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Lesson guide gr. 3 chapter i -subtraction v1.0

1) The document is a lesson guide for grade 3 elementary mathematics on subtraction. 2) It covers subtracting 3-digit and 4-digit numbers from 4-digit and 5-digit numbers without and with regrouping in the tens, hundreds, thousands, and ten thousands places. 3) The guide provides learning objectives, content, experiences, and activities to teach subtraction skills and apply them to word problems, including estimating differences and mental subtraction. It integrates values, multiple intelligences techniques, and higher-order thinking skills.

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Lesson Guide In Elementary Mathematics Grade 3 Reformatted for distribution via DepEd LEARNING RESOURCE MANAGEMENT and DEVELOPMENT SYSTEM PORTAL DEPARTMENT OF EDUCATION BUREAU OF ELEMENTARY EDUCATION in coordination with ATENEO DE MANILA UNIVERSITY 2010 Chapter I Whole Numbers Subtraction INSTRUCTIONAL MATERIALS COUNCIL SECRETARIAT, 2011
Lesson Guides in Elementary Mathematics Grade III Copyright © 2003 All rights reserved. No part of these lesson guides shall be reproduced in any form without a written permission from the Bureau of Elementary Education, Department of Education. The Mathematics Writing Committee GRADE 3 Region 3 Agnes V. Canilao – Pampanga Josefina S. Abo – Tarlac City Alma Flores – Bataan Region 4 - A Cesar Mojica – Regional Office Marissa J. de Alday – Quezon Henry P. Contemplacion – San Pablo City Region 4 – B Felicima Murcia – Palawan National Capital Region (NCR) Laura N. Gonzaga – Quezon City Dionicia Paguirigan – Pasig/San Juan Yolita Sangalang – Pasig/San Juan Bureau of Elementary Education (BEE) Elizabeth J. Escaño Galileo L. Go Nerisa M. Beltran Ateneo de Manila University Pacita E. Hosaka Support Staff Ferdinand S. Bergado Ma. Cristina C. Capellan Emilene Judith S. Sison Julius Peter M. Samulde Roy L. Concepcion Marcelino C. Bataller Myrna D. Latoza Eric S. de Guia - Illustrator Consultants Fr. Bienvenido F. Nebres, SJ – President, Ateneo de Manila University Ms. Carmela C. Oracion – Principal, Ateneo de Manila University High School Ms. Pacita E. Hosaka – Ateneo de Manila University Project Management Yolanda S. Quijano – Director IV Angelita M. Esdicul – Director III Simeona T. Ebol – Chief, Curriculum Development Division Irene C. Robles – OIC - Asst. Chief, Curriculum Development Division Virginia T. Fernandez – Project Coordinator EXECUTIVE COMMITTEE Jesli A. Lapus – Secretary, Department of Education Teodosio C. Sangil, Jr. – Undersecretary for Finance and Administration Jesus G. Galvan – OIC - Undersecretary for Programs and Projects Teresita G. Inciong – Assistant Secretary for Programs and Projects Printed By: ISBN – 971-92775-2-1
iii TABLE OF CONTENTS Introduction ..................................................................................................................................iv Matrix ........................................................................................................................................v I. WHOLE NUMBERS A. Subtraction Subtracting Numbers without Regrouping  3-Digit Numbers from 4- to 5-Digit Numbers .................................................... 1  4-Digit Numbers from 4- to 5-Digit Numbers .................................................... 7 Subtracting Numbers with Regrouping in the:  Tens Place ........................................................................................................ 15  Hundreds Place ................................................................................................. 21  Thousands Place .............................................................................................. 27  Ten Thousands Place ....................................................................................... 32 Subtracting Numbers with Zero Difficulty ....................................................................... 38 Estimating Differences ................................................................................................... 45 Subtracting Mentally without Regrouping ...................................................................... 49 Solving Word Problems .................................................................................................. 55 Solving Word Problems Mentally ................................................................................... 61 Solving 2-Step Word Problems involving Addition and Subtraction including Money ................................................................................................ 65
iv I N T R O D U C T I O N The Lesson Guides in Elementary Mathematics were developed by the Department of Education through the Bureau of Elementary Education in coordination with the Ateneo de Manila University. These resource materials have been purposely prepared to help improve the mathematics instruction in the elementary grades. These provide integration of values and life skills using different teaching strategies for an interactive teaching/learning process. Multiple intelligences techniques like games, puzzles, songs, etc. are also integrated in each lesson; hence, learning Mathematics becomes fun and enjoyable. Furthermore, Higher Order Thinking Skills (HOTS) activities are incorporated in the lessons. The skills are consistent with the Basic Education Curriculum (BEC)/Philippine Elementary Learning Competencies (PELC). These should be used by the teachers as a guide in their day-to-day teaching plans.
v MATRIX IN ELEMENTARY MATHEMATICS Grade III COMPETENCIES VALUES INTEGRATED STRATEGIES USED MULTIPLE INTELLIGENCES TECHNIQUES With HOTS I. Whole Numbers A. Subtraction of Whole Numbers 1. Comprehension of Subtraction 1.1 Subtract 3 to 4 digit numbers from 4 to 5 digit numbers with minuends up to 100 000 without and with regrouping and with zero difficulty 1.1.1 Subtract 3 digit numbers from 4 to 5 digit numbers with minuends up to100 000 without regrouping Cooperation Modeling Simplifying the problem Diagrams and chart (Spatial) Cooperative groups (Interpersonal)  1.1.2 Subtract 4 digit number from 4 to 5 digit numbers with minuends up to 100 000 without regrouping Cooperation Draw pictures Simplifying the problem Puzzle (Logical mathematics) Diagrams and chart (Spatial) Cooperative groups(Interpersonal  1.1.3 Subtract 3 to 4 digit numbers from 4 to 5 digit numbers with regrouping 1.1.3.1 in the tens place Helpfulness and following rules Draw pictures Body movements (Bodily kinesthetic) Manipulative (Bodily kinesthetic) Diagram (Spatial)  1.1.3.2 in the hundreds place Cooperation Simplifying the problem Song (Musical) Manipulative (Bodily kinesthetic)  1.1.3.3 in the thousands place Helpfulness Draw pictures Simplifying the problem Cooperative groups(Interpersonal) Puzzle (Logical mathematics)  1.1.3.4 in the ten thousand place Cooperation Draw pictures Simplifying the problem Cooperative groups(Interpersonal) Manipulative (Bodily kinesthetic)  1.1.3.5 with zero difficulty in either tens or hundreds place Helpfulness Polya's steps in problem solving Acting out the problems Body movements (Bodily kinesthetic) 
vi 1.1.4 Estimate the difference of two numbers with 3 to 4 digits Following simple directions Simplifying the problem Puzzle (Logical mathematics)  1.2 Subtracts mentally 2 digit numbers with minuends up to 99 without regrouping Speed and accuracy Simplifying the problem Number Puzzle (Logical mathematics) Illustrations (Spatial) Body movements (Bodily kinesthetic)  2. Application of Subtraction 2.1 Solve 1 step word problems involving subtraction of whole numbers including money with minuends up to100 000 without and with regrouping following the steps in problem solving Cooperation/Helpfulness Drawing pictures/figures Polya's steps in problem solving Song (Musical) Body movements (Bodily kinesthetic)  2.2 Solve mentally 1 step word problems involving subtraction without regrouping Speed and accuracy Draw the problem Body movements (Bodily kinesthetic) Illustrations (Spatial)  1. Application of Addition and Subtraction 3.1 Solve 2 step word problems involving addition and subtraction of whole numbers including money following the steps in problem solving Active participation Polya's steps in problem solving Cooperative groups (Interpersonal) 
1 Subtracting Numbers without Regrouping I. Learning Objectives Cognitive: Subtract 3-digit numbers from 4- to 5-digit numbers with minuends up to 99 999 without regrouping. Psychomotor: Write correctly the numeral in vertical column according to their place value. Affective: Work cooperatively during the class and group activities II. Learning Content Skill: Subtracting numbers without regrouping Reference: BEC PELC I.C.1.1.1 Materials: 0-9 number cards, place value pocket chart, flash cards of basic subtraction Value: Cooperation III. Learning Experiences A. Preparatory Activities 1. Drill: (flashcards of basic subtraction) 2. Review – Game Divide the children into 5 groups. Distribute place value pocket charts and number cards. The teacher will give instructions on what number they will form. The group who answers first will have the point and the group with the highest points will be the winner. Tell the pupils to do the following: Ask: Form the largest 3-digit number without repetition Form the smallest 3-digit number without repetition Form the largest 4-digit number without repetition Form the smallest 4-digit number without repetition. Using the digits 4, 7, 3 and 0, what is the largest number you can form? the smallest number you can form? 3. Motivation: Who among you has a bank account? What are you doing with your savings? What happens to your money if you deposit and withdraw? Is it okay to withdraw money from your savings account? Why? 8 - 5 3 - 2 9 - 7 6 - 2 5 - 3 7 - 4 2 - 1 4 - 0 10 - 6 1 - 1
2 B. Developmental Activities Present the table: Number of Trees Planted in Barangay Malinis Trees Number of Trees Acacia 3 875 Narra 2 554 Molave 432 How many more acacia trees are there than molave trees? 1. Presentation a. Compare the number of acacia trees to the number of molave trees. Which has more trees, acacia or molave? How many trees more? What process are we going to use to find the answer? What is the number sentence? Ask a pupil to write the number sentence on the board. (3 875 – 432 = N) Which is the minuend? the subtrahend? b. Let the pupils work in pairs. Ask them to represent the minuend through their cubes, flats, longs and ones. cube long flat 1 flat = (100 cubes) 1 block = (1000 cubes) Activity 1 – Using Manipulatives – Working by pairs
3 Let us solve the problem by using manipulative. Let us do it by pairs. How many acacia trees are there? What about molave trees? How many more acacia trees are there than molave trees? Ask: How will you represent 3 875 using the cubes, flats, longs and ones? How many cubes, flats, longs and ones will you use? (3 blocks, 8 flats, 7 longs and 5 cubes) Thousands Hundreds Tens Ones What about our subtrahend, 432? How many flats, longs and cubes will there be? (4 flats, 3 longs and 2 cubes) Since 432 is the number to be taken away, let’s get it from 3 875. (Let the pupil get 4 flats, 3 longs and 2 cubes from 3 blocks, 8 flats, 7 longs and 5 cubes.) How many blocks, flats, longs and cubes were left? (3 blocks, 4 flats, 4 longs and 5 cubes) How will you read blocks, flats, longs and ones in numeral? How will you write it in figure? 3 443 So, what is 3 875 – 432? 3 443 Activity 2 – Using the expanded form Here is another way of subtracting numbers by Expanded Form. 3 875 3 000 + 800 + 70 + 5 - 432 400 + 30 + 2 3 000 + 400 + 40 + 3 = 3 443 What is the difference? 3 443 X X X XX X X X X
4 Activity 3 – Short Cut Method Let us represent the same number through the place value chart. How will you write the numerals in the place value chart. Short Form: 3 875 minuend - 432 subtrahend N Thousands Hundreds Tens Ones 3 8 7 5 - 4 3 2 3 4 4 3 1. Subtract the ones. (5 – 2 = 3) 2. Subtract the tens. (7 tens – 3 tens = 4 tens) 3. Subtract the hundreds. (8 hundreds – 4 hundreds = 4 hundreds) 4. Subtract the thousands. (3 thousands – 0 thousands = 3 thousands) So, 3 875 – 432 is 3 443. c. Give again another problem. Group the class into three. Let the 1 st group solve it by manipulative (blocks, flats, long and cubes); the 2 nd group by expanded form (value form) and, the 3 rd group by short-cut form (short form-place value chart). Expected Answer: 1 st Group: 4 blocks, 1 flat, 1 long and 3 cubes = 4,113 2 nd Group: 4 356 4 000 + 300 + 50 + 6 - 243 200 + 40 + 3 4 000 + 100 + 10 + 3 = 4 113 3 rd Group: Th H T O 4 3 5 6 – 2 4 3 4 1 1 3 Did you get the same difference? 2. Guided Practice a. Group Work – (4 members per group) Let the pupils group themselves with 4 members each. Ask them to answer the following numbers using only their blocks, flats, long and cubes. Then they will put their answers in the place value pocket chart with the use of their number cards. What is 4 356 minus 243? Number Cards 0 1 2 3 4 5 6 7 8 9 Place Value Pocket Chart Th H T O
5 1) 3 674 2) 4 356 3) 5 243 4) 6 532 5) 8 547 - 532 - 143 - 112 - 321 - 217 Did you get all the answers right? Why? b. Work by pairs Use the expanded form method in solving the number problem. You will work now in pairs. 1) 19 236 2) 24 379 3) 17 874 4) 26 728 5) 36 745 - 220 - 234 - 762 - 312 - 233 Did you get all the answers right? Why? c. Individual Work Let us use the short-cut method. 1) 7 419 2) 7 923 3) 8 465 4) 24 936 5) 35 985 - 306 - 412 - 254 - 224 - 865 Did you get all the answers correctly? Which of the three methods do you prefer or like? Why? Why do you think you got the right answer easily? Which group got all correct answers first? Why do you think they got it easily? What did the group do to make their work easy? 3. Generalization: How do we subtract numbers without regrouping? How do we write the numeral when subtracting? Where do we start subtracting? Why do you think subtracting is very important? Remember: In subtracting 3-digit numbers from 4-digit numbers, the digits must be aligned according to their place value. Then, subtract the ones first, then the tens, the hundreds and the thousands. C. Application Individual work (Use of show-me-board, chalk and flashcards) Subtract the numbers I’m going to show you. Then write the difference on your show-me- board. 1) 8 537 2) 3 489 3) 7 642 - 315 - 158 - 132 (Note to the teacher: Make the materials ready before the activity)
6 4) 5 783 5) 9 857 6) 16 476 - 241 - 315 - 324 7) 22 879 8) 34 364 9) 21 976 - 524 - 134 - 235 10) 19 752 - 421 IV. Evaluation A. Work by pairs. Find the missing numbers. 1) 8 362 2) 2 514 3) 4 _ _2 4) 3 2_5 - _50 - 1_ _ - 261 - _3_ 8 21_ 2 _11 4 63_ 3 063 5) 7 384 6) 12 _ _ _ 7) 4 _ _2 8) 3 2_5 - _ _ _ - 315 - 261 -_3_ 7 120 2 _11 4 63_ 3 063 9) 8 362 10) 2 514 - _50 - 1_ _ 8 21_ 2 _11 B. Individual Work Find what number is being asked. 1. What is the difference between 8 753 and 213? 2. What number is 320 less than 1 975? 3. Subtract 514 from 2 758. 4. What is 6 788 less 351? 5. What number is 502 less than 4 735? 6. Take away 485 from 13 596. 7. What is 24 359 minus 134? 8. What is the difference between 523 and 21 785? V. Assignment Do as indicated. 1. What is the difference between the largest 4-digit number without repetition and the smallest 3- digit number without repetition? 2. What is the difference between the largest 4-digit number with repetition and the smallest 3-digit number without repetition? 3. What is the difference between the largest 4-digit number with repetition and the largest 3-digit number with repetition?
7 Subtracting Numbers without Regrouping I. Learning Objectives Cognitive: Subtract 4-digit numbers from 4-5 digit numbers with minuends up to 100 000 without regrouping. Psychomotor: Write correctly the numeral in vertical column according to their place value. Affective: Work cooperatively during the class and group activities II. Learning Content Skill: Subtracting numbers without regrouping Reference: BEC PELC I.C.1.1.2 Materials: maze, play money (money kit) Value: Cooperation, Helpfulness III. Learning Experiences A. Preparatory Activities 1. Drill – Maze Procedure: a. The teacher will post the maze on the board. There will be 2 teams with 10 members each. b. Each member will unblock the path on the maze by answering the subtraction sentence written inside the box. c. Each member will answer one at a time. A member goes to the board only upon the return of the member before him/her. d. The first group to finish and unblock the path wins the game. (Note to the teacher: Each box should have basic subtraction fact written inside)
8 2. Review a. Find the difference 7 436 3 853 8 789 2 432 5 859 - 215 - 701 - 237 - 102 - 325 b. Checking of Assignment 3. Motivation: Present a problem opener. The Boy and Girl Scouts Drama Group presented a play. On the first day, they earned 4,865. On the second day, they earned 5,985. How much more did they earn on the second day than on the first day? B. Developmental Activities 1. Presentation a. Let us analyze and solve the problem. - Who presented the play in the problem? (The Boy and Girl Scout Drama Group) - How much did they earn on the 1 st day? 2 nd day? (1 st day- 4,865; 2 nd day- 5,985) - What operation are we going to use to solve the problem? (subtraction) - What will be our number sentence? ( 5,985 – 4,865 = N) - How much more did they earn on the second day than on the first day? ( 1,120)
9 Activity 1. Using Play Money/Drawing Pictures – Work in pairs Ask the pupils to work in pairs. Let them get their money kit and represent the money earned on the first day and on the second day. 1 st Day 2 nd Day 4,865 5,985 1,000 1,000 1,000 1,000 500 100 100 100 50 10 5 1,000 1,000 1,000 1,000 1,000 500 100 100 100 100 50 10 10 10 5
10 From the money kit can you tell how much more they earned on the second day than on the 1 st day? Why/Why not? Let them pair the money earned on the 1 st day to the money earned on the second day. 1 st Day 2 nd Day 4,865 5,985 Do all the money earned on the first day have pairs on the 2 nd day? 1,000 1,000 1,000 1,000 500 100 100 100 50 10 5 1,000 1,000 1,000 1,000 5 1,000 500 100 100 100 100 50 10 1 0 1 0 has no pair has no pair has no pair has no pair
11 What about the other way around? Do all the money earned on the 2 nd day have pairs on the first day? How much money do not have pairs? 1,000 + 100 + 10 + 10 = 1,120 Therefore, how much more money did they earn on the 2 nd day? 1,120 Does our answer make sense? Activity 2 – Expanded Form: Let’s recall the problem, “How much more did they earn on the second day than on the first day?” What process are we going to use? Subtraction Why did you say subtraction? Let’s write the number sentence. (Ask the pupil to write the number sentence on their drill board and show it to the teacher.) Ask the pupils to write the given numerals in expanded form. 5 985 5 000 + 900 + 80 + 5 - 4 865 4 000 + 800 + 60 + 5 1 000 + 100 + 20 + 0 = 1 120 partial differences Subtract each number vertically, then add the partial differences horizontally. Activity 3 – Short Form: Let us use the short cut method. Place the minuend and subtrahend in the place value chart. Short Form 5 985 - 4 865 1 120 1 st – Subtract the ones (5 – 5 = 0) 2 nd – Subtract the tens (8 tens – 6 tens = 2 tens) 3 rd – Subtract the hundreds (9 hundreds – 8 hundreds = 1 hundreds) 4 th – Subtract the thousands (5 thousands – 4 thousands = 1 thousands) Did we get the same answer from the 3 activities? a. Group Work Group 1 will answer no. 1, Group 2, no. 2 and Group 3, no. 3 Group 1 will use the drawing method either by one to one pairing or crossing-out just like what we did yesterday. Use _______ for 1000, for 100, for 10 and __ for 1 Group 2 will use the expanded form method. Group 3 will use the short-cut method 1. What is the difference between 2 532 and 8 975? 2. Subtract 3 526 from 64 729 3. From 78 324, take away 5 302 Expected Answers: 4 th 3 rd 2 nd 1 st Th H T O 5 9 8 5 4 8 6 5 1 1 2 0
12 1. Drawing (Pairing) Drawing (crossing-out) 8975 2 532 8 975 2. 64 729 60 000 + 4 000 + 700 + 20 + 9 - 3 526 - 3 000 + 500 + 20 + 6 = 60 000 + 1 000 + 200 + 0 + 3 = 61 203 3. 78 324 Ten Thousands Hundreds Tens Ones - 5 302 Thousands 7 8 3 2 4 - 5 3 0 2 7 3 0 2 2 Which group finished first? Why do you think they have done the activity easily? What did each member do to make their work easy? no pair How many have no pairs? 1 000 1 000 1 000 1 000 1 000 1 000 100 100 100 100 100 10 10 10 10 1 6 000 400 40 3 6 443 Take away 2 532 How many were left? 1 000 + 1 000 + 1 000 + 1 000 + 1 000 + 1 000 + 100 + 100 + 100 + 100 + 10 + 10 + 10 + 10 + 1 + 1 + 1 = 6 443
13 2. Guided Practice a. Work in pairs Subtract the following. Use the short-cut method 1) 7 635 2) 2 304 3) 6 287 4) 6 789 5) 4 236 - 3 413 - 1 203 - 6 152 - 3 436 - 2 225 6) 98 325 7) 88 766 8) 83 293 9) 72 844 10)54 678 - 3 103 - 2 513 - 1 021 - 1 342 - 1 325 a. Group Work – (with 3 members) Number Puzzle – (Provide each group with number puzzle to work on.) Subtract the following numbers and write your answer on the number puzzle. You have 5 minutes to complete it. a b c d e f g h i j k Across a. 6 898 – 4 353 d. 1 215 less than 4 885 f. 6 548 minus 1 240 g. 5 487 less 4 035 i. 1 270 – 1 230 j. What is the difference between 4 562 and 4 510? k. Subtract 1 231 from 2 477 Down b. What number is 1 000 less than 6 755? c. From 5 244, subtract 1 212 d. 5 346 – 2 132 e. 3 866 minus 2 014 h. The difference between 2 726 and 1 325 Did you get the answers right? Did your team work together to finish the puzzle fast? How did you subtract easily? Which method did you use? 3. Generalization How do we subtract 4-digit numbers from 4 to 5-digit numbers? Where do we start subtracting? Do you think there is a technique in doing this? How?
14 Remember In subtracting 4-digit numbers, the numbers must be aligned properly according to their place value. Then start subtracting from ones first, then tens, hundreds and thousands. C. Application a. Find the missing numbers 1) 4 921_ 2) 69 4_ _ 3) 32 9_8 - _ 112 - 3 _12 - 2 _0_ 45 _ _1 6_ 220 3_ 135 b. Do as indicated 1. What number is 2 541 less than 87 876? 2. Subtract 3 487 from 56 899. IV. Evaluation (To be done individually) Paper and pencil Write in column then subtract 1) 4 732 – 2 301 = N 3) 7 857 – 3 412 = N 5) 8 576 – 4 253 = N 7) 5 436 – 1 034 = N 9) 6 258 – 2 153 = N 2) 73 259 – 1 143 = N 4) 62 987 – 2 543 = N 6) 25 737 – 3 705 = N 8) 48 635 – 2 125 = N 10) 75 557 – 5 423 = N V. Assignment Write in expanded form then subtract. 1) 59 875 = _____ + _____ + _____ + _____ + _____ - 4 362 = _____ + _____ + _____ + _____ + _____ 2) 37 589 = _____ + _____ + _____ + _____ + _____ - 3 251 = _____ + _____ + _____ + _____ + _____ 3) 87 639 = _____ + _____ + _____ + _____ + _____ - 3 318 = _____ + _____ + _____ + _____ + _____
15 Subtracting Numbers with Regrouping in the Tens Place I. Learning Objectives Cognitive: Subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the tens place. State the rules in subtracting numbers with regrouping Psychomotor: Follow the rules in subtracting numbers with regrouping in the tens place and use the body-number coding (kinesthetic math) properly. Affective: Follow simple rules correctly. Practice helpfulness at all times. II. Learning Content Skill: Subtracting numbers with regrouping in the tens place Reference: BEC PELC I-C 1.1.3.1 Materials: chart of the body number coding, problem chart, flash cards of basic subtraction, Popsicle sticks or straws Value: Following simple rules correctly/Helpfulness III. Learning Experiences A. Preparatory Activities 1. Drill – Body Number Coding Let the pupils do the coding of numbers through their hands and body. (Write the code on a manila paper) Digit Movement 0 1 2 3 4 5 6 7 8 9 - Forefinger and thumb together forming zero - Right arm forward closed fist - Left arm forward closed fist - Left and right arms bend forward close to the body - Hands on waist - Right hand on the chest - Bend forward to pick something - Stand straight - Arms obliquely upward - Do McDonald sign The teacher will show some flashcards about basic subtraction and the pupils will give the answer through their body action without giving the answer. Example: 7 – 3 = 4 (They have to act the code for number 4 which is hands on waist) 2. Motivation – Present a problem opener. Mang Pedro brought 2 752 eggs to sell in the public market. Danny, his eldest son, helped him sell 1 345 eggs. How many eggs were left? 8 - 7 5 - 1 3 - 0 5 - 5 6 - 4 10 - 5 9 - 2 8 - 2 9 - 1 10 - 1
16 B. Developmental Activities 1. Presentation a. What do you think is the work of Mang Pedro? What did he sell in the public market? Who is his eldest son? What kind of son is he? Are you also helpful? In what ways are you helpful? How many eggs did Mang Pedro bring? How many eggs were sold by his eldest son? What is asked in the problem? How are we going to solve it? What process are we going to use? What will be our number sentence? b. Let a pupil write the number sentence on the board. 2 752 – 1 345 = N (Pre-Activities) Note to the Teacher: (The pupils should have their Math Kit where they can place their Popsicle sticks/straws, rubber bands, counters, etc. A place value containers should always be inside their classroom. If possible, the place value containers should be made as a project of the pupil.) Place Value Containers  Guide the pupils to bundle 10 straws which should be placed in the tens place of the place value container.  Let them bundle 10 groups of 10 straws each which will be placed in the hundreds place of the place value container.  Lastly, let them bundle 10 groups of 100 straws to be placed in the thousands place of the place value container.  Let them see and observe how many is 1 ten, 1 hundred and 1 thousand. Activity 1 – Using Manipulatives and Drawings/Diagram  Tell the pupils to work in groups with 5 members each.  Let them represent the number of eggs brought by Mang Pedro through their straws/Popsicle sticks and place value containers. Ask: How will you represent 2 752? 2 bundles of 1 000 straws 7 bundles of 100 straws 5 bundles of 10 straws 2 pieces of straws
17 Thousands Hundreds Tens Ones A B C 1 4 0 7 So, 2 752 therefore, 1 407 eggs were left. - 1 345 1 407 Now, let us take away the number of eggs sold by Danny. How many eggs were sold by Danny? 1 345 eggs How will you represent 1 345 in bundled straws? 1 bundle of 1 000 straws, 3 bundles of 100 straws each, 4 bundles of 10 straws each and 5 pieces of straws)  Ask the pupils to take away 1 345 from 2 752.  Did you get all the straws in each place value containers?  In what place value container did you find it difficult to get the straws?  Can you get 5 straws from 2 straws? You cannot subtract 5 from 2;  Therefore, we will regroup 1 group of ten straws from the tens cup and place it in the ones cup.  But we cannot still get 5 straws because the straws are still in bundle.  So, what should we do? (Unbundle the tens straws)  So, how many straws are there in the ones container now? 12  How many group of tens straws were left at the tens container?  Can you get 4 bundles of 10 straws from it? What about 3 bundles of 100 straws each, can you get it from the hundreds container?  What about a bundle of 1 000 straws, can you get it from the thousands container?  So, how many straws were left in each container?  How will you read it in numeral?  So, how many eggs were left? Does our answer make sense?
18 Activity 2 – Using Expanded Form 1) Let us try solving the same problem using the Expanded Form. Let us see if we can get the same difference. 1. Subtract the ones. 2 752 2 000 + 700 + 50 + 2 - 1 345 1 000 + 300 + 40 + 5 2. Regroup the tens. 2 000 + 700 + (50 – 10) + (10 + 2) - 1 000 + 300 + 40 + 5 _ 2 000 + 700 + 40 + 12 - 1 000 + 300 + 40 + 5 7 3. Subtract the tens. 2 000 + 700 + 40 + 12 - 1 000 + 300 + 40 + 5 0 + 7 4. Subtract the hundreds. 2 000 + 700 + 40 + 12 - 1 000 + 300 + 40 + 5 400 + 0 + 7 5. Subtract the thousands. 2 000 + 700 + 40 + 12 - 1 000 + 300 + 40 + 5 1 000 + 400 + 0 + 7 = 1407 Did we get the same difference? 1407 eggs were left. 2) Let us try using the short cut method or the short form. Th H T O 2 7 4 5 1 2 - 1 3 4 5 1 4 0 7 1. Subtract the ones. But since you cannot subtract 5 ones from  2 ones; we will regroup the tens place.  5 tens becomes 4 tens and 1 ten; then 1 ten becomes 10 ones  then, we will rename the ones place.  10 ones + 2 ones equals 12 ones Then subtract the ones place. (12 ones – 5 ones = 7 ones) 2. Subtract the tens. (4 tens – 4 tens = 0 ten) 3. Subtract the hundreds. (7 hundreds – 3 hundreds = 4 hundreds) 4. Subtract the thousands. (2 thousands – 1 thousand = 1 thousand) Did we get the same difference? 1 407 eggs were left. You cannot subtract 5 from 2; therefore, regroup one 10 from the tens column and add it to 2. Subtract 5 from 12 Subtract 40 from 40 Subtract 300 from 700 Subtract 1000 from 2000. Add all the partial differences. 2 752 - 1 345 N 2 7 4 5 12 2 - 1 3 4 5 1 4 0 7
19 2. Guided Practice Group work with 5 members each a. Solve by using the place value containers and straws/Popsicle sticks. 1) 1 343 – 236 = N 2) 2 491 – 1 358 = N 3) 2 635 – 1 217 = N Work in Triads b. Solve the following by Expanded Form Method. 1) 3 942 – 719 = N 2) 7 363 – 247 = N 3) 6 475 – 2 136 = N 4) 32 635 – 2 217 = N 5) 25 136 – 4 018 = N Work in Dyads b. Subtract the following using the Short Form Method. 1) 5 785 – 349 = N 2) 15 324 – 2 106 = N 3) 3 642 – 235 = N 4) 26 483 – 3 248 = N 5) 4 384 – 248 = N 6) 56 587 – 2 359 = N 7) 8 252 – 4 036 = N 8) 43 462 – 1 357 = N 9) 7 461 – 3 237 = N 10) 34 677 – 2 338 = N Were you able to finish all the exercises? Why? How did each of your member work to come up with the correct answer? Did you help each other during the activities? Which method do you like best? Why? 3. Generalization: How do we subtract numbers with regrouping in the tens place? To subtract whole numbers, start with the ones column. If the digit in the minuend is smaller than the digit in the subtrahend, regroup from the next column to the left. To check the difference, add it to the subtrahend to get the minuend. C. Application a. Work in Dyads – (Use flash cards and show me board.) The teacher will flash some cards and the pupils will give the answer using their show me board. 1) 2) 3) 4) 5) 3 521 - 417 8 463 - 237 7 482 - 158 5 366 - 139 6 834 - 318
20 IV. Evaluation A. Group work (with 4 members each) – Body Number Coding and flash cards Form groups with 4 members each. Let the pupils answer on a piece of paper the exercise on the flash card. They will give the answer orally using the body-number coding. One pupil will act out the ones digit, the other one on the tens digit, the next one will act out the hundreds digit and the 4 th member will act out the thousands digit. 1) 2) 3) 4) 5) B. Individual Work – (Paper and Pencil) Subtract the following. 1) 67 893 2) 25 876 3) 37 735 4) 49 852 5) 57 651 - 5 376 - 2 138 - 1 317 - 5 214 - 3 425 V. Assignment A. Find the missing minuend, subtrahend or difference. 1) 3 462 2) 5 463 3) _____ 4) 8 364 5) _____ - 345 - _____ - 134 - _____ - 418 _____ 5 227 7 228 8 227 6 124 6) _____ 7) 9 594 8) _____ 9) 5 866 10) 3 425 - 3 158 - _____ - 2 136 - 1 437 - 1 207 3 224 6 358 2 559 _____ _____ B. Write the missing numerals. 1) 2) 3) 8 5 - 3 2 6 8 4 0 4 7 5 2 - 2 4 4 7 6 7 3 - 2 3 1 6 5 3 9 4) 5) 3 4 5 - 1 7 6 3 3 1 5 7 5 8 2 - 3 1 2 7 3 5 7 853 -3 614 2 746 -1 327 3 745 -1 316 4 853 -1 315 8 597 -4 319
21 Subtracting Numbers with Regrouping in the Hundreds Place I. Learning Objectives Cognitive: Subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the hundreds place Psychomotor: State the rule in subtracting whole number with regrouping Affective: Work cooperatively with others in finding the difference of the given number with accuracy II. Learning Content Skill: Subtracting numbers with regrouping in the hundreds place Reference: BEC PELC I.C.1.1.3.2 Materials: flash cards of subtraction (2-digit by 1), Math kit (cubes, flats, longs and ones), Show Me Board, place value pocket chart, chart of exercises Value: Cooperation III. Learning Experiences A. Preparatory Activities 1. Drill – Mental Computation 2. Review Checking of assignment. 3. Motivation Song: Math Time (Tune: It’s a Small World) Chorus: Oh, it’s Math time after all (3x) Come together and come all. There is just one class We enjoy so much Where our mind think hard And compute a lot Though the drills are so fast And the problem so tough We enjoy our class in Math (Repeat Chorus) Do you really enjoy our Math class? Why? What are the things we do in Math? 12 - 5 17 - 8 15 - 6 11 - 7 13 - 4 19 - 9 14 - 7 16 - 9 18 - 5 15 - 8
22 B. Developmental Activities 1. Presentation a. Let us read and analyze this number sentence. Subtract 275 from 1 359 = N b. Ask the pupils which is the minuend and the subtrahend in the number sentence. Let them write the numerals in column and analyze it. 1 359 - 275 Ask: Can we subtract the ones place? What is the answer? What about the tens place? Can we subtract 7 from 5? 1. Activity 1 – Manipulatives (cubes, longs, flats and blocks) c. Now, ask the pupils to get their Math kit and get their cubes, longs, flats and blocks. Let them do it by pairs. Let them represent first the minuend. Ask: How many blocks, flats, longs and cubes can make 1 359? d. Ask the pupils to take away 275 from the blocks, flats, longs and cubes. Ask: How many flats, longs and cubes will make 275? Do I have enough cubes to take away 5 from it? How many cubes will be left? What about the longs, do I have enough to take away 7 from it? What shall we do then? = 1,359 (blocks) (flats) (longs) (cubes)
23 Thousands Hundreds Tens Ones X X X X X X X X X X
24 1 0 8 4 So, we will regroup 1 flat and rename it as longs. How many longs will there be in 1 flat? (10) So, how many longs do we have now? Can we not get 7 longs from it? How many longs were left? e. Now, ask the pupils to focus on flats. Let them take away 2 flats from it. Ask how many flats remain in the flats column. Then, ask if they are going to take away anything from the blocks column and then ask why. Let the pupils express their answers. f. Let them now count the number of blocks, flats, longs and cubes that were left in each column. How do you read the numeral? Let’s solve the same problem using the expanded form method. 2. Activity 2 – Expanded Form Method 1 359  - 275  1 000 + 300 + 50 + 9 - 200 + 70 + 5 a. Subtract 5 from 9. b. Subtract 70 from 50. Is it possible? (No) ? + 4 Rename  1 000 + 200 + 100 + 50 + 9 c. Rename 300 into 200 and 100. Regroup 100 with 50. Regroup  1 000 + 200 + 150 + 9 - 200 + 70 + 5 d. Subtract 70 from 150. 80 + 4 1 000 + 200 + 150 + 9 - 200 + 70 + 5 e. Then, subtract 200 from 200 and bring down 1 000. 1 000 + 0 + 80 + 4 = 1 084 f. Lastly, add the partial differences. Let’s solve it again using the short form. Write the numeral in the place value chart.
25 Th H T O 1) Subtract the ones (9 – 5 = 4) 1 3 5 9 - 2 7 5 2) Subtract the tens. Can you take away 7 tens from 5 tens? Why not? 4 Th H T O Regroup 3 hundreds into 2 hundreds and 10 tens. Then rename the tens. How many tens are there now? Can we subtract 7 tens from it? Then subtract. How many hundreds were left? 1 2(3) 15(5) 9 - 2 7 5 1 0 8 4 3) Subtract the hundreds. (2 hundreds – 2 hundreds = 0 hundreds) 4) Then bring down the digit in the thousands place because you will not subtract anything from it. Did we get the same difference? Which of the three methods do you like best? Why? 2. Guided Practice a. Group Work 1. Divide the class into 3 groups and the members of the groups will work in pairs. 2. The first group will use the manipulative method to find the difference. 3. The 2 nd group will use the expanded method. 4. The 3 rd group will use the short form method. 5. Then they are going to report to the class the answer they got. Write in column then subtract. Group 1 Group 2 Group 3 3 735 – 562 8 628 – 4 253 56 816 – 3 745 b. Work in Pairs The teacher will show some numbers to be subtracted. The pupils will write their answer on their Show Me Board. They will use the short form method. 8 237 - 162 5 648 - 353 7 525 - 281 4 419 - 345 9 456 5 645 8 266 7 538 - 7 271 - 2 183 - 1 173 - 3 252 25 325 15 815 32 546 47 679 - 4 151 - 2 732 - 1 476 - 2 385 1. Which pairs got the most number of correct answers? 2. What do you think they did to get all the correct answers?
26 3. Did they work cooperatively? 4. Did they get the correct answer fast by working in pairs? Do you think regrouping is important? Why? Why not? 3. Generalization How do we subtract 3- to 4-digit numbers with regrouping? Where do we start? Remember this:  Regroup the numeral in the hundreds place of the minuend when necessary  Rename the numeral in the tens place  Then, start subtracting from the right going to the left. (Start with ones place, then tens place, etc.) C. Application Subtract the following: 1) th h t o 2) th h T o 7 4 2 5 8 5 3 6 - 3 5 3 - 1 6 2 3) tth th h t o 4) tth th h T o 2 8 6 1 4 4 5 6 4 6 - 4 2 4 2 - 3 2 7 1 5) hth tth th h t o 3 2 6 3 4 8 - 4 1 5 3 IV. Evaluation A. Write in column then subtract. 1) 4 537 – 352 2) 2 913 – 771 3) 6 435 – 2 152 4) 2 854 – 1 692 5) 13 429 – 2 275 B. Write the missing minuend, subtrahend or difference. 1) 7 325 2) . 3) 8 526 4) 53 436 5) . - _ . - 2 391 - _ . - _ . - 3 145 7 172 1 072 4 153 52 074 24 171
27 V. Assignment A. Fill in the blanks with the correct numerals then subtract. 1) 3 538 = ____ + ____ + ____ + ____  ____ + ____ + (____ + ____) + ____ - 253 = 200 + 50 + 3___ -____ + ____ __ ____ + ____ _____________ _____ +____ + ____ __ ____ + ____ = ___________________ 2) 5 627 = ____ + ____ + ____ + ____  ____ + ____ + (____ + ____) + ____ - 4 353 = 4000 + 300 + 50 + 3___ -_____ + ____ + ____ _ ____ + ____ _______________________________ ____ + ____ + ____ _ ____ + ____ = ___________________ 3) 47 859 = ____ +___ + ___+ ____ +___  ____ + ____ + ____ + (___ + ___) + ____ - 5 383 = 5 000 + 300 + 80 + 3__ - ____ + ____ + ________ + ____ ___________________________________ _____ +_ ____ + ____+ ________ + ____ = ___________________ B. Fill in the box with the missing numeral. 1) 3   9 2) 7  5 2 6 3) 5 8 5 3  - 1 2 7 3 - 4 3 4  - 2 3   2  2 4  7 2  1   3 8 4 C. Complete the table. Subtract the numerals in the first column from the numerals in the first row. 9 537 9 835 87 563 273 9 562 3 181 6 356 7 393 80 170 Subtracting 3- to 4-Digit Numbers from 4- to 5-Digit Numbers with Regrouping in the Thousands Place I. Learning Objectives Cognitive: Subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the thousands place Psychomotor: Write numbers neatly and correctly Affective: Practice helpfulness
28 II. Learning Content Skills: Subtracting 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the thousands place Reference: BEC PELC I C 1.1.3.3 Materials: flash cards, show me board, leaf cut-outs, puzzle board Value: Helpfulness III. Learning Experiences A. Preparatory Activities 1. Drill (Basic Subtraction Facts) Using the flashcards, ask the children to give the answer orally. 10 7 12 16 11 15 8 14 - 2 - 4 - 6 - 9 - 3 - 9 - 3 - 7 Check the assignment. 2. Review  Subtraction with regrouping in the hundreds place Have a group game, boys against girls. Ask each group to answer number problems written on a chart. Ask them to write their answers on show me board. 1) 349 2) 765 3) 734 4) 649 5) 6 734 - 76 - 194 - 282 - 82 - 291 ____ ____ ____ ____ ____ 3. Motivation Present a problem through storytelling. Ask children to listen to the story problem.  Edgar is a vendor. He received 25 855 newspapers. At the end of the day, 3 935 newspapers were left. How many newspapers were sold? B. Developmental Activities 1. Presentation a. Have a comprehension check-up about the story problem presented in the motivation. Ask:  Who’s the newspaper boy?  Have you seen a boy like Edgar? Why do you think he is selling newspapers?  Do you think he can help his parents by doing this kind of work? How? b. Let’s try solving the problem using these steps. Step 1: ■ Understand the problem a. How many newspapers did Edgar receive? b. How many were left? c. What is asked in the problem?
29 Step 2: ■ Plan a. What process is involved in the problem? b. What helps you decide to use this process? Step 3: ■ Carry out the plan Ask a pupil to write the number sentence. (25 855 – 3 935 = N) Activity 1: Let’s solve the problem using the indicated method. Expanded form: 4 000 1 800 . 25 855 = 20 000 + 5 000 + 800 + 50 + 5 - 3 935 = 3 000 + 900 + 30 + 5 = 20 000 + 1 000 + 900 + 20 + 0 = 21 920 newspapers sold In what place did we have the regrouping? Why? Step 4: ■ Looking back a. Have we answered the problem? b. Is our answer sensible? c. Did we place the correct label? Activity 2: Now, let’s use the short method. Compare the digits in the minuend and subtrahend in each place where regrouping is needed. 1. Start from the ones. Subtract 5 ones from 5 ones. 25 855 - 3 935 0 2. Subtract 3 tens from 5 tens. 25 855 - 3 935 20 3. Regroup 1 thousand from 5 thousands as 1 thousand. Rename 8 as 18 hundreds. 4 18 25 855 - 3 935 920 4. Subtract 3 thousands from 4 thousands. 4 18 25 855 - 3 935 1 920 5. Bring down the last digit 2. 4 18 25 855 - 3 935 21 920 Answer: There were 21 920 newspapers sold. 21 920 difference + 3 935 subtrahend 25 855 minuend To check: Add the difference and the subtrahend to get the minuend. Give more examples. Ask pupils to explain how the difference was obtained.
30 9 736 8 245 9 364 75 864 8 369 - 924 - 813 - 2 721 - 2 942 - 1 925 8 812 7 432 6 643 72 922 6 444 2. Guided Practice a. Work in pairs. Give each pair a leaf cut-out with a number problem. Ask them to write their answers on a piece of paper. 3 486 7 645 26 598 5 345 54 394 - 924 - 813 - 1 732 - 1 824 - 2 653 b. Work in groups of 4. Each group will be given a puzzle board. Ask them to complete the puzzle using subtraction. The first group to finish wins. 1) 9 7 6 2) 8 4 3) 5 3 4 9 2 8 1 3 2 2 8 4 2 4 2 6 4 3 4) 7 8 4 5) 6 3 3 9 2 9 4 1 2 7 2 2 2 6 5 2 4 Is regrouping important? Why? 3. Generalization: How do we subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the thousands place? Remember: To subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the thousands place, we do the following:  Compare the digits in the minuend and subtrahend.  Start subtracting from the ones, then the tens.  If the subtrahend in the hundreds place is greater than the minuend, regroup 1 thousand.  Rename the hundreds place and the thousands place, then subtract up to the last digit.  To check: add the difference and the subtrahend. C. Application Match the number problem with the correct answer on the right. 1) 3 695 - 934 2) 78 478 - 59 264 3) 5 633 - 811 a. 4822 b. 74 322 c. 6961
31 4) 76 146 - 1 824 5) 7 686 - 725 IV. Evaluation Solve these problems: 1) The pupils in Tucop Elementary School need to collect 7 345 instant noodles wrappers for their school project. They had collected 4 531 wrappers. How many more wrappers do they need to collect? Answer: ________________ 2) Lyn bought 1 355 eggs. She sold 822 eggs. How many eggs were left? Answer: ________________ 3) 76 895 - 7 443 4) 98 674 - 9 432 5) 86 738 - 7 424 V. Assignment A. Do as indicated. Write the answer on the blank. 1. The difference between 9 349 and 825 ___________ 2. Subtract 8911 from 29 834 __________ 3. From 36 384 take away 4 962 _________ 4. 9 369 minus 3 924 _________ 5. Take away 5 925 from 38 567 ___________ B. Fill in the box with the correct difference. 1. 7 349 – 826 2. 9 298 – 3 436 3. 24 364 – 2 952 4. 59 462 – 7 621 5. 73 398 – 964 d. 2761 e. 19 214 = _ _ _ _ _ = _ _ _ _ _ = _ _ _ _ _ = _ _ _ _ _ = _ _ _ _ _
32 Subtracting Numbers with Regrouping in the Ten Thousands Place I. Learning Objectives Cognitive: Subtract 4-digit numbers from 5-digit numbers with regrouping in the ten thousands place. Psychomotor: Write the numbers vertically according to their place value. Affective: Work cooperatively in the class during the activities and discussion. Choose the leader wisely. II. Learning Content Skill: Subtracting numbers with regrouping in the ten thousands place Reference: BEC PELC IC 1.1.3.4 Materials: problem chart, exercises chart, colored chalk, picture chart for coloring activity, regrouping game chart. Value: Wise choice of leader III. Learning Experiences A. Preparatory Activities 1. Drill – Regrouping Game Divide the class into 5 groups. Choose a leader for each group. Give each group a regrouping activity sheet. Ask them to match the numeral in column A with the renamed numerals in column B by drawing a line that will connect them. The first group who will post their work on the board with all answers correct will be the winner. A B 1. 41 325 •  a. 4 ten thousands + 16 thousands + 3 hundreds + 85 ones 2. 32 853 •  b. 3 ten thousands + 13 thousands + 584 ones 3. 56 385 •  c. 1 ten thousands + 17 thousands + 26 tens + 7 ones 4. 27 267 •  d. 3 ten thousands + 11 thousands + 325 ones 5. 43 584 •  e. 2 ten thousands + 12 thousands + 85 tens + 3 ones 2. Review – Checking of assignment 3. Motivation: Are you familiar with the word “election?” When do we hold election here in our country? If you are going to elect a candidate, what good qualities of a leader/candidate would earn your vote? Why?
33 B. Developmental Activities 1. Presentation In an election, Mr. Santos received 21 785 votes. His opponent, Mr. Gomez, received 9 465 votes. How many more votes did Mr. Santos receive than Mr. Gomez? a. Ask: Who were the candidates in the story problem? How many votes did Mr. Santos receive? How many votes did Mr. Gomez receive? Who won in the election? How many more votes did Mr. Santos receive than Mr. Gomez? What process are we going to use to get the answer? What will be our number sentence? b. Let a pupil write the number sentence on the board. 21 785 – 9 465 = N Activity 1 – Drawing/Pictorial Let us draw the problem to see how many more votes Mr. Santos received than Mr. Gomez. Mr. Santos Mr. Gomez Now ask the pupil to draw again the diagram vertically starting with Mr. Santos. Then let them do the pairing. 10 000 1000 10 000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100 100 100 100 100 100 100 100 100 100 100 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 1 10 000 1000 10 000 100 100 100 100 100 100 100 1000 1000 1000 1000 1000 1000 1000 1000 1000 100 100 100 100
34 What have you observed with the thousands drawing? Does Mr. Santos have enough thousands to compare or pair with Mr. Gomez? What shall we do? 10 10 1010 10 10 10 10 1 1 11 1 10 10 10 10 10 10 1 1 11 1 10 000 10 000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Regroup 1 ten thousand from the ten thousands drawing and rename it as thousands. How many thousands are there in 1 ten thousand? 10 How many thousands do we have now? Can we now pair it with Mr. Gomez’s thousands? How many ten thousands drawing were left? 10 000 1000 100 100 100 100 100 100 100 10 10 1010 10 10 10 10 100 100 100 100 10 10 10 10 10 10 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
35 Which of the candidates has drawings with no pairs at all? Let us count how many of each was left with Mr. Santos. How many were left? 1 = 10 000 How many were left? 2 = 2 000 How many were left? 3 = 300 How many were left? 2 = 20 How many were left? 0 = 0 How many in all were left? 12 320 How many more votes did Mr. Santos receive than Mr. Gomez? 12 320 votes Does our answer make sense? c. Let us use the Expanded Method 21 785 20 000 + 1000 + 700 + 80 + 5 - 9 465 9000 + 400 + 60 + 5 N 20 000 + 1000 + 700 + 80 + 5 Regroup : 10 000 + (10 000 + 1000) + 700 + 80 + 5 Rename : 10 000 + 11 000 + 700 + 80 + 5 Subtract : 9000 + 400 + 60 + 5 Difference : 10 000 + 2 000 + 300 + 20 + 0 = 12 320 Did we get the same difference? Activity 3 – Short Form Method d. Let us use the Short form method. TTh Th H T O 21 785 2 1 7 8 5 21 785 - 9 465 9 4 6 5 - 9 465 N ? 3 2 0 ? 320 Steps: 1. Subtract the ones. (5 ones – 5 ones = 0 ones) 2. Subtract the tens. (8 tens – 6 tens = 2 tens) 3. Subtract the hundreds. (7 hundreds – 4 hundreds = 3 hundreds) 4. Subtract the thousands. Can you subtract them? Why not? 1 1 11 1 1 1 11 1 1 1 10 10 100 100 1000 1000 10 000 10 000
36 TTh Th H T O 1 + 1 10 + 1 2 1 7 8 5 9 4 6 5 3 2 0  Rename the ten thousands. 2 ten thousands becomes 1 ten thousands + 1 ten thousands How many thousands are there in 1 ten thousands? 10 thousands?  Regroup 1 ten thousands to the thousands place.  Rename the thousands. 10 thousands + 1 thousands becomes 11 thousands or 10 000 + 1000 = 11 000 Can we now subtract 9 thousands from it? TTh Th H T O 1 11 21 785 2 1 1 11 7 8 5 21 785 - 9 465 9 4 6 5 - 9 465 ? 3 2 0 12 320  Then, subtract the thousands place. (11 thousands – 9 thousands = 2 thousands) 5. Bring down the digit that was left in the ten thousands. How many more votes did Mr. Santos receive than Mr. Gomez? Did we also get the same difference? 2. Guided Practice a. The pupils will work in groups with 4 members each. They are going to solve the following numbers using the three methods. 1) 34 659 – 9 327 2) 51 485 – 2 135 3) 23 764 – 5 321 Ask: Which method do you like best? Why? Were you able to finish the activity faster when you used that method? Why? Work in pairs – Written b. Write the following in column then subtract. Use the short method. 1) 73 864 – 7 321 2) 65 492 – 8 252 3) 51 276 – 3 214 4) 83 472 – 7 122 5) 31 597 – 4 132 6) 24 856 – 6 313 7) 32 583 – 6 321 8) 53 642 – 7 120 9) 81 731 – 7 401 10) 44 367 – 6 135 Ask: Were you able to finish all the exercises? Why? How did you work as a pair so that you will come up with the correct answer? Did you help each other during the activities?
37 3. Generalization: How do we subtract numbers with regrouping in the ten thousands place? Remember: To subtract numbers with regrouping in the ten thousands place: 1. Write the numbers vertically to align the digits in each place value. 2. Regroup the ten thousands place and rename the thousands place. 3. Subtract from right to left, starting with the ones. C. Application The table below shows the accumulated points of NCR, Region 4 and Region 3 during the Palarong Pambansa. Palarong Pambansa Team Scores Team Points NCR 12 535 Region 4 8 302 Region 3 9 421 1. Which team scored the highest points? the lowest points? 2. How many more points does Region 3 have than Region 4? 3. How many more points does NCR have than Region 3? 4. Knowing the differences, can you tell the winner? IV. Evaluation A. Do what is asked. 1. Subtract 4 312 from 73 852. 2. What is 26 321 – 9120? 3. Take away 7313 from 42 763. 4. What is 5 235 less than 51 659? 5. How much more is 36 859 than 8 312? 6. What is 25 867 minus 8 314? 7. From 72 859, subtract 9 424. 8. What is the differences between 13 598 and 4 323? B. Complete the table. Find each output Rule: Subtract 7 537 from each input. Rule: Subtract 8 231 from each input. Input Output Input Output a. 41 215 b. 35 136 c. 24 523 d. 73 213 e. 56 105 a. 92 587 b. 34 346 c. 75 973 d. 23 832 e. 16 763
38 V. Assignment Find the difference then compare. Write >, < or = in the Box 1) 72 859 – 9 424 _____ 68 633 2) 27 613 _____ 32 789 – 6 413 3) 21 473 – 7 152 _____ 14 321 4) 75 272 _____ 82 659 – 7 417 5) 24 593 – 5 321 _____ 19 275 Subtracting Numbers with Zero Difficulty in Either Tens or Hundreds Place I. Learning Objectives Cognitive: Subtract 3– to 4-digit numbers from 4– to 5-digit numbers with zero difficulty in either tens or hundreds place. Psychomotor: State the rule in subtracting whole numbers with zero difficulty in the tens or hundreds place Affective: Help others in doing group activities II. Learning Content Skill: Subtracting numbers with zero difficulty in either tens or hundreds place Reference: BEC PELC I C 1.1.3.5 Materials: flash cards of basic subtraction, chart of body-number coding, cut-outs of different geometrical shape with number value, secret message activity sheets, strips of cartolina with subtraction sentences Value: Helpfulness III. Learning Experiences A. Preparatory Activities 1. Drill : Kinesthetic Math Review the body symbols for digits 0 – 9. Then the teacher will show some basic subtraction facts (flash cards) and the pupils will act out the answer. Digit Movement 0 - Forefinger and thumb together forming zero 1 - Right arm forward closed fist 2 - Left arm forward closed fist 3 - Left and right arms folded vertically closed to the body 4 - Hands on waist 5 - Right hand on the chest 6 - Bend forward to pick something 7 - Stand straight 8 - Arms obliquely upward 9 - Do the McDonald sign 7 - 3 9 - 7 10 - 1 8 - 3 5 - 2 6 - 5 5 - 5 10 - 3 10 - 4 10 - 2
39 2. Motivation : Present a problem opener The Grade Three class collected bottle caps for their doormat project. The boys collected 3 234 caps while the girls collected 5 405 caps. How many more caps did the girls collect than the boys? B. Developmental Activities 1. Presentation a. Ask: What was the project of the grade three class? Do you know what a doormat is? Is the project of the grade three pupils a good project? Why? What benefit can we get from it? Is it an expensive project? Is it helpful and useful in our lives? b. Let us solve the problem using Polya’s 4 steps in problem solving. ■ Understand the problem a. How many bottle caps did the grade three boys collect? b. How many caps did the grade three girls collect? c. Who collected more caps? d. How many more caps did the girls collect than the boys? e. What process are we going to use? ■ Make a plan What operation will be used to solve the problem? ■ Carry out the plan Ask a pupil to write the number sentence on the board. 5 405 – 3 234 = N Activity 1 – Acting Out the problem  The class forms 5 groups. Each group chooses a leader.  Give each group a set of different geometric shapes with different number value written on it. Let them illustrate the number of caps collected by the grade three boys and the number of caps collected by the grade three girls through acting out. Girls Boys 1000 100 10 1 1000 1000 1000 1000 100 100 100 100 1000 1 1 1 1 1 1000 1000 1000 100 100 1 1 1 1 10 10 10
40 10 10 100 10 100 100  Let them use pairing technique wherein the number of caps collected by the grade three boys will be paired to the number of caps collected by the grade three girls. Starting with the s place, how many s were left with no pair? Girls Boys  Pair the s. Did you find it easy to do so? Why not? Since the girls’ number of caps do not have s, what shall we do?  Borrow one in the s place. Rename it as . How many s are there in 1 ? 10 s Girls Boys  How many s were left with no pair?  Pair the s and s. How many s and s were left with no pairs? Girls 11 1000 100 10 1 1000 1000 1000 1000 100 100 100 100 1000 1 1 1 1 1 1000 1000 1000 100 100 1 1 1 1 10 10 10 XX XX XX XX 10 10 1000 100 10 1 1000 1000 1000 1000 100 100 100 100 1000 1 1 1 1 1 1000 1000 1000 100 100 1 1 1 1 10 10 10 XX XX XX XX 10 10 10 10 10 10 10 10 10 10 10 100 1000 1000 1000 100 10 1 1000 1000 1000 1000 100 100 100 1000 1 1 1 1 1 XX XX 10 10 10 10 10 10 10 10 10 10X X X X X X X X 100
41 1 Boys No pair Answer 2 1 7 1  Count how many s, s, s and s were left with no pair at all?  How will you read it in numerals?  So, how many more caps did the girls collect than the boys? ■ Look back Is your answer sensible? What is the correct label? Did all the groups get the same difference? Activity 2: Expanded Form Method Let the children solve the same problem using the expanded form. Will you get the same difference? a. Subtract the ones. 5 405 5 000 + 400 + 0 + 5 - 3 234 3 000 + 200 + 30 + 4 1 b. Subtract the tens. 5 000 + 400 + 0 + 5 - 3 000 + 200 + 30 + 4 ? + 1 5 000 + (400 – 100) + (100 + 0) + 5 - 3 000 + 200 + 30 + 4 ? + 1 5 000 + 300 + 100 + 5 - 3 000 + 200 + 30 + 4 70 + 1 c. Subtract the hundreds. 5 000 + 300 + 100 + 5 - 3 000 + 200 + 30 + 4 100 + 70 + 1 d. Subtract the thousands. 5 000 + 300 + 100 + 5 - 3 000 + 200 + 30 + 4 2 000 + 100 + 70 + 1 1000 1000 1000 100 100 1 1 1 1 10 10 10 XX XXX X X X X X X X 1000 1000 100 110 10 10 10 10 1010 1000 100 10 Subtract 4 from 5. You cannot subtract 30 from 0; therefore borrow 100 from the hundreds column and put it in the tens column Subtract 30 from 100. Subtract 200 from 300. Subtract 3 000 from 5 000. Add all the partial differences.
42 So, we get the same difference. Activity 3 – Short form method Solve the same problem using the short cut method. Th H T O 5 405 5 4 0 5 5 405 - 3 234 3 2 3 4 - 3 234 N 1 1 Steps: a. Put the numerals in the place value chart or align them according to their place value. b. Subtract the ones. (5 ones – 4 ones = 1 ones) c. Subtract the tens. Is it possible to subtract 3 tens from 0 tens? Th H T O Checking : 3 + 1 10 + 0 310 5 405 5 4 0 5 5 405 3 234 - 3 234 3 2 3 4 - 3 234 + 2 171 N 1 2 171 5 405  Regroup the hundreds. 4 hundreds = 3 hundreds + 1 hundreds.  Transfer 1 hundreds to the tens place. How many tens are there in 1 hundred?  Rename the tens. 10 tens + 0 tens = 10 tens  Can we now subtract 3 tens from it? (10 tens – 3 tens = 7 tens) d. Subtract the hundreds. (3 hundreds – 2 hundreds = 1 hundreds) e. Subtract the thousands. (5 thousands – 3 thousands = 2 thousands)  Did we get the same difference? 4. Solve the number sentence. What is 37 067 – 2 532?  Divide the class into 3 groups. Each group will work by partners.  The first group will solve it using the geometric cutouts with numbers written on it.  The 2 nd group will solve it using the expanded form.  The 3 rd group will solve it using the short cut method. Ask:  Did we get the same difference?  Which of the three methods do you like best? Why?
43 2. Guided Practice a. SECRET MESSAGE – To be done by groups with 4 members each. The teacher will provide each group with the secret message activity. Directions: Find the secret message. Find the difference of the number sentences in the box of Activity A. The difference will give the letters. Then use them in Activity B to decode the message. Activity A 4 305 8 607 5 906 5 037 - 142 - 473 - 283 - 516 A B C E 2 086 7 049 3 608 4 509 6 907 23 075 - 423 - 635 - 1 273 - 1 393 - 2 273 - 2 532 H I N O R S 32 095 47 032 54 308 38 053 12 507 - 1 731 - 3 412 - 135 - 4 531 - 1 242 T U W Y Z Activity B SECRET MESSAGE: 33 522 3 116 43 620 4 163 4 634 4 521 4 163 Y O U A R E A 20 543 43 620 8 134 30 364 4 634 4 163 5 623 30 364 6 414 3 116 2 335 54 173 1 663 6 414 11 265 W H I Z b. Math kinesthetic – (Body Number Coding) Group work with 5 members in each group. The teacher shows some subtraction sentences written in strips of cartolina. Each group will solve the number sentence on their paper. When they get the correct difference, each member acts out the answer using the body number coding. (To be written in strips of cartolina) 1. What is 3 050 minus 1 322? 2. Subtract 3 435 from 28 078? 3. Find the difference of 735 and 8 809. 4. Take away 1 345 from 8 907? 5. What is 3 253 less than 8 094? SS U B OR A C T IT N
44 c. Dyads Ask the pupils to write some subtraction sentences in a piece of paper. The pair exchanges their work with the other pair. Both pairs answer the problem they are holding. Let them show their answers for the class to check. What makes you enjoy the activities we had? What happens to your work when you help one another? 3. Generalization: How do we subtract numbers with zero difficulty in tens or hundreds? What do you always bear in mind when a digit in the minuend is zero and the corresponding digit in the subtrahend is a non-zero number? Remember: To subtract numbers with zero difficulty in tens or hundreds: 1. Align the numerals according to their place value. 2. Subtract starting with the ones place. 3. If the tens digit in the minuend is smaller than the subtrahend, regroup the hundreds then rename the tens. 4. To check: Add the difference and the subtrahend. The sum should be equal to the minuend. C. Application Individual work – Written Find the difference using the short cut method. 1) 3 059 - 432 2) 7 306 - 132 3) 6 059 - 1 325 4) 15 025 - 4 321 5) 27 309 - 4 132 IV. Evaluation Work by pairs Find the missing minuend, subtrahend or difference. 1) 3 059 - 432 ____ 2) 4 603 - ____ 2 471 3) ____ - 2 823 622 4) 13 087 - ______ 11 355 5) 24 809 - 1 372 ______ V. Assignment A. Write in column then subtract. 1) 3 405 – 393 2) 7 049 – 1 323 3) 25 306 – 2 134 4) 16 087 – 3 053 5) 73 059 – 2 124 B. Fill in the box with missing numeral 1) 5 _05 - 79_ 5 1_2 2) _ 087 - 1 _43 4 7_4 3) 8 _ _3 - 132 7 27_ 4) 1_ 03_ - 2 _34 15 9_3 C. Read and solve. 1. What should your minuend be if you have 45 453 as difference and 2 173 as subtrahend?
45 2. Patrick was able to save P5,430 from his monthly allowance. He wants to buy a cabinet that costs P9,050. How much more does he need to save so that he can buy the cabinet? 3. Bicycles are popular all over the world. The first bicycle was invented about 1790. How many years ago was the first bicycle invented? Estimating Differences I. Learning Objectives Cognitive: Estimate the difference of two numbers with 3- to 4-digits Psychomotor: State the rules in estimating differences Affective: Follow the rules in estimating differences correctly II. Learning Content Skill: Estimating differences Reference: BEC PELC I.C.1.1.4 Materials: flash cards, Show Me Board, word problem chart, cards with subtraction sentences and estimated difference, puzzle, table chart Value: Following simple directions correctly III. Learning Experiences A. Preparatory Activities 1. Drill (flash cards) Flashcards with numerals written on it. The pupils will read the numeral and tell the place value of the underlined digit. 2. Review a. Checking of assignment. b. Rounding Numbers Round the following numbers to the nearest: Hundreds Thousands 1) 253 _____________ 2) 3 437 _____________ 3) 125 _____________ 4) 6 053 _____________ 5) 478 _____________ 6) 4 857 _____________ 7) 659 _____________ 8) 8 210 _____________ 9) 304 _____________ 10) 7 489 _____________ 3. Motivation a. Guessing Game 1. Present a bottle filled with multicolored buttons. Ask: How many buttons do you think are there in this bottle? 4 753 1 543 84 387 47 259 547 203 3 575 4 385 59 367 38 732
46 2. Give 10 seconds for the pupils to give their guesses. Let them write their answers on the show-me-board. 3. Call 1 or 2 pupils to count the number of buttons in the bottle. The one who can give the closest guess will be the winner. Ask: How did you come up with the correct/nearest answer? Why is it not possible to get the exact answer immediately?  There are times that we do not need the exact answer to a problem. All we need is just the closest possible answer. b. Present a Problem Opener Mr. Cruz has 782 square metres of land planted with corn and 575 square metres planted with palay. About how many square metres more of land were planted with palay than with corn? B. Developmental Activities 1. Presentation a. Let us understand the problem. 1. How many square metres of land was planted corn? 2. How many square metres of land was planted palay? 3. What is asked in the problem? 4. Do we need an exact answer? 5. What word clues tell that we do not need an exact answer?  The phrase “about how many” tell us that we should estimate the answer. 6. What operation are we going to use? b. Let us plan on how we can solve the problem. 1. What will be the number sentence for the problem? 2. Ask a pupil to write the number sentence on the board. c. Let us execute our plan. 1. To find the estimated difference, round each number to the greatest place value 782 - 575 800 - 600 2. Then subtract. 800 - 600 3. Around 200 square metres of land were planted to palay than corn. d. Check your work. Exact Difference Estimated Difference 1. Did I answer the question? 2. Compare the estimated difference with the exact difference. 782 - 575 207 800 - 600 200 3. Is my answer sensible? 207 is close to 200 e. The teacher will give more exercises for the pupils to solve. Round each number then estimate the difference.
47 845 - 458  ____?____  ____?____ 7 541 - 1 825  ____?____  ____?____ Is the estimate difference close to the exact one? 2. Guided Practice a. Individual Work (flashcards and show me board) 1. Teacher shows some flashcards with subtraction sentences. 2. The pupils give the numerals rounded to the highest place value and then find their difference. Let them write the answer on their show me board. B. Game: Finding Patterns 1. Divide the class into 2. Give sets of cards with subtraction sentence in one group and cards with estimated difference in another group. 2. The first pair who matched the correct sentence with the correct estimated difference wins. Subtraction Sentence Cards Estimated Difference Cards:  Did you find your partner easily?  How did you do it?  Did you follow the rules in estimating difference?  Did you get the correct answer? 483 - 124 536 - 275 296 - 154 748 - 334 882 - 416 4 615 - 3 243 6 427 - 3 281 7 086 - 2 540 8 937 - 4 352 6 836 - 2 595 534-357 919-422 856-580 8 545-7 903 7 581-2 614 842-221 667-308 5 049-2 836 858-139 425-186 893-754 7 145-3 780 7 943-3 607 8 605-2 807 9 145-1 863 9 045-1405 100 200 300 400 500 600 700 800 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 900 9 000Joker cards:
48 3. Generalization a. What are the steps in estimating the difference? b. Why do we need to estimate? c. In what situation in life is estimation important? Remember: To estimate the difference: a. Round the minuend and the subtrahend to their greatest place value. b. Subtract the rounded numbers. C. Application Individual Work (Written) 1. Write the puzzle on the board. 2. Complete the puzzle boxes by estimating. The answer in the bottom right corner of each box will be the same when subtracting across or down. 1 287 891 888 641 IV. Evaluation Work by Pairs (Written) Estimate the difference by rounding the numbers to its highest place value then subtract. Write the answer in your notebook. 1) 673  _______ 2) 846  _______ 3) 558  _______ - 448  _______ - 551  _______ - 98  _______ _______ _______ _______ 4) 452  _______ 5) 758  _______ 6) 8 435  _______ - 125  _______ - 174  _______ - 2 526  _______ _______ _______ _______ 7) 9 071  _______ 8) 4 892  _______ 9) 8 465  _______ - 2 052  _______ - 1 261  _______ - 3 259  _______ _______ _______ _______ 10) 4 936  _______ - 2 143  _______ _______ V. Assignment A. Answer the following questions based on the table below.
49 LAND AREAS OF SOME PROVINCES Province Area (sq. km) Oriental Mindoro 4 365 Leyte 6 268 Bohol 4 117 Marinduque 959 Tawi-Tawi 1 087 1. About how much bigger is Oriental Mindoro than Leyte? 2. Estimate the difference between the areas of Tawi-Tawi and Marinduque. 3. About how much smaller is Marinduque than Leyte? B. Write a good estimate after each problem, then solve. 1. Mr. Reyes wanted to sell 302 tickets for a cultural show. He sold 191 tickets. About how many more tickets should he sell? Estimate by rounding to the nearest hundreds: ___________ Answer: ___________ 2. There are 8 936 books in Manuel L. Quezon Elementary School. Manuel Roxas Elementary School has 7 642 books in its library. How many more books does Manuel L. Quezon Elementary School have than Manuel Roxas Elementary School? Estimate by rounding to the nearest thousands: ___________ Answer: ___________ Subtracting Mentally 2-Digit Numbers without Regrouping I. Learning Objectives Cognitive: Subtract mentally 2-digit numbers with minuends up to 99 without regrouping Psychomotor: Tell the difference without using paper and pencil Affective: Show speed and accuracy when working in the activities II. Learning Content Skill: Subtracting mentally 2-digit numbers without regrouping Reference: BEC PELC I.C.1.2 Materials: spinner numbered 0 to 9 and 10 to 18, drill boards, flash cards, number coding chart Value: Speed and accuracy III. Learning Experiences A. Preparatory Activities 1. Drill Conduct a drill on basic subtraction facts using spinners. Provide a pair of spinners as shown below.
50 a. First, use the 0 to 9 spinner to generate two single-digit subtraction facts. b. Then call two pupils. c. Let pupil A spin Spinner 1 and pupil B spin Spinner 2 to generate 2-digit minuends such as 18-4 and other subtraction facts. (15-6, 12-2) d. The rest of the class answer them on their drill boards. e. At a given signal they show their answer to the teacher and to their seatmates. 2. Review Distribute 2 sets of strips of cartolina with numbers written on it. Then ask the pupils to find the expanded form of the number on their strips. The first partner to find each other wins. (The teacher may add more to the given strips) 3. Motivation Present a problem opener. Dick gathered 56 shells at the beach. He gave 24 shells to his friend. How many shells were left? B. Developmental Activities 1. Presentation a. Have you been to a beach? What are the things you saw there? In our story problem, who gathered shells? What did he do after gathering some shells? What kind of friend is he? Are you also kind to your friends? In what ways? How many shells did Dick gather? How many shells did he give to his friends? How many shells were left? What operation are we going to use? What will be our number sentence? b. Let a pupil write the number sentence on the board. 56 – 24 = N Ask somebody to write the number in vertical column. 56 - 24 N Say: Today, we will not use paper and pencil to find the difference but instead we will try to compute it mentally. Think of how we subtract numbers. In what direction do we follow when we subtract numbers? Subtract mentally the ones, then the tens 59 87 68 76 95 74 50 + 9 80 + 7 60 + 8 70 + 6 90 + 5 70 + 4
51 Think: 5 6 5 6 - 2 4 2 4 2 3 2 c. The teacher will give more example. 8 4 8 4 8 4 - 2 1 2 1 2 1 63 3 6 3 7 8 7 8 7 8 - 3 5 - 3 5 - 3 5 43 3 4 3 2. Guided Practices a. Let the pupils study the coding of numbers. Let them do it afterwards and memorize if possible (To be written in manila paper) Digit Movement 0 - Say “Yo!” 1 - Clap once 2 - Clap twice 3 - Clap thrice 4 - Raise your left hand 5 - Raise your right hand 6 - Say “Ole” 7 - Do the yes clap 8 - Say “Mabuhay!” 9 - Say “Be Happy!” (To be done by pairs) Direction: Find the missing number in the difference. Use the number coding. (Use flashcards) 1. 46 2. 88 3. 96 4. 78 5. 98 - 21 - 25 - 24 - 35 - 35 2_ _3 7_ _3 6_ Then give the difference 32 So, 32 shells were left to Dick. Is this the correct answer? Is it sensible?
52 6. 95 7. 29 8. 59 9. 62 10. 39 - 25 - 19 - 20 - 51 - 11 _0 1_ 3_ _1 2_ b. Cross number puzzle – (Individual work) Subtract mentally the following numbers to solve the puzzle. (Make 1 copy of the puzzle for every pupil.) a b c d e f g h I j k Across Down a. 95 – 63 a. 42 – 12 b. 72 – 20 b. 68 – 11 c. 89 – 29 c. 84 – 21 d. 68 – 21 d. 79 – 34 e. 98 – 33 e. 99 – 32 g. 49 – 12 f. 68 – 43 h. 35 – 20 h. 25 – 21 j. 28 – 14 i. 92 – 20 k. 56 – 33 j. 49 – 33 d. Telephone Game – (By Group) Directions: Group the pupils by column with 10 members each. The teacher gives subtraction sentence written on a piece of paper to the last pupil in every
53 column. On cue, the pupils who received the piece of paper simultaneously solve the subtraction sentence mentally. Then he/she whispers the answer to the next pupil until it reaches the pupils in front. The pupils in front will then write the answer on the board. The group with the correct answer gets a point. The first group to get 5 points wins. Illustration: The following subtraction sentences should be written on a strip of paper as many as the number of groups formed. 1) 85 2) 79 3) 67 4) 59 5) 89 - 24 - 34 - 35 - 32 - 25 6) 79 7) 94 8) 83 9) 99 10) 68 - 45 - 72 - 23 - 26 - 34 Did you do it fast? Were all your answers correct? 3. Generalization How do we subtract mentally? How did you do it? Where do we start subtracting? Remember: To subtract mentally 2-digit numbers mentally without regrouping, subtract the ones first, then the tens. Then give the difference. C. Application Subtract mentally. (Use drill board and flash cards) Chalk Board
54 1) 35 2) 56 3) 94 4) 48 5) 68 - 12 - 32 - 72 - 25 - 34 IV. Evaluation A. Subtract the following mentally. 1) 74 2) 86 3) 97 4) 94 5) 79 - 12 - 35 - 84 - 72 - 45 B. Game – Rally Robin Pupils will make their own subtraction sentence. Then they will pass it to their right and the pupils on the right answer the question. Then, they will do the reverse way. The one who answered correctly will also make a subtraction sentence and pass it to her/his right. V. Assignment A. Subtract mentally. Write only the answer. 1) 36 2) 89 3) 56 4) 67 5) 83 - 12 - 36 - 34 - 45 - 51 B. Find the difference of the numbers on the fruits by subtracting them mentally. 76 89 86 68 95 - 24 - 36 - 41 - 43 - 62 ___ ___ ___ ___ ___ C. Have the pupils subtract each number from 86 using mental arithmetic and write their answers in the triangles. 86 43 34 22 57
55 Solving Word Problems involving Subtraction I. Learning Objectives Cognitive: Solve 1-step word problems involving subtraction of whole numbers including money with minuends up to 100 000 without and with regrouping Psychomotor: Write the number sentence correctly Affective: Work cooperatively by helping one another in the group activities II. Learning Content Skill: Solving word problems involving subtraction Reference: BEC PELC I.C.2.1 Materials: flash cards of basic subtraction facts, chart of the song, problems written on manila papers, activity answer sheet, activity cards, play money, geometric cutouts with value written on it Value: Cooperation and helpfulness III. Learning Experiences A. Preparatory Activities 1. Drill: Kinesthetic Math The teacher will show flashcards (butterfly design) of basic subtraction facts and the pupils will act out the answer through body number coding. Digit Movement 0 Forefinger and thumb together forming zero 1 Right arm forward, closed fist 2 Left arm forward, closed fist 3 Both fists folded vertically close to the body 4 Hands on waist 5 Right hand on the chest 6 Bend forward to pick something 7 Stand straight 8 Arms obliquely upward 9 Do Mcdonald sign 4 8 10 9 7 5 - 2 - 3 - 4 - 1 6 2 6 9 10 8 - 2 - 2 - 1 - 8 2. Review Checking of assignment.
56 3. Motivation A. Song: This is the Time (Tune: This is the Day) This is the time (2x) That we’re waiting for (2x) We’ll learn our Math (2x) And apply them all (2x) So this is the time That we solve problems We’ll learn them all And apply them well. This is the time (2x) That we’re waiting for 1) Did you like the song? 2) What is the song all about? 3) What are we going to do with the problems? B. Present a problem opener. Two of the highest mountains in the Philippines are Mt. Apo in Mindanao which is 2 954 metres high and Mt. Pulog in Luzon which is 2 928 metres high. How many metres higher is Mt. Apo than Mt. Pulog? B. Developmental Activities 1. Presentation a. Let a pupil read the problem aloud to the class while the rest follow silently. b. Ask: Have you seen a mountain? Where? What happened to some of our mountains? What can we do to preserve our natural resources especially mountains? c. Let us analyze and solve the word problem using Polya’s 4 steps. ■ Understand the problem a. What are the two highest mountains in the Philippines? b. Where can you find Mt. Apo? What about Mt. Pulog? c. What are given? How high is Mt. Apo? How high is Mt. Pulog? d. What is being asked? e. What operation is needed to solve the problem? f. Why did you say so? What keywords/word clues were used? ■ Plan What equation will solve the problem? ■ Solve Ask a pupil to write the equation on the board. 2 954 – 2 928 = N d. Let the pupils draw the given height of the 2 mountains using the following geometric shapes and their equivalent values.
57 Shape Value 1000 500 100 10 1 Mt. Apo = Mt. Pulog =  Cross out the drawings that will make a pair.  What were left? How many are there?  I I I = 10 + 10 + 3 = 23  How many metres higher is Mt. Apo than Mt. Pulog? 23 metres ■ Look Back a. Did you use the correct operation? b. Does the answer make sense? c. Did you label the answer correctly? d. Mt. Apo is 23 metres higher than Mt. Pulog. e. Present another word problem for the pupils to analyze and solve. There were 2 995 people who went to see the basketball game. Nine hundred eighty-six were in the front rows and the rest were in the back rows. How many were left in the back rows? ■ Understand a. What are given? What do we already know? b. What is being asked? c. What operation is needed to solve the problem? d. Why did you say so? What keywords/word clues were used in the problem? ■ Plan What equation will represent the problem? ■ Solve a. Ask a pupil to write the equation on the board. 2 995 – 986 = N b. Write the number sentence in vertical column. The numerals must be aligned according to their place value. Subtract starting from ones column. If the minuend is smaller than the subtrahend, borrow 1 from the next column on the left. 8 15 2 995 2 995 - 986 - 986 2 009 ■ Look Back a. Did you use the correct operation?
58 b. Does the answer make sense? c. Did you label the answer correctly? 2 009 people were left in the back rows 2. Guided Practice Group Work Divide the class into small groups, around 3-4 members in a group. Have them answer the following problems cooperatively using the different strategies suggested. Then, discuss the solutions to the problems with the whole class. To be written in an index card: 1. The baker baked 3948 cupcakes. He sold 2437 of them. How many cupcakes were left? Instructions: Solve the problem through illustration. Use the following geometric shapes as representation. Shape Value - 1 000 - 500 - 100 - 10 - 1 2. Aling Maria earned 4,976 from selling meat. She spent 3,365 for the family’s food. How much money were left? Instructions: Solve the problem by acting it out. Use play money as your materials. 3. Cora sold 5 485 raffle tickets. Four thousand three hundred seventy-three of them were paid. How many raffle tickets were not paid? Instructions: Solve the problem by acting it out. Use geometric cutouts with value written on it. Ex.: 1 000 10 100 1
59 4. Mang Rexon harvested 6 884 ears of corn. He sold 4 693. How many ears of corn were unsold? Instruction: Solve the problem using the 4 steps of Polya. 5. Fely picked 3 953 flowers for the festival. She used 1 842. How many flowers were unused? Instruction: Use the 4-step in solving problems by Polya. 6. Ask the pupils about their feelings during the group activity.  How did you work with your group?  Did you help one another? Did you cooperate with the group?  What happened to your work when everybody is cooperative and helpful?  Were you able to arrive at the correct answer? 3. Generalization How do we analyze and solve word problems involving subtraction? What are the 4 steps in solving problems? What are the questions under each step? C. Application Group Work (5 members in each group) The teacher will give each group an activity card where a problem is written, and an activity answer sheet where they are going to write their answer. The group will report to the class about their work/solution for the class to check. Example of an activity answer sheet: Answer Sheet for Problem #1 ■ Understand a. What are the given facts? b. What is being asked? c. What are the necessary information or facts? d. What words tell what operation to use? e. What operation will you use? Polya’s 4 steps in solving problems are: a. UNDERSTAND – Understand the problem. What do I know? What do I need to find? b. PLAN – Make a plan. What shall I do? c. SOLVE – Carry out the plan. I will put my plan to work. d. LOOK BACK – Look back. Have I answered the question? Is my answer sensible?
60 ■ Plan What equation will solve the problem? ■ Solve Solve the equation. ■ Look Back a. Did you use the correct operation? b. Does the answer make sense? c. Did you label the answer correctly? IV. Evaluation A. Read, analyze and solve the following problems. 1. Mrs. Castro wants to buy a washing machine for 5,795. She saved 3,273. How much more does she need? 2. In a basketball game, 1 735 people watched the game. After the first half of the game 214 left. How many people stayed to watch the game? 3. Rhona wanted to sell 1 876 tickets for a dance exhibition. She has sold 934 tickets. How many more tickets should she sell? 4. During the local elections. Mr. Gonzales received 7 859 votes while Mr. Manzano received 6 347 votes. How many more votes did Mr. Gonzales receive than Mr. Manzano? 5. A morning newspaper has 29 347 subscribers. An afternoon newspaper has only 8 732 subscribers. How many more subscribers do the morning newspaper has than the afternoon newspaper? B. Written – Triads The problems below have no numbers. Decide how you would solve each one. If it will help you, fill in reasonable numbers. 1. Mario saved some money by buying a book of movie passes rather than individual tickets. How can he figure out how much money he had saved? 2. John knows the weight and price of two different sizes of boxes for dog food. How can he figure out which of the two is a better buy? 3. Anna bought a pair of rubber shoes. She went to the cashier to pay for it. How will she know how much change she had received? 4. Rebecca wanted to buy a refrigerator. She only save a certain amount. How can she figure out how much more does she need to save? 5. Laura made some circles. She colored some of them red and the rest blue. How will she know how many circles were colored blue? (The group will publish their work on the board for the class to check.) C. Work in Pairs Ask the pupils to create their own problem, then let her/his partner answer it. Then they are going to publish their work for the class to check. V. Assignment Read, analyze and solve. Use the 4 steps of Polya. 1. A total of 1750 tourists went to Baguio City in April and 639 in May. How many more tourists went to Baguio in April than in May? 2. Mother had 1,590. She bought groceries worth 1,587. How much was her change?
61 3. Robert harvested 1 659 cavans of palay from his farm. He sold 735 cavans. How many cavans of palay were left? Solving Word Problem Mentally I. Learning Objectives Cognitive: Solve mentally 1-step word problems involving subtraction without regrouping Psychomotor: State the complete answer Affective: Show speed and accuracy in solving word problems II. Learning Content Skill: Solving word problem mentally Reference: BEC PELC I.C.2.2 Materials: problem chart, flash cards, body number coding chart Value: Speed and accuracy III. Learning Experiences A. Preparatory Activities 1. Drill: Mental Computation Use flashcards. 2. Review Name the place value of the underlined digit. 3. Motivation Ask the pupils to subtract each number in the outer circle from the number in the inner circle. 8 - 5 4 - 2 10 - 7 18 - 7 12 - 5 29 - 8 17 - 8 485 376 109 362 785 87 32 41 2556 43 11 21 1233 75 32 20 5314 96 37 52 5634
62 B. Developmental Activities 1. Presentation Fely helped her mother sold pineapples in the market. She had 48 pineapples to sell. She sold 36 pieces in the morning. How many pineapples were not sold? Let us analyze and solve the problem mentally. What is asked in the problem? What are the given facts? What operation are you going to use? What will be the number sentence? How will you solve it mentally? Activity 1 Try to draw the problem in your mind. Does the answer make sense? Is it reasonable? Activity 2 – Expanded Form 48 - 36 = 40 + 8 = 30 + 6 10 + 2 Subtract the ones  8 – 6 = 2. Subtract the tens  40 – 30 = 10. Then add the two differences = 2 + 10 = 12. Activity 3 – Short Cut Form To solve mentally  Subtract the ones, then the tens. 10 1 1 1 1 1 1 1 1 1010 10 10 1 1 1 1 1 1 1 1 1010 10  48 pineapples (number of pineapples to be sold)  12 pineapples (number of pineapples left) Think
63 48 48 48 - 36 - 36 - 36 2 12 12 12 pineapples were not sold. Let us have another problem. Arlene has 98 in her wallet. She bought a kilogram of sugar for 32. How much was left with her? To solve mentally  Subtract the ones, then the tens. 98 98 - 32 - 32 6 66 66 was left with Arlene. 2. Guided Practices a. Individual Work The pupils will solve the problems mentally then write their answer on their show me board. After 5 seconds, they will show their answer to their teacher and classmates. a. Aling Nena washed 14 pieces of clothes while Rosa washed 26 pieces. How many more pieces did Rosa wash? a. The following day, Aling Nena ironed 34 pieces of clothes. Of the 34 pieces, 12 were blouses and the rest were t-shirts. How many t-shirts did she iron? b. A flower vendor had 85 roses to sell. She sold 63 roses in the morning and the remaining roses in the afternoon. How many roses did she sell in the afternoon? c. Mr. Santos planted 38 tomato seedlings and 15 eggplant seedlings. How many more tomato seedlings did Mr. Santos plant? d. There are 98 pupils in the school ground. Forty-two of them are Grade Three and the rest are Grade Four. How many Grade Four pupils are there? Kinesthetic Math – Body Coding Number To be done by pairs. The pupils will solve the problems mentally then they will act out the answer by pairs. One pupil will act out the tens place digit and the other will act out the ones place. a. Mother gave Agnes 95. She bought a notebook for 35. How much money was left? b. Kim had 78 marbles. He gave his brother 32 marbles. How many were left to him? c. Laura’s tomato plants have 89 ripe tomatoes. She picked 28 ripe tomatoes. How many ripe tomatoes were left? d. Maris counted 36 flowers in their school garden. Fely counted 98 flowers in the flower shop. How many more flowers did Fely count than Maris? e. Robert gathered 56 shells at the beach. He gave 24 shells to his friend. How many shells were left to Robert? Think
64 Creative Math – To be done by group with 3 members. Ask the pupils to make their own problem and solve it using the given data. 1) 76 flower pots to sell; 42 pots were sold 2) 99 hen’s eggs; 65 duck’s eggs 3) 58 Math books; 32 Science books 4) 67 Grade 3 pupils; 35 are boys 5) 95 pink balloons; 60 white balloons Did you do it fast? Were your answers correct? 3. Generalization How do we solve mentally 1-step word problems without regrouping? How did you do it? Remember: In solving word problem mentally involving subtraction, analyze the problem first, then subtract the ones places and the tens place. C. Application Individual Work Solve the problems mentally. Write your answer on a piece of paper or in your notebook. 1. Cindy had 95. She spent 30 for juice and biscuits. How much money was left? 2. Sarah has 78 baseball cards. Tricia has 40 cards. Who has more cards? How many more? 3. The sum of two numbers is 75. One number is 32. What is the other number? 4. Give the number that is 21 less than the other number, if the other number is 57. 5. The farmer gathered 93 bananas in his orchard. 42 bananas were yellow. How many were not yellow? IV. Evaluation Solve the following problems. At the market, Mar, Kim, Mae and Ken helped their mother count the vegetables she has to sell. They recorded the vegetables they counted. Name Eggplants Tomatoes Mar 88 76 Kim 32 54 Mae 59 67 Ken 27 15 Answer the following questions: 1. How many more eggplants did Mar count than Kim? 2. How many more eggplants did Mae count than Ken? 3. How many more tomatoes did Mar count than Kim? 4. How many more tomatoes did Mae count than Ken?
65 5. How many more eggplants than tomatoes did Mae count? Did you all get the answers correctly? What should you always remember every time you solve a problem? Is it good to work fast? Why? V. Assignment Study the price list of fruits per kilogram then answer the questions that follow. 1. Which fruit is the cheapest? 2. Which fruit is the most expensive? 3. How much more expensive are apples than mangoes? 4. How much cheaper are oranges than ponkan? 5. How much cheaper are bananas than ponkan? 6. How much more expensive are mangoes than oranges? 7. Which is cheaper, mangoes or ponkan? How much cheaper? 8. Which is more expensive, oranges or bananas? How much more expensive? Solving Two-Step Word Problems involving Addition and Subtraction of Whole Numbers including Money I. Learning Objectives Cognitive: Solve two-step word problems involving addition and subtraction of whole numbers including money Psychomotor: Tell what is asked, what are given and the word clue/s to be able to write the equation that will solve the problem Affective: Participate actively in class activities II. Learning Content Skills: Solving two-step word problems involving addition and subtraction of whole numbers including money Reference: BEC PELC I C 3.1 Materials: flash cards Value: Active participation III. Learning Experiences A. Preparatory Activities
66 1. Drill (Mental Computation) Conduct a drill in the basic subtraction and addition facts using flashcards with the shape of a flower. 2. Review “Subtraction with zero difficulty” Two students compete with each other, trying to answer the equation mentally. Sample equations: 600 – 426 = ______ 900 – 810 = ______ 2 000 – 1 593 = ______ Strategy: a. Mentally, deduct one from the hundreds digit; change zeros to 9, except in the ones. Change 0 in the ones place to 10. Ex. 5 9 10 6 0 0 - 4 2 6 b. Subtract: 59 (10) - 42 6 174 3. Motivation Present a two-step word problem. Mang Carlos picked 115 yellow mangoes and 73 green mangoes. He sold 56 mangoes in all. How many mangoes were left to him? B. Developmental Activities 1. Presentation a. At this point, ask the class to recall the 4-steps on problem solving according to George Polya: Understand  Plan  Solve  Look Back b. Looking at the problem, elicit from the students the following: ■ Understand a. What is asked? Number of mangoes left to Mang Carlo b. What are given? 115 yellow mangoes, 73 green mangoes, sold 56 in all
67 ■ Plan At this point, ask what question do we have to answer first to get the final answer? This question is called “hidden question.” ■ Solve What operation/s are needed to solve the problem? Addition; subtraction. What equation will solve the problem? 115 + 73 – 56 = n Which do we perform first? Addition: 115 + 73 188 then subtract 188 - 56 132 mangoes ■ Look back Does our answer make sense? Yes, since 132 is less than the total. Yes, since the 2 steps used were to find the total number of mangoes first, then the number of mangoes left. Did we label it correctly? c. Give another problem. Regina has 80 eggs to sell. She sold 25 eggs in the morning and 46 eggs in the afternoon. How many more eggs does she need to sell? d. Ask: 1. What are given? 80 eggs in all to sell 25 eggs sold in the morning and 46 eggs in the afternoon 2. What is being asked? Number of eggs Regina need more to sell 3. What operations are needed? Addition and subtraction or subtraction only. 4. What equation will solve the problem? 80 – (25 + 46) = n or 80 – 25 – 46 = n 5. Solve: 25 80 80 55 + 46 - 71 or - 25 - 46 71 9 55 9 6. Check if the answer makes sense and if labeled properly. 2. Guided Practice a. Activity: Column Relay Present the following problem. Daniel earned 35 by delivering water to several houses. He gave 15 of his earnings to his mother and 12 to his sister. How much money was left to him? Directions: 1. Divide the class into 6 groups. Each member will answer one column. 2. Give the first pupil a copy of the questions. He answers the question then passes the copy to the second pupil. The second pupil answers the end question and then passes the copy to the 3 rd pupil and so on. 3. Read the problem posted on the board, then answer each question below: a. What are given? ___________________________________ ________________________________________________ b. What is being asked? _______________________________
68 ________________________________________________ c. What operation/s is/are needed to solve? _______________ ________________________________________________ d. What equation will represent the problem? _________________ e. Solve the operation: f. Label and look back. b. Cooperative Learning Activity: “Rally Table” 1. Group the class in pairs; players A and B. 2. Each member of the pair takes turn in answering the questions posted on the board. 3. Present these problems on the board. Rules:  Player A writes the hidden question.  Player B answers the hidden question.  Player A writes the equation that will solve the problem.  Player B answers/solves the equation. 1. Mang Carlos raised 35 piglets for sale. He sold 10 piglets to his mother and 5 piglets to his friend. How many piglets were left to him? 2. Danilo arranged 564 books in the library. The next day, he arranged 345 books. There are 1 500 books in the library. How many more books will Danilo arrange? 3. In the pupils’ government election, Alexis received 112 votes. Brylle received 186 votes. The winner Joric received 312 votes. How many more votes did Joric receive than Alexis and Brylle? Do you think you can solve the problems without following the steps? Was your solutions correct? Was your answer correct? If your answer was not correct, in what part did you commit a mistake? 3. Generalization What are the 4 important steps in solving word problems? a. Understand the problem. - Find the hidden question. b. Make a plan. c. Solve/carry out plan. d. Look back. C. Application Direction.  Give each group a copy of the problems below on strips of paper.  Let each group solve the problems.  Write their solutions on the board.  Present the work afterwards 1. Mr. Javier has to deliver 760 sacks of rice. He delivered 510 to Mr. Rosales and 140 to Mr. Acosta. How many more sacks of rice will be delivered?
69 2. After spending 75.00 for a shirt and 125.00 for a pair of pants, Michelle had 50.00 left in her wallet. How much money did she have at first? 3. There are 246 yellow mangoes and 152 green ones. Out of these, 120 are in the basket and the rest are in the crate. How many are in the crate? 4. Mang Luis is a farmer who sells coconuts and watermelons. He earned 843.00 from selling coconuts and 832.00 from watermelons. Before going home, he bought 1 kilo of pork for 120.00. How much money was left to him? 5. Mother and Lito picked tomatoes in their vegetable garden. Mother picked 19 tomatoes and Lito picked 12. Mother used 5 tomatoes for cooking. How many tomatoes were left? IV. Evaluation Answer the following problems using Polya’s strategy. 1. Mr. Reyes gathered 365 mangoes on Monday and 453 on Tuesday. He sold 650 mangoes on Wednesday. How many mangoes were left unsold? 2. A farmer harvested 425 sacks of palay. He sold 258 sacks to Buyer A and 120 to Buyer B and kept the rest for his family. How many sacks of palay were left? 3. Rita bought a dress for 235.00 and a pair of shoes for 574.00. She gave a 1000-peso bill to the cashier. How much is her change? 4. Alex wants to buy a T-shirt worth 185.00 and a school bag worth 240.00. He has only 300.00. How much more money does he need? V. Assignment Solve the following: 1. There are 262 boys and 528 girls in Grade Three. Out of these, 174 pupils are 10 years old. How many pupils are not 10 years old? 2. Pia spelled 26 words correctly on Monday, 25 on Wednesday and 37 on Friday. If there are 100 words to be spelled, how many words did she misspell? 3. Rosalinda bought a bag for 165.00 and a pair of shoes for 395.00. How much change did she get from 1,000.00? 4. A shoe factory in Marikina produced 235 pairs of shoes in one week and 324 pairs in another week. If 450 pairs were delivered to a department store, how many pairs were not delivered? 5. Rose had a balance of 3,500.00 in her account in the bank. She deposited 1,200.00 the following month and withdrew 950.00. How much was left in her account?

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Lesson guide gr. 3 chapter i -subtraction v1.0

  • 1.
    Lesson Guide In Elementary Mathematics Grade3 Reformatted for distribution via DepEd LEARNING RESOURCE MANAGEMENT and DEVELOPMENT SYSTEM PORTAL DEPARTMENT OF EDUCATION BUREAU OF ELEMENTARY EDUCATION in coordination with ATENEO DE MANILA UNIVERSITY 2010 Chapter I Whole Numbers Subtraction INSTRUCTIONAL MATERIALS COUNCIL SECRETARIAT, 2011
  • 2.
    Lesson Guides inElementary Mathematics Grade III Copyright © 2003 All rights reserved. No part of these lesson guides shall be reproduced in any form without a written permission from the Bureau of Elementary Education, Department of Education. The Mathematics Writing Committee GRADE 3 Region 3 Agnes V. Canilao – Pampanga Josefina S. Abo – Tarlac City Alma Flores – Bataan Region 4 - A Cesar Mojica – Regional Office Marissa J. de Alday – Quezon Henry P. Contemplacion – San Pablo City Region 4 – B Felicima Murcia – Palawan National Capital Region (NCR) Laura N. Gonzaga – Quezon City Dionicia Paguirigan – Pasig/San Juan Yolita Sangalang – Pasig/San Juan Bureau of Elementary Education (BEE) Elizabeth J. Escaño Galileo L. Go Nerisa M. Beltran Ateneo de Manila University Pacita E. Hosaka Support Staff Ferdinand S. Bergado Ma. Cristina C. Capellan Emilene Judith S. Sison Julius Peter M. Samulde Roy L. Concepcion Marcelino C. Bataller Myrna D. Latoza Eric S. de Guia - Illustrator Consultants Fr. Bienvenido F. Nebres, SJ – President, Ateneo de Manila University Ms. Carmela C. Oracion – Principal, Ateneo de Manila University High School Ms. Pacita E. Hosaka – Ateneo de Manila University Project Management Yolanda S. Quijano – Director IV Angelita M. Esdicul – Director III Simeona T. Ebol – Chief, Curriculum Development Division Irene C. Robles – OIC - Asst. Chief, Curriculum Development Division Virginia T. Fernandez – Project Coordinator EXECUTIVE COMMITTEE Jesli A. Lapus – Secretary, Department of Education Teodosio C. Sangil, Jr. – Undersecretary for Finance and Administration Jesus G. Galvan – OIC - Undersecretary for Programs and Projects Teresita G. Inciong – Assistant Secretary for Programs and Projects Printed By: ISBN – 971-92775-2-1
  • 3.
    iii TABLE OF CONTENTS Introduction..................................................................................................................................iv Matrix ........................................................................................................................................v I. WHOLE NUMBERS A. Subtraction Subtracting Numbers without Regrouping  3-Digit Numbers from 4- to 5-Digit Numbers .................................................... 1  4-Digit Numbers from 4- to 5-Digit Numbers .................................................... 7 Subtracting Numbers with Regrouping in the:  Tens Place ........................................................................................................ 15  Hundreds Place ................................................................................................. 21  Thousands Place .............................................................................................. 27  Ten Thousands Place ....................................................................................... 32 Subtracting Numbers with Zero Difficulty ....................................................................... 38 Estimating Differences ................................................................................................... 45 Subtracting Mentally without Regrouping ...................................................................... 49 Solving Word Problems .................................................................................................. 55 Solving Word Problems Mentally ................................................................................... 61 Solving 2-Step Word Problems involving Addition and Subtraction including Money ................................................................................................ 65
  • 4.
    iv I N TR O D U C T I O N The Lesson Guides in Elementary Mathematics were developed by the Department of Education through the Bureau of Elementary Education in coordination with the Ateneo de Manila University. These resource materials have been purposely prepared to help improve the mathematics instruction in the elementary grades. These provide integration of values and life skills using different teaching strategies for an interactive teaching/learning process. Multiple intelligences techniques like games, puzzles, songs, etc. are also integrated in each lesson; hence, learning Mathematics becomes fun and enjoyable. Furthermore, Higher Order Thinking Skills (HOTS) activities are incorporated in the lessons. The skills are consistent with the Basic Education Curriculum (BEC)/Philippine Elementary Learning Competencies (PELC). These should be used by the teachers as a guide in their day-to-day teaching plans.
  • 5.
    v MATRIX IN ELEMENTARYMATHEMATICS Grade III COMPETENCIES VALUES INTEGRATED STRATEGIES USED MULTIPLE INTELLIGENCES TECHNIQUES With HOTS I. Whole Numbers A. Subtraction of Whole Numbers 1. Comprehension of Subtraction 1.1 Subtract 3 to 4 digit numbers from 4 to 5 digit numbers with minuends up to 100 000 without and with regrouping and with zero difficulty 1.1.1 Subtract 3 digit numbers from 4 to 5 digit numbers with minuends up to100 000 without regrouping Cooperation Modeling Simplifying the problem Diagrams and chart (Spatial) Cooperative groups (Interpersonal)  1.1.2 Subtract 4 digit number from 4 to 5 digit numbers with minuends up to 100 000 without regrouping Cooperation Draw pictures Simplifying the problem Puzzle (Logical mathematics) Diagrams and chart (Spatial) Cooperative groups(Interpersonal  1.1.3 Subtract 3 to 4 digit numbers from 4 to 5 digit numbers with regrouping 1.1.3.1 in the tens place Helpfulness and following rules Draw pictures Body movements (Bodily kinesthetic) Manipulative (Bodily kinesthetic) Diagram (Spatial)  1.1.3.2 in the hundreds place Cooperation Simplifying the problem Song (Musical) Manipulative (Bodily kinesthetic)  1.1.3.3 in the thousands place Helpfulness Draw pictures Simplifying the problem Cooperative groups(Interpersonal) Puzzle (Logical mathematics)  1.1.3.4 in the ten thousand place Cooperation Draw pictures Simplifying the problem Cooperative groups(Interpersonal) Manipulative (Bodily kinesthetic)  1.1.3.5 with zero difficulty in either tens or hundreds place Helpfulness Polya's steps in problem solving Acting out the problems Body movements (Bodily kinesthetic) 
  • 6.
    vi 1.1.4 Estimate thedifference of two numbers with 3 to 4 digits Following simple directions Simplifying the problem Puzzle (Logical mathematics)  1.2 Subtracts mentally 2 digit numbers with minuends up to 99 without regrouping Speed and accuracy Simplifying the problem Number Puzzle (Logical mathematics) Illustrations (Spatial) Body movements (Bodily kinesthetic)  2. Application of Subtraction 2.1 Solve 1 step word problems involving subtraction of whole numbers including money with minuends up to100 000 without and with regrouping following the steps in problem solving Cooperation/Helpfulness Drawing pictures/figures Polya's steps in problem solving Song (Musical) Body movements (Bodily kinesthetic)  2.2 Solve mentally 1 step word problems involving subtraction without regrouping Speed and accuracy Draw the problem Body movements (Bodily kinesthetic) Illustrations (Spatial)  1. Application of Addition and Subtraction 3.1 Solve 2 step word problems involving addition and subtraction of whole numbers including money following the steps in problem solving Active participation Polya's steps in problem solving Cooperative groups (Interpersonal) 
  • 7.
    1 Subtracting Numbers withoutRegrouping I. Learning Objectives Cognitive: Subtract 3-digit numbers from 4- to 5-digit numbers with minuends up to 99 999 without regrouping. Psychomotor: Write correctly the numeral in vertical column according to their place value. Affective: Work cooperatively during the class and group activities II. Learning Content Skill: Subtracting numbers without regrouping Reference: BEC PELC I.C.1.1.1 Materials: 0-9 number cards, place value pocket chart, flash cards of basic subtraction Value: Cooperation III. Learning Experiences A. Preparatory Activities 1. Drill: (flashcards of basic subtraction) 2. Review – Game Divide the children into 5 groups. Distribute place value pocket charts and number cards. The teacher will give instructions on what number they will form. The group who answers first will have the point and the group with the highest points will be the winner. Tell the pupils to do the following: Ask: Form the largest 3-digit number without repetition Form the smallest 3-digit number without repetition Form the largest 4-digit number without repetition Form the smallest 4-digit number without repetition. Using the digits 4, 7, 3 and 0, what is the largest number you can form? the smallest number you can form? 3. Motivation: Who among you has a bank account? What are you doing with your savings? What happens to your money if you deposit and withdraw? Is it okay to withdraw money from your savings account? Why? 8 - 5 3 - 2 9 - 7 6 - 2 5 - 3 7 - 4 2 - 1 4 - 0 10 - 6 1 - 1
  • 8.
    2 B. Developmental Activities Presentthe table: Number of Trees Planted in Barangay Malinis Trees Number of Trees Acacia 3 875 Narra 2 554 Molave 432 How many more acacia trees are there than molave trees? 1. Presentation a. Compare the number of acacia trees to the number of molave trees. Which has more trees, acacia or molave? How many trees more? What process are we going to use to find the answer? What is the number sentence? Ask a pupil to write the number sentence on the board. (3 875 – 432 = N) Which is the minuend? the subtrahend? b. Let the pupils work in pairs. Ask them to represent the minuend through their cubes, flats, longs and ones. cube long flat 1 flat = (100 cubes) 1 block = (1000 cubes) Activity 1 – Using Manipulatives – Working by pairs
  • 9.
    3 Let us solvethe problem by using manipulative. Let us do it by pairs. How many acacia trees are there? What about molave trees? How many more acacia trees are there than molave trees? Ask: How will you represent 3 875 using the cubes, flats, longs and ones? How many cubes, flats, longs and ones will you use? (3 blocks, 8 flats, 7 longs and 5 cubes) Thousands Hundreds Tens Ones What about our subtrahend, 432? How many flats, longs and cubes will there be? (4 flats, 3 longs and 2 cubes) Since 432 is the number to be taken away, let’s get it from 3 875. (Let the pupil get 4 flats, 3 longs and 2 cubes from 3 blocks, 8 flats, 7 longs and 5 cubes.) How many blocks, flats, longs and cubes were left? (3 blocks, 4 flats, 4 longs and 5 cubes) How will you read blocks, flats, longs and ones in numeral? How will you write it in figure? 3 443 So, what is 3 875 – 432? 3 443 Activity 2 – Using the expanded form Here is another way of subtracting numbers by Expanded Form. 3 875 3 000 + 800 + 70 + 5 - 432 400 + 30 + 2 3 000 + 400 + 40 + 3 = 3 443 What is the difference? 3 443 X X X XX X X X X
  • 10.
    4 Activity 3 –Short Cut Method Let us represent the same number through the place value chart. How will you write the numerals in the place value chart. Short Form: 3 875 minuend - 432 subtrahend N Thousands Hundreds Tens Ones 3 8 7 5 - 4 3 2 3 4 4 3 1. Subtract the ones. (5 – 2 = 3) 2. Subtract the tens. (7 tens – 3 tens = 4 tens) 3. Subtract the hundreds. (8 hundreds – 4 hundreds = 4 hundreds) 4. Subtract the thousands. (3 thousands – 0 thousands = 3 thousands) So, 3 875 – 432 is 3 443. c. Give again another problem. Group the class into three. Let the 1 st group solve it by manipulative (blocks, flats, long and cubes); the 2 nd group by expanded form (value form) and, the 3 rd group by short-cut form (short form-place value chart). Expected Answer: 1 st Group: 4 blocks, 1 flat, 1 long and 3 cubes = 4,113 2 nd Group: 4 356 4 000 + 300 + 50 + 6 - 243 200 + 40 + 3 4 000 + 100 + 10 + 3 = 4 113 3 rd Group: Th H T O 4 3 5 6 – 2 4 3 4 1 1 3 Did you get the same difference? 2. Guided Practice a. Group Work – (4 members per group) Let the pupils group themselves with 4 members each. Ask them to answer the following numbers using only their blocks, flats, long and cubes. Then they will put their answers in the place value pocket chart with the use of their number cards. What is 4 356 minus 243? Number Cards 0 1 2 3 4 5 6 7 8 9 Place Value Pocket Chart Th H T O
  • 11.
    5 1) 3 6742) 4 356 3) 5 243 4) 6 532 5) 8 547 - 532 - 143 - 112 - 321 - 217 Did you get all the answers right? Why? b. Work by pairs Use the expanded form method in solving the number problem. You will work now in pairs. 1) 19 236 2) 24 379 3) 17 874 4) 26 728 5) 36 745 - 220 - 234 - 762 - 312 - 233 Did you get all the answers right? Why? c. Individual Work Let us use the short-cut method. 1) 7 419 2) 7 923 3) 8 465 4) 24 936 5) 35 985 - 306 - 412 - 254 - 224 - 865 Did you get all the answers correctly? Which of the three methods do you prefer or like? Why? Why do you think you got the right answer easily? Which group got all correct answers first? Why do you think they got it easily? What did the group do to make their work easy? 3. Generalization: How do we subtract numbers without regrouping? How do we write the numeral when subtracting? Where do we start subtracting? Why do you think subtracting is very important? Remember: In subtracting 3-digit numbers from 4-digit numbers, the digits must be aligned according to their place value. Then, subtract the ones first, then the tens, the hundreds and the thousands. C. Application Individual work (Use of show-me-board, chalk and flashcards) Subtract the numbers I’m going to show you. Then write the difference on your show-me- board. 1) 8 537 2) 3 489 3) 7 642 - 315 - 158 - 132 (Note to the teacher: Make the materials ready before the activity)
  • 12.
    6 4) 5 7835) 9 857 6) 16 476 - 241 - 315 - 324 7) 22 879 8) 34 364 9) 21 976 - 524 - 134 - 235 10) 19 752 - 421 IV. Evaluation A. Work by pairs. Find the missing numbers. 1) 8 362 2) 2 514 3) 4 _ _2 4) 3 2_5 - _50 - 1_ _ - 261 - _3_ 8 21_ 2 _11 4 63_ 3 063 5) 7 384 6) 12 _ _ _ 7) 4 _ _2 8) 3 2_5 - _ _ _ - 315 - 261 -_3_ 7 120 2 _11 4 63_ 3 063 9) 8 362 10) 2 514 - _50 - 1_ _ 8 21_ 2 _11 B. Individual Work Find what number is being asked. 1. What is the difference between 8 753 and 213? 2. What number is 320 less than 1 975? 3. Subtract 514 from 2 758. 4. What is 6 788 less 351? 5. What number is 502 less than 4 735? 6. Take away 485 from 13 596. 7. What is 24 359 minus 134? 8. What is the difference between 523 and 21 785? V. Assignment Do as indicated. 1. What is the difference between the largest 4-digit number without repetition and the smallest 3- digit number without repetition? 2. What is the difference between the largest 4-digit number with repetition and the smallest 3-digit number without repetition? 3. What is the difference between the largest 4-digit number with repetition and the largest 3-digit number with repetition?
  • 13.
    7 Subtracting Numbers withoutRegrouping I. Learning Objectives Cognitive: Subtract 4-digit numbers from 4-5 digit numbers with minuends up to 100 000 without regrouping. Psychomotor: Write correctly the numeral in vertical column according to their place value. Affective: Work cooperatively during the class and group activities II. Learning Content Skill: Subtracting numbers without regrouping Reference: BEC PELC I.C.1.1.2 Materials: maze, play money (money kit) Value: Cooperation, Helpfulness III. Learning Experiences A. Preparatory Activities 1. Drill – Maze Procedure: a. The teacher will post the maze on the board. There will be 2 teams with 10 members each. b. Each member will unblock the path on the maze by answering the subtraction sentence written inside the box. c. Each member will answer one at a time. A member goes to the board only upon the return of the member before him/her. d. The first group to finish and unblock the path wins the game. (Note to the teacher: Each box should have basic subtraction fact written inside)
  • 14.
    8 2. Review a. Findthe difference 7 436 3 853 8 789 2 432 5 859 - 215 - 701 - 237 - 102 - 325 b. Checking of Assignment 3. Motivation: Present a problem opener. The Boy and Girl Scouts Drama Group presented a play. On the first day, they earned 4,865. On the second day, they earned 5,985. How much more did they earn on the second day than on the first day? B. Developmental Activities 1. Presentation a. Let us analyze and solve the problem. - Who presented the play in the problem? (The Boy and Girl Scout Drama Group) - How much did they earn on the 1 st day? 2 nd day? (1 st day- 4,865; 2 nd day- 5,985) - What operation are we going to use to solve the problem? (subtraction) - What will be our number sentence? ( 5,985 – 4,865 = N) - How much more did they earn on the second day than on the first day? ( 1,120)
  • 15.
    9 Activity 1. UsingPlay Money/Drawing Pictures – Work in pairs Ask the pupils to work in pairs. Let them get their money kit and represent the money earned on the first day and on the second day. 1 st Day 2 nd Day 4,865 5,985 1,000 1,000 1,000 1,000 500 100 100 100 50 10 5 1,000 1,000 1,000 1,000 1,000 500 100 100 100 100 50 10 10 10 5
  • 16.
    10 From the moneykit can you tell how much more they earned on the second day than on the 1 st day? Why/Why not? Let them pair the money earned on the 1 st day to the money earned on the second day. 1 st Day 2 nd Day 4,865 5,985 Do all the money earned on the first day have pairs on the 2 nd day? 1,000 1,000 1,000 1,000 500 100 100 100 50 10 5 1,000 1,000 1,000 1,000 5 1,000 500 100 100 100 100 50 10 1 0 1 0 has no pair has no pair has no pair has no pair
  • 17.
    11 What about theother way around? Do all the money earned on the 2 nd day have pairs on the first day? How much money do not have pairs? 1,000 + 100 + 10 + 10 = 1,120 Therefore, how much more money did they earn on the 2 nd day? 1,120 Does our answer make sense? Activity 2 – Expanded Form: Let’s recall the problem, “How much more did they earn on the second day than on the first day?” What process are we going to use? Subtraction Why did you say subtraction? Let’s write the number sentence. (Ask the pupil to write the number sentence on their drill board and show it to the teacher.) Ask the pupils to write the given numerals in expanded form. 5 985 5 000 + 900 + 80 + 5 - 4 865 4 000 + 800 + 60 + 5 1 000 + 100 + 20 + 0 = 1 120 partial differences Subtract each number vertically, then add the partial differences horizontally. Activity 3 – Short Form: Let us use the short cut method. Place the minuend and subtrahend in the place value chart. Short Form 5 985 - 4 865 1 120 1 st – Subtract the ones (5 – 5 = 0) 2 nd – Subtract the tens (8 tens – 6 tens = 2 tens) 3 rd – Subtract the hundreds (9 hundreds – 8 hundreds = 1 hundreds) 4 th – Subtract the thousands (5 thousands – 4 thousands = 1 thousands) Did we get the same answer from the 3 activities? a. Group Work Group 1 will answer no. 1, Group 2, no. 2 and Group 3, no. 3 Group 1 will use the drawing method either by one to one pairing or crossing-out just like what we did yesterday. Use _______ for 1000, for 100, for 10 and __ for 1 Group 2 will use the expanded form method. Group 3 will use the short-cut method 1. What is the difference between 2 532 and 8 975? 2. Subtract 3 526 from 64 729 3. From 78 324, take away 5 302 Expected Answers: 4 th 3 rd 2 nd 1 st Th H T O 5 9 8 5 4 8 6 5 1 1 2 0
  • 18.
    12 1. Drawing (Pairing) Drawing(crossing-out) 8975 2 532 8 975 2. 64 729 60 000 + 4 000 + 700 + 20 + 9 - 3 526 - 3 000 + 500 + 20 + 6 = 60 000 + 1 000 + 200 + 0 + 3 = 61 203 3. 78 324 Ten Thousands Hundreds Tens Ones - 5 302 Thousands 7 8 3 2 4 - 5 3 0 2 7 3 0 2 2 Which group finished first? Why do you think they have done the activity easily? What did each member do to make their work easy? no pair How many have no pairs? 1 000 1 000 1 000 1 000 1 000 1 000 100 100 100 100 100 10 10 10 10 1 6 000 400 40 3 6 443 Take away 2 532 How many were left? 1 000 + 1 000 + 1 000 + 1 000 + 1 000 + 1 000 + 100 + 100 + 100 + 100 + 10 + 10 + 10 + 10 + 1 + 1 + 1 = 6 443
  • 19.
    13 2. Guided Practice a.Work in pairs Subtract the following. Use the short-cut method 1) 7 635 2) 2 304 3) 6 287 4) 6 789 5) 4 236 - 3 413 - 1 203 - 6 152 - 3 436 - 2 225 6) 98 325 7) 88 766 8) 83 293 9) 72 844 10)54 678 - 3 103 - 2 513 - 1 021 - 1 342 - 1 325 a. Group Work – (with 3 members) Number Puzzle – (Provide each group with number puzzle to work on.) Subtract the following numbers and write your answer on the number puzzle. You have 5 minutes to complete it. a b c d e f g h i j k Across a. 6 898 – 4 353 d. 1 215 less than 4 885 f. 6 548 minus 1 240 g. 5 487 less 4 035 i. 1 270 – 1 230 j. What is the difference between 4 562 and 4 510? k. Subtract 1 231 from 2 477 Down b. What number is 1 000 less than 6 755? c. From 5 244, subtract 1 212 d. 5 346 – 2 132 e. 3 866 minus 2 014 h. The difference between 2 726 and 1 325 Did you get the answers right? Did your team work together to finish the puzzle fast? How did you subtract easily? Which method did you use? 3. Generalization How do we subtract 4-digit numbers from 4 to 5-digit numbers? Where do we start subtracting? Do you think there is a technique in doing this? How?
  • 20.
    14 Remember In subtracting 4-digitnumbers, the numbers must be aligned properly according to their place value. Then start subtracting from ones first, then tens, hundreds and thousands. C. Application a. Find the missing numbers 1) 4 921_ 2) 69 4_ _ 3) 32 9_8 - _ 112 - 3 _12 - 2 _0_ 45 _ _1 6_ 220 3_ 135 b. Do as indicated 1. What number is 2 541 less than 87 876? 2. Subtract 3 487 from 56 899. IV. Evaluation (To be done individually) Paper and pencil Write in column then subtract 1) 4 732 – 2 301 = N 3) 7 857 – 3 412 = N 5) 8 576 – 4 253 = N 7) 5 436 – 1 034 = N 9) 6 258 – 2 153 = N 2) 73 259 – 1 143 = N 4) 62 987 – 2 543 = N 6) 25 737 – 3 705 = N 8) 48 635 – 2 125 = N 10) 75 557 – 5 423 = N V. Assignment Write in expanded form then subtract. 1) 59 875 = _____ + _____ + _____ + _____ + _____ - 4 362 = _____ + _____ + _____ + _____ + _____ 2) 37 589 = _____ + _____ + _____ + _____ + _____ - 3 251 = _____ + _____ + _____ + _____ + _____ 3) 87 639 = _____ + _____ + _____ + _____ + _____ - 3 318 = _____ + _____ + _____ + _____ + _____
  • 21.
    15 Subtracting Numbers withRegrouping in the Tens Place I. Learning Objectives Cognitive: Subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the tens place. State the rules in subtracting numbers with regrouping Psychomotor: Follow the rules in subtracting numbers with regrouping in the tens place and use the body-number coding (kinesthetic math) properly. Affective: Follow simple rules correctly. Practice helpfulness at all times. II. Learning Content Skill: Subtracting numbers with regrouping in the tens place Reference: BEC PELC I-C 1.1.3.1 Materials: chart of the body number coding, problem chart, flash cards of basic subtraction, Popsicle sticks or straws Value: Following simple rules correctly/Helpfulness III. Learning Experiences A. Preparatory Activities 1. Drill – Body Number Coding Let the pupils do the coding of numbers through their hands and body. (Write the code on a manila paper) Digit Movement 0 1 2 3 4 5 6 7 8 9 - Forefinger and thumb together forming zero - Right arm forward closed fist - Left arm forward closed fist - Left and right arms bend forward close to the body - Hands on waist - Right hand on the chest - Bend forward to pick something - Stand straight - Arms obliquely upward - Do McDonald sign The teacher will show some flashcards about basic subtraction and the pupils will give the answer through their body action without giving the answer. Example: 7 – 3 = 4 (They have to act the code for number 4 which is hands on waist) 2. Motivation – Present a problem opener. Mang Pedro brought 2 752 eggs to sell in the public market. Danny, his eldest son, helped him sell 1 345 eggs. How many eggs were left? 8 - 7 5 - 1 3 - 0 5 - 5 6 - 4 10 - 5 9 - 2 8 - 2 9 - 1 10 - 1
  • 22.
    16 B. Developmental Activities 1.Presentation a. What do you think is the work of Mang Pedro? What did he sell in the public market? Who is his eldest son? What kind of son is he? Are you also helpful? In what ways are you helpful? How many eggs did Mang Pedro bring? How many eggs were sold by his eldest son? What is asked in the problem? How are we going to solve it? What process are we going to use? What will be our number sentence? b. Let a pupil write the number sentence on the board. 2 752 – 1 345 = N (Pre-Activities) Note to the Teacher: (The pupils should have their Math Kit where they can place their Popsicle sticks/straws, rubber bands, counters, etc. A place value containers should always be inside their classroom. If possible, the place value containers should be made as a project of the pupil.) Place Value Containers  Guide the pupils to bundle 10 straws which should be placed in the tens place of the place value container.  Let them bundle 10 groups of 10 straws each which will be placed in the hundreds place of the place value container.  Lastly, let them bundle 10 groups of 100 straws to be placed in the thousands place of the place value container.  Let them see and observe how many is 1 ten, 1 hundred and 1 thousand. Activity 1 – Using Manipulatives and Drawings/Diagram  Tell the pupils to work in groups with 5 members each.  Let them represent the number of eggs brought by Mang Pedro through their straws/Popsicle sticks and place value containers. Ask: How will you represent 2 752? 2 bundles of 1 000 straws 7 bundles of 100 straws 5 bundles of 10 straws 2 pieces of straws
  • 23.
    17 Thousands Hundreds TensOnes A B C 1 4 0 7 So, 2 752 therefore, 1 407 eggs were left. - 1 345 1 407 Now, let us take away the number of eggs sold by Danny. How many eggs were sold by Danny? 1 345 eggs How will you represent 1 345 in bundled straws? 1 bundle of 1 000 straws, 3 bundles of 100 straws each, 4 bundles of 10 straws each and 5 pieces of straws)  Ask the pupils to take away 1 345 from 2 752.  Did you get all the straws in each place value containers?  In what place value container did you find it difficult to get the straws?  Can you get 5 straws from 2 straws? You cannot subtract 5 from 2;  Therefore, we will regroup 1 group of ten straws from the tens cup and place it in the ones cup.  But we cannot still get 5 straws because the straws are still in bundle.  So, what should we do? (Unbundle the tens straws)  So, how many straws are there in the ones container now? 12  How many group of tens straws were left at the tens container?  Can you get 4 bundles of 10 straws from it? What about 3 bundles of 100 straws each, can you get it from the hundreds container?  What about a bundle of 1 000 straws, can you get it from the thousands container?  So, how many straws were left in each container?  How will you read it in numeral?  So, how many eggs were left? Does our answer make sense?
  • 24.
    18 Activity 2 –Using Expanded Form 1) Let us try solving the same problem using the Expanded Form. Let us see if we can get the same difference. 1. Subtract the ones. 2 752 2 000 + 700 + 50 + 2 - 1 345 1 000 + 300 + 40 + 5 2. Regroup the tens. 2 000 + 700 + (50 – 10) + (10 + 2) - 1 000 + 300 + 40 + 5 _ 2 000 + 700 + 40 + 12 - 1 000 + 300 + 40 + 5 7 3. Subtract the tens. 2 000 + 700 + 40 + 12 - 1 000 + 300 + 40 + 5 0 + 7 4. Subtract the hundreds. 2 000 + 700 + 40 + 12 - 1 000 + 300 + 40 + 5 400 + 0 + 7 5. Subtract the thousands. 2 000 + 700 + 40 + 12 - 1 000 + 300 + 40 + 5 1 000 + 400 + 0 + 7 = 1407 Did we get the same difference? 1407 eggs were left. 2) Let us try using the short cut method or the short form. Th H T O 2 7 4 5 1 2 - 1 3 4 5 1 4 0 7 1. Subtract the ones. But since you cannot subtract 5 ones from  2 ones; we will regroup the tens place.  5 tens becomes 4 tens and 1 ten; then 1 ten becomes 10 ones  then, we will rename the ones place.  10 ones + 2 ones equals 12 ones Then subtract the ones place. (12 ones – 5 ones = 7 ones) 2. Subtract the tens. (4 tens – 4 tens = 0 ten) 3. Subtract the hundreds. (7 hundreds – 3 hundreds = 4 hundreds) 4. Subtract the thousands. (2 thousands – 1 thousand = 1 thousand) Did we get the same difference? 1 407 eggs were left. You cannot subtract 5 from 2; therefore, regroup one 10 from the tens column and add it to 2. Subtract 5 from 12 Subtract 40 from 40 Subtract 300 from 700 Subtract 1000 from 2000. Add all the partial differences. 2 752 - 1 345 N 2 7 4 5 12 2 - 1 3 4 5 1 4 0 7
  • 25.
    19 2. Guided Practice Groupwork with 5 members each a. Solve by using the place value containers and straws/Popsicle sticks. 1) 1 343 – 236 = N 2) 2 491 – 1 358 = N 3) 2 635 – 1 217 = N Work in Triads b. Solve the following by Expanded Form Method. 1) 3 942 – 719 = N 2) 7 363 – 247 = N 3) 6 475 – 2 136 = N 4) 32 635 – 2 217 = N 5) 25 136 – 4 018 = N Work in Dyads b. Subtract the following using the Short Form Method. 1) 5 785 – 349 = N 2) 15 324 – 2 106 = N 3) 3 642 – 235 = N 4) 26 483 – 3 248 = N 5) 4 384 – 248 = N 6) 56 587 – 2 359 = N 7) 8 252 – 4 036 = N 8) 43 462 – 1 357 = N 9) 7 461 – 3 237 = N 10) 34 677 – 2 338 = N Were you able to finish all the exercises? Why? How did each of your member work to come up with the correct answer? Did you help each other during the activities? Which method do you like best? Why? 3. Generalization: How do we subtract numbers with regrouping in the tens place? To subtract whole numbers, start with the ones column. If the digit in the minuend is smaller than the digit in the subtrahend, regroup from the next column to the left. To check the difference, add it to the subtrahend to get the minuend. C. Application a. Work in Dyads – (Use flash cards and show me board.) The teacher will flash some cards and the pupils will give the answer using their show me board. 1) 2) 3) 4) 5) 3 521 - 417 8 463 - 237 7 482 - 158 5 366 - 139 6 834 - 318
  • 26.
    20 IV. Evaluation A. Groupwork (with 4 members each) – Body Number Coding and flash cards Form groups with 4 members each. Let the pupils answer on a piece of paper the exercise on the flash card. They will give the answer orally using the body-number coding. One pupil will act out the ones digit, the other one on the tens digit, the next one will act out the hundreds digit and the 4 th member will act out the thousands digit. 1) 2) 3) 4) 5) B. Individual Work – (Paper and Pencil) Subtract the following. 1) 67 893 2) 25 876 3) 37 735 4) 49 852 5) 57 651 - 5 376 - 2 138 - 1 317 - 5 214 - 3 425 V. Assignment A. Find the missing minuend, subtrahend or difference. 1) 3 462 2) 5 463 3) _____ 4) 8 364 5) _____ - 345 - _____ - 134 - _____ - 418 _____ 5 227 7 228 8 227 6 124 6) _____ 7) 9 594 8) _____ 9) 5 866 10) 3 425 - 3 158 - _____ - 2 136 - 1 437 - 1 207 3 224 6 358 2 559 _____ _____ B. Write the missing numerals. 1) 2) 3) 8 5 - 3 2 6 8 4 0 4 7 5 2 - 2 4 4 7 6 7 3 - 2 3 1 6 5 3 9 4) 5) 3 4 5 - 1 7 6 3 3 1 5 7 5 8 2 - 3 1 2 7 3 5 7 853 -3 614 2 746 -1 327 3 745 -1 316 4 853 -1 315 8 597 -4 319
  • 27.
    21 Subtracting Numbers withRegrouping in the Hundreds Place I. Learning Objectives Cognitive: Subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the hundreds place Psychomotor: State the rule in subtracting whole number with regrouping Affective: Work cooperatively with others in finding the difference of the given number with accuracy II. Learning Content Skill: Subtracting numbers with regrouping in the hundreds place Reference: BEC PELC I.C.1.1.3.2 Materials: flash cards of subtraction (2-digit by 1), Math kit (cubes, flats, longs and ones), Show Me Board, place value pocket chart, chart of exercises Value: Cooperation III. Learning Experiences A. Preparatory Activities 1. Drill – Mental Computation 2. Review Checking of assignment. 3. Motivation Song: Math Time (Tune: It’s a Small World) Chorus: Oh, it’s Math time after all (3x) Come together and come all. There is just one class We enjoy so much Where our mind think hard And compute a lot Though the drills are so fast And the problem so tough We enjoy our class in Math (Repeat Chorus) Do you really enjoy our Math class? Why? What are the things we do in Math? 12 - 5 17 - 8 15 - 6 11 - 7 13 - 4 19 - 9 14 - 7 16 - 9 18 - 5 15 - 8
  • 28.
    22 B. Developmental Activities 1.Presentation a. Let us read and analyze this number sentence. Subtract 275 from 1 359 = N b. Ask the pupils which is the minuend and the subtrahend in the number sentence. Let them write the numerals in column and analyze it. 1 359 - 275 Ask: Can we subtract the ones place? What is the answer? What about the tens place? Can we subtract 7 from 5? 1. Activity 1 – Manipulatives (cubes, longs, flats and blocks) c. Now, ask the pupils to get their Math kit and get their cubes, longs, flats and blocks. Let them do it by pairs. Let them represent first the minuend. Ask: How many blocks, flats, longs and cubes can make 1 359? d. Ask the pupils to take away 275 from the blocks, flats, longs and cubes. Ask: How many flats, longs and cubes will make 275? Do I have enough cubes to take away 5 from it? How many cubes will be left? What about the longs, do I have enough to take away 7 from it? What shall we do then? = 1,359 (blocks) (flats) (longs) (cubes)
  • 29.
    23 Thousands Hundreds TensOnes X X X X X X X X X X
  • 30.
    24 1 0 84 So, we will regroup 1 flat and rename it as longs. How many longs will there be in 1 flat? (10) So, how many longs do we have now? Can we not get 7 longs from it? How many longs were left? e. Now, ask the pupils to focus on flats. Let them take away 2 flats from it. Ask how many flats remain in the flats column. Then, ask if they are going to take away anything from the blocks column and then ask why. Let the pupils express their answers. f. Let them now count the number of blocks, flats, longs and cubes that were left in each column. How do you read the numeral? Let’s solve the same problem using the expanded form method. 2. Activity 2 – Expanded Form Method 1 359  - 275  1 000 + 300 + 50 + 9 - 200 + 70 + 5 a. Subtract 5 from 9. b. Subtract 70 from 50. Is it possible? (No) ? + 4 Rename  1 000 + 200 + 100 + 50 + 9 c. Rename 300 into 200 and 100. Regroup 100 with 50. Regroup  1 000 + 200 + 150 + 9 - 200 + 70 + 5 d. Subtract 70 from 150. 80 + 4 1 000 + 200 + 150 + 9 - 200 + 70 + 5 e. Then, subtract 200 from 200 and bring down 1 000. 1 000 + 0 + 80 + 4 = 1 084 f. Lastly, add the partial differences. Let’s solve it again using the short form. Write the numeral in the place value chart.
  • 31.
    25 Th H TO 1) Subtract the ones (9 – 5 = 4) 1 3 5 9 - 2 7 5 2) Subtract the tens. Can you take away 7 tens from 5 tens? Why not? 4 Th H T O Regroup 3 hundreds into 2 hundreds and 10 tens. Then rename the tens. How many tens are there now? Can we subtract 7 tens from it? Then subtract. How many hundreds were left? 1 2(3) 15(5) 9 - 2 7 5 1 0 8 4 3) Subtract the hundreds. (2 hundreds – 2 hundreds = 0 hundreds) 4) Then bring down the digit in the thousands place because you will not subtract anything from it. Did we get the same difference? Which of the three methods do you like best? Why? 2. Guided Practice a. Group Work 1. Divide the class into 3 groups and the members of the groups will work in pairs. 2. The first group will use the manipulative method to find the difference. 3. The 2 nd group will use the expanded method. 4. The 3 rd group will use the short form method. 5. Then they are going to report to the class the answer they got. Write in column then subtract. Group 1 Group 2 Group 3 3 735 – 562 8 628 – 4 253 56 816 – 3 745 b. Work in Pairs The teacher will show some numbers to be subtracted. The pupils will write their answer on their Show Me Board. They will use the short form method. 8 237 - 162 5 648 - 353 7 525 - 281 4 419 - 345 9 456 5 645 8 266 7 538 - 7 271 - 2 183 - 1 173 - 3 252 25 325 15 815 32 546 47 679 - 4 151 - 2 732 - 1 476 - 2 385 1. Which pairs got the most number of correct answers? 2. What do you think they did to get all the correct answers?
  • 32.
    26 3. Did theywork cooperatively? 4. Did they get the correct answer fast by working in pairs? Do you think regrouping is important? Why? Why not? 3. Generalization How do we subtract 3- to 4-digit numbers with regrouping? Where do we start? Remember this:  Regroup the numeral in the hundreds place of the minuend when necessary  Rename the numeral in the tens place  Then, start subtracting from the right going to the left. (Start with ones place, then tens place, etc.) C. Application Subtract the following: 1) th h t o 2) th h T o 7 4 2 5 8 5 3 6 - 3 5 3 - 1 6 2 3) tth th h t o 4) tth th h T o 2 8 6 1 4 4 5 6 4 6 - 4 2 4 2 - 3 2 7 1 5) hth tth th h t o 3 2 6 3 4 8 - 4 1 5 3 IV. Evaluation A. Write in column then subtract. 1) 4 537 – 352 2) 2 913 – 771 3) 6 435 – 2 152 4) 2 854 – 1 692 5) 13 429 – 2 275 B. Write the missing minuend, subtrahend or difference. 1) 7 325 2) . 3) 8 526 4) 53 436 5) . - _ . - 2 391 - _ . - _ . - 3 145 7 172 1 072 4 153 52 074 24 171
  • 33.
    27 V. Assignment A. Fillin the blanks with the correct numerals then subtract. 1) 3 538 = ____ + ____ + ____ + ____  ____ + ____ + (____ + ____) + ____ - 253 = 200 + 50 + 3___ -____ + ____ __ ____ + ____ _____________ _____ +____ + ____ __ ____ + ____ = ___________________ 2) 5 627 = ____ + ____ + ____ + ____  ____ + ____ + (____ + ____) + ____ - 4 353 = 4000 + 300 + 50 + 3___ -_____ + ____ + ____ _ ____ + ____ _______________________________ ____ + ____ + ____ _ ____ + ____ = ___________________ 3) 47 859 = ____ +___ + ___+ ____ +___  ____ + ____ + ____ + (___ + ___) + ____ - 5 383 = 5 000 + 300 + 80 + 3__ - ____ + ____ + ________ + ____ ___________________________________ _____ +_ ____ + ____+ ________ + ____ = ___________________ B. Fill in the box with the missing numeral. 1) 3   9 2) 7  5 2 6 3) 5 8 5 3  - 1 2 7 3 - 4 3 4  - 2 3   2  2 4  7 2  1   3 8 4 C. Complete the table. Subtract the numerals in the first column from the numerals in the first row. 9 537 9 835 87 563 273 9 562 3 181 6 356 7 393 80 170 Subtracting 3- to 4-Digit Numbers from 4- to 5-Digit Numbers with Regrouping in the Thousands Place I. Learning Objectives Cognitive: Subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the thousands place Psychomotor: Write numbers neatly and correctly Affective: Practice helpfulness
  • 34.
    28 II. Learning Content Skills:Subtracting 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the thousands place Reference: BEC PELC I C 1.1.3.3 Materials: flash cards, show me board, leaf cut-outs, puzzle board Value: Helpfulness III. Learning Experiences A. Preparatory Activities 1. Drill (Basic Subtraction Facts) Using the flashcards, ask the children to give the answer orally. 10 7 12 16 11 15 8 14 - 2 - 4 - 6 - 9 - 3 - 9 - 3 - 7 Check the assignment. 2. Review  Subtraction with regrouping in the hundreds place Have a group game, boys against girls. Ask each group to answer number problems written on a chart. Ask them to write their answers on show me board. 1) 349 2) 765 3) 734 4) 649 5) 6 734 - 76 - 194 - 282 - 82 - 291 ____ ____ ____ ____ ____ 3. Motivation Present a problem through storytelling. Ask children to listen to the story problem.  Edgar is a vendor. He received 25 855 newspapers. At the end of the day, 3 935 newspapers were left. How many newspapers were sold? B. Developmental Activities 1. Presentation a. Have a comprehension check-up about the story problem presented in the motivation. Ask:  Who’s the newspaper boy?  Have you seen a boy like Edgar? Why do you think he is selling newspapers?  Do you think he can help his parents by doing this kind of work? How? b. Let’s try solving the problem using these steps. Step 1: ■ Understand the problem a. How many newspapers did Edgar receive? b. How many were left? c. What is asked in the problem?
  • 35.
    29 Step 2: ■ Plan a.What process is involved in the problem? b. What helps you decide to use this process? Step 3: ■ Carry out the plan Ask a pupil to write the number sentence. (25 855 – 3 935 = N) Activity 1: Let’s solve the problem using the indicated method. Expanded form: 4 000 1 800 . 25 855 = 20 000 + 5 000 + 800 + 50 + 5 - 3 935 = 3 000 + 900 + 30 + 5 = 20 000 + 1 000 + 900 + 20 + 0 = 21 920 newspapers sold In what place did we have the regrouping? Why? Step 4: ■ Looking back a. Have we answered the problem? b. Is our answer sensible? c. Did we place the correct label? Activity 2: Now, let’s use the short method. Compare the digits in the minuend and subtrahend in each place where regrouping is needed. 1. Start from the ones. Subtract 5 ones from 5 ones. 25 855 - 3 935 0 2. Subtract 3 tens from 5 tens. 25 855 - 3 935 20 3. Regroup 1 thousand from 5 thousands as 1 thousand. Rename 8 as 18 hundreds. 4 18 25 855 - 3 935 920 4. Subtract 3 thousands from 4 thousands. 4 18 25 855 - 3 935 1 920 5. Bring down the last digit 2. 4 18 25 855 - 3 935 21 920 Answer: There were 21 920 newspapers sold. 21 920 difference + 3 935 subtrahend 25 855 minuend To check: Add the difference and the subtrahend to get the minuend. Give more examples. Ask pupils to explain how the difference was obtained.
  • 36.
    30 9 736 8245 9 364 75 864 8 369 - 924 - 813 - 2 721 - 2 942 - 1 925 8 812 7 432 6 643 72 922 6 444 2. Guided Practice a. Work in pairs. Give each pair a leaf cut-out with a number problem. Ask them to write their answers on a piece of paper. 3 486 7 645 26 598 5 345 54 394 - 924 - 813 - 1 732 - 1 824 - 2 653 b. Work in groups of 4. Each group will be given a puzzle board. Ask them to complete the puzzle using subtraction. The first group to finish wins. 1) 9 7 6 2) 8 4 3) 5 3 4 9 2 8 1 3 2 2 8 4 2 4 2 6 4 3 4) 7 8 4 5) 6 3 3 9 2 9 4 1 2 7 2 2 2 6 5 2 4 Is regrouping important? Why? 3. Generalization: How do we subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the thousands place? Remember: To subtract 3- to 4-digit numbers from 4- to 5-digit numbers with regrouping in the thousands place, we do the following:  Compare the digits in the minuend and subtrahend.  Start subtracting from the ones, then the tens.  If the subtrahend in the hundreds place is greater than the minuend, regroup 1 thousand.  Rename the hundreds place and the thousands place, then subtract up to the last digit.  To check: add the difference and the subtrahend. C. Application Match the number problem with the correct answer on the right. 1) 3 695 - 934 2) 78 478 - 59 264 3) 5 633 - 811 a. 4822 b. 74 322 c. 6961
  • 37.
    31 4) 76 146 -1 824 5) 7 686 - 725 IV. Evaluation Solve these problems: 1) The pupils in Tucop Elementary School need to collect 7 345 instant noodles wrappers for their school project. They had collected 4 531 wrappers. How many more wrappers do they need to collect? Answer: ________________ 2) Lyn bought 1 355 eggs. She sold 822 eggs. How many eggs were left? Answer: ________________ 3) 76 895 - 7 443 4) 98 674 - 9 432 5) 86 738 - 7 424 V. Assignment A. Do as indicated. Write the answer on the blank. 1. The difference between 9 349 and 825 ___________ 2. Subtract 8911 from 29 834 __________ 3. From 36 384 take away 4 962 _________ 4. 9 369 minus 3 924 _________ 5. Take away 5 925 from 38 567 ___________ B. Fill in the box with the correct difference. 1. 7 349 – 826 2. 9 298 – 3 436 3. 24 364 – 2 952 4. 59 462 – 7 621 5. 73 398 – 964 d. 2761 e. 19 214 = _ _ _ _ _ = _ _ _ _ _ = _ _ _ _ _ = _ _ _ _ _ = _ _ _ _ _
  • 38.
    32 Subtracting Numbers withRegrouping in the Ten Thousands Place I. Learning Objectives Cognitive: Subtract 4-digit numbers from 5-digit numbers with regrouping in the ten thousands place. Psychomotor: Write the numbers vertically according to their place value. Affective: Work cooperatively in the class during the activities and discussion. Choose the leader wisely. II. Learning Content Skill: Subtracting numbers with regrouping in the ten thousands place Reference: BEC PELC IC 1.1.3.4 Materials: problem chart, exercises chart, colored chalk, picture chart for coloring activity, regrouping game chart. Value: Wise choice of leader III. Learning Experiences A. Preparatory Activities 1. Drill – Regrouping Game Divide the class into 5 groups. Choose a leader for each group. Give each group a regrouping activity sheet. Ask them to match the numeral in column A with the renamed numerals in column B by drawing a line that will connect them. The first group who will post their work on the board with all answers correct will be the winner. A B 1. 41 325 •  a. 4 ten thousands + 16 thousands + 3 hundreds + 85 ones 2. 32 853 •  b. 3 ten thousands + 13 thousands + 584 ones 3. 56 385 •  c. 1 ten thousands + 17 thousands + 26 tens + 7 ones 4. 27 267 •  d. 3 ten thousands + 11 thousands + 325 ones 5. 43 584 •  e. 2 ten thousands + 12 thousands + 85 tens + 3 ones 2. Review – Checking of assignment 3. Motivation: Are you familiar with the word “election?” When do we hold election here in our country? If you are going to elect a candidate, what good qualities of a leader/candidate would earn your vote? Why?
  • 39.
    33 B. Developmental Activities 1.Presentation In an election, Mr. Santos received 21 785 votes. His opponent, Mr. Gomez, received 9 465 votes. How many more votes did Mr. Santos receive than Mr. Gomez? a. Ask: Who were the candidates in the story problem? How many votes did Mr. Santos receive? How many votes did Mr. Gomez receive? Who won in the election? How many more votes did Mr. Santos receive than Mr. Gomez? What process are we going to use to get the answer? What will be our number sentence? b. Let a pupil write the number sentence on the board. 21 785 – 9 465 = N Activity 1 – Drawing/Pictorial Let us draw the problem to see how many more votes Mr. Santos received than Mr. Gomez. Mr. Santos Mr. Gomez Now ask the pupil to draw again the diagram vertically starting with Mr. Santos. Then let them do the pairing. 10 000 1000 10 000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100 100 100 100 100 100 100 100 100 100 100 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 1 10 000 1000 10 000 100 100 100 100 100 100 100 1000 1000 1000 1000 1000 1000 1000 1000 1000 100 100 100 100
  • 40.
    34 What have youobserved with the thousands drawing? Does Mr. Santos have enough thousands to compare or pair with Mr. Gomez? What shall we do? 10 10 1010 10 10 10 10 1 1 11 1 10 10 10 10 10 10 1 1 11 1 10 000 10 000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Regroup 1 ten thousand from the ten thousands drawing and rename it as thousands. How many thousands are there in 1 ten thousand? 10 How many thousands do we have now? Can we now pair it with Mr. Gomez’s thousands? How many ten thousands drawing were left? 10 000 1000 100 100 100 100 100 100 100 10 10 1010 10 10 10 10 100 100 100 100 10 10 10 10 10 10 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
  • 41.
    35 Which of thecandidates has drawings with no pairs at all? Let us count how many of each was left with Mr. Santos. How many were left? 1 = 10 000 How many were left? 2 = 2 000 How many were left? 3 = 300 How many were left? 2 = 20 How many were left? 0 = 0 How many in all were left? 12 320 How many more votes did Mr. Santos receive than Mr. Gomez? 12 320 votes Does our answer make sense? c. Let us use the Expanded Method 21 785 20 000 + 1000 + 700 + 80 + 5 - 9 465 9000 + 400 + 60 + 5 N 20 000 + 1000 + 700 + 80 + 5 Regroup : 10 000 + (10 000 + 1000) + 700 + 80 + 5 Rename : 10 000 + 11 000 + 700 + 80 + 5 Subtract : 9000 + 400 + 60 + 5 Difference : 10 000 + 2 000 + 300 + 20 + 0 = 12 320 Did we get the same difference? Activity 3 – Short Form Method d. Let us use the Short form method. TTh Th H T O 21 785 2 1 7 8 5 21 785 - 9 465 9 4 6 5 - 9 465 N ? 3 2 0 ? 320 Steps: 1. Subtract the ones. (5 ones – 5 ones = 0 ones) 2. Subtract the tens. (8 tens – 6 tens = 2 tens) 3. Subtract the hundreds. (7 hundreds – 4 hundreds = 3 hundreds) 4. Subtract the thousands. Can you subtract them? Why not? 1 1 11 1 1 1 11 1 1 1 10 10 100 100 1000 1000 10 000 10 000
  • 42.
    36 TTh Th HT O 1 + 1 10 + 1 2 1 7 8 5 9 4 6 5 3 2 0  Rename the ten thousands. 2 ten thousands becomes 1 ten thousands + 1 ten thousands How many thousands are there in 1 ten thousands? 10 thousands?  Regroup 1 ten thousands to the thousands place.  Rename the thousands. 10 thousands + 1 thousands becomes 11 thousands or 10 000 + 1000 = 11 000 Can we now subtract 9 thousands from it? TTh Th H T O 1 11 21 785 2 1 1 11 7 8 5 21 785 - 9 465 9 4 6 5 - 9 465 ? 3 2 0 12 320  Then, subtract the thousands place. (11 thousands – 9 thousands = 2 thousands) 5. Bring down the digit that was left in the ten thousands. How many more votes did Mr. Santos receive than Mr. Gomez? Did we also get the same difference? 2. Guided Practice a. The pupils will work in groups with 4 members each. They are going to solve the following numbers using the three methods. 1) 34 659 – 9 327 2) 51 485 – 2 135 3) 23 764 – 5 321 Ask: Which method do you like best? Why? Were you able to finish the activity faster when you used that method? Why? Work in pairs – Written b. Write the following in column then subtract. Use the short method. 1) 73 864 – 7 321 2) 65 492 – 8 252 3) 51 276 – 3 214 4) 83 472 – 7 122 5) 31 597 – 4 132 6) 24 856 – 6 313 7) 32 583 – 6 321 8) 53 642 – 7 120 9) 81 731 – 7 401 10) 44 367 – 6 135 Ask: Were you able to finish all the exercises? Why? How did you work as a pair so that you will come up with the correct answer? Did you help each other during the activities?
  • 43.
    37 3. Generalization: How dowe subtract numbers with regrouping in the ten thousands place? Remember: To subtract numbers with regrouping in the ten thousands place: 1. Write the numbers vertically to align the digits in each place value. 2. Regroup the ten thousands place and rename the thousands place. 3. Subtract from right to left, starting with the ones. C. Application The table below shows the accumulated points of NCR, Region 4 and Region 3 during the Palarong Pambansa. Palarong Pambansa Team Scores Team Points NCR 12 535 Region 4 8 302 Region 3 9 421 1. Which team scored the highest points? the lowest points? 2. How many more points does Region 3 have than Region 4? 3. How many more points does NCR have than Region 3? 4. Knowing the differences, can you tell the winner? IV. Evaluation A. Do what is asked. 1. Subtract 4 312 from 73 852. 2. What is 26 321 – 9120? 3. Take away 7313 from 42 763. 4. What is 5 235 less than 51 659? 5. How much more is 36 859 than 8 312? 6. What is 25 867 minus 8 314? 7. From 72 859, subtract 9 424. 8. What is the differences between 13 598 and 4 323? B. Complete the table. Find each output Rule: Subtract 7 537 from each input. Rule: Subtract 8 231 from each input. Input Output Input Output a. 41 215 b. 35 136 c. 24 523 d. 73 213 e. 56 105 a. 92 587 b. 34 346 c. 75 973 d. 23 832 e. 16 763
  • 44.
    38 V. Assignment Find thedifference then compare. Write >, < or = in the Box 1) 72 859 – 9 424 _____ 68 633 2) 27 613 _____ 32 789 – 6 413 3) 21 473 – 7 152 _____ 14 321 4) 75 272 _____ 82 659 – 7 417 5) 24 593 – 5 321 _____ 19 275 Subtracting Numbers with Zero Difficulty in Either Tens or Hundreds Place I. Learning Objectives Cognitive: Subtract 3– to 4-digit numbers from 4– to 5-digit numbers with zero difficulty in either tens or hundreds place. Psychomotor: State the rule in subtracting whole numbers with zero difficulty in the tens or hundreds place Affective: Help others in doing group activities II. Learning Content Skill: Subtracting numbers with zero difficulty in either tens or hundreds place Reference: BEC PELC I C 1.1.3.5 Materials: flash cards of basic subtraction, chart of body-number coding, cut-outs of different geometrical shape with number value, secret message activity sheets, strips of cartolina with subtraction sentences Value: Helpfulness III. Learning Experiences A. Preparatory Activities 1. Drill : Kinesthetic Math Review the body symbols for digits 0 – 9. Then the teacher will show some basic subtraction facts (flash cards) and the pupils will act out the answer. Digit Movement 0 - Forefinger and thumb together forming zero 1 - Right arm forward closed fist 2 - Left arm forward closed fist 3 - Left and right arms folded vertically closed to the body 4 - Hands on waist 5 - Right hand on the chest 6 - Bend forward to pick something 7 - Stand straight 8 - Arms obliquely upward 9 - Do the McDonald sign 7 - 3 9 - 7 10 - 1 8 - 3 5 - 2 6 - 5 5 - 5 10 - 3 10 - 4 10 - 2
  • 45.
    39 2. Motivation :Present a problem opener The Grade Three class collected bottle caps for their doormat project. The boys collected 3 234 caps while the girls collected 5 405 caps. How many more caps did the girls collect than the boys? B. Developmental Activities 1. Presentation a. Ask: What was the project of the grade three class? Do you know what a doormat is? Is the project of the grade three pupils a good project? Why? What benefit can we get from it? Is it an expensive project? Is it helpful and useful in our lives? b. Let us solve the problem using Polya’s 4 steps in problem solving. ■ Understand the problem a. How many bottle caps did the grade three boys collect? b. How many caps did the grade three girls collect? c. Who collected more caps? d. How many more caps did the girls collect than the boys? e. What process are we going to use? ■ Make a plan What operation will be used to solve the problem? ■ Carry out the plan Ask a pupil to write the number sentence on the board. 5 405 – 3 234 = N Activity 1 – Acting Out the problem  The class forms 5 groups. Each group chooses a leader.  Give each group a set of different geometric shapes with different number value written on it. Let them illustrate the number of caps collected by the grade three boys and the number of caps collected by the grade three girls through acting out. Girls Boys 1000 100 10 1 1000 1000 1000 1000 100 100 100 100 1000 1 1 1 1 1 1000 1000 1000 100 100 1 1 1 1 10 10 10
  • 46.
    40 10 10 100 10 100 100  Let themuse pairing technique wherein the number of caps collected by the grade three boys will be paired to the number of caps collected by the grade three girls. Starting with the s place, how many s were left with no pair? Girls Boys  Pair the s. Did you find it easy to do so? Why not? Since the girls’ number of caps do not have s, what shall we do?  Borrow one in the s place. Rename it as . How many s are there in 1 ? 10 s Girls Boys  How many s were left with no pair?  Pair the s and s. How many s and s were left with no pairs? Girls 11 1000 100 10 1 1000 1000 1000 1000 100 100 100 100 1000 1 1 1 1 1 1000 1000 1000 100 100 1 1 1 1 10 10 10 XX XX XX XX 10 10 1000 100 10 1 1000 1000 1000 1000 100 100 100 100 1000 1 1 1 1 1 1000 1000 1000 100 100 1 1 1 1 10 10 10 XX XX XX XX 10 10 10 10 10 10 10 10 10 10 10 100 1000 1000 1000 100 10 1 1000 1000 1000 1000 100 100 100 1000 1 1 1 1 1 XX XX 10 10 10 10 10 10 10 10 10 10X X X X X X X X 100
  • 47.
    41 1 Boys No pair Answer 21 7 1  Count how many s, s, s and s were left with no pair at all?  How will you read it in numerals?  So, how many more caps did the girls collect than the boys? ■ Look back Is your answer sensible? What is the correct label? Did all the groups get the same difference? Activity 2: Expanded Form Method Let the children solve the same problem using the expanded form. Will you get the same difference? a. Subtract the ones. 5 405 5 000 + 400 + 0 + 5 - 3 234 3 000 + 200 + 30 + 4 1 b. Subtract the tens. 5 000 + 400 + 0 + 5 - 3 000 + 200 + 30 + 4 ? + 1 5 000 + (400 – 100) + (100 + 0) + 5 - 3 000 + 200 + 30 + 4 ? + 1 5 000 + 300 + 100 + 5 - 3 000 + 200 + 30 + 4 70 + 1 c. Subtract the hundreds. 5 000 + 300 + 100 + 5 - 3 000 + 200 + 30 + 4 100 + 70 + 1 d. Subtract the thousands. 5 000 + 300 + 100 + 5 - 3 000 + 200 + 30 + 4 2 000 + 100 + 70 + 1 1000 1000 1000 100 100 1 1 1 1 10 10 10 XX XXX X X X X X X X 1000 1000 100 110 10 10 10 10 1010 1000 100 10 Subtract 4 from 5. You cannot subtract 30 from 0; therefore borrow 100 from the hundreds column and put it in the tens column Subtract 30 from 100. Subtract 200 from 300. Subtract 3 000 from 5 000. Add all the partial differences.
  • 48.
    42 So, we getthe same difference. Activity 3 – Short form method Solve the same problem using the short cut method. Th H T O 5 405 5 4 0 5 5 405 - 3 234 3 2 3 4 - 3 234 N 1 1 Steps: a. Put the numerals in the place value chart or align them according to their place value. b. Subtract the ones. (5 ones – 4 ones = 1 ones) c. Subtract the tens. Is it possible to subtract 3 tens from 0 tens? Th H T O Checking : 3 + 1 10 + 0 310 5 405 5 4 0 5 5 405 3 234 - 3 234 3 2 3 4 - 3 234 + 2 171 N 1 2 171 5 405  Regroup the hundreds. 4 hundreds = 3 hundreds + 1 hundreds.  Transfer 1 hundreds to the tens place. How many tens are there in 1 hundred?  Rename the tens. 10 tens + 0 tens = 10 tens  Can we now subtract 3 tens from it? (10 tens – 3 tens = 7 tens) d. Subtract the hundreds. (3 hundreds – 2 hundreds = 1 hundreds) e. Subtract the thousands. (5 thousands – 3 thousands = 2 thousands)  Did we get the same difference? 4. Solve the number sentence. What is 37 067 – 2 532?  Divide the class into 3 groups. Each group will work by partners.  The first group will solve it using the geometric cutouts with numbers written on it.  The 2 nd group will solve it using the expanded form.  The 3 rd group will solve it using the short cut method. Ask:  Did we get the same difference?  Which of the three methods do you like best? Why?
  • 49.
    43 2. Guided Practice a.SECRET MESSAGE – To be done by groups with 4 members each. The teacher will provide each group with the secret message activity. Directions: Find the secret message. Find the difference of the number sentences in the box of Activity A. The difference will give the letters. Then use them in Activity B to decode the message. Activity A 4 305 8 607 5 906 5 037 - 142 - 473 - 283 - 516 A B C E 2 086 7 049 3 608 4 509 6 907 23 075 - 423 - 635 - 1 273 - 1 393 - 2 273 - 2 532 H I N O R S 32 095 47 032 54 308 38 053 12 507 - 1 731 - 3 412 - 135 - 4 531 - 1 242 T U W Y Z Activity B SECRET MESSAGE: 33 522 3 116 43 620 4 163 4 634 4 521 4 163 Y O U A R E A 20 543 43 620 8 134 30 364 4 634 4 163 5 623 30 364 6 414 3 116 2 335 54 173 1 663 6 414 11 265 W H I Z b. Math kinesthetic – (Body Number Coding) Group work with 5 members in each group. The teacher shows some subtraction sentences written in strips of cartolina. Each group will solve the number sentence on their paper. When they get the correct difference, each member acts out the answer using the body number coding. (To be written in strips of cartolina) 1. What is 3 050 minus 1 322? 2. Subtract 3 435 from 28 078? 3. Find the difference of 735 and 8 809. 4. Take away 1 345 from 8 907? 5. What is 3 253 less than 8 094? SS U B OR A C T IT N
  • 50.
    44 c. Dyads Ask thepupils to write some subtraction sentences in a piece of paper. The pair exchanges their work with the other pair. Both pairs answer the problem they are holding. Let them show their answers for the class to check. What makes you enjoy the activities we had? What happens to your work when you help one another? 3. Generalization: How do we subtract numbers with zero difficulty in tens or hundreds? What do you always bear in mind when a digit in the minuend is zero and the corresponding digit in the subtrahend is a non-zero number? Remember: To subtract numbers with zero difficulty in tens or hundreds: 1. Align the numerals according to their place value. 2. Subtract starting with the ones place. 3. If the tens digit in the minuend is smaller than the subtrahend, regroup the hundreds then rename the tens. 4. To check: Add the difference and the subtrahend. The sum should be equal to the minuend. C. Application Individual work – Written Find the difference using the short cut method. 1) 3 059 - 432 2) 7 306 - 132 3) 6 059 - 1 325 4) 15 025 - 4 321 5) 27 309 - 4 132 IV. Evaluation Work by pairs Find the missing minuend, subtrahend or difference. 1) 3 059 - 432 ____ 2) 4 603 - ____ 2 471 3) ____ - 2 823 622 4) 13 087 - ______ 11 355 5) 24 809 - 1 372 ______ V. Assignment A. Write in column then subtract. 1) 3 405 – 393 2) 7 049 – 1 323 3) 25 306 – 2 134 4) 16 087 – 3 053 5) 73 059 – 2 124 B. Fill in the box with missing numeral 1) 5 _05 - 79_ 5 1_2 2) _ 087 - 1 _43 4 7_4 3) 8 _ _3 - 132 7 27_ 4) 1_ 03_ - 2 _34 15 9_3 C. Read and solve. 1. What should your minuend be if you have 45 453 as difference and 2 173 as subtrahend?
  • 51.
    45 2. Patrick wasable to save P5,430 from his monthly allowance. He wants to buy a cabinet that costs P9,050. How much more does he need to save so that he can buy the cabinet? 3. Bicycles are popular all over the world. The first bicycle was invented about 1790. How many years ago was the first bicycle invented? Estimating Differences I. Learning Objectives Cognitive: Estimate the difference of two numbers with 3- to 4-digits Psychomotor: State the rules in estimating differences Affective: Follow the rules in estimating differences correctly II. Learning Content Skill: Estimating differences Reference: BEC PELC I.C.1.1.4 Materials: flash cards, Show Me Board, word problem chart, cards with subtraction sentences and estimated difference, puzzle, table chart Value: Following simple directions correctly III. Learning Experiences A. Preparatory Activities 1. Drill (flash cards) Flashcards with numerals written on it. The pupils will read the numeral and tell the place value of the underlined digit. 2. Review a. Checking of assignment. b. Rounding Numbers Round the following numbers to the nearest: Hundreds Thousands 1) 253 _____________ 2) 3 437 _____________ 3) 125 _____________ 4) 6 053 _____________ 5) 478 _____________ 6) 4 857 _____________ 7) 659 _____________ 8) 8 210 _____________ 9) 304 _____________ 10) 7 489 _____________ 3. Motivation a. Guessing Game 1. Present a bottle filled with multicolored buttons. Ask: How many buttons do you think are there in this bottle? 4 753 1 543 84 387 47 259 547 203 3 575 4 385 59 367 38 732
  • 52.
    46 2. Give 10seconds for the pupils to give their guesses. Let them write their answers on the show-me-board. 3. Call 1 or 2 pupils to count the number of buttons in the bottle. The one who can give the closest guess will be the winner. Ask: How did you come up with the correct/nearest answer? Why is it not possible to get the exact answer immediately?  There are times that we do not need the exact answer to a problem. All we need is just the closest possible answer. b. Present a Problem Opener Mr. Cruz has 782 square metres of land planted with corn and 575 square metres planted with palay. About how many square metres more of land were planted with palay than with corn? B. Developmental Activities 1. Presentation a. Let us understand the problem. 1. How many square metres of land was planted corn? 2. How many square metres of land was planted palay? 3. What is asked in the problem? 4. Do we need an exact answer? 5. What word clues tell that we do not need an exact answer?  The phrase “about how many” tell us that we should estimate the answer. 6. What operation are we going to use? b. Let us plan on how we can solve the problem. 1. What will be the number sentence for the problem? 2. Ask a pupil to write the number sentence on the board. c. Let us execute our plan. 1. To find the estimated difference, round each number to the greatest place value 782 - 575 800 - 600 2. Then subtract. 800 - 600 3. Around 200 square metres of land were planted to palay than corn. d. Check your work. Exact Difference Estimated Difference 1. Did I answer the question? 2. Compare the estimated difference with the exact difference. 782 - 575 207 800 - 600 200 3. Is my answer sensible? 207 is close to 200 e. The teacher will give more exercises for the pupils to solve. Round each number then estimate the difference.
  • 53.
    47 845 - 458  ____?____ ____?____ 7 541 - 1 825  ____?____  ____?____ Is the estimate difference close to the exact one? 2. Guided Practice a. Individual Work (flashcards and show me board) 1. Teacher shows some flashcards with subtraction sentences. 2. The pupils give the numerals rounded to the highest place value and then find their difference. Let them write the answer on their show me board. B. Game: Finding Patterns 1. Divide the class into 2. Give sets of cards with subtraction sentence in one group and cards with estimated difference in another group. 2. The first pair who matched the correct sentence with the correct estimated difference wins. Subtraction Sentence Cards Estimated Difference Cards:  Did you find your partner easily?  How did you do it?  Did you follow the rules in estimating difference?  Did you get the correct answer? 483 - 124 536 - 275 296 - 154 748 - 334 882 - 416 4 615 - 3 243 6 427 - 3 281 7 086 - 2 540 8 937 - 4 352 6 836 - 2 595 534-357 919-422 856-580 8 545-7 903 7 581-2 614 842-221 667-308 5 049-2 836 858-139 425-186 893-754 7 145-3 780 7 943-3 607 8 605-2 807 9 145-1 863 9 045-1405 100 200 300 400 500 600 700 800 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 900 9 000Joker cards:
  • 54.
    48 3. Generalization a. Whatare the steps in estimating the difference? b. Why do we need to estimate? c. In what situation in life is estimation important? Remember: To estimate the difference: a. Round the minuend and the subtrahend to their greatest place value. b. Subtract the rounded numbers. C. Application Individual Work (Written) 1. Write the puzzle on the board. 2. Complete the puzzle boxes by estimating. The answer in the bottom right corner of each box will be the same when subtracting across or down. 1 287 891 888 641 IV. Evaluation Work by Pairs (Written) Estimate the difference by rounding the numbers to its highest place value then subtract. Write the answer in your notebook. 1) 673  _______ 2) 846  _______ 3) 558  _______ - 448  _______ - 551  _______ - 98  _______ _______ _______ _______ 4) 452  _______ 5) 758  _______ 6) 8 435  _______ - 125  _______ - 174  _______ - 2 526  _______ _______ _______ _______ 7) 9 071  _______ 8) 4 892  _______ 9) 8 465  _______ - 2 052  _______ - 1 261  _______ - 3 259  _______ _______ _______ _______ 10) 4 936  _______ - 2 143  _______ _______ V. Assignment A. Answer the following questions based on the table below.
  • 55.
    49 LAND AREAS OFSOME PROVINCES Province Area (sq. km) Oriental Mindoro 4 365 Leyte 6 268 Bohol 4 117 Marinduque 959 Tawi-Tawi 1 087 1. About how much bigger is Oriental Mindoro than Leyte? 2. Estimate the difference between the areas of Tawi-Tawi and Marinduque. 3. About how much smaller is Marinduque than Leyte? B. Write a good estimate after each problem, then solve. 1. Mr. Reyes wanted to sell 302 tickets for a cultural show. He sold 191 tickets. About how many more tickets should he sell? Estimate by rounding to the nearest hundreds: ___________ Answer: ___________ 2. There are 8 936 books in Manuel L. Quezon Elementary School. Manuel Roxas Elementary School has 7 642 books in its library. How many more books does Manuel L. Quezon Elementary School have than Manuel Roxas Elementary School? Estimate by rounding to the nearest thousands: ___________ Answer: ___________ Subtracting Mentally 2-Digit Numbers without Regrouping I. Learning Objectives Cognitive: Subtract mentally 2-digit numbers with minuends up to 99 without regrouping Psychomotor: Tell the difference without using paper and pencil Affective: Show speed and accuracy when working in the activities II. Learning Content Skill: Subtracting mentally 2-digit numbers without regrouping Reference: BEC PELC I.C.1.2 Materials: spinner numbered 0 to 9 and 10 to 18, drill boards, flash cards, number coding chart Value: Speed and accuracy III. Learning Experiences A. Preparatory Activities 1. Drill Conduct a drill on basic subtraction facts using spinners. Provide a pair of spinners as shown below.
  • 56.
    50 a. First, usethe 0 to 9 spinner to generate two single-digit subtraction facts. b. Then call two pupils. c. Let pupil A spin Spinner 1 and pupil B spin Spinner 2 to generate 2-digit minuends such as 18-4 and other subtraction facts. (15-6, 12-2) d. The rest of the class answer them on their drill boards. e. At a given signal they show their answer to the teacher and to their seatmates. 2. Review Distribute 2 sets of strips of cartolina with numbers written on it. Then ask the pupils to find the expanded form of the number on their strips. The first partner to find each other wins. (The teacher may add more to the given strips) 3. Motivation Present a problem opener. Dick gathered 56 shells at the beach. He gave 24 shells to his friend. How many shells were left? B. Developmental Activities 1. Presentation a. Have you been to a beach? What are the things you saw there? In our story problem, who gathered shells? What did he do after gathering some shells? What kind of friend is he? Are you also kind to your friends? In what ways? How many shells did Dick gather? How many shells did he give to his friends? How many shells were left? What operation are we going to use? What will be our number sentence? b. Let a pupil write the number sentence on the board. 56 – 24 = N Ask somebody to write the number in vertical column. 56 - 24 N Say: Today, we will not use paper and pencil to find the difference but instead we will try to compute it mentally. Think of how we subtract numbers. In what direction do we follow when we subtract numbers? Subtract mentally the ones, then the tens 59 87 68 76 95 74 50 + 9 80 + 7 60 + 8 70 + 6 90 + 5 70 + 4
  • 57.
    51 Think: 5 65 6 - 2 4 2 4 2 3 2 c. The teacher will give more example. 8 4 8 4 8 4 - 2 1 2 1 2 1 63 3 6 3 7 8 7 8 7 8 - 3 5 - 3 5 - 3 5 43 3 4 3 2. Guided Practices a. Let the pupils study the coding of numbers. Let them do it afterwards and memorize if possible (To be written in manila paper) Digit Movement 0 - Say “Yo!” 1 - Clap once 2 - Clap twice 3 - Clap thrice 4 - Raise your left hand 5 - Raise your right hand 6 - Say “Ole” 7 - Do the yes clap 8 - Say “Mabuhay!” 9 - Say “Be Happy!” (To be done by pairs) Direction: Find the missing number in the difference. Use the number coding. (Use flashcards) 1. 46 2. 88 3. 96 4. 78 5. 98 - 21 - 25 - 24 - 35 - 35 2_ _3 7_ _3 6_ Then give the difference 32 So, 32 shells were left to Dick. Is this the correct answer? Is it sensible?
  • 58.
    52 6. 95 7.29 8. 59 9. 62 10. 39 - 25 - 19 - 20 - 51 - 11 _0 1_ 3_ _1 2_ b. Cross number puzzle – (Individual work) Subtract mentally the following numbers to solve the puzzle. (Make 1 copy of the puzzle for every pupil.) a b c d e f g h I j k Across Down a. 95 – 63 a. 42 – 12 b. 72 – 20 b. 68 – 11 c. 89 – 29 c. 84 – 21 d. 68 – 21 d. 79 – 34 e. 98 – 33 e. 99 – 32 g. 49 – 12 f. 68 – 43 h. 35 – 20 h. 25 – 21 j. 28 – 14 i. 92 – 20 k. 56 – 33 j. 49 – 33 d. Telephone Game – (By Group) Directions: Group the pupils by column with 10 members each. The teacher gives subtraction sentence written on a piece of paper to the last pupil in every
  • 59.
    53 column. On cue,the pupils who received the piece of paper simultaneously solve the subtraction sentence mentally. Then he/she whispers the answer to the next pupil until it reaches the pupils in front. The pupils in front will then write the answer on the board. The group with the correct answer gets a point. The first group to get 5 points wins. Illustration: The following subtraction sentences should be written on a strip of paper as many as the number of groups formed. 1) 85 2) 79 3) 67 4) 59 5) 89 - 24 - 34 - 35 - 32 - 25 6) 79 7) 94 8) 83 9) 99 10) 68 - 45 - 72 - 23 - 26 - 34 Did you do it fast? Were all your answers correct? 3. Generalization How do we subtract mentally? How did you do it? Where do we start subtracting? Remember: To subtract mentally 2-digit numbers mentally without regrouping, subtract the ones first, then the tens. Then give the difference. C. Application Subtract mentally. (Use drill board and flash cards) Chalk Board
  • 60.
    54 1) 35 2)56 3) 94 4) 48 5) 68 - 12 - 32 - 72 - 25 - 34 IV. Evaluation A. Subtract the following mentally. 1) 74 2) 86 3) 97 4) 94 5) 79 - 12 - 35 - 84 - 72 - 45 B. Game – Rally Robin Pupils will make their own subtraction sentence. Then they will pass it to their right and the pupils on the right answer the question. Then, they will do the reverse way. The one who answered correctly will also make a subtraction sentence and pass it to her/his right. V. Assignment A. Subtract mentally. Write only the answer. 1) 36 2) 89 3) 56 4) 67 5) 83 - 12 - 36 - 34 - 45 - 51 B. Find the difference of the numbers on the fruits by subtracting them mentally. 76 89 86 68 95 - 24 - 36 - 41 - 43 - 62 ___ ___ ___ ___ ___ C. Have the pupils subtract each number from 86 using mental arithmetic and write their answers in the triangles. 86 43 34 22 57
  • 61.
    55 Solving Word Problemsinvolving Subtraction I. Learning Objectives Cognitive: Solve 1-step word problems involving subtraction of whole numbers including money with minuends up to 100 000 without and with regrouping Psychomotor: Write the number sentence correctly Affective: Work cooperatively by helping one another in the group activities II. Learning Content Skill: Solving word problems involving subtraction Reference: BEC PELC I.C.2.1 Materials: flash cards of basic subtraction facts, chart of the song, problems written on manila papers, activity answer sheet, activity cards, play money, geometric cutouts with value written on it Value: Cooperation and helpfulness III. Learning Experiences A. Preparatory Activities 1. Drill: Kinesthetic Math The teacher will show flashcards (butterfly design) of basic subtraction facts and the pupils will act out the answer through body number coding. Digit Movement 0 Forefinger and thumb together forming zero 1 Right arm forward, closed fist 2 Left arm forward, closed fist 3 Both fists folded vertically close to the body 4 Hands on waist 5 Right hand on the chest 6 Bend forward to pick something 7 Stand straight 8 Arms obliquely upward 9 Do Mcdonald sign 4 8 10 9 7 5 - 2 - 3 - 4 - 1 6 2 6 9 10 8 - 2 - 2 - 1 - 8 2. Review Checking of assignment.
  • 62.
    56 3. Motivation A. Song:This is the Time (Tune: This is the Day) This is the time (2x) That we’re waiting for (2x) We’ll learn our Math (2x) And apply them all (2x) So this is the time That we solve problems We’ll learn them all And apply them well. This is the time (2x) That we’re waiting for 1) Did you like the song? 2) What is the song all about? 3) What are we going to do with the problems? B. Present a problem opener. Two of the highest mountains in the Philippines are Mt. Apo in Mindanao which is 2 954 metres high and Mt. Pulog in Luzon which is 2 928 metres high. How many metres higher is Mt. Apo than Mt. Pulog? B. Developmental Activities 1. Presentation a. Let a pupil read the problem aloud to the class while the rest follow silently. b. Ask: Have you seen a mountain? Where? What happened to some of our mountains? What can we do to preserve our natural resources especially mountains? c. Let us analyze and solve the word problem using Polya’s 4 steps. ■ Understand the problem a. What are the two highest mountains in the Philippines? b. Where can you find Mt. Apo? What about Mt. Pulog? c. What are given? How high is Mt. Apo? How high is Mt. Pulog? d. What is being asked? e. What operation is needed to solve the problem? f. Why did you say so? What keywords/word clues were used? ■ Plan What equation will solve the problem? ■ Solve Ask a pupil to write the equation on the board. 2 954 – 2 928 = N d. Let the pupils draw the given height of the 2 mountains using the following geometric shapes and their equivalent values.
  • 63.
    57 Shape Value 1000 500 100 10 1 Mt. Apo= Mt. Pulog =  Cross out the drawings that will make a pair.  What were left? How many are there?  I I I = 10 + 10 + 3 = 23  How many metres higher is Mt. Apo than Mt. Pulog? 23 metres ■ Look Back a. Did you use the correct operation? b. Does the answer make sense? c. Did you label the answer correctly? d. Mt. Apo is 23 metres higher than Mt. Pulog. e. Present another word problem for the pupils to analyze and solve. There were 2 995 people who went to see the basketball game. Nine hundred eighty-six were in the front rows and the rest were in the back rows. How many were left in the back rows? ■ Understand a. What are given? What do we already know? b. What is being asked? c. What operation is needed to solve the problem? d. Why did you say so? What keywords/word clues were used in the problem? ■ Plan What equation will represent the problem? ■ Solve a. Ask a pupil to write the equation on the board. 2 995 – 986 = N b. Write the number sentence in vertical column. The numerals must be aligned according to their place value. Subtract starting from ones column. If the minuend is smaller than the subtrahend, borrow 1 from the next column on the left. 8 15 2 995 2 995 - 986 - 986 2 009 ■ Look Back a. Did you use the correct operation?
  • 64.
    58 b. Does theanswer make sense? c. Did you label the answer correctly? 2 009 people were left in the back rows 2. Guided Practice Group Work Divide the class into small groups, around 3-4 members in a group. Have them answer the following problems cooperatively using the different strategies suggested. Then, discuss the solutions to the problems with the whole class. To be written in an index card: 1. The baker baked 3948 cupcakes. He sold 2437 of them. How many cupcakes were left? Instructions: Solve the problem through illustration. Use the following geometric shapes as representation. Shape Value - 1 000 - 500 - 100 - 10 - 1 2. Aling Maria earned 4,976 from selling meat. She spent 3,365 for the family’s food. How much money were left? Instructions: Solve the problem by acting it out. Use play money as your materials. 3. Cora sold 5 485 raffle tickets. Four thousand three hundred seventy-three of them were paid. How many raffle tickets were not paid? Instructions: Solve the problem by acting it out. Use geometric cutouts with value written on it. Ex.: 1 000 10 100 1
  • 65.
    59 4. Mang Rexonharvested 6 884 ears of corn. He sold 4 693. How many ears of corn were unsold? Instruction: Solve the problem using the 4 steps of Polya. 5. Fely picked 3 953 flowers for the festival. She used 1 842. How many flowers were unused? Instruction: Use the 4-step in solving problems by Polya. 6. Ask the pupils about their feelings during the group activity.  How did you work with your group?  Did you help one another? Did you cooperate with the group?  What happened to your work when everybody is cooperative and helpful?  Were you able to arrive at the correct answer? 3. Generalization How do we analyze and solve word problems involving subtraction? What are the 4 steps in solving problems? What are the questions under each step? C. Application Group Work (5 members in each group) The teacher will give each group an activity card where a problem is written, and an activity answer sheet where they are going to write their answer. The group will report to the class about their work/solution for the class to check. Example of an activity answer sheet: Answer Sheet for Problem #1 ■ Understand a. What are the given facts? b. What is being asked? c. What are the necessary information or facts? d. What words tell what operation to use? e. What operation will you use? Polya’s 4 steps in solving problems are: a. UNDERSTAND – Understand the problem. What do I know? What do I need to find? b. PLAN – Make a plan. What shall I do? c. SOLVE – Carry out the plan. I will put my plan to work. d. LOOK BACK – Look back. Have I answered the question? Is my answer sensible?
  • 66.
    60 ■ Plan What equationwill solve the problem? ■ Solve Solve the equation. ■ Look Back a. Did you use the correct operation? b. Does the answer make sense? c. Did you label the answer correctly? IV. Evaluation A. Read, analyze and solve the following problems. 1. Mrs. Castro wants to buy a washing machine for 5,795. She saved 3,273. How much more does she need? 2. In a basketball game, 1 735 people watched the game. After the first half of the game 214 left. How many people stayed to watch the game? 3. Rhona wanted to sell 1 876 tickets for a dance exhibition. She has sold 934 tickets. How many more tickets should she sell? 4. During the local elections. Mr. Gonzales received 7 859 votes while Mr. Manzano received 6 347 votes. How many more votes did Mr. Gonzales receive than Mr. Manzano? 5. A morning newspaper has 29 347 subscribers. An afternoon newspaper has only 8 732 subscribers. How many more subscribers do the morning newspaper has than the afternoon newspaper? B. Written – Triads The problems below have no numbers. Decide how you would solve each one. If it will help you, fill in reasonable numbers. 1. Mario saved some money by buying a book of movie passes rather than individual tickets. How can he figure out how much money he had saved? 2. John knows the weight and price of two different sizes of boxes for dog food. How can he figure out which of the two is a better buy? 3. Anna bought a pair of rubber shoes. She went to the cashier to pay for it. How will she know how much change she had received? 4. Rebecca wanted to buy a refrigerator. She only save a certain amount. How can she figure out how much more does she need to save? 5. Laura made some circles. She colored some of them red and the rest blue. How will she know how many circles were colored blue? (The group will publish their work on the board for the class to check.) C. Work in Pairs Ask the pupils to create their own problem, then let her/his partner answer it. Then they are going to publish their work for the class to check. V. Assignment Read, analyze and solve. Use the 4 steps of Polya. 1. A total of 1750 tourists went to Baguio City in April and 639 in May. How many more tourists went to Baguio in April than in May? 2. Mother had 1,590. She bought groceries worth 1,587. How much was her change?
  • 67.
    61 3. Robert harvested1 659 cavans of palay from his farm. He sold 735 cavans. How many cavans of palay were left? Solving Word Problem Mentally I. Learning Objectives Cognitive: Solve mentally 1-step word problems involving subtraction without regrouping Psychomotor: State the complete answer Affective: Show speed and accuracy in solving word problems II. Learning Content Skill: Solving word problem mentally Reference: BEC PELC I.C.2.2 Materials: problem chart, flash cards, body number coding chart Value: Speed and accuracy III. Learning Experiences A. Preparatory Activities 1. Drill: Mental Computation Use flashcards. 2. Review Name the place value of the underlined digit. 3. Motivation Ask the pupils to subtract each number in the outer circle from the number in the inner circle. 8 - 5 4 - 2 10 - 7 18 - 7 12 - 5 29 - 8 17 - 8 485 376 109 362 785 87 32 41 2556 43 11 21 1233 75 32 20 5314 96 37 52 5634
  • 68.
    62 B. Developmental Activities 1.Presentation Fely helped her mother sold pineapples in the market. She had 48 pineapples to sell. She sold 36 pieces in the morning. How many pineapples were not sold? Let us analyze and solve the problem mentally. What is asked in the problem? What are the given facts? What operation are you going to use? What will be the number sentence? How will you solve it mentally? Activity 1 Try to draw the problem in your mind. Does the answer make sense? Is it reasonable? Activity 2 – Expanded Form 48 - 36 = 40 + 8 = 30 + 6 10 + 2 Subtract the ones  8 – 6 = 2. Subtract the tens  40 – 30 = 10. Then add the two differences = 2 + 10 = 12. Activity 3 – Short Cut Form To solve mentally  Subtract the ones, then the tens. 10 1 1 1 1 1 1 1 1 1010 10 10 1 1 1 1 1 1 1 1 1010 10  48 pineapples (number of pineapples to be sold)  12 pineapples (number of pineapples left) Think
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    63 48 48 48 -36 - 36 - 36 2 12 12 12 pineapples were not sold. Let us have another problem. Arlene has 98 in her wallet. She bought a kilogram of sugar for 32. How much was left with her? To solve mentally  Subtract the ones, then the tens. 98 98 - 32 - 32 6 66 66 was left with Arlene. 2. Guided Practices a. Individual Work The pupils will solve the problems mentally then write their answer on their show me board. After 5 seconds, they will show their answer to their teacher and classmates. a. Aling Nena washed 14 pieces of clothes while Rosa washed 26 pieces. How many more pieces did Rosa wash? a. The following day, Aling Nena ironed 34 pieces of clothes. Of the 34 pieces, 12 were blouses and the rest were t-shirts. How many t-shirts did she iron? b. A flower vendor had 85 roses to sell. She sold 63 roses in the morning and the remaining roses in the afternoon. How many roses did she sell in the afternoon? c. Mr. Santos planted 38 tomato seedlings and 15 eggplant seedlings. How many more tomato seedlings did Mr. Santos plant? d. There are 98 pupils in the school ground. Forty-two of them are Grade Three and the rest are Grade Four. How many Grade Four pupils are there? Kinesthetic Math – Body Coding Number To be done by pairs. The pupils will solve the problems mentally then they will act out the answer by pairs. One pupil will act out the tens place digit and the other will act out the ones place. a. Mother gave Agnes 95. She bought a notebook for 35. How much money was left? b. Kim had 78 marbles. He gave his brother 32 marbles. How many were left to him? c. Laura’s tomato plants have 89 ripe tomatoes. She picked 28 ripe tomatoes. How many ripe tomatoes were left? d. Maris counted 36 flowers in their school garden. Fely counted 98 flowers in the flower shop. How many more flowers did Fely count than Maris? e. Robert gathered 56 shells at the beach. He gave 24 shells to his friend. How many shells were left to Robert? Think
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    64 Creative Math –To be done by group with 3 members. Ask the pupils to make their own problem and solve it using the given data. 1) 76 flower pots to sell; 42 pots were sold 2) 99 hen’s eggs; 65 duck’s eggs 3) 58 Math books; 32 Science books 4) 67 Grade 3 pupils; 35 are boys 5) 95 pink balloons; 60 white balloons Did you do it fast? Were your answers correct? 3. Generalization How do we solve mentally 1-step word problems without regrouping? How did you do it? Remember: In solving word problem mentally involving subtraction, analyze the problem first, then subtract the ones places and the tens place. C. Application Individual Work Solve the problems mentally. Write your answer on a piece of paper or in your notebook. 1. Cindy had 95. She spent 30 for juice and biscuits. How much money was left? 2. Sarah has 78 baseball cards. Tricia has 40 cards. Who has more cards? How many more? 3. The sum of two numbers is 75. One number is 32. What is the other number? 4. Give the number that is 21 less than the other number, if the other number is 57. 5. The farmer gathered 93 bananas in his orchard. 42 bananas were yellow. How many were not yellow? IV. Evaluation Solve the following problems. At the market, Mar, Kim, Mae and Ken helped their mother count the vegetables she has to sell. They recorded the vegetables they counted. Name Eggplants Tomatoes Mar 88 76 Kim 32 54 Mae 59 67 Ken 27 15 Answer the following questions: 1. How many more eggplants did Mar count than Kim? 2. How many more eggplants did Mae count than Ken? 3. How many more tomatoes did Mar count than Kim? 4. How many more tomatoes did Mae count than Ken?
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    65 5. How manymore eggplants than tomatoes did Mae count? Did you all get the answers correctly? What should you always remember every time you solve a problem? Is it good to work fast? Why? V. Assignment Study the price list of fruits per kilogram then answer the questions that follow. 1. Which fruit is the cheapest? 2. Which fruit is the most expensive? 3. How much more expensive are apples than mangoes? 4. How much cheaper are oranges than ponkan? 5. How much cheaper are bananas than ponkan? 6. How much more expensive are mangoes than oranges? 7. Which is cheaper, mangoes or ponkan? How much cheaper? 8. Which is more expensive, oranges or bananas? How much more expensive? Solving Two-Step Word Problems involving Addition and Subtraction of Whole Numbers including Money I. Learning Objectives Cognitive: Solve two-step word problems involving addition and subtraction of whole numbers including money Psychomotor: Tell what is asked, what are given and the word clue/s to be able to write the equation that will solve the problem Affective: Participate actively in class activities II. Learning Content Skills: Solving two-step word problems involving addition and subtraction of whole numbers including money Reference: BEC PELC I C 3.1 Materials: flash cards Value: Active participation III. Learning Experiences A. Preparatory Activities
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    66 1. Drill (MentalComputation) Conduct a drill in the basic subtraction and addition facts using flashcards with the shape of a flower. 2. Review “Subtraction with zero difficulty” Two students compete with each other, trying to answer the equation mentally. Sample equations: 600 – 426 = ______ 900 – 810 = ______ 2 000 – 1 593 = ______ Strategy: a. Mentally, deduct one from the hundreds digit; change zeros to 9, except in the ones. Change 0 in the ones place to 10. Ex. 5 9 10 6 0 0 - 4 2 6 b. Subtract: 59 (10) - 42 6 174 3. Motivation Present a two-step word problem. Mang Carlos picked 115 yellow mangoes and 73 green mangoes. He sold 56 mangoes in all. How many mangoes were left to him? B. Developmental Activities 1. Presentation a. At this point, ask the class to recall the 4-steps on problem solving according to George Polya: Understand  Plan  Solve  Look Back b. Looking at the problem, elicit from the students the following: ■ Understand a. What is asked? Number of mangoes left to Mang Carlo b. What are given? 115 yellow mangoes, 73 green mangoes, sold 56 in all
  • 73.
    67 ■ Plan At thispoint, ask what question do we have to answer first to get the final answer? This question is called “hidden question.” ■ Solve What operation/s are needed to solve the problem? Addition; subtraction. What equation will solve the problem? 115 + 73 – 56 = n Which do we perform first? Addition: 115 + 73 188 then subtract 188 - 56 132 mangoes ■ Look back Does our answer make sense? Yes, since 132 is less than the total. Yes, since the 2 steps used were to find the total number of mangoes first, then the number of mangoes left. Did we label it correctly? c. Give another problem. Regina has 80 eggs to sell. She sold 25 eggs in the morning and 46 eggs in the afternoon. How many more eggs does she need to sell? d. Ask: 1. What are given? 80 eggs in all to sell 25 eggs sold in the morning and 46 eggs in the afternoon 2. What is being asked? Number of eggs Regina need more to sell 3. What operations are needed? Addition and subtraction or subtraction only. 4. What equation will solve the problem? 80 – (25 + 46) = n or 80 – 25 – 46 = n 5. Solve: 25 80 80 55 + 46 - 71 or - 25 - 46 71 9 55 9 6. Check if the answer makes sense and if labeled properly. 2. Guided Practice a. Activity: Column Relay Present the following problem. Daniel earned 35 by delivering water to several houses. He gave 15 of his earnings to his mother and 12 to his sister. How much money was left to him? Directions: 1. Divide the class into 6 groups. Each member will answer one column. 2. Give the first pupil a copy of the questions. He answers the question then passes the copy to the second pupil. The second pupil answers the end question and then passes the copy to the 3 rd pupil and so on. 3. Read the problem posted on the board, then answer each question below: a. What are given? ___________________________________ ________________________________________________ b. What is being asked? _______________________________
  • 74.
    68 ________________________________________________ c. What operation/sis/are needed to solve? _______________ ________________________________________________ d. What equation will represent the problem? _________________ e. Solve the operation: f. Label and look back. b. Cooperative Learning Activity: “Rally Table” 1. Group the class in pairs; players A and B. 2. Each member of the pair takes turn in answering the questions posted on the board. 3. Present these problems on the board. Rules:  Player A writes the hidden question.  Player B answers the hidden question.  Player A writes the equation that will solve the problem.  Player B answers/solves the equation. 1. Mang Carlos raised 35 piglets for sale. He sold 10 piglets to his mother and 5 piglets to his friend. How many piglets were left to him? 2. Danilo arranged 564 books in the library. The next day, he arranged 345 books. There are 1 500 books in the library. How many more books will Danilo arrange? 3. In the pupils’ government election, Alexis received 112 votes. Brylle received 186 votes. The winner Joric received 312 votes. How many more votes did Joric receive than Alexis and Brylle? Do you think you can solve the problems without following the steps? Was your solutions correct? Was your answer correct? If your answer was not correct, in what part did you commit a mistake? 3. Generalization What are the 4 important steps in solving word problems? a. Understand the problem. - Find the hidden question. b. Make a plan. c. Solve/carry out plan. d. Look back. C. Application Direction.  Give each group a copy of the problems below on strips of paper.  Let each group solve the problems.  Write their solutions on the board.  Present the work afterwards 1. Mr. Javier has to deliver 760 sacks of rice. He delivered 510 to Mr. Rosales and 140 to Mr. Acosta. How many more sacks of rice will be delivered?
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    69 2. After spending75.00 for a shirt and 125.00 for a pair of pants, Michelle had 50.00 left in her wallet. How much money did she have at first? 3. There are 246 yellow mangoes and 152 green ones. Out of these, 120 are in the basket and the rest are in the crate. How many are in the crate? 4. Mang Luis is a farmer who sells coconuts and watermelons. He earned 843.00 from selling coconuts and 832.00 from watermelons. Before going home, he bought 1 kilo of pork for 120.00. How much money was left to him? 5. Mother and Lito picked tomatoes in their vegetable garden. Mother picked 19 tomatoes and Lito picked 12. Mother used 5 tomatoes for cooking. How many tomatoes were left? IV. Evaluation Answer the following problems using Polya’s strategy. 1. Mr. Reyes gathered 365 mangoes on Monday and 453 on Tuesday. He sold 650 mangoes on Wednesday. How many mangoes were left unsold? 2. A farmer harvested 425 sacks of palay. He sold 258 sacks to Buyer A and 120 to Buyer B and kept the rest for his family. How many sacks of palay were left? 3. Rita bought a dress for 235.00 and a pair of shoes for 574.00. She gave a 1000-peso bill to the cashier. How much is her change? 4. Alex wants to buy a T-shirt worth 185.00 and a school bag worth 240.00. He has only 300.00. How much more money does he need? V. Assignment Solve the following: 1. There are 262 boys and 528 girls in Grade Three. Out of these, 174 pupils are 10 years old. How many pupils are not 10 years old? 2. Pia spelled 26 words correctly on Monday, 25 on Wednesday and 37 on Friday. If there are 100 words to be spelled, how many words did she misspell? 3. Rosalinda bought a bag for 165.00 and a pair of shoes for 395.00. How much change did she get from 1,000.00? 4. A shoe factory in Marikina produced 235 pairs of shoes in one week and 324 pairs in another week. If 450 pairs were delivered to a department store, how many pairs were not delivered? 5. Rose had a balance of 3,500.00 in her account in the bank. She deposited 1,200.00 the following month and withdrew 950.00. How much was left in her account?