lesson plans (repaired) (repaired) (repaired)

Numbers from 100 001 through Millions/Billions

I. Learning Objectives

Cognitive: Identify numbers from 100 001 through millions/billionsPsychomotor: Write numbers from 100 001 through millions/billionsAffective: Practice carefulness in writing numbers through millions/billions

II. Learning Content

Skills: 1. Identifying numbers from 100 001 through millions/billions2. Writing numbers from 100 011 through millions/billions

References: BEC – PELC I.A. 1.2Textbooks in Math 4

Materials: flash cards, chart, place value chart, set of numbers written on cards with cordValue: Carefulness

III. Learning Experiences

A. Preparatory Activities

1. DrillAsk for 10 volunteers. Give each a number tag. Have them wear the cord with

numbers from 0 to 9. Guide the pupils to form 3 – 6 – digit numbers. Ask the pupils who are sitting to read the numbers orally.

Example: a)

b)

c)

d)

e)

2. Review

Pick out the numbers less than 100 001 from the sets of numbers posted on the houses.

7 3 2 1 4

2 4 7

5 8 6 0 9

8 2 7 9 5

5 4 6 3 2 1

45 489

8 432 10 100

6 789 436 132

634 312

7 364 99 999

100 000 436 849

123 421

7 364 99 999

100 000 436 849

3. MotivationStart by playing “Guess What Number”. The teacher places the following statements

on the board.

a. My telephone number is “III II II – II III IIII”.b. The space capsule is circling the earth every “> > > IIIIII”c. I traveled “CDLXXIV” kilometers by motorcycle.

Do you think the sentences are easy to read and understand? Why?What numbers do you think these numerals represent?

B. Developmental Activities

1. Presentation

a. Read the data.

1) What is the given number? (2 904 487)2) How do we read it? (2 million, 904 thousand, 487)3) How do we write it in words? (Two million, nine hundred four thousand, four

hundred eighty-seven)4) Is the number easy to read and understand? Why? (Yes, because it is written in

standard form.)b. Presenting the place value chart.

MILLIONS THOUSANDS UNITShundreds tens ones hundreds tens ones hundreds tens ones

2 9 0 4 4 8 72

millions9 hundred thousands

0 ten thousands

4 thousands

4 hundreds

8 tens 7 ones

1) Give the digit in the one millions place, in hundred thousands place, ten thousands lace and so on.

2) Give the expanded form then give the value of each digit.

2. Guided Practice

Activity 1

Put a check (√) if the number is in millions and a cross (x) if it is in billions.

___ a) 6 386 798

Traffic in Metro Manila is heavy because nearly one-half of the 2 904 487 vehicles in the country are registered here.

___ b) 76 998 289 584___ c) 17 633 549

Activity 2

Write M if the number is in millions and B if it is in billions.___a) 89 679 289 548___b) 3 386 798___c) 456 126 834

Activity 3

Write a number on your paper that has 11 digits.1) 7 in the ten billions place.2) A digit that is 5 less than 8 in the one thousands place.3) 4 in the hundred millions place.

3. GeneralizationHow do you identify a number in million or in billion?

C. Application

Read the data. Write the number words in figures.1. One drop of blood contains about five million red blood cells.2. The human eye can see more than seven million, five hundred thousand color

differences.3. During an average lifetime, human heart beats about two billion, five hundred million

times.IV. Evaluation

A. Write T if the number is in thousands, M if it is in millions and B if it is in billions.

___ 1) 6 034 597 ___ 4) 52 758 137___ 2) 145 793 000 ___ 5) 425 010___ 3) 206 000 371 148

B. Examine the given numbers below. Write them in the proper place where they should belong. Be sure that the numbers in each column are written from the smallest to the greatest.

Million has three periods. It contains 7, 8 or 9 digits.

Billion has four periods. It contains 10, 11, or 12 digits.

15 086 912 305 674 981 643 212 002

17 196 741 014 357 296 324 899 120 741 019

BILLIONS MILLIONS THOUSANDS

V. Assignment

A. Study the given numbers. Copy the number which does not belong to the group.

1) 718 345 210 340; 151 968 254; 219 742 0362) 50 307 501; 500 897 621 543; 15 718 260 3453) 258 154; 508 476; 8 696 425 4) 3 274 503; 310 608; 2 830 4585) 450 187 402; 897 500 126; 2 247 364 869

B. Arrange each of the following sets of numbers starting from thousands, millions and billions place. Rewrite them on your paper.1) 4 759 248 804; 541 298; 532 689 012 4) 29 673 000; 127 683; 1 542 678 7252) 205 946 101; 423 543 103 811; 988 415 5) 75 942 376 055; 24 673 503; 898 1453) 726 054; 7 685 004 208; 8 684 452

Place Value


Cognitive: Give the place value/value of each digit in a 6- or more digit numberPsychomotor: Read and write numerals up to the hundred billions placeAffective: Participate actively


Skills: 1. Identifying the place value and value of each digit in a 6- or more digit number2. Reading and writing numerals up to the hundred billions

References: BEC – PELC I.A. 1.1Textbooks in Math 4

Materials: place value chart, number cards, number words, flash cardsValues: Active participation and being considerate

185 451 9 273 050 357 296 234 8 095 403 002


A. Preparatory Activities1. Drill

Have a drill in the form of a game

“Number Tag Game”a. Each group will have a set of numbers from 0 to 9.b. Pupils will form the number given by the teacher.

The number must be less than 6 digits.Example: 79 384

c. First group to form the digit will be the winner.

2. Review

Reading and writing numerals in the standard form using different ways.

“Matching Game”

Mechanics:Divide the class into 2 groups. A representative from each group takes turn in

answering or matching the numeral with its number name or word name.

A B37 1 thousand 3 hundreds 5 tens

6 ones145 Thirty-seven

1356 Eight hundred twenty-six thousand, one hundred forty-one

24 295 1 hundred 4 tens 5 0nes826 141 20 000 + 4 000 + 200 + 90 + 5

3. MotivationAsk the pupils why smaller pupils are seated in front while the bigger pupils are

seated at the back. Help the pupils realize that people must be considerate to get along well with others.


1. Presentation

a. Tell the pupils that numbers are like people. They can be grouped in many ways.b. Discuss the three ways in representing the numbers in standard form.

3 765

1) Word form: three thousand, seven hundred sixty-five2) Number and abbreviation form: 3th 7h 6t 5 ones3) Number and word: 3 thousands 7 hundreds 6 tens 5 ones

c. Show a place value chart which is up to the hundred billions place. Tell the pupils that our system of numeration has digits grouped in threes, we call them PERIODS.

Billions Millions Thousands UnitsHundred

sTens Ones Hundreds Tens Ones Hundred

sTens Ones Hundred

sTens Ones

2 0 6 4 3 7 6 1 2 9 7 5

2. Group Activity

a. Groups will be given activity sheets with the data below written on them.b. Tell them to follow the directions in writing the data.

Directions: give the place value and the value of the underlined digits

2 3 7 9 8 7 4 3 2 1 4 2

Digit Place Value Value

c. Showing more exercises in identifying the place value and value of each digit in a 6- or more digit numeral using number cards. (This will be done orally.)

Give the place value and the value of the digit 6 in each numeral:

a) 864 439 b) 826 453c) 6 82 975d) 86 451 197e) 126 458 360f) 26 974 431 100

d. Have a game on the different skills learned for the day.Do blackboard relay.

Divide the class in columns. Each pupil takes turn in writing the correct answer on the board. The column with the most number of correct points wins.Questions:1) What is the value of 6 in 64 395?2) What is the value of 4 in 1 462 587?3) In the numeral 45 376 192, what digit is in the one millions place?

4) What is the standard form of sixty-five billion, one hundred four million, two hundred thirty-seven thousand, eighty six?

5) What is the standard form for 9m 6hth 3tth 8h 7ones?

3. GeneralizationHow do you tell the place value and the value of each digit in a given number?

Valuing: Did you participate in the activities today?

Rate yourself: 5-highest and 1-lowest

C. Application

Write each digit of the given number in the place value chart.1) 144 7852) 27 436 1923) 3 007 518 692

Billions Millions Thousands UnitsH T O H T O H T O H T O

1)2)3)

IV. Evaluation

A. Give the value of each digit in the number 27 436 198.1) 2 ____ 5) 6 ____2) 7 ____ 6) 1 ____3) 4 ____ 7) 9 ____4) 3 ____ 8) 8 ____

B. Answer the following questions.

1. What is the place value of 6 in 642 321 104?a. Millionsb. Billionsc. Ten millionsd. Hundred billions

2. Give the place value of 3 in 77 585 230.a. Tensb. Thousandsc. Millionsd. Hundreds

3. What is the place value of the underlined digit in 72 490 321?

a. Hundredsb. Ten thousandsc. Hundred thousandsd. Tens

4. Give the place value of 0 in 70 243 265.a. Billionsb. Thousandsc. Millionsd. Hundreds

5. In 762 241 513 214, what digit has the place value of ten billions?a. 2b. 4c. 7d. 6

V. Assignment

Write the numbers up to millions/billions in the standard form.

Reading and Writing Numbers through Millions/Billions in Symbols and in Words


Cognitive: Read and write numbers through millions/billions in symbols and in wordsPsychomotor: Write numbers in words correctlyAffective: Participate actively in different activities


Skill: Reading and writing numbers through millions/billions in symbols and in wordsReferences: BEC – PELC I.A. 1.2Materials: flash cards, chartsValue: Cooperation

III. Learning ExperiencesA. Preparatory Activities

1. Drill

Reading of numbers.

242 186 246 386 187 623

305 160 65 187

2. Review

Teacher will dictate these numbers and pupils will write them in their show-me-cards.

682 468 23 694

3 743 7 218

946 569

3. MotivationHow many digits has 723 964 157 368?Can you write the number in words?


1. Presentation

a. Discuss1) How many square kilometers is the lad surface? Write it on the board.2) How many square kilometers have the water surface? Write it on the board.3) How many digits have the land surface area? How about the water surface area?4) Read the numbers.5) Write the numbers in words.

b. Read and write the word name for each numeral.1) 389 152 2472) 2 714 683 3893) 1 186 792 0534) 9 544 416 9365) 7 110 313 425

2. Group ActivitiesLet’s have a contest. “Groups 1 and 2 form your line. 5 members each group. ” (Infuse the

value of the active participation.) Get a number card in the box and match it with the word names in the pocket chart. Those who finish first should be commended.a) 85 312 914 677b) 18 000 777 283c) 109 067 214 511d) 87 782 570 308e) 5 112 914 000

3. Fixing Skills/PracticeRead and answer the following:a. The Bureau of Forest Development donated three seedlings each for school children all

over the country. The total number of seedlings was 15 223 564 821. Write this figure in words.

The land surface of the earth is 148 892 864 square kilometers and the water surface is 362 011 332 square kilometers.

b. Mrs. Luna’s shell craft factory used five hundred eighty-six million, three hundred twenty-four thousand, three hundred eighty-two shells in one year, write the number of shells in symbols.

c. Zero has no value. Can we just leave the space for zero vacant? Why?d. Is zero important in writing numbers?e. How would you write 204 000 785 083 in words?

Valuing: Did you participate in the activity? How? What did you share with your group? Do you also

practice this at home? How?

4. GeneralizationHow are numbers written in words?

IV. Evaluation

Read this numbers in words then write in symbols.

1. Four hundred thirty million, two hundred thousand, two hundred seventy___________

2. Fifty three billion, nine hundred twelve million, forty-five thousand, eight hundred seventeen___________

3. Write nine hundred fourteen thousand two hundred sixteen in figure.___________

4. How will you write twenty-nine million, eight hundred forty thousand, thirty-six in symbol?___________

5. Write six million, two hundred eighty thousand, two hundred sixty in symbol___________

Answer the following:

1. Write 8 352 641 in words.2. Which is the correct number words for 8 631 262?

a. Eight million six hundred thirty-one thousand two hundred sixty-oneb. Eight million sixty-one thousand two hundred sixty twoc. Eight million two hundred sixty twod. Eight million two hundred thousand

3. Write 265 386 426 in words.4. What is the number word for 721 326 117 214?5. Write 120 416 317 in words.

V. Assignment

The numbers are written in words in the same way that they are read.

A. Write the number in words.a. 6 463 342 264b. 520 175 786c. 23 596 384 103

B. Write the number words in symbols.a. Two billion, three million, five hundred thirty thousand, thirty-eightb. Five hundred one billion, one hundred seventy-six thousand

Rounding Numbers to the Nearest Tens


Cognitive: Round numbers to the nearest tensPsychomotor: Use a number line to show rounded off numbersAffective: Cooperate during group activities


Skills: Rounding numbers to the nearest tensReferences: BEC – PELC I.A. 2.1

Textbooks in Math 4Materials: charts, activity cards, number linesValue: Cooperation



2. Drill“Guessing Game”

Divide the class into 2 groups. All pupils will solve the given problem as fast as they can.The first pupil who gives the correct answer wins.a. My ones digit is 2. My tens digit is thrice the ones digit. My hundreds digit is four times the ones digit and my thousand digit is the sum of the ones and the tens digit. What number am I?b. I am an 8 digit number. My thousands digit is 9. My ten millions digit is 3. My hundreds digit is 6. The other digits are 0. What number am I?

3. Review

Write the place value and the value of the underlined digit in each of the following numbers.35 492 73 985789 143 785 19 432 156 000

4. Motivation

Read a news item that shows estimation.

Examples: Last week, a company manager called for a meeting. Almost 50 employees came.

Did the actual number of employees attend the meeting? What word was used which expressed an estimate? (almost)

The population in our school is about 2000 pupils. What word in the sentence expresses an estimate? (about)


1. Presentation

a. Read the problem carefully and then answer the question briefly.

1) Who is Rica? What does Rica need?2) How much money does she need for the school project?3) Where did she get the money?4) How much is her savings?5) What kind of a girl is Rica?

b. Present a number line showing numbers from 20 to 30.Draw a ring around 27. Ask: Is 27 closer to 20 or 30?

20 21 22 23 24 25 26 27 28 29 30

2. Analysis/Abstraction

Looking back at the number line, is 27 nearer to 20 or to 30? Number 27 is nearer to 30 than 20. So, if we round 27 to the nearest tens, it will become 30.

Valuing: How did you find the activity? What kind of a girl is Rica? Are you like Rica? Do you also save a certain amount from your daily allowance?

3. Fixing Skills

Let the pupils group themselves into 4 and perform the activities in the activity sheet. Emphasize the value of cooperation. Let them relate how they cooperate with other members of their group.

Group 1

Rica, a Grade 4 pupil needs 27php for her school project. She did not ask money from her parents because she has saved 30php from her daily allowance. What kind of a girl is Rica?

Original Number Rounded to the nearest tens154379326487

Group 2

Original Number Rounded to the nearest tens126342568269644853

Group 3

Original Number Rounded to the nearest tens1 3494 7848 6323 7867 755

Group 4

Original Number Rounded to the nearest

tens16 27728 16356 78833 15417 416

1.12

4. Generalization

How do we round off numbers to the nearest tens?

In rounding numbers to the nearest tens, look at the digit at the right of the tens digit. If the number is 5 or more, add 1 to the tens place, if the digit is less than 5, retain the tens digit. Change the ones digit to zero.

C. Application

Round the following to the tens place.

a. 342b. 4 638c. 5 419d. 28 326e. 49 749

IV. Evaluation

A. Answer the following questions.

1. Lyla has 38 rubber bands. Around how many rubber bands did Lyla have?a. 40b. 38c. 30d.45

2. Mother bought 44 apples. Around how many apples did mother have?a. 44b. 50c. 40d. 55

3. When 83 is rounded off to the nearest tens, 83 will become ____________.a.80b. 85c. 83d. 90

4. Round off 264 to the nearest tens.5. Round off 76 to the nearest tens.6.

B. Answer each question by rounding the given number to the nearest tens.

a. Lydia has 37 rubber bands. Around how many rubber bands does Lydia have?b. Mother bought 43 bananas. Around how many bananas did mother buy?c. Mang Tony gathered 94 eggs in the poultry farm. About how many eggs did Mang Tony

gather?d. If rounded to the nearest tens, 769 become ___.

V. Assignment

Round the following numbers to the nearest tens.

In rounding numbers to the nearest tens, look at the digit at the right of the tens digit. If the number is 5 or more, add 1 to the tens place, if the digit is less than 5, retain the tens digit. Change the ones digit to zero.

a. 362 f. 11 211b. 837 g. 18 788c. 5 742 h. 4 985d. 6 424 i. 343e. 9 654 j. 96

Rounding Numbers through Hundred Thousands


Cognitive: Round numbers to the nearest hundreds, thousands, ten thousands and hundred thousands

Psychomotor: State the rules in rounding numbers correctlyAffective: Find joy in working with others and doing something for others


Skill: Rounding numbers to the nearest hundreds, thousands, ten thousands and hundred thousands

References: BEC – PELC I.A. 2.2.2Textbooks in Math 4

Materials: chart, number cardsValues: Cooperation and friendliness



Teacher picks out numbers one at a time from a box. The task of each pupil is to round these numbers to the nearest tens.

Example: 37 rounds to 40

21 rounds to 20

2. ReviewHow do we round numbers to the nearest tens? Show examples on the board. What

are the rules in rounding numbers to the nearest tens?

3. Motivation

Which of the following numbers can be rounded to 400? 600?385 349 562 515 571

37

37


1. Presentation

Look at the table below and examine how the numbers 371 582 and 256 454 have been rounded.

Number Nearest Hundreds

Nearest Thousands

Nearest Ten Thousands

Nearest Hundred Thousands

371 582 371 600 372 000 370 000 400 000256 454 256 500 256 000 260 000 300 000


Discuss the given problem.a. What cities benefited from the Clean and Green Program of the government?b. How many residents benefited in the city of Makati? Pasay City?c. Round 371 582 to the nearest hundreds, thousands, hundred thousands.d. Round 256 454 to the nearest thousands, ten thousands, hundred thousands.

Let us try rounding numbers to the nearest: hundreds, thousands, ten thousands, hundred thousands.

3. Group Activities1. Round the numbers to the nearest hundreds and to the nearest thousands.2. Round the numbers to the nearest ten thousands and to the nearest hundred

thousands.c. 831 732d. 925 501e. 655 321 100f. 531 841 215g. 736 386 133

4. GeneralizationHow do we round numbers to the nearest hundreds, thousands, ten thousands and

hundred thousands.

C. Application

There are 371 582 residents in the city of Makati and 256 454 residents in Pasay City who are benefiting from the Clean and Green Program of the government.

Round up if the digit to the right of the digit to be rounded is 5, 6, 7, 8, and 9.

Round down if the digit to the right of the digit to be rounded is 0, 1, 2, 3, and 4

1. Round the following numbers to the nearest ten thousands then answer the questions that follow.a. 25 743 = _____ Did you round up or down?b. 15 652 = _____ Is your answer 20 000? How did you get the answer?c. 34 730 = _____ How will you round to the nearest thousands?d. 76 348 = _____ Did you roundup? Why?e. 89 192 = _____ Is the answer 80 000? Why? State the rule.

2. Read the following situations below. Tell whether the number has an exact value or an estimated value.a. Mrs. Reyes lives at 10 Monte de Piedad Street.b. There were 1 275 people at the auditorium.c. Karen’s student number is 15 031.d. In school, there were about 150 seats at the cafeteria.

IV. EvaluationA. Encircle the letter of the correct answer.1. If you round 9 477 to the nearest hundred, what is the answer?

a. 4 000b. 9 000c. 9 400d. 9 500

2. Round off 394 634 to the nearest thousands.a. 395 000b. 394 000c. 390 000d. 396 000

3. 1 745 384 rounded to the nearest ten thousand is ______.a. 174 540b. 1 745 000c. 1 700 000d. 1 750 000

4. When you round off 137 573 to the nearest ten thousands, it will be _______.5. The population of Brgy. Masikap is 637 268.

Round off the figure to the nearest hundred thousands. _________

B. Round each of the following to its nearest specific place value.

Numbers Ten Thousands Hundred Thousands1) 127 5632) 486 1703) 816 3424)374 1395)732 256

V. Assignment

Round the number to the place value of the underlined digit.

a. 238 789 d. 793 948b. 3 94 634 e. 943 431c. 545 381

Rounding Numbers to the Nearest Millions and Billions


Cognitive: Round numbers to the nearest millions and billionsPsychomotor: Tell numbers rounded off to the nearest millions and billionsAffective: Appreciate the importance of being thrifty

II. Learning ContentSkills: 1. Rounding numbers to the nearest millions and billions

2. Identifying numbers rounded off to the nearest millions and billionsReferences: BEC – PELC I.A. 2.2.3

Textbooks in Math 4Materials: flash cards, activity cardsValue: Thriftiness



1. DrillReading numbers through millions/billions

2. ReviewHow do we round numbers to the nearest hundred thousands?Recall the steps in rounding numbers to its nearest specific place value.

3. MotivationHave you been to a cement factory? What did you see there? Do you have an idea

about the number of bags of cement that can be manufactured in a month?

B. Developmental Activities1. Presentation

Read and understand the story on the activity card carefully.

Mary’s Cement is a big factory. It supplies cements to the whole country. Last year, Mary’s Cement delivered a total of 64 768 117 bags to Visayas and Mindanao. About how many bags of cement were delivered in all?

a. What products does Mary’s Cement Factory have?

b. Is cement manufacturing a good business? Why?c. Why do most people buy cement?d. What was the actual number of cement delivered to Visayas and Mindanao?e. What will the number be if rounded off to the nearest ten millions?f. How did you get 60 000 000?g. Which of these rules do you use?

Round up if the digit to the right of the digit in the millions place is 5, 6, 7, 8, or 9.Round down if the digit to the right of the millions place is 0, 1, 2, 3, or 4.

Show and discuss another problem in the class.

One of the wealthiest men in Asia opened a savings account in the Philippine bank with an initial deposit of 25, 643, 914, 377php. About how much is his deposit in the bank?

a. Who opened a savings account in a bank?b. Why do you think he keeps his money in the bank?c. About how many billions was his initial deposit?

Valuing:

If you have a plenty of money, what will you do? Will you save some of it? If you have a little money, will you still save? Why?

How would your savings affect your life in the future?

Let the pupils show their work on activities 1 & 2 on the board.

Activity 1

Number64 768 117

Nearest Millions65 000 000

Activity 2

Number25, 643, 914, 377php

Nearest Billions26 000 000 000php

2. Guided PracticeLet us play a game. For 2 groups of pupils, the yellow group and the red group. The

group who can round the numbers first to the nearest millions wins. Are you ready now? The numbers are inside the boxes in front of your group.a. 8 856 000 f. 23 431 785b. 4 180 374 g. 42 683 360 c. 9 793 205 h. 75 413 000d. 6 316 348 i. 17 938 172e. 2 630 539 j. 136 715 340

Do the same in billions. Call on the pupils who did not participate in the first game then give them the same directions stated in the first activity. The numbers are inside the box. Play blackboard relay.

a. 2 942 628 f. 23 592 176 302b. 5 341 707 333 g. 47 234 346 532c. 14 603 100 784 h. 92 739 316 035d. 6 421 125 000 i. 16 484 148 703e. 17 725 823 421 j. 345 800 000 145

Winners should be commended.

3. GeneralizationHow do we round numbers to the nearest millions/billions?

C. Application

Round off to the nearest millions/billions.

Number Nearest Millions Nearest Billions6 831 462 126 a. f.2 124 549 314 b. g.8 314 183 512 c. h.27 573 976 249 d. i.15 439 873 831 e. j.

IV. EvaluationA. Choose the letter of the correct answer.

1. During the Christmas season, a hotdog company delivered 3 745 000 bags of hotdogs to 3 986 rolling stores all over the Metro Manila. Round 3 745 000 to the nearest millions.a. 4000b. 3 000 000c. 4 000 250d. 4 000 000

2. A certain tire supplier distributes different sizes of tires all over the country. The number of tires is supplied 236 435 677. How will you round this number to the nearest hundred millions?a. 236 000 000b. 200 000 000c. 240 000 000d. 300 000 000

B. Name the place value in which the following numbers are rounded. 1. 287 455 rounded to 290 000 _________2. 27 643 189 rounded to 28 000 000 _________3. 458 096 245 rounded to 500 000 000 _________

Round up if the digit to the right of the millions/billions place is 5, 6, 7, 8 and 9.

Round down if the digit to the right of the place to be rounded is 0, 1, 2, 3 and 4.

4. 35 613 827 549 rounded to 35 610 000 000 _________5. 57 924 603 285 rounded to 58 000 000 000 _________

V. AssignmentThe table gives the distance of the five planets from the sun. Round the figures to the nearest hundred millions and nearest billions.

Planet Distance from the sun in kilometers

Nearest Hundred Millions

Nearest Billions

1. Jupiter 778 300 0002. Saturn 1 427 000 0003. Uranus 2 869 600 0004. Neptune 4 496 700 0005. Earth 150 000 000

Adding Numbers through Billions without Regrouping


Cognitive: Add 6- or more digit numbers with 4- or more addends with sums through billions without regrouping.

Psychomotor: Write large numbers in column and add them correctlyAffective: Show accuracy with numbers

II. Learning ContentSkills: 1. Adding 6- or more digit numbers with 4- or more addends without

regrouping2. Writing large numbers in column.

References: BEC – PELC I.B. 1.1Textbooks in Math 4

Materials: chart with exercises, drill cards, picture of vegetable gardenValues: Accuracy and diligence



1. DrillBasic addition factsAdminister A – 1 card. Record pupils’ errors.

2. Review a. Review or have a game on identifying the terms used in addition. (sum, addends, plus,

put together, more, more than, combine, total, add, added to)b. Solve this math problem.

What is the sum of 450 712 and 113 210? Discuss the steps in adding large numbers.3. Motivation

Show a picture of vegetable garden. What vegetables are planted in the garden? Do you want to read a short story about this?

B. Developmental Activities1.Presentation

Problem Opener

How will you find the answer? Guide the pupils in stating the mathematical sentence 230 212 + 120 413 + 111 201 + 111 142 = n, where n is the total number of kilograms of vegetables.

Ask the pupils to write the numbers in column.

Add the ones Add the tens Add the hundreds

Add the thousands

Add the ten thousands

Add the hundred thousands

230 212 230 212 230 212 230 212 230 212 230 212120 413 120 413 120 413 120 413 120 413 120 413111 201 111 201 111 201 111 201 111 201 111 201110 142 110 142 110 142 110 142 110 142 110 142

8 68 968 1 968 71 968 571 968Check by adding upward.

230 212120 413111 201111 142 571 968

Valuing:Stress the value of accuracy and diligence when writing each digit in its proper column.

2. Guided PracticeGroup yourselves into 4 groups. Add the addends to get the sum. Do it as fast as you can with accuracy. The first group to finish the exercise will do the “bomb clap”.

a. 1 041 002 b. 2 152 1012 301 025 1 304 0243 113 210 34 101 641

+ 2 120 241 + 51 012 033

c. 23 612 111 d. 3 016 215 21051 024 125 1 151 030 02412 152 021 2 530 410 153

+ 501 201 532 + 1 202 234 502

Mt. Province is home for what we call Baguio Vegetables. Everyday, it produces 230 212 kilograms of potatoes, 120 413 kilograms of beans, 111 201 kilograms of cabbage and 110 142 kilograms of carrots. How many kilograms of vegetables does the province produce daily?

Give more exercises. Write in column then add.a. 410 + 102 123 + 201 021 + 104 213b. 3 240 120 + 1 211 103 + 50 213 132 + 424 104 213c. 102 022 011 + 301 531 120 + 3 421 013 104 + 2 103 213 453

3. Generalization

How do we add large numbers?

C. ApplicationSolve this problem.

A progressive farmer kept an accurate record of his sales in his vegetable garden for five years. His yearly sales amounted to 156 572php, 400 203php, 10 102php, 211 001php and 121 121php. What was the total amount of his sales for the last five years?

IV. EvaluationRead the following then choose the letter of the correct answer.

1. When you add 12 301; 23 135; 13 352 and 215 053. What is the sum?a. 236 741b. 263 741c. 263 147d. 237 641

2. What is the total number of 202 268; 102 963 and 400 738?a. 705 989b. 405 989c. 705 998d. 750 989

3. If you put together 194 870 cans of milk and 102 201 cans of sausages, what is the result?a. 707 291b. 972 071c. 792 107d. 297 071

4. Add 87 593 to the sum of 903 846 and 815 489.5. What is 2 243 more than the sum of 13 458 and 21 387?

V. Assignment

Write in column then add.a. 313 112 + 201 003 + 8 241 301 + 71 203 021

In adding large numbers, write the addends in column, add the digits in the ones first, then the tens, the hundreds and so on. Continue up to the last digit. Write the sum under each column.

b. 24 321 213 + 721 034 120 + 102 512 504 + 7 112 021 012c. 27 123 614 + 111 222 331 + 110 141 303 + 6 221 232 241d. What is the result when 8 256 115, 987 140 and 12 721 234 are put together?e. A number added to 87 463 gives a result of 298 685. What is the number?

Adding Numbers through Billions with Regrouping

I. Learning ObjectivesCognitive: Add 6- or more digit numbers with 4- or more addends with sums through billions

with regroupingPsychomotor: Give the sum of 6- or more digit numbers with 4 addends with sums through

billions with regroupingAffective: Help the community in the “clean and green ” project

II. Learning ContentSkills: 1. Adding 6- or more digit numbers with 4- or more addends with sum through

billions with regrouping2. Giving the sum of 6- or more digit numbers with 4 addends with sums through billions with regrouping

References: BEC – PELC I.B. 1.2Textbooks in Math 4

Materials: flash cards, chart with problemsValue: Helpfulness


1. DrillBasic Addition Factsa. Do the relay game.b. Divide the class in groups of 10. Each pupil in the group will take turn in answering the

flash cards with addition facts on the board. The group who finishes first with the most number of correct points wins.

2. ReviewAdd the following:

1 203 121 0232 102 312 1122 351 213 312

+ 3 121 000 121

3. MotivationHave you experienced staying in the field harvesting fruits? What things did you

see around? What did you feel when staying in the place with fresh air and plenty of fruits?

Valuing: What should you do to keep your community clean and green?


Read the problem silently. Answer the questions that follow.

Questions:

a. How many towns harvested a big number of coconuts?b. How many coconuts were harvested by the farmers in the first town, second, third and fourth?c. What is asked in the problem?d. What are we going to do to solve the problem?e. What will you add?f. What is the answer to the problem?g. What is the label for the final answer?

Discussion:Present the table to the pupils. Ask them to follow the steps by column to illustrate the process in adding the numbers.

Add the ones

Add the tens

Add the hundreds

Add the thousands

Add the hundred

thousands

Add the one millions

Add the ten

millions

Add the hundred millions

1434 136 724158 122 386

3 150 924+ 1 425 260

4

1434 136 724158 122 386

3 150 924+ 1 425 260

94

11434 136 724158 122 386

3 150 924+ 1 425 260

294

211434 136 724158 122 386

3 150 924+ 1 425 260

5 294

1211434 136 724158 122 386

3 150 924+ 1 425 260

35 294

11211434 136 724158 122 386

3 150 924+ 1 425 260

835 294

112 11434 136 724158 122 386

3 150 924+ 1 425 260

6 835 294

1 112 11434 136 724158 122 386

3 150 924+ 1 425 260

596 835 294

a. What are the given facts?b. What operation did you use to find the answer?c. What did you do when the sum in each place value is 10 or more?d. What is the final answer?

What can you say about the farmers of the 4 towns? (industrious, hardworking)

2. Guided Practice (Group Activities)

Find the sum.

Farmers in the 4 towns of Quezon harvested a big number of coconuts. Farmers in the first town harvested 434 136 724 coconuts, the second 158 122 386, the third 3 150 924 and the fourth 1 425 260. Find the total number of coconuts harvested by the farmers in the 4 towns.

You and your partners will add in two ways. One going down and the other are going up. As soon as you have finished, say the word “yes!”

a. 132 416 430 b. 186 433 840329 854 932 249 678 432461 503 006 123 456 789

+ 892 756 834 + 148 385 108

c. 400 600 500 d. 302 120 612 700 300 899 674 531 421456 832 627 61 478 523

+ 863 442 816 + 527 347 618

e. If the addends are 87 463 129, 458 645 and 35 185 687, what is the sum?f. What is the sum of 275 146 and 3 798 347?

3. Generalization

How do we add large numbers with regrouping?

C. Application

Find the answer.

IV. EvaluationRead then find the sum.

1. The sum of 1 245 368; 997 465 and 943 524 is ______________.a. 2 557 889b. 2 000 557 889c. 755 988d. 5 257 889

2. Put together 746 257 835; 844 758 560; 348 369 102 and 561 567 134. ________________.a. 2 005 952 361b. 5 205 925 361c. 2 500 952 631d. 5 200 259 136

In adding large numbers with regrouping, add the ones first, the tens, the hundreds, and continue up to the millions and billions. Regroup in all places if necessary.

As a Christmas project for the needy, the government spent 223 300php for rice, 121 000php for sugar, 524 050 for sardines and 405 270 for milk. What was the total expense of the government for its Christmas project?

3. Find the total number of 136 031 647; 330 141 445; and 341 319 303. ______________a. 749 802 599b. 807 294 395c. 708 294 593d. 807 492 395

4. If you will add 312 964 758; 574 532 643; 628 345 124 and 843 237 412. What is the answer?5. 583 236 205 more than the sum of 123 841 523; 481 325 108 and 248 248 316. ___________

V. Assignment

Solve this problem.

1. What are the canned goods stated in the problem?2. What canned good has the biggest number?3. Write the number sentence.4. Solve for the sum.

Commutative Property of Addition

I. Learning ObjectivesCognitive: Identify the commutative property of addition used in an equationPsychomotor: 1. Write commutative property in two ways

2. Supply the missing number in a given equationAffective: Manifest thoughtfulness during special occasions

II.Learning ContentSkill: Comprehension of the commutative/order property of additionReferences: BEC – PELC I.B.2.1

Textbooks in Math 4Materials: bean seeds, corn seeds, stones, marbles, bottle caps, straw, popsicle sticksValue: Thoughtfulness

III.Learning Experiences


1. DrillWarm up Exercises (Number game involving addition)“I am thinking of a number”Example:I am thinking of a number, my first digit is 5 and the second is 6, what number am I?

A big warehouse has stocks of canned goods. There are 623 405 234 cans of sardines, 731 065 823 cans of milk, 136 291 629 cans of corned beef, 786 341 098 cans of green peas, and 600 493 587 cans of meatloaf. If you were the stockman, how would you know the total number of canned goods?

2. ReviewAddition facts using flash cards.

3. Motivation

What did Ana give?

If somebody asks you about the total number of roses, what should you do?


a. How many red roses were given? How about the white roses? What is the total number of roses?

b. Write the number sentence.1. (red + white)2. (white + red)

c. Does the sum change? Why?Let’s find out.

2. Group Activity

Divide the pupils into 3 groups.

Group 1Illustrate the given facts in the problem by following these directions.a. Draw the given data.

Write the number sentence for the given data.b. Change the positions of the given data, does the sum change? Why?

Group2a. Express the mathematical sentence using the mathematical sticks.b. Change the order of the data, tell if the sum changes also.c. Explain why the sum did not change.

Group 3a. Use the bean seeds to express the mathematical phrase for the problem.b. Change the order of the given data.c. Tell if the sum changes.

3. Analysis/AbstractionHow did you write the given data?

36 +44

44 +36

62 +29

29 +62

Ana gave her teacher 9 white roses and 8 red roses because it’s her birthday. How many roses did she give her?

How did you draw it?Can you change the position of the data or the given facts?What happens to the sum if you change the order of the numbers?

+

4. Practice ExercisesWrite each of the following in its opposite order.

a. + = _____ + _____

b. + = _____ + _____

c. _____ + _____ = 10 + 12

d. 15 + 10 = _____ + _____

e. Mario gathered 25 blue marbles and 18 yellow marbles. How many marbles were gathered? Express/give the mathematical sentence in two ways.

5. GeneralizationWhat is commutative property of addition?

C. Application

Give the missing numbers.

1. 17 + ____ = 9 + 172. 20 + 45 = ____ + 203. ____ + 19 = 19 + 184. 23 + ____ = 17 + 235. 68 + 49 = 49 + ____6. Jose gathered 48 big bamboos and 28 small bamboos for his poultry house. How many

bamboos did he gather? Show the addition sentence in two ways.

9 + 8 = 178 + 9 = 17

9 8+8 + 917 17

IIIII III

00000000

00000

Commutative property of addition – Changing the order of the addends does not change the sum.

IV. Evaluation

Give the missing numbers.1. 46 + ____ = 93 + 462. 60 + 80 = 80 + ____3. 23 + ____ = 17 +234. 60 + 94 = 94 + ____5. Fred mixed 28 kilograms of corn grits and 25 kilograms of soya beans. How many kilograms of

feeds did he mix? Show the addition sentence in two ways.6. 73 + 20 = ____ + 737. 24 + ____ = 12 + ____8. ____ + 18 = ____ + 139. 124 + 27 = 27 + ____10. 79 + ____ = 25 + ____

V. AssignmentA. Write the addition sentence in 2 ways.

1.

+

2.

+

B. Give the missing numbers.

1. 7 + 10 = ____ + 72. 17 + ____ = 10 + 17

C. Ben harvested 73 eggplants and 94 pieces of okra. How many pieces of vegetables were harvested? (Show your solutions in two ways.)

Associative Property of Addition


Cognitive: Show the associative property of additionPsychomotor: Supply for the missing numberAffective: Participate actively in any group activity

II. Learning Content:

Skills: 1. Showing the associative property of addition2. Supplying the missing number

References: BEC – PELC I.B.2.2Materials: chart, activity sheet, drill cards, cutout of shapesValues: Cooperation and active participation



1. Drill/Review

Mental Activity

Supply the missing number (asking one another).

a. 9 + ____ = 16 d. 24 + ____ = 30____ + 9 = 16 ____ + 24 = 30

b. ____ + 6 = 15 e. ____ + 23 = 486 + ____ = 15 23 + ____ = 48

c. 18 + ____ = 35 f. 32 + 40 = ________ + 18 = 35 40 + 32 = ____

What property of addition did you apply? State the rule.

2. Motivationa. How will you learn better? b. How can your group perform well?


Activity SheetRead carefully and do as instructed.a. Inside the envelope are cutout materials which you are going to use in the activity.b. Make a group of three green shapes, 4 red shapes and 7 yellow shapes. What is the

sum? Write the addition sentence for this.c. Show 2 ways in finding the sum without changing the order of the numbers. Explain

how you grouped the numbers.d. What can you say about the sum of the numbers after grouping them in two different

ways?

e. Write the two ways of grouping the numbers.

2. Discussion/Abstraction

(Each group presents and explains their work.)(3 + 4) + 7 = 3 + (4 + 7) 15 + (10 + 3) = (15 + 10) + 3

7 + 7 = 3 + 11 15 + 13 = 25 + 3 14 = 14 28 = 28

In the given addition sentences, which are the same? What are different? When you change the way in which the addends are grouped, does the sum change? Why?

3. Guided Practice1) Give the missing number.

Example:

(3 + 4) + 6 = 3 + (4 + 6) = 13 7 + 6 = 3 + 10 = 13

a. (8 + 3) + 5 = 8 + (___+ 5) = ______ + 5 = 8 + ___ = 16

b. 4 + (9 + 7) = (4 + 9) + ___ = ___4 + ___ = ___ + 7 = ___

c. (12 + 3) + ___ = 12 + (3 + 8) = ___15 + ___ = ___ + 11 = ___

2) Use the associative property for the following:a. Use the addends 9, 8, and 5. Write two different addition sentences then

solve each.b. Use 35 as your sum. The first addend is 17. What are the two addends, if

the second is 2 more than the first addend? Solve it in two ways.

4. Generalization

What is the associative property of addition?

Changing the grouping of addends does not affect the sum.

C. Application

Write the missing number.a. ___ + (3 + 4) = 12 b. 6 + (___ + 4) = 20 e. 7 + (9 + ___) = 21

(___ + 3) + 4 = 12 (6 + ___) + 4 = 20 (7 + 9) + ___ = 21

c. 7 + (9 + ___) = 21 d. (___ + 6) + 2 = 15(7 + 9) + ___ = 21 ___ + (6 + 2) = 15

IV. Evaluation

Write the missing number.a. 7 + (5 + 6) = (7 + 5) + 6 b. (7 + 3) + 12 = 7 + (3 + 12)

7 + ___ = ___ + 6 ___ + 12 = 7 + ___ ___ = ___ ___ = ___

c. (9 + 7) + 20 = 9 + (7 + 20) d. What is the other addend if one group is 9 + 8 ___ + 9 = 9 + ___ and the sum is 45? Write the number ___ = ___ sentence and solve it.

e. (13 + 6) + 9 = 13 + (6 + 9) f. (10 + 7) + 3 = 10 + (7 + 3)___ + 9 = 13 + ___ ___ + 3 = 10 + ___ ___ = ___ ___ = ___

V. AssignmentIdentify the property of addition used in each equation. Write your answer on the blank provided for.

a. 3 + 4 = 4 + 3 _________b. 9 + (8 + 7) = (9 + 8) + 7 _________c. 20 + 47 = 47 + 20 __________d. 35 + 18 = 18 + 35 __________e. 76 + (30 + 70) = (76 + 30) + 70 _________

Identity Property of Addition

I. Learning ObjectivesCognitive: Identify the identity property of addition used in an equationPsychomotor: 1. Write the addition sentences showing the identity property of addition

2. Supplying the missing number in a given equationAffective: Show sportsmanship during games/activities

II. Learning ContentSkills: 1. Identifying the identity property of addition

2. Supplying the missing number

Reference: BEC – PELC I.B.2.3Materials: flash cards, written exercises on a cartolinaValue: Sportsmanship


1. Drill (Emphasize sportsmanship during the game)

Do the following exercises in the form of a race. Form two lines. Teacher shows the flash cards. Pupils give the answers orally. Pupils make one step forward for every correct answer.a. 26 54 43 35 46 51 24 +53 +33 +24 +44 +42 +28 +63

b. 55 28 37 31 62 35 63 +33 +41 +30 +57 +27 +57 +34

2. Review

Give the property of addition shown in each equation below. Write your answer on the blank provided for.a. 23 + 68 = 68 + 23 ________b. 13 + (10 + 30) = (13 + 10) + 30 ________c. 96 + 22 = 22 + 96 _________d. 38 + 19 = 19 + 38 _________e. (50 + 12) + 6 = 50 + (12 + 6) ________

3. Motivation Ask what happens if a number is added to zero. Show the equations on the board.

I II10 + 0 = ______ 0 + 70 = ______192 + 0 = ______ 0 + 66 = ______35 + 0 = ______ 0 + 37 = ______62 + 0 = ______ 0 + 88 = ______


a. Read the exercises written on a cartolina or in the blackboard.b. Answer the exercises as fast as you can.

c. Ask: What do you observe about the equations under column I? What can you say about the equations in column II?

d. Focus the children’s attention on the numeral 0. Ask: What is the sum when zero (0) is added to a number? What about when a number is added to zero?

e. Introduce the term identity property of addition.

2. Group Activities

a. Fill the correct 1) 6 + 0 = ___2) 3 + ___ = 33) 12 + ___ = 124) ___ + 69 = 695) 80 + ___ = 80

b. Put a check (√) on the blank provided for if the equation shows the identity property of addition and a cross (x) if it does not.______1. (36 + 21) + 5 = 36 + (21 + 5)______2. (13 + 19) + (65 + 25) = (65 + 25) + (13 + 19)______3. 1888 + 0 = 1888______4. (67 + 93) + 16 = 16 + (67 + 93)______5. 0 + 820 = 820

c. Supply the missing number then write the property of addition shown on the blank before each number.

______1. 88 + 0______2. (86 + 39) + 7 = ___+ (39 + 7)______3. ___ + 270 = 270______4. 78 + ___ = 78______5. 3000 + 0 = ___

3. Generalization

What is identity property of addition?

C. Application

Fill in the correct answer.1. 8 + ___ = 82. 45 + 0 = ___3. ___ + 21 = 214. 5 + 0 = ___5. 36 + 0 = ___

IV. Evaluation

Zero is the identity element for addition. When zero is added to any number, the sum is the number.

A. Supply the missing number that will make each equation correct.1. 628 + 0 = ___2. ___ + 711 = 7113. 564 + ___ = 5644. ___ + 128 = 1285. 323 + 0 = ___

B. Encircle the number of the equation showing the identity property of addition1. 420 + 0 = 4202. 926 + 24 = 24 + 9263. 372 + (35 + 63) = (372 + 35) + 634. 0 + 306 = 3065. 821 + 0 = 821

C. Complete each equation. Write IPA on the blank if the equation shows the identity property of addition.______1. 150 + 0 = _________2. 370 + ___ = 370______3. 26 + 800 = 800 + 26______4. (85 + ___) + 90 = 85 + (20 + 90)______5. ___ + 922 = 922

V. AssignmentA. Write the number that will make each equation correct.

1. 62 + 0 = ___ 6. ___ + 1250 = 12502. 121 + ___ = 121 7. 728 + ___ = 7283. 550 + 0 = ___ 8. 230 + ___ = 2304. 236 + ___ = 236 9. ___ + 552 = 5525. ___ + 801 = 801 10. 525 + ___ = 525

B. Write 10 equations showing the identity property of addition.

Estimating the Sum

I. Learning ObjectivesCognitive: Estimate the sum of 6- or more digit addendsPsychomotor: Illustrate how to find the estimated sum of 6- digit addendsAffective: Appreciate the importance of working hard

II. Learning ContentSkill: Estimating the sum of 6- or more digit numbersReferences: BEC – PELC I.B.2

Textbooks in Math 4Materials: pictures, pocket chart, colored chalk, show-me-card or drill board

Values: Hard work, perseverance



1. DrillBasic addition facts using flash cards.

9 +7 9 + 4 4 + 7 9 + 68 + 3 8 +6 6 + 5 8 + 87 + 5 7 + 9 8 + 5 7 + 9

2. Review“Rounding off numbers to the nearest 10 000 to 100 000”

Play “Pass the paper game.” Each pupil in the column takes turns in rounding numbers as fast as correctly as they can. Check answers in class.

3. Motivation

Show picture of farmers working in a farm or coconut plantation. What do you see in the picture? What does the farmer do to have a good quality harvest? Can you tell the number of coconuts seen in the drawing?


Mang Mario has a coconut plantation. He usually works in his farm the whole day. He harvested 11 389 coconuts in the first month and 15 481 coconuts on the second month. About how many coconuts did he harvest in 2 months?

Analyze and solve the given problem.a. What is asked in the problem?b. What are the given facts?c. What is the operation needed?d. What is the number sentence?e. What kind of a farmer is Mang Mario? What benefits could we get if we work hard?

If you’re given a task, do you work on it? 11 389 10 000 First round the addends to the nearest+ 15 481 20 000 ten thousand then add the rounded

30 000 numbers to get the estimated sum

2. Group Activitiesa. Work with a partner. One will get the exact sum and the other will estimate the sum

to the highest place value. (Use your drill board.)1) 594 2) 3 978 3) 5 928 4) 783 5) 1 397+ 678 +5 697 +1 436 +492 + 1 280

b. Estimate the sum of each to the highest place value.1) 25 635 2) 36 403 3) 43 321 4) 18 476 5) 611 175

+46 780 + 53 296 +52 085 + 20 581 + 258 806

c. Below are the prices of some school supplies. Use your estimation skills to answer each of the questions without using paper and pencil.Ballpen 4.50 Glue 18.50Pad paper 19.00 Pencil case 21.25Ruler 10.50 Math notebook 21.25Pentel pen 35.25 Pencil 5.25Crayons 28.25

1. About how much will a box of crayons and a pencil case cost?2. Randy has 50.00php. Has he enough money to buy one pad paper, crayons and a

math notebook?3. You have 50.00php. What three things can you buy?4. What can you buy if you have 20.00 bill?5. You have 100.oophp. How many math notebooks and pad paper can you buy?

3. GeneralizationWhat are the steps involved in estimating sums of 6 or more digit addends? How

do you estimate? How would you come up with a good estimate?

C. Application

Solve the problem.

Mrs. Dayo’s poultry farm produced 236 378 eggs in 1997 and 147 932 eggs in 1998. About how many hundred thousands of eggs were produced in two years?

IV. EvaluationA. Round each addend to the highest place value. Then add.

a. 713 156 b. 138 819 c. 514 912 d. 614 346 e. 192 143+291 724 +861 412 +813 125 + 201 223 + 361 414

B. Estimate the sum of the following numbers:1. Estimate the sum of 56 435 and 90 845.

a. 150 000b. 350 000c. 500 000d. 100 000

2. If you will use your estimation skills in addition, what is the answer for 287 254 and 245 812?

Round addends to the nearest highest place value then add. A good estimate is a little less or more than the exact answer.

a. 250 000b. 300 000c. 500 000d. 600 000

3. When you add 54 231; 30 685 and 33 751. What is the estimated sum?a. 100 000b. 200 000c. 110 000d. 210 000

4. What is the approximate total of 1 010 000, 298 000 and 165 380? ________5. Find the estimated sum of 61 241, 21 836 and 45 091. _______

V. Assignment

A. Estimate then find the exact sum.1) 56 435 2) 456 412 3) 74 825 4) 21 165 5) 63 729

+ 90 845 +141 708 + 9 567 + 3 270 + 23 878

B. Write the addends in column then estimate the sum.1. 156 + 290 8452. 829 + 246 7233. 871 702 + 249 5814. 379 405 + 845 563

Adding Mentally 2- to 3-Digit Numbers with Sums Up to 300

I. Learning ObjectivesCognitive: Add 2- to 3-digit numbers mentally with sums up to 300 without

regroupingPsychomotor: solve for the sum of 2- to 3-digit numbers mentallyAffective: Appreciate the value of trees and other plants around us

II. Learning ContentSkill: Adding mentally 3- digit numbers with sums up to 300References: BEC – PELC I.B.3

Textbooks in Math 4Materials: flash cards, number cards, window cardsValue: Appreciation of nature



113 + 174 =

111 + 178 = 186 + 113 =

124 + 165 =100 + 200 =

165 + 123 =

140 + 140 =

152 + 36 = 116 + 170 =125 + 34 =

1. Drill

“Game in Basic Addition Facts Using Flashcards”

Relay game by pairs.

2. ReviewEstimate the sum of each item orally.

312 143 163 192 676 780 816 136 376 762+ 291 + 414 + 681 + 271 + 215 + 342 +415 + 861 + 213 + 134

3. MotivationAre trees and other plants important to us? Why? What do trees and other plants give us? Do you take care of our trees and plants? In what way?


1. PresentationProblem Opener

2. Group Activitiesa. Activity 1

1. What kind of trees is found in the orchard?2. Can you name them?3. How would you get the total number of trees in the orchard?4. Do you need to use paper and pencil?5. Can you solve for the final answers mentally? How?

b. Activity 2

Let us help the baby go up and down the stairs by adding the equations mentally as fast as you can.

In an orchard, there are 125 avocadoes and 173 mango and santol trees. How many trees are there in all?

3. Generalization

What is the fastest way in solving for the sum mentally? Recall once again the steps.

C. Application

Add the following numbers mentally.1) 246 2) 270 3) 153 4) 146 5) 134

+52 + 25 + 136 +150 + 45

6) 278 7) 189 8) 164 9) 123 10) 265 + 10 + 100 + 133 + 76 + 34

Use window cards with 2- to 3-digit numbers with sum up to 300.

IV. EvaluationA. Teacher will flash a card one at a time in class. The task of each pupil is to write the sum on

their paper.a. 115 b. 213 c. 241 d. 186 e. 153

+ 174 + 182 + 50 + 111 + 146

B. Add mentally using flash cards or dictation.1. What is the total of 50 and 42?2. Combine 143 and 123, the result is _______.3. Put together 131 and 12, you get _______.4. Father gathered 250 guavas in the morning and 132 guavas in the afternoon. How many

guavas did father gather in all?5. Jose sold 120 sampaguita garlands. Rosa sold 135 sampaguita garlands, how many did

they sell in all?

Solving Word Problems Involving Addition

I. Learning ObjectivesCognitive: Solve word problems involving addition of whole numbers including money

with sums through millions and billions without and with regrouping following the steps in problem solving

Psychomotor: Analyze and solve word problems accurately

Affective: Share one’s ideas and materials with others

II. Learning ContentSkill: Analyzing and solving word problems involving addition of whole numbersReferences: BEC – PELC I.B.4.1

Textbooks in Math 4Materials: story problems, charts, pictures, strips of cartolinaValue: Sharing



1. DrillPost addition equations on the board. Solve the sum mentally as fast and as

correct as they can.32 45 16 44 64 35 42 25 66

+ 2 + 11 + 43 + 23 + 33 + 12 + 26 + 32 + 11

2. ReviewMatch the appropriate phrase suited to the given facts and statement below.

Write the letter of the correct answer on the blank provided for.

_____1. The total population for both schools._____2. 13 486 + 23 465 = n_____3. Addition_____4. 13 486 + 23 465 = 36 951

3. MotivationSong (Sing to the tune of “Planting Rice”.)

Learning math is really fun I am glad, you are gladNew ideas every time For your answer are all rightThere is joy for everyone We all feel that we are brightProblem solving satisfies Solving problems makes us wise

a. Operation neededb. Given factsc. Number sentenced. Solution and answere. Asked in the problem


Materials:Drawing of trees with figures shown on the trunk of each tree as mentioned in the problem.

2. Group WorkActivity 1A representative will act as facilitator to discuss the questions presented by the teacher.a. Who are the families mentioned in the problem?b. What kind of families are they?c. What did they donate?d. How many trees were donated by the Estrada family?e. What kinds of trees were donated by Cruzado family? Estrada family?

Valuing: At your age, do you share things with others? What things do you share with others? What do you feel?

Activity 2

Call another representative in class to ask and discuss the following questions

a. What is being asked in the problem?b. What are the given facts?c. What operation will you use to solve the problem? Why? Explain your answer.d. Give the number sentence that will help you solve the problem.e. Show the solution to the problem on the board.

Example: 126 896 acacia and ipil–ipil trees + 351 724 molave and narra trees

442 620 total trees donated by the 2 familiesActivity 3Materials: chalk, mini-boardsThe group will give the answer to the problem by supplying the information below.a. The given facts are ______b. The process to be used is _______c. The answer is _______

3. Fixing Skills/Practice

Read the problem carefully then answer the following questions.

The Estrada’s and Cruzado’s are 2 generous families. They donated tree seedlings to the different barangays of the country. The Estrada family donated 126 896 acacia and ipil-ipil tree seedlings. The Cruzado family donated 315 724 molave and narra tree seedlings. How many seedlings were donated by the 2 families?

a. There was a benefit show for the orphans. 512 761.00php was earned. On the second day, 726 895.00php was the proceed. How much was generated by the show in 2 days?

b. The Math club of Barrio Obrero Elementary School started a news paper drive to raise funds for the poor children of Sapang Palay. If one group brought 434 253 old news papers and the other group brought625 250 old news papers, how many old news papers would there be in all?

c. Last year, Manny deposited 1 276 718.00php in the bank. This year, he deposited 991 221.00php. How much did he deposit in 2 years?

4. GeneralizationHow do you solve problems? What are the steps involved in solving story problems? Elicit the steps.

IV. EvaluationRead and solve the problems carefully.

1. It was reported that the total population in Benguet is 541 817 and in Kalinga is 154 145. What was the total population of Benguet and Kalinga?

2. Quezon City has a population of 8 424 262 while Manila has 11 189 people. What is the combined population of the two cities?

3. The Marcela Cooperative Farms earned 17 342 262.00php while Barangay Bayambang Cooperative earned 48 159 926.00php. Altogether, how much money did the two cooperatives earn?

4. During the best of seven series in the basketball game, there were 1 211 125 tickets sold in the fifth game while 2 179 600 in the sixth game. How many tickets were sold in the two games?

5. Mr. Domingo Sy earned 1 224 663.00php in the year 2001 while Mrs. Ellen Sy earned 926 175.00php for the same year. How much did they earn altogether? Look at the earnings of a certain food company. Then answer the questions that follow:

Milk products 378 584.00Fruit juices 198 475.00Meat products 326 421.00Other products 178 623.00

In solving word problems involving addition of numbers with sums up to millions and billions, the following steps are to be followed:

a. Read and understand the problem.b. Plan on what to do.c. Solve the problem.d. Look back to check if the answer to the problem is correct.

9 2

1 5

3 7

6

+11

6 3

8 5

9 2

7 1

+12

3 5

6 4

9 7

8 1

+11

a. What are the total earnings for meat products and fruit juices?b. What are the total earnings for meat and milk products?

V. Assignment

Solve the following problems carefully.1. Mr. Reyes purchased a pair of shoes worth 4 179.00php and a jacket which costs 725.00php at

SM Megamall. How much did he pay the cashier?2. There are 2 big central schools in Mindanao. In the first school, population was 4 486 while 3

654 in the second school. What is the total population of the 2 schools?3. A car dealer had this sales summary for the last quarter of 2000.

October – 653 410.00phpNovember – 585 688.00phpDecember – 890 462.00php

What was his total sale in 3 months?

Solving Mentally 1-Step Word Problems

I. Learning ObjectivesCognitive: Solve mentally 1-step word problems involving addition with sums up

to 300 without regroupingPsychomotor: Tell the answer to the problems accuratelyAffective: Appreciate the beauty of nature

II. Learning ContentSkill: Solving 1-step word problems mentallyReferences: BEC – PELC I.B.4.2

Textbooks in Math 4Value: Love for nature



1. Drill

Complete the addition wheel

2. Review

Solve the following math sentences.

a. What is the sum of 78 and 71?b. What is 74 more than 24?c. What is the result when 87 is added to 23?d. What is 18 more than the sum of 35 and 47?e. Add 35 to the sum of 43 and 69.

3. MotivationWho is your favorite newscaster? Why did you choose him/her? If given a chance, would you like to be like him/her? Why?


1. Presentation

a. Call a pupil to report the problem in class.

Discussion:

1) Who went to the park?2) What did they do there?3) If you were to visit a park, will you do what they did? Explain.4) What are the flowers mentioned in the problem?5) How many flowers were counted by the boys?6) How many flowers were counted by the girls?7) How many flowers are there in all?8) How did you get the answer?9) What is the fastest way of solving the given problem?10) How will you solve the problem mentally? Draw out the steps.

b. Solve mentally

One sunny day, Mrs. Almonte and her pupils went to the park. They enjoyed looking at the different flowers. On their way home, the decided to count all the flowers they saw. A group of boys reported that there were 71 roses and daisies while the girls reported 128 gumamela, camia and yellow bells. How many flowers were there in all? This is (name of student) reporting.

1) A crowd of 162 people watched the first day of the football game. The next day, 138 attended the game. How many people watched the games?

2) Ramon had 175.00php. His father gave him 123.00php. how much does he have now?


Divide the class into groups. Assign a leader to act as the facilitator in the discussion of the problem.

Group 1Jeff collected 145 stamps while Alvin collected 153 stamps. How many stamps did

they collect altogether?

Group 2Sheila used 147 bond paper. Irene used 132 bond paper. How many sheets of

bond paper did Sheila and Irene used altogether?

Group 3At Basilan Elementary School, there are 110 members of Science Club and 181

members of Math Club. How many members are there altogether?

3. Generalization

How do you solve story problems mentally?

C. Application

You can do these orally. Try them.1. Kevin picked 135 santols. Marie picked 161 santols. How many santols were picked in all?2. Lyn has 137 stamps in her album. Alma has 151. How many stamps do they have in all?3. Marlin walked 138 metres north and 160 metres south. How many metres did she walk in

all?4. Father drove 162 km from their home. After an hour, he drove 35 kilometres more in the

same direction. How far is he from his starting point?5. Mang Igme received an order of 175 baskets. After 5 days, there was an order of 124

baskets more. How many order for baskets did he received in all?

IV. Evaluation

A. Study the table then answer the following questions below.

In solving word problems mentally, give the answers to the problems accurately without using paper and pencil.

1. How many pupils are enrolled in Grades 1 and 2 altogether?2. The total number of pupils enrolled in Grades 4 and 5 is ______3. What is the sum of the enrollment of grades 5 and 1?4. The combined enrollment of Grades 3 and 4 is ______

B. Think and solve mentally.

1. Kalawaan Elementary School has 35 classes. Pasig Elementary School has 24 more classes than Kalawaan Elementary School. How many classes does Pasig Elementary School have in all?

2. Jenny is 35 years old now. Her mother is 41 years older. How old is her mother now?3. The weight of Benjie is 74 pounds. His friend is 22 pounds heavier than him. What is the

total weight of Benjie’s friend?

V. Assignment

1. Read and answer.a. Rosa sells fruits in the market. She earned 275.00php for her mangoes and 126.00php for

the papayas. How much did she earn from the fruits she sold?b. My aunt went shopping last Saturday. She bought a blouse for 280.00 and an umbrella for

125.00php. How much did my aunt spend in shopping?

Subtracting without Regrouping

I. Learning ObjectivesCognitive: Subtract 5- or more digit numbers from 6- or more digit numbers without

regroupingPsychomotor: Find the difference of 5- or more digit numbers from 6- or more digit

numbers without regroupingAffective: Show concern in cleaning and greening of the community

II. Learning ContentSkill: Subtracting 5- or more digit numbers from 6- or more digit numbers

without regroupingReferences: BEC – PELC I.C.1.1

Dr. Sixto Elementary School Grade 1 – 140 Grade 4 - 120 Grade 2 – 115 Grade 5 - 144 Grade 3 - 152

Textbooks in Math 4Materials: flash cards, pocket cardsValue: Environmental concern



Basic addition facts using flash cards

2. Review/Mental Computationa. What is 45 more than the sum of 12 and 13?b. Tony picked 35 apples. His friend gave him 11 more. How many apples were there in

all?

3. MotivationWhat do children of your age do to help the barangay officials in their campaign

for the clean and green program? What activities would you suggest to promote the clean and green program of your barangay?


1. Presentation

a. Activity 1

1. What is asked in the problem?2. What are the given facts?3. What operation is to be used?4. What is the number sentence?5. Solution (help the pupils solve the problem)

In support of the clean and green campaign of our government, the officials and constituents of Barangay Kalawaan decided to raise a total amount of 685 976.00php to buy ornamental plants, flowering plants, grass and some garden materials. During the recent fund drive they conducted, they were able to raise a net amount of 234 802.00php. How much more should they raise in order to meet the target amount for their beautification project?

Strategy 1

Subtract the ones Subtract the tens Subtract the hundreds

685 976 685 976 685 976- 243 802 - 234 802 - 234 802

4 74 174

Subtract the Subtract the Subtract the Thousands ten thousands hundred thousands

685 976 685 976 685 976- 243 802 - 234 802 - 234 802

1 174 51 174 451 174

Let us familiarize ourselves with the terms we used in subtraction.

685 976 (minuend)- 234 802 (subtrahend)451 174 (difference)

How do we check if our answer is correct? Do this by adding the difference and the subtrahend. If the minuend and the sum are the same, then our difference is correct.

451 174 (difference)+ 234 802 (subtrahend) 685 976Strategy 2

Use of expanded notation.

685 976 = 600 000 + 80 000 + 5 000 + 900 + 70 + 6- 234 802 = 200 000 + 30 000 + 4 000 + 800 + 0 + 2

400 000 + 50 000 + 1 000 + 100 + 70 + 4 = 451 174

b. Activity 2

1. Use your drill board to find the difference of each

a. 62 716 b. 78 914 c. 386 112 d. 297 564 e. 687 312 - 41 302 - 12 513 - 125 011 - 126 231

- 574 211

2. Answer and check with the class.

a. Subtract 633 420 from 955 420.b. Take away 59 104 from 89 108.

c. What is 475 634 minus 243 522?d. What is the difference between 878 945 and 25 714?e. 961 837

-351 425

f. 457 791-231 661

2. Generalization

How would you find the difference of 5- or more digit numbers from 6- or more digit numbers without regrouping?

C. Application

Subtract.

a. 27 892 b. 287 196 c. 279 124 d. 78 465 e. 754 683 - 16 574 - 163 164 - 59 113 -52 431 -310 521

Find the missing numbers.

a. 85 421 b. 75 436 c. 495 837 d. 787 251 e. 893 526- 1 - 12 - 7 2 - 1 3 - 7 1

IV. Evaluation

A. Find the difference. Choose the letter of the correct answer.

1. Find the difference between 936 635 and 473 215.a. 363 420b. 436 420c. 463 420d. 453 240

2. What is 18 467 less 14 235?a. 4 132b. 4 232c. 5 132d. 5 232

In subtracting 5- or more digits from 6- or more digits without regrouping, subtract from the ones until the last given digit.

3. Subtract 234 802 from 685 976.a. 451 174b. 514 471c. 415 174d. 154 417

4. Take away 15 061 from 27 892. ___________5. Find the missing numbers in

85 421- 1

B. Find the difference.

1. 67 071 2. 70 184 3. 871 976 4. 987 726 5. 876 752-15 061 -30 174 -341 275 -765 115 -561 331

V. Assignment

Find the difference. Check your answer.

8 184 21 748 95 614 72 114 65 718 -6 153 - 11 136 - 34 512 - 31 002 - 23 416

Solve for n.

a. 38 415 – 27 304 = nb. N – 24 923 = 53 024c. 17 556 – (2 475 + 625) = nd. 875 122 – 764 111 = ne. 693 952 – 512 841 = n

Subtracting Large Numbers with Zero Difficulty


Cognitive: Subtract 5- or more digit numbers from 6- or more digit numbers with 3 continuous or non-continuous zeros in both the minuend and the subtrahend with regrouping

Psychomotor: Solve for the difference of 6- or more digit numbers with zero difficultyAffective: Support organizations that help poor people


Skill: Subtracting large numbers with zero difficultyReferences: BEC – PELC I.C.1.2

Textbooks in Math 4Materials: flash cards, charts, pocket chartsValue: Helpfulness


1. Drill

Subtract.17 18 21 17 23 35 41 19

- 10 - 11 - 16 - 12 - 19 - 11 - 21 - 19

2. ReviewFind the difference.

= =

=

3. Motivation

What government organizations help poor people? Have you experienced asking help from some organizations?


1. Presentation

a. Who sells tickets?b. Why do they sell tickets?

Valuing:

As a student, how will you help this organization? Is it right to help them? Why?

Discuss the solution to the problem.

9 9 1 10 10 10 1 10 10 10

74 814

3 876

1 968

47 765

59 732

Red Cross is an organization which helps the poor people. During the Red Cross Week, Garita Elementary School was given 12 000 tickets to sell for a benefit show. The school was able to sell 9 032 tickets. How many tickets were not sold?

800 120

400 050

70 625500 200

621 000711 000

12 000 1 2 0 0 0 1 2 0 0 0 - 9 032 - 9 0 3 2 - 9 0 3 2

2 9 6 8

2. Group Activity

a. Find the difference by subtracting the indicated numbers from 800 120.

b. Follow the arrows to fill up the boxes by subtracting the numbers until you reach 93 100.

- =

- =

- =

3. Generalization

How can you subtract numbers with 3 continuous or non-continuous zeros in both minuends and subtrahends and with regrouping in any places?

C. Application

93 150 000 13 281 600

176 105

79 092 200 93 100

When there are continuous zeros or non-continuous zeros, we regroup first in places that need regrouping, starting at the leftmost digit, then proceed to subtraction

Find the difference.a. 780 004 b. 2 357 000 c. 9 856 000 d. 900 603

-36 842 - 26 453 - 500 032 - 590 407

e. 700 080 f. 7 800 000 g. 97 000 136 h. 160 080 000 - 345 000 - 1 156 000 - 6 002 179 - 42 165 000

IV. Evaluation

A. Find the differencea. 900 034 b. 867 000 c. 320 400

-720 004 - 123 000 - 10 009

d. 98 000 000 e. 65 000 000 - 15 900 050 - 9 261 000

B. Subtract 5 digit numbers from 6 or more digit numbers with continuous zeros.

1. Take away 3 006 from 206 000.a. 302 994b. 203 494c. 202 994d. 202 499

2. Decrease 1 600 from 700 067.a. 696 467b. 896 467c. 986 476d. 689 476

3. Subtract 36 842 from 780 004.a. 734 162b. 743 162c. 734 261d. 437 261

4. Find the difference between 700 080 and 345 000. ________5. What is the difference between 800 000 and 156 000? _________

V. Assignment

Write in column and subtract.1) 901 060 006 – 9 300 518 = n2) 100 000 000 – 85 643 214 = n3) 80 000 000 – 1 234 567 = n4) 421 300 048 – 216 321 832 = n

5) 726 140 009 – 402 124 000 = n

Estimating the Difference of Two Numbers


Cognitive: Estimate the difference of two numbers with four to six digitsPsychomotor: Solve for the difference mentallyAffective: Show love and concern for parents

II. Learning ContentSkill: Estimating the difference of two numbers with four to six digitsReferences: BEC – PELC I.C.1.3

Textbooks in Math 4Materials: flash cards, chartValue: Thoughtfulness



1. Drill Find the difference

65 – 22 = 10 – 6 = 9 – 5 = 17 – 10 =127 – 105 = 7 – 3 = 12 – 6 = 18 – 11 =396 – 254 = 17 – 9 = 11 – 8 = 12 – 7 =

2. ReviewRound the following numbers to the nearest tens and thousands.

Nearest Tens Nearest Thousandsa. 74 325 ____________ _____________b. 25 936 ____________ _____________c. 127 547 ____________ _____________d. 31 247 ____________ _____________e. 743 426 ____________ _____________

3. MotivationWhat would you do if you cannot afford to buy a greeting card or gifts for your loved ones? What do you feel?


1. Presentation

The grade 4 pupils of Maybunga Elementary School made 2 568 greeting cards for their parents while the grade 3 pupils made 1 756 cards. About how many more greeting cards did the grade 4 pupils make than grade 3?

a. Who made greeting cards?b. Why did they make the cards?c. Who among them made more cards?

Valuing:

To whom will they give the cards? Do you also give cards to your parents? When? Why?

2. Group Activity

Activity 1a. What is asked in the problem?b. What are the given facts?c. What operation is to be used?d. What is the number sentence?

To estimate the difference, round off the minuend and subtrahend to the highest place value then subtract.

2 568 3 000 2 568 - 1 756 - 2 000 - 1 756

1 000 - estimated difference 812 -actual difference

Activity 2Estimate to the highest place value then find the difference.

a. 54 798 b. 95 895 c. 349 258 d. 4 912 - 42 991 - 72 521 - 121 123 - 3 165

e. 6 861 f. 5 762 g. 25 376 h. 265 - 4 136 - 3 223 - 14 213 - 142

i. 4 632 j. 5 134 k. 72 571 - 1 482 - 1 675 - 61 933

3. Generalization

How do you estimate the difference of two numbers with four to six digits?

C. Application

To estimate the difference of two numbers with four to six digits, round each of the numbers to highest place value then subtract.

1. Round each minuend and subtrahend to the nearest a) tens b) hundreds c) thousands and d) ten thousands, then find its estimated difference

78 528 78 530 - 43 187 - 43 190

2. Estimate the difference to its highest possible place value.

a. 6 348 b. 8 888 c. 13 429 d. 52 634 e. 73 287 - 3 344 - 2 929 - 12 363 - 19 584 -48 896

IV. Evaluation

A. Estimate the difference by rounding to the nearest ten thousands.

1. 85 946 2. 34 879 3. 59 679 - 52 346 - 16 843 - 37 051

B. Estimate then find the difference.

1. Estimate the difference between 6 213 and 4 362.a. 2 000b. 3 000c. 4 000d. 6 000

2. What is the estimated answer if 1 236 is subtracted from 2 705?a. 1 000b. 3 000c. 2 000d. 4 000

3. The sponsor of the play prepared 4 230 tickets; 2970 were sold. About how many were not sold?a. 3 000b. 4 000c. 2 000d. 1 000

4. Estimate the difference between 7 452 and 5 602. ___________5. Get the estimated difference between 87 625 and 5 362. __________

V. Assignment

1. Ask the actual income of the family. Estimate the difference of the family’s monthly expenses from their actual income.

2. Estimate the difference by rounding to the nearest a) tens b) hundreds c) thousands d) ten thousands.

194 385 - 168 651

3. Estimate the difference by rounding to the highest possible place value.5 672 67 935 84 764

- 5 219 - 61 398 - 84 159

Subtracting Numbers Mentally without Regrouping


Cognitive: Subtract mentally numbers with minuends up to 300 without regroupingPsychomotor: Give the correct answer mentally and orallyAffective: Show the value of helpfulness when given a task


Skill: Subtracting mentally with minuends up to 300 without regroupingReferences: BEC – PELC I.C.2

Textbooks in Math 4Materials: flash cards, chart window card, pocket chartValue: Helpfulness



1. DrillBasic subtraction facts.Each pupil take turns in answering the basic subtraction facts written on each strip of manila paper. Check the answers in the class.

10 - 2

10 - 9

10- 7

15- 6

16- 7

12- 8

10- 9

2. ReviewThis may be done in form of a game. Let a pupil pick one petal of the flowers (one at a time) and have him/her answer the equation.

45- 20

47- 16

87- 64

53- 32

37- 26

78- 24

83- 23

75- 21

66- 12

67- 33

99- 11

99- 83

3. Motivation

During weekends, what do you do to help your parents earn extra income? Guide the pupils to see the value of helpfulness.


1. Presentation of lesson

2. Discussion

a. How many mangoes did Leah have in the morning?b. How many mangoes did she have at the end of the day?c. What will you do to get the answer?d. What is the fastest way of solving for the final answer?e. How many mangoes were sold?


a. Relay Game

Mechanics:Group the pupils into 5. Let them form a line outside or inside the room.

Teacher writes all the exercises in a rolled paper and pastes it on the board. When the teacher says “go”, pupils takes turns in going to the board. The first group who correctly answers the questions wins.

During weekends, Leah helps her mother sell mangoes in the market. One morning, she had 275 mangoes. At the end of the day, she had 55 mangoes left. How many mangoes were sold?

Group 1 Group 2 Group 3 Group 4 Group 5

1. 276 2. 239 3. 179 4. 264 5. 148 - 132 - 135 - 146 - 153 - 46

b. Supply the missing numbers orally.

1) 2) 3) 4) 171 5) 247

- 102 - 132 - 275 - - 104 141 33 210 102

c. Find the missing numbers to complete the puzzle. Subtract horizontally and vertically.1) 2)

274 ____ 142____ 21 ____131 ____ 20

4. Generalization

How can you subtract mentally? Give the steps.

C. Application

1. Subtract mentally.a. 284 – 174 = nb. 340 – 130 = nc. 182 – 130 = nd. 488 – 242 = ne. 575 – 273 = n

2. Subtract mentally the following numbers.a. 299 b. 299 c. 266 d. 278 e. 265

- 183 - 153 - 155 -178 - 152

IV. Evaluation

____ 248 44143 112 ____149 ____ 13

A. Give the difference orally.

1. 300 2. 239 3. 270 4. 290 5. 239 - 200 - 105 - 120 - 190 - 133

B. Subtract mentally.

1. The difference between 298 and 56?2. What remains between 876 and 543?3. Less 13 from 126.4. What is left between 178 and 152?5. What is 715 minus 236?

V. Assignment.

Subtract mentally.

1. 762 2. 838 3. 174 4. 174 5. 294 - 241 - 712 - 100 - 74 - 253

6. 120 7. 150 8. 159 9. 249 10. 678 - 110 - 140 - 147 - 123 - 423

Solving Mentally 1 – Step Word Problems Involving Subtraction without Regrouping


Cognitive: Solve mentally 1-step word problems involving subtraction without regrouping

Psychomotor: Solve problems mentallyAffective: Show appreciation for God’s creation


Skill: Solving mentally 1-step word problems involving subtraction without regrouping

References: BEC – PELC I.C.3.2Textbooks in Math 4

Materials: flash cards, picture, chart, activity sheets, paper, crayonsValue: Appreciation of God’s creation



1. Drill

Mental ComputationSolve for the difference mentally as fast and as correct as you can.

96 85 874 305 4 248 - 54 - 61 - 523 - 202 - 2 125

2. Review

Answer orally.Jose sold 120 sampaguita garlands. Rosa sold 135 sampaguita garlands. How many

more sampaguita garlands did Rosa sell than Jose?

3. Motivation

Show pictures of trees, skies, land, fish, people, etc.

Valuing: Who created these things? Can we be like God? Why or why not?


1. Presentation

2. Discussion

Guide the pupils in the discussion of the problem by answering the following questions.a. What is asked in the problem?b. What are given?c. What operation is needed to solve the problem?d. What is the fastest way of solving for the final answer?e. What is the final answer?

Group the pupils by pairs. Distribute activity sheets to each pair. Their task is to help each other solve the problems carefully.

a. Edgar helps his father in the farm. There were 150 coffee seedlings. If 90 seedlings have been planted, how many more does he need to plant?

Marc has 78 fishes in his aquarium. His mother transferred 25 fishes into another aquarium. How many fishes were left?

b. Aling Norma has 12 children. Ten of her children went to America. How many children still lives with Aling Norma?

c. If Carlo accidentally broke 12 of his 24 crayons, how many crayons were not broken?d. Loren has 15 guavas. She gave 12 guavas to her sister. How many has she left?e. Mother baked 28 cookies. Lita ate 12 of the cookies. How many cookies were left?

3. GeneralizationHow do we solve problems involving subtraction mentally? What are the rules to remember in solving problems mentally?

C. Application

Solve mentally. Write the answers on your paper.1. Danny planted 54 upo seedlings. Ernie planted 65 ampalaya seedlings. Who planted

more?2. Nancy planted 39 patani seedlings. If 13 of them did not grow, how many seeds grew?

IV. EvaluationSolve the problem mentally.

1. There are 20 buses in the bus terminal. Only 15 are checked to be in good condition. How many are left for repair?

2. Mia bought 15 candies. On her way home, she ate 5 of the candies. How many candies did she bring home?

3. Jerry weighs 182 lbs. randy weighs 120 lbs. how much more is Jerry’s weight than Randy?4. Mang Isko baked 30 cookies. Ronald ate 20 of the cookies. How many cookies were left?5. Carlo broke 10 of his 24 crayons, how many crayons were not broken?

V. Assignment

Create your own story problem involving subtraction. You may exchange problems with your partners then try to solve it accurately. Discuss solutions in class.

Word Problems Involving Subtraction


In solving word problems involving mental subtraction, follow the following steps:

Understand, think and give your answer without using pencil and paper, then look back to check your answer.

Cognitive: Solve one step word problems involving subtraction of numbers including money, with and without regrouping

Psychomotor: Write the number sentence for a given story problemAffective: Practice wise decision-making


Skills: 1. Writing number sentences for story problems2. Solving word problems involving subtraction of whole numbers including money with and without regrouping


Materials: flash cards, chart on problem solvingValue: Intelligent decision in voting



1. Drill

Have a short drill on selected subtraction facts.35 18 16 31 34

- 5 - 7 - 8 - 9 - 6

2. Review

Find the difference.7 367 6 380 7 125 2 375 9 245

- 2 314 - 2 629 - 5 443 - 1 142 - 6 730

3. Motivation

How many registered voters are there?How many male voters are there?How many are female?

Valuing: If you are to vote for your student government, how are you going to select a

good leader? Why?


Purok Masagana has 7 206 registered voters. If 3 271 are male voters, how many are female voters?

1. Presentation

a. What is asked in the problem?b. What is/are given in the problem?c. What operation will you use? Is there a clue word?d. What is the number sentence for the problem?e. How is the solution done?

2. Group Activity

Group the pupils into 4 groups. Have each group solve the problems then present their work to the class.

Group 11. The pineapple planters of Laguna gathered 4 276 pineapples last month. This

month, they harvested 6 278 pineapples. How many more pineapples did they harvest this month than last month?

2. Mrs. Posadas wants to buy a washing machine worth 5 785.00php. She has 2 356.00php cash on hand. How much more money does she need in order to buy the washing machine?

Group 21. A fish dealer sold 232 152 kg of assorted fish in one week. If 156 218 kg were

sold in 4 days, how many kg of fish were sold in 3 days?2. Mr. Perez bought a car that costs 356 826.00php. After five years, she decided

to sell the old car for 186 738.00php. How much is the cost difference? Group 3

1. A farmer harvested a total of 10 404 watermelons last year. This year, he was able to harvest 22 098 watermelons. What is the difference between the watermelons harvested this year and last year?

2. A big library has 38 459 books in the shelves. There are 7 079 Science books. How many books are not Science books?

Group 41. There were 450 computers in St. Mary’s school. After the school year, it was

discovered that 86 were not functioning. How many computers were in good condition?

2. Aling Precy sold fruit at a public market. She had 2 056 mangoes. At the end of the day, she had only 94 left. How many mangoes were sold on that day?

Provide provisions foe word clues leading to the solutions of the word problems, specifically for the slow groups.

3. Generalization

What are the steps to follow in problem solving?What clues are needed to solve word problems involving subtraction?

C. Application

Solve the following word problems.

1. In a week, Mang Carlos earned 4 265.00php for catching fish. He gave 1 500.00php to his wife and deposited the rest in the bank. How much did he deposit in the bank?

2. Mrs. Malvar and her eldest daughter watched a songfest. There were 10 206 who watched the said competition if 6 259 were females, how many were males?

3. Mariano’s cottage industry exported a total of 250 756 native slippers and bags. Of these products, 75 903 were native bags, how many native slippers were exported?

4. Mr. Cortez has 527 968.00php in a savings bank. He withdrew 35 500.00 for his children’s school expenses. How much money is left in the bank?

IV. Evaluation

Read and solve the following problems.

A.1. Virgie collected 1 280 local and international stamps. If 452 were local stamps, how many were international stamps?2. The school property custodian distributed 4 758 English and Math books for grade IV pupils. If 2 307 are English books, how many are Math books?

B. 1. Emmy bought 60 sacks of corn that cost a total 15 940.00php. If she had 32 075.00 in her wallet, how much more was left?2. During the local election for Mayor, Atty. Roxas received 32 708 votes while Mr. Reyes received 21 926 votes. How many more votes did Atty. Roxas receive than Mr. Reyes?

C.1. A garment factory earned 858 928.00php. The workers were paid 28 968.00php. How much was left for the factory’s other expenses?2. Mr. Gomez plans to buy a car for 55 726.00php. He already has 48 905.00php. How much more does he need to be able to buy the car?

V. Assignment

Read and solve the following word problems.

1. To sustain and maintain the Clean and Green Project, the city hired 315 new workers. If they need 1 210 new workers, now many more should be hired?

2. The Junior Red Cross members of Bagong Silang Elementary School collected old news papers and bottles. They sold the old news papers for 1 090.00php and the bottles for 2 115.00php. How much more did the Junior Red Cross earn from selling bottles than newspapers?

3. The Bantayog Ladies Circle invited several women to participate in a beautification project. The women were able to raise 100 000.00php for the improvement of the town park. They spent 46 000.00php for making a flower garden and the rest they spent for playground equipments. How much was spent for the playground equipments?

4. Quezon City had a Clean and Green Project. All the barangays planted a total of 32 500 seedlings of fruit trees. The school children planted about 25 000 ornamental plants in their homes and school yards. How many more were fruit trees than ornamental plants?

5. The food committee ordered 15 000 doughnuts. Only 13 269 were sold. How many doughnuts were left?

Analyzing 2-Step Word Problems Involving Addition and Subtraction Including Money


Cognitive: Analyze word problems involving addition and subtraction including money

Psychomotor: Solving problems involving addition and subtraction including moneyAffective: Appreciate the value of hardwork


Skill: 1. Analyzing word problems2. Telling what is asked, what are given, the word clues, the hidden question and the operation to be used3. Transforming the word problem into a number sentence4. Using the correct operation5. Solving for the final answer with the necessary label

References: BEC – PELC I.C.4.1.1Textbooks in Math 4

Materials: charts, strips of cartolina, manila paper, markersValue: Value of hardwork



1. DrillDo merry-go-round. Divide the class into groups of 5. Each pupil takes turn in solving for the sum/difference mentally to be written in an activity sheet. Check answers in class.

25 37 74 65 46 98 64 37 + 86 + 43 +28 + 13 - 33 - 75 - 49 - 18

2. Review

What are the steps in solving word problem?

3. Motivation

Rica’s father earns 2 500.00php a week. Her mother earns 1 800.00php. They set aside 3 500.00php for their weekly expenses. How much money was left for their savings?

What do you know about the word earnings, savings and expenses?

Valuing:

Why do people work? Do you spend all your earnings? Why do you have to save?


1. Presentation

Guide the students in analyzing and solving the problem in class. Refer to the questions below.a. What is asked in the problem?

The total savings for the week.b. What are given?

2 500.00 1 800.00 3 500.00c. What is the hidden question?

How much do they earn altogether?d. What words were used to help solve the problem?

Money left as savingse. What operations will you use?

Addition and subtractionf. What is the number sentence?

(2 500 + 1 800) – 3 500 = ng. What is the answer?

800.00php in a weekGive more problems to be discussed in class.

2. Group Activity

Divide the class into groups of 3s. Distribute a sheet with problems on it. The task of the students is to help each other solve the problems. Assign a representative/leader to report and discuss solutions made by their group in class.

a. Mr. Nicolas bought a house for 350 000.00php. He spent 120 000.00php for its repair. Then, he sold the house for 670 000.00php. How much did he gain?

b. In November, Mrs. Rizon spent 8 200.00php for household expenses and 1 750.00php for her children’s allowance. In October, she spent 8 550.00php for the same expenses. How much more does she spend in November than in October?

c. On the first day, there were 1 415 children vaccinated at the Health Center and 1 054 on the second day. Of these, 1 459 were boys. How many were girls?

Adrian bought a bag for 500.00php and a raincoat for 250.00php. Maria bought an umbrella for 230.00php. How much more did Adrian spend than Maria?

3. Practice Exercises

Solve the following problems using the steps in problem solving.a. Some pupils donated seedlings for their plant-a-tree project. The girls donated 2 518

seedlings while the boys donated 1 736 seedlings. Of these seedlings, 1 385 withered. How many plants did not wither?

b. Jay watched two movies and paid 60.00php each as admission fee. Then, he ate at a restaurant and paid 120.00php for a pizza and a glass of juice. If he spent 10.00php for transportation, how much money was left if he had 400.00php at the start?

4. Generalization

How do we solve word problems?What are the steps involved?

C. Application

Read each problem and solve on your paper.1. In a town’s fund-raising drive, several organizations raised the following amounts: Knights

of Rizal, 18 176.00php, daughters if Isabela 12 735.00php and the Women’s Club 10 487.00php. After deducting the expenses of 7 385.00php incurred, how much did they raise altogether?

2. In 1990, the number of overseas workers in the country was 41 730, in 1992 it went up by 12 768. In 1995, it went up to 782 297. What was the increase in the number of overseas workers from 1990 to 1995?

IV. Evaluation

Solve the problems by following the steps in problem solving.

1. Precy went shopping. She wants to buy a pair of pants which cost 395.00php and a blouse which costs 250.00php. how much would be her change if she gave the cashier 1 000.00php?

2. The school auditorium can hold 5 000 people. Of the school population, 3 246 boys and 1 362 girls went to see the basketball game. How many more students can the auditorium accommodate?

V. Assignment

Write your analysis of these problems by answering the 7 questions in the presentation part.

1. Mrs. Reyes collected 8 345 seashells from Luzon, Visayas and Mindanao. She collected 3 420 from Luzon and 3 058 from Mindanao. How many seashells did Mrs. Reyes collect from Visayas?

2. You have 200.00php. How much change would you receive if you paid all the items below?Ballpens and pencils 48.00Notebooks 75.00Crayons 24.00Pad paper 20.00Art papers 31.00

Solving 2-Step Word Problems Involving Addition and Subtraction Including Money


Cognitive: Solve 2-step word problems involving addition and subtraction including money

Psychomotor: Solve problems accuratelyAffective: Show love for books


Skill: Solving 2-step word problems involving addition and subtraction including money


Materials: flash cards, chartsValue: Love for books



1. Drill

Use flash cards for the basic addition and subtraction facts.3 9 5 6 9 4 8

+ 8 + 2 + 7 + 4 + 8 + 7 + 8

12 11 6 15 18 17 - 5 - 8 - 2 - 7 - 8 - 9

2. Review

Find the sum. Write the answers in your math notebooks.

238 277 364 811 675 +215 +124 +125 + 278 + 324

128 248 899 278 367 - 114 - 231 - 176 - 72 - 56

3. Motivation

Have you gone to the library?What do you see in the library?


1. Presentation

Let 2 or 3 pupils show the solution on the board. Discuss the solutions on the board.

10 000 – (238 + 215) = n

10 000 – 453 = n

n = 9 547 books

Valuing:

What kind of girls are Glenda and Girlie? Do you also enjoy reading books? What kind of books do you love to read? Is reading books a good hobby? Why?

2. Group Activity

a. Activity 1Divide the class into groups/columns. Let the pupils help each other solve the

problem. Show the solution.

1. Aling Naty picked 25 tomatoes from her vegetable garden on Monday and 43 tomatoes on Tuesday. She used 12 of these for cooking. How many tomatoes were left?

2. Nita needs 100.00php for her project. Father gave her 25.00php and her mother gave her 55.00php. How much more does she need?

3. Janice collected 300 shells and Riza collected 250 shells on the beach. On their way home, they lost 120 shells. How many shells were they able to bring home?

b. Activity 2

Glenda and Girlie love to read books. They always go to the library to read books. Glenda had read 238 books and Girlie read another 215 books. If their library has 10 000 books, how many more books do they still need to read?

Divide the pupils into 3 groups. The first group to give the correct answer will get the points.1. For the month of January, a department store received 4 838 denim pants and 3

746 slacks. If 6 220 pants were sold, how many were left?2. Mother baked 365 cookies in the morning and 273 in the afternoon. She sold 526

cookies to her neighbors. How many cookies were left?3. Lani deposited 1 350.00 in November and 3 175.00 in December. She withdrew

2 000.00 in January. How much money is left in the bank?

3. Generalization

What do we have to do before we can solve a problem?

C. Application

Group the pupils. The leader of each group will pick a problem using the “Wheel of Fortune”. They will be given 2 minutes to solve the problem. If the answer is correct, they will be given points.

1. Mr. and Mrs. Ignacio planned to buy a house and lot worth 31 486 875.00php and a car worth 1 755 930.00php. If they have 25 950 395.00php, how much more money do they have to raise to be able to buy the house and lot and the car?

2. In 1998, the population of barangay San Antonio was 5 786. In 1999, there were 1 296 newborns and 325 deaths. What is the population of barangay San Antonio at the end of 1999?

3. Portland Industries earned 17 836 109.00 in the year 2001 and 21 350 865.00 in 2002. Because of fire, they spent 16 650 370.00 to rebuild their factory. How much of their earnings were left?

IV. Evaluation

Solve the following problems.

1. Lino sold empty bottles in Saturday and received 18.00. On Sunday, he received 21.00. He spent 15.00 for food. How much money was left?

2. Rafael earned 45.00 for washing cars and 55.00 for running errands. He bought a box of crayon for 24.00. How much money was left?

3. Mandy caught 148 fishes in the morning and 216 in the afternoon. He gave 56 of these to her mother for dinner. How many fishes were left to be sold in the market?

Follow the steps in analyzing and solving a problem.

a. Thinkb. Planc. Solved. Look back

4. Mrs. Cruz bought canned goods worth 375.00 and garments worth 950.00. She gave the cashier 1 500.00. How much change did she get?

5. Bonifacio Elementary School had 3 568 Grade 1 pupils and 3 756 Grade 2 pupils in 2001. If the enrollment was 17 324, how many pupil were in the other grade levels?

6. Mr. Del Rosario’s monthly income is 20 150.00 while his wife’s monthly income is 16 720.00. If their monthly expenses are 26 450.00, how much is their monthly savings?

V. Assignment

Solve the problem. Show your solution.

1. A mineral water company produced 15 476 bottles of mineral water for the month of June and 21 658 for the month of July. They were able to sell 33 274 bottles of mineral water. How many bottles were unsold?

2. A soft drink factory was able to manufacture 48 357 bottles for January and 55 219 for February. The factory was able to sell 84 379 bottles. How many were not sold?

Properties of Multiplication


Cognitive: Show the different properties of multiplication Commutative property Associative property Zero property One/Identity property

Psychomotor: 1. Solve for the product mentally2.Supply for the missing numbers in a given situation

Affective: Show love for reading


Skill: Identifying the properties of multiplicationReferences: BEC – PELC I.D.IaMaterials: counters, cartolina strips, chartValue: Love for reading



1. Drill Answer as fast as you can. (number sentences written on cartolina strips)

9 + 6 4+ 75 + (3 + 6) 7 + 46 + 9 (2 + 5) + 6(5 + 3) + 6 9 + (4 + 2)

2. Review

Write each number on the left as a product of two numbers in different ways.18 = 6X3 3X6 9X2 2X9 1X1820 =32 =25 =42 =

3. MotivationMiss Daisy has 25 pupils. She required each pupil to read two books for

home reading per month. How many books will the children read in 10 months?

Valuing: What do you think will be developed among the pupils of Miss Daisy? What do you think shall we get from reading many books?


1. Presentation

25 x 2 = 50

What are the factors? Do you think that if we interchange the factors, the product will still be the same? Let us see.

2 x 25 = 50 50 = 50

Therefore: 25 x 2 = 2 x 25

Materials: countersGroup size: pairsProcedure:

Distribute 40 counters to each pair. Say 2 multiplication problems using the same factors (e.g. 3 x 6, 6 x 3). Each pupil in pair shows and solves one of the problems using counter. Pupils compare the products and discuss. Repeat activity (5 – 10 mins.).

a. Distribute cards to all the pupils. Each card contains a different multiplication fact such as 4 x 2 = 8 and 2 x 4 = 8. Each child will look for his/her partner. Include in the multiplication facts 0 and 1, factors like 0 x 1 = 0, 1 x 0 = 0, 3 x 1 = 3, 1 x 3 = 3

b. Based on the activities done, present the following:

A B C9X4 = 36 7X0 = 0 2X1 = 24X9 = 36 0X7 = 0 1X2 = 2

8X3 = 24 9X0 = 0 6X1 = 63X8 = 24 0X9 = 0 1X6 = 6

7X9 = 63 15X0 = 0 12X1 = 129X7 = 63 0X15 = 0 1X12 = 12

What have you observed in Group A? if the order of the factors are changed, does the product also change or remain the same? (Then present the commutative property of multiplication) Does addition also have this property?

How about column B? What have you observed? (Introduce the zero property.)How about column C? What can you say about the numbers multiplied by 1? (Introduce the identity property.)

c. Present 2 cartolina strips showing:(4 x 2) x 5 = 8 x 5 = 404 x (2 x 5) = 4 x 10 = 40

40 = 40Therefore, (4 x 2) x 5 = 4 x (2 x 5)

6 x (4 x 3) = 6 x 12 = 72(6 x 4) x 3 = 24 x 3 = 72

72 = 72Therefore, 6 x (4 x 3) = (6 x 4) x 3

What have you observed? Do the groupings of the factors affect the product? (Introduce the associative property)

2. Group Activity

Distribute activity cards.Each group will answer the exercises in the activity card and report. (Identify what

property is illustrated.)

a. 3 x 6 = 6 x 3 d. 18 x 9 = 9 x 18b. 1 x 12 = 12 e. 6 x 0 = 0c. (8 x 4) x 5 = 8 x (4 x 5) f. 12 x (2 x 5) = (12 x 2) x 5

3. Generalization

What are the properties of multiplication? Define each.

Commutative Property – changing the order of the factors does not change the product.

Associative Property – changing the grouping of the factors does not change the product.

C. Application

Mang Tonyo prepares his harvest to be brought to the market. He has 5 baskets of tomatoes. If each basket contains 300 tomatoes, how many tomatoes are there in all? (Prove your answer by showing the commutative property)

Solution: 5 x 300 = 300 x 5 1 500 = 1 500

IV. Evaluation

A. Encircle the letter of your answer.

1. Which equation shows the Identity Property of Multiplication?a. 238 x 0 = 0b. 14 x 23 = 23 x 14c. 85 x 1 = 85d. (2 x 3) x 4 = (3 x 4)

2. Among the equations below, which shows or describe the zero property of multiplication?a. 39 x 0b. 45 x 1c. (9 x 8) x 2 = 9 x (8 x 2)d. 15 x 3 = 3 x 15

3. Commutative Property of multiplication is best shown by the equation __________.a. 34 x 2 = 2 x 34b. 65 x 1 = 65c. (3 x 7) x 8 = (7 x 8) x 3d. 370 x 0 = 0

4. The equation ________, shows the Associative Property of Multiplication?a. 48 x 62 = 62 x 48b.b. 1 x 4 271 = 4 271c. 9 x (5 x 6) = (9 x 5) x 6d. 99 x 0 = 0

5. Give example of Associative property of multiplication. ___________

B. Solve for the answer and indicate the property of multiplication.

Commutative Property – changing the order of the factors does not change the product.

Associative Property – changing the grouping of the factors does not change the product.

1. 7 x 8 = 8 x 72. (4 x 8) x 3 = 4 x (8 x 3)3. 120 x 04. 29 x 15. (14 x 5) x 8 = 14 x (5 x 8)

V. Assignment

Solve and fill in the blanks the correct answer.1. 5 x 8 = 8 x 5 6. (2 x 3) x 6 = 2 (3 x 6)

___ = ___ ___ x 6 = 2 x ___2. 9 x 4 = 4 x 9 ___ = ___

___ = ___ 7. 14 x 1 = ___3. 6 x 0 = ___ 8. 100 x 0 = ___4. 80 x 1 = ___ 9. 4 x 9 = ___ x ___5. (3 x 8) x 4 = 3 x (8 x 4) 10. 7 x 3 = 3 x 7

___ x 4 = 3 x ___ ___ = ______ = ___

Distributive Property of Multiplication over Addition


Cognitive: Identify the distributive property of multiplication over additionPsychomotor: 1. Supply the missing number

2. Solve for the product mentallyAffective: Demonstrate love for work


Skill: Showing the distributive property of multiplication over additionReferences: BEC – PELC I.D.1.B

Textbooks in Math 4Materials: flash cards, chart, picture, counters, activity cardsValue: Dignity of labor



1. Drilla. Have the pupils answer orally the basic multiplication facts using flash cards.

2. Review

b. Identify the property of multiplication being illustrated. Complete the equations as necessary.1. 6 x 2 = 2 x 6 9. (6 x 0) x 5 = 6 x (0 x 5)2. (4 x 8) x 2 = 4 x (8 x 2) 10. (4 x 1) x 9 = 4 x (1 x 9)3. 9 x 0 = 11. 4 x 12 = 12 x 44. 1 x 25 = 12. 36 x 1 = 1 x 365. 7 x 6 = 6 x 7 13. 4 x 10 = 10 x 46. 9 x 0 = 14. 300 x 0 = 7. 75 x 1 = 15. 95 x 1 =8. (3 x 9) x 6 = 3 x (9 x 6) 16. (1 x 7) x 8 = 1 x (7 x 8)

3. Motivation

Valuing:

What kind of person is Rene? How many jobs does he have? How many days does he work a week? Would you want to be like Rene?


1. Presentation

a. Study the problemWhat are the jobs of Rene? Answer: Dishwasher and as CookHow much does he earn as dishwasher? Answer: P120.00How much does he earn as cook? Answer: P250.00How many days does he work in a week? 5What is the number sentence? (5 x P120) + (5 x P250) = n or

5 (p120.00 + P250.00) = n

b. Present the following illustrations.

Write the number sentence below the illustration.

3 x 4 + 3 x 5

Rene works every morning as a dishwasher at Chefoo restaurant earning P120.00 per day and every afternoon as cook at Gardenia garden Restaurant earning P250.00 per day. If he works for 5 days a week in both restaurants, how much is his earning for a week?

(3 x 4) + (3 x 5)

(3 x 4) + (3 x 5) = 3 x (4 + 5)

12 + 15 = 3 x 9

27 = 27

Ask: Did the answers change in the two illustrations? What was done in the second illustration? (the stars were grouped together)]

c. Study the next illustration.

What is the number sentence?

4 x (4 + 3) = 4 x 7 = 28

4 x 4 + 4 x 3

(4 x 4) + (4 x 3) = 16 + 12 = 28

Therefore, 4 x (4 + 3) = (4 x 4) + (4 x 3)

Explain why the answers are the same.

2. Group Activity

a. Divide the class into 3 groups. Give them counters. Distribute the activity cards. Show by means of counters the following combination facts showing the distributive property of multiplication over addition.A 2 x (4 + 8) = (2 x 4) + (2 x 8)B 5 x (6 + 7) = (5 x 6) + (5 x 7)C 4 x (5 + 9) = (4 x 5) + (4 x 9)

b. Draw in your manila paper your work and explain it to the class. (Advise the pupils to use crayons to make their work nice and presentable.)


Solve using the distributive property of multiplication. The example is given to you.(3 + 4) x 8 = (3 x 8) + (4 x 8)

= 24 + 32 = 56

a. 6 x (3 + 3)b. 4 x (5 + 4)c. (6 + 3) x 7d. (2 x 7) x 8e. (3 + 2) x 4f. (3 + 6) x 9g. (2 + 5) x 7h. 9 x (4 + 4)i. 8 x (3 + 3)j. 3 x (2 + 7)

4. Generalization

What is the distributive property of multiplication?

C. Application

Lisa and Marie have 3 dolls and 4 stuffed toys each. How many toys do they have in all?

IV. Evaluation

Distributive property of multiplication over addition is also known as “breaking apart”. The product will not change if one factor is expressed as the sum of two addends then multiplied by the other factor.

A. Give the missing numbers.1) 3 x (7 + 4) = (___ x 7) + (3 x 4) = ____2) 9 x (3 + 4) = (9 x 3) + (9 x ___) = ____3) 5 x (10 + 3) = (___ x 10) + (5 x 3) = ____4) 6 x (4 + 4) = (6 x 4) + (___ x 4) = ____5) (3 + 4) x 5 = (3 x 5) + (___ x 5) = ____

B. Rename the second factor as two addends and find the product.1) 6 x 122) 8 x 253) 5 x 144) 3 x 135) 7 x 9

V. Assignment

1. Show the distributive property of multiplication over addition then solve for the product.Example: 6 x 7 = 6 x (4 + 3)

= (6 x 4) + (6 x 3) = 24 + 18 = 42

a. 9 x 15b. 3 x 21c. 2 x 9d. 8 x 18e. 4 x 10

2. Write the number sentence for each problem, then solve.a. There were 8 pupils who helped the science teacher. Each of them carried 3 beakers and 2

alcohol lamps. How many things did the pupils carry?b. Each of the 9 families in our street has 4 fruit trees and 2 shade trees. How many trees are

there in our street?c. Jojo and his 4 friends were given 4 guavas and 3 chicos each by their Uncle Bert. How

many fruits did they get?

Multiplying 5- or More Digit Factors by 3- Digit Factors without and with Regrouping


Cognitive: Multiply 5- or more digit factors by 3- digit factors without and with regrouping

Psychomotor: illustrate multiplying by 5- or more digit factors using partial product method

Affective: Appreciate the importance of trees


Skill: Multiplying of 5- or more digit factors by 3-digit factors with and without regrouping

References: BEC – PELC I.D.2Textbooks in Math 4

Materials: drill cards, picture, manila paper, markersValue: Conservation of trees



1. Drill

Basic multiplication facts using drill cards

2. Review

What are the parts of a multiplication sentence?

Solve for the product mentally as fast and correct as they can.12 23 17 13 42

x 5 x 3 x 4 x 7 x 8

3. Motivation What can you see in the picture? Do you have fruit trees in your farm/backyard? Is it good to plant trees? Why?


1. Presentation

Analyze the problem.

a. How many mangoes did Mang Ambo and his co-workers gather in one day?b. What is asked in the problem?c. How can we solve the problem?d. Show the solution by using the sum of partial products.

12 234 12 234 12 234 12 234 x 123 x 123 x 123 x 12336 702 36702 36702 36 702

Mang Ambo and his co-workers can deliver 12 234 coconuts in a day. How many coconuts can they deliver in 123 days?

24468 24468 24468 + 12234 + 12234__

1504782

Step 1 Step 2 Step 3Multiply 12 234 Multiply 12 234 Multiply 12 234By 3 by 2 by 1

Step 4Add the partial Products

More practice

Show the solution.a. 14 213 b. 16 821 c. 23 568

x 132 x 424 x 238

Study the multiplication algorithm.

625 543x 3521251086

3127715 + 1876629_ 220191136

Let the children have more practice.a. 68 214 b. 52 183 c. 821 145 d. 21 963 e. 72 584

2. Group ActivityEach group will be given activity sheets/cards containing 3 items. Each

group that finishes the work will display them on the board. The group with the most number of correct answers will be given a prize.

65 218 21 465 392 146 24 693 24 986x 456 x 382 x 781 x 423 x 142

421 826 95 218 76 542 621 483x 321 x 523 x 352 x 218

3. Generalization

How do we multiply 5- or more digit factors by 3- digit factors without and with regrouping?

C. Application

Mr. Mendoza can gather 12 350 eggs in a week from his poultry farm. How many eggs can he gather in 12 weeks?

IV. Evaluation

A. Solve for the products. Choose the letter of the correct answer.

1. Find the product of 32 122 and 112.a. 3 579 664b. 3 597 664c. 7 359 664d. 5 397 664

2. What is the product of 13 211 and 121?a. 1 958 531b. 1 895 531c. 1 598 531d. 1 351 895

3. If the factors are 49 325 and 631, what is the product?a. 31 124 075b. 31 241 750c. 31 421 075d. 31 142 075

4. What is 32 143 repeated 215 times? ________5. Add 1 394 to the product of 42 632 and 134, what is the result? ________

V. Assignment

Give the products.1) 85 354 2) 82 806 3) 49 236 4) 421 832 5) 678 322

x 978 x 814 x 314 x 175 x 387

We multiply 5- or more digit factors by 3- digit factors by multiplying all the digits in the multiplier by the ones digit of the multiplicand to get the first partial product, then by the tens digit to get the second partial product and the hundreds digit to get the third partial product and so on. Then add the partial products to get the final product.

6) What is the product of 2 876 and 489?7) What is 27 654 added to the product of 32 145 and 237?

Multiplying Numbers having Zeros in both Factors without Regrouping


Cognitive: Multiply 5- or more digit factors having 1 to 3 zeros in both factors without regrouping

Psychomotor: Find the product using the process of long multiplication with ease Affective: Show carefulness in doing other activities


Skill: Multiplying 5- or more digit factors having 1 t 3 zeros in both factors without regrouping

References: BEC – PELC I.D.2.3Textbooks in Math 4

Materials: M-1 window cardsValue: Carefulness



1. DrillDrill on basic multiplication facts using window cards. Give the exact time (number

of minutes) to finish the drill card.

2. Mental Computation

Answer the following on your notebook.213 842 524 400 523x 3 x 2 x 3 x 7 x 10

3. ReviewShow how to solve for the product using the long method on the board. Elicit the steps. Be sure that the pupils follow correctly and carefully the steps in multiplying using the long method.

Valuing:

Are you also careful in doing other things aside from our activities in Math? How?

Find the product.

65 432x 765

What did you do to get the correct product?

4. Motivation

Sing the song (tune: Are you sleeping).

Mathematics! Mathematics!How it thrills, how it thrillsAddition, SubtractionMultiplication, DivisionMental Math! Mental Math!(Repeat)


1. Presentation

a. Analyze the problem. How many trucks of rice did the company deliver? How many sacks are in each truck? What is asked? What is the operation to be used? Show the solution

b. Write on the board.40 000

x 30012 000 000 sacks of rice

c. Written exercises10 411 20 011 20 500 80 003x 200 x 60 x 40 x 200

40 004 95 000 70 100x2 000 x 100 x 300

How did you come up with the answers? Is there a faster way to solve for the product? Elicit the patterns.

The Zoom Rice Milling Company delivered 300 trucks of rice in Metro Manila. If each truck contains 40 000 sacks, how many sacks did the company deliver in all?

2. Group activity

Divide the class into two groups.Give them activity sheets where the exercises are written. Each group will report

their answers.60 002 30 052 21 220 23 001x 300 x 1001u x 40 x 200

11 000 21 200 30 022x 500 x 400 x 30

Dyad

Pair the children. Each pair will work on these exercises.32 000 10 052 50 012 52 003 3 002x 300 x 101 x 400 x 100 x 303

3. Generalization

How do we multiply 5- or more digit factors having 1 to 3 zeros in both factors without regrouping?

C. Application

There are 12 300 members of Barangay Masikap. If each member contributed 30 packs of noodles for the Lutong Bayan Project, how many packs of noodles were collected?

IV. Evaluation

A. Find the product.44 000 60 021 32 011 34 000x 21 x 302 x 101 x 21

43 002 2 340X 321 x 21

B. Answer the following:1. Multiply 7 400 and 200. What is the product?2. What is 23 100 added 40 times?3. If the factors are 4 500 and 90, what is the product?4. What is 61 002 multiplied by 400?

V. Assignment

Find the product.

Any number multiplied by zero equals zero. If the zeros in both factors are found at the end, multiply the given numbers then count the number of zeros found at the end of the factors and write them in the answer.

a. 30 002 b. 42 102 c. 21 004 d. 60 002 e. 32 102x 320 x 43 x 102 x 41 x 403

Multiplying Numbers having Zeros in both Factors with Regrouping


Cognitive: Find the product of 5- or more digit factors having 1 to 3 zeros in both factors with regrouping

Psychomotor: Multiply 5- or more digit factors having 1 to 3 zeros in both factors with regrouping in all places

Affective: Show cooperation during class activities


Skill: Multiplying 5- or more digit factors having 1 to 3 zeros in both factors with regrouping in all places


Materials: window cardsValue: Cooperation


1. Drilla. Basic multiplication facts using window drill cards (Record each pupil’s time.)b. Mental Math

2 004 30 100 80 020 7 001 70 200x 320 x 43 x 102 x 41 x 50 x 403

600x400

2. Review

Find the product.80 100 93 002 72 000 80 100 61 003x 50 x 30 x 40 x 50 x 30

3. Motivation

Game: Multiplication Relay

61 001 81 012 61 001 70 200 31 100

x 400 x 60 x 200 x 40 x 60


1. Presentation

a. Analyze the problem. How many laborers are there in the show factory? What is the salary per year of each laborer? What is asked in the problem? What is the operation to be used? How will the problem be solved?

b. Show the solution of the problem. 31 200.00x 501 560 000.00

2. Group Activities

Cooperative Exercise

Complete the table.

x 40 50 60 70 8086 000 4 300 00090 042 7 203 360

809 051 56 633 570700 800

Divide the class into three groups. Give each group an activity card/sheet. The members of the group will help each other answer the following exercises shown below.

64 000 70 800 80 700 90 050 80 007x 30 x 40 x 150 x 203 x 701

460 010 391 021 3 620 400 1 210 055x 50 x 100 x 720 x 302

3. Generalization

How do we multiply 5- or more digit factors having 1 to 3 zeros in both factors with regrouping in all places?

A shoe factory pays each laborer 31 200.00 annually. How much does the owner pay for its 50 laborers?

C. Application

IV. Evaluation

Multiply the following.

1. Multiply 86 000 and 2001, what is the product?a. 17 002 000b. 17 200 000c. 17 020 000d. 170 002 000

2. What is 441 000 repeated 60 times?a. 24 460 000b. 24 604 000c. 24 406 000d. 246 000 000

3. What is 63 004 multiply to 500?a. 31 520 000b. 31 025 000c. 31 502 000d. 31 205 000

4. What is 39 600 times 50? _______5. If the factors are 45 000 and 90, what is the product? _______

V. AssignmentFind the product.

61 002 370 501 462 003 1 874 002 20 621 000 x 40 x 50 x 800 x 108 x 306

Solve the following math problems.1. What is 37 100 times 50?2. Multiply 700 to the difference of 2 100 and 355.3. If the factors are 20 710 and 40, what is the product?

Remember:

1. Use the same steps in multiplying.2. Regroup whenever necessary.3. Write zero in the product if zero is multiplied by any number or bring down

the terminal zeros of the factors and proceed with multiplying the non-zero digits.

Ralph is a salesman of electrical appliances. His average sales for a month is 23 005.00 what is his sales for 105 months?

Multiplying Numbers by Multiples of 10, 100, and 1000


Cognitive: Multiply 5- or more digit factors by multiples of 10, 100 and 1000Psychomotor: Write the product of factors of 5- or more digit by multiples of 10, 100 and

1000Affective: Show kindness to other people in times of need


Skill: Multiplying 5- or more digit factors by multiples of 10, 100 and 1000References: BEC – PELC I.D.2.4Materials: flash cards, charts, number wheelValue: Kindness and helpfulness


1. Drill

Basic multiplication facts using flash cards


4 x 10 8 x 10 9 x 1000 16 x 10 25 x 1007 x 10 36 x 100 4 x 1000 11 x 10 35 x 1000

3. Review

Have the class count together by tens up to 100, and by hundreds up to 1000.

4. Motivation

Show pictures of people of families hit by calamities like typhoon or earthquake.

Valuing: How does our government help the people during typhoon or earthquake? How

about you, how do you help others during heavy typhoon, fire and the like?


1. Presentation

Barrio San Agustin was hit by typhoon Lucing last October. The president promised to give each family 12 250.00. If there were 100 families in the barrio, how much will be given to the families in Barrio San Agustin?

Analyze the problem.

a. What calamity hit Barrio San Agustin?b. What did the president promise each family in the barrio?c. How many families are there in the barrio?d. What is asked in the problem?e. What operations will help solve the problem?f. What is the answer? Show and discuss the solution on the board.

A. 52 163 x 4 = 208 652 B. 21 846 x 3 = 65 53852 163 x 40 = 2 086 520 21 846 x 30 = 655 38052 163 x 400 = 20 865 200 21 846 x 300 = 6 553 80052 163 x 4 000 = 208 652 000 21 846 x 3 000 = 65 538 000

Ask: What pattern did you observe? How do we multiply numbers by multiples of 10?

2. Group Activities

1) Answer the following.a. 21 882 b. 23 635 c. 21 245 d. 53 421 e. 38 456

x 40 x 30 x 500 x 200 x 3 000

f. 32 185 g. 24 683 h. 12 832 i. 32 145 j. 18 321x 10 x 100 x 1 000 x 500 x 7 000


Complete the table

X 60 400 2 000a. 24 345b. 21 632c. 25 998d. 32 529e. 37 292

4. Generalization

How do we multiply numbers by multiples of 10? 100? 1 000?

C. Application

Multiply the multiplicand by the non-zero digits of the multiplier, then annex to the product as many terminal zeros as there are in the multiplier to get the final product.

Solve this problem.Miss Lim receives a monthly salary of 10 625.00. How much can she earn in 10 months?

IV. Evaluation

Multiply the following.

1. What is the product of 21 450 and 50?

a. 1 072 500b. 1 720 005c. 1 270 050d. 1 072 400

2. What is 52 183 multiply by 300 times 2?a. 31 903 800b. 31 093 800c. 31 309 800d. 31 903 008

3. Multiply 80 to the sum of 32 000 and 180.a. 2 475 400b. 2 754 400c. 2 745 400d. 2 574 400

4. What is 319 000 minus the product of 376 120 and 800? ________5. The product of 12 836 and 100 is added to 23 916. ________

V. Assignment

X 60 1 200 6 000a. 21 345b. 53 466c. 25 364d. 51 528e. 85 432

Solve the following math problems.1. Multiply 80 to the sum of 320 and 180.2. What is the product of 2 145 and 50?3. What is 319 000 minus the product of 376 and 800?

Estimating Products


Cognitive: Estimate the product of two factors with 5- or more digits and 2- to 3- digit numbers

Psychomotor: 1. Tell the importance of caring for our environment2. Find the estimated product of two factors with 5- or more digits and 2- to 3- digit numbers

Affective: Show love for nature


Skill: Estimating the products of two factors with 5- or more digits and 2- to 3- digit numbers

References: BEC – PELC I.D.3Textbooks in math 4

Materials: cutouts, chart, activity cards, number wheel, picturesValue: Love for nature



1. Drill

Basic Multiplication FactsGame: “Picking Guavas”

A pupil picks a guava with a multiplication fact. He/she answers as fast as he/she can. A correct answer gets a candy.

2. Review

Review rounding off numbers.Round off to the nearest:

Tens Hundreds Thousands Ten Thousands

Hundred Thousands

213 685172 29436 42869 123

3. Motivation

a. Show the picture of three baskets full of mangoes. About how many mangoes do you think are contained in the baskets? (Pupils are expected to give different numbers.)

b. Explain that what they give are just estimates of the number of mangoes in the baskets. They are not sure and did not actually count the number of mangoes in the baskets.


1. Presentation

The garden club is selling orchid plants at 12 323.00 a pot to collect funds. If 123 pots were sold, about how much money did the club get?

a. How much is a pot of orchid plant?b. How many pots were sold?c. What phrase in the problem indicates that what is asked is an estimated product?

Let us study how to estimate products.1. 12 323 10 000 2. 10 000

x 123 x 100 x 100 1 000 000

How do we estimate products? What do we do first?

Valuing: Orchids are beautiful flowers. What do they do to our surroundings? Are they

important to us? Why?

2. Group Activity

Estimate the products.a. The Girl Scouts of Cavite is engaged in rose gardening. They gather 55 125 roses a

day and sell them. How many flowers can they gather in 24 days?b. An environmentalist distributed gift envelopes to 24 565 school children. If each

envelope contained 17 plant-a-tree bookmarks, how many bookmarks were distributed?

c. The Sangley Nursery grows 33 284 santan every month. How many santan will it produce in 212 months?

Analyze and discuss the answers of each group. Ask the children why we need to grow plants.

3. Guided Practice

Estimate the product by rounding each factor to the nearest tens.a. 14 325 b. 21 178 c. 56 683 d. 47 928

x 42 x 43 x 62 x 37

e. 34 625 f. 51 321 g. 32 182 h. 52 146x 63 x 28 x 33 x 45

i. 45 682 j. 21 456x 78 x 81

4. Generalization

How do you estimate the product of 2 factors?

C. Application

Solve each problem.1. A nursery sells 34 296 seedlings a day. About how many seedlings can be sold in 23 days?2. A town has an average of 81 989 number of trees. Give the estimated total number of

trees of 12 towns.IV. Evaluation

Estimate the product.

1. Estimate the product of 34 231 and 62.a. 18 000 000b. 1 800 000c. 1 008 000d. 180 000 000

2. Round off 184 599 and 586 to the highest place value and find the estimated product.a. 100 000 000b. 120 000 000c. 600 000 000d. 500 000 000

3. Use the number sentence 48 214 x 34 = n. Estimate the product.a. 2 000 000b. 1 000 000c. 1 500 000d. 1 005 000

4. If we round off 265 463 to the greatest place value is equal to the 300 000 and 371 to 400. What is the estimated product? ________

5. Barangay San Vicente plans to raise 14 563.00 weekly from recycled waste materials. About how much would they be able to raise in 13 years? ________

V. Assignment

Estimate the product.a. 631 236 b. 184 599 c. 265 463

x 143 x 586 x 371

d. 572 169 e. 491 641x 39 x 334

Multiplying Mentally without Regrouping

To estimate the products, round the factors to the highest/greatest place value then multiply the rounded factors.


Cognitive: Multiply mentally 2- digit numbers with products up to 200 without regrouping

Psychomotor: Practice speed and accuracyAffective: Tell the importance of fruits to our body


Skill: Multiplying mentally 2- digit numbers with products up to 200 without regrouping

Reference: BEC – PELC I.D.4Materials: textbook, flash cards, activity cardsValue: Health consciousness



1. Drill

Basic multiplication facts using flash cards


13 24 12 16 22 11x 3 x 2 x 4 x 1 x 4 x 7

3. Review

Estimate the products.32 465 12 365 72 146 31 654 46 123

x 28 x 47 x 52 x 32 x 81

4. Motivation

Do you like fruits? What is your favorite fruit? What food nutrients do we get from fruits? Which do you prefer to eat chocolate candies or fruits? Why? Why do we have to eat fruits everyday?


1. Presentation

a. Present this word problem

How much is a kilo of mango? What is the cost of 2 kilos? What did you do to solve the problem? Can you solve it without using paper and pencil?b. Give the products orally.

42 54 31 43 64 21 54x 3 x 2 x 5 x 3 x 2 x 8 x 2

c. Copy and complete the table.

Factor 14 22 41 21 32 40Factor 2 3 2 4 2 2Product ? ? ? ? ? ?

2. Group Activity

Divide the class into three groups. Give each group an Activity Card like one below. Record which group answered first, the second and the third. Answers will be written on the other square.

2 X3 X4 X

Answers

3. Generalization

How do you multiply mentally 2- digit numbers by 1- digit number without regrouping?

A kilo of mango cost 80.00. How much will you pay for 2 kilos?

22 63 52 43 32 7221 41 3044 126 104

129 96 21684 164 120

C. Application

Solve mentally.1. There are four rows of chairs in Miss Luna’s class. If there are 10 chairs in each row,

how many chairs are there in all?2. Rizal Primary School has three sections in Grade 4. Each section has 42 pupils. How

many Grade 4 pupils are there in Rizal Primary School?

IV. Evaluation

Multiplying mentally:

1) 102 multiply by 2 is equal to _____2) What is the product of 20 and 10? _____3) In number sentence 40 x 5 = n, what is n?4) What is the product of 20 x 5, multiply by 2? 5) Rizal Primary School has 4 sections for grade 4. Each section has 50 pupils. How many grade 4

are there in Rizal Primary School?

Multiply mentally.

23 x 3 = 21 x 4 = 3 x 62 =2 x 50 = 21 x 9 = 4 x 50 =

V. Assignment

A. Multiply mentally. 61 20 43 64 72x 3 x 10 x 3 x 2 x 2

24 36 73 54 82x 2 x 1 x 2 x 2 x 2

B. Orall drill. Test your speed in multiplying each number mentally. 12 22 23 11 12x 2 x 3 x 1 x 4 x 3

32 11 43 33 50x 3 x 7 x 2 x 3 x 2

C. Create two word problems involving multiplying numbers mentally.

Numbers in Exponential Form


In multiplying mentally, multiply first the ones and then the tens, without using paper and pencil.

10 33 42

22

6

42

Cognitive: Write numbers in exponential formPsychomotor: Express numbers in exponential formAffective: Practice cooperation in group activities


Skill: Writing numbers in exponential formReferences: BEC – PELC I.D.5

Textbooks in Math 4Materials: flash cards, activity sheetValue: Cooperation



1. Drill

Use flash cards in conducting this drill. Select two to three volunteers/pupils to act as contestants. Whoever answers first will be given points until the time limit has been consumed.

Example:

25 36 22 81 18 50x 2 x 4 x 3 x 2 x 5 x 4

2. Review

Write the missing numbers in the factor tree.

a. 6 b. 12 c. 30

d. 48

3. Motivation

Look at the given data below. Notice how the numbers are written.

Standard Form Product of Factors Exponential Form2 = 2 21

4 = 2 x 2 22

8 = 2 x 2 x 2 23

16 = 2 x 2 x 2 x 2 24

32 = 2 x 2 x 2 x 2 x 2 25

64 = 2 x 2 x 2 x 2 x 2 x 2 26

What did you observe about how the numbers are written?


1. Presentation

Group 11. Look at the numbers in the table. How is 2 related to 4 and 4 to 8?2. Write your observations on the chart.

Given Data Observationsa. 2b. 4c. 8d. 16e. 32f. 64

Group 2a. Tell something about the illustration.b. How many times is number 2 being written?

Exponential Form Product

2

2 x 2

1

2

3

2 x 2 x 2

2 x 2 x 2 x 2

2 x 2 x 2 x 2 x 2

2 x 2 x 2 x 2 x 2 x 2

Group 3

a. What did you observe about the way 2 is written?b. Observe from the first to the sixth number.

Group 4

a. Compare the following data to those of the power of 2. Do they show a pattern? How?

b. Write your observations below.3 = 39 = 3 x 327 = 3 x 3 x 381 = 3 x 3 x 3 x 3243 = 3 x 3 x 3 x 3 x 3729 = 3 x 3 x 3 x 3 x 3 x 3

Observations: _____________________________________

2. Analysis and DiscussionAsk the pupils the following questions:

a. What happens to 2 when multiplied by another 2? By another 2?b. What did you observe about the numbers from 2 up to 64? How about the factors?

Illustrations:

2 4 8 16 32 64

What is the relation of the first number to the second number?What happens when you double 2, 4 and so on?Does it form a pattern?Do you know that any number can also express in exponential form? How are we going to do this?

40 = 1 - Any non-zero number raised to zero power is always 1.51 = 5 - A number raised to the first power is always equal to itself.

4

5

6

62 = 36 – Any number raised to the second power is always multiplied by itself.

Exponent62 = 36 (standard form) = 6 x 6 (product)

Base

Based on the work of group 4, 3 to the third power is obtained by multiplying 3 by itself three times. It is written as 33

Valuing: How did you work with the other members in your group? It is important to cooperate with each other while working on something?

Why?

3. Group Activity

a. Write the exponential form.1) 7 x 7 3) 9 x 9 x 9 x 92) 8 x 8 x 8

b. Write each as a product of equal factors.1) 642) 125

4. Generalizationa. What is exponent?b. How do you write numbers in exponential form?

C. Application1. Write the standard form.

a. 24

b. 43

c. 74

d. 85

e. 94

The exponent tells how many times the base is used as a factor. A non-zero number raised to the zero power is always 1.

A number raised to the first power is always itself; the second power is also called squared and so on.

4 = 2 x 2 = 22 Exponent (tells how many times the base is multiplied by itself)

Factors Base (the factor to be multiplied)

2. Write in exponential form.a. 2 x 2 x 2 x 2b. 3 x 3 x 3 x 3c. 4 x 4 x 4d. 7 x 7 x 7 x 7 x 7 x 7e. 9 x 9 x 9 x 9 x 9 x 9 x 9

IV. EvaluationA. Match column A with column B.

A B1) 53 a. three cubed2) 45 b. fived cubed3) 22 c. five to the seventh power4) 57 d. two squared5) 33 e. four to the fifth powerB. Write the standard form.

1) 35

2) 54

3) 63

V. Assignment

Select the letter of the correct answer.1) 7 x 7 x 7 x 7 x 7 =

a. 77 b. 75 c. 57

2) 9 x 9 x 9 x 9 =a. 49 b. 94 c. 99

3) 10 =a. 100 b. 101 c. 102

4) 43 =a. 12 b. 16 c. 64

5) 64 = a. 82 b. 28 c. 88

Numbers from Standard Form to Scientific Notation


Cognitive: Write numbers from standard form to scientific notationPsychomotor: Compute accurately the power of a numberAffective: Show accuracy in giving answers


Skill: 1. Writing numbers in scientific notation2. Computing the power of a number

References: BEC – PELC I.D.6.1

Textbook in Math 4Materials: flash cards, chart, learning activity sheetsValue: Accuracy



1. Drill

Find each product.a. 10 x 10 = ___

10 x 10 x 10 = ___10 x 10 x 10 x10 = ___

b. 1) 1 x 10 = ___ 10 x 10 = ___2) 3 x 200 = ___ 30 x 200 = ___3) ___ x 40 = 20 x 80 30 x 100 = ___ x 50

2. Review

Write the standard form for the following:a. 23 b. 34 c. 42 d. 53 e. 65

3. Motivation

The teacher shows a picture of solar system and asks the following questions:a. What is the composition of the solar system?b. What is the closest planet to the sun?c. How far is this planet from the sun? do you know what planet this is? It is

Mercury.

Problem:

Valuing: How are you going to answer the different exercises? Why? How do you feel if you get a correct answer?


1. Presentation

Introduce the lesson through illustration/drawing.

Mercury is the planet closest to the sun. It is about 60 000 000 kilometres to the sun. How far is it from the sun?

Mercury is 60 000 000 km away from the sun.

Look at this illustration:

60 000 000 6 x 107

Example #2

Standard Form Scientific Notation500 5 x 102

Example #3How many zeros are there? Why is it 10 raised to the 4th

power?40 000 4 x 104

Example #4360

Sun Mercury

Standard Form

In what form is 60 000 000 written?

Is it in standard form? How many zeros are there?

There are 7 zeros.

Scientific Notation

Where can we find 6?

Is it the 8th digit of the number? Is it a number greater than 1 but

less than 10? The scientific notation consists of

two factors, the first factor is number 1 or greater but less than 10.

So, 6 is the first factors. The second factor is a power of 10.

What is the power of 10?

60 000 000 = 6 x 107 exponent

7 zeros (shows the number of zeros)

Think: 360 is between 300 and 400.300 = 3 x 102

400 = 4 x 102

Shortcut method:3. 6. 0. = 3.6 x 102

A number greater than or equal to one but less than

ten


Dyad GroupingWrite in scientific notation.

a. 30b. 600c. 7 400

3. Generalization

How do we write numbers from standard form to scientific notation?

C. Application

Triad Grouping

Write in scientific notation.

1) 3002) 6 0003) 40 0004) 800 0005) 700 000 000

IV. Evaluation

1. Fill in the missing number.a. 600 = ___ x 102

b. 7 000 = 7 x 10 ___

move the decimal point 2 places to the left. (you have to move the decimal point 2 places to the left so the first factor is more than 1 but less than 10)

Standard numerals are written in scientific notation as a product of 2 factors. The first factor is greater than or equal to 1 but less than 10 and the second factor is a power of 10.

c. 160 000 = 16 x 10 ___d. 12 000 000 = ___ x 106

e. 250 000 000 = 25 x 10 ___

2. Write in the scientific notation.a. 80b. 500c. 240d. 6 700e. 31 000

V. Assignment

Express in scientific notation.

1) 564 0002) 3 120 0003) 6 400 000 000

Numbers in Scientific Notation to Standard Form


Cognitive: Write numbers in scientific notation to standard formPsychomotor: Use powers of 10 to write numbers in exponential formAffective: Show cooperation in group activities


Skills: 1. Writing numbers in scientific notation2. Using powers of 10 to write numbers in exponential form


Materials: flash cards, chart, learning activity sheetsValue: Cooperation



1. Drill

Mental computation using multiplication facts.

2. Review

Write the numbers in exponential form.a. 6 000b. 7 000 000c. 80 000 000d. 860 000e. 3 800 000

3. Motivation

Mercury is the planet closest to the sun. It is about 60 000 000 km from the sun.a. How far is Mercury from the sun?b. What did we study yesterday?c. What did we do with the number?


1. Presentation

60 000 000 is in what form of the number?6 x 107, what is this form?How did we express the numbers?

Suppose, we do it this way:6 x 107 60 000 000

How did I write the given number?Do you know how to do it?

2. Group Activity

a. Present this number.

What is the exponent?

Based on previous lesson, the exponent shows the number of zeros 60 000 000 has.

What is this form?- Scientific Notation

How about this?- Standard form

Pupils’ Activity: DyadExample:

4 x 10 7 40 000 0007 x 10 6 7 000 000

b. Show the changing of exponential form to standard form.

6 x 107 60 000 000

6 x 107

60 000 000

1.2 x 104 = 1. 2 000 12 000

1. The exponent is 4. Move the decimal point 4 places to the right.2. What happened to the number when the decimal point is moved to the right using the

exponent?3. Give other examples for dyad activity

3.1 x 106 3. 1 00000 3 100 000

7.31 x 106 7 3 1 0000000 7 310 000 0003. Practice Exercises

Write in standard form (group activity).a. 3 x 103

b. 4 x 106

c. 6 x 108

d. 6.1 x 103

e. 9.3 x 106

4. Generalization

How do we write numbers in scientific notation to standard form?

C. Application

Write in standard numerals.8 x 104

9 x 102

1.2 x 105

2.81 x 103

IV. Evaluation

1. Match column A with column B.A B

1) 6 x 102 a. 6 0002) 6 x 104 b. 60 0003) 6 x 103 c. 6004) 6 x 105 d. 6 000 0005) 6 x 106 e. 600 000

2. Write in standard form.

To change scientific notation to standard numerals, move the decimal point to the right of the decimal point adding zeros after the last non-zero digit depending on the exponent to make it a whole number.

a. 8 x 102

b. 8.1 x 102

c. 2.16 x 105

d. 3.49 x 108

e. 6.11 x 107

V. Assignment

Write in standard form.1) 3 x 103

2) 4 x 104

3) 9.3 x 106

4) 12 x 103

5) The earth is about 1.5 x 108 km from the sun.

Solving Problems Involving Multiplication


Cognitive: Solve word problems involving multiplication of whole numbers including money

Psychomotor: Follow correctly the steps in solving word problemsAffective: Realize the importance of backyard gardening for the family


Skill: Solving word problems involving multiplication of whole numbers including money


Materials: flash cards, chart, learning activity sheetValue: Industry



1. Drill

a. Basic multiplication facts using window cards.b. Solve for the product of factors with multiples of 10 and 100.

Examples: 40 x 9 = ___ 400 x 30 = ___

50 x 30 = ___ 20 x 90 = ___20 x 700 = ___ 500 x 8 = ___600 x 8 = ___ 60 x 20 = ___

2. Review

What are the steps in solving a problem?

a. Have a game on rearranging the steps in analyzing word problems that are written on strips of cartolina.

b. The group who finishes ahead of the others is declared the winner.

3. MotivationHow many of you have gardens at home? What are planted in your

garden? Are they in rows? How do farmers plant seedlings in a farm?

Valuing:

Is it important to have gardens at home? Why?


1. Presentation

The teacher specifies that to solve a word problem, the pupils must always think of the steps in solving a word problem. Let us use the following guide in solving word problems.

a. What is asked?b. What are given?c. What operations are to be used?d. Write the number sentence.e. Do the operation.f. What is the answer?g. Check if your answer makes sense?

2. Group Activity

Remind the pupils of the importance of analyzing the problems first before solving for the answer.

a. Group the pupils.

An orchard contains 8 rows of trees. If there are 10 trees in a row, how many trees are there?

b. Each group is given an activity sheet with a problem written on it.c. They will solve the problems using the steps in problem solving.

Activity 1

Supply the missing information below.

a. What is asked?b. What are given?c. What operations are to be used?d. Write the number sentence.e. What is the answer?

Activity 2

Illustrate the problem.

Activity 3

Write the given data and solve for the answer.

a. What is asked?b. What are given?c. What operations are to be used?d. Write the number sentence.e. What is the answer?


The teacher gives problems and lets the pupils solve for the answer by following the steps.

a. Mang Julio’s jeepney uses 175 litres of gasoline in a week. How many litres of gasoline can it consume in 15 weeks?

b. A basket of lanzones costs 1 285.00. How much do 25 baskets of lanzones cost?c. There are 1 648 shoppers who go to Mabuhay Department Store everyday. How many

shoppers go to the store in 59 days?d. There are 953 names listed in each guest book of the National Museum. How many

names are listed in 52 guest books?

4. Generalization

What are the steps in solving word problems?

C. Application

Read and solve on your paper.1. Mrs. Dizon, the school nurse examined 48 pupils per day. How many pupils did she

examine in 5 days?2. Alissa and her classmates used 5 packs of cornstarch for their maja blanca recipe. Each

pack cost them 19.00. How much did they spend for cornstarch?

IV. Evaluation

Solve the following problems.

1. Norma saved 128.00 from her daily allowance for 22 days. How much was her daily earnings?2. Each bag contains 20 kg of lanzones. If each kilogram of lanzones costs 120.00, how much

does a bag of lanzones costs?3. Empty bottles are brought at 8.00 each bottle. How much money does one earn in selling 4

280 empty bottles?4. Jose earned 48.00 a day. How much did he earn in one week?5. It was Lara’s 7th birthday. Her mother bought 15 kilos of pork. If each kilo costs 120.00, how

much will her mother spend for pork?

V. Assignment

Solve.1. Aling Rosa sells flowers. She can sell 12 dozens of roses a day. How many roses can she sell in

two weeks?2. It was Joan’s 10th birthday. Her mother bought 10 kilos of pork. If each kilo costs 200.00, how

much will her mother spend for pork?

Solving 2-Step Word Problems


Cognitive: Solve 2- step word problems involving multiplication and either addition or subtraction

Psychomotor: Write the solution to the problem accuratelyAffective: Work cooperatively with the group


Skill: Solving 2- step word problems involving multiplication and either addition or subtraction


Materials: textbook, flash cards, chart, learning activity sheetValue: Cooperation



1. Drill

Write the numeral mentioned in the blank provided.Story:

The statue of Liberty is one hundred fifty-one (_____) feet tall. The tip of the torch is three hundred five (______) feet above the ground. It is made with over three hundred (______) thin sheets of copper. To climb the top of the statue, there are one hundred sixty-eight (_______) steps.

a. The largest number in the story is ______.b. The smallest number in the story is _______.c. The numbers in the story that are less than 186 are ____ and ____.d. The numbers in the story that are greater 200 are ____ and ____.

2. Review

Ask the pupils about the different steps in solving word problems.

3. Motivation

Do you know what a mailman is?What is his work?What do you notice on the mail envelope?Is this important? Why?

Here is the problem about stamps. Let us find what it is all about.Problem:


1. Presentation

Children, if you are to solve the problem, what are you going to do?If I will let you work in groups, what are you going to do? Why?

Marie had 153 pages in her stamp album. There were 12 stamps on each page. She gave 63 stamps to her friend. How many stamps were left with her?

Activities – Discovery Approach

Group 1

Acting out the problems.

Materials: magazines, pieces of art paperThe pupils are to present the problem by acting it out. One member will act as

Marie and others will help in answering the problem using improvised album and stamps.

Group 2

Solving the problem (Computation)Materials: chalk, mini-boardsThe group is allowed to have a direct computation based on their understanding about the problem. The group should come out with only one common answer.

Group 3

Picture illustrations about the problem.Materials: manila paper, mini board, chalk, crayons, marker penThe group is to give the answer to the problem by illustrating it through pictures.They should indicate the given data. Report their answer.

Group 4

Solve the problem by answering the guide questions.a. What are given?b. What is asked?c. What are the operations to be used?d. Write the number sentence?e. How will you do the operations?f. What is the answer?


Teacher will use the data presented by the pupil.a. Who collects stamps?b. What did she do with her stamps?c. Did she give all her stamps? How many stamps were given?d. Do you know the number of stamps? What do you think you will do?e. Is the final answer correct? Why?

3. Practice Exercises – Dyad

Solve the problems carefully.

a. Many had 3 boxes of paper plates. Each box contains 36 plates. He used 73 paper plates for the birthday party of his son. How many paper plates were left?

b. There were 27 children who went to the library in the morning and 16 children in the afternoon. Each child read 7 books. How many books were read by them?

4. Generalization

How do you solve 2- step word problems involving multiplication and addition/subtraction?

In solving 2- step word problems involving multiplication and addition/subtraction, follow the following steps:

C. Application

Solve and give the correct answer.1. Naty has a vegetable garden. Last week, she sold 65 pieces of papaya for 10.00 each and 90

pieces of ampalaya for 5.00 each. How much was her total sales last week?2. Pacita bought 6 kilograms of rice at 24.00 a kilogram and 4 bars of laundry soap at 19.00

each. How much did she pay in all?

IV. Evaluation

Solve and give the correct answer.1. Rey bought 3 boxes of apples. Each box contained 321 apples. He gave 480 apples to his

brothers and sisters. How many were left with Rey?2. Letty bought 15 kilos of rice at 25.00 per kilo. How much should be her change if she gave

500.00?3. A pre-school teacher charges 125.00 per person for one hour of tutorial class. The teacher

pays 35.00 per hour for the rental of her place. How much does she earn for a 12-hour tutorial class with one pupil?

4. Rica sold 785.00 worth of beauty products. The products she sold were make-up kits and lipsticks. She was able to sell 6 make-up kits at 95.00 each. How much was her sales for the lipsticks?

5. Marie and Peping bought the following goods for their picnic: two cakes at 15.00 each, 4 bags of potato chips at 14.00 each, 3 boxes of chocolate candies at 25.00 per box. How much did he pay for the goods? Is 150.00 enough?

V. Assignment

a. Readb. Understandc. Plan d. Solvee. Look back to check the answer

Solve the following word problems and label your answers.1. Jubal packed 12 pillowcases in a box. Each pillowcase costs 25.00. How much would 3 boxes of

pillowcase cost?2. A group of balikbayan rented 3 cottages at 1 275.00 each. They also rented 2 extra beds at

475.00 each. How much did the group pay for the cottages and the extra beds?

Dividing Numbers by 3- Digit Numbers without Remainder


Cognitive: Divide 5- or more digit numbers by 3-digit numbers without remainderPsychomotor: Solve problems with ease and accuracyAffective: Practice helpfulness and cooperation


Skill: Dividing 5- or more digit numbers by 3-digit numbers without remainderReferences: BEC – PELC I.E.1.1Materials: window cards, butterfly cutoutsValue: Helpfulness and cooperation



1. Drill

Game – Catching the Butterflies (butterfly cutout from a garden of flowers and answer the combination at the back) Each pupil will get one butterfly cutout

20 ÷ 5 24 ÷ 4 35 ÷ 7 15 ÷ 310 ÷ 2 36 ÷ 6 21 ÷ 3 28 ÷ 742 ÷ 6 18 ÷6

2. Review

“Mix and Match”Teacher prepares several pairs of number sentences.Example:

707 ÷ 7 = 101

303 ÷ 3 = 1016006 ÷ 6 = 1001

1269 ÷ 9 = 141

Pupils will get one card each.Teacher announces, “mix” and pupils will mix around with their classmates.Teacher calls, “pair” and the pupils will find a partner to match their cards.

3. Motivation

A while ago, we used cutouts of butterflies. Where do butterflies stay? Why is it that they love to stay in the garden? What do we find in this place? Present the lesson through this problem:

Valuing: What kind of a boy is Ruben? Are you like Ruben? Are you also helpful at home?

What do you do to help?


1. Presentation

a. Answer the following.

How many tomatoes did he gather? What did he do to the tomatoes? How many bags were used?

b. The pupils present their work and have them explain how they arrived at the answer.

c. Showing the illustration

divisor 215 /671 875 dividend (number to be divided)(number used to divide)

1) What are you going to do?2) What is the number that you are going to divide?

e. How many 215s are there in 671?Use: 215 (trial and error)

x 4860

9660 ÷ 3 = 3220

Ruben helped his father in gathering tomatoes in their vegetable farm. If he gathered 671 875 tomatoes and placed 215 in each bag, how many bags did Ruben use?

Or repeated addition 215+ 215 430+ 215 645

1) Which is the correct answer? 3 or 4? Why?2) Where did I write 3? Why?3) What do you call 3?4) What will you do to 3 and 215?5) How about 671 and 645?6) How do we know if the answer is correct?7) Follow the same questions until the time the answer is given

The long method 3 125

215 / 671 875- 645 268 - 215 537 - 430

1075 - 1075

0

f. Solve individually.162 ÷ 213


Solve: “Quad Group”a. 52 216 ÷ 122b. 266 299 ÷ 473c. Mr. Francisco subdivided his coconut farm in Cavite whose area is 37 800 square

metres. It will be used as a resettlement area for 120 landless families in a squatters area in Metro Manila. How many square metres will each family get?

3. Generalization

How will you divide numbers without remainder?

In dividing 5 digit numbers by 3-digit numbers:

a. Divide the number formed by the first three digits of the dividend from the highest place by the divisor. If the first three digits of the dividend is less than the divisor use the first 4 digits of the dividend.

b. Multiply the partial quotient by the divisor then write the answer below the first digits used in the dividend.

c. Subtract the partial product from the first partial dividend.

C. Application

Find the quotient.1. 76 622 ÷ 4212. 57 024 ÷ 1323. A furniture factory delivered 42 875 chairs to 175 schools. Each school got an equal

number of chairs. How many chairs did each receive?

IV. Evaluation

1. Divide the following:a. 39 751 ÷ 127 =b. 237 744 ÷ 312 =c. 50 924 ÷ 116 = d. 240 118 ÷ 422 =e. 167 072 ÷ 368 =

2. Read and solve.1. What number will you get if you divide 91 372 by 431?2. If you divide 66 248 by 292, what quotient will you get?3. 223 136 divided by 608 equals ___4. 188 020 divided by the sum of 345 and 250 = ___

V. Assignment

Find the quotient.1) 213 906 ÷ 926 2) 663 552 ÷ 864 3) 554 552 ÷ 673

In dividing 5 digit numbers by 3-digit numbers:

a. Divide the number formed by the first three digits of the dividend from the highest place by the divisor. If the first three digits of the dividend is less than the divisor use the first 4 digits of the dividend.

b. Multiply the partial quotient by the divisor then write the answer below the first digits used in the dividend.

c. Subtract the partial product from the first partial dividend.

lesson plans (repaired) (repaired) (repaired)

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