 pineapples to sell.
She sold 36 pieces in the morning. How many pineapples were not sold?
Let us analyze and solve the problem mentally.
What is asked in the problem?
What are the given facts?
What operation are you going to use?
What will be the number sentence?
How will you solve it mentally?
Activity 1
Try to draw the problem in your mind.
Does the answer make sense?
Is it reasonable?
Activity 2 – Expanded Form
48
- 36
= 40 + 8
= 30 + 6
10 + 2
Subtract the ones 8 – 6 = 2.
Subtract the tens 40 – 30 = 10.
Then add the two differences = 2 + 10 = 12.
Activity 3 – Short Cut Form
To solve mentally
Subtract the ones, then the tens.
10
1 1 1 1
1 1 1 1
1010 10
10
1 1 1 1
1 1 1 1
1010 10
48 pineapples
(number of pineapples to
be sold)
12 pineapples
(number of pineapples left)
Think
69. 63
48 48 48
- 36 - 36 - 36
2 12 12
12 pineapples were not sold.
Let us have another problem.
Arlene has 98 in her wallet. She bought a kilogram of sugar for 32. How much
was left with her?
To solve mentally
Subtract the ones, then the tens.
98 98
- 32 - 32
6 66
66 was left with Arlene.
2. Guided Practices
a. Individual Work
The pupils will solve the problems mentally then write their answer on their show me
board. After 5 seconds, they will show their answer to their teacher and classmates.
a. Aling Nena washed 14 pieces of clothes while Rosa washed 26 pieces. How many
more pieces did Rosa wash?
a. The following day, Aling Nena ironed 34 pieces of clothes. Of the 34 pieces, 12 were
blouses and the rest were t-shirts. How many t-shirts did she iron?
b. A flower vendor had 85 roses to sell. She sold 63 roses in the morning and the
remaining roses in the afternoon. How many roses did she sell in the afternoon?
c. Mr. Santos planted 38 tomato seedlings and 15 eggplant seedlings. How many more
tomato seedlings did Mr. Santos plant?
d. There are 98 pupils in the school ground. Forty-two of them are Grade Three and the
rest are Grade Four. How many Grade Four pupils are there?
Kinesthetic Math – Body Coding Number
To be done by pairs. The pupils will solve the problems mentally then they will act out
the answer by pairs. One pupil will act out the tens place digit and the other will act out
the ones place.
a. Mother gave Agnes 95. She bought a notebook for 35. How much money
was left?
b. Kim had 78 marbles. He gave his brother 32 marbles. How many were left to him?
c. Laura’s tomato plants have 89 ripe tomatoes. She picked 28 ripe tomatoes. How
many ripe tomatoes were left?
d. Maris counted 36 flowers in their school garden. Fely counted 98 flowers in the
flower shop. How many more flowers did Fely count than Maris?
e. Robert gathered 56 shells at the beach. He gave 24 shells to his friend. How many
shells were left to Robert?
Think
70. 64
Creative Math – To be done by group with 3 members.
Ask the pupils to make their own problem and solve it using the given data.
1) 76 flower pots to sell; 42 pots were sold
2) 99 hen’s eggs; 65 duck’s eggs
3) 58 Math books; 32 Science books
4) 67 Grade 3 pupils; 35 are boys
5) 95 pink balloons; 60 white balloons
Did you do it fast?
Were your answers correct?
3. Generalization
How do we solve mentally 1-step word problems without regrouping? How did you do it?
Remember:
In solving word problem mentally involving subtraction, analyze the problem first, then
subtract the ones places and the tens place.
C. Application
Individual Work
Solve the problems mentally. Write your answer on a piece of paper or in your notebook.
1. Cindy had 95. She spent 30 for juice and biscuits. How much money was left?
2. Sarah has 78 baseball cards. Tricia has 40 cards. Who has more cards? How many more?
3. The sum of two numbers is 75. One number is 32. What is the other number?
4. Give the number that is 21 less than the other number, if the other number is 57.
5. The farmer gathered 93 bananas in his orchard. 42 bananas were yellow. How many were not
yellow?
IV. Evaluation
Solve the following problems.
At the market, Mar, Kim, Mae and Ken helped their mother count the vegetables she has to sell.
They recorded the vegetables they counted.
Name Eggplants Tomatoes
Mar 88 76
Kim 32 54
Mae 59 67
Ken 27 15
Answer the following questions:
1. How many more eggplants did Mar count than Kim?
2. How many more eggplants did Mae count than Ken?
3. How many more tomatoes did Mar count than Kim?
4. How many more tomatoes did Mae count than Ken?
71. 65
5. How many more eggplants than tomatoes did Mae count?
Did you all get the answers correctly? What should you always remember every time you solve a
problem? Is it good to work fast? Why?
V. Assignment
Study the price list of fruits per kilogram then answer the questions that follow.
1. Which fruit is the cheapest?
2. Which fruit is the most expensive?
3. How much more expensive are apples than mangoes?
4. How much cheaper are oranges than ponkan?
5. How much cheaper are bananas than ponkan?
6. How much more expensive are mangoes than oranges?
7. Which is cheaper, mangoes or ponkan? How much cheaper?
8. Which is more expensive, oranges or bananas? How much more expensive?
Solving Two-Step Word Problems involving Addition and Subtraction of Whole
Numbers including Money
I. Learning Objectives
Cognitive: Solve two-step word problems involving addition and subtraction of
whole numbers including money
Psychomotor: Tell what is asked, what are given and the word clue/s to be able to
write the equation that will solve the problem
Affective: Participate actively in class activities
II. Learning Content
Skills: Solving two-step word problems involving addition and subtraction of
whole numbers including money
Reference: BEC PELC I C 3.1
Materials: flash cards
Value: Active participation
III. Learning Experiences
A. Preparatory Activities
72. 66
1. Drill (Mental Computation)
Conduct a drill in the basic subtraction and addition facts using flashcards with the shape
of a flower.
2. Review
“Subtraction with zero difficulty”
Two students compete with each other, trying to answer the equation mentally.
Sample equations: 600 – 426 = ______
900 – 810 = ______
2 000 – 1 593 = ______
Strategy:
a. Mentally, deduct one from the hundreds digit; change zeros to 9, except in the ones.
Change 0 in the ones place to 10.
Ex. 5 9 10
6 0 0
- 4 2 6
b. Subtract: 59
(10)
- 42 6
174
3. Motivation
Present a two-step word problem.
Mang Carlos picked 115 yellow mangoes and 73 green mangoes. He sold 56 mangoes in
all. How many mangoes were left to him?
B. Developmental Activities
1. Presentation
a. At this point, ask the class to recall the 4-steps on problem solving according to George
Polya:
Understand Plan Solve Look Back
b. Looking at the problem, elicit from the students the following:
■ Understand
a. What is asked? Number of mangoes left to Mang Carlo
b. What are given? 115 yellow mangoes, 73 green mangoes, sold 56 in all
73. 67
■ Plan
At this point, ask what question do we have to answer first to get the final answer?
This question is called “hidden question.”
■ Solve
What operation/s are needed to solve the problem? Addition; subtraction.
What equation will solve the problem?
115 + 73 – 56 = n
Which do we perform first?
Addition: 115
+ 73
188
then subtract 188
- 56
132 mangoes
■ Look back
Does our answer make sense?
Yes, since 132 is less than the total.
Yes, since the 2 steps used were to find the total number of mangoes first, then
the number of mangoes left.
Did we label it correctly?
c. Give another problem.
Regina has 80 eggs to sell. She sold 25 eggs in the morning and 46 eggs in the
afternoon. How many more eggs does she need to sell?
d. Ask:
1. What are given? 80 eggs in all to sell
25 eggs sold in the morning and 46 eggs in the
afternoon
2. What is being asked? Number of eggs Regina need more to sell
3. What operations are needed? Addition and subtraction or subtraction only.
4. What equation will solve the problem? 80 – (25 + 46) = n or
80 – 25 – 46 = n
5. Solve: 25 80 80 55
+ 46 - 71 or - 25 - 46
71 9 55 9
6. Check if the answer makes sense and if labeled properly.
2. Guided Practice
a. Activity: Column Relay
Present the following problem.
Daniel earned 35 by delivering water to several houses. He gave 15 of his
earnings to his mother and 12 to his sister. How much money was left to him?
Directions:
1. Divide the class into 6 groups. Each member will answer one column.
2. Give the first pupil a copy of the questions. He answers the question then passes the
copy to the second pupil. The second pupil answers the end question and then
passes the copy to the 3
rd
pupil and so on.
3. Read the problem posted on the board, then answer each question below:
a. What are given? ___________________________________
________________________________________________
b. What is being asked? _______________________________
74. 68
________________________________________________
c. What operation/s is/are needed to solve? _______________
________________________________________________
d. What equation will represent the problem? _________________
e. Solve the operation:
f. Label and look back.
b. Cooperative Learning Activity:
“Rally Table”
1. Group the class in pairs; players A and B.
2. Each member of the pair takes turn in answering the questions posted on the
board.
3. Present these problems on the board.
Rules:
Player A writes the hidden question.
Player B answers the hidden question.
Player A writes the equation that will solve the problem.
Player B answers/solves the equation.
1. Mang Carlos raised 35 piglets for sale. He sold 10 piglets to his mother
and 5 piglets to his friend. How many piglets were left to him?
2. Danilo arranged 564 books in the library. The next day, he arranged 345
books. There are 1 500 books in the library. How many more books will
Danilo arrange?
3. In the pupils’ government election, Alexis received 112 votes. Brylle
received 186 votes. The winner Joric received 312 votes. How many more
votes did Joric receive than Alexis and Brylle?
Do you think you can solve the problems without following the steps?
Was your solutions correct? Was your answer correct?
If your answer was not correct, in what part did you commit a mistake?
3. Generalization
What are the 4 important steps in solving word problems?
a. Understand the problem.
- Find the hidden question.
b. Make a plan.
c. Solve/carry out plan.
d. Look back.
C. Application
Direction.
Give each group a copy of the problems below on strips of paper.
Let each group solve the problems.
Write their solutions on the board.
Present the work afterwards
1. Mr. Javier has to deliver 760 sacks of rice. He delivered 510 to Mr. Rosales and 140 to
Mr. Acosta. How many more sacks of rice will be delivered?
75. 69
2. After spending 75.00 for a shirt and 125.00 for a pair of pants, Michelle had
50.00 left in her wallet. How much money did she have at first?
3. There are 246 yellow mangoes and 152 green ones. Out of these, 120 are in the basket
and the rest are in the crate. How many are in the crate?
4. Mang Luis is a farmer who sells coconuts and watermelons. He earned 843.00 from
selling coconuts and 832.00 from watermelons. Before going home, he bought 1 kilo
of pork for 120.00. How much money was left to him?
5. Mother and Lito picked tomatoes in their vegetable garden. Mother picked 19 tomatoes
and Lito picked 12. Mother used 5 tomatoes for cooking. How many tomatoes were left?
IV. Evaluation
Answer the following problems using Polya’s strategy.
1. Mr. Reyes gathered 365 mangoes on Monday and 453 on Tuesday. He sold 650 mangoes
on Wednesday. How many mangoes were left unsold?
2. A farmer harvested 425 sacks of palay. He sold 258 sacks to Buyer A and 120 to Buyer B
and kept the rest for his family. How many sacks of palay were left?
3. Rita bought a dress for 235.00 and a pair of shoes for 574.00. She gave a 1000-peso
bill to the cashier. How much is her change?
4. Alex wants to buy a T-shirt worth 185.00 and a school bag worth 240.00. He has only
300.00. How much more money does he need?
V. Assignment
Solve the following:
1. There are 262 boys and 528 girls in Grade Three. Out of these, 174 pupils are 10 years old.
How many pupils are not 10 years old?
2. Pia spelled 26 words correctly on Monday, 25 on Wednesday and 37 on Friday. If there are
100 words to be spelled, how many words did she misspell?
3. Rosalinda bought a bag for 165.00 and a pair of shoes for 395.00. How much change
did she get from 1,000.00?
4. A shoe factory in Marikina produced 235 pairs of shoes in one week and 324 pairs in another
week. If 450 pairs were delivered to a department store, how many pairs were not delivered?
5. Rose had a balance of 3,500.00 in her account in the bank. She deposited
1,200.00 the following month and withdrew 950.00. How much was left in her account?
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