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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 II Rational Numbers Fractions 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 II. RATIONAL NUMBERS A. Division Identifying Fractions Less Than One .............................................................................. 1 Telling the Relationship Between Fractions Less than One ........................................... 5 Ordering Fractions Less than One Having One as Numerators..................................... 9 Identify Fractions Equal to One....................................................................................... 13 Identify Fractions More than One.................................................................................... 16 Ordering Fractions Equal to One, Less than One and More than One with the same Denominators..................................................................................................... 20 Finding the GCF (Greatest Common Factor) of Two Given Numbers ........................... 25 Reducing Fractions to Lowest Terms ............................................................................. 29 Finding Fractional Part of a Set/Region.......................................................................... 33
- 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. Rational Numbers A. Comprehension of Fractions 1. Order fractions less than one/equal to one/more than one 1.1 Identify fractions less than one Sharing Modeling Drawing pictures Drawing (Spatial) 1.2 Order fractions less than one Active participation Drawing pictures Modeling Play (Bodily kinesthetic) Drawing (Spatial) 1.2.1 Tell the relationship between fractions less than one Health consciousness Simplifying the problem Modeling Drawing pictures Cooperative groups(Interpersonal) Drawing (Spatial) 1.3 Identify fractions equal to one Neatness Modeling Write equation Games (Bodily kinesthetic) 1.4 Identify fractions more than one Concern for others Simplifying the problem Drawing pictures Song (Musical) "Looking for a Partner" Game(Bodily kinesthetic) Drawing (Spatial) Game "Giant Step" (Bodily kinesthetic) Cooperative groups(Interpersonal) 1.5 Order fractions less than one/equal to one/more than one Health consciousness Modeling/drawing pictures "Giant Step" Game (Bodily kinesthetic) Cooperative groups(Interpersonal) 2. Change fractions to lower forms 2.1 Tell the greatest number by which two given numbers can exactly be divided 2.1.1 Give the GCF (Greatest Common Factor) of 2 given numbers Thriftiness Listing Games (Bodily kinesthetic) Cooperative groups(Interpersonal) 2.2 Reduce fractions to lowest terms Sharing Simplifying the problem Illustrations (Spatial) Song (Musical
- 6. vi 3. Find the fractional part of set/regions e.g. 1/3 of 12 1/4 of 20 1/2 of 8 Helpfulness Acting out the problem Games (Bodily kinesthetic) Cooperative groups(Interpersonal)
- 7. 1 Identifying Fractions Less Than One I. Learning Objectives Cognitive: Identify fractions less than one Psychomotor: Read and write fractions less than one Affective: Practice the habit of sharing II. Learning Content Skills: 1. Identifying fractions less than one 2. Reading and writing fractions less than one Reference: BEC PELC II A.1.1 Materials: textbooks, flash cards, coloring materials Value: Sharing III. Learning Experiences A. Preparatory Activities: 1. Drill Name the shaded part/unshaded part 2 1 3 1 4 2 8 3 2. Review – Parts of a fraction 1. What does 1 mean in 2 1 ’ 3 1 ; 2 in 4 2 ; 3 in 8 3 ? 2. What do you call them? 3. What does 2 mean in 2 1 ? 3 in 3 1 ? 3 in 8 3 ? 4. What do you call them? 3. Motivation Show a cake model. On Mary’s birthday, her mother baked a cake. She divided it into 8 equal parts to be shared among her friends. What do you call one of the equivalent parts? 8 1 Who can write the fraction in figure? 8 1 Write it in words. One eighth
- 8. 2 Mary is a generous girl because she shares the cake to her friends. Do you also share things to your friends and family? What are the things that you share to your friends? Your family? B. Developmental Activities: 1. Presentation a. Show an illustration of the cake on the board b. Let the pupil shade two of the eight equivalent parts. How many parts are shaded? The shaded parts were given to Rose and Josie. What part of the whole cake was given to Rose and Josie? Who can represent the shaded parts in figures? 8 2 Read the fraction. How do we write it in words? Two eighths Now, what part of the whole cake was left? 8 6 six eighths Ask the pupil to write the fraction in figures and in words. Let the pupils shade the whole region. What fraction represents the whole region? 8 8 Is 8 8 equal to the whole region? Write: 8 8 = 1 Is 8 2 less than 8 8 ? Is 8 6 less than 8 8 ? c. Comparing parts of whole region (use cut-out of shapes) Present the figures below. Let the pupils observe the figures. Ask: How many equivalent parts does each figure have? Have the pupils write the numerals representing the number of equal parts each figure has. Let the pupils write the numerals representing the shaded parts in their show me cards. Ask the pupils to match their show me cards with the cut-out shapes. Let the pupils compare the fraction by using the symbols >, <. Which is greater? 4 1 or 3 2 , 4 3 or 4 1 , 5 3 or 4 1 , 3 2 or 4 3
- 9. 3 4 1 or 4 4 , 5 3 or 5 5 , 3 2 or 3 3 2. Guided Practice a. Drawing regions for the given numerals. Let the pupils draw regions to represent the following fractions. 4 1 3 2 4 3 5 1 6 1 b. Comparing parts of a fraction (Numerator and Denominator) What do we call? 1 in 4 1 , 2 in 3 2 , 3 in 4 3 etc. What does the numerator represent? What does the denominator tell us? c. Using a number line, ask pupils to divide it into 5 equivalent parts. 5 1 5 2 5 3 5 4 5 5 Into how many equivalent parts is the line segment divided? What do you call 2 of the equivalent parts? Write the fraction in figure and in words. 5 2 two fifths You can see in the illustration that 1 is equal to 5 5 , read all the fractions less than one or 5 5 . What can you say about the numerators of these fractions in relation to their denominators? The numerators are less than the denominators. We call these, fractions less than one. 3. Generalization How do we know if a fraction is less than one? A fraction is less than one when the numerator is less than the denominator. C. Application A. Play “Who Am I?” 1. I am a fraction equal to one. My denominator is 9. Who am I? 2. I am a fraction that shows 5 of 9 equal parts. Who am I? 3. I am a fraction whose denominator is 4 and my numerator is 2 of the equivalent parts. Who am I? B. Pair Square 1. Find all possible fractions in which the sum of the numerator and denominator is greater than the numerator. What do you notice? 2. Find a fraction in which the difference of the numerator and denominator is 3 and the sum is 8.
- 10. 4 IV. Evaluation A. Do what is asked. a. Divide the following into halves, thirds and fourths. a. Shade one of the equivalent parts. c. Write the fraction name for the shaded part. B. Write √ if the fraction is less than one and x if it’s is not less than one. _____ 1) 3 2 _____ 2) 12 4 _____ 3) 3 4 _____ 4) 7 8 _____ 5) 9 7 _____ 6) 10 11 _____ 7) 11 8 _____ 8) 7 3 _____ 9) 10 12 _____ 10) 2 3 V. Assignment: A. Circle the fractions less than 1. 1) 4 2 , 3 5 , 4 4 2) 6 6 , 10 12 , 5 1 3) 8 5 , 7 9 , 5 6 4) 2 1 , 2 3 , 3 4 5) 5 5 , 7 3 , 4 6
- 11. 5 B. Draw and shade to show the fraction. 1. 2. 3. 4. 5. Telling the Relationship Between Fractions Less Than One I. Learning Objectives Cognitive: Tell the relationship between fractions less than one Psychomotor: Show relationship between fractions by using the symbols > and < Affective: Practice eating the right kinds of food II. Learning Content Skills: 1. Telling the relationship between fractions less than one 2. Reading and writing fractions less than one Reference: BEC PELC II A.1.2.1 Materials: cut-outs with color shaded parts, diagram showing fractions less than one Value: Health consciousness III. Learning Experiences A. Preparatory Activities 1. Drill - Naming fractions less than one. 1. Show cut-outs of regions with shaded parts 2. Ask the pupils to name the shaded parts. 2. Review - What do you call fractions whose numerators are less than the denominators? 5 4 6 5 3 2 4 2 8 1
- 12. 6 3. Motivation Do you like vegetables? What particular vegetable do you like? Why do we eat vegetables? Problem illustration Corn is grown in 6 2 of a farm and vegetables in 6 1 . Which is greater, the part where corn is grown or the part where vegetables are planted? B. Developmental Activities: 1. Presentation a. Show a representation of the problem. Ask the pupils to shade the part where corn is grown and the part where vegetables are planted. Write the fraction representing the part where corn is grown. 6 2 Write the fraction representing the part where vegetables are planted. 6 1 What part of the farm is not planted? 6 3 What fraction represents the whole farm? 6 6 Which of these fractions is less than one? 6 2 6 1 6 3 Why do we call these fractions less than one? b. Have pupils compare the fractions representing the parts of the farm. 1. Which is greater, the part where corn is grown or the part where vegetables are planted? Which is lesser the part representing where nothing is planted or the part where corn is grown? 2. Show the relationship of the fractions by using symbols > and <. 6 2 > 6 1 6 3 > 6 2 6 1 < 6 2 6 2 < 6 3 This figure is a representation of the farm in the problem. Part where corn is grown. Part where vegetables are planted.
- 13. 7 c. Observing illustrations and comparing fractions less than one. Show 2 cut-out of fractions. Write the fractions in figures and in words. 4 1 one-fourth 3 1 one-third Which is greater 4 1 or 3 1 ? Which expression tells correctly the relationship between the 2 fractions? 1. 4 1 > 3 1 2. 4 1 < 3 1 3. 4 1 = 3 1 d. Ask the pupils to illustrate the problem below. One-third of Tom’s vegetable plot is planted to camote and two-sixths to mongo seedlings? Show the relationship of the fraction by using > and <. To what food groups do camote, camote tops and mongo belong? Go, glow or grow? Why do we need to eat these kinds of food? Do you eat enough of these kinds of food daily? 2. Guided Practice a. Use of number line Ask the pupils to divide the line segment into 5 equivalent parts. 5 1 5 2 5 3 5 4 5 5 b. Show the relationship by using > or <. Group pupils into learning barkadas. Distribute illustrations of regions and number lines representing fractions less than one. Ask pupils to write the fractions in figures and in words. Ask other pupils to show the relationship of the fractions by using > and <. 3. Generalization What symbols do we use to show relationships between fractions less than one? We use the symbol > (is greater than) and < (is less than) to show relationship between fractions less than one.
- 14. 8 C. Application A. Compare the following fractions. Write <, > on the blanks. 1) 2 1 ___ 4 2 3) 4 3 ___ 2 1 5) 5 4 ___ 9 8 2) 8 1 ___ 10 2 4) 5 2 ___ 9 1 B. Prove that the relationship is true or false. 1. 4 3 > 5 4 = ______ 2. 5 4 < 6 3 =______ 3. 3 2 > 6 4 = ______ 4. 4 1 < 8 1 = ______ 5. 9 2 > 7 3 = ______ C. Pair Square 1. Three-eights of a class built a diorama; 20 5 built a wishing well. Which activity had more members? 2. Mrs. Reyes has 5 3 gallon of water. Mrs. Lopez has 8 6 gallon of water. Who has more water? Why? IV. Evaluation A. Look at the illustrations. Compare the shaded part. Use > or <. 1) 4 1 ___ 8 4 2) 3 1 ___ 4 1 3) 8 4 ___ 3 1 B. Show by illustrations the relationship of the following fractions. 1) 8 7 3 1 2) 6 5 6 3 3) 3 2 4 2
- 15. 9 4) 4 1 2 1 5) 5 1 4 3 V. Assignment A. Ring the fraction in column B which is greater than the given fraction in column A. A B 1) 2 1 4 1 5 1 3 2 2) 4 3 8 1 10 9 2 1 3) 8 2 5 2 4 1 8 3 4) 4 1 2 1 5 4 3 2 5) 3 2 6 4 7 2 5 1 B. Write < or > on the blank to make each sentence true. 1) 6 1 ______ 4 3 2) 6 2 ______ 3 2 3) 3 1 ______ 6 4 4) 9 3 ______ 8 4 5) 8 3 ______ 8 4 Ordering Fractions Less Than One having 1 as Numerators I. Learning Objectives Cognitive: Order fractions less than one having 1 as numerators Psychomotor: Shade parts of whole regions and write their fraction names Affective: Participate actively in group activities II. Learning Content Skill: Ordering fractions less than one having 1 as numerators Reference: BEC PELC II A 1.2 Materials: textbooks, fraction kit, flash cards, coloring materials, Show Me Cards Value: Active participation in group activities
- 16. 10 III. Learning Experiences A. Preparatory Activities 1. Drill: Distribute “Show me cards” to the pupils with fraction names. As the teacher flashes the cards, the pupil shows the fraction name of the shaded part of each region. 2. Review: What are fractions less than one? Is 2 1 a fraction less than one? Why? 3. Motivation Introductory questions: Do you have friends/barkada? Do you invite them in your house? What are the things you do? A group of friends was given a rice cake. Mary ate 2 1 , Rose 6 1 , Carol 8 1 and Camille 4 1 . Who consumed the most? the least? B. Developmental Activities 1. Presentation a. Problem illustration using regions 1. Distribute fraction circles to pupils. Let them divide the circular regions by showing the amount of cake consumed by each. Ask the pupils to shade the designated part using crayons. Mary 3 1 Carol 8 1 Camille 4 1 Rose 6 1 Who consumed the least? Who consumed the greatest? 2. Arrange a diagram to compare fractions less than one. b. Observing a diagram to compare fractions less than one 1. From the diagram, write 2 fractions on the board and compare them using the symbols > and <. 2 1 3 1 4 1 5 1 6 1 7 1 8 1
- 17. 11 2. Order the fractions on the diagram from least to greatest. c. Problem illustration using a number line In the fable, “The Turtle and the Hare”, the hare had covered a distance of 2 1 from the starting point to the end point before it decided to take a nap. Meanwhile the persistent turtle has covered 8 1 . Show the distance covered using the number line 8 1 2 1 Which is greater, 2 1 or 8 1 2. Guided Practice a. Game – Using cut-outs and show me cards. 1. Distribute cut-outs to pupils with fractions printed on them. 2. Tell them to read the direction at the back of the cut-out. 3. Have them write their answer on their show me cards. Directions: Order the fractions from greatest to least Order the fractions from least to greatest b. Cooperative Learning – group activities – contest 1. Group pupils into learning barkadas 2. Distribute cut-outs showing fractions with shaded parts. 3. Let the pupils arrange them from least to greatest and vice-versa. 4. Ask them to read the fractions as they move forward to show the regions. 5. The fastest group to form the line in correct order wins the game. 3. Generalization How do we order fractions less than one? When ordering fractions less than one with one as the numerators, remember that the greater the denominator the lesser is the value of the fraction. C. Application 1. In a pie-eating contest, Mary ate 2 1 of a pie, Lori 4 1 and Mercy 8 1 . Who ate the most? the least? 2. Contest – Let the pupils participate in a softdrink drinking contest, Measure the amount of liquid consumed by each contestant. Write the fraction names. 4 1 3 1 2 1 8 1 9 1 5 1 10 1 9 1 6 1 2 1 3 1 2 1 4 1 3 1 5 1 6 1 7 1 6 1 8 1 12 1 9 1 2 1 4 1 4 1 7 1 3 1 2 1 6 1 10 1 8 1 5 1
- 18. 12 IV. Evaluation 1. Draw regions showing 2 1 , 3 1 , 4 1 , 5 1 and 6 1 . Color the shaded parts and arrange them from least to greatest. 2. Arrange the fractions from least to greatest. 1) 7 1 5 1 2 1 3 1 3) 4 1 3 1 6 1 2 1 5) 9 1 8 1 10 1 4 1 2) 9 1 10 1 4 1 3 1 4) 8 1 2 1 3 1 7 1 3. Prove that the fractions are arranged from least to greatest. Reason 1) 9 1 7 1 15 1 3 1 2 1 = ___________________ 2) 10 1 8 1 5 1 3 1 2 1 = ___________________ 3) 12 1 13 1 14 1 15 1 16 1 = ___________________ V. Assignment a. Do what is asked. 1. Show the following fractions by using rectangular regions. 2 1 3 1 4 1 5 1 and 6 1 2. Color the part being considered. 3. Arranged them from least to greatest. b. Arrange the fractions from greatest to least. 8 1 9 1 2 1 4 1 5 1 c. Arrange the fractions from least to greatest. 3 1 6 1 7 1 10 1 5 1
- 19. 13 Identifying Fractions Equal to One I. Learning Objectives Cognitive: Identify fractions equal to one Psychomotor: Read and write fractions equal to one Affective: Develop the habit of writing neatly II. Learning Content Skills: Identifying fractions equal to one Reading and writing fractions equal to one Reference: BEC PELC II A.1.2 Materials: fraction circles, fractional bars, activity sheet, coloring materials Value: Neatness III. Learning Experiences A. Preparatory Activities 1. Drill – Fractions less than one Give the fractions for the shaded parts. 2. Review – Part of a fraction What are the parts of a fraction? Which part of a fraction represents the number of equal parts? Which part represents the number parts being considered? 3. Motivation Do you like fruits? What fruits do you like? Why? Game: Pupil describes a fruit and let their classmates give the name of the fruit. B. Lesson Proper 1. Presentation a. Use a real object for problem illustration. 1. Show a papaya and cut it equally into halves. Into how many parts is the papaya divided? 2 How will you write one of the equal parts? 2 1 How will you write two halves? 2 2 Are two halves equal to one? 2 2 = 1
- 20. 14 2. Let the pupils write the fractions in figures and in words. 2 1 one half 2 2 two halves 3. Compare the fractions. What kind of fraction is 2 1 ? Fraction less than one What about 2 2 ? Fraction equal to one What can you say about the numerator and denominator of 2 2 ? They are the same b. Use of cut-outs 1. Distribute cut-outs of different parts of a cake to the pupils. 2. The pupils put the parts together to form a whole. 3. Ask: Into how many parts is the whole divided? What do you call each part? 4. Guide the pupils in recognizing the whole as six-sixths. How many 6 equal parts has the whole region? 6 The whole region is equal to 6 6 . We say six-sixths and write 6 6 Is 6 6 equal to one? What can you say about the numerator and denominator of the fraction? They are the same. c. Observing illustrations and identifying fractions equal to one. 2 2 4 4 5 5 1. Let pupils shade each part one after the other. 2. Ask them to identify the shaded parts. 3. When all the parts have been shaded, ask them to write the fraction names for the shaded parts. 4. Is 2 2 equal to 1? 4 4 ? 5 5 ? 5. What do you notice about the numerators and denominators of fractions equal to one? They are the same. 2. Guided practice a. Let the pupils identify which fractions are equal to one. Write the fraction name for the shaded parts and encircle the fraction equal to one. (At this point remind the pupils to write their numbers neatly and legibly). b. Distribute fraction words and figures to the pupils. Call out a fraction and ask the pupils holding the fraction figure and fraction word to stand side by side in front of the class. 2 2 Two halv es 4 4 Four fourt hs 5 5 Five fifths 6 6 Six sixth s
- 21. 15 c. Ask the pupils to read the numbers. 3. Generalization How do we know that fractions are equal to one? Fractions are equal to one when their numerators and denominators are the same. C. Application Ring the fractions equal to one 1) 4 4 4 2 3) 6 3 6 6 5) 3 2 3 3 2) 5 5 5 3 4) 9 3 9 9 IV. Evaluation A. Write the fraction numerals for the following. 1. five-fifths _____ 2. two-halves ____ 3. four-fourths ____ 4. eight-eights ____ 5. six-sixths ____ B. Encircle the fractions equal to one. 1) 3 2 6 2 2 2 4 2 3) 10 7 8 5 5 4 3 3 5) 6 4 4 4 9 4 12 4 2) 7 7 6 7 8 3 6 3 4) 9 4 4 3 5 5 6 8 V. Assignment A. Write 5 fractions having a value of one.
- 22. 16 B. Write the fraction words for the following: 1) 6 6 ________ 3) 4 4 ________ 5) 9 9 ________ 2) 8 8 ________ 5) 7 7 ________ C. Identify the fractions equal to one in the given set. Set A 7 3 ’ 7 5 ’ 7 7 ’ 9 3 ’ 9 7 ’ 9 9 ’ 10 3 ’ 10 5 ’ 10 10 Set B 8 2 ’ 8 6 ’ 8 8 ’ 12 5 ’ 12 7 ’ 12 12 ’ 15 6 ’ 15 9 ’ 15 15 Identifying Fractions More Than One I. Learning Objectives Cognitive: Identify fractions more than one Psychomotor: Read/Write fractions more than one Affective: Be considerate to others/Work well with others II. Learning Content Skills: Identifying fractions more than one Reading/Writing fractions more than one Reference: BEC PELC II A 1.4 Materials: textbooks, cut-outs, activity cards, coloring materials Value: Concern for others III. Learning Experiences A. Preparatory Activities 1. Drill - "Climbing the Ladder" a. Call on 2 pupils. b. Let them have a race in climbing the ladder by checking out all fractions less than one. (note: The ladder should have the same fractions) c. The first pupil to come up with the most number of correct answers wins the game (At this point give some safety precautions to pupils like telling them not to push each other.
- 23. 17 2. Review – When is a fraction less than one? A fraction is less than one when the numerator is less than the denominator. 3. Motivation Let the pupils sing a fraction song to the tune of "The Farmer in the Dell" One whole, one whole, one whole Divided into 2 One part is called 2 1 (Substitute 2 1 with other unit fraction) And so the other too. B. Developmental Activities 1. Presentation a. Problem Illustration 1. Present the following with all parts shaded. (cut-outs) A C B Into how many equal parts is figure A divided? Figure B? Figure C? What fractional parts are shaded? What do you call the fractions 2 2 , 4 4 , and 6 6 ? 8 2 2 3 3 4 9 1 6 2 7 3 5 5 4 8 10 3 4 1 8 2 2 3 3 4 9 1 6 2 7 3 5 5 4 8 10 3 4 1
- 24. 18 2. Remind the pupils that fractions equal to one have the same numerators and denominators. 3. Present other figures. (Cut-outs) D E F a. How many fourths does Figure D show? b. How many halves does Figure E show? c. How many thirds does Figure F show? d. Write the fraction for the shaded parts of D, E and F. 4 5 , 2 3 , 3 5 e. Are these fractions less than one? equal to one? more than one? f. What do you notice about the numerators and denominators of fractions more than one? 2. Guided Practice a. What kind of fractions are the following: 2 3 , 3 4 , 4 7 , 6 8 , 7 8 1. Are these fractions more than one? Why? 2. What do you notice about their numerators and denominators? b. Game - "Looking for a Partner" Distribute cut-outs of regions divided into equal parts. a. Let the pupils find their partners by showing their cut-outs to the others. b. Ask them to look for the regions with shapes similar to their cut-outs. c. When everybody has found his partners, let them stand side by side and show their regions and say the fraction represented by their cut-outs. 2 3 4 7
- 25. 19 3. Generalization: How do we identify fractions more than one? Fractions are called fractions more than one when their numerators are greater than the denominators. C. Application 1. Draw regions showing the following fractions. 1) 4 6 2) 3 5 3) 2 3 4) 6 7 5) 5 8 2. Put a check mark before fractions equal to one, a cross mark after fractions more than one and encircle fractions less than one 1) 2 2 2) 3 9 3) 6 3 4) 10 12 5) 4 5 6) 5 2 7) 6 6 8) 7 7 9) 7 8 10) 8 10 IV. Evaluation A. Write the fraction for these names 1. Five-halves _____________ 2. Six-thirds ______________ 3. Five-fourths ___________ 4. Nine-eighths ____________ 5. Twelve-tenths ___________ B. Circle the fractions which are equal to one. Box the fractions which are greater than one. 3 2 4 4 6 6 5 7 5 3 9 8 8 9 8 8 7 7 3 4 4 3 7 2 9 7 7 9
- 26. 20 V. Assignment Write the following fractions in words. 1) 2 6 ___________ 2) 4 5 ___________ 3) 5 7 ___________ 4) 6 8 ___________ 5) 3 9 ___________ Ordering Fractions Equal to One, Less Than and More Than One with the same Denominators I. Learning Objectives Cognitive: Order fractions equal to one, less than and more than one with the same denominators Psychomotor: Write fractions from least to greatest and vice versa Affective: Practice good health habits II. Learning Content Skills: Ordering fractions equal to one, less than and more than one with the same denominators Writing fractions equal to one, less than and more than one from greatest to least and vice versa Reference: BEC PELC II A.1.4 Materials: textbooks, fraction circles, activity cards, cut-outs Value: Health consciousness III. Learning Experiences A. Preparatory Activities 1. Drill – Identifying fractions equal to one, more than and less than one 1. Play “Giant Step” (Pupils play in pairs) 2. The teacher flashes the cards containing fraction numerals. (equal to one, more than one and less than one) 3. Tell whether the fraction is equal to one, more than one or less than one. 4. The contestants beat each other in giving the correct answer. 5. The first pupil who gives the correct answer takes one step forward. 6. The first pupil to reach the finish line wins the game.
- 27. 21 2. Review: Circle all fractions less than one, box all fractions more than one and cross all that are equal to one. 3. Motivation Do you eat your breakfast before going to school? How many meals do you eat everyday? (Show picture of Go, Grow and Glow foods) Which of these food do you eat everyday? Are these foods good for the body? Why? B. Developmental Activities 1. Presentation a. Problem illustration Are fruits good for the body? Show two apples, an orange and papaya cut in fourths. Into how many equal parts is the orange divided? Get 2 pieces of the equal parts and show them. How many fourths are there? 2 Write the fraction for the pieces. 4 2 What kind of fraction is 4 2 ? Into how many equal parts is the papaya divided? Get all the pieces and show them. What fraction names the parts? 4 4 What kind of fraction is 4 4 ? Into how many equal parts are the apples divided? Get 5 pieces of the sliced apples and show them. Can we get one whole from these pieces? What fraction names the pieces? 4 5 What kind of fraction is 4 5 ? Which is greater, 4 2 or 4 4 ? 4 5 or 4 4 ? 4 2 or 4 5 ? Arrange the fractions from greatest to least. 4 3 5 7 4 3 2 2 12 10 9 1 10 4 17 8 5 5 8 12 5 6 11 11 6 8 9 4 5 2
- 28. 22 4 2 4 4 4 5 b. Use the regions 1. Write a numeral for the shaded parts. A = 4 2 B = 4 5 C = 4 4 D = 4 7 2. Compare the fractions by using > or < 4 2 < 4 4 , 4 5 > 4 4 , 4 5 < 4 7 3. Arrange the fractions from least to greatest. 4 2 4 4 4 5 4 7 4. Arrange the fractions from greatest to least 4 7 4 5 4 4 4 2 5. How do we order fractions with the same denominators? c. Use number lines. 0 5 1 5 2 5 3 5 4 5 5 0 5 1 5 2 5 3 5 4 5 5 0 5 1 5 2 5 3 5 4 5 5 5 6 1. Observe the distances covered in the number line. 2. Compare the distances covered by using > or < 5 3 < 5 5 , 5 6 > 5 5 , 5 6 > 5 3 , 5 5 > 5 6 A B C D
- 29. 23 3. Arrange the fractions from greatest to least. 5 6 5 5 5 3 4. How do we order fractions with the same denominator? 2. Guided Practice a. Cooperative learning – group pupils into learning barkadas (triads) 1. Show flashcards with fractions arranged from least to greatest and vice versa. 2. Using their show me cards, the pupils will write More if the fractions are arranged from greatest to least and Less, if arranged from least to greatest. 3 2 3 3 3 5 3 8 3 10 less 9 2 9 5 9 9 9 12 9 15 less 5 6 5 5 5 4 5 2 5 1 more 7 2 7 4 7 6 7 7 7 9 less 8 1 8 4 8 5 8 8 8 10 less 10 9 10 7 10 5 10 3 10 1 more C. Application A. Write the fractions in order from least to greatest 1) 8 2 8 4 8 1 8 8 8 10 ______________ 2) 5 1 5 8 5 5 5 3 5 4 ______________ 3) 10 3 10 10 10 15 10 4 10 1 ______________ B. Read, analyze and solve. Marlyn bought 3 whole buko pies. Each buko pie was divided into 8 equal parts. She gave 8 4 to Ken, 8 8 to a friend, 8 7 to her brothers and sisters and ate the rest. Who got the biggest share? Who got the least share? C. Work with a partner. Pupils will be paired with learning partners. Write the fractions in order from smallest to biggest and vice versa Pupil 1 Learning Partner Greatest to Least Least to Greatest 1) 8 2 8 4 8 1 8 8 8 6 ______________ _______________ 2) 5 1 5 5 5 3 5 4 5 8 ______________ _______________
- 30. 24 3) 6 7 6 4 6 5 6 6 6 1 ______________ _______________ 3. Generalization How do we order fractions less than one, equal to one and more than one? When ordering fractions less than one, equal to one and more than one with the same denominator, remember that the greater the numerator, the greater is the value of the fraction. IV. Evaluation A. Draw regions to represent these fractions. Arrange the region as directed. 1) 2 1 , 2 2 , 2 3 2) 3 2 , 3 5 , 3 3 3) 9 4 , 9 9 , 9 12 B. Which sets of fractions are written in order from greatest to least? 1) 5 2 5 1 5 4 5 6 3) 4 5 4 4 4 3 4 2 5) 6 9 6 6 6 5 6 2 2) 8 7 8 5 8 4 8 3 4) 7 7 7 6 7 8 7 5 V. Assignment: A. Answer the problem Karen bought 2 whole big pizzas. Each pizza was divided into 12 equal parts. She gave 12 3 to Karie, 12 12 to her friends, 12 5 to her brothers and sisters and ate the rest. Who got the biggest share? Who got the least share? B. Inside the boxes are fractions and shaded portions of regions representing fractions. Arrange the fractions from least to greatest by writing numbers 1 to 7 on top of the boxes. 8 7 8 5 8 1 greatest to leastleast to greatestgreatest to least
- 31. 25 C. Arrange the following fractions from greatest to least 1) 6 3 6 1 6 4 6 5 6 6 6 8 6 2 2) 9 4 9 9 9 1 9 6 9 5 9 2 9 8 3) 7 2 7 4 7 7 7 9 7 1 7 3 7 8 Finding the GCF (Greatest Common Factor) of Two Given Numbers I. Learning Objectives Cognitive: Find the GCF (Greatest Common Factor) of two given numbers Psychomotor: Tell/Write the GCF of two given numbers Affective: Spend money wisely II. Learning Content Skills: Finding the GCF (Greatest Common Factor) of two given numbers Telling/Writing the GCF of two given numbers Reference: BEC PELC II A 2.1 Materials: Learning Activity Sheets, cut-outs Value: Thriftiness III. Learning Experiences A. Preparatory Activities 1. Mental Computation There are 56 boxes with 8 crayons in each box. How many crayons are there in all? 2. Drill: Games a. The pupils give the product as the teacher points to the combinations in the number wheel. b. The teacher gives a product and the pupils give the factors.
- 32. 26 3. Review – Term used in Multiplication a. Write a multiplication sentence on the board. 9 x 8 = 72 b. Pupils read the sentence. c. What do we call 9 and 8, the numbers that we multiplied? Factors d. What do we call 72? Product 4. Motivation Julie has 3 piggy banks. If she has 8 in each bank, how much does she have? Who among you have piggy banks at home? What do you do if you have extra money from your baon? Do you put them in your piggy bank? Is it good to save money for the future? Why? B. Developmental Activities 1. Presentation a. What shall we do to solve our problem? Multiply 3 x P8 = 24 3 and 8 are factors of 24. 24 is the product of 3 and 8. b. Distribute cut-outs to pupils. 1. Aside from 3 and 8, what 2 numbers when multiplied will give a product of 24? 2. Call on the pupils holding the cut-outs to compare the numbers and come up with a pair of cut-outs which are factors of 24. 6 x 4 = 24 2 x 12 = 24 1 x 24 = 24 3. Who can give all the factors of 24? 1, 2, 4, 6, 12, 24, How many factors has 24? 6 c. Listing of and comparing factors of given numbers. Ask the pupils to list the factors of 12. What are the factors of 12? List them from least to greatest. 1, 2, 3, 4, 6, 12 Tell the pupils to compare the factors of 24 and 12 on the board, you can see the factors of 12 and 24. 6 2 4 12 1 24
- 33. 27 24 12 1 1 1. How many factors has 12? 24? 2 3 4 6 8 12 24 2 3 4 12 2. Look at the list and find the common factors of the numbers. Circle the factors. 3. What are the common factors of 24 and 12? 1, 2, 3, 4, and 12 4. From the common factors, put a check mark beside the greatest number common to both 24 and 12. 5. What is the greatest common factor of 24 and 12? 12 6. 12 is the greatest common factor of 12 and 24. 7. 12 is the GCF of 12 and 24. 2. Guided Practice a. Use of cut-outs Distribute cut-outs of petals of flowers with printed numerals. Group pupils into 3’s. Ask them to form a flower from the petals and post the petals around the circle cut- outs posted on the board. The numeral on the circle cut-out is the pupils’ cue for the products. The pupils will select petals with numerals that are factors of the number on the circle cut-out. Ask pupils to select 2 products and write the GCF on the show me cards. Let them say: The GCF of 15 and 20 is 5. The GCF of 10 and 15 is 5. The GCF of 16 and 8 is 8. The GCF of 10 and 20 is 10. b. Use of activity cards Form 2 teams. Distribute activity cards. Two cards per group. 2 9 6 3 5 18 1 7 4 18 18 1 3 2 4 7 8 6 12 9 36 10 36 24 5 6 7 2 3 12 4 8 1 24 5 40 1 9 8 3 4 7 40 In each card, circle or ring all the factors of the given numbers. Then ask the pupils to supply the missing data on the board. Number Total no. of factors Common factors GCF 18 36 8 6 1, 2, 3 6, 9, 18 18 18 is the GCF of 18 and 36.
- 34. 28 Number Total no. of factors Common factors GCF 24 40 8 6 1, 4, 8 8 8 is the GCF of 24 and 40. 3. Generalization How do you find the GCF of 2 given numbers? What are the steps in finding the GCF of 2 given numbers? a. List down the factors of each number. b. Find the common factors of the given numbers. c. Look for the greatest factor common to the numbers. C. Application A. Use the number in the box to answer each of the questions. 1 2 4 6 9 10 12 14 15 24 27 28 1. Which pair of numbers has a GCF 5? 2. Which pair of numbers has a GCF 6? 3. Which pair of numbers has 12 as GCF? 4. Which pair of numbers has 4 as GCF? 5. Which pair of numbers has 9 as GCF? B. Read, analyze and solve 1. Jenny has two pieces of ribbon. One is 8 dm long and the other is 12 dm long. What is the longest length wherein she can cut both pieces into equal length without wasting any part of the ribbon? 2. Henny has two pieces of rope with lengths of 24 m and 27 m. How long will he cut each piece to get pieces of equal length and the longest possible without wasting any rope? IV. Evaluation A. Find the GCF. 1) 6 and 12 2) 12 and 18 3) 15 and 21 4) 12 and 16 5) 10 and 20 8 dm 12 dm 24 m 27 m
- 35. 29 B. Match Column A with Column B by drawing a line. A – Given Numbers B - GCF 1) 24 and 12 a. 25 2) 28 and 32 b. 5 3) 25 and 50 c. 8 4) 10 and 15 d. 4 5) 8 and 24 e. 12 V. Assignment: A. Find the missing pair of each number: Pair of Numbers GCF 1) 2 and _____ 6 2) _____ and 10 10 3) 24 and _____ 8 4) 48 and _____ 6 5) _____ and 15 5 B. Write the GCF of the following pairs of numbers on the blank. 1) 8, 12 _______ 2) 56, 48 _______ 3) 32, 24 _______ 4) 64, 16 _______ 5) 18, 36 _______ Reducing Fraction to Lowest Forms I. Learning Objectives Cognitive: Reduce fractions to lowest forms Psychomotor: Express/write fraction in lowest forms Affective: Practice the habit of sharing II. Learning Content Skills: Reducing fractions to lowest forms Writing fractions to lowest forms Reference: BEC PELC II A.2.2 Materials: textbooks, cut-outs, activity sheets, coloring materials Value: Sharing III. Learning Experiences A. Preparatory Activities 1. Drill – Giving the common factors of 2 given numbers. Show a flash card one at a time. Ask the pupils to give the common factors of the numbers. 12 and 16 15 and 18 10 and 20 27 and 1818 and 24
- 36. 30 2. Review – Writing the GCF of 2 given numbers. Distribute cut-outs of fruits with printed numerals, each having a pair of numbers. Ask the pupils to show their cut-outs and give the GCF of the pairs of numbers. 3. Motivation Song (Tune: The Farmer in the Dell) One whole, one whole, one whole Divided into 2 One part is called 2 1 And so the other too. B. Developmental Activities: 1. Presentation a. Present a problem Aling Beatriz bought a whole piece of buko pie. She cut it as shown on the picture. given to Alice given to Zeny What part of the buko pie did Alice receive? 2 1 What part was given to Zeny? Both girls received parts of the buko pie. If you were Zeny and Alice would you share your buko pie to others? Why? b. Analysis of the problem Did both girls receive the same size of buko pie? Yes Do 2 1 and 4 2 have the same size? Since 2 1 and 4 2 have the same size, they are called equivalent fractions. What do we call fractions showing the same size? Equivalent Fractions A fraction can be expressed in lowest terms. 2 1 is the lowest term of 4 2 Observe how 4 2 is reduced to lowest term in the example below: 4 2 ÷ 2 2 = 2 1 What is the GCF of the denominators?
- 37. 31 What is done with the GCF to find the lowest terms of the fraction? The numerator and denominator are divided by the GCF. c. Problem Illustration Look at the pieces of sticks. How is the 2 nd piece of stick divided? Do 3 1 and 6 2 show the same parts? What is the GCF of the denominators? Using the same pattern above let's see how 6 2 is reduced to 3 1 6 2 2 2 = 3 1 What did we do with the fraction and the GCF to reduce it to lowest terms? d. Use of fraction bars 2 1 2 1 4 1 4 1 4 1 4 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 How many fourths are there in 2 1 ? Are 4 2 and 2 1 the same? How many eights are there in 2 1 ? Are 8 4 and 2 1 the same? How many eights are there in 4 1 ? Are 8 2 and 4 1 the same? Show how 8 2 , 4 2 and 8 4 are reduced to lowest terms. 8 2 ÷ 2 2 = 4 1 4 2 ÷ 2 2 = 2 1 8 4 ÷ 4 4 = 2 1 2. Guided Practice a. Divide the class into triads. One of the pupils will read the fraction. The second pupil will give the GCF and the third pupil will give the lowest term of the fraction. Each correct answer merits one point. The team with the highest no. of points wins. Ex. 6 3 GCF = 3 LT = 2 1 b. Group the class into dyads. Each player takes turn in answering questions about the exercises. Which is the lowest term of the following fractions? 1) 6 3 = ( 2 1 , 4 3 , 6 2 ) 2) 8 2 = ( 4 2 , 3 1 , 4 1 )
- 38. 32 3) 10 2 = ( 2 1 , 4 1 , 5 1 ) 4) 20 5 = ( 3 1 , 10 2 , 4 1 ) c. Try these: 1) 8 6 ÷ 2 2 = ___ 2) 12 9 ÷ 3 3 = ___ 3) 15 10 ÷ 5 5 = ___ 3. Generalization How do we reduce fractions to lowest terms? To express the lowest terms of a fraction, divide both the numerator and the denominator by the GCF. C. Application Read the problems and answer the questions. 1. Linda bought 12 eggs. She boiled 6 2 of the eggs and fried 8 2 of them. What are 6 2 and 8 2 in lowest terms? 2. Mother cooked 2 1 kg of chicken and 12 4 kg of beef. Did she cook the same amount of meat? Why? 3. Aling Rosa cut a large squash into 6 equal parts. She gave 6 3 to her neighbors and kept 2 1 for family use. Did she keep the smaller part of the squash? What kind of person is Aling Rosa? Is she generous to her neighbors? Do you also share some food to your neighbors and friends? IV. Evaluation A. Express each fraction in lowest terms by supplying the missing number. 1) 12 4 = 3 3) 24 9 = 3 5) 24 8 = 3 2) 12 3 = 1 4) 15 6 = 2 B. Write the missing number in each box. 1) 4 2 ÷ = 2 1 3) 15 3 ÷ = 5 1 2) 14 7 ÷ = 2 1 4) 10 2 ÷ = 5 1 C. Solve the following: 1) Express 20 15 as a fraction with a denominator of 5. 2) How many fifths as there in 15 9 ?
- 39. 33 3) How many fourths as there in 100 25 ? 4) Change 18 3 to sixths. 5) Three twenty-fourth is equal to how many eights? V. Assignment A. Copy the fractions that are not in the lowest form. Then find the GCF and change them to lowest terms. 3 2 , 3 1 , 10 4 , 4 2 , 5 2 , 8 4 , 9 6 , 18 5 B. Choose the lowest terms of the given fractions. 1) 15 6 a. 5 2 b. 3 2 c. 2 1 d. 3 1 3) 24 8 a. 4 1 b. 3 1 c. 2 1 d. 10 2 5) 12 9 a. 5 3 b. 8 3 c. 4 3 d. 2 1 2) 15 10 a. 3 2 b. 5 2 c. 5 3 d. 8 3 4) 21 7 a. 6 1 b. 5 1 c. 4 1 d. 3 1 Finding Fractional Part of a Set/Region I. Learning Objectives Cognitive: Find fractional part of a set/region Psychomotor: Write the fractional part of a number Affective: Help do household chores II. Learning Content Skills: Finding fractional part of a set/region Writing the fractional part of a number Reference: BEC PELC II.A.3
- 40. 34 Materials: textbooks, set of real objects, geometric regions activity sheets, coloring materials Value: Helpfulness III. Learning Experiences A. Preparatory Activities 1. Drill – Basic Division Facts (Flash cards) Game "Giant Steps" a. Call 2 or 3 contestants at a time. b. Flash the cards. c. The pupil who gives the correct answer first gets a point. d. The first pupil to reach the finish line wins the game. Review - Naming the shaded parts of figures. Writing the fractions in words e. Call on 2 pupils. f. One of the pupils will name the shaded part of the figure. g. The other one will write the fraction word on the board. 2. Motivation What are the things that we use when eating our meals? Show sets of glasses, saucers, cups, spoons, forks, etc. Do you help in washing the dishes at home? Who among you help in the household chores at home? What are the household chores that you do at home? B. Developmental Activities 1. Presentation a. Using Fractional Parts of Set (Real Objects) 1. Arrange 14 glasses on the table. 2. Let the pupils fill 7 glasses with water. 3. Present this problem: One-half of the 14 glasses are full. How many glasses are full? 4. Write 2 1 of 14 = ___ 5. How many glasses are full? 2 1 of 14 = 7 6. Let pupils arrange 16 saucers on the table. How many saucers are there? 7. Let them put candies on 8 saucers. 8. Ask: How many saucers have candies? 9. Write 2 1 of 16 = ___ 2 1 of 16 = 8 10. Do the same procedure with the cups. What is 3 1 of 9?
- 41. 35 b. Grouping Elements of Sets 1. Group pupils into learning barkadas. 2. Distribute activity sheets to the groups. Group by 5s 5 1 of 15=3 Group by 6s 6 1 of 18 = 3 Group by 8s 8 1 of 24 = 3 Group by 4s 4 1 of 16 = 4 . Group by 7s 7 1 of 21 = 3 Group by 4’s 4 1 of 20=5 3. Ask the pupils to group the elements as directed. 4. Let them observe the number of group formed. 5. Ask: How many groups are formed after grouping the hearts by fives? 6. 5 1 of 15 = 3 7. Do the same procedure with the other sets. 2. Guided Practice a. Let the pupils observe the number sentences. 1) 2 1 of 14 = 7 2) 2 1 of 16 = 8 3) 5 1 of 15 = 3 4) 4 1 of 16 = 4 5) 7 1 of 21 = 3
- 42. 36 b. In the first example, what is the whole number? the denominator? What did we do with the whole number and the denominator to get the answer? c. Use the same procedure in analyzing the other number sentences. d. Group pupils in dyads. e. The pupils take turn in writing the answers on the output column. Find 5 1 of the input Find 4 1 of the input Input Output Input Output 15 3 12 3 25 8 30 20 10 16 f. Game - "Come and Get Me" 1. Call on 3 contestants at a time. 2. Arrange fractions & whole numbers written on cut-outs of shapes on the table. 3. Ask pupils to select cut-outs which will produce a number sentence and post them on the board. The pupil with the most number of sentences wins the game. 3. Generalization How do we find the fractional part of a number? To find the fractional part of a number, divide the whole number by the denominator. C. Application Read the problems and answer the questions that follow. 1. Aling Dolores buys 20 oranges for her children. 2 1 of them are ripe. How many are ripe? _________ 2. Raymund had 30. He gave 2 1 of it to his brother. How much did he give his brother?_________ 3. Thirty-six children went to the resort. 6 1 just watched the others swim. How many children did not go swimming?________ 10 2 1 =5 3 1 21 =7 4 1 20 =5 6 1 18 =3 of of of of
- 43. 37 IV. Evaluation A. Complete the tables by finding fractional part of a number. Fraction 10 8 6 16 24 28 2 1 Fraction 9 12 15 21 27 30 3 1 B. Find the missing numbers. 1) 5 1 of 15 = ____ 2) 4 1 of 20 = ____ 3) 2 1 of 12 = ____ 4) 3 1 of 30 = ____ 5) 6 1 of 24 = ____ C. Read, analyze and solve 1. Mr. Contemplacion had 360. He spent 3 1 of his money in movie ticket. How much money was left? 2. There are 50 children in a park. If 5 1 are boys, how many are girls? 3. Of 90 glasses, 9 1 were used by the visitors in audio-visual room. How many visitors came? V. Assignment A. Find the missing numbers. 1) 8 1 of ___ = 2 2) 3 1 of ___ = 3 3) 10 1 of 50 = ___ 4) 4 1 of 100 = ___ 5) 6 1 of ___ = 8 B. Write the answer on the box under output. Follow the rule. Rule: Find 4 1 of the input Find 2 1 of the input. 1. Input Output 2. Input Output 16 18 20 6

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