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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 Division 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. Division Dividing 2- to 3- digit numbers by renaming ................................................................... 1 Dividing 2- to 3- digit numbers by 1- digit numbers without remainder........................... 6 Dividing 2- to 3- digit numbers by 1- digit numbers with remainder................................ 11 Dividing 2- to 3- digit numbers by multiples of 10 up to 90............................................. 15 Dividing 2- to 3- digit numbers by 1- to 2- digit numbers with zero difficulty................... 21 Dividing 3- to 4- digit numbers by 1- to 2- digit numbers without remainder .................. 26 Dividing 3- to 4- digit numbers by 1- to 2- digit numbers with remainder ....................... 32 Dividing 3- to 4- digit numbers by 2- to 3- digit numbers with zero difficulty................... 36 Dividing whole numbers by 5 .......................................................................................... 43 Dividing whole numbers by 10 and 100.......................................................................... 48 Dividing mentally 2- digit numbers through 99 by 1- digit number without remainder........................................................................................................... 54 Solving 1- step word problems involving division of 2- to 4- digit numbers by 1- to 2- digit numbers including money.............................................................. 59 Solving 2- step word problems involving division and anyone of the fundamental operations including money ............................................................................... 63 Solving 3- step word problems involving division and any two of the other fundamental operations including money .......................................................... 67
- 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. Division of Whole Numbers 1. Comprehension of Division 1.1 Divide 2 to 4 digit numbers by 1 to 2 digit numbers without or with remainder and with zero difficulty 1.1.1 Divide 2 to 3 digit number without/with numbers by 1 digit remainder with/without remainder 1.1.1.1 Show that renaming 2 to 3 digit numbers help make computation easy Industry Simplifying the problem Song (Musical) Cooperative groups(Interpersonal) 1.1.1.2 Divide 2 to 3 digit numbers by 1 digit number without remainder Sharing Acting out the problem Making a table Cooperative groups(Interpersonal) 1.1.1.3 Divide 2 to 3 digit numbers by 1 digit number with remainder Honesty Simplifying the problem Manipulative (Bodily kinesthetic) 1.2 Divide 2 to 3 digit numbers by multiples of 10 up to 90 Physical fitness Modeling Simplifying the problem Diagram (Spatial) Maze (Logical math) 1.3 Divide 2 to 3 digit numbers by 1 to 2 digit numbers with zero difficulty Eating the right kind of food Modeling Drawing pictures Cooperative groups(Interpersonal) 1.4 Divide 3 to 4 digit numbers by 1 to 2 digit numbers without or with remainder and with zero difficulty 1.4.1 Divide 3 to 4 digit numbers by 1 digit number without remainder Eating the right kind of food Drawing pictures Making a table Cooperative groups(Interpersonal) 1.4.2 Divide 3 to 4 digit numbers by 1 to 2 digit numbers with remainder Kindness/Friendliness Acting out the problem Polya's steps in problem solving Chart (Spatial) Manipulative (Bodily kinesthetic) 1.4.3 Divide 3 to 4 digit numbers by 1 to 2 digit numbers with zero difficulty Politeness Polya's steps in problem solving Ladders (Spatial) 1.4.4 Divide whole numbers by 5 Cooperation Acting out the problem Puzzle (Logical mathematics) 1.4.5 Divide whole numbers by 10 and 100 Helpfulness Simplifying the problem Maze (Logical math) Number chart (Spatial)
- 6. vi 1.5 Divide mentally 2 digit numbers through 99 by 1 digit numbers without remainder Accuracy Simplifying the problem Number wheels (Logical Math) Manipulative (Bodily kinesthetic) 2. Application of Division 2.1 Solve 1 step word problem involving division of 2 to 4 digit numbers by 1 to 2 digit numbers including money Industry/Love of work Acting out the problem Polya's steps in problem solving Maze (Logical math Song (Musical)) 3. Application of the Four Fundamental Operations 3.1 Solve 2 step word problems involving division and any one of the fundamental operations including money Helpfulness/ Industry Polya's steps in problem solving Acting out the problem Movements (Bodily Kinesthetic Cooperative groups(Interpersonal) 3.2 Solve 3 step word problems involving division and any two of the other fundamental operations including money Wise use of time Polya's steps in problem solving Making a table Illustrations (Spatial) Cooperative groups(Interpersonal)
- 7. 1 Dividing 2- to 3-Digit Numbers by Renaming I. Learning Objectives Cognitive: Show that renaming 2- to 3-digit numbers help make computation easy in division Psychomotor: Write the expanded form of numbers Affective: Be industrious II. Learning Content Skill: Renaming 2- to 3-digit numbers make computation easy in division Reference: BEC PELC I.E.1.1 Materials: cut-outs, flash cards, number cards, show me cards Value: Industry III. Learning Experiences A. Preparatory Activities 1. Drill: Division Basic Facts Contest – “Giant Steps” a. The teacher calls on 4 pupils at a time. b. She flashes the number cards and the pupils outdo each other by giving the correct answers. c. The first pupil to give the correct answer will take one step forward. d. The first pupil to reach the finish line wins the game. 64 ÷ 8 = __ 72 ÷ 9 = __ 25 ÷ __ = 5 32 ÷ 4 = __ 48 ÷ __ = 6 30 ÷ 6 = __ 2. Review – Renaming Numbers a. The teacher flashes the number cards. b. The pupils write the expanded form of the number in their show me cards. 126 100 + 20 + 6 935 900 + 30 + 5 473 400 + 70 + 3 228 200 + 20 + 8 564 500 + 60 + 4 3. Motivation Introduce the song “I’m Mathematics” to the tune of “Skip to my Loo” (I’m mathematics, how do you do?) 2x Who are you, tell me true I’m just a child, but I know you. You know addition, yes I do Multiplication, yes I do Even division, yes I do Let’s get together, I like you
- 8. 2 What are the operation mentioned in the song? Addition, Multiplication and Division Let’s see if you can tell the operation that we shall use in solving the problem on the chart. B. Developmental Activities 1. Presentation a. Present problem 1 (2 digits dividend) Tony and Peter wanted to help their family in earning a living. They planted mustard seedlings in their garden plots. There are 36 seedlings. They planted 6 seedlings in each row, how many rows of mustard seedlings did they have? b. Analysis ● Who wanted to help their family in earning a living? ● What did they do to increase the family income? ● Do you also help your family in earning a living? ● What kind of children are Tony and Peter? ● Are they industrious? ● How many seedlings do they have? ● How many seedlings did they plant in each row? ● What shall we do to answer the problem? c. Solve the problem through illustration. Let us look at the seedlings on the chart. How many seedlings are there in all? How many rows are there? How many seedlings are there in each row? Write the division sentence. 36 ÷ 6 = 6 6 6 36 36 0 d. Solve the problem by renaming the dividend (use of expanded form). Let’s solve the problem with the use of the expanded form. Write the number sentence. 36 ÷ 6 = N
- 9. 3 Rename 36 using the expanded form of the number 30 + 6 = 36 6 36 30 ÷ 6 = 5 6 ÷ 6 = 1 5 + 1 = 6 e. Solve the problem using the short form. 6 36 Step 1 6 is not contained in 3. so, take 36 36 ÷ 6 = 6 Step 2 Multiply 6 by 6. 6 x 6 = 36 subtract 36 – 36 = 0 f. Present problem 2 (3 digits dividend) There are 248 pupils in grade 3. They are distributed equally among 4 classes. How many pupils are there in each class? How many pupils are there? Into how many classes are they distributed equally? Write the number sentence. 248 ÷ 4 = N Rename the dividend and solve. 4 248 200 + 40 + 8 200 ÷ 4 = 50 40 ÷ 4 = 10 8 ÷ 4 = 2 50 + 10 + 2 = 62 Let’s show it in another way. 4 21050 200 840200 0 40 40 0 8 8 0 Who can compute the answer using the short form? 4 62 248 = 62 Step 1 Divide the hundreds. 4 is not contained in 2 so take 24, 24 ÷ 4 = 6 Step 2 Multiply 4 by 6. 4 x 6 = 24 subtract 24 from 24 24 – 24 = 0 4 6 24 248 0
- 10. 4 Did we get the same answer when we divide 248 by 4 using the expanded notation and the short form? Which method is easy to use? Why? 2. Guided Practice a. Work in pairs Game “Compute Me” Distribute number cards with division problem written on them. The pupils answer the problem by renaming the dividend as a sum of hundreds, tens and ones. (expanded form) Instruct them to write their answer at the back of the number card. The first pair to give the correct answer wins the game. b. Group the pupils into Learning Barkadas. (LBs) Game – “Come and Get Me” The teacher arranges number cards on the chalkboard. Then she distributes activity cards to the LBs. The pupils will answer the problem in the activity card by renaming the dividend using the expanded form. After answering the problem, they will look for the answer on the chalkboard. The first LB to get the correct answer from the chalkboard wins. Step 3 Bring down 8. 8 ÷ 4 = 2 Multiply 4 by 2. 2 x 4 = 8 Subtract 8 – 8 = 0 4 62 24 248 08 8 0 5 155 3 633 5 525 6 336 2 42 4 84 3 93 3 366
- 11. 5 3. Generalization How do we make our computation in division easy? We can make computation in division easy by renaming the dividend with the use of the expanded form. What are the steps in division of numbers using the expanded form? 1. Rename the dividend using the expanded form. 2. Divide each number by the divisor. 3. Add the partial quotients. C. Application A. Write the missing numbers. 1) 2 844 800 + ____ + 4 800 ÷ ____ = ____ 40 ÷ 2 = _______ ______ ÷ 2 = _____ 2) 2 252 200 + 50 + 2 =252 200 ÷ 2 = _______ 50 ÷ 2 = _______ 2 ÷ 2 = _____ _____ + _____ + _____ = _____ 3) 5 255 5 550200 0 50 __ 0 5 _ 0 B. Read, Analyze and Solve Show your solution by renaming the dividend. There are 648 cans of sardines that is to be distributed in 2 evacuation centers of flood victims. How many sardines were given equally among the evacuation center? = ___
- 12. 6 IV. Evaluation Rename the dividend, then divide. The first one is done for you. 2 488 2 440200 400 880400 0 80 80 0 8 8 0 1) 3 633 2) 5 525 3) 3 963 4) 5 245 5) 3 393 V. Assignment A. Fill the blank with the correct answer. 1) 5 285 285 = ______+ ______ + ______ ______ ÷ 5 = ______ ______ ÷ 5 = ______ ______ ÷ 5 = ______ ______ + ______ + ______ = ______ 2) 2 542 542 = ______+ ______ ______ ÷ 2 = ______ ______ ÷ 2 = ______ ______ ÷ 2 = ______ ______ + ______ + ______ = ______ B. Rename, then find the quotient. 1) 5 655 2) 4 88 3) 2 46 Dividing 2- to 3-Digit Numbers by 1-Digit Number without Remainder I. Learning Objectives Cognitive: Divide 2- to 3-digit numbers by 1-digit numbers without remainder Psychomotor: Write the expanded form of given numbers Affective: Share one’s blessings to others
- 13. 7 II. Learning Content Skill: Dividing 2- to 3-digit numbers by 1- to 2-digit numbers without remainder Reference: BEC PELC IE 1.2 Materials: flash cards, number cards, show me boards Value: Sharing III. Learning Experiences A. Preparatory Activities 1. Drill: Division Basic Facts The teacher writes the following division sentence on the board. 15 ÷ 3 = 5 Ask volunteers to identify the dividend, divisor and quotient. The teacher calls on 5 players. She flashes the cards with division sentence on them. One of the numbers in the sentence is underlined. Ask the pupils to identify the underlined numbers. 18 ÷ 6 = 3 Dividend The first player to get the most number of correct answers wins the game. 2. Review “Rename Me” Rename the following numbers: 35 = 30 + 5 186 = 100 + 80 + 6 47 = 40 + 7 96 = 90 + 6 458 = 400 + 50 + 8 293 = 200 + 90 + 3 The teacher groups the pupil into LBs. Then she gives a number. The pupils write the expanded form of the number on the board. The LB with the most number of correct answer wins the game. 3. Motivation Noli has some bananas. He wants to share 10 bananas equally to his 5 friends. How many bananas will he give to each of them? How many bananas does Noli want to share with his 5 friends? Do you also share your blessings to your friends? B. Developmental Activities 1. Presentation a. Acting out the problem. Call on 6 pupils. Ask one pupil to act as Noli, and the rest, his 5 friends. Let Noli distribute the 10 bananas equally to his friends.
- 14. 8 How many bananas are there in all? 10 How many friends will these be distributed? 5 Write 10 ÷ 5 = 2. How many will each friend get? b. Division as repeated subtraction 10 ÷ 5 means how many 5s are there in 10? Let us subtract 5 from 10 until we get 0. 10 How many times did we subtract - 5 - 1 five from ten? 2 5 - 5 - 1 0 Division is repeated subtraction. c. Present another problem. A department store had 336 pairs of socks. The socks were sold in packages of 3 pairs. How many packages were there? How many pairs of socks has the department store? How were the socks sold? What operation shall we use to solve the problem? 3 336 Which is the dividend? Which is the divisor? 1) Group the pupils into 2. Let them solve the problem in 2 ways. Group 1 3 210100 300 630300 0 30 - 30 0 6 - 6 0 = 112 Steps 1. Divide the hundreds. 2. Divide the tens. 3. Divide the ones.
- 15. 9 Group 2 3 112 3 336 3 - 3 0 6 - 6 0 Did we get the same answer even if we used 2 ways of solving the problem? Let’s check if the quotient is correct. How do we check if our answer is correct? 112 - quotient x 3 - divisor 336 - dividend 2) Solve the problem below using the short method. 6 14 6 876 27 - 24 36 - 36 0 2. Guided Practice/Fixing Skill A. Work in triads Supply the missing numbers in the box. 1. 4 4 48 2. 8 8 96 8 16 - 8 - 16 0 0 Steps 1. Divide 3 by 3. 3 ÷ 3 = 1 Write 1 in the hundreds place. 2. Multiply 1 by 3. 1 x 3 = 3 3. Subtract 3 from 3. 3 – 3 = 0 4. Bring down 3. 3 ÷ 3 = 1 Write 1 in the tens place. 5. Multiply 1 by 3. 1 x 3 = 3 6. Subtract 3 from 3. 3 – 3 = 0 7. Bring down 6. 6 ÷ 3 = 2 8. 2 x 3 = 6 9. 6 – 6 = 0 Multiply the quotient by the divisor. If the answer is exactly the same as the dividend, the answer is correct. 8 ÷ 6 = 1 1 x 6 = 6 8 – 6 = 2 2 < 6 Bring down 7 27 ÷ 6 = 4 4 x 6 = 24 27 – 24 = 3 3 < 6 Bring down 6 36 ÷ 6 = 6 6 x 6 = 36 36 – 36 = 0 (__ x 4) (__ x 4) (__ x 8) (__ x 8)
- 16. 10 3. 6 30 318 4. 9 27 288 _ _ 18 - 18 - 18 0 0 A. Read, Analyze and Solve 1. If you divide my number by 4, you get a quotient of 37. What is my number? 2. A scoutmaster has 75-metre piece of rope. How many pieces- each of which is 6 m long- can be cut from it? 3. What number am I? If you divide me by 5 then add 3, you get 25. 3. Generalization How do we divide 2- to 3-digit numbers by 1 digit number? To divide 2- to 3-digit numbers by 1 digit number, follow these steps: Divide, multiply, subtract, compare and bring down, until all the digits in the dividend are divided. C. Application 1. Work in group of four Divide. Fill in the _ with the correct number. Do this on your drill board. a. 4 4 68 b. 5 5 75 _ _ 25 - _ _ - _ _ _ _ c. 4 28 312 d. 3 21 234 _ _ 24 - _ _ - 24 _ 0 e. 4 20 212 12 - 12 0 (__ x 6) (__ x 6) (__ x 9) (__ x 9) (4 x 1) (4 x 7) (5 x 1) (5 x 5) (4 x 7) (4 x 8) (3 x __) (3 x __) (4 x __) (4 x __)
- 17. 11 IV. Evaluation 1. Divide pupils into LBs. 2. Distribute activity cards to the LBs. 3. Let them solve the division exercises. 4. Ask them to supply the missing numbers in the table. (Dividend, Divisor, Quotient) 5. The first LB to present the table with the correct answer wins the contest. LB1 LB2 Dividend Divisor Quotient Dividend Divisor Quotient 126 2 62 365 5 43 V. Assignment Divide. Then check if the answer is correct. 1) 2 126 2) 3 291 3) 5 365 4) 4 432 5) 6 294 Divide 2- to- 3 Digit Number by 1- Digit Number with Remainder I. Learning Objectives Cognitive: Divide 2- to 3-digit numbers by 1-digit number with remainder Psychomotor: Tell the meaning of remainder Affective: Practice the habit of being honest II. Learning Content Skills: Meaning of Remainder Division of 2- to 3-digit numbers with remainder Reference: BEC PELC I.E.1.1.1.3 Materials: textbook, Math kit, 1 bottle can, popsicle stick Value: Honesty 2 126 3 231 6 294 5 365 5 480 6 66 5 75 4 212 6 198 7 147
- 18. 12 III. Learning Experiences A. Preparatory Activities 1. Drill: Basic division facts 2. Review 2 24 4 96 7 64 8 64 9 63 4 36 B. Developmental Activities 1. Presentation a. Present the story problem Mr. Golez packed 54 tomatoes into small boxes. If 4 tomatoes can be placed in each box, how many boxes did he fill? How many tomatoes were left out? 1) Ask the children to bring out their counters (stones, popsicle sticks, etc) Let’s show this problem using our counters. - How many tomatoes are there? 54 - How many tomatoes can be placed in a small box? 4 - How many boxes will be filled? 2) Have the children illustrate the problem using their counters. 13 boxes were filled 2 tomatoes were not put in the box We call 2 as the remainder. 3) Let’s solve the problem using the steps in problem solving. ■ Understand What are given? 54 tomatoes in small boxes 4 tomatoes in each box What is being asked? How many boxes did he fill? How many were left out? What operation will solve the problem? Division ■ Plan What equation will represent the problem? 54 ÷ 4 = N ■ Solve Guide the children in solving the problem following the steps:
- 19. 13 4 13 4 54 14 - 12 2 Ask: How many boxes were filled? ■ Look Back How many tomatoes were not included? Does your answer make sense? b. Present another problem. This time with 3-digit by 1-digit using Polya’s method. Mang Tasyo divided 848 mangoes equally into 6 big baskets. How many mangoes were there in each basket? Divide to find the answer. 6 848 What are given? What is being asked? What operation will solve the problem? What equation will solve the problem? Show how this is done. 1. Divide hundreds 8 ÷ 6 Multiply, subtract and compare. 6 __1 848 - 6 2 2. Bring down the tens. Divide tens (24 ÷ 6 = 4) Multiply (4 x 6 = 24) Subtract and compare. 6 14 848 - 6 . 24 - 24 8 3. Bring down the ones. Divide ones 6 ÷ 8 = 1 Multiply, subtract/compare. 6 141 848 - 6 . 24 - 24 8 - 6 2 2. Guided Practice A. Solve the following number sentences. 1) 2 345 2) 4 87 3) 3 67 4) 4 745 5) 5 394 Divide: How many 4s are in 5? Multiply: 1 x 4 = 3 Subtract: 5 – 4 = 1 Bring down 4 beside 1 How many 4s are in 14? Multiply 3 x 4 = 12 Subtract 14 – 12 = 2 remainder
- 20. 14 B. Read, analyze and solve 1. If you divide my number by 6, you get a quotient of 25 and remainder of 3. What is my number? 2. How many fours are there in 130? 3. What will be the remainder if 261 is divided by 5? 3. Generalization How do we divide 3-digit by 1-digit number? What is the meaning of remainder? We divide the hundreds, then the tens and the ones. Then we multiply and subtract. Remainder – is the left-over. C. Application Solve the following: 1) 3 619 2) 9 813 3) 7 432 4) 5 617 5) 4 914 IV. Evaluation Divide and write the letters above the given quotients to answer these questions. What is another word for left over? R 5 23 N 9 613 S 2 313 A 4 217 M 6 39 B 7 236 E 5 62 D 3 214 I 8 821 ____ ____ ____ ____ ____ ____ ____ ____ ____ 4r3 12r2 6r3 54r1 102r5 68r1 71r1 12r2 4r3 V. Assignment Divide 1) 2 126 2) 3 231 3) 4 232 4) 5 365 5) 6 253
- 21. 15 Dividing 2- to 3-Digit Numbers by Multiples of 10 up to 90 I. Learning Objectives Cognitive: Divide 2-to 3-digit numbers by multiples of 10 up to 90 Psychomotor: Write the quotient accurately Affective: Practice the habit of keeping healthy II. Learning Content Skill: Dividing 2-to 3-digit numbers by multiples of 10 up to 90 Reference: BEC PELC I E 1.4 Materials: activity cards, flash cards, show me boards Value: Keeping physically fit III. Learning Experiences A. Preparatory Activities 1. Drill: Division Basic Facts a. Distribute flashcards with division number sentences to the pupils. b. The teacher shows a number card one by one. (The number in the card is a quotient which is an answer to the division exercises of the pupils.) c. The pupil who has the division sentence will raise the card. 2 6 12 ÷ 3 = N 3 7 30 ÷ 5 = N 4 8 63 ÷ 9 = N 5 9 81 ÷ 9 = N 25 ÷ 5 = N 48 ÷ 6 = N 18 ÷ 3 = N 2. Review – Dividing 2- to 3-digit numbers by 1-digit divisor. Form 2 groups. Group 1 – Divide 355 by 5 using the expanded form. 5 11060 300 550300 0 50 50 0 5 5 0 Group 2 – Divide 355 by 5 using the short form. Note: The quotient/answer may have 1 or more division sentence. = 71
- 22. 16 5 71 35 355 05 5 0 What are the steps in dividing whole numbers using the short form? 1. Divide 2. Multiply 3. Subtract 4. Compare and bring down 5. Repeat the procedure until all the digits in the dividend are divided. 3. Motivation Present the story problem. Mr. Flores did some brisk walking. In 10 minutes he was able to walk a distance of 50 metres. How far did he walk in one minute? What did Mr. Flores do? Who can demonstrate how to walk briskly? Do you know that brisk walking is good for the heart? If done regularly, it keeps a person physically fit. Do you exercise to make yourself healthy? B. Developmental Activities 1. Presentation a. Use of number line. 10 20 30 40 50 60 700 How many metres did Mr. Flores walk in 10 minutes? 50 m How far did he walk in one minute? Write the number sentence: 50 ÷ 10 = N Let’s show with the use of number line that division is a repeated subtraction. 50 – 10 = 40 40 – 10 = 30 30 – 10 = 20 20 – 10 = 10 10 – 10 = 0 How many times did we subtract 10 from 50? 50 ÷ 10 = 5 How far did Mr. Flores walk in 1 minute? Let’s see if the answer is correct? 5 x 10 = 50 Quotient x divisor = dividend quotient divisor dividend 5 4 3 2 1
- 23. 17 b. Use of the short method Step 1 Divide Step 2 Multiply Step 3 Subtract Check: 5 x 10 = 50 Quotient Divisor Dividend c. Present another problem. Masantol Elementary School has 20 booths for the School Foundation Day. The school buys 346 prizes. Each booth will share the prizes equally. How many prizes should each booth get? Are there any left over prizes? How many booths does Masantol Elementary School have for the School Foundation Day? How many prizes did the school buy? What shall we do to solve the problem? Write the number sentence. 346 ÷ 20 = N 20 346 Call on 8 pupils. Tell them to fall in line, in single file. The pupils will take turns in solving the problem following the steps in dividing whole numbers. Pupil 1 – Step 1 Divide the hundreds by 20. 20 1 346 3 cannot be divided by 20. Divide 34 by 20. 34 can be divided by 20. 34 ÷ 20 = 1 Write 1 in the tens place. Pupil 2 – Step 2 Multiply 1 x 20 = 20. 20 1 20 346 10 5 50 10 5 50 50 5 cannot be divided by10 50 can be divided by 10 5 x 10 = 50 10 5 50 50 0 50 – 50 = 0
- 24. 18 Pupil 3 – Step 3 Subtract 34 – 20 = 14. 20 1 20 346 14 Pupil 4 – Step 4 Bring down 6. 20 1 20 346 146 Pupil 5 – Step 5 Divide 146 by 20. 20 17 20 346 146 - 140 Pupil 6 – Step 6 Multiply 7 x 20. Pupil 7 – Step 7 Subtract 146 – 140. 20 17 20 346 146 - 140 6 Pupil 8 – Step 8 Write the remainder. What shall we do to check if the answer is correct? 17 x 20 340 + 6 346 2. Guided Practice a. Work in Pairs – Content Group pupils by 2. Each pair will be given a card with number equation. The first pair to solve the equation wins. b. Work in groups of 5. 1) Each group will be given a copy of the mailbox trails. 2) Trace the path on the trail and look for the message at the end of the trail. 3) Look for a card in the box and drop the answer in the correct mailbox from START. 4) Follow the arrow until you reach the FINISH LINE. Multiply the quotient and the divisor. Then add the remainder. If the answer is the same as the dividend, then the answer is correct. 80 ÷ 40 = N 63 ÷ 30 = N 990 ÷ 30 = N 680 ÷ 60 = N 500 ÷ 20 = N 623 ÷ 20 = N
- 25. 19 5) The first group to come up with the most number of correct answers will get the message from the teacher and wins the contest. The message is HAPPY MATHEMATICKING. 6) The teacher calls the attention of the pupils with divisors and dividends having terminal zeros. 7) Make them realize that computation will be easy if the terminal zeros in the divisor and dividend are cancelled first before dividing the numbers. The Mailbox Trail 3. Generalization What are the steps in dividing 2- to 3-digit numbers by multiples of 10? Step 1 – Divide. Step 2 – Multiply. Step 3 – Subtract. Step 4 – Compare and bring down. Step 5 – Repeat the procedure until all the digits in the dividend are divided. Step 6 – Check the answer by multiplying the quotient with the divisor. If there are terminal zeros in the divisor and dividend, what shall we do with them before dividing the numbers? Cancel the terminal zeros in the divisor and dividend. The number of zeros to be cancelled in the divisor and dividend must be equal.
- 26. 20 C. Application A. Write the answers on the blanks. 1. The divisor is 50. The dividend is 300. What is the quotient? ______ 2. In 625 ÷ 10, the quotient is ______. 3. The remainder in 865 ÷ 20 is ______. 4. The quotient is 30, the dividend is 900, what is the divisor? ______ 5. 800 ÷ 80 is ______. B. Read, analyze and solve 1. In a camp, a scoutmaster had 140 canned goods. He distributed the canned goods equally to 20 patrols. How many did each patrol have? 2. There are 240 boxes of chalk to be shared equally among 30 teachers. How many boxes will each teacher get? IV. Evaluation A. Solve the problem below. 1. If Ricky walked 240 metres in 20 minutes, how many metres did he walk in 1 minute? ________ 2. Rosa gathered 400 popsicle sticks to make flower vases. She used 40 popsicle sticks for each flower vase. How many flower vases did she make? ________ 3. Mr. Santos bought 60 pads of paper to be given to 30 poor children. If they will be given equal share, how many pads will each child get? 4. Mr. dela Cruz bought 500 mahogany seedlings. If the seedlings will be planted equally in ten rows, how many seedlings will each row have? 5. One hundred twenty Grade VI pupils will have a field trip. If there are 10 adults, how many pupils will each adult take care of? B. Find the quotients. 1) 20 40 2) 30 60 3) 10 50 4) 40 938 5) 50 750 6) 60 863 7) 30 586 8) 20 380 9) 10 89 10) 70 788 V. Assignment Divide. 1) 50 500 2) 30 630 3) 20 780 4) 20 690 5) 40 560
- 27. 21 Dividing 2- to 3-Digit Numbers by 1 to 2-Digit Numbers with Zero Difficulty I. Learning Objectives Cognitive: Divide 2- to 3-digit numbers by 1- to 2-digit numbers with zero difficulty Psychomotor: Write the division sentence in vertical column Affective: Eating the right kinds of food regularly II. Learning Content Skills: 1. Dividing 2- to 3-digit numbers by 1- to 2-digit numbers with zero difficulty 2. Writing the division sentence in vertical column Reference: BEC PELC I E 1.5 Materials: cut outs of stars, diagrams Value: Eating the right kind of foods III. Learning Experiences A. Preparatory Activities 1. Drill Light up each bulb mentally every time you get an exact quotient by dividing the middle number by the other number. 2. Review: Find the quotient and remainder if any. 1) 5 694 3) 6 917 5) 7 2561 2) 12 5871 4) 35 9645 3. Motivation Do you eat vegetables? What kind of vegetables do you like to eat most? Do you eat carrots? Why should you eat carrots? Don’t you know that carrots are good for our eyes? 12 8 4 24 3 25 96 40 10 5 3 28 72 8 4 3 96
- 28. 22 B. Developmental Activities 1. Presentation a. Present this problem. A farmer puts 30 carrots in 2 bags equally. How many carrots are in each bag? To solve the problem, follow these steps: ■ Understand Know what is asked. Number of carrots in each bag. Know the given facts. 30 carrots, 2 bags Know the word clue. each bag ■ Plan Decide what process to use. Division Draw a picture for the problem. Write the mathematical sentence. 30 ÷ 2 = N ■ Solve Solve the equation 30 ÷ 2 = 15 Write the complete answer 15 carrots Answer: There are 15 carrots in each bag. 30 carrots 15 15 carrots in each bag Step 1 2 1 2 30 10 Step 2 2 15 2 30 10 - 10 0 Divide 3 ÷ 2 = 1 Write 1 in the tens place Multiply 1 x 2 = 2 Subtract 3 – 2 = 1 Bring down 0 Divide 10 ÷ 2 = 5 Write 5 in the ones place Multiply 5 x 2 = 10 Subtract 10 – 10 = 0
- 29. 23 ■ Look back See if the answer makes sense. Check by multiplying. Multiplying 2 by 15 gives 30. There are 15 carrots in each bag. b. Present another problem. An auditorium has 240 seats in all. If there were 12 rows of seats, how many seats were there in each row? To solve the problem, follow these steps ■ Understand Know what is asked. Number of seats in each row Know the given facts. 240 seats, 12 rows Know the word clue. each row ■ Plan Decide what process to use. Division Write the mathematical sentence. 240 ÷ 12 = N ■ Solve Solve the equation. 240 ÷ 12 = 20 Step 1 12 2 24 240 0 Step 2 12 20 24 240 00 - 0 0 Write the complete answer: there are 20 seats in each row. Each time you bring down a digit, you must write a digit in the quotient. Sometimes that digit is zero. ■ Check and Look back See if the answer makes sense. Check by multiplying. Multiplying 12 by 20 gives 240. There are 20 seats in each row. 2. Guided Practice a. Write the missing numeral in each step on your paper. 1. Step 1 Step 2 5 15 160 5 15 160 1 10 Divide 24 tens by 12 = 2 tens. Write 2 in the tens place. Multiply 2 x 12 = 24 Subtract 24 – 24 = 0 Bring down 0. Divide 0 ÷ 12 = 0 Write 0 in the ones place. Multiply 2 x 12 = 0 Subtract 0 – 0 = 0 __ x 5 __ x 5
- 30. 24 - 10 0 2. Step 1 Step 2 7 7 105 7 7 105 3 35 - 35 0 3. Step 1 Step 2 Step 3 3 3 306 3 3 306 3 3 306 0 0 0 - 0 - 0 6 6 - 6 4. Step 1 25 50 51 1 5. Step 1 Step 2 8 72 720 8 72 720 0 0 - 0 __ b. Food Facts These food facts may or may not be true! Divide and decide if the quotient is true or false. If the quotient is true, then the fact is true! 1. The shape of a pretzel was invented by a priest who gave “pretzels to children when they memorized prayers. 90 ÷ 3 = 30 True False 2. Cracker Jack was the brainchild of a man named Jack Cracker, who invented the snack after some popcorn got stuck in his tooth. 208 ÷ 12 = 16 r.4 True False 3. Hot dogs can be traced back 3,500 years ago, when Babylonians stuffed animal intestines with spicy meat. 950 ÷ 5 = 190 True False 4. Pasta was first made in China from rice and bean flour. 700 ÷ 15 = 46 r.10 True False 5. Ketchup became popular when Alice White dropped a tomato and dipped some French fries in the juice. 560 ÷ 3 = 186 r.1 True False __ x 3 __ x 3 __ x 3 __ x 25 r. 1 __ x 8
- 31. 25 c. Discover the message. Use the letter code. 40 ÷ 8 = a 120 ÷ 12 = n 80 ÷ 2 = f 830 ÷ 12 = s 401 ÷ 16 = h 607 ÷ 11 = t 300 ÷ 5 = i 302 ÷ 3 = u 760 ÷ 9 = m M A T H I S F U N 84 R.4 5 55 R.2 25 R.1 60 69 R.2 40 100 R.2 10 3. Generalization: How do we divide 2- to 3-digit numbers by 1- to 2-digit numbers with zero difficulty? C. Application A. Fill in the missing numerals. 1) 5 0 20 200 2) 4 4 50 3) 8 24 306 0 10 66 - 0 - 8 - 64 0 __ __ 4) 16 32 420 5) 23 46 508 100 48 - 96 - 46 __ 2 B. Read, analyze and solve 1. If I divide 40 pupils in groups of 8, how many groups shall I form? 2. If you separate 81 desks into rows with 27 desks each, how many rows will you have? 3. Mico had 144 stamps. He pasted them on 12 pages of his album, how many stamps did he place on each page? r.__ r.__ r.__ r.__ In dividing whole numbers divide multiply subtract bring down if the dividend is less than the divisor put zero.
- 32. 26 IV. Evaluation A. Find the quotient. 1) 3 60 2) 11 403 3) 4 500 4) 12 860 5) 21 701 B. Solve the following problems: 1. The 150 Grade Three pupils were divided into 6 equal groups to participate in a dance contest. How many pupils were there in each group? 2. A class of 60 pupils was divided into 3 equal groups to participate in different activities for the “Clean and Green” project of their barangay. How many pupils were in each group? 3. Imon and Bato harvested 109 pieces of camote. They placed them equally in 15 baskets. How many pieces of camote were in each basket? 4. There are 360 books to be given equally among 4 classes. How many books will be given to each class? 5. Arnel place 70 books equally in 5 shelves. How many books were in each shelf? V. Assignment A. Divide. 1) 13 80 2) 5 600 3) 11 780 4) 22 220 5) 15 301 B. Solve. 1) (88 – 8) ÷ 4 2) (765 + 44) ÷ 32 3) (149 + 11) ÷ 8 4) (15 x 8) ÷ 4 5) (500 x 3) ÷ 13 C. Divide then check the answer. 1) 4 800 2) 8 90 3) 14 620 4) 11 403 5) 21 610 Dividing 3- to 4-Digit Numbers by 1- to 2-Digit Numbers without Remainder I. Learning Objectives Cognitive: Divide 3- to 4-digit numbers by 1- to 2-digit numbers without remainder Psychomotor: Write division equation correctly. Affective: Practice eating the right kind of foods.
- 33. 27 II. Learning Content Skills: Dividing 3- to 4-digit numbers by 1- to 2-digit numbers without remainder Writing division equation correctly. Reference: BEC PELC I E 1.4.1 Materials: Show me board, wheel card, cut-outs of fruits/baskets Value: Being healthy III. Learning Experiences A. Preparatory Activities 1. Drill: Basic Division Facts Write the quotients in the outer circle. 2. Review – Dividing 2 to 3-digit numbers by 1-digit divisor Divide the following numbers. Use “Show-Me-Board.” 1) 2) 3) 4) 5) 6) 3. Motivation Present a problem opener. Anne bought 120 mangoes in the market. She placed the mangoes equally in 3 baskets. How many mangoes were placed in each basket? B. Developmental Activities 1. Presentation a. Ask: Who bought mangoes? How many mangoes did she buy? Where did she place the mangoes? Why do you think Anne bought mangoes? Is it good to eat mangoes? Why? 36 ÷ 2 = 39 ÷ 3 = 51 ÷ 3 = 44 ÷ 4 = 86 ÷ 2 = 64 ÷ 2 =
- 34. 28 a. Solve the problem using the 4 steps in problem solving. ■ Understand the problem Where did Anne buy mangoes? How many mangoes did she buy? How many baskets did she use? How many mangoes were placed in each basket? What process are we going to use? ■ Make a plan What operation will solve the problem? ■ Carry out the plan Ask a pupil to write the number sentence: 120 ÷ 2 = N Activity 1 1) Divide the class into 4 teams. 2) Each team will show the solution by using paper cut outs of mangoes and baskets. Answer: Each basket will have 60 mangoes. Did each team get the correct answer? Prove your answer. Activity 2 Solve the problem in another way using expanded notation: How many hundreds are there in 120? How many tens are there? How many ones are there? 120 ÷ 2 = 2 01050 020100 ■ Look back: Is the answer correct? What should be the correct label? Let us try to solve the problem using another way. Step 1 2 6 12 120 0 Step 2 2 60 12 120 0 0 0 Answer: 60 mangoes were placed in each basket. = 60 mangoes Divide the tens. 12 tens ÷ 2 = 6 tens Write 6 in the tens place Multiply: 6 x 2 = 12 Write 12 under 12. Subtract 12 – 12. Bring down 0. Divide the ones. 0 ones ÷ 2 = 0 ones Write 0 in the ones place. Multiply: 0 x 2 = 0 Write 0 under 0. Subtract 0 – 0 = 0.
- 35. 29 To check: Multiply: 60 quotient x 2 divisor 120 dividend b. Give more examples. a) 2 171 2 342 b) 12 46 48 552 c) 6 1609 6 9654 d) 21 352 63 7392 14 72 36 109 14 72 36 105 2 0 5 42 2 0 42 0 54 0 54 0 2. Guided Practice a. Work in groups of four. Divide: Fill in the blank with the correct number. Do this on your paper. 1) 4 664 - 4 (4 x 1) - _ (4 x 6) - _ (4 x 6) 2) 15 375 - 30 (15 x 2) - _ (15 x 5) 3) 3 5868 - 3 (3 x 1) - _ (3 x 9) - _ (3 x 5) - _ (3 x 6) 4) 32 9984 - 96 (32 x 3) - _ (32 x 1) - _ (32 x 2)
- 36. 30 Work in pairs: (Dyads) Solve the number problem in each box. Then find the answer written in the cut outs of apples. Place the apples in their correct box. 1) a. 684 2) b. 15 3) c. 377 4) d. 193 5) e. 53 f. 25 3. Generalization What should you remember in dividing 3- to 4-digit numbers by 1- to 2-digit divisor? To divide 3- to 4-digit numbers by 1- to 2-digit divisor: Step 1: Take the first number at the left of the dividend. If the first digit of the dividend is less than the divisor, take the first two digits. Step 2: Divide, multiply, subtract and bring down. Repeat the same procedure up to the last digit in the dividend. To check the answer: Multiply the quotient by the divisor The answer is correct if the product is equal to the dividend. 386 ÷ 2 195 ÷ 13 4788 ÷ 7 9425 ÷ 25 636 ÷ 12
- 37. 31 C. Application Analyze the table below. Divide the given numbers to find the number of trays to be used if each tray holds 12 eggs. Then complete the table with the correct answers. 360 432 1 524 1 008 8 940 eggs eggs eggs eggs eggs IV. Evaluation A. Divide each number problem. Check if the quotient is correct. Write True if it is correct and False if it is not. 1) 596 ÷ 4 = 149 2) 975 ÷ 15 = 95 3) 1 234 ÷ 2 = 617 4) 5 682 ÷ 21 = 362 5) 4 806 ÷ 54 = 89 B. Analyze and solve 1. 620 divided by 25. What is the result? 2. What is the quotient of 896 divided by 16? 3. How many 27 are there in 1245? C. Solve each problem. 1. Alyssa has a vegetable garden in their farm. If she planted 819 okra seeds in 9 rows. How many seeds were in each row? Answer: ___________ 2. Father gathered 1 500 guavas. He placed them equally in 12 baskets. How many guavas were there in each basket? Answer: ___________ V. Assignment A. Complete the division problem by putting the correct number in each circle. 1. 2 432 2. 27 1134 3. 4 6352 - _ - _ - _ 3 54 23 - _ - 54 - _ 12 0 35 - 12 - _ 0 32 - 32 0
- 38. 32 B. Divide and check: 1) 5 535 2) 21 630 3). 52 7904 4). 78 7644 Dividing 3- to 4-Digit Numbers by 1- to 2-Digit Numbers with Remainder I. Learning Objectives Cognitive: Divide 3- to 4-digit numbers by 1- to 2-digit numbers with remainder Psychomotor: Perform division of whole numbers with accuracy Affective: Practice the habit of sharing and being friendly II. Learning Content Skill: Dividing 3- to 4-digit numbers by 1- to 2-digit numbers with remainder Reference: BEC PELC I E 1.4.2 Materials: real objects (popsicle sticks), flash cards, chart Value: Friendliness/Kindness III. Learning Experiences A. Preparatory Activities 1. Drill – Basic Division Facts The teacher will show a chart containing division number problems. Message in the Boxes 56 ÷ 8 40 ÷ 8 50 ÷ 5 54 ÷ 6 32 ÷ 8 A 7 E 5 H 10 O 9 R 4 48 ÷ 6 15 ÷ 5 6 ÷ 6 18 ÷ 9 36 ÷ 6 S 8 T 3 U 1 W 2 Y 6 2 9 2 3 10 7 3 8 1 4 5 2 7 8 W O W T H A T S U R E W A S 5 7 8 6 E A S Y For the teacher: To decode the message in the boxes, let the children answer the division problems. Match the answer with the letters. Write the letters under the answers and form the message.
- 39. 33 2. Review: Terms used in divisions of whole numbers. The teacher distributes strips of paper with questions. The pupils take turns in getting a strip of paper and answer the question. a. In 488 ÷ 8 = 61 what do we call 488? 8? 61? b. Which number should be greater, the divisor or the dividend? c. To check if our answer in division is correct, what shall we multiply? d. To find the divisor, what shall we do with the dividend and quotient? e. What do we call the left over number after all the digits in the dividend were divided? 3. Motivation Present a word problem. Henry collected 152 popsicle sticks. He distributed the sticks to his 9 friends equally. How many sticks did each of his friends get? How many were left? B. Developmental Activities 1. Presentation a. Comprehension check-up ● Who picked popsicle sticks? ● What did he do with the sticks? ● What character traits did Henry show? ● Is it good to share what you have with your friends? Why? Activity 1: Role Playing ● Ask a pupil to get 152 sticks. Then tell him to call 9 of his friends. Ask him to distribute the sticks to them. How many sticks did each of his friends receive? Did each child get equal number of sticks? Were there sticks left? How many sticks were left? b. Let us solve the problem using Polya’s 4 steps in problem solving. ■ Understand the problem a. How many sticks did Henry collect? b. How many friends had he? c. What process are we going to use?
- 40. 34 ■ Plan Decide what operation will be used to solve the problem. ■ Carry Out the Plan Write the number sentence. 152 ÷ 9 = N Activity 2: (Short Form Method) Let’s solve the problem using another way: Step 1: 9 1 9 152 62 Step 2: 9 16 9 152 62 54 8 Answer: 16 r. 8 popsicle sticks ■ Look back To check: multiply 16 quotient x 9 divisor 144 + 8 remainder 152 dividend c. Give more examples 1) 5 151 5 756 2) 12 540 60 6487 3) 7 1423 7 9962 25 48 29 25 48 28 6 7 16 5 0 14 1 7 22 21 1 Check: Check : Check: 151 540 1423 x 5 x 12 x 7 755 1080 9961 + 1 540_ + 1 756 6480 9962 + 7 6487 Divide: 15 ÷ 9 = 1 Write 1 in the tens place. Multiply: 1 x 9 = 9 Write 9 under 15. Subtract: 15 – 9 = 6 Bring down 2. Divide: 62 ÷ 9 = 6 Write 6 in the ones place. Multiply: 9 x 6 = 54 Write 54 under 62. Subtract: 62 – 54 = 8 Is there any remainder? What is the remainder? r. 8 Is the answer reasonable?
- 41. 35 2. Guided Practice a. Work by teams. 1. Each team will be given an activity card to work on. The team who will get the most number of correct answers wins. Activity Card: Read and understand each question. Write your answers on a sheet of paper. 1. What is the remainder if we divide 956 by 8? ______ 2. Divide 543 by 42. 3. 21 278 4. 15 305 5. 12 604 B. Work in groups of four: (Chalkboard Challenge) 1. Each would be given a challenge. 2. Solve the challenge on the chalkboard. 3. The first group to finish with the right answers wins. 1) 3) 2) 3. Generalization: How do we divide 3 to 4-digit numbers by 1 to 2-digit divisors with remainder? What do we do with the remainder? How do we check if the answer is correct? Remember: To divide 3- to 4-digit numbers by 1- to 2-digit divisors with remainder: Start dividing digit with the highest place value. If it is less than the divisor take the next digit. Then multiply, subtract and bring down. Repeat the same procedure up to the last digit of the dividend. Indicate the remainder in the quotient. To Check Multiply the quotient by the divisor. Add the remainder, to get the complete answer. 546 ? ÷ 9 3453 ? ÷ 8 3942 ? ÷ 32
- 42. 36 C. Application A. Divide and check: 1) 8 642 2) 13 9678 3) 21 439 4) 5 7638 5) 36 4989 B. Analyze and solve 1) If we divide 565 by 15 what will be the remainder? 2) What will be the remainder in 2079 ÷ 11? 3) 2436 divided by 48 will give you a remainder of ______. IV. Evaluation Find the quotient and the remainder. Then complete the table below. Number Problem Quotient Remainder 1) 639 ÷ 4 = _____________ ______________ 2) 948 ÷ 25 = _____________ ______________ 3) 7631 ÷ 8 = _____________ ______________ 4) 6349 ÷ 14 = _____________ ______________ 5) 7872 ÷ 28 = _____________ ______________ V. Assignment Read and analyze the problem. Answer the questions that follow: There were 1479 pupils in Dinalupihan Elementary School. They were divided equally into 12 groups for “Share for a Cause” school activity. How many pupils were there in each group? How many pupils were left to join any of the groups? 1. What process is involved in the problem? _________________________ 2. Write the number sentence. _________________________ 3. Solve the problem. _________________________ 4. Is there a remainder? What is the remainder? _________________________ Dividing 3- to 4- Digit Numbers by 2- to 3-Digit Numbers with Zero Difficulty I. Learning Objectives Cognitive: Divide 3- to 4-digit numbers by 2- to 3-digit numbers with zero difficulty Psychomotor: Write division sentences in different ways. Affective: Show politeness while answering.
- 43. 37 II. Learning Content Skills: 1. Dividing 3- to 4-digit numbers by 2- to 3-digit numbers with zero difficulty 2. Writing division sentences in different ways. Reference: BEC PELC I E 1.6.3 Materials: crayons, flash cards, show me card, diagrams, number cards Value: Politeness III. Learning Experiences A. Preparatory Activities 1. Drill Direction: For the teacher a. The teacher distributes number cards to the pupils cut from old calendars. b. She shows a number chart on the board. (See number chart below.) c. The pupils analyze the number chart. d. Those holding the correct number card for each of the number problems will place the card under the appropriate numbers. ÷ 12 15 18 21 24 ÷ 8 12 16 20 24 28 32 36 3 4 4 ÷ 10 15 20 25 30 35 45 5 ÷ 6 12 18 24 30 36 42 6 2. Review a. Divide the following numbers. b. Pupils will solve for the answer on the “show me card.” 1) 2 90 2) 13 405 3) 11 308 4) 6 203 5) 9 400 3. Motivation Have you gone on a field trip? What did you take to reach the place? (bus, jeeps) B. Developmental Activities 1. Presentation a. Present this problem. A group of 2 860 pupils went on a field trip. Their teacher hired some buses to transport them. Each bus can carry 55 pupils. How many buses were hired?
- 44. 38 To solve the problem, follow these steps: ■ Understand a. Know what is asked. number of hired buses. b. Know the given facts. 2 860 pupils, 55 pupils c. Know the word clue. each bus ■ Plan a. Decide what process to use. division b. Write the mathematical sentence. 2860 ÷ 55 = N ■ Solve Solve the equation. 2860 ÷ 55 = 52 Step 1 55 5 275 2860 11. Step 2 55 52 275 2860 110 - 110 0 Complete answer There are 52 buses hired. ■ Check and Look Back Does your answer make sense? Check by multiplying Multiplying 55 by 52 gives 2 860. There are 52 buses hired. b. Present another problem. Mrs. de Castro has 207 pencils to be given to her pupils. There are 29 pupils. How many pencils can she give to each pupil? To solve the problem, follow these steps: ■ Understand a. Know what is asked. number of pencils to be given to each pupil. b. Know the given facts. 207 pencils, 29 pupils c. Know the word clue. each pupil ■ Plan a. Decide what process to use. division b. Write the mathematical sentence. 207 ÷ 29 = N Divide 286 ÷ 55 = 5 Multiply 5 x 55 = 275 Subtract 286 – 275 = 11 Bring down 0. Divide 110 ÷ 55 = 2 Multiply 2 x 55 = 110 Subtract 110 – 110 = 0
- 45. 39 ■ Solve Solve the equation Step 1 29 7 203 207 4 Step 2 29 7 203 207 4 Answer: Each pupil was given 7 pencils and there were 4 pencils left. ■ Check and Look Back Does you answer make sense? Check. Multiplying 7 by 29 gives 203. Adding 203 and 4 gives 207. Each pupil was given 7 pencils. There are still 4 pencils left to Mrs. de Castro. c. Give more examples 1) 3 253 6 760 2) 12 174 12 2090 3) 23 217 46 5000 16 . 89 40 - 15 . - 84 - 23 10 50. 170 - 9 - 48. - 161 1 2. 9 2. Guided Practice (Dyads) a. Write the missing numerals in the boxes. 1) 15 03 054 2) 12 61 102 - _ _ - _ _ 0 _ 1 - 0 - _ _ 0 _ Divide 207 ÷ 29 = 7 Multiply 7 x 29 = 203 Subtract 207 – 203 = 4 Write the remainder.r. 4 r. 1 r. 2 r. 9 Check: 30 x 15 ___ Check: 16 x 12 ___ + ___ ___ r. 9
- 46. 40 3) 25 221 7603 - _ _ _ 6 - _ _ _ _ - _ _ _ _ 4) 12 424 2905 5) 32 432 3057 - _ _ - _ _ 2 9 1 1 0 - _ _ - _ _ _ _ _ _ 3 . - _ _ - _ _ _ . 4 15 b. Work in group with 4 members. Divide. Use the code. Match your answers with the letters. Write the answers on the lines. Read the message. 1) 10 3005 2) 11 5011 3) 13 9046 4) 16 475 5) 35 7008 6) 21 2036 7) 20 750 8) 43 658 CODE O O O G R W D K 96 r. 20 695 r. 11 455 r. 6 300 r. 5 37 r. 10 200 r. 8 29 r.11 15 r.13 ____ ____ ____ ____ ____ ____ ____ ____ Answer: Good Work c. Triads Division Patterns Directions: 1. Solve the division problems. 2. Then color the squares. 3. Look for the pattern created by the answers. Check: 122 x 25 ___ + ___ ___ r. 17 Check: 424 x 12 ___ + ___ ___ Check: 234 x 32 ___ + ___ ___ r. 15r. 4 402 ÷ 24 3 060 ÷ 21 300 ÷ 12 7 302 ÷ 35 280 ÷ 14 6 001 ÷ 31
- 47. 41 Color the squares below that answer the division problems. 38 r. 9 16 r. 18 208 r. 22 145 r. 15 140 r. 7 475 r. 3 75 r. 3 20 251 196 r. 28 280 25 365 r. 8 68 r. 5 901 193 r. 18 473 175 r. 21 32 r. 1 175 r. 5 What pattern do the colored squares make? _______ (ans. Figure 9) 3. Generalization: How do we divide whole numbers with zero difficulty? Stress politeness while answering. In dividing whole numbers with zero difficulty Follow the steps in dividing whole numbers. a. Divide, multiply, subtract, bring down (Repeat the same procedure until all digits in dividend are divided.) Write 0 in the quotient if the trial dividend is less than the divisor. Check you answer by multiplying the quotient by the divisor. - Add the remainder if needed. C. Application A. Find the missing digits. 4 030 ÷ 23 6 300 ÷ 32 4 200 ÷ 15 7 603 ÷ 16
- 48. 42 1) 42 252 260 2) 12 84 905 __ 65 - 60 __ 3) 11 33 4003 4) 32 64 6502 70 10 - 66 - 0 4_. 102. - 33. - 96. 10. 6. 5) 12 72 8061 86 - 84 _1 - 12 9 B. Read, analyze and solve A well-known cap company made 3 436 caps and put the same number of caps in 36 boxes. a. How many caps are there in each box? b. If 20 more caps were added how many caps are there in each box? IV. Evaluation 4 Groups It’s Trivia Time. Directions Divide the equations inside each box. Then use the code below to answer the question. CODE P N M A T O U 48 r. 14 105 13 r. 5 168 r. 27 83 r. 35 352 r. 8 500.8 10 5008 15 200 21 7400 20 2100 36 3023 r. __ r. __ r. 10 r. __ r. 9 What is the tallest mountain in the Philippines?
- 49. 43 42 7083 17 830 21 7400 Answer: Mount Apo Divide the following. 1) 14 906 2) 14 340 3) 21 1660 4) 20 8302 5) 15 2170 V. Assignment A. Divide and check by multiplying 1) 14 603 2) 25 750 3) 19 1203 4) 24 6709 5) 11 3201 B. Solve the following problems. 1. Miss Caponpon distributed 302 squares of cloth equally among 16 girls to make a table cover. How many squares of cloth did each girl get? 2. Each box contains 12 handkerchiefs. If 1260 handkerchiefs were placed in boxes, how many boxes were used? 3. There are 4660 peanuts to be packed in 14 boxes. Each box will contain the same number of peanuts. How many peanuts will there be in each box? Dividing Whole Numbers by 5 I. Learning Objectives Cognitive: Divide whole numbers by 5 Psychomotor: Write division facts with 5 as divisor Affective: Cooperate actively in the activities II. Learning Content Skills: 1. Dividing whole numbers by 5 2. Counting by 5’s (forward and backward) Reference: BEC PELC I E 2 Materials: cut outs of leaves, pocket charts, flash cards Value: Cooperation
- 50. 44 III. Learning Experiences A. Preparatory Activities 1. Drill Supply the missing number in series. a. 5 ___ 15 20 ___ 30 35 ___ 45 ___ 55 ___ 65 ___ 75 80 ___ 90 ___ ___ b. Count backward. Start at 50. 50 45 40 35 30 25 20 15 10 5 2. Review – Checking of Assignment 3. Motivation Divide the class into 4 groups. Give each group an envelope with the strips. The pupils will be looking for the card that represents 5. Then they will put them in the pocket chart. The first to complete the set will win the game. Give time limit. -Cards inside the envelope- B. Developmental Activities 1. Presentation At the summer camp, children share happy times singing their favorite songs. Sometimes they take turns singing in groups. Around the campfire, 20 campers are singing in groups of 5. How many groups of 5 are there? Let us analyze and solve the problem. ■ Read a. What is asked in the problem? How many groups of 5 are there? b. What are the given facts? 20 campers, 5 groups c. What is/are the word clue/s? groups of 5 ■ Plan a. What is the operation needed? Division b. What is the mathematical sentence? 20 ÷ 5 = N V 8 x 3 9 - 4 7 - 3 6 - 1 2 + 3 IIII IV 4 + 1 5 ones 6 + 3 5 x 1 2 + 8
- 51. 45 ■ Do Activity 1: ACTING OUT - Call out 20 pupils from the class. - Let them group themselves into 5. - How many pupils were there in each group? (4) Activity 2: SHORT CUT METHOD 20 ÷ 5 = 4 or 5 4 20 20 0 ■ Check 1. Think: 20 campers, 5 in a group. There are 4 groups. 4 groups of 5 equals 20, or 4 x 5 = 20 so 20 ÷ 5 = 4 5 4 20 There are 4 groups of campers. 2. Give another example. Write a division fact for each. a. 25 campers 5 in each group How many groups are there? (25 ÷ 5 = 5) b. 40 campers 5 in each group How many groups are there? (40 ÷ 5 = 8) c. 60 mangoes 5 in each basket How many are in each basket? (60 ÷ 5 = 12) d. 90 marbles 5 in each box How many are in each box? (90 ÷ 5 = 18) 2. Guided Practice (Dyads) Give cut outs of the leaves to each pair. Tell them to write the correct quotient for each on their show me board. groups
- 52. 46
- 53. 47 Play the game blockbuster using the game board below. Direction 1. Divide the class into two groups. Assign a colored marker to each group. One group will use blue markers, the other group, red markers. Have a representative from each group toss a die. The group who gets the highest number play first. 2. The first team member chooses a slot on the game board and answers the division sentence. If his/her answer is correct, he/she places his/her group’s marker on the game board. The play continues with the next team member as long as the answer is correct. If a wrong answer is given the other team will have the chance to play. 3. The first team to make a chain of correct answers from end to end (whether from top to bottom or side to side) wins the game. 50 ÷ 5 10 ÷ 5 100 ÷ 5 40 ÷ 5 75 ÷ 5 45 ÷ 5 750 ÷ 5 35 ÷ 5 30 ÷ 5 55 ÷ 5 15 ÷ 5 65 ÷ 5 85 ÷ 5 90 ÷ 5 5 ÷ 5 10 ÷ 5 95 ÷ 5 300 ÷ 5 425 ÷ 5 500 ÷ 5 20 ÷ 5 60 ÷ 5 80 ÷ 5 25 ÷ 5 130 ÷ 5 140 ÷ 5 3. Generalization: How do you divide whole numbers by 5? Dividing whole numbers by 5 is like counting by 5. C. Application A. Divide 1) 30 ÷ 5 = __ 2) 35 ÷ 5 = __ 3) 5 ÷ 5 = __ 4) 15 ÷ 5 = __ 5) 5 20 6) 5 40 7) 5 10 8) 5 45 9) 5 90 10) 5 120
- 54. 48 B. Find the missing input or output DIVIDE BY 5 INPUT OUTPUT 25 5 ___ 8 60 ___ 95 ___ ___ 33 IV. Evaluation A. Write a division fact for each 1. 30 campers 5 in each group How many groups? 2. 45 campers 5 in each group How many groups? 3. 115 rubber bands 5 in each box How many boxes of rubber bands? 4. 180 shells 5 in each group How many groups? 5. 300 mangoes 5 in each plastic bag How many plastic bags of mango? B. Write division facts for each. 1) 4, 5, 20 2) 3, 5, 15 3) 5, 7, 35 4) 5, 16, 130 5) 245, 49, 5 V. Assignment 1. Write a division fact with 5 as the divisor and 8 as the quotient. What is the dividend? Explain how you did it? 2. Draw a picture to solve this problem. There are 30 campers in 5 tents. Each tent has the same number of campers. How many campers are in each tent? Dividing Whole Numbers by 10 and 100 I. Learning Objectives Cognitive: Divide whole numbers by 10 and 100 Psychomotor: Cancel the same number of zeros from both the divisor and dividend Affective: Help each other in doing the group activities
- 55. 49 II. Learning Content Skills: 1. Dividing whole numbers by 10 and 100 2. Canceling the same number of zeros from both the divisor and the dividend Reference: BEC PELC I E 3 Materials: roulette, diagrams Value: Helpfulness III. Learning Experiences A. Preparatory Activities 1. Drill Spin a wheel then multiply. 2. Review Divide the class into 2 groups. Let each group compete by spinning the roulette with multiples of 10 and 100. The first group works on multiples of 10, the second group on multiples of 100. The first group to finish wins the game. Write these on the board. Ask the pupils to write the indicative multiples inside the box. Multiples of 10 Multiples of 100 3. Motivation (Problem Opener) The Tulungan Credit Union granted loans of 5 000 to its member-farmers. If the loans were paid by the farmers in equal monthly payments, how much would each pay for: a. 10 monthly payments? b. 100 monthly payments? B. Developmental Activities 1. Presentation What is the name of the union? In your place, do you also have a credit union? What help does credit union can give to its members? How much was the loan granted by Tulungan Credit Union to its members?
- 56. 50 Let us analyze and solve the problem. ■ Read a. What is asked in the problem? number of payments for 10 equal monthly payments 100 equal monthly payments b. What are the given facts? 5 000 loan granted 10 equal monthly payments, 100 equal monthly payments c. What are the clue words? equal monthly payments ■ Plan d. What operation is needed to solve the problem? division e. What is the mathematical sentence? 5 000 ÷ 10 = N 5 000 ÷ 100 = N ■ Do 5 000 ÷ 10 = N Step 1 10 5 50 5000 0 Step 2 10 50 50 5000 0 - 0 0 Step 3 10 500 50 5000 0 - 0 0 - 0 0 5000 ÷ 100 = N Long Method Divide: 50 ÷ 10 = 5 Multiply: 5 x 10 = 50 Subtract: 50 – 50 = 0 Bring down zero in the tens place. Divide: 0 ÷ 10 = 0 Multiply: 0 x 10 = 0 Subtract: 0 – 0 = 0 Bring down zero in the ones place. Divide: 0 ÷ 10 = 0 Multiply: 0 x 10 = 0 Subtract: 0 – 0 = 0
- 57. 51 Step 1 100 5 500 5000 0 Step 2 100 50 500 5000 0 - 0 0 Cancel 1 zero in the dividend and the divisor. 5 000 ÷ 10 500 ÷ 1 = 500 5 000 ÷ 100 = NCancel 2 zeros 5 000 ÷ 100 50 ÷ 1 = 50 Remember: Cancel the same number of zeros from the dividend and the divisor. Answer: Each monthly payment was a.) 500 b.) 50 ■ Check: Did you copy the numbers from the problem correctly? Did you follow the correct steps? Is your answer reasonable? Since 500 x 10 = 5 000 and 50 x 100 = 5 000, the answers are reasonable. Other examples: Cancel zeros from both the dividend and the divisor. 4 200 ÷ 100 = 42 390 ÷ 10 = 39 7 800 ÷ 10 = 780 8 000 ÷ 100 = 80 2. Guided Practice a. Follow the number paths. Work in pairs (Stress the value of helpfulness.) 1. 2. Divide: 500 ÷ 100 = 5 Multiply: 5 x 100 = 500 Subtract: 500 – 500 = 0 Bring down zero. Divide: 0 ÷ 100 = 0 Multiply: 0 x 100 = 0 Subtract: 0 – 0 = 0 Short Cut Method 300 START 30 0÷ 10 X 10 ÷ 100 X 10 ? END 700 START X 10 ÷ 100 ÷ 10 ? END x 100
- 58. 52 3. 4. 5. b. Work in Group (4 groups) SPOT THE QUOTIENTS Directions: Solve then encircle the answer in the box. The answers may go down, backward, across and diagonally. 2 4 0 0 9 1 6 6 2 9 5 4 3 3 5 7 7 8 6 8 6 7 4 3 9 3 4 6 4 7 8 8 5 2 6 0 0 7 5 0 1 1 4 8 5 2 5 8 1 2 0 4 0 0 0 1 4 7 4 1 5 9 3 6 1 7 1 5 1 9 9 1 5 4 0 6 6 8 6 0 1 ? START X 10 ÷ 100 ÷ 10 2000 END x 100 2500 START X 10 ÷ 100 ÷ 10 ? END ? START X 10÷ 100 ÷ 10 8000 END ÷ 100 10 360 100 8000 10 7500 1000 456000 100 73800 100 24000 100 48500 10 2800 10 4000 10 660 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
- 59. 53 c. Solve each problem. (Four in each group) 1. Four hundred ninety pupils are going on a field trip. They will be distributed into 10 buses. How many pupils will be in each bus? 2. One thousand four hundred books are to be packed in 100 boxes. How many books will be packed in each box? 3. There are 730 mangoes to be placed equally in 10 baskets. How many mangoes will be in each basket? 4. There are 3 000 kilos of rice to be distributed among 100 typhoon victims. How many kilos of rice will each victim receive? 5. There are 11 000 fingerlings (young fish) to be evenly placed in 10 fish ponds. How many fingerlings will be in each pond? 3. Generalization: How do we divide whole numbers by 10 and 100? To divide whole numbers by 10 and 100, cancel the same number of zeros in both the dividend and the divisor. Divide. C. Application A. Find the quotient. Cancel the correct number of zeros. 1) 400 ÷ 100 4) 9 300 ÷ 100 2) 1 800 ÷ 100 5) 620 ÷ 10 3) 2 900 ÷ 10 B. Analyze and solve 1) How many 100 are there in 600? 2) Two thousand and five hundred has how many hundreds? 3) 5 000 is how many hundreds? 4) How many hundreds are there in 4 900? 5) 400 is equal to how many tens? IV. Evaluation A. Give the missing number. 1) 650 ÷ 10 = _______ 2) 3 900 ÷ ___ = 39 3) 7 800 ÷ ___ = 78 4) 2 000 ÷ ___ = 200 5) 180 ÷ ___ = 18 B. Divide and check by multiplication. 1) 100 5200 2) 100 8500 3) 100 9000 4) 10 6000 5) 10 3570
- 60. 54 V. Assignment A. Divide mentally. Write the quotients 1) 630 ÷ 10 = _____ 2) 5400 ÷ 100 = ____ 3) 480 ÷ 10 = ____ 4) 63000 ÷ 100 = ____ 5) 3600 ÷ 10 = ____ B. Solve each problem 1) There were 3 400 sacks of sand donated to Barangay Matulungin for the repair of its foot bridge. If there were 100 donors, how many sacks of sand did each one donate? 2) A sack of cement costs 100. How many sacks can one buy with 6 200? 3) If the 3 400 sacks were used by 10 groups of workers, how many sacks did each group use? 4) Operation Pagtatanim distributed 8 400 different kinds of seedlings equally among 10 elementary schools. How many seedlings did each school receive? 5) Edgar has 230 as school allowance for 10 days. How much is his daily allowance? Dividing Mentally 2-Digit Numbers through 99 by 1-Digit Number without Remainder I. Learning Objectives Cognitive: Divide mentally 2-digit numbers through 99 by 1-digit number without remainder Psychomotor: Solve word problems involving division mentally Affective: Show accuracy in solving mentally II. Learning Content Skills: 1. Dividing mentally 2-digit numbers through 99 by 1-digit number without remainder 2. Solving word problems involving division mentally Reference: BEC PELC I E 1.5 Materials: counters, roulette, flash cards Value: Accuracy III. Learning Experiences A. Preparatory Activities 1. Drill Have a drill on basic division facts. 1) 36 ÷ 9 2) 42 ÷ 6 3) 7 ÷ 7 4) 49 ÷ 7 5) 9 ÷ 0 6) 5 ÷1
- 61. 55 2. Review Spin any of the roulettes. Then multiply. Give the factors. 36 = ___ x ___ 63 = ___ x ___ 72 = ___ x ___ 48 = ___ x ___ 3. Motivation (Use the counters-pebbles) How many ways can you group equally 24 pebbles. B. Developmental Activities 1. Presentation a. Miss Rosas distributed 48 Math books equally among the 4 rows in her class. How many books were given to each row?
- 62. 56 - What did Miss Rosas do? - How many rows were there in her class? - How many Math books were distributed? - How will you solve this problem? You can divide 48 by 4 mentally. Rename 48 as 40 + 8 40 ÷ 4 = 10 divide the tens 8 ÷ 4 = 2 divide the ones 10 + 2 = 12 add the answer Answer: Twelve (12) Math books were given to each row. b. A farmer puts 36 carrots in 2 bags. He puts the same number in each bag. How many carrots are in each bag? Divide 36 by 2. (36 ÷ 2 = N) Rename 36 as 20 + 16 20 ÷ 2 = 10 16 ÷ 2 = 8 10 + 8 = 18 Answer: Each bag has 18 carrots. c. The teacher will give more examples. Divide mentally. (written on card) a. 24 ÷ 8 = N f. 36 ÷ 6 = N b. 42 ÷ 2 = N g. 26 ÷ 2 = N c. 48 ÷ 4 = N h. 38 ÷ 2 = N d. 18 ÷ 3 = N i. 16 ÷ 4 = N e. 24 ÷ 6 = N j. 45 ÷ 3 = N 2. Guided Practice b. Divide each number by the center number. Write the answer in the empty spaces.
- 63. 57 c. Game – “Giant Step” 1. The teacher calls on 4 pupils at a time. 2. She flashes the number cards and the pupils outdo each other by giving the correct answers. 3. The first pupil to give the correct answer will take one step forward. 4. The first pupil to reach the finish line wins the game. d. Career Changes - Many Filipinos change careers during their lives. Even our heroes have different jobs. - What jobs/career do you think these Filipinos had before they became heroes? - Your job is to find out. Instruction for the activity 1. Divide mentally, then match the quotient. 2. The quotient will tell you the job/career of the heroes. Divide Mentally Quotient and Career 1. Jose P. Rizal 99 ÷ 3 = ___ 9 Writer 2. Andres Bonifacio 72 ÷ 2 = ___ 15 Lawyer 3. Apolinario Mabini 81 ÷ 9 = ___ 33 Doctor–Ophthalmologist 4. Manuel L. Quezon 90 ÷ 6 = ___ 8 Priest 5. Gomburza 72 ÷ 9 = ___ 36 Fan Vendor 3. Generalization: How do we divide mentally 2-digit numbers through 99 by 1-digit number without remainder? 1. Rename mentally. 2. Then divide. C. Application Give the answers orally 1) 24 ÷ 6 2) 28 ÷ 7 3) 49 ÷ 7 4) 36 ÷ 6 5) 48 ÷ 8 6) 40 ÷ 8 7) 56 ÷ 8 8) 18 ÷ 6 9) 14 ÷ 2 10) 32 ÷ 8 50 ÷ 2 64 ÷ 4 39 ÷ 3 80 ÷ 4 75 ÷ 5 35 ÷ 7 72 ÷ 8 45 ÷ 3 20 ÷ 5 90 ÷ 3
- 64. 58 IV. Evaluation A. Solve mentally then compare using >, < or =. Put your answer inside the box. 1) 48 ÷ 6 ___ 63 ÷ 7 2) 42 ÷ 7 ___ 48 ÷ 8 3) 56 ÷ 7 ___ 24 ÷ 3 4) 28 ÷ 7 ___ 36 ÷ 6 5) 35 ÷ 7 ___ 16 ÷ 4 B. Solve the following problems mentally. Be accurate. 1) Lina works in a slipper factory. Her work is to pair slippers. There are 86 slippers for her to pair In the morning. How many pairs does she make in the morning? 2) There are 80 pupils. They will be distributed equally in 4 classes. How many pupils will be in each class? 3) Mrs. Medina will teach a Muslim dance to 56 Grade III children for the school’s Field Day. She wants to make groups of 4 children. How many groups can she make? 4) There are 24 chairs to be divided evenly into 2 rows. How many chairs will be in each row? 5) A farmer picked 81 pineapples. He has 9 boxes. If he will put equal numbers in each box, how many pineapples will each box have? V. Assignment A. Find the quotients of the following. Do it mentally. 1) 36 ÷ 9 2) 48 ÷ 6 3) 63 ÷ 7 4) 16 ÷ 8 5) 63 ÷ 9 B. Choose one divisor and one dividend to make a division sentence. You may use each number more than once. Divisor Dividend 3 2 4 16 56 54 8 96 51 Construct a division sentence whose quotient is: 1) 17 2) 12 3) 18 4) 8 5) 14 C. Solve each problem mentally. 1. Mother divided 20 oranges equally among her 4 children. How many oranges did each child receive? 2. The grade three class has 2 booths for the school Foundation Day. The class buys 88 prizes. Each booth will share the prizes equally. How many prizes should each booth get? 3. Marsha has 48 shells for each of her three friends. How many shells does each of her friends get? 4. There are 54 tomatoes. There are 9 tomatoes in each box. How many boxes are there?
- 65. 59 Solve 1-Step Word Problems involving Divisions of 2- to 4- Digit Numbers by 1- to 2- Digit Numbers including Money I. Learning Objectives Cognitive: Solve 1- step word problems involving divisions of 2- to 4- digit numbers by 1- to 2- digit numbers including money Psychomotor: Tell the word clues/operations to be used. Use the correct operation in solving word problems Affective: Show love of work II. Learning Content Skill: Solve 1-step word problems involving divisions of 2- to 4- digits numbers by 1- to 2- digits including money Reference: BEC PELC I E 6.1 Materials: chart, paper money, drawing Value: Love of work III. Learning Experiences A. Preparatory Activities 1. Drill (mental division) Flash card with division facts, let the pupil solve mentally. 2. Motivation Present the song: “Top of the World” Come and join our Mathematics class. You will surely enjoy being here with us Mastering basic facts, multiply, add, subtract. Everything is being learned the easy way. Solve a problem in many ways, we know… Number sentence helps Ask the questions how Learn with ease and success Make us do our very best Our Math today is nice if it is like this. We’re on the top of the world solving… Down in our land of numbers learning concepts By discovery. It’s the love that we found Right from very start and come let’s be Happy learning Math Ask the following questions: 1. What does the song tell us? 2. What do we do in Mathematics class? 3. What do you enjoy doing in your Math class? 32 ÷ 4 48 ÷ 6 25 ÷ 5 21 ÷ 7
- 66. 60 B. Developmental Activities 1. Presentation a. Storytelling Present the story with a hand puppet. Nestor sells newspapers after class. He earns 36.00 a day. He divides his earnings to his 3 brothers for their baon. How much does each of his brothers get? Ask. Who earned money from selling newspaper? How much does he earn? Let’s solve this problem using POLYA’s 4-steps in problem solving. How does he earn money? Do you think he love his work? Why? ■ Understand a. What are given? b. What is asked? c. What operation will solve the problem? ■ Plan What equation will solve the problem? ■ Solve Solve the equation. Strategy – (acting out the problem) The pupil will use play money to demonstrate the story problem. 1) How much money did each child get? ( 12.00) ■ Look back Does the answer make sense? Yes. b. Story 2 Present another word problem: Laura picked 124 guavas. She placed them equally in 2 plastic bags. How many guavas were placed in each bag? Let’s solve this problem using the expanded form. 2 21050 100 420100 20 - 20 4 - 4 0 = 62 guavas
- 67. 61 2. Guided Practice a. Work in groups of 5. Distribute index cards with problems to solve. Let them answer the following questions: ■ Understand: a. What are given? b. What is asked? c. What are the necessary information or facts needed to solve the problem? d. What words tell what operation to use? e. What operations will you use? ■ 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? Problem 1 – (written on ¼ Manila Paper) Michelle has 873 chicos. She puts the same number of chicos in 4 baskets. How many chicos are in each basket? Problem 2 – Raffy bought 132 pieces of comic magazines. If he puts them equally in 12 envelopes, how many magazines will each envelope have? Problem 3 – A baker bakes 1 720 cookies. He placed 25 pieces in each plastic bag. How many plastic bags of cookies were there in all? b. Secret Place Rina and Apol are going to a “Secret Place” Let us join them in their fun. - The teacher will draw similar maze on 8 bond papers. Each group leader will be given one, and the first to solve the problem in the maze wins.
- 68. 62 Problems 1. Vilma received 375.00 for 5 baskets of chicos. How much did each basket cost? 2. Mr. Reyes’ store had 144 pairs of socks. The socks were sold in packages of 12 pairs. How many packages were there? 3. Mrs. Villamor has 945.00 to be divided equally among her 3 children for their school needs. How much did each child get? 4. Seven boys ate their lunch at a restaurant. The meal cost 238. They agreed to share equally the expenses. What was the share of each boy? 3. Generalization: What are the steps in analyzing and solving word problem? How do we solve word problems involving division of 2 to 4 digit number by 1 to 2 digit number including money? Steps to be followed in solving one-step word problems are: 1. Understand 2. Plan 3. Do 4. Look Back C. Application Let us solve the problem. 1. Miss Canilao has 135 pupils in her P.E. class. They form 5 groups. How many pupils are in each group? 2. A small pack of biscuits costs 4.00. How many packs of biscuits could one buy with 120.00?
- 69. 63 IV. Evaluation 1. Harris is making plant hangers. She needs 7 beads for each hanger. She has 427 beads. How many hangers can she make? Number sentence: ________________ Complete Answer: ________________ 2. Edgardo spent 326.00 for 2 chairs. How much did each chair cost? Number sentence: ________________ Complete Answer: ________________ 3. Mrs. Abo sells 3 orchid plants for 195.00. What is the price of 1 orchid? Number sentence: ________________ Complete Answer: ________________ 4. A sampaguita vendor gathered 800 sampaguita flowers. She used 10 flowers to make a garland. How many garlands did she make? Number sentence: ________________ Complete Answer: ________________ V. Assignment Read and solve the problem 1. Nine high school students contributed 720.00 to buy their seedlings from a nearby plant nursery. How much did each of them pay? 2. A family drove 7285 kilometres in 5 hours. How many kilometres did they drive in one hour? Solving 2-step Word Problems involving Division and any one of the Fundamental Operations including Money I. Learning Objectives Cognitive: Solve 2-step word problems involving division and any one of the fundamental operations including money Psychomotor: Write the number sentences Affective: Help parents in earning daily living. Cooperate in group activities II. Learning Content Skills: Solving 2-step word problems involving division and any one of the fundamental operations including money Writing number sentences Reference: BEC PELC I – E 6.2 Materials: textbooks, problem chart, activity sheet Value: Helpfulness, industriousness III. Learning Experiences A. Preparatory Activities 1. Drill – Basic Division Facts 81 ÷ 9, 64 ÷ 8 56 ÷ 7 42 ÷ 6 35 ÷ 5
- 70. 64 2. Review – Steps in solving problems In a store for school supplies, 480 sheets of bond paper were placed equally in 20 envelopes. How many sheets of paper were placed in each envelope? What are the steps in solving one-step word problems? ■ Understand a. What is asked in the problem? Number of sheets of paper placed in each envelope. b. What are given? 480 sheets of bond paper, 20 envelopes ■ Plan a. What is the operation to be used in solving the problem? Division b. Write the number sentence. 480 ÷ 20 = N ■ Solve Write the answer. N = 24 ■ Look back Is my answer reasonable? correct? 3. Motivation Mr. Santos gathered 384 eggs from his poultry farm. He kept 24 eggs for home use and sold the rest equally to 3 vendors. How many eggs were sold to each vendor? B. Developmental Activities 1. Presentation a. Problem analysis Have the class read the problem. Ask: What is asked in the problem? number of eggs sold to the vendor. What are given? 384, 24, 3 What is the hidden question? number of eggs left after Mr. Santos kept 24 for home use What operation shall we use to answer the hidden question? subtraction Write the number sentence for the hidden question. 384 – 24 = N What operations shall we use to answer the given question? subtraction and division Write the number sentence for the given question. (384 – 24) ÷ 3 = N Give the answer. N = 12 Is the answer reasonable? b. Acting out a problem. 1. Present another problem to the pupils. 2. Let them act out the problem (role playing)
- 71. 65 Cora and Rene helped their parents earn money by selling newspapers and magazines. Cora earned 640.00 while Rene earned 940.00. They divided their earnings equally between their father and mother. How much did each of them get? How did Cora and Rene help their parents earn money? What kind of children are they? Are they industrious? Helpful? Who among you help your parents? 3. Call on 6 pupils. Let them form a line. Assign each one of them to answer a question about the problem. Pupil 1 – What is asked? 2 – What are given 3 – What is the number sentence for the hidden question? 4 – Write the number sentence for the hidden question. 5 – Write the number sentence for the given questions. 6 – Solve the problem. 2. Guided Practice a. Divide the class into learning barkadas b. Distribute activity cards to different groups. c. Let the group match the answers to the questions. Nena prepared 284 sandwiches. Rita prepared 368 sandwiches. They distributed the sandwiches equally among the 4 classes. How many did each class receive? A B 1. What are given? a. 284 + 368 = N 2. What is asked? b. addition 3. What is the hidden question? c. total number of sandwiches 4. What operation to be used to find the hidden question? d. 284, 368, 4 e. number of sandwiches that each class received5. What is the number sentence of the hidden question ? f. (284 + 368) ÷ 4 = N 6. What is the number sentence of the given question? g. addition and division h. 163 7. What operations to be used to find the answer? 8. What is the answer?
- 72. 66 3. Generalization: How do we solve 2-step word problems? What are the steps in solving 2-step word problems? Understand What is asked in the problem? What are given? What is the hidden question? Plan What is the operation to be used to find the answer to the hidden question? given question? Write the number sentences: hidden question, given question. Solve Write the answer. Look Back Is my answer reasonable? C. Application Group Work – Work in Triads 1. Distribute activity cards to the pupils. 2. Have them answer the questions on the sheets. 3. Let them post their answers on the board. Activity Card IV. Evaluation Read and solve each problem. 1. Amanda Flower Shop used 159 flowers to make 3 bouquets that had the same number of flowers. How many flowers were used for 2 bouquets? 1. What is asked? ___________________ 2. What are given? ___________________ 3. What is the hidden question? ___________________ 4. Write the number sentence. Hidden question __________________ Given question __________________ 5. Write the answers. ___________________
- 73. 67 2. Ralph and Laurel paid 45 each for their hair cut every month. By the time they spent 540, how many months would they have had their hair cut? 3. Mrs. Laura Gonzales earns 2,130, for 6 days a week. If she works only 4 days in one week, how much will she be paid? 4. Carlos put 212 tennis balls into 4 wire baskets. He put the same number of balls in each basket. He brought 3 baskets of balls to the tennis court. How many balls did Carlos bring? 5. Four boys work 6 hours in one day. If the job takes 192 hours to complete, how many days will the boys have to work? V. Assignment Read the problems and answer the questions that follow. 1. Ronie picked 240 santols while Mario picked 260. They placed the santols equally in 50 baskets. How many santols will there be in each basket? 2. Olive baked 6 cakes for 245 each. If she shared her earnings equally with her brother and sister, how much did each of them get? Solving 3- Step Word Problems involving Division and any two of the other Fundamental Operations including Money I. Learning Objectives Cognitive: Solve 3-step word problems involving division and any two of the other fundamental operations including money Psychomotor: Write the complete answer. Affective: Use time wisely II. Learning Content Skills: 1. Solving 3- step word problems involving division and any two of the other fundamental operations including money 2. Writing complete answer Reference: BEC PELC I E 3.2 Materials: textbooks, problem chart, number cards, flash cards Value: Wise use of time III. Learning Experiences A. Preparatory Activities 1. Drill – Division, multiplication, subtraction and addition basic facts The teacher divides the class into 2 groups. She designates a leader and let all members form a straight line. Then she distributes number cards and asks the pupils to look for the answer of their number combinations from the cut-outs on the chalkboard. The first group to get all the correct answers wins the race. 54 ÷ 9 = __ 7 x 8 = __ 5 x __ = 20 __ ÷ 6 = 7
- 74. 68 2. Review Have a review in analyzing and solving 2-step word problem. a. Group the pupils in fours b. Each group will answer a set of word problems. c. Before the pupils answer the word problems, guide them to analyze an example. Buddy saved 80, 90 and 100 for 3 months. What was his average monthly savings? ■ Understand a. Draw a picture about the problem 80 90 100 b. What is asked in the problem? c. What information is needed to solve the problem? d. Can you find the answer to the problem at once? e. What do you need to do? Find the hidden question. ■ Plan a. What process will you use to find the hidden question? b. What process will you use to find the given question? c. Who can write the number sentence? ■ Solve Solve the problem. Step 1 80 + 90 + 100 = 270 Step 2 270 ÷ 3 = 90 ■ Look back Does the answer make sense? 3. Motivation – Present a problem. Johnny worked in a factory. He receives daily salary of 350 and 150 overtime pay. If he receives the same rate, how much will he receive for 1 week and 2 days? a. Where does Johnny work? b. Is Johnny an industrious person? c. Did he use his time wisely? d. Read the part of the problem showing that Johnny is industrious. e. Does it pay to be industrious? Why? B. Developmental Activities 1. Presentation a. Analysis 1. What are the given facts that can help us solve the problem? 2. What is asked in the problem? 3. Can you find the answer to the problem at once? 16 - 8 = __ 63 ÷ __ = 9 9 + __ = 18 64 ÷ __ = 8 6 56 4 42 8 7 8 9
- 75. 69 4. Look for the hidden question. 5. What process/processes will you use to answer the hidden question? 6. Write the number sentence for the hidden question. 7. What other operation will you use to answer the given question? 8. Write the number sentence for the given question. 9. Solve the problem. Step 1 300 + 150 = 450 Step 2 Change 1 week to days 1 week = 5 days 5 + 2 = 7 days Step 3 450 x 7 3 150 10. Does the answer make sense? b. Organize the data in a table The teacher distributes strips of paper with the steps in problem solving written on them. Then she posts the 4 big steps on the board. UNDERSTAND PLAN SOLVE LOOK BACK 1. What are given? 1. What are the processes to be used to solve the hidden and given questions? Solve the number sentence 1. Is my answer reasonable?2. What is asked? 3. What is the hidden question? 2. Write the number sentence. The teacher asks the pupils to post the strips of paper under the appropriate column. 2. Guided Practice a. Contest – Working in pairs 1. Group pupils in pairs. 2. Give them problems to work on. 3 Each pair will work cooperatively. 4. Ask them to write their answers on the board. 5. The team to get the most number of correct answers wins the contest.
- 76. 70 Word Problems 1. Forty-two children gathered two bags of shells with 336 shells in each bag in the morning and 3 bags of shells with 420 shells in each bag in the afternoon. If they divided the shells equally, how many shells will each one get? 2. There were 3 rows of lights with 148 lights in each row. 34 busted out and the rest were kept. If each box has 10 lights. How many boxes were used? b. Work in group of 6. 1. Form groups with 6 members. 2. Give each group a problem. 3. Ask each group to solve the problem and report their output to the class by supplying the data called for in the table below. Given Asked Processes to be used Number Sentence (Hidden Question) Number Sentence (Given Question) Answers Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 4. The group who gets the most number of correct answers wins the game. 3. Generalization: What are the steps to be followed in solving 3-step word problems? Understand Plan Solve Look Back Read and understand the problem. Find out what are given. Find out what is asked. Know the hidden question. Decide the process to be used. Write the number sentence. Solve the problem. Check if the answer is reasonable/correct.
- 77. 71 C. Application Read and solve the following problems. 1. The teaching force of an elementary school has 85 male and 97 female teachers. If 26 are special teachers and the rests are assigned equally in 6 grades, how many teachers are there in each grade? 2. The grade III pupils went on a field trip to Tagaytay. They hired a bus for 2,445 and a minibus for 1,235. The school gave 1,120 and the rest was shared equally by among the 32 pupils. How much did each pupil pay? IV. Evaluation Write the missing data on the blanks. In the children’s store, 285 blue notebooks and 325 red notebooks were delivered. Out of these, 190 notebooks were sold and the rest were arranged in 15 shelves. How many notebooks were in each shelf? 1. Given ____________________ 2. Asked ___________________ 3. Hidden Question ___________ 4. Number sentence for the hidden question ____________ 5. Number sentence for the given question ____________ 6. Answer _________________ V. Assignment Read, analyze and solve the problem. 1. For the school fund-raising projects, the primary classes collected 89 kg of old newspapers, and the intermediate classes collected 125 kg. The children sorted out the old and crumpled newspapers which weighed 6 kg. They bundled the remaining newspapers at 8 kilograms per bundle. How many bundles were made?

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