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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 Multiplication 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. Multiplication Changing the Order or Regrouping in Multiplication ...................................................... 1 Multiplying 2- to 4- digit numbers by 1- to 2- digit numbers Without regrouping............................................................................................. 6 With grouping..................................................................................................... 11 Multiplying 2- digit numbers by 1- digit number with zero in the multiplicand..... 16 Multiplying 3- to 4- digit numbers by 1- digit numbers with zero in the multiplicand. ..................................................................................................... 20 Multiplying 2- to 4- digit numbers by multiples of 10......................................... 25 Multiplying 2- to 4- digit numbers by multiples of 100....................................... 30 Estimating the product of 2- to 3- digit numbers by 1- to 2- digit numbers........ 35 Estimating the product of 4- digit numbers by 1- to 2- digit numbers................ 39 Multiplying mentally 2- digit numbers with products up to 100 without regrouping............................................................................................ 43 Solving word problems involving multiplication of whole numbers including money.................................................................................................. 47 Solving 2- to 3- step word problems involving multiplication and any one of addition/subtraction......................................................................................... 50
- 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. Multiplication of Whole Numbers 1. Comprehension of Multiplication 1.1 Multiply 2 to 4 digit numbers by 1 to 2 digit numbers without and with regrouping in all places 1.1.1 Multiply 2 to 4 digit numbers without and with regrouping 1.1.1.1 Show that changing the order and/or regrouping in multiplication makes computation easy Industry Concept development Simplifying the problem Singing (Musical) Climbing the ladder (Bodily Kinesthetic) Game Drawing (Spatial) 1.1.1.2 Multiply 2 to 4 digit numbers by 1 to 2 digit numbers without regrouping Accuracy/carefulness Simplifying the problem Game "Giant Step" (Bodily kinesthetic) 1.1.1.3 Multiply 2 to 4 digit numbers by 1 to 2 digit numbers with regrouping Speed and accuracy Simplifying the problem "Solve and Deliver" Game(Bodily kinesthetic) 1.1.1.4 Multiply 2 digit numbers by 1 digit number with zero in the multiplicand Care and concern for the Environment Drawing pictures Movements (Bodily Kinesthetic 1.1.1.5 Multiply 3 to 4 digit numbers by 1 digit numbers with zero in the multiplicand Following rules and regulations Simplifying the problem Song (Musical) Game "Flaglet Race"(Bodily kinesthetic) 1.1.1.6 Multiply 2 to 4 digit numbers by multiples of 10 Develop the habit of being independent Looking for patterns "Skip" movement (Bodily kinesthetic) 1.1.1.7 Multiply 2 to 4 digit numbers by multiples of 100 Cooperation Looking for patterns Cooperative groups(Interpersonal) 1.1.2 Estimate the product of 2 to 3 digit numbers by1 to 2 digit numbers Neatness Simplifying the problem Cooperative groups(Interpersonal) 1.1.3 Estimate the product of 4 digit numbers by 1 to2 digit numbers Active participation Simplifying the problem Listening to music while doing the game (Musical) 1.1.4 Multiply mentally 2 digit numbers by 1 digit numbers without regrouping with products up to 100 Cooperation and Independence Drawing pictures Puzzle (Logical mathematics) Coloring (Spatial) Manipulation (Bodily kinesthetic) 2. Application of Multiplication
- 6. vi 2.1 Solve word problems involving multiplication of whole numbers including money following the steps in problem solving Thriftiness/Cooperation Polya's steps in problem solving Drawing table Cooperative groups(Interpersonal) 3. Application of Multiplication and any one of Addition/Subtraction 3.1 Solve 2-3 step word problems involving multiplication and any one of addition/subtraction following the steps in problem solving Honesty Acting out the problem Polya's steps in problem solving Diagram (Spatial) Cooperative groups(Interpersonal)
- 7. 1 Changing the Order or Regrouping in Multiplication I. Learning Objectives Cognitive: Show that changing the order and/or regrouping in multiplication makes computation easy Psychomotor: Illustrate multiplication in different orders of factors Affective: Show sportsmanship when working in the activities II. Learning Content Skill: Changing the order or regrouping in multiplication Reference: BEC PELC I.D1.1.1.1 Materials: counters, flash cards, cut-outs of a rabbit and a frog, cut-outs of rectangular arrangements, drawings Value: Sportsmanship III. Learning Experiences A. Preparatory Activities 1. Drill “Climbing the Ladder” Call two pupils to answer the multiplication facts as fast as they can. The one who makes a mistake will fall from the ladder. 6 x 6 4 x 8 3 x 5 8 x 3 6 x 4 2. Review In 3 x 4 = 12, what are 3 and 4? Give the factors of: 10, 16 3. Motivation What game/sport do you enjoy playing? If you do not win in a game, how would you feel? What will you do to show that you are a good sport? Is it good to engage in sports? Why? 18 21 32 24 16
- 8. 2 Let all the pupils stand and form - two lines - three lines - four lines Ask: Did the number of pupils change as they change their position/groupings? B. Developmental Activities 1. Presentation a. In a race, Lady rabbit takes 4 hops of 3. Mr. Frog takes 3 hops of 4. Who is ahead? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Discuss: - How many hops did Lady Rabbit take? - How about Mr. Frog? Who won the race? - Why did you say it’s a tie? - Compare the number of hops done. - Ask some pupils to hop as what Lady Rabbit and Mr. Frog did. Lady Rabbit 4 hops of 3 Mr. Frog 3 hops of 4 Transform 4 hops of 3 into addition and multiplication sentence. 3 + 3 + 3 + 3 = 12 4 x 3 = 12 Transform 3 hops of 4 into addition and multiplication sentence. 4 + 4 + 4 = 12 3 x 4 = 12 Is 4 x 3 the same as 3 x 4? Why? b. Present another activity. ● Have the pupils get 8 counters. Let them group the counters by 4s ● Ask: How many groups of 4 did you get? Give the multiplication sentence. ● This time, have the pupils group the counters by 2s ● Ask: How many groups of 2s did you get? What is the multiplication sentence for this? ● Guide the pupils to analyze the number sentence on the board. a.) 2 x 4 = 8 b.) 4 x 2 = 8 ● What are the factors of 8? Which factor comes first in sentence a, 2 or 4? How about in sentence b? What did we do to the order of the factors? Did the product change? c. Mang Tony prepared 2 groups of sugarcane seedlings for his plantation. Each group had seedlings. He cut each seedling into 3 pieces. How many pieces were there in all? Lady rabbit Mr. Frog
- 9. 3 Sometimes a number pattern can help when we multiply three or more numbers. (2 x 8) x 3 = 48 thirds of sugar cane seedlings 2 x (8 x 3) = 48 thirds of sugar cane seedlings Give more examples: (4 x 2) x 3 = 24 4 x (2 x 3) = 24 (6 x 3) x 2 = 36 6 x (3 x 2) = 36 (5 x 3) x 3 = 45 5 x (3 x 3) = 45 2. Guided Practice a. Write two multiplication sentences for the following. 4 sets of 3 3 sets of 4 5 sets of 2 2 sets of 5 16 16 x 3 = 48 24 24 x 2 = 48 ______ x _____ ______ x _____ ______ x _____ ______ x _____
- 10. 4 4 sets of 6 6 sets of 4 3. Generalization: Does the product change when we change the order of the factors? Can you have product if you don’t have factors? Changing the order of the factors does not affect the product. Regrouping of the factors makes computation easy. C. Application 1. Fill in the blanks to complete each equation. 1) 5 x 3 = __ x 5 3) 6 x 2 = __ x 6 5) __ x 5 = 5 x 7 2) 6 x 8 = 8 x __ 4) __ x 5 = 5 x 7 6) Write the multiplication sentence: 2. Activity The learners are asked to examine a set of rectangular arrangements and explore the situation. Activity Card Directions: Examine the following figures. How many squares does each figure have? _______ Hold it in vertical and horizontal positions and take note how the number of rows and column change. NOTE: Do these in all rectangles. Rectangle cut outs ______ x _____ ______ x _____ ______ x _____ ______ x _____
- 11. 5 a. Write all the possible multiplication sentences. Rectangle A 3 x 6= 18 6 x 3 = 18 Rectangle B ___________ ___________ Rectangle C ___________ ___________ Rectangle D ___________ ___________ Rectangle E ___________ ___________ b. How many multiplication sentences did you form in each rectangle? _____ c. Complete the table Rectangle Write the multiplication sentences based on the rectangle. What are the factors in each multiplication sentence? What is their product? A B C D E d. Compare the two multiplication sentences for each rectangle. What do you observe about their factors? 3. Draw a if the number sentence is correct and a if it is wrong. ____ 1) (3 x 4) x 2 = 3 x (4 x 2) ____ 2) 2 x (8 x 3) = (3 x 7) x 2 ____ 3) 4 x (5 x 2) = 4 x (7 x 3) ____ 4) 8 x (6 x 2) = (8 x 6) x 2 ____ 5) 10 x (2 x 3) = (10 x 2) x 4 4. Find the missing numbers. 1) 2 x (3 x 9) = (2 x _) x 9 2) (5 x 4) x _ = 5 x (4 x 8) 3) (7 x 8) x 3 = _ x (8 x 3) 4) (6 x 2) x 9 = 6 x (_ x 9) 5) 8 x (3 x 1) = (_ x 3) x 1 Rectangle A Rectangle B Rectangle C Rectangle D Rectangle E
- 12. 6 IV. Evaluation A. Complete the following. 1) (4 x 2) x 3 = 4 x (__ x 3) 2) 2 x (2 x 4) = (2 x 2) x __ 3) 8 x (3 x 5) = (8 x __) x 5 4) (6 x 7) x 4 = __ x (7 x 4) 5) 9 x (6 x __) = (9 x 6) x 3 B. Group the following in two ways. Find the product. 1) 2 x 5 x 8 = ______ 2) 3 x 3 x 10 = ______ 3) 3 x 4 x 2 = ______ 4) 6 x 2 x 5 = ______ 5) 7 x 2 x 10 = ______ V. Assignment A. Perform the operations. Multiply the numbers inside the parenthesis first. 1) (4 x 5) x 7 3) (6 x 5) x 4 5) (7 x 3) x 8 2) (9 x 4) x 2 4) (3 x 2) x 6 B. Let N represent the missing number in each sentence. Find N. 1) 9 x 8 = N x 9 2) (2 x 3) x 5 = N x (3 x 5) 3) N x 3 = 3 x 7 4) 5 x 6 = N x 6 5) (5 x 8) x 2 = 5 x (N x 2) Multiplying 2- to 4- Digit Numbers by 1- to 2- Digit Numbers without Regrouping I. Learning Objectives Cognitive: Multiply 2- to 4- digit numbers by 1- to 2- digit number without regrouping Psychomotor: Compute the product of 2 numbers with accuracy Affective: Show accuracy/carefulness in solving number problems II. Learning Content Skill: Multiplying 2- to 4- digit numbers by 1- to 2- digit numbers without regrouping Reference: BEC PELC I.D.1.1.1.2 Materials: flash cards, problem written on manila paper Value: Accuracy/Carefulness
- 13. 7 III. Learning Experiences A. Preparatory Activities 1. Drill: Basic multiplication facts 8 3 4 9 5 10 x 1 x 7 x 0 x 2 x 6 x 4 2. Review Recall the importance of accuracy and carefulness in doing things. In 8 x 3 = 24. What do you call 8? 3? 24? Put the factors and the products in the correct box. 4 x 2 = 8 12 x 3 = 36 9 x 5 = 45 6 x 7 = 42 5 x 5 = 25 10 x 6 = 60 11 x 3 = 33 9 x 8 = 72 13 x 3 = 39 FACTORS PRODUCTS 3. Motivation Message in Boxes Multiply. Write the letter that is next to each answer in the correct box below. Read the secret message. 9 4 3 9 5 x 2 x 9 x 4 x 7 x 2 A E H O R 9 5 9 9 6 x 8 x 9 x 9 x 3 x 9 S T U W Y 27 63 27 45 12 18 45 72 81 10 36 W O W T H A T S U R E 27 18 72 36 18 72 54 W A S E A S Y
- 14. 8 B. Developmental Activities 1. Presentation a. Present this problem Andres Bonifacio Elementary School received 12 boxes of toys from the governor of the province. Each box had 24 assorted toys. How many toys were there in all? Let us analyze the problem ■ Understand the problem What is asked in the problem? Number of toys in all. What are given? 12 boxes of toys, 24 assorted toys. What process will you use? Multiplication. ■ Plan What is the number sentence? What is your answer? Did you do it this way? 12 x 24 = N 24= 20 + 4 x 12= 10 + 2 ■ Carry out the plan Tell the pupils that the following solutions used expanded notation. Step 1: Step 2: Step 3: 20 + 4 20 + 4 24 = 20 + 4 x 10 + 2 x 10 + 2 x 12 = 10 + 2 40 + 8 200 + 40 40 + 8 2 x 4 = 8 10 x 4 = 40 + 200 + 40 2 x 20 = 40 10 x 20 = 200 240 + 48 = 288 toy planes Introduce now the short method. Multiply the multiplicand by the ones in the multiplier. Write the product (48) beginning from the ones place. Multiply the multiplicand by the tens in the multiplier. Write the product (240) Multiply by ones Multiply by tens 24 24 24 x 12 x 2 x 10 48 48 240 240 Add the two partial products 24 x 12 48 partial products + 240 288 product ■ Look back Did you answer correctly the given problem? Check your answer.
- 15. 9 Let the class do these on the board. 1) 22 2) 322 3) 31 4) 1 243 x 11 x 3 x 33 x 21 Let the pupils do these exercises on their seats. 1) 23 2) 23 3) 223 4) 312 x 22 x 12 x 23 x 12 2. Guided Practice a. Game (GIANT STEP) Teacher will call on 5 pupils. Provide each pupil illustration board and chalk. They will stand and start from the back. The teacher will flash the multiplication. The first one who will give the correct answer will step forward, the one who reaches first the front desk wins the contest. 1) 232 2) 24 3) 231 4) 321 5) 4 321 x 2 x 22 x 32 x 33 x 2 6) 1 431 7) 324 8) 33 x 12 x 22 x 22 b. Group Activity: (4 groups) Give each group an activity card. Each group will present their work after 3 minutes. After working, ask questions that will emphasize the value of accuracy and carefulness. Group I = 124 6321 21 x 2 x 12 x 21 Group II = 221 32 412 13 x 4 x 12 x 12 Group III = 212 4 213 14 x 13 x 12 x 2 Group IV = 212 2 134 23 x 3 x 12 x 13 c. Problem Solving 1. Miss Cruz arranges 142 books in every shelf in the library. If there are 12 shelves, how many books are there in all? 2. Gerry spent his vacation working in a supermarket. He worked 8 hours a day for 11 days. How many hours did he work in all? 3. Marnelyn counted 24 small chocolate bars in a package. If there were 21 packages in the shelf, how many chocolate bars were there? 4. Marlon delivers 50 letters each day. How many letters does Marlon deliver in 3 days? 5. Tony has 4 packs of pencils. There are 20 pencils in each pack. How many pencils does Tony have?
- 16. 10 3. Generalization How do you multiply 2- to 4- digit numbers by 1- to 2- digit number without regrouping? In multiplying 2- to 4- digit numbers by 1- to 2- digit numbers without regrouping, start with the ones, then the tens, then the hundreds, and lastly the thousands. C. Application 1. What is the greatest product you can get using the digits 3, 2, 1, 4 as factors? Write in the boxes the factors that will give the largest product. Product = _______ 2. Pick a number from box X. Multiply it by a number from box Y to find the given answers. Box X Box Y 42 22 123 21 12 32 23 31 431 24 33 20 1) 483 2) 8620 3) 3936 X = _______ X = _______ X = _______ Y = _______ Y = _______ Y = _______ 4) 504 5) 528 6) 1023 X = _______ X = _______ X = _______ Y = _______ Y = _______ Y = _______ IV. Evaluation A. Find the missing digits. 1) 2 3 4 2) 4 3 2 1 3) 2 4 2 2 x 2 3 x 1 1 +4 _ 8 1 2 9 _ _ 2 _ _ 6 8 _ 8 _ 4 2 _ _ _ _ 5 _ 4 8 9 9 _ 8 3 _ 6 4 4) 3 2 5) 1 2 3 x 1 2 x 1 3 _ _ _ 6 9 _ 2 _ 1 2 _ _ 3 8 4 1 _ 9 9 __ __ x __ __
- 17. 11 B. Find the product: 1) 234 2) 143 3) 322 x 2 x 21 x 13 4) 2 233 5) 6 321 x 32 x 3 V. Assignment A. Find the product. 1) 452 2) 313 3) 23 x 11 x 13 x 21 4) 2 431 5) 421 x 22 x 21 B. Solve the following problems. 1. Ellen has 23 pages of stamps. Each page has 112 pieces. How many stamps does she have in all? 2. Mang Mario needs 4 poles for his vegetable garden. Each pole should be 122 centimetres long. What will be the total length of 4 poles? 3. The bookstore received a shipment of 13 boxes of books. Each box contained 112 books. How many books were in the shipment? 4. Puring and Linda are going home after visiting their grandmother. The trip takes 3 hours. If the bus travels 122 kilometres an hour, how far away is their house? 5. Edith bought 231 pieces of linen paper at P3 each. How much did she spend for the linen paper? Multiplying 2- to 4- Digit Numbers by 1- to 2- Digit Numbers with Regrouping I. Learning Objectives Cognitive: Multiply 2- to 4- digit numbers by 1- to 2- digit numbers with regrouping Psychomotor: Write the product of 2- to 4- digit numbers by 1- to 2- digit numbers Affective: Compute the product of two numbers with speed and accuracy II. Learning Content Skill: Multiplying 2- to 4- digit numbers by 1- to 2- digit numbers with regrouping Reference: BEC PELC I.D.1.1.1.3 Materials: chalkboard, flash cards, activity cards Value: Speed and accuracy
- 18. 12 III. Learning Experiences A. Preparatory Activities 1. Drill : (Multiplying by 1-digit number) 2. Review Give the factors of the given number. 72 = (9 x 8) 24 = ? 36 = ? 81 = ? 64 = ? 18 = ? 45 = ? 90 = ? 3. Motivation (Song) Be alert in answering the multiplication sentence while singing. (Tune: Skip to My Love) Teacher: I’m Mathematics how do you do? Children: I’m Mathematics how do you do? Teacher: Who are you? Tell me too? Children: I’m just a child but I know you. Teacher: Speak, speak, 7 x 7 Children: _____ (The pupils will answer) Teacher: Speak, speak, 5 x 8 Children: _____ All: It’s so easy I tell you. B. Developmental Activities 1. Presentation a. There are 36 newspapers in a bundle. How many newspapers are in 125 bundles? Analyze the problem with the pupils to determine the solution. To find the answer, we multiply 125 by 36. Multiply 125 by 6 ones Multiply 125 by 3 tens 125 125 x 36 x 6 750 750 125 x 30 3750 Add the partial products. 125 x 36 750 + 3 750 There are 4 500 newspapers. 4 500 - Emphasize that the multiplier 36 in the example means multiplying the multiplicand by 6 ones and by 3 tens. (30) 25 x 2 20 x 4 43 x 2 32 x 4 11 x 6
- 19. 13 b. Copy then complete. 2 4 0 x 2 5 12 0 0 4 8 0 0 _ _ _ _ 2 5 6 x 2 4 1 0 2 4 5 1 2 _ _ _ _ _ 2. Guided Practice a. Write the missing numbers. 22 x 39 198 _ _ _ _ _ _ 232 x 16 1392 _ _ _ _ _ _ _ _ 8721 x 24 34884 _ _ _ _ _ _ _ _ _ _ 32 x 15 160 _ _ _ _ _ _ 128 x 22 256 _ _ _ _ _ _ _ _ b. Show a chart “How many Fruits Are There in All.” Group the pupils into 4. Each group will work on one fruit. Ask each group to present their work on the board. Number of Baskets Fruits and Number per Basket Mangoes 24 Avocados 146 Atis 36 Melon 18 25 baskets 30 baskets 12 baskets 36 baskets 24 x 25 = 600 e. Game (SOLVE AND DELIVER). Be fast and accurate while answering the multiplication sentences. Why is it necessary to be accurate in solving any problem? 1. Get a partner. 2. Pretend you are cousins who live in the same house. Your grandmother is sick. You are asked to bring food to her. Just like Little Red Riding Hood, you will meet lots of danger and obstacles along the way. These obstacles are in the form of multiplication exercises like the ones below. 3. Cut and place them on the table upside down. Take turns with your partner in picking up a card. 4. Answer the problem in the card. If you get the correct answer, you will move one step forward towards grandma’s house. 5. If your answer is wrong, you will move one step backward. Use a marker to indicate your position. Let us see who can deliver the food to grandma. 45 x 23 18 x 46 29 x 51 84 x 70 92 x 12 15 x 65 24 x 62 77 x 14 32 x 56 40 x 63
- 20. 14 3. Generalization: How do we multiply 2- to 4- digit numbers by 2- digit numbers with regrouping? Multiply the 2- to 4- digit multiplicand by the ones of the multiplier. Regroup if needed. Multiply the multiplicand by the tens of the multiplier. Regroup if needed. Add the partial products to get the final product. C. Application a. Find the product: 1) 32 x 15 2) 42 x 52 3) 25 x 35 4) 821 x 52 5) 1503 x 22 b. Follow the arrows. Fill in the missing numbers. 1) 73 x ___ 365 - ___ 305 x 9 = ___ 2) ___ x 8 200 + ___ 449 x 6 = ___ 3) 39 x ___ 78 + 294 ___ x 7 = ___ 4) ___ x 4 256 – 178 ___ x 5 = ___ 5) The sum of all four numbers is ____.
- 21. 15 IV. Evaluation A. Multiply 1) 179 x 12 2) 643 x 12 3) 370 x 16 4) 145 x 18 5) 224 x 10 B. Find the missing digits 1) 33_ x 16 2_22 33_ _ 5_9_ 2) 60_ x _8 4_32 1_08_ 169_ _ 3) _48 x 36 2 6 _ _ 1 _4 _6 12 8 4) _8 x 1_ _34 78_ 10_ _ 5) 4_0 x 3_ _52_ _260_ 15_ _0 V. Assignment A. Find the missing digits. 1) 3 9 x 1 4 1 5 6 _ 9_ _ _ 6 2) 25 x 31 _5 75_ 775 3) 2 4 7 x 3 6 1 4 8 2 7 4 1_ _ _ _ _ 4) 261 x 13 _83 261_ 339_ 5) 1 8 3 x 2 5 9 _ _ _ 6 6_ _ 5 _ 5 B. Find the products. 1) 137 x 12 2) 4500 x 38 3) 538 x 26 4) 763 x 46 5) 1256 x 49
- 22. 16 Multiplying 2-Digit Numbers by 1-Digit Number with Zero in the Multiplicand I. Learning Objectives Cognitive: Multiply 2-digit numbers by 1-digit number with zero in the multiplicand Psychomotor: Apply basic skills in multiplying numbers Affective: Show care and concern for the environment II. Learning Content Skills: a. Multiplying 2-digit numbers by 1-digit number with zero in the multiplicand b. Applying basic skills in multiplying numbers Reference: BEC PELC I.D.1.1.1.4 Materials: number wheel, flash card, strips, drawing Value: Care and concern for the environment III. Learning Experiences A. Preparatory Activities 1. Drill : Conduct a contest by spinning the wheels and giving the product. 2. Review If (4 x 3) x 2 = 24, then 4 x (3 x 2) = N If (6 x 1) x 7 = 42, then 6 x (1 x 7) = N If 4 x (2 x 5) = 40, then (4 x 2) x 5 = N If 3 x (2 x 4) = 24, then (3 x 2) x 4 = N Name the missing factors. 8 x 3 = 3 x ___ 8 x 4 = ___ x 8 5 x 4 = ___ x 5 6 x 8 = ___ x 6 12 x 2 = ___ x 12 15 x 7 = ___ x 15 3. Motivation Present a problem opener. Mang Ato harvested 5 crates of mangoes. If each crate has 50 mangoes, how many mangoes were there in all? What trees do you have in your backyard? Why are trees important? What do you think will happen if there are no trees around us? 1 2 3 45 6 7 8 x 7 1 2 3 45 6 7 8 x 8 1 2 3 45 6 7 8 x 9
- 23. 17 B. Developmental Activities 1. Presentation a. Analyze the problem. How many crates of mangoes did Mang Ato harvest? How many mangoes were there in each crate? What is asked in the problem? What facts are given? What process is to be used? (Steps in solving the problem) Step 1 50 x 5 0 Step 2 50 x 5 250 - Remind the pupils about the zero property of multiplication. Any number multiplied by zero, the product is zero. b. Present another problem. Mr. de Alday gave 90 santol seedlings to each of the 8 classes, how many seedlings were given out? What seedlings did Mr. de Alday give to each of the 8 classes? How many santol seedlings did each class receive? What is asked in the problem? What are the given facts? What process will you use? How will you solve the problem? 90 90 x 8 8 0 720 santol seedlings More examples: 1) 70 70 x 7 7 0 490 2) 60 60 x 5 5 0 300 3) 20 20 x 8 8 0 160 4) 40 40 x 9 9 0 360 5) 90 90 x 6 6 0 540 2. Guided Practice a. Let the pupils study the coding of numbers. Let them do it afterwards. Multiply the ones on the multiplicand by the multiplier. Now multiply the tens on the multiplicand by the multiplier.
- 24. 18 Digit Movement 0 1 2 3 4 5 6 7 8 9 - - Forefinger and thumb together forming zero - - Right arm forward closed fist - - Left arm forward closed fist - - Left and right arm folded vertically - - Hands on waist - - Right hand on the chest - - Bend forward to pick something - - Stand straight - - Arms obliquely upward - - Do the McDonald sign Work in Dyads Direction: Find the missing number in the product. Use the number coding in answering. 1) 50 x 4 20_ 2) 90 x 3 _70 3) 70 x 6 4_0 4) 20 x 8 _ _0 5) 60 x 6 36_ 6) 30 x 9 _70 7) 80 x 5 4_0 8) 10 x 7 _0 9) 40 x 6 _40 b. Group Activity - Draw Lots The teacher will prepare a box with word problems inside. Any member of the group will draw 1 strip inside the box, then the group will answer it afterwards. The group will be given 2 minutes to answer the problem. The group with the highest points wins. Sample problems: 1. There are 50 passengers in one provincial bus. How many passengers are there in 8 buses? 2. Jean saves 90 a month. How much will she save in 5 months? 3. Celia can sell 50 sampaguita garlands a day. How many garlands can she sell in 9 days? 4. Mang Dianong has 9 rows of corn plants in his farm. There are 20 plants in each row. How many corn plants are there? 5. Aldy planted 30 pechay seedlings in each plot. How many seedlings did he plant in 8 plots? What should you remember in multiplying a number with zero? c. (Little Brother Approach) Let the fast learners develop their own simple word problems, They’ll answer these together with the slow learners. 1. Mang Andy saves __ a day. How much will he save in __ days? 2. Jojo has __ piles of tanzan. Each pile has ___ tanzans. How many tanzans are there in all? 3. There were __ students in the library. Each student borrowed ___ books. How may books were borrowed by the students? 4. Maris has __ boxes of chalk. Each box contains __ pieces of halk. How many pieces of chalk does Maris have? 5. Edith earned __ a day in selling newspaper. How much will she earn in __ days? 3. Generalization: How do we multiply 2-digit numbers by 1-digit number with zero in the multiplicand?
- 25. 19 a. Multiply the ones in the multiplicand by the multiplier. b. Multiply the tens in the multiplicand by the multiplier. Any number multiplied by zero is equal to zero. C. Application Solve the following problems. 1. A baker bakes 60 pieces of bread in one day. How many pieces of bread will he bake in 7 days? 2. Aling Marta has 8 baskets of tomatoes. If each basket contains 90 tomatoes, how many tomatoes will she have in all? 3. Mang Ading harvested 20 mangoes from each of the 9 mango trees. How many mangoes did he harvest in all? 4. There are 30 cans of milk in a box. If there are 9 boxes, how many cans of milk will there be in all? 5. A Mathematics Dictionary cost 80.00. How much will 6 Mathematics Dictionary cost? IV. Evaluation A. Give the product. 1) 80 x 5 = 2) 60 x 4 = 3) 50 4) 70 5) 90 x 6 x 5 x 6 B. SECRET MESSAGE 1. Find the product. Write the answer on the boxes. A. 70 x 4 10 x 9 50 x 8 90 x 4 90 x 7 A C E H I 40 x 4 20 x 9 35 x 2 30 x 2 40 x 7 L M N O P 20 x 4 30 X 8 60 x 5 70 x 7 80 x 9 60 x 7 R T U W Y Z 2. Write the letter that matches with the numbers. 720 60 300 280 80 400 280 Y O U A R E A 180 300 160 240 630 280 160 630 90 280 240 630 60 70 M U L T I P L I C A T I O N 490 360 630 420 W H I Z
- 26. 20 3. What is the secret message? V. Assignment A. Fill in the box with correct answer. 1) 90 x 7 6_0 2) 60 x 6 36_ 3) 40 x 7 2_0 4) 80 x 8 _40 5) 50 x 8 4_ _ B. Write >, < or = in the box. 1) 80 x 6 ___ 60 x 8 2) 40 x 5 ___ 20 x 9 3) 50 x 7 ___ 70 x 4 4) 30 x 6 ___ 40 x 6 5) 70 x 5 ___ 90 x 2 Multiplying 3- to 4-Digit Number by 1-Digit Number with Zero in the Multiplicand I. Learning Objectives Cognitive: Multiply 3- to 4-digit numbers by 1-digit number with zero in the multiplicand Psychomotor: Apply basic skills in multiplying numbers Affective: Follow the rules and regulations in every activity II. Learning Content Skills: Multiplying 3- to 4-digit number by 1-digit number with zero in the multiplicand Applying basic skills in multiplying numbers Reference: BEC PELC I.D.1.1.1.5 Materials: pictures, flaglets, box Value: Following rules and regulations III. Learning Experiences A. Preparatory Activities 1. Drill (Song) Multiply (Tune: Mary Had a Little Lamb) Let us learn to multiply Multiply, multiply Let us learn to multiply
- 27. 21 Table 2 and 3 (Pupils will recite table 2 and 3) 2 x 1 3 x 1 2 x 10 3 x 10 We had learn to multiply Multiply, multiply Table 2 and 3. Pupils recite the other multiplication tables. 2. Review Spin any of the roulettes. Then multiply the number at the center with the number where the arrow points. 3. Motivation Show a picture of a boy in a library. Talk about the picture. Ask: Have you been to a library? How should you behave when you’re in a library? What should you do in the library? What are some of the rules to be followed while you are in the library? Do you always follow them? Why? B. Developmental Activities 1. Presentation a. Present the problem. Manolito is a student assistant in the school library. He is counting the Mathematics books in the shelf. There are 120 books in each shelf. How many Mathematics books are there in the 6 shelves? b. Ask the following questions to the pupils. Who is the student assistant? How many books are there in each shelf? What is asked in the problem? What facts are given? What process is to be used? How will you solve the problem? - To find the number of Mathematics books, multiply 6 by 120
- 28. 22 Step 1 – Multiply the ones by 6 120 x 6 0 Step 2 – Multiply the tens by 6. Regroup the product. 120 x 6 20 Step 3 – Multiply the hundreds by 6. Add the regrouped hundreds. 6 hundreds + 1 hundred = 7 hundreds. 120 x 6 720 Mathematics books Ask: How many Mathematics books are there in all? c. Present another problem. A bookstore sold 2 105 greeting cards each month for three successive months. How many cards were sold altogether? Ask the following: - Have you received any greeting card? What kind of greeting card was it? - How many greeting cards did the bookstore sell in one month? - How many successive months did the bookstore sell greeting cards? - How will you find the answer? (Guide the pupils in answering the problem.) Step 1 2 105 x 3 5 Step 2 – Multiply the tens by 3. Add the regrouped ten. Zero ten + 1 ten = 1 ten 2 105 x 3 15 Step 3 – Multiply the hundreds by 3. 2 105 x 3 315 Step 3 – Multiply the thousands by 3. 2 105 x 3 6 315 The bookstore sold 6 315 greeting cards in 3 successive months. 2. Guided Practice a. Game: (Flaglet Race) Divide the class into 4 teams. A representative from each group will get a flaglet which has multiplication sentence written on it. The first one who can answer it can claim that flag. Do these with the other members of the group. The group who will earn more flaglets wins the game. b. Another activity (Find a Partner) Multiply the ones by 3. Regroup the product. 15 ones is 1 ten and 5 ones.
- 29. 23 Let the individual pupil get one number from the box. The numbers in the box are the multiplicands and the multipliers written separately on a strip of paper. The 1- digit number represents the multiplier, while the 2-3-digit numbers represent as the multiplicand. Every pupil will find a partner as – Multiplicand to multiplier and vice versa. Partners will solve it together. Multiplicand Multiplier 450 , 205 , 4501 1009 , 2380 , 8026 8 9 4 7 6 5 c. RIDDLE “What is the term used when giraffes going in one direction get mixed-up with giraffes going in another direction? Here’s how to get the answer. 1. Find the products of the exercises given below. 2. Then cross out the letters that show the same products in the boxes found on the next page. 3. The remaining letters spell the answer to our riddle. 1) 405 x 3 2) 360 x 8 3) 1204 x 5 4) 830 x 2 5) 310 x 8 6) 2035 x 6 7) 4510 x 4 8) 7068 x 9 9) 3205 x 5 4 305 1 660 18 040 1 215 8 550 7 065 16 025 A I T S G I U 15 270 2 480 4 501 7 782 8 900 2 880 4 320 R R A F F A I 2 670 12 210 7 028 6 020 4 950 63 612 3 201 C B J E A T M Answer: A G I R A F F I C J A M 3. Generalization: How do we multiply 3- to 4-digit numbers by 1-digit number with zero in the multiplicand? Multiply the ones, tens, hundreds and thousands in the multiplicand by the multiplier. Regroup when necessary. Zero times any number is zero and zero plus any number equals the same number.
- 30. 24 C. Application Solve the following problems. 1. A baker bakes 1 052 pieces of bread in one day. How many pieces of bread will he bake in 7 days? 2. Aling Marta has 8 baskets of tomatoes. If each basket contains 405 tomatoes, how many tomatoes will she have in all? 3. Mang Ading harvested 105 mangoes from each tree in his orchard. How many mangoes did he harvest from 7 trees? from 9 trees? 4. Pinky can read 260 words in 1 minute. If she spends 4 minutes reading, how many words can she read? IV. Evaluation Seatwork A. Fill in the blanks with the missing number. 1) 302 x 4 1 2_8 2) 4 510 x 6 2_ 0_0 3) 820 x 3 2 46_ 4) 905 x 7 6 _ _5 5) 1 075 x 8 8 _00 B. Check the multiplication problems and encircle any incorrect solution. 1) 408 x 5 2 040 2) 3 450 x 7 20 157 3) 6 071 x 8 48 568 4) 4 095 x 3 12 126 5) 5 708 x 4 22 832 C. Solve the following problems. 1. Miss de Alday arranges 140 books in every shelf in the library. There are 9 shelves. How many books are there in all? 2. Brylle collects 8 pages of stamps. Each page has 306 pieces. How many stamps are there in all? 3. Gloria helps her mother sell calamansi in the market. She puts 150 calamansi in each bag. How many calamansi are there in 7 bags? 4. Mrs. Pantoja bought 3 kilos of meat at 130 per kilo. How much did she pay the vendor? 5. There are 250 apples in a box. If an apple cost 5, how much will the apples cost? V. Assignment A. Multiply the following 1) 360 x 5 2) 4 008 x 2 3) 7 005 x 3
- 31. 25 4) 6 041 x 4 5) 5 730 x 6 B. Cross number puzzle Multiply the following number to solve the puzzle. a b c d g e f h i Across a. 170 x 5 b. 160 x 3 d. 320 x 8 h. 8 702 x 4 i. 108 x 2 Down a. 406 x 2 c. 3 520 x 2 e. 506 x 8 f. 1 620 x 3 g. 908 x 7 Multiplying 2- to 4-Digit Numbers by Multiples of 10 I. Learning Objectives Cognitive: Multiply 2 to 4 digit numbers by multiples of 10 Psychomotor: Solve multiplication sentence accurately Affective: Show the value of doing work independently II. Learning Content Skills: Multiplying 2 to 4 digit numbers by multiples of 10 Solving multiplication sentence accurately Reference: BEC PELC I. D.1.1.1.6 Materials: flash cards, activity cards Value: Independence III. Learning Experiences A. Preparatory Activities 1. Drill: Have a drill on multiplication basic facts using flashcards. 4 3 1 4 8 9 x 5 x 6 x 5 x 9 x 7 x 3
- 32. 26 5 2 5 3 2 3 x 7 x 9 x 0 x 8 x 7 x 5 2. Review Find the product. a) 21 b) 122 c) 3 012 d) 4 024 e) 313 x 5 x 6 x 4 x 2 x 3 3. Motivation Let all the pupils stand and do the skip movement on the floor. As they skip, let them count by 10s. (Say “10, 20, 30, 40, 50, 60, 70…) Ask: What do you observe about these numbers? (Possible answers are: “These numbers end in zero; or, These numbers can be divided by 10.”) Can you give other numbers that end in zero or that can be divided by 10? (Accept possible answers.) Say, “These numbers are called multiples of 10.” B. Developmental Activities 1. Presentation a. Present this problem. 1) In a toy factory, a group of workers filled the 21 boxes with 50 toy cars each How many toy cars were filled in all the boxes? 2) Analyze the problem. Ask: What is asked? (The total number of toy cars that were filled in all the boxes) What are the given facts? (21 boxes and 50 toy cars) What shall we do to find the answer? (multiply) What is the number sentence for the problem? (21 x 50 = N) 3) Discuss with the pupils the three steps of multiplication. Step 1 Ask, “What shall we do first? 21 (Multiply 21 by 0) x 50 00 Step 2 “What shall we do next? 21 (Multiply 21 by 5) x 50 00 105_
- 33. 27 Step 3 21 x 50 “What shall we do with the partial 00 products?” + 105_ (Add the partial products to get the 1 050 final product.) “So, what’s the answer to the problem?” (1050 toy cars were filled in all the boxes.) b. Now, let them study other examples. This time, help them discover a pattern that will help them multiply by multiples of 10 easily. 25 22 210 3140 x 10 x 30 x 40 x 40 250 660 8400 125 600 Ask,” How many zeros are there in the factors in the first and second examples? (1 zero) in the product? (1 zero) How about in the 3 rd and 4 th examples, how many zeros are there in the factors? (2 zeros each) in the product? (2 zeros) Point out that the number of zeros in the factors is equal to the number of zeros in the product. Say, “Multiply the non-zero digits and then annex zeros in the product. The number of zeros in both factors is equal to the number of zeros in the product. c. Now look at the number line. 0 | | | | | | | | | | | | | 10 20 30 40 50 60 70 80 90 100110120130 How many zeros are there in 12 tens? 12 x 10 = 120 How many zeros are there in 10? (1) What did you do with zero? 12 x 10 or 12 x 10 = 120 120 (Do the same process/procedure in the remaining numbers in the number line?) d. Error Analysis – For some exercises, some pupils might do this: 20 x 5 = 10 Have pupils who made this error look first at the product to see if it made sense. Ask: “Can 5 twenties be equal to 10? (No) Then have the pupils concentrate first on the product of 5 and 2 (10), then on writing the correct number of zeros after the product. 2. Guided Practice a. Divide the class into 3 groups. Let each group do the following: Look for the hidden message by solving each problem. Find the letter in the code that matches each answer. Write the correct letters in the boxes. (Each group will work independently.)
- 34. 28 1) 10 2) 80 3) 10 4) 560 5) 10 x 7 x 10 x 37 x 10 x 20 6) 70 7) 80 8) 90 9) 70 10) 80 x 5 x 70 x 30 x 80 x 50 11) 90 12) 300 13) 630 14) 72 o.) 640 x 70 x 70 x 10 x 30 x 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ayou are Math Whiz Code A – 5 600 I – 2 160 T – 4 000 K – 700 V – 40 Z – 12 800 H – 6 300 X – 210 M – 2 700 L – 560 R – 200 P – 240 W – 21 000 E – 350 U – 370 Y – 70 O – 800 S – 720 b. Investigation Divide the class into 2 groups. Give them activity card. ACTIVITY CARD # 1 Investigate, then write your investigation afterwards. 6 x 10 = 60 3 x 30 = 90 7 x 20 = 140 4 x 40 = 160 Questions: 1. How many zeros are there in each factor? ______ 2. How about the zeros in the products? ______ 3. Do they have the same number of zeros? 4. What is your investigation about it? ACTIVITY CARD # 2 Investigate, then write your investigation afterwards. 5 x 20 = 100 2 x 50 = 100 5 x 40 = 200 8 x 50 = 400 Questions: 1. How many zeros are there in each factor? ______ 2. How about the zeros in each product? ______ 3. Are the number of zeros in the factors the same with the number of zeros in the product? ________ 4. What is your investigation about it? __________ How did you answer your activity?
- 35. 29 Did you copy from the other group? Why? Stress the value of doing ones work independently. 3. Generalization How do we multiply 2- to 4-digit numbers by multiples of 10? a. To multiply by a multiple of 10, multiply the non-zero digits first, and then annex zeros in the product. b. The number of zero in the factors is equal to the number of zeros in the product. Is there a short cut for this? C. Application Solve the following problems. 1. There are 165 trays of oranges. Each tray has 20 oranges. How many oranges are there in all? 2. Grade Three SPED A class has 43 pupils. Each pupil has 10 books each. How many books did they have altogether? 3. If there are 24 bottles in a case, how many bottles will there be in 30 cases? IV. Evaluation A. Encircle the letter of the correct product. 1) 36 a. 36 b. 360 c. 3 610 x 10 2) 25 a. 2 520 b. 2 500 c. 500 x 20 3) 45 a. 1 350 b. 1 530 c. 1 340 x 30 4) 232 a. 2 320 b. 6 420 c. 4 640 x 20 5) 9 201 a. 276 030 b. 270 603 c. 273 060 x 30 B. Write >, <, or = in the blank. 1) 55 x 10 _____ 25 x 20 2) 500 x 70 _____ 50 x 70 3) 315 x 30 _____ 154 x 50 4) 750 x 20 _____ 20 x 750 5) 81 x 10 _____ 75 x 10 C. Solve the following problems. 1. A vendor sold 15 boxes of soap. Each box has 20 bars of soap. How many bars of soap did he sell? 2. Mang Ben gathered 213 baskets of mangoes. Each basket has 30 mangoes. How many mangoes did he gather?
- 36. 30 V. Assignment A. Answer the following: 1) 73 x 10 = 2) 25 x 30 = 3) 15 x 10 = 4) 62 x 10 (<, >, =) 60 x 10 5) 43 x 20 (<, >, =) 53 x 10 B. Find the product. 1) 77 x 10 = 2) 250 x 20 = 3) 2 248 x 20 = 4) 1 623 x 30 = 5) 4 132 x 40 = Multiplying 2- to 4- Digit Numbers by Multiples of 100 I. Learning Objectives Cognitive: Multiply 2- to 4- digit numbers by multiples of 100 Psychomotor: Annex the same number of zeros in the factors to the product Affective: Show cooperation in doing the activities II. Learning Content Skill: Multiplying 2- to 4- digit numbers by multiples of 100 Reference: BEC PELC D.I.1.2.3 Materials: flash cards, picture, bean bags Value: Cooperation III. Learning Experiences A. Preparatory Activities 1. Drill Present the TIC-TAC-TOE GAME. Divide the class into 2 groups. Show flash cards on multiplication by tens. To determine which group will play first, show a card to the representative of each group and the first one to answer correctly after a go signal will have his/her turn first. The group will choose another representative to answer the first card. If he/she gets it rig -Tac-Toe board: if not, the group will get an X. 2. Review Show cards 1 to 10 for the pupils to multiply mentally by 10s. Tell them that they will just add 1 zero after the number. 40 x 6 20 x 2 60 x 3 40 x 3 40 x 8 50 x 5 40 x 5 50 x 7
- 37. 31 3. Motivation Show a picture of an Indian. Ask: Have you seen an Indian? Say: Long ago a man in India decided to write a small dot to mean “zero”. Later the small dot became a circle. The circle is now called zero Working Together: Each member should cooperate. ● Work in a small group. Pretend zero does not exist. Try to write the numbers below without using zero. Talk about what you do. one hundred twenty one thousand, and two one thousand, two hundred one hundred two What if the man in India had never invented zero? What symbol would you use to stand for nothing? Say: Now we are going to work with zeros. B. Developmental Activities 1. Presentation a. Present this problem. A pharmacy ordered 100 packs of surgical gloves. Each pack contained 15 pairs of surgical gloves. How many pairs were delivered to the pharmacy? Show number card again and now multiply with 100. 100 x 15 = ____ To find the answer, we count by 100s. Long Method Step 1 100 x 15 (Multiply 100 by 5) 500 Step 2 100 x 15 (Multiply 100 by 1) 500 100_ Step 3 100 x 15 (Add the partial products to get 500 the final product) + 100_ 1 500 1 500 pairs of surgical gloves were delivered Short method 100 x 15 (Multiply the non-zero digits 15 by 1) 15__ 100
- 38. 32 x 15 (Affix the number of zeros to the product) 1 500 b. Present this number sentence. 1 100 x 100 = N How many zeros are there in 11 hundreds? 100? What are the non-zero digits in 11 x 100? After multiplying the non-zero digits, what did you do with zeros? 2. Guided Practice a. Give this activity sheet to the group. The Bean Bag Game Materials: 2 bean bags (x 100) Have the children play a toss game to practice multiplying by hundreds. Tape the numbered squares of paper to the floor as shown below. 2 324 175 231 3 561 25 38 74 15 Divide the class into 2 teams. Provide each team with 1 bean bag. The bean bags represent the factor 100. The teacher calls out a product 17 500. Since the factors of 17 500 are 175 and 100, a player from each team tosses the bean bag to the correct number on the grid (175) and earns one point for his/her team. For the product 1 500, the bean bag should be tossed to the number 15 on the grid. The first team to score 10 points wins the game. b. Divide the class into 4 groups. Let each representative of the group do the “Jack en Poy” game. The first one to win can choose the problem which he think is easier to solve. This will be done respectively by all the representatives of the group. Problems: 1. Cheryl bought 400 boxes of cough syrup from the drugstore. Each box contained 18 bottles. How many bottles of cough syrup did she buy? 2. Eva needs 300 packs of lozenges. Each pack contains 26 tablets. How many lozenges does she need in all? 3. Mary ordered 200 bags of syringes. Each bag has 114 syringes. How many syringes did she order? 4. Glenda will distribute 18 bedsheets in every room in the hospital. How many bedsheets will she need in all if there are 100 rooms?
- 39. 33 Solutions Problem No. 1 Problem No. 2 400 300 x 18 x 26 7 200 7 800 Problem No. 3 Problem No. 4 114 100 x 200 x 18 22 800 1 800 c. Problem solving using a table The table shows how some of the fastest vehicle in the world. Vehicle Speed (k/h) (rounded to the nearest hundreds) Hayaba Motorcycle 300 SSC Ultimate Aero Car 400 Spirit of Australia Water Vessel 500 French TGV Train 600 (Source: www.bukisa.com/47080) 1. If Hayaba Motorcycle run for 3 hours without stopping how far could it go? 2. If SSC Ultimate Aero Car travel for 2 hours, how far could it go? 3. If French TGV Train travel for 5 hours, how many kilometres could it reach? 4. If Spirit of Australia Water Vessel take a trip for 3 hours, how many kilometres could it travel? 3. Generalization: How do we multiply 2- to 4- digit numbers by multiples of 100? Multiply the non-zero digits. Then affix to the product the number of zeros from both the factors. C. Application Solve each problem. 1. There are 500 bags of peanuts. If each bag of peanuts contains 125 peanuts, how many peanuts will there be in all? 2. Jack delivers 25 magazine to 400 customers. How many magazines does he deliver in all? 3. One volume of encyclopedia has 400 pages. How many pages are there in 3 volumes? 4. When one-digit number is multiplied by 100, the product is 720 more than the product of the number and 10. What is the number? Answer: 8 x 100 = 800 720 more 8 x 10 = 80 The number is 8.
- 40. 34 IV. Evaluation A. Write the missing number. 1) 13 x 3 hundreds = ___ hundreds 13 x 300 = ___ 2) 24 x 2 hundreds = ___ hundreds 24 x 200 = ___ 3) 16 x 7 hundreds = ___ hundreds 16 x 700 = ___ 4) 14 x 8 hundreds = ___ hundreds 14 x 800 = ___ 5) 15 x 6 hundreds = ___ hundreds 15 x 600 = ___ B. Encircle the letter of the correct answer. 1) 219 multiplied by 100 gives the product of ___ a. 21 900 b. 25 c. 2 500 d. 2 600 2) 25 times 100 equals ___ a. 250 b. 25 c. 2 500 d. 2 600 3) 24 times 200 = ___ what number should be placed in the box. a. 2 400 b. 4 800 c. 2 242 d. 24 000 4) What number when multiplied by 100 gives the product of 2800? a. 28 b. 2 807 c. 280 000 d. 2 888 5) What is the missing number in this sentence? 36 x ___ = 3 600 a. 10 b. 100 c. 1 000 d. 120 C. Supply with the multiples of 100. 1) 5 x ___ = 3 500 2) 8 x ___ = 7 200 3) 4 x ___ = 2 400 4) 12 x ___ = 6 000 5) 23 x ___ = 13 800 V. Assignment A. Multiply mentally. Write the product. 1) 800 x 24 2) 600 x 17 3) 900 x 25 4) 300 x 18 5) 700 x 24 B. Write >, < or = in the blank. 1) 9 x 900 ___ 9 x 8000 2) 600 x 7 ___ 70 x 600 3) 70 x 500 ___ 50 x 70
- 41. 35 4) 500 x 81 ___ 50 x 800 5) 800 x 21 ___ 31 x 900 Estimating the Product of 2- to 3-Digit Numbers by 1- to 2-Digit Numbers I. Learning Objectives Cognitive: Estimate the product of 2- to 3-digit numbers by 1- to 2-digit numbers Psychomotor: Follow the steps in estimating the product Affective: Show neatness in one’s computation II. Learning Content Skill: Estimating the product of 2- to 3-digit numbers by 1- to 2-digit numbers Reference: BEC PELC I.D.1.1.2 Materials: chart, activity sheets, flash cards, roulette Value: Neatness III. Learning Experiences A. Preparatory Activities 1. Drill Give a drill on multiplication using flashcard. Present the Give-Me-The-Card Game to the class. Arrange the cards on the chalk ledge. The teacher will give the product and the pupils from each team will find the card of its factors. The first one to get the correct card wins a point. 2. Review Let the pupils spin the roulette then round off the numbers to the nearest tens, hundreds and thousands. 9 x 6 8 x 7 9 x 6 3 x 7 9 x 9 7 x 4 5 x 8 2 x 8 8 x 3 9 x 10 Nearest Tens 75 46 23 68 84 32 Nearest Hundreds 372 296 734 524 850 415
- 42. 36 3. Motivation (Show a picture of a school garden.) What vegetables grow in the school garden? How many okra plants are there? Estimate the numbers of each kind of plants. What should you do to make your plants healthy and robust? B. Developmental Activities 1. Presentation a. Let us read this problem. A farmer prepares 15 plots for vegetables. About how many seedlings will be needed if each plot could be planted with 9 seedlings? How many plots are being prepared by the farmer? How many seedlings could be planted in one plot? What is the mathematical sentence? Multiply: 9 x 15 = N Think: 15 x 9 rounded to 20 x 9 180 estimated product 15 x 9 rounded to 15 x 10 150 estimated product therefore 15 x 10 150 nearest estimated product b. Let’s have another problem. Mang Delfin harvested 263 sacks of rice in one hectare. About how many sacks of rice will be harvested in 12 hectares? Multiply: 263 x 12 = N Estimate the product. Think: 263 x 12 rounded to 300 x 10 600 3 000 3 600 263 x 12 rounded to 263 x 10 2 630 263 x 12 rounded to rounded to 300 x 10 3 000 nearest estimated product
- 43. 37 c. Here are some examples. 491 x 4 is rounded off to 500 x 4 2 000 estimated product Remember that we do not round off a 1-digit number. 98 x 23 is rounded off to 100 x 20 2 000 estimated product 832 x 67 is rounded off to 800 x 70 56 000 estimated product 2. Guided Practice a. Estimate each product. Please avoid too many erasures. 1) 73 2) 87 3) 74 4) 473 5) 664 x 5 x 6 x 4 x 6 x 8 6) 38 7) 76 8) 526 9) 89 10) 479 x 23 x 44 x 48 x 23 x 29 b. Group pupils into pairs then have them perform the activity shown below. MANIPULATIVE ACTIVITY CARD 19 Activity: Estimating Products Materials: number cards (1-10) Group Size: Pairs Procedure: Distribute number cards to each pair, face down, in pile. Write on board: 374, 438, 152, 297. Partner 1 draws number card (e.g. 6). Partners write multiplication example using the number on the board and number card. (374 x 6) Partner 1 rounds up 374 and finds the product (400 x 6); Partner 2 rounds down and finds the product. (300 x 6) Continue the activity with the remaining numbers on the board. (5-10 min.) c. Perfect Score Pamela Perfect would like you to check her Math problems so she can get a perfect score. Estimate to check the product. Encircle any incorrect solution. Ex.: 325 300 X 12 x 10 3000 1) 22 2) 163 3) 573 x 16 x 5 x 45
- 44. 38 4) 465 5) 727 6) 26 x 15 x 36 x 14 7) 982 8) 230 9) 318 x 43 x 75 x 48 3. Generalization How do we estimate the product of 2- to 3-digit numbers multiplied by 1- to 2-digit numbers? To estimate the product: Round either the multiplicand or multiplier or both to its greatest place value. Multiply the rounded factors. Why is estimation useful? C. Application Estimate and solve each problem. 1. There are 5 cages. Each cage has 38 birds. About how many birds are there? 2. There are 35 pupils in a class. Each pupil collected 125 copies of old newspapers. About how many copies of newspapers did the class collect? 3. Mang Celso gathered 285 eggs from his poultry farm in one day. About how many eggs would he gather in one week? 4. Simon spends 645 for his transportation per month. About how much would his total transportation expenses be for 18 months? 5. A movie theater can accommodate 375 people in each show. About how many people can the theater accommodate in 24 shows? IV. Evaluation A. Estimate the products. 1) 83 2) 67 3) 365 x 12 x 41 x 77 4) 622 5) 776 6) 634 x 56 x 52 x 59 B. Multiply then estimate to check the product. 1) 183 x 6 = ___ x ___ = _____ 2) 698 x 7 = ___ x ___ = _____ 3) 68 x 71 = ___ x ___ = _____ 4) 236 x 18 = ___ x ___ = _____ 5) 732 x 5 = ___ x ___ = _____
- 45. 39 V. Assignment A. Find the factors that when multiplied will give each estimated product on the left. 1) 60 6 x 14 5 x 18 5 x 13 2) 150 4 x 34 4 x 36 5 x 28 3) 270 9 x 24 9 x 26 8 x 31 4) 360 6 x 53 7 x 47 6 x 58 5) 4500 8 x 542 7 x 684 9 x 487 B. Estimate the products then compare using <, > or =. 1) 321 x 6 119 x 23 2) 506 x 12 605 x 9 3) 159 x 4 591 x 18 4) 679 x 4 663 x 4 5) 872 x 37 834 x 27 Estimating the Product of 4-Digit Numbers by 1- to 2- Digit Numbers I. Learning Objectives Cognitive: Estimate the product of 4-digit numbers by 1- to 2- digit numbers Psychomotor: Follow the steps in estimating the product Affective: Participate actively in the discussion II. Learning Content Skills: a. Estimating the product of 4-digit numbers by 1- to 2- digit numbers b. Following the steps in estimating the product Reference: BEC PELC I D 1.1.3 Materials: roulette, word problems written on manila paper Value: Active participation III. Learning Experiences A. Preparatory Activities 1. Drill : Spin a roulette. Multiply the numbers by 10.
- 46. 40 2. Review Round off the following numbers. Number Nearest tens Nearest hundreds Nearest thousands 9 375 9 380 9 400 9 000 12 478 13 265 24 563 46 814 3. Motivation (Problem Opener) A bookstore sold 2 165 greeting cards each month for 3 successive months. About how many cards were sold in these months? B. Developmental Activities 1. Presentation a. How many successive months did the bookstore sell greeting cards? How many greeting cards were sold in each month? To find out, estimate the product. Circle the thousands digit in the multiplicand. Round off the multiplicand to the place value of that digit. Then multiply to estimate the product. 2165 x 3 2 000 x 3 6 000 Round off to the nearest thousand. About 6 000 cards were sold in 3 months. We can also use estimation to check the answer. - How many digits does the multiplicand have? Into what place are you going to round off 2 165? Do we need to round off 3? Why? b. Let’s try another example. Aling Cora sells big watermelons in the market every summer. If she can sell 1 023 watermelons in a month, about how many watermelons can she sell in 12 months? Step 1: Round the multiplicand and the multiplier to the highest place value. 1 025 x 12 watermelons months 1 000 x 10 Step 2: Multiply to find the product. 1 000 x 10 10 000 Estimated number of watermelons. c. Examine carefully how the estimated products of these examples are found. 4 735 x 28 5 000 x 30 150 000 6 423 x 6 6 000 x 6 36 000 In example A, did you round off both the multiplicand and the multiplier? Into what places were they rounded off? In example B did you round off the multiplier? Why?
- 47. 41 2. Guided Practice a. Let all the pupils chant with the “Pass it On” music Let the pupils form a big circle. They are going to pass a rolled strip of cartolina. When the music stops, the one who holds the strip will answer what is written on it through estimation. b. Estimate to solve each problem. 1) A bus travels 1 263 kilometres in a week. About how many kilometres does it travel in 6 weeks? 2) Mang Simon spends 2 645 for his transportation per month. About how much will be spend for 3 months? 3) A movie theater can accommodate 3 405 people in each show. About how many people will it be able to accommodate in 24 shows? 4) The Sport Club ordered 1 171 boxes of basketball. Each box contains 4 balls. About how many balls did they order? 5) Sta. Catalina Central School received 35 boxes of pencils from a rich balikbayan. Each box contains 2 356 pencils. About how many pencils did the school receive? c. Round the multiplicands to their highest place, then find the estimated products. Write the answers on your paper. 1) 1 208 2) 3 946 3) 6 854 4) 8 309 x 8 x 5 x 3 x 7 5) 9 287 x 9 d. Try harder. Find the actual and the estimated products. Write the answers on your paper. 1) 5 456 2) 7 812 3) 8 743 4) 1 090 5) 6 731 x 2 x 16 x 41 x 7 x 8 3. Generalization: How do we estimate the product of a 4-digit number by 1- to 2- digit numbers? When we estimate a product, we round off the factor to its highest place value, then multiply. We do not need to round off a one-digit factor. 3 882 x 26 1 392 x 38 7 056 x 2 4 481 x 12 6 970 x 78
- 48. 42 C. Application Solve each problem. 1. Mang Mario can harvest 1 252 ears of corn from his farm a day. About how many ears of corn can he harvest in 3 days? 2. Mang Delfin harvested 2 637 sacks of rice in one hectare. About how many sacks of rice will be harvested in 12 hectares? 3. Last year, a car manufacturer shipped 3 705 cards to each of his 14 dealers. About how many cars were shipped in all? 4. There are 1 203 subdivisions in Cavite. Each subdivision has 85 houses. About how many houses are there in Cavite? 5. Chris delivers 1 710 letters each month. About how many letters will Chris deliver in 9 months? IV. Evaluation A. Find the factors that when multiplied will give each estimated product on the left. 1) 12 000 6 x 1 561 5 x 1 842 5 x 3 423 2) 15 000 7 x 2 165 3 x 4 583 6 x 1 252 3) 24 000 4 x 5 983 3 x 9 754 5 x 8 392 4) 45 000 8 x 5 425 7 x 6 846 9 x 4 873 5) 200 000 42 x 4 868 49 x 4 869 34 x 4 863 B. Estimate each product. 1) 8 025 2) 3 676 3) 4 236 4) 7 632 5) 6 423 x 4 x 12 x 23 x 35 x 82 V. Assignment A. Estimate the products. 1) 6 620 x 8 2) 7 676 x 28 3) 3 812 x 28 4) 8 905 x 34 5) 9 135 x 36
- 49. 43 Multiplying Mentally 2-Digit Numbers with Products up to 100 without Regrouping I. Learning Objectives Cognitive: Multiply mentally 2-digit numbers by 1-digit number with product up to 100 without regrouping Psychomotor: Solve mentally word problems involving multiplication Affective: Work well with classmates II. Learning Content Skill: Multiplying mentally 2-digit numbers with product up to 100 without regrouping Reference: BEC PELC I.D.1.1.4 Materials: flash cards, drawing, crayon Value: Cooperation and independence III. Learning Experiences A. Preparatory Activities 1. Drill Game: Salute Materials: set of number cards (1 digit-number) 1. Each group is composed of three members. 2. Two members will get each card and put it on their head (two members facing each other) as the remaining member of the group says “salute”. 3. The one who says salute will give the product of the two numbers written on the cards. 4. The first to give the number on his/her head gets the point. 5. The team with the highest point wins. 2. Review GAME: Color the Mailbox – 2 Groups Teacher will call out 2 pupils, one from each group. She will flash combination of numbers. Then the pupils will give the estimated product. The first one who can give the correct answer will have the chance to color the first figure in the mailbox. The teacher will repeat the process until the group had completed coloring the figures in the mailbox. The first group to complete coloring the mailbox wins the game. Flashcards: 1 212 x 2 326 x 5 4 213 x 12 3 214 x 25 1 432 x 32
- 50. 44 Group I Group II 3. Motivation Astronomers sometimes need calculators and computers in their study of space. When do you need a calculator? When is mental Math a faster way to find an answer? Find these products as quickly as you can. 9 x 3 8 x 9 6 x 8 7 x 7 B. Developmental Activities 1. Presentation a. Present this problem. Four boys helped their teacher return some workbooks to the library. Each boy carried 12 workbooks. How many workbooks did they carry altogether? Multiply 12 by 4. Do it mentally. Think: Multiply the ones by ones. Multiply the tens by ones. Give the product. 1 2 12 X 4 x 4 8 48 The product is 48. So, 48 workbooks were carried by the boys. Marlon picked avocados from their farm. He put them in 3 bags. If there are 13 avocados in each bag, how many avocados did Marlon pick? Think: 1 3 13 X 3 x 3 9 39 1 4 3 5 7 8 6 2 1 4 3 5 7 8 6 2
- 51. 45 b. The teacher will give more examples. 11 1 1 11 X 5 x 5 x 5 5 55 22 2 2 22 X 3 x 3 x 3 6 66 13 1 3 13 X 2 x 2 x 2 6 26 12 1 2 12 X 2 x 2 x 2 4 24 2. Guided Practice a. Divide the class into four groups then assign a leader in each group. Each group will be given an activity sheet with word problems to be answered mentally. The first group to finish shall post their work on the board. What should you do when you work in groups? Will it give better results? Why? ACTIVITY SHEET Find the answer as fast as you can by multiplying mentally. There are 22 eggs in a tray. How many eggs are there in 4 trays? Tina has 3 pencil cases. If there are 12 pencils in each case, how many pencils does she have? Fifteen pupils are seated in a row. If there are 4 rows in the classroom, how many pupils are there? Thirty two guavas were placed in a basket. If there are 4 baskets, how many guavas are there in all? After 5 minutes, post your work on the board. Which group got the highest score? What does it mean? b. Work in Pairs Answer mentally. 13 12 20 23 13 12 x 3 x 4 x 1 x 2 x 2 x 3 c. Treasure Hunting Have you experienced hunting treasures? Do you want to experience it? Well, trace the path by passing the obstacles. Look for a card in the box and tape the answer in the correct tree from the START. Follow the arrow until you reach the finish line. 55 66 26 24
- 52. 46 3. Generalization How do you multiply mentally 2-digit numbers by 1-digit number without regrouping? To multiply mentally 2-digit numbers without regrouping ● Multiply the ones by ones. ● Multiply the tens by ones. ● Then give the product. C. Application What did the boy say when he met his teacher? Look at the hidden message by solving the exercises. Find the letter in the code that matches each answer. Write the letter inside the circles. 12 13 23 11 12 13 13 26 20 22 23 x 5 x 2 x 2 x 4 x 3 x 2 x 3 x 1 x 3 x 2 x 3 A – 36 B – 28 C – 59 D – 54 E – 69 F – 66 G – 53 H – 39 I – 60 J – 77 K – 61 L – 30 M – 44 N – 48 O – 34 P – 38 Q – 41 R – 42 S – 46 T – 26 U – 72 Z – 2 V – 94 W – 76 X – 89 Y – 57
- 53. 47 IV. Evaluation A. Listen to these multiplication sentences. Find their products without using paper and pencil. Answer as fast as you can. 1) 34 2) 23 3) 44 4) 20 5) 13 x 2 x 3 x 2 x 3 x 3 B. Solve each problem. 1. Elvie planted 3 rows of sampaguita. Each row had 12 sampaguita plants. How many sampaguita plants did she plant in all? 2. Francis planted 11 plots with eggplant seedlings. Each plot has 8 eggplant seedlings. How many eggplant seedlings did he plant? 3. A jeepney driver charges each passenger 20 for a sight-seeing trip. How much will he earn if he has 5 passengers? 4. A farmer prepares 11 plots for vegetables. How many seedlings will be needed if each plot is planted with 9 seedlings? 5. You need 2 oranges to make a glass of orange juice. How many oranges do you need to make 13 glasses of orange juice? V. Assignment A. Solve mentally. 1) 11 2) 12 3) 23 4) 24 5) 13 x 7 x 2 x 3 x 2 x 3 B. Cut out colorful pictures from magazines and paste them on 2 1 index card. Write a word problem involving multiplication of 2-digit by 1-digit without regrouping. Answer each problem mentally. Write the answer at the back of the card. Solving Word Problems Involving Multiplication of Whole Numbers Including Money I. Learning Objectives Cognitive: Solve word problems involving multiplication of whole numbers including money Psychomotor: Write the solution to the problem correctly Affective: Practice being thrifty II. Learning Content Skills: Solving word problems involving multiplication of whole numbers including money Giving solution to the problems correctly Reference: BEC PELC I D 2.1 Materials: textbook, flash cards, roulette, chart, activity cards, pictures of plants Value: Thrift III. Learning Experiences A. Preparatory Activities
- 54. 48 1. Drill: Basic multiplication facts using this double roulette. 2. Review: Transform this problem into number sentence. Ask: Who helped father in the garden? What did they plant? How many tomato seedlings did they plant in a row? How many rows were planted with tomatoes? What are you going to look for in this problem? What are the given data? What is the number sentence? 3. Motivation Present this story problem. Cheena saves 15.00 a day. How much will she save in 5 days? Ask: How much does Cheena save in a day? For how many days will Cheena save? Who among you are like Cheena? How much do you save in a day? Is it good to save? Why? B. Developmental Activities 1. Presentation a. Group the children into four. Using the problem, let each group illustrate the problem. Present this guide to the children in analyzing and illustrating the problem. Problem: What is asked for? What are the given information? Draw/illustrate the problem. What is the process or operation to be used? What word/s help you determine the operation to use. Write the number sentence. Jobette helped his father in the garden. They planted 63 tomato seedlings in a row. How many tomato seedlings did they plant in 7 rows?
- 55. 49 Let the pupils show their work and explain it. Involve the class in checking to see whether what the group did is correct or not. If you were to solve the problem, what process would you use? Is there a word or words in the problem that tell what process or operation to use? b. Present problems that used different keywords or word clues to determine the operation to be used. Let them analyze. 1. A vendor buys 85 boxes of candies. Each box has 100 candies. How many candies are there in all? 2. Nena bought 12 sets of baby dresses. Each set costs 185. How much did she pay for all the dresses? 3. Mr. Santos is a postman. He has to deliver 178 letters in a day. How many letters will he deliver in 25 days? Problem 1 Problem 2 Problem 3 How many candies; in all How much; for all How many What operations will you use if you see these words? c. Assign the problems to three group. Let them solve the problem showing the correct solution and operation. Ex. What is asked? Total number of candies What data/facts are given? 85 boxes of candies 100 candies in each box What is the operation/process to be used? Multiplication What is the number sentence? 85 x 100 = n Solve the number sentence. 85 x 100 = 8 500 What is the complete answer? There are 8 500 candies in all. 2. Guided Practice Using the strategy – multiplication concentration. Materials: 12 cards with multiplication problems 12 cards with their products Procedures: Shuffle all 24 cards and place them face down in four rows of six cards each. Players take turns turning over two cards. If one shows a problem and the other card shows its product, the player keeps those cards. If the cards do not match, the player will read the problem in the cards and solve it showing the correct solution and operations. - The player with the most cards or who solve the most number of problems will be declared winner. 3. Generalization What did you do to solve/get the correct answer? What are the steps that we should follow in solving problems.
- 56. 50 C. Application Read and understand each problem. Solve using Polya’s method. 1. Mang Berto picked 25 small baskets of atis. If each basket contained 45 atis, how many atis were there in all? 2. If each basket of atis costs 120.00, how much will Mang Berto receive for 25 small basket of atis? 3. Mr. Lee sells mangoes by baskets. Each basket contains 26 mangoes. How many mangoes does 34 baskets have? 4. Alma saves 25.00 a day in her piggy bank. How much money will she save in twelve days? 5. Pet could read 75 pages of his favorite pocket book in a day. If he would read for 12 days, how many pages would he finish? IV. Evaluation A. Read and solve the following. 1. Grandma gave her 6 grandsons 100 each last Christmas. How much did she give-away in all? 2. Mr. Cruz deposits 2 500 every month. How much will be his deposit in 8 months? 3. A tray contains 30 eggs. How many eggs will there be in 115 trays? 4. A one-way plane ticket to Cebu costs 1 540. If there were 100 passengers with one-way tickets, how much did all their tickets cost? 5. A dictionary costs 1 345.00 pesos each. A teacher needs a dictionary for her class. How much will it costs her to buy the dictionary? V. Assignment Read and solve. 1. A bus can accommodate 72 passengers. How many passengers can be accommodated in 15 buses? 2. Three vendors sold small flags at 3.00 at Luneta during the Independence Day celebration. These vendors were able to sell 320 flags. How much was the total sale of the three vendors? 3. The Grade III class of 45 pupils used bottle caps for their project. Each child used 25 pieces of bottle caps. How many bottle caps did the children use? 4. Simon spends 645 for his transportation per month. How much is his total transportation expenses for 9 months? 5. Nancy can type 32 words per minute. How many words can she type in 400 minutes? Solving 2- to 3-Step Word Problems involving Multiplication and any one of Addition/Subtraction I. Learning Objectives Cognitive: Solve 2- to 3-step word problems involving multiplication and any one of addition/subtraction Psychomotor: Follow the steps in problem solving Affective: Practice the habit of being honest
- 57. 51 II. Learning Content Skill: Solving 2-3 step word problems involving multiplication and any one of addition/subtraction Reference: BEC-PELC I.D.3.1 Materials: Textbooks, charts, flash cards, “Show Me Card”, real objects Value: Honesty III. Learning Experiences A. Preparatory Activities 1. Drill The teacher flashes the flashcards and the children write their answers on their “Show Me” board. 32 20 83 42 21 x2 x4 x3 x2 x2 2. Review a. Present the problem written on Manila paper. Laura made 56 sampaguita garlands. Each garlands has 13 pieces of sampaguita. How many pieces of sampaguita did she use in all? Ask: Who made sampaguita garlands? How many sampaguita garlands did she make? What is asked in the problem? What are given? What is the operation to be used to solve the problem? Let the children solve the problem and show the answer in their “Show Me Board.” b. Add in the review multiplication of numbers with decimal point (including money). 3. Motivation Present the word problem. Gally bought 5 shirts for 94.50 each. If he had 475.00, how much change would he get? Ask: Who bought 5 shirts? How much did each shirt cost? How much money had he? How much would he spend for his five shirts? The salesgirl happened to give a change more than what Gally should receive? If you were Gally, what would you do? Why?
- 58. 52 Is it good to return the money that does not belong to you? Why? B. Developmental Activities 1. Presentation a. Using the problems in the motivation, ask the pupils to act out through “Play Store” wherein pictures or objects like shirts, play money, etc are used. A pupil will go to the store and buy shirts. b. Present the problem using a diagram. ■ Read How many shirts were bought? How much did a shirt cost? How much money did Gally have? ■ Plan What is the hidden question? the cost of 4 shirts What is asked? change Gally would get What operation should be used? What is the number sentence? 475 - ( 94.50 x 5) = N ■ Solve STEP 1 - Look for the cost of 5 shirts. 94.50 cost of 1 shirt X 5 number of shirts bought 472.50 cost of 4 shirts STEP 2 475.00 money of Gally -472.50 costs of 4 shirts 2.50 change ■ Check Go over the solution. Is it correct? Is your answer reasonable? Is it complete? 2. Guided Practice Learning Barkadas LBs will be given 5 two-step word problems to solve. The first LBs who will get the most points wins. Solve each problem.
- 59. 53 1. Allan and Andy have one garden plot each, Allan has 4 rows of 12 pechays in each row. Andy has 5 rows of 10 pechay in each row. How many pechay plants do they have altogether? 2. Rafael is saving money for a new pair of pants worth 386.00. He has been saving 20.00 a day for ten days. How much more has he to save to buy new pants? 3. Mr. Rey went on a vacation. He bought 35 pasalubong items for his relatives and friends. If each item costs 50.00 and he gave the seller 2 000, how much change would he get? 4. In the canteen’s refrigerator, there were four trays of eggs. Each tray had 12 eggs. The cook got 15 eggs. How many eggs were left in the refrigerator? 3. Generalization What are the important points to consider in solving 2-step word problems? In solving 2-step word problems, first answer the hidden question then the given question. The operation inside the parenthesis is done first. C. Application Solve the following problems. 1. A “litson manok” vendor uses 2 sacks of charcoal a day. How much will be paid for charcoal in 30 days, if each sack costs 80.00? 2. Cherry has 500.00. She bought 3 books at 150.00 each. How much did she pay for the books? How much money was left ? IV. Evaluation Read and solve the following problems. 1. Joseph earned 35.00 each day for 5 days. He spent 55.00 for his snacks. How much money was left? 2. Alyssa bought three kilograms of sugar at 26.00 per kilogram and a bottle of chocolate for 25.00. How much did she spend in all? Using the table below, answer the questions that follow. sandwich 25.00 pineapple juice 15.00 cookies 10.00 3. Alma bought 2 sandwiches and a can of pineapple juice. How much did she spend in all? 4. If Josie bought 3 cookies, how much change would she get from her 50.00? 5. If Marlon bought two packs of pineapple juice and gave the vendor 100.00, how much change would he get?
- 60. 54 V. Assignment Solve these problems. 1. Fely packed bottles of honey in 8 boxes. Each box had 3 layers of 12 bottles. How many bottles did Fely pack? 2. Jun bought 18 baskets of mabolo. Each basket costs 90.00. How much change would he get from his 2,000.00?

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