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- 1. Lesson Guide In Elementary Mathematics Grade 3 Reformatted for distribution via DepEd LEARNING RESOURCE MANAGEMENT and DEVELOPMENT SYSTEM PORTAL DEPARTMENT OF EDUCATION BUREAU OF ELEMENTARY EDUCATION in coordination with ATENEO DE MANILA UNIVERSITY 2010 Chapter I Whole Numbers Addition INSTRUCTIONAL MATERIALS COUNCIL SECRETARIAT, 2011
- 2. 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
- 3. iii TABLE OF CONTENTS Introduction ..................................................................................................................................iv Matrix ........................................................................................................................................v I. WHOLE NUMBERS A. Addition Adding 4- to 5- Digit Numbers up to four addends with Sums up to 100 000 without regrouping in short form ........................................................................1 Adding 4- to 5- digit numbers up to four addends with regrouping in the tens and hundreds ............................................................................................ 4 Adding 4- to 5- digit numbers up to four addends with sums up to 100 000 with regrouping in the thousands and en thousands place................................ 8 Estimating sums of 3- to 5- digit addends ...................................................................... 11 Adding mentally 1- to 2- digit numbers with sum up to 100 without regrouping ............ 15 Mental computation of 1-step word problems involving addition ................................... 21 Solving word problems involving addition....................................................................... 25
- 4. iv I N T R O D U C T I O N The Lesson Guides in Elementary Mathematics were developed by the Department of Education through the Bureau of Elementary Education in coordination with the Ateneo de Manila University. These resource materials have been purposely prepared to help improve the mathematics instruction in the elementary grades. These provide integration of values and life skills using different teaching strategies for an interactive teaching/learning process. Multiple intelligences techniques like games, puzzles, songs, etc. are also integrated in each lesson; hence, learning Mathematics becomes fun and enjoyable. Furthermore, Higher Order Thinking Skills (HOTS) activities are incorporated in the lessons. The skills are consistent with the Basic Education Curriculum (BEC)/Philippine Elementary Learning Competencies (PELC). These should be used by the teachers as a guide in their day-to-day teaching plans.
- 5. v MATRIX IN ELEMENTARY MATHEMATICS Grade III COMPETENCIES VALUES INTEGRATED STRATEGIES USED MULTIPLE INTELLIGENCES TECHNIQUES With HOTS I. Whole Numbers A. Addition of Whole Numbers 1. Comprehension of Addition 1.1 Add 4- to 5-digit numbers up to four addends with sums up to 100 000 1.1.1 Without regrouping in short forms Cleanliness Simplifying the problem Clean and Green campaign Global theme (Naturalist) Chart (Spatial) 1.1.2 With regrouping in 1.1.2.1 Tens and hundreds places Recycling Simplifying the problem Cooperative groups(Interpersonal) Chart (Spatial) 1.1.2.2 Thousands and ten thousands places Forest conservation Simplifying the problem Global theme (Naturalist) Cooperative groups(Interpersonal) Chart (Spatial) 1.2 Estimate the sums of 3 to 5 digit addends Active participation Simplifying the problem Storytelling (linguistic) Cooperative groups(Interpersonal) 1.3 Add mentally 1 to 2 digit numbers with sums up to 100 without regrouping Active participation Puzzle (Logical mathematics) 2. Application of Addition 2.1 Solve word problems involving addition of whole numbers with sums up to100 000 including money following the steps in problem solving Cooperation Polya's steps in problem solving Acting out the problems Song (Musical) Diagram (Spatial) Movements (Bodily kinesthetic) 2.2 Solve mentally 1 step word problems involving addition with sums up to 100 without regrouping Speed and accuracy Polya's steps in problem solving Cooperative groups (Interpersonal)
- 6. 1 Adding 4- to 5- Digit Numbers up to 4 Addends with Sums up to 100 000 without Regrouping in Short Form I. Learning Objectives Cognitive: Add 4- to 5- digit numbers up to four addends with sums up to 100 000 without regrouping in short form Psychomotor: Write numbers in proper column before adding Affective: Show cleanliness in doing assigned tasks II. Learning Content Skill: Adding 4- to 5- digit numbers up to 4 addends with sums up to 100 000 without regrouping in short form. Reference: BEC PELC I.B.1.1.1 Materials: textbooks, flash cards, picture of a model community, place value chart Value: Cleanliness III. Learning Experiences A. Preparatory Activities 1. Drill – Addition Basic facts Game “Sit down” a. Ask all the pupils to stand near their desks/chairs. b. The teacher flashes some combinations of numbers. c. The first pupil to give the correct answer will sit down. 2. Review Find the sum. 3214 7845 3847 4654 789 + 4623 + 2023 + 2120 + 5211 + 200 3. Motivation Show picture of a clean community. How would you help maintain cleanliness in your community? How about in our school? Let‟s see whose desk will remain clean up to the last minute of the class. A. Developmental Activities 1. Presentation a. Present this problem In response to the government‟s “Clean and Green” campaign, the Boy and Girl Scouts of Region IV held a tree planting activity. They planted 5 143 narra seedlings, 5 000 mahogany seedlings, 3 010 molave seedlings and 4 835 ipil-ipil seedlings. How many seedlings did they plant in all? b. Lead the pupils in analyzing the word problem. c. Put the given numbers in the place value chart before adding them. Emphasize that the numbers must be written in proper column, otherwise they will arrive at the wrong answers.
- 7. 2 Thousands Hundreds Tens Ones 5 5 3 4 1 0 0 8 4 0 1 3 3 0 0 5 Do the steps one by one. 5 143 add 5 143 add the 5 143 add the 5 000 the 5 000 hundreds 5 000 ones 3 010 tens 3 010 3 010 4 835 4 835 4 835 8 88 988 add the 5 143 thousands 5 000 3 010 4 835 17 988 d. Present more examples. Do the steps again one by one. Stress that the numbers must be written first in proper column. 2. Guided Practice Working with learning partner. Game: Let‟s build the house Two houses will be built by the boys and the girls. One correct answer will contribute one pillar or post to the house. Give each learning partner a number problem to solve. The teacher will check the answer. 3. Generalization How do we add 4- to 5- digit numbers up to four addends? Where do we start adding? To add whole numbers with 4 to 6 digits, add the ones digit first, then the tens, then the hundreds and so on. 1 2 3 4 6985 7
- 8. 3 C. Application Add. 52 345 90 000 25 036 82 101 80 502 52 121 60 231 93 230 10 210 + 92 320 + 60 122 12 230 IV. Evaluation A. Write the numbers in column, then add. 1) 63 114 + 21 020 + 22 431 = 2) 25 041 + 13 102 + 61 213 + 11 323 = 3) 31 124 + 22 101 + 31 310 + 13 001 = 4) 11 301 + 14 003 + 30 200 + 10 222 = 5) 42 131 + 11 021 + 10 102 + 10 011 = B. Answer each question below. Use the chart. Sales at de Luna Farm Animal 1996 1997 1998 1999 chickens 11 302 11 511 12 021 12 121 ducks 10 021 11 021 12 022 12 234 pigs 12 111 12 034 12 221 12 333 goats 10 222 13 230 13 121 13 200 Find: 1. Total sales in 1996, in 1997, in 1998 and in 1999. 2. Total sale of chickens; of ducks; of pigs; and of goats. V. Assignment Look at the pictures then answer the questions that follow. WATERMELON SQUASH PEANUTS PILI How many nuts are there altogether? 1. watermelon, squash, peanuts and pili nuts 2. watermelon, squash, and pili nuts 3. watermelon, peanuts and pili nuts 4. squash, peanuts and pili nuts 5. peanuts, pili nuts and watermelon
- 9. 4 Adding 4- to 5- Digit Numbers up to Four Addends with Regrouping in the Tens and Hundreds I. Learning Objectives Cognitive: Add 4- to 5- digit numbers up to four addends with sums up to 100 000 with regrouping in tens and hundreds place Psychomotor: Regroup in the tens and hundreds digit correctly Affective: Appreciate the value of recycling II. Learning Content Skill: Adding 4- to 5- digit numbers up to four addends with regrouping in tens and hundreds digit Reference: BEC PELC I B-1.1.2.1 Materials: textbooks, small basin with sand, rubber band, sticks, place value chart Value: Recycling III. Learning Experiences A. Preparatory Activities 1. Drill – Basic addition facts (The teacher will prepare a small basin with sand. Under the sand are 20 rubber bands. On the rubber bands are basic addition sentences which the pupils will answer correctly.) a. Call a pupil and ask him/her to get one rubber band from the basin using a stick. b. Once he gets a rubber band, he reads the sentence and gives the correct answer. c. They may do this in the form of a contest. 2. Review Working in dyads: Add. 2 514 11 310 12 461 53 322 12 434 5 423 42 301 31 203 25 012 32 234 + 2 041 11 211 42 122 10 231 11 001 21 107 +12 212 +11 122 +12 120 3. Motivation Who among you reads newspaper? What does your family do with old newspaper? Why do we need to recycle them? B. Developmental Activities 1. Presentation a. Present this problem. The pupils of Mogpog Central School brought old newspapers to support the school‟s “Newspaper Fund Drive.”
- 10. 5 The table shows the contribution of newspapers per section in Grade Three. Newspaper Fund Drive Section Contribution (in kg) Masunurin Malinis Masinop Maunlad 12 721 13 372 12 526 12 270 How many kilograms of newspaper did the Grade Three pupils bring? What will you do to find the sum? b. Lead the pupils in analyzing the problem. Let the pupils put the number in the place value chart. Ten Thousands Thousands Hundreds Tens Ones 1 2 7 2 1 1 3 3 7 2 1 2 5 2 6 1 2 2 7 0 c. Stress the importance of putting the numbers in proper column. d. Add the numbers carefully. What are we going to add first? The ones What is the answer? 9 Now let us add the tens. What can you say about the sum? What is the answer? Is this one group of one hundred and 8 tens? Let us regroup it into the hundreds place. What number remains in the tens place? Repeat the process up to the last place value. Regroup when necessary. e. Present other examples. 2 973 2 321 6 415 2 553 etc. + 5 732 2 125 + 2 432 Repeat the process as what you did in c and d. 2. Guided Practice Working in triads. Stress that each member must cooperate with the group. Arrange the numbers in the windmill in column then add and check.
- 11. 6 Individual Activity. Peer checking. Add: 54 432 35 678 21 265 24 324 10 526 14 125 11 432 10 421 3. Generalization How do we add 4- to 5- digit numbers with 4 or 5 addends? Where do we usually start? What do we do if the answer in each column is 10 or more? C. Application Add: 2 973 21 471 2 321 6 415 22 342 2 553 +5 732 21 421 2 125 +11 424 +2 432 IV. Evaluation A. Look at the letter number chart below. Each letter has an equivalent point. Find out the total number of points for a word. Then find the sum. Example: MANILA M 13 A 1 N 14 I 9 L 12 A 1 50 points Letter Number chart A – 10 461 O – 11 347 B – 21 354 P – 11 621 C – 11 425 R – 10 434 E – 10 324 S – 10 467 I – 10 341 T – 10 467 L – 10 357 U – 11 464 M – 10 212 Y – 11 521 N – 21 565 Z – 24 894
- 12. 7 Find the number of points for the following: 1. CEBU 2. PASAY C = P = E = A = B = S = U = A = Total Y = Total 3. TANAY 4. RIZAL T = R = A = I = N = Z = A = A = Y = L = Total Total 5. CUBAO C = U = B = A = O = Total Find the sum. 1) 2 316 2) 3 561 3) 80 612 1 284 1 426 14 768 + 4 844 + 2 729 + 3 252 4) 23 805 5) 32 743 42 127 11 846 12 996 16 421 V. Assignment Get a partner and answer these at home. 1) 4 657 2) 2 793 2 328 4 308 + 1 472 + 1 411 3) 23 472 4) 15 278 12 563 11 470 +11 421 +11 561 5) 32 571 22 432 12 473 +11 261
- 13. 8 Adding 4- to 5- Digit Numbers up to Four Addends with Sums up to 100 000 with Regrouping in the Thousands and Ten Thousands Place I. Learning Objectives Cognitive: Add 4- to 5- digit numbers up to four addends with sums up to 100 000 with regrouping in the thousands and ten thousands place Psychomotor: Regroup in the thousands and ten thousands places correctly Affective: Show concern for the environment by giving the importance of forest conservation II. Learning Content Skill: Adding 4- to 5- digit numbers up to four addends with sums up to 100 000 with regrouping in the thousands and ten thousands place Reference: BEC PELC B-1.1.2.2 Materials: textbooks, charts Value: Concern for the environment III. Learning Experiences A. Preparatory Activities 1. Drill – Basic addition facts Game: 2 Groups Pick two fruits from the tree. Open them and look for the numbers. Give the total of the two numbers. (If the child gives the correct answer he gets the fruits. The group that picks more fruits wins the game. (Provide as many fruits as you can.) 2. Review Working in triads: Add. 12 345 43 254 26 541 16 278 15 781 31 578 10 578 + 10 257 40 525 + 10 625 + 11 525 3. Motivation Who among you have gone to a forest or mini-forest? What did you feel when you were in this place? Did you feel cold? What must pupils like you do to save our forest? Why is it important to conserve our forests? B. Developmental Activities 1. Presentation a. Present this problem. Mr. Go initiated a reforestation project in Marinduque. He donated all the seedlings that were planted: 10 147 mahogany seedlings, 6 130 narra, 7 322 lauan and 25 400 fruit bearing trees. How many tree seedlings were planted in all?
- 14. 9 b. Lead the class in analyzing the problem. Write the numbers in a place value chart first to emphasize the need to write the numbers in column. Ask: What are we going to add first? If the sum is ten or more, what will you do? Ask the same question up to the ten thousands digit. Ten Thousands Thousands Hundreds Tens Ones 1 0 1 4 7 6 1 3 0 7 3 2 2 2 5 4 0 0 Add the ones first. Add the tens. Add the hundreds. 10 147 10 147 10 147 6 130 6 130 6 130 7 322 7 322 7 322 + 25 400 25 400 25 400 9 99 999 Add the thousands. Add the ten thousands. Regroup. Regroup when necessary. 10 147 10 147 6 130 6 130 7 322 7 322 + 25 400 25 400 8 999 48 999 Final Answer c. Bring out a bowl which contains strips of numbers like the ones below. Ask each pupil to draw numbers up to 4 addends then do the addition cooperatively. 3 742 22 025 19 102 4 304 25 421 10 252 2 613 14 320 18 342 4 220 16 101 24 100 2. Guided Practice a. Working in dyads: Write in column and add. (Regroup in all places) 1) 24 157 + 38 621 + 15 254 + 10 268 2) 32 476 + 12 784 + 21 468 + 15 211 3) 17 434 + 23 245 + 31 254 + 18 201 4) 25 319 + 30 218 + 19 264 + 11 785 5) 48 215 + 15 211 + 15 612 + 18 785
- 15. 10 b. Form several groups of 5 members each. Each group will answer one column. Then together they will check their work. Provide at least 3 number problems to be answered by them. 3. Generalization Where do we usually start in adding four to five digit numbers up to 4 addends with regrouping? If the sum is 10 or more, what do we do? We start adding with the ones period. We regroup if the answer in each column is 10 or more. C. Application Write in column and then add. 1) 21 654 + 21 114 + 21 864 + 14 676 = 2) 7 846 + 21 241 + 45 216 + 24 3561 = 3) 14 201 + 24 567 + 35 432 + 11 673 = 4) 12 654 + 24 641 + 11 200 + 34 544 = IV. Evaluation A. Write in column and then add. 1) 24 157 + 37 974 + 15 678 + 12 321 2) 32 784 + 12 534 + 22 233 + 15 712 3) 16 148 + 21 372 + 35 622 + 4 212 4) 14 035 + 23 572 + 18 404 + 24 156 5) 15 367 + 42 194 + 17 509 + 13 506 B. The 2009 Palarong Pambansa was held in Tacloban City. It was participated and attended by athletes and visitors. The table below shows the number of people who attended the affair each day. Use the table in solving the answer to each question. PALARONG PAMBANSA DAY NUMBER OF PEOPLE Sun 23 475 Mon 18 904 Tues 20 648 Wed 19 053 Thu 24 186 Fri 17 509 Sat 14 136 How many people came to see the Palaro on the following days? 1. Sunday, Monday, Tuesday 2. Monday, Tuesday, Wednesday and Thursday 3. Tuesday, Wednesday, Thursday, Friday 4. Wednesday, Thursday, Friday, Saturday
- 16. 11 5. Thursday, Friday, Saturday, Sunday 6. Sunday, Saturday, Monday and Friday 7. Monday, Saturday, Friday, Thursday 8. Wednesday, Sunday, Saturday and Tuesday 9. Sunday, Monday and Thursday 10. Saturday, Wednesday, Thursday, Monday V. Assignment Below are leaves that fall from a tree. Pick up at least four dry leaves and copy the numbers on them. Add the numbers. Do this at home. Estimating Sums of 3- to 5- Digit Addends I. Learning Objectives Cognitive: Estimate the sums of 3- to 5- digit addends Psychomotor: Round numbers to the indicated place correctly Affective: Participate actively in group activities II. Learning Content Skill: Estimating sums of 3- to 5- digit addends Reference: BEC PELC 1.B.1.2 Materials: textbooks, charts, picture of a palace, king, wicked woman Value: Active Participation
- 17. 12 III. Learning Experiences A. Preparatory Activities 1. Drill Answer as fast as you can 10 100 1 000 400 7 000 + 20 + 400 + 7 000 + 500 + 6 000 etc. 2. Review Contest between boys and girls. “Climb the ladder” Each member of the group will round the number flashed by the teacher to the highest place value. Correct answer means one step in the ladder. The first to reach the top of the ladder wins. 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 3. Motivation Let us pretend that we are in a palace. In a faraway palace lived a king, a prince, followers of the kings and a wicked woman. One day, the wicked woman got angry because one of the soldiers killed her cat. She turned everybody into stone except the prince. The wicked woman told the prince, “Everything will become normal again after you answer this problem correctly”. The prince consulted the wise men in the neighboring kingdom to be able to come up with the correct solution. B. Developmental Activities 1. Presentation a. Here is the problem given by the wicked woman. There are 25 678 girls and 13 211 boys in the palace. About how many children are there in the palace? 25 678 rounded to 30 000 13 211 rounded to 10 000 40 000 – estimated sum b. Let us analyze the problem given by the wicked woman and the solutions done by the wise men. In estimating what do we do first with the addends? After rounding the addends what is the next step?
- 18. 13 c. Let us go back to the story. The wicked woman did not fulfill her promise. Instead she told the little prince, “You still need to solve this problem. Since the reign of your father, 19 254 soldiers have died. Now the palace has only 37 634 living soldiers. About how many soldiers were in this palace before?” Solution: 19 254 rounded to 20 000 37 634 rounded to 40 000 60 000 2. Guided Practice (stress here the need for active participation in group activities) Form 4 groups. Give each group an activity to perform. Group A Read each problem carefully, then give the estimated sum. a. Edward and Fred played chess for 173 minutes before lunch and 167 minutes after lunch. About how many minutes did they play? b. The Blue Team and the Red Team played basketball. The Blue Team had a score of 172 while the Red Team had a score of 242 points. About how many points did they make in all? c. There were 284 boys and 302 girls at the program. About how many children were at the program? d. Mr. Luna spent 16,575 for the appliances and 54,567 for the house down payment. About how much did Mr. Luna spend? e. In 1999, there were 96 200 cable subscribers while in 2000 there were 15 968. Estimate the total number of cable subscribers in 1999 and 2000. Group B Encircle the letter of the estimated sum. 1. 67,857 a. 90,000 + 23,269 b. 80,000 2. 78,293 a. 120,000 + 47,179 b. 130,000 3. 51,476 a. 90,000 + 39,174 b. 100,000 4. 86,478 a. 140,000 + 51,976 b. 130,000 5. 27,464 a. 110,000 + 78,248 b. 120,000 Group C Estimate the sum. 1) 1 267 2) 8 320 3) 35 784 + 7 340 + 6 780 + 48 961
- 19. 14 4) 57 611 5) 31 811 + 61 112 + 48 988 Oral Practice. Estimate the sum of the following addends. 1) 284 2) 756 3) 524 4) 634 5) 374 +534 +381 +678 +194 +430 6) 3246 7) 1874 8) 6781 9) 15 678 10) 11 465 +6784 +3981 +7891 +14 278 +16 878 3. Generalization How do we estimate? In estimating 3- to 5-digit addends, first we round the addends to the highest place value then we add. Why do we estimate? C. Application Estimate each sum by rounding the numbers. Estimated Sum 1) 211 and 271 is about the same as 200 + 300 = 500 2) 333 + 321 is about the same as ___________ = ______ 3) 17 781 + 16 211 is about the same as _________ = ______ 4) 61 478 + 78 211 is about the same as _________ = ______ 5) 31 182 + 49 511 is about the same as _________ = ______ IV. Evaluation A. Look for the hidden message by solving each problem. Round the answer to its highest place value. Find the letter in the code that matches each answer. Write the correct letters in the boxes. 1 2 3 4 5 6 7 8 9 10 I L O V E M A T H ! 1) 62 784 2) 17 321 3) 33 171 4) 34 154 + 35 321 + 65 478 + 43 251 + 48 587 5) 72 534 6) 10 578 7) 43 000 8) 24 134 + 63 254 + 13 000 + 15 000 + 28 578 9) 17 321 10) 31 578 + 13 576 + 12 634 LEGEND: 20 000 - M 30 000 - H 40 000 - ! 50 000 - T 60 000 - A 70 000 - O 80 000 - V 90 000 - L 100 000 - I 130 000 - E
- 20. 15 B. Refer to the given table for the problems below. Activity Club Number of Members Volleyball 13 578 Basketball 75 254 Tennis 34 786 Art 66 931 Cooking 58 561 Softball 42 154 a. Estimate the combined number of members of the following: 1. volleyball and basketball 2. volleyball and tennis 3. volleyball and art 4. volleyball and cooking 5. volleyball and softball 6. basketball and tennis 7. basketball and art 8. basketball and cooking 9. basketball and softball 10. tennis and art 11. tennis and cooking 12. tennis and softball 13. art and cooking 14. art and softball 15. cooking and softball V. Assignment Estimate the sum. 1. There are 187 Girl Scouts in grade five and 135 Girl Scouts in grade six. About how many Girl Scouts are there in grades five and six? 2. There were 2 421 Mathematics textbooks and 3 578 workbooks delivered to Boac North Central School. About how many Mathematics books were delivered in all? 3. Mr. Nicolas harvested 6 755 coconuts from his plantation. His brother harvested 8 461. About how many coconuts did they harvest altogether? 4. Aida‟s class sold 5 678 tickets for a benefit show for the handicapped children in their town while Nelly‟s class sold 3 415 tickets. Estimate the total number of tickets sold. 5. Aling Norma bought a television set at 18,565 and a washing machine at 6,543. About how much did she pay the cashier? Adding Mentally 1- to 2- Digit Numbers with Sums up to 100 without Regrouping I. Learning Objectives Cognitive: Add mentally 1- to 2- digit numbers with sums up to 100 without regrouping Psychomotor: Give the sum of 1- to 2- digit numbers without using paper and pencil Affective: Participate actively in the different activities
- 21. 16 II. Learning Content Skill: Adding mentally 1- to 2- digit numbers with sums up to 100 without regrouping Reference: BEC PELC I B 1.3 Materials: Show me board, puzzle, square chips Value: Active participation III. Learning Experiences A. Preparatory Activities 1. Drill The age of each “number persons” can be found by adding the person‟s numbers. How old is each? After knowing each age make combination of numbers like 7 + 7 = 14 and so on. 2. Review Contest: boys and girls “Put-together Puzzles” a. Give 10 square chips of the same size to each of the two groups. b. Using these chips the pupils will form at least two 5-square figures like the one below. How to play the game The teacher will call on two pupils – one from each group. She will flash combination of numbers. Pupils will give the correct estimated sum. The pupil who is able to give the correct answer first will be given the chance to paste the first square until they were able to form 5 square figures. The first to complete the two figures wins the game. Remember. One side of the square must touch the other square. Example 1 Letter C Letter L After completing the figure, the members of the group will recognize the figure formed. 3. Motivation Who among you watch game shows? Why do you watch such program? As young children like you, what TV program should you watch?
- 22. 17 Today we have lots of games and activities. I‟m sure you‟ll enjoy them. What should you do when you‟re in a group? (Participate actively) Why should you participate in group activities? B. Developmental Activities 1. Presentation A. Form groups of five members each. Give one Show Me Board. B. Explain the mechanics of the game. Emphasize the time limit. 1. First Round (5 seconds only) Answer Correct or Incorrect (2 points each) 1) 56 + 23 = 79 2) 78 + 21 = 98 3) 35 + 43 = 79 4) 65 + 24 = 89 5) 38 + 51 = 89 6) 36 + 21 = 56 7) 47 + 21 = 68 8) 34 + 51 = 85 9) 33 + 66 = 96 10) 78 + 20 = 98 2. Second Round – Solve Me Mentally (2 pts.) (5 seconds only) I will read the problem once. Listen carefully. When I say go, That‟s the time for you to write your answer. When the buzzer rings, raise your Show Me Board. a. There are 23 adult passengers and 45 youth passengers in the bus station. How many passengers are there in the bus station? b. Mang Rico harvested 48 chicos and 31 mangoes. How many fruits did he harvest? c. Nonoy sold 45 sampaguita garlands. Rita sold 22 sampaguita garlands. How many sampaguita garlands did the two sell? d. Peter picked 32 chicos on Sunday. He picked 41 chicos on Wednesday. How many chicos did he pick in two days? e. Nena made 46 paper dolls in one week. She made 22 in another week. How many dolls did she make in two weeks? f. Rita prepared 26 tuna sandwiches and 13 chicken sandwiches. How many sandwiches did she prepare in all? g. Nolan sold 73 bananas and 22 mangoes. How many fruits did he sell in all? h. The Grade III pupils went on a field trip. 65 were boys and 34 were girls. How many went on a field trip? i. Regina has 80 eggs to sell. Roger has 15 more to sell. How many eggs do they have to sell altogether? j. The Grade III class registered 28 boy scouts and 71 girls scouts. How many scouts did they register in all? 3. Round 3 (under time limit – one minute) Make at least five combinations of numbers with the sum of 75.
- 23. 18 2. Guided Practice Regroup the class into 3 groups. Have them do this activity. They will do this as fast as they can. For the other group just change the sentences. Mechanics: Have you received a letter from a friend? Well, trace the path and look for it. Look for a card in the box and drop the answer in the correct mailbox from START. Follow the arrow until you reach the FINISH LINE.
- 24. 19 Working in dyads. (under time limit) What did the girl say when she met her teacher? Look for the hidden message by solving the exercises. Find the letter in the code that matches each answer. Write the correct letter in the last row. 31 62 32 42 21 74 61 51 22 21 63 + 33 32 33 40 23 20 32 43 42 61 36 I ‘T S M A T H T I M E A – 44 F – 72 K – 16 P – 50 U – 68 B – 76 G – 55 L – 39 Q – 83 V – 80 C – 17 H – 93 M – 82 R – 13 W – 56 D – 30 I – 64 N – 22 S – 65 X – 46 E – 99 J – 95 O – 15 „T – 94 Y – 11 Z – 90 Ask: Class, did you enjoy our lesson today? Why? 3. Generalization How do we add mentally? What do you think are the advantages of knowing how to add mentally accurately?
- 25. 20 C. Application 1. Number puzzle Look at the numbers which I am going to flash. Encircle the answer from the number puzzle. Find the sum of the encircled numbers in the first line, second line and so on. 1. 5 9 5 8 5 7 6 7 4 3 2 2. 8 1 9 8 9 7 9 6 9 5 9 3. 7 8 7 9 7 5 7 6 7 4 7 4. 7 6 7 7 7 5 7 8 8 7 4 5. 5 6 8 8 8 7 8 6 8 9 8 6. 9 6 9 5 9 4 9 1 9 8 9 7. 9 6 9 5 8 4 9 1 9 0 9 8. 7 6 7 7 7 8 7 9 7 1 7 9. 5 1 5 0 5 2 5 6 5 4 5 10. 8 6 8 3 8 1 8 6 8 7 8 Add mentally. 1) 33 2) 71 3) 23 4) 33 + 51 + 45 + 26 + 21 5) 62 6) 42 7) 31 8) 54 + 27 + 24 + 22 + 54 9) 35 10) 67 + 21 + 20 IV. Evaluation A. Look at the flashcards and answer it quickly. 1) 61 2) 71 3) 54 4) 38 5) 51 + 28 + 23 + 15 + 21 + 24 6) 33 7) 54 8) 61 9) 34 10) 81 + 24 + 31 + 27 + 64 + 14 V. Assignment Make 5 addition sentences for each sum. 1) 87 2) 76 3) 64 4) 57 5) 96 6) 84 7) 88 8) 76 9) 64 10) 53
- 26. 21 Mental Computation: 1-Step Word Problems Involving Addition I. Learning Objectives Cognitive: Solve mentally 1-step word problems involving addition with sums up to 100 without regrouping Psychomotor: Write an equation correctly Affective: Show speed and accuracy in solving problems mentally II. Learning Content Skill: Mental computation 1-step word problems involving addition Reference: BEC PELC 1.B.2.2 Materials: textbook, flashcards, manila paper Value: Speed and accuracy III. Learning Experiences A. Preparatory Activities 1. Drill – Add mentally (use flashcard) 8 9 4 7 3 8 7 + 3 + 6 + 5 + 5 + 9 + 9 + 6 2. Review (Recall the steps in solving word problems involving addition) Group the pupils into 4 teams. Each team will analyze the word problem then answers the questions. Chona has 35 stamps. Her friend gives her 49 more. How many stamps does she have in all? What is asked? What are given? What are the word clues? What process should be used? Write the number sentence? 3. Motivation Liza was invited by her friend Anne to attend a birthday party. But Liza‟s mother told her to clean the house. If you were Liza, what would you do? Do you encounter problems in life? How do you solve them? B. Developmental Activities 1. Presentation Present problem opener: Chito was arranging the social hall for the grade 3 program. He arranged 60 chairs in rows. Then he added 40 more chairs in rows. How many chairs did he arrange altogether?
- 27. 22 A. Let us solve the problem using Polya‟s 4steps in problem solving. ■ Understand a. What are given? 60 chairs and 40 chairs b. What is being asked? Total number of chairs Chito arranged c. What operation will solve the problem? Addition ■ Plan What equation will solve the problem? 60 + 40 = N ■ Solve ■ Look Back Does the answer make sense? Yes What is the correct label? 100 chairs Stress accuracy and speed B. Divide the class into 4 teams. Solve the problems that the teacher will read. Write your answer on the “Show Me Board.” The group with more points wins the game. Give the sum of the following: 1. There are 10 straws and 24 bottles in a case. How many straws and bottles are there altogether? 2. A box contains counters to be used in Math class. There are 27 stones, 18 sticks and 30 marbles. How many counters are there in the box? 3. Alex arranged his stamp collection in his scrap book. There were 40 U.S. stamps, 25 Philippine stamps and 78 other stamps. How many stamps were there in the scrap book? 4. Joy, Kim and Jake gathered sea shells during their Lakbay Aral in Boracay. Joy collected 38 sea shells, Kim gathered 20, and Jake had 55. How many sea shells had they collected in all? 5. Father harvested fruits in his garden. He had 62 chicos, 30 mangoes and 43 guavas. How many fruits did Father harvest altogether? Were you able to give the sum at once without using pencil and paper? Why? 2. Guided Practice a. Work in groups of four. Give each group a show-me-board. Solve the problems written on a chart mentally. 1. Edmar bought 12 red roses and 12 white roses. How many roses did he buy in all? Trivia: George Polya is the father of Problem Solving. He listed 4 simple steps to use when solving any given problem. These are: UNDERSTAND – PLAN – SOLVE – LOOK BACK Lead the pupils to note that the addends end in 0. The tens digits add up to 10. This equation maybe solved mentally by simply adding the tens digits and annexing a 0 60 + 40 100
- 28. 23 2. Mary collected 50 shells last Saturday and 60 more last Sunday. How many shells did she collect in all? 3. Mang Andres harvested 95 cavans in July and 98 cavans in August. How many cavans of palay did he harvest altogether? 4. A fisherman caught 80 fish in the morning and 55 fish in the afternoon. How many fish did he catch in all? 5. Nelda picked 75 guavas while Yoly picked 25 guavas. How many guavas did they pick altogether? b. Work in groups of 8. Play “Aim High.” Each group will be given strips of colored papers. Group 1 – red Group 3 – blue Group 2 – yellow Group 4 – orange The teacher will post a problem on the board. Pupils read the problem silently. The first group who gives the correct answer will have a chance to paste the strips of colored paper on the ladder. Repeat the same procedure until a group reaches the top. 7 6 5 4 3 2 1 110 mangoes and 200 santols. There are _______ fruits in all? 300 members last year. 70 more joined this year. How many in all? Gathered 150 pebbles yesterday; 40 more today. How many in all? Counted 54 blue pens, counted 60 red pens. How many pens in all? Planted 60 okra seedlings and 45 tomato seedlings. How many seedlings were planted altogether? c. Work in pairs Give short story problems written on manila paper and have each pair answer them mentally in their notebook or on paper. 1. Gally gathered 45 eggs the first day and 50 eggs the second day. How many eggs did they gather in 2 days? 2. Joey picked 54 star apples in the morning and 60 in the afternoon. How many star apples did he pick? 3. Hazel and Shara brought pasalubong for their grandfather, 44 chocolate cookies and 45 butter cookies. How many cookies did they bring for their grandfather? 4. Rico went fishing. He caught 34 fish before lunch and 22 more after lunch. How many fish did Rico catch? 5. Ester has 420 stamps. Joyce gave her 175 stamps more. How many stamps has she? Were you accurate in adding mentally? Did you add quickly? red yellow blue orange
- 29. 24 3. Generalization: What is the technique of doing mental addition? What are Polya‟s 4 steps in problem solving? C. Application Look at the table below and answer the questions that follow. An orchard in Brgy. Sto. Niño has the following fruit-bearing trees: Trees Number of Trees star apple 50 avocado 45 macopa 30 guava 22 santol 20 1. How many star apple and avocado trees are there in all? 2. How many macopa, guava and santol trees are there in all? 3. How many avocado, santol and macopa trees are there in all? 4. How many guava and star apple trees are there in all? 5. How many fruit-bearing trees are there in all? IV. Evaluation Solve these problems as fast as you can. (Compute mentally) 1. Mother sold 150 pieces of calamansi and 100 pieces of caimito. How many calamansi and caimito did she sell altogether? 2. What number when added to 200 is equal to 500? 3. A balut vendor sold 110 balut last Saturday and 120 last Sunday. How many balut did she sell in two days? 4. In San Miguel Central Elementary School there are 550 boys and 420 girls. How many pupils are there in all? 5. The baker sold 700 pandesal on Monday and 800 on Tuesday. How many pandesal did he sell in two days? V. Assignment Give the sum by computing mentally. 1) 20 cups 20 saucers ? 2) 40 duck‟s eggs 55 hen‟s eggs ? 3) 34 yellow buttons 45 white buttons ? 4) 80 spoons 80 forks ? 5) 55 plates 50 glasses ? 6) 45 pens 45 pencils ? 7) 50 bottles 36 cases ? 8) 90 red balloons 65 yellow balloons ? 9) 42 Math Books 36 Science books ? 10) 53 flowers 40 fruits ? Understand Plan Solve Look back
- 30. 25 Solving Word Problems Involving Addition I. Learning Objectives Cognitive: Solve 1-step word problems involving addition of whole numbers with sums up to 100 000 including money Psychomotor: Tell what is/are given, the word clue/s and the operation to be used in the problem Write the number sentence/equation correctly Affective: Participate actively and work cooperatively in group/class activities II. Learning Content Skill: Solving word problems involving addition Reference: BEC PELC I.B.2 Materials: flash cards, problem chart, play money, cut-out of trees and fruits Value: Active participation and cooperation III. Learning Experiences A. Preparatory Activities 1. Drill Mental Computation Give the sum orally. (flashcards) Set A 20 80 70 50 40 30 60 20 80 50 + 40 + 90 + 60 + 70 + 90 + 80 + 30 + 90 + 70 + 60 Set B 300 500 600 800 200 400 600 + 200 + 800 + 70 + 50 + 700 + 700 + 800 2. Motivation Present a problem opener. Jose and Nilo helped their family in their poultry farm. They gathered 2 509 eggs in January and 3 488 eggs in February. How many eggs did they gather in all?
- 31. 26 B. Developmental Activities 1. Presentation a. Let the pupils read the problem silently. Ask: Who are the children in the story? What can you say about them? Are you also helpful at home? In what ways are you helpful? Activity 1 – Polya‟s 4 steps Now, let us analyze and solve the problem using Polya‟s 4 steps. ■ Understand a. What are given? What do we already know? b. What is being asked? c. What operation is needed to solve the problem? ■ Plan What equation will solve the problem? 2 509 + 3 488 = N ■ Solve 2 509 + 3 488 5 997 ■ Look Back Did you use the correct operation? Does the answer make sense? Did you label the answer correctly? 5 997 eggs b. Let us analyze and solve another problem. Susan collected 1 085 shells while Ellen collected 589 more shells than Susan. How many shells did Ellen collect? Activity 2 – Using table Person in the Story Number of Shells Collected Susan 1 085 Ellen Susan‟s + 589 = ? ■ Understand a. Who collected shells in the story?
- 32. 27 b. How many shells were collected by Susan? c. What about Ellen‟s collections? Do you know exactly the number of shells she collected? d. What condition was given about Ellen‟s collection? 589 more than Susan e. How can we find the total shells collected by Ellen? f. What word clues tell what operation to be used? ■ Plan What operation are we going to use? What equation? Susan‟s + 589 1 085 + 589 = N ■ Solve 1 085 + 589 1 674 ■ Look Back Did you use the correct operation? Does the answer make sense? Did you label the answer correctly? 1 674 shells were collected by Ellen. c. Present another problem. Mrs. Gonzales bought a TV set worth 9,300, a refrigerator worth 18,500 and a washing machine worth 5,150. How much did she spend in all? What did Mrs. Gonzales buy in the story? How much did each cost? What is asked in the problem? What word clue/s tell what operation to use? What operation are we going to use? What will be the number sentence? Strategy – Acting Out the problem Let the pupils solve the problem by acting it out using play money as their materials. Then let them report the answer to the class. Expected answer: 9,300 18,500 5,150 32,950 - total amount spent by Mrs. Gonzales Look back Is their answer right? Did they write the correct label? Is the answer sensible?
- 33. 28 2. Guided Practice Group work Divide the class into 5 groups. Each group will choose their leader, pick a fruit from the tree and solve the problem written on the fruit. Problems written on each fruit. (It should be written first on a bond paper and pasted at the back of each fruit) 1. When the “Clean and Green Campaign” was launched in Quezon City, 3 425 boys and 5 342 girls from different schools joined the parade. How many pupils joined the parade? 2. If Dino picked 2 452 siniguelas from one tree and 1 535 siniguelas from another tree, how many siniguelas would he picked in all? 3. There were 2 421 Mathematics textbooks and 3 233 Mathematics workbooks delivered to Baclaran Central Elementary School. How many Mathematics books were delivered in all? 4. The secretary of Mr. Virgilio Cruz can type 39 840 words in the morning and 40 765 words in the afternoon. How many words can the secretary type in one day? Instruction: Use Polya‟s steps to answer the problem. Report your work to the class. 5. Mr. Cruz harvested 72 850 coconuts from his plantation. His brother harvested 25 730 coconuts. How many coconuts did they harvest altogether? Instruction: Answer the following questions. Then report your answer to the class. a. What is asked in the problem? b. What are the needed data to solve the problem? c. What words tell what operation to use? d. What operation will you use? What will be the equation? e. Solve the equation. f. Look back. Ask the pupils about their feeling during the group activity. Did they participate and cooperate with the group? What happened to the work when everybody is cooperating? Which strategy do you like best? Why? Why do we need to analyze the problem?
- 34. 29 3. Generalization: How do we analyze and solve word problems involving addition of whole numbers? What are the questions we ask to analyze word problems? What are the 4 steps of Polya in solving word problems? Remember: To analyze and solve word problems, we can use Polya‟s 4 steps in solving them. The steps are: UNDERSTAND : Understand the problem What are given? What do we already know? What is being asked? What operation is needed to solve the problem? What word clue/s tell what operation to be used? PLAN : Make a plan. What operation will solve the problem? SOLVE : Work your plan. Strategies can be: 1. Using table, manipulatives, cutouts 2. Drawing/Illustrations 3. Acting out the problem 4. Direct solving LOOK BACK : Check you work. Did you use the correct operation? Does the answer make sense? Did you label the answer correctly? C. Application Written: Directions: Read the problem. Write what is asked, the given facts, word clues, operation to be used and the number sentence/equation for the problems. Then solve. 1. There are 2 135 victims of the volcanic eruption and 1 124 typhoon victims. How many people in all need help? 2. Candy factory A manufactures 8 196 candies a day. Factory B manufactures 1 783 more candies than factory A. How many candies does factory B manufacture in a day? 3. The pupils of Juan Luna Elementary School went on a field trip. The Grade 4 pupils paid 2,420 for their bus fare. The Grade V pupils paid 3,115 and the Grade VI pupils paid 2,142. How much was the total bus fare? 4. In a certain district, there are 4 325 boys and 5 648 girls. What is the total population of the district? 5. There were 4 485 boys and 5 318 girls who watched the Laguna Art Exhibit on its opening day. How many children in all watched the exhibit on the first day?
- 35. 30 IV. Evaluation Group work with 4 members each Create simple problems using the given data below. Then solve the problem you have created. 1. 3,553 – 1 st day 5,382 – 2 nd day 2,420 – 3 rd day 2. Central Visayas Region Bohol – 4 117 square kilometres Cebu – 5 088 square kilometres Negros Oriental – 5 402 square kilometres Siquijor – 344 square kilometres 3. Mr. Lopez – 26 482 votes Mr. Cruz – 25 907 votes 4. TV set – 12,500 Typewriter – 3,700 Radio – 1,300 5. Narra trees – 37 280 Mahogany trees – 12 415 Eucalyptus trees – 11 528 Ipil-Ipil trees – 14 236 Work in pairs The pairs will create one-step word problem and exchange their work with other pairs. Then they will solve it and show their work for the class to check. V. Assignment Answer the problems using Polya‟s 4 steps. Don‟t forget to “look back.” 1. The earth‟s diameter is 12 762 kilometres, while that of the moon is 3 482 kilometres. What is the total diameter of the earth and the moon? 2. Father earned 25,400 in selling dressed chickens last November and 39,300 last December. How much did he earn in all? 3. Workers from different sectors attended a peace rally. If 12 342 people were from the south, 5 694 people from the north, 7 269 from the east and 6 492 people from the west attended the rally, how many people were in the rally? 4. Mr. Bautista bought a sofa for 6,500, a bed for 5,350 and a cabinet for 4,950. How much did Mr. Bautista spend for his furniture? 5. Two farmers in Laguna planted their fields to corn. The first farmer harvested 2 386 ears of corn and the second farmer harvested 3 129. How many ears of corn did they harvest altogether? Problems for Enrichment: 1. Nitoy saved 956 in 3 months. Carlo saved 548. How much did they save together? 2. Mang Jerry harvested 3192 calamansi. Mang Noli harvested 876. How many calamansi did the 2 men harvest altogether?

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