Lesson Guides Book 7 v0.2

8/11/2019 Lesson Guides Book 7 v0.2

1/41

Lesson Guide

In

Elementary MathematicsGrade 6

Reformatted for distribution viaDepEd LEARNING RESOURCE MANAGEMENT and DEVELOPMENT SYSTEM PORTAL

INSTRUCTIONAL MATERIALS COUNCIL SECRETARIAT, 2011

DEPARTMENT OF EDUCATIONBUREAU OF ELEMENTARY EDUCATION

in coordination with

ATENEO DE MANILA UNIVERSITY

2010

Chapter II

Rational Numbers

Fractions


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Lesson Guides in Elementary Mathematics

Grade VI

Copyright 2003All rights reserved. No part of these lesson guides shall be reproduced in any form without a writtenpermission from the Bureau of Elementary Education, Department of Education.

The Mathematics Writing Committee

GRADE 6

Region 3

Dolores A. UmbinaOlongapo CityZenaida P. GomezPampangaTeresita T. TungolPampanga

Region 4-AMargarita RosalesLucena City

Segundina B. GualbertoBatangasEstelita AraulloRizalHenry P. ContemplacionSan Pablo City

National Capital Region (NCR)Teresita L. LicardoQuezon CityLilia T. SantosQuezon CityEleanor InteriaQuezon CityElfrida V. MarquezManilaVictoria C. TafallaValenzuela

Bureau of Elementary Education (BEE)

Rogelio O. DoesRobesa Hilario

Ateneo de Manila University

Girlie N. Salvador

Support Staff

Ferdinand S. BergadoMa. Cristina C. Capellan

Emilene Judith S. SisonJulius Peter M. SamuldeRoy L. ConcepcionMarcelino C. BatallerMyrna D. LatozaEric S. de GuiaIllustrator

Consultants

Fr. Bienvenido F. Nebres, SJPresident,Ateneo de Manila University

Carmela C. OracionAteneo de ManilaUniversity

Pacita E. HosakaAteneo de ManilaUniversity

Project Management

Yolanda S. QuijanoDirector IVAngelita M. EsdiculDirector III

Simeona T. EbolChief, Curriculum Development DivisionIrene C. de RoblesOIC-Asst. Chief, Curriculum Development Division

Virginia T. FernandezProject Coordinator

EXECUTIVE COMMITTEE

Jesli A. LapusSecretary, Department of EducationJesus G. GalvanUndersecretary for Finance and AdministrationVilma L. LabradorOIC, Undersecretary for Programs and ProjectsTeresita G. InciongAssistant Secretary for Programs and Projects

Printed By:

ISBN971-92775-5-6


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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.


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MATRIX IN ELEMENTARY MATHEMATICSGrade VI

COMPETENCIES VALUES INTEGRATED STRATEGIES USED MULTIPLE INTELLIGENCESTECHNIQUES With HOTS

II. Rational Numbers

F. Comprehension of Fractions

1. Write the factor described involving Cooperation Drawing picture Games, Individual work

regions, sets, and number line

2. Rename fractions as decimals and Helpfulness Concept development Whole class activity

vice-versa

3. Form equivalent fractions Care for the body Modeling, Listing Independent hands-on activity

4. Solve for the missing terms in a pair

of equivalent fractions

5. Reduce fractions to lowest terms Sharing Modeling Games, Whole class activity

6. Change mixed numbers to improper Helpfulness Drawing, Use of tables Games, Group work

fractions and vice-versa Independent study

7. Estimate fractions close to 3. Respectfulness Independent study

1 /2 of 1 Helpfulness

8. Find the least common denominator Fairness Drawing picture Drawing, Independent study

(LCD) of a set of fractions Concept development Concept development Scientific method , Sharing

Listing, Simplifying the Listing, Simplifying the ideas/Speaking

problem problems

9. Compare fractions and mixed forms

using different methods

9.1 fraction sense, visual reasoning,

renaming to like forms

9.2 Cross products method Helping others Guess, Drawing number Comparing, Speaking

line Manipulative

9.3 LCD method

10. Order fractions in simple and mixed Wise use of money and Draw a picture Game, Group work

forms in ascending or descending time modeling Manipulative, Diagramsorder using different methods

11. Solve mentally word problems Wise use of time Simplifying the problem Independent study, Logic

involving fractions

11.1 Reduce final answer to lowest

Term


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1

Writing Fractions

I. Learning Objectives

Cognitive: Name the fraction or mixed number described by a shaded region,set, or point on the number line

Psychomotor: Write the fraction or mixed number described by a shaded region,set, or point on the number line

Affective: Work cooperatively with a learning partner

II. Learning Content

Skill: Writing the fractions or mixed numbers describedReference: PELC IV G-1Materials: Math textbook, flash cards, number line, pictorials, magazines,

newspapers, scissors, glue, bond paperValue: Cooperation

III. Learning Experiences

A. Preparatory Activities

1. Mental Computation DrillSolving for the GCF/LCM of a set of numbers

Play: Agawan Panyoa) Divide the class into 2 groups.b) A representative from each group is asked to stand at the back of the room, on

the center side.c) A volunteer is also asked to be the arbiter. He/she holds a handkerchief, lets it

dangle in his/her hand, and stays in front of the room.d) Teacher flashes a card with a set of numbers and the representative of each

group solves mentally for the GCF.Ex. 10

1520GCF

e) The first to grab the handkerchief from the arbiter gives his/her answer. If theanswer is correct, his/her group gets 1 point. If not, the other player gets to steal.

f) Repeat the same procedure for another round, this time with each player solvingmentally for the LCM of a set of numbers.

g) The group with more number of points wins.

2. ReviewReview previous lesson. Give one to two examples.


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3. Motivationa) Show the following figures:

A. B. C.

b) Ask the following questions:

1. Which region shows a fraction whose value is less than 1? Name the

fraction.2. Which region shows a fraction whose value is equal to 1? Give the fraction.3. Which region shows a fraction whose value is greater than 1? Name the

fraction.

B. Developmental Activities

1. Presentation

Activity 1Introduce the following:

a) proper fractions

b) improper fractionsc) mixed numbers

Describe each kind of fraction. Elicit examples.

Name the fraction for the shaded part.

1 2 3


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Give more examples.

Show the number line below. Let some students name the fraction (or mixednumber) for each indicated point on the number line.

0 A 1 B 2 C D 3

Next, show the sets of objects below. Call on some volunteers to name afraction for each shaded region.

Give more examples on naming fractions (or mixed numbers) to describe shadedregions, sets, or points on the number line.

Activity 2 (By Pairs)

a) Ask the students to cut out articles in newspapers or magazines that show a

fraction or mixed number.b) Ask them to make a collage of these articles on bond paper.c) Ask them to highlight with a marker the fractions or mixed numbers in the

articles.d) Discuss the value of cooperation with a learning partner.

Elicit from the pupils how best they could show cooperation in everything they doin school and the effect of it in the task on hand.

FractionsGreaterThan 1

MixedForm


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2. Fixing Skills1) Look at the figure.

a. Give two fractions to tell what part of therectangular region is shaded red.

b. Give two fractions to tell what part of therectangular region is shaded blue.

c. What part of the region is not shaded?

d. Give two fractions to describe the part ofthe region that lies to the left of the redregion.

2) What fraction names point B?

3. Generalization

What is a fraction? What does the numerator of the fraction tell? What does thedenominator of the fraction tell? What are the kinds of fractions we discussed? Howdo we name fractions given shaded regions, sets, and number lines?

C. Application

What would you do in this situation?

You have a piece of cake. Two of your classmates do not have baon. What wouldyou do? Into how many parts would you divide your piece of cake? What fractional partwould you give to your classmates? What fractional part would be left for you? Whatgood thing did you do in this situation?

IV. Evaluation

1. Look at the illustration:

a. Give two fractions to tell what part of the set of children are girls.b. Give two fractions to tell what part of the set of children are boys.c. Give two fractions to tell what part of the set of children are wearing glasses.d. What fractional part of the set of children are wearing hair ribbons?

red

blue

1 2 3B


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2) Divide the grid equally into 4 equal parts.

3) Ask: How many small squares is4

1 ?4

2 ?4

3 ?

2

1 = 25 small squares

4

2 = 50 small squares

4

3

= 75 small squares4) Answer the question in the problem? Explain?

5) Guide the pupils to see how a fraction can be changed to decimal. (4

3 is a

fraction which also means division, the numerator is the dividend and the

denominator is the divisor, hence4

3 34 ).

75

0034

.

. therefore 43 is equal 0.75

2 8 .2020

6) Is4

3 equal to 0.71 in our problem? Explain.

b. Activity 2Use of a Grid

1) Use the 10 by 10 grid in Activity 1.2) Ask the pupils to shade or color certain small squares.

Example: color/shade 7 grids

How many grids are shaded of the 100 parts? ( 1007 ) Guide them to see that

100

7 can also be written as decimal (0.07). Lead them to see how it is done.3) Continue the activity until pupils can answer succeeding questions with ease.

c. Activity 31) Change the fraction to decimal.

a. 53 b. 83 c. 125 d. 41 e. 65 2) Discuss: How did you change decimal to fraction?3) Change the decimal to fractions.

Example: 0.6 = 106

22 = 5

3 a. 0.35 b. 0.04 c. 0.36 d. 0.57 e. 3.4

4) Discuss: How did you change decimal to fraction?

2. Fixing Skills

A. Change to decimals.

1) 2015 2) 5

4 3) 127 4) 20

9 5) 4015

6) 1216

7) 415

8) 712

9) 513

10) 812

B. Change to fractions.

1) 0.07 2) 0.58 3) 0.55 4) 0.006 5) 0.0126) 1.5 7) 3.4 8) 4.09 9) 6.005 10) 5.015


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3. Generalization

How do you change fractions to decimals?How do you change decimals to fractions?

C. Application

1) Ann helped her mother clean the house 53

of an hour. How will you express this indecimal?

2) While cleaning she found out that one of their pails is2

1 full of water. Express the

contents in decimal.3) After her work, she read an article which says: Of the total population only 0.09 own a

vehicle. The average length of a trip to the work place is 10.9 km. Write thenumbers read by Ann in fraction form.

IV. EvaluationA. Rename the fractions as decimals.

1) 2521 2) 40

7 3) 5018 4) 20

93 5) 25

311

B. Rename the decimals as fractions.

1) 0.7 2) 0.16 3) 0.03 4) 7.24 5) 4.005

V. Assignment

Rename as fractions or decimals.

1) 85

2) 507

12

3) 25089

44

4) 2519

9

5) 50017

2

6) 0.001

7) 0.56

8) 50.8

9) 9.025

10) 11.004

Solving for the Missing Term in Equivalent Fractions


Cognitive: Solve for the missing term in a pair of equivalent fractionsPsychomotor: Form equivalent fractionsAffective: Keep oneself healthy


Skill: Forming and solving for the missing term in a pair of equivalent Fractions

Reference: BEC PELC II.G.3.3-3.4Materials: strips of paper, fraction bars, activity cardsValues: Care for the body



1. Drill: Naming fractional partsExample: 50 pupils in a class


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By what number will you divide 15 to get 3? (15 5 = 3)

Hence 1510 = 3

2 Allow them to do it with several fractions until they can generalize how toform equivalent fractions?

Activity 4

Working by Learning Team

Give activity card for each group to work on.

1) 31 =

6

2) 18 = 32

3) 52 = 4

4) 1000100 = 10

5)12

= 63

6) 43 =

16

7) 6050 =

6

8) 82 = 12

9) 81 = 2

10) 364 =

9

2. Fixing Skills

a) Tell whether each pair of fractions is equivalent or not. If not, make it equivalent.

1) 427 = 6

1 2) 85 = 16

9 3) 43 = 50

30

4) 75 = 35

25 5) 53 = 15

8

b) Solve for the missing term.

1) 32 =

9 2) 7

6 = 28 3) 95 = 25

4) 9 = 8163 5) 4 = 2016

3. Generalization

How do you solve for the missing term in equivalent fractions.

C. Application

1) A recipe needs 32 cup of flour. You are going to make 3 recipes. How many cups of

flour do you need?

2) You need 43 tbsp of sugar for a glass of lemonade. You are going to make 4

glasses. How much sugar do you need?


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IV. Evaluation

Solve for the missing term.

1) 42 =

8

2) 5040 = 4

3) 9 = 43

4) 21 = 9

5)5

= 2520

6) 8 = 2824

7) 109 = 81

8) 7 = 3530

9) 65 =

30

10) 54 = 24

V. AssignmentUse the numbers in the box to form equivalent fractions. You can use the number more thanonce.

8 14 1 4

12 2 3 18

1) 123

2) 123

3) 62

4) 126

5) 76

6) 84

7) 31

8) 128

9) 128

10) 97

Reducing Fractions to Lowest Terms


Cognitive: Reduce fractions to lowest termsPsychomotor: Write the lowest term of a given fractionAffective: Share a fraction of ones time to help at home


Skill: Reducing fractions to lowest termsReference: BEC-PELC II.G.5Materials: flash cardsValue: Sharing a fraction of a time to help

III. Learning ExperiencesA. Preparatory Activities

1. Drill: Finding Equivalent Fractions

Activity 1Partner Huntinga) Teacher prepares on small cards 2 sets of fractions that are equivalent.


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e.g.

12

9,

4

3,

4

2,

2

1

b) Divide the class into two teams with 10 players each. A player in the team isgiven a fraction card.

c) At the signal Go, each player in the team looks for a fraction equivalent to whathe/she is holding from among his/her teammates.

d) The first team to finish partner-hunting falls in line with their partners.e) The team with the higher score wins.

2. Review: Solving for the Missing Term in a Pair of Equivalent FractionsMATCHING GAME

a) Teacher prepares on flash cards equivalent fractions with a missing term, andnumber cards from 1 to 20.e.g.

164

3 n=

b) Divide the class into two teams with 10 players each.c) Teacher flashes an equation, say

164

3 n=

.

d) At the signal Go, the first player in each team gets a number from a set ofnumbers posted on the board and matches it to the missing term.Note: Teacher should make sure that answers range from 1 to 20 only.

e) The team with the higher score wins.

3. Mental Computation Drill: Finding GCFa) Teacher prepares two numbers on flash cards whose GCF is to be given by the

players, e.g., 6 and 9.b) Divide the class into two teams with 10 players each. Each team forms a line on

opposite sides of the table. A scorer is assigned on the board.c) Teacher shows a flash card.d) The player in front of the line taps the table to signal he wants to answer. The

player who is first to signal gives the GCF. If the answer is correct the teamearns a point. If not, the other student from the other team has the chance toanswer.

e) The team that gets the higher score wins.


1. Presentation

Look at this fraction.

12 (1, 2, 3 , 6, 12)15 (1, 3 , 5, 15)

a. What are the factors of 12? (1 x 12, 3 x 4, 6 x 2)


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b. What are the factors of 15? (1 x 15, 3 x 5)c. What is the largest number that is a factor of 12 and also a factor of 15? (3)d. Divide the numerator and the denominator by the greatest common factor 3.

12 3 415 3 5

e. What is now the Greatest Common Factor of 4 and 5?When the numerator and the denominator of a fraction have no commonfactor other than 1, the fraction is in lowest terms.

f. Show another example:Look at 8. (1, 2, 4, 8)

9 (1, 3, 9)What are the factors of 8? What are the factors of 9? What is the greatest

common factor of 8 and 9? Is9

8in lowest terms?

2. Practice Exercisesa) List the factors of the numerator and the denominator. Encircle the greatest

common factor. Number 1 is done for you.1) 8 (1, 2, , 8)

12 (1, 2, 3, , 6,12)

2) 24

3) 39

4) 5

9

5) 916

6) 1415

7) 1618

8) 1220

9) 1528

10) 2434

b) Divide the numerator and the denominator of the fractions under Exercise I bytheir GCF and express in lowest terms. Number 1 is done for you.

1)3

2

4

4

12

8 2)

4

2

c) Tell whether these fractions are in lowest terms.1) 1

62) 8

173) 9

124) 6

105) 9

15

6) 815

7) 1018

8) 924

9) 1520

10) 1021

11) 2530

12) 1518

13) 17102

14) 1833

15) 3051

16) 1523

17) 1945

18) 1768

19) 3075

20) 1944

d) Give the lowest terms for each set of fractions.1) 2, 3, 4 5) 14, 21, 28

4

4


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6 9 12

2) 6, 9, 1220 30 40

3) 10, 15, 2014 21 28

4) 2, 3, 412 18 24

16 24 32

6) 18, 27, 3620 30 40

7) 2, 3, 416 24 32

8) 10, 20, 3012 24 36

3. GeneralizationWhen is a fraction in lowest terms? How do you reduce fractions to lowest terms?

C. Application

Listen to this problem:On weekdays, Irene enjoys helping her mother with the home chores. She cleans

the house, waters the plants, helps in washing the clothes, preparing the meals, andwashing the dishes. She spends about 4 hours doing these various chores. Whatfraction of the day does she use in helping at home? State your answer in lowest terms.

Who among you also enjoy helping your mother in the home chores like Irene? Howdoes your mother feel when you help her?

What kind of girl is Irene? Are you helpful also? Why should you help in the homechores?

IV. Evaluationa. Determine whether the fraction is in lowest terms. Write Yes or No.

1) 35

2) 2

6

3) 410

4) 512

5) 6

10

6) 15

7) 78

8) 12

15

9) 1318

10) 2128

11) 35

41

12) 4245

13) 1720

14) 28

51

15) 1927

b. Choose the GCF of the numerator and denominator.

1) 2 (1, 2, 3, 5)10

2) 4 (2, 3, 4, 6)12

3) 6 (2, 3, 4, 5)15

4) 7 (1, 3, 4, 7)9

5) 8 (2, 4, 6, 8)12

6) 10 (1, 2, 5, 10)25

7) 36 (3, 4, 6, 9)81

8) 56 (4, 6, 8, 12)64

9) 60 (5, 10, 12, 15)84

10) 60 (5, 10, 20, 30)90


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c. Reduce the following fractions to lowest terms.

1) 312

2) 26

3) 410

4) 520

5) 610

6) 1050

7) 79

8) 852

9) 1028

10) 658

11) 1236

12) 1448

13) 1856

14) 5070

15) 2545

16) 2751

17) 2149

18) 4263

19) 2258

20) 1868

21) 5490

22) 3952

23) 2454

24) 3681

25) 4977

26) 32128

27) 64144

28) 102220

29) 120140

30) 84128

V. AssignmentWrite each fraction in lowest terms.

1)12

9 4)

10

4 7)

12

8 10)

98

12 13)

100

75

2)32

24 5)

16

10 8)

50

6 11)

72

18 14)

124

32

3)65

25 6)

24

10 9)

108

9 12)

64

32 15)

120

104

Changing Mixed Numbers to Improper Fractions and Vice-Versa


Cognitive: Change mixed numbers to improper fractions and vice-versaPsychomotor: Write mixed numbers to improper fractions and vice-versaAffective: Help the family in any simple way you can.


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Skill: Changing mixed numbers to improper fractions and vice-versaReference: BEC PELC II.G.6Materials: Math textbooks, real objects, drawings,flash cardsValue: Helpfulness



1. Mental Computation

a. Strategy 1: Tapping GameReducing fraction to lowest terms1) The teacher prepares flash cards with fractions to be changed to lowest

terms.2) The class is divided into 2 groups.3) The first player is determined by a tossed coin.4) The teacher raises a flash card and the first player gives the lowest term of

the fraction. If he answers correctly, he taps the next player from his groupwho will answer next.

5) If the player answers incorrectly, the other group will play.6) A correct answer will earn a point for the group. The group that scores more

wins.

b. Strategy 2: Ball Catching Identifying Proper, Improper Fraction, andMixed Numbers1) Teacher fills the board with 3 kinds of fractions - proper, improper, and mixed

number.2) She numbers each fraction.3) The class is divided into 2 groups.4) Teacher throws the ball to the group and calls a number of a fraction on the

board.

5) The student who catches the ball identifies the fraction.6) The scorer gives a point to each correct answer.7) The group that has more number of correct answers wins.

2. ReviewUse flash card.

Give the missing term.

1) 3 = 95

2) 20 = 10

36

3) 1 =4 8

4) 4 =

3 9

5) 9 = 312

6)= 80

5 100

7)= 648 12

8) 2 =

3 15

9) 5 = 25 30

10) 20 = 10

36 B. Developmental Activities

1. Presentation

a. Strategy 1: Use a Problem Opener

Mother gathered 10 flowers in her garden. She arranged them by 3s inflower vases. How many groups of 3 did she make? How many were leftover?


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c. Strategy 3: Whole Class DiscussionProblem Situation:

Girlie helps her sister bake some cakes. Her sister asks her to measure 21

3

cups of flour. Can you give another name for 21

3 ?Guide the pupils to see the process.

(3 x 2) + 12How is a mixed number changed to improper fraction?How is an improper fraction changed to a mixed number?

Ex. 27

7 2 = 3; 3 x 2 = 6; 76 = 1

The quotient is 3 and the remainder is 1. The fraction 27

is written as a mixed

number2

13 .

Follow this with a discussion.

2. Fixing Skills

A. Write an improper fraction for each mixed number.1) 2 1 = (2 x 6) + 1 = 136 6 6

2) 3 24

3) 5 28

4) 6 46

5) 7 12

6) 4 35

7) 6 24

8) 5 56

9) 7 24

10) 3 79

11) 6 58

12) 9 49

13) 9 78

14) 18 38

15) 19 49

B. Write the mixed number for each. Express the fractions in lowest terms.1) 54

82) 40

123) 57

84) 38

45) 37

9

6) 78

87) 42

98) 59

69) 39

910) 81

4

11) 75

612) 102

813) 177

914) 102

815) 148

163. Generalization

How are improper fractions changed to mixed numbers?How are mixed numbers changed to improper fractions?

C. Application

Edna, a grade VI pupil, helps her mother to earn extra income. She wakes up earlyand helps gather roses in their garden. Everyday she gathers 25 roses and ties 3 rosesto a bundle. The roses are sold by her mother in the market. How many bundles doesEdna make everyday? What good traits does Edna possess? Do you help your family?How do you help your family? Why?

= 27

213 =


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1. Drill: Identifying Fractional Parts

2. Review

Rounding Numbers

Do you still remember the rules in rounding numbers? Heres a game onrounding numbers.

Who Travels Faster?

a) Teacher prepares on flash cards whole numbers to be rounded.e.g. 4, 8, 13, 15, 17, 28, 0.21, 0.89, 3.75

b) Two sets of equal number of players start at the end of the room. The first playeris determined by a tossed coin.

c) Whenever a player in a team gives a correct answer, he makes one small stepforward. If the second/next player gives a correct answer, the first player movesforward while the second/next player takes his place. This process goes on untila horizontal line is formed.

d) A player who answers incorrectly does not move.e) Answering is done alternately between the two groups.f) The group that is first to form a horizontal line wins.

3. Motivation

Have you ever helped an elderly person carry her heavy load? For example awoman has 3 bags of groceries. Will it lighten her load if you help her carry 2 of herbags? How would you feel after helping a person?


1. Presentation

a. Activity 1Making Strips of Number Lines with a Partner

1) Teacher asks pupils to cut four strips of paper, 12 inches or 1-foot long.2) The pupils fold the four strips into 2 equal parts. On the 4 strips, mark oneend 0 and the other end 1.

3) On the first strip, mark2

0 ,2

1 , and2

2 .

4) Fold the second strip into 4 equal parts and mark4

3

4

2

4

1

4

0,,, , and

4

4.


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5) Fold the last strip into 16 equal parts.Note: Strips of paper will look like this.

DISCUSS:1) Compare the fractions with 1. How can you tell whether a fraction is equal to

2

1 ? Is 2 equal to2

1 ? Are they equivalent fractions?

How can you tell whether a fraction is less than 1? Greater than2

1 ? Why?

2) Look at your second strip. Is 1 close to 0 or2

1 ? Since4

1 is2

1 of4

2 , and

0.25 in decimal,4

1 is closer to2

1 than 0. Is4

3 closer to2

1 or to 1?4

3 is 0.75

in decimal, so it is closer to 1 than2

1 .

3) Look at your third strip. What fractions are closer to 0 than to2

1 ? Is8

2

closer to 0 or8

4 which is2

1 ? What two fractions are close to2

1 ? Is8

5 close

to 1 or2

1 ? Where is8

6 and8

7 close to? Why?

4) What fractions are close to 0? What fractions are close to2

1 ? What

fractions are close to 1?

5) What is the reference point to determine whether the fraction is close to 0,2

1 ,

or 1?

b. Activity 2

Which fractions are close to 0? Which are close to 1? Which are close to2

1

?

1)8

1 2)21

11 3)50

7 4)10

9 5)20

3

6)20

3 7)20

9 8)30

5 9)31

15 10)15

7

11)8

7 12)17

8 13)100

7 14)20

18


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1) When is a fraction close to 0?

2) When is a fraction close to2

1 ?

3) When is a fraction close to 1?

4) Which is greatera fraction close to 0 or 1? a fraction close to 0 or 21

? a

fraction close to2

1 or 1?

5) If two fractions are both close to2

1 , how would you tell which is greater or

less?6) What other methods can we use to compare fractions?

Fractions are close to 1 if the numerator and denominator are close to each

other. Fractions are close to2

1 if the numerator is close to half the denominator.

Fractions are close to 0 if the numerator and denominator are very much apart

from each other.c. Activity 3

GAME: Where Do You Belong?1) Teacher prepares fractions on flash cards.

She divides the board in 3 parts and writes:

02

1 1

2) Any number of players.3) Teacher holds up a fraction.

4) The players estimate if the fraction is close to 0,2

1 , or 1.

5) The player goes to where the fraction is close to. If his estimate is wrong, he

gets out of the game.6) The players who stay in the game win.

2. Fixing Skills

EXERCISE 1Illustrate the following fractions with a number line. Estimate if the fraction is close to 0,

2

1 , or 1.

1)6

4

3)9

2

5)6

1

7)10

7

9)6

2

2)12

2

4)12

5

6)12

8

8)6

4

10)9

7


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EXERCISE 2

State whether the fraction is close to 0,2

1 , or 1.

1)5

3

3)3

2

5)5

1

7)7

5

9)11

5

2)13

2

4)15

5

6)15

9

8)12

8

10)15

12

3. Generalization

What is the reference point to estimate fractions close to 0, 21

, or 1?

C. ApplicationHave you done something like this?

Susie was on her way to school when an elderly woman who looked worried andtired called her and said, Ive been walking for half an hour trying to find the municipalbuilding.Youre too far from it, Maam. Ill pass that way. Would you like to go with me? saidSusie as she helped the woman carry her bag.

Was the woman far or close to the municipal building? Why do you say so?

*ValuingIf you were Susie, would you have done the same thing? Have you helped a

stranger? What help did you give to the stranger? What good trait does Susie have?

IV. Evaluation

Indicate if the fraction is close to 0,2

1 , or 1.

1)7

1

4)8

6

7)16

2

10)5

4

13)3

1

2)12

9

5)15

14

8)18

2

11)20

18

14)18

16

3)30

3

6)28

4

9)35

32

12)50

5

15)27

3


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V. Assignment

A) Use a number line to estimate the fractions close to 0,2

1 , or 1.

1) 78 2) 212 3) 512 4) 912 5) 214

B) Give 10 examples each of fractions close to 0,2

1 , and 1.

Finding the Least Common Denominator (LCD)


Cognitive: Find the least common denominator (LCD) of a set of fractions

Psychomotor: Write the least common denominator (LCD) of a set of fractionsAffective: Deal with people fairly


Skill: Find the least common denominator (LCD) of a set of fractionsReference: BEC PELC II.G.8Materials: flash cards, Show Me BoardValue: Fairness



Activity 1A game to review LCM1. Teacher prepares pairs of numbers for pupils to find the LCM.2. Form two sets of 10 pairs of players. Each pair is given one minute to compute for

the answer. Each correct answer earns a point for the team. The team to play first isdetermined by a tossed coin.

3. Teacher shows a pair of numbers for pupils to find the LCM.4. The team that earns more points wins.

1) 9 and 122) 9 and 15

3) 8 and 124) 7 and 5

5) 7 and 66) 12 and 9

7) 7 and 288) 27 and 54

9) 25 and 2010) 36 and 9

Activity 2Individual WorkGive the LCM orally. (Use of Show Me Board)

1) 6 and 72) 4 and 12

3) 6 and 84) 4 and 12

5) 9 and 186) 2, 4, 6

7) 9, 3, 188) 5, 6, 10


1. Presentation

a. Activity 1Problem Opener


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Mrs. Reyes bought two boxes of pizza for her guests. After serving

them, she had2

1 pizza left in one box and4

1 in the other. How will she

slice these so that each of her 3 children will get the same size?Here is the diagram of the problem:

2

1 4

1 4

2 +4

1 =4

3

Expected answer:

Mrs. Reyes will slice the2

1 pizza into 2 equal pieces. Each piece is

4

1 of the whole pizza. So, she will have 3 equal slices.

1) What did Mrs. Reyes serve her guests? What Filipino trait did Mrs. Reyes

show?2) What part of the pizza did each child receive?3) Do you think mother was fair in sharing the pizza? Why? In what situations

can you practice fairness?Discuss:1) How did mother make the fractions similar?2) How can we change dissimilar fractions to similar fractions?Find the Least Common Denominator or LCD. Heres how to find the LCD.Find the Least Common Multiple (LCM) of the denominators 2 and 4.

One way is to list the multiples and find the least common number:

2 = 2, 4, 6

4 = 4, 8, 12 so 4 is the LCD of 2 and 4

Exercise:Find the LCD.1)

3

2

6

1

3)2

1

8

3

5)3

2

12

4

7)3

2

9

1

2)4

2

8

3

4)7

3

14

3

6)2

1

6

1

8)4

3

16

1

b. Activity 2

Find the LCD of2

1 ,4

1 , and6

1 .

1) What are the denominators?2) Get the multiples of each denominator. (The list will look like this.)

22, 4, 6, 8, 10, 12, 14, 16, 44, 8, 12, 16, 20, 66, 12, 18, 24,

3) What is the smallest number that can be found in the list? (12), 12 is the LCDof 2, 4, and 6.


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Exercise: Find the LCD.

1)5

2

43

2)6

1

83

3)2

1

74

4)12

5

83

5)6

1

97

6)4

1

3

2

6

1

7)8

3

3

1

4

3

8)2

1

4

1

5

3

9)2

1

3

2

4

1

10)4

3

8

1

6

1

c. Activity 3

Find the LCD of5

2 ,12

1 , and3

1 .

Use prime factorization.

Prime factors of:5 = 5 x 112 = 3 x 2 x 23 = 3 x 1

LCD of 5, 12, and 3 is 5 x 3 x 4 = 60Process:Multiply all the prime factors. If there are the same prime factors, use the onewith the highest exponent.

e.g. 12 = 3 x 2 x 22 x 2 = 22

2. Fixing Skills

Exercise 1:

Find the LCD.

1)8

7 ,6

5 ,5

4 2)8

2 ,16

5 ,18

3

3)6

5 ,7

6 ,4

3 4)7

2 ,28

3 ,28

3

Exercise 2:

Find the LCD.

1)4

3 ,6

5 2)9

1 ,4

4 3)4

1 ,2

1 ,6

5

4) 31

, 51

, 63

5) 81

, 163

, 42

6) 51

, 123

, 104

7)7

3 ,14

5 ,21

1 8)20

6 ,12

9 9)12

5 ,4

3

10)16

9 ,24

3


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3. Generalization

How do we find the LCD of two fractions?What are the methods of finding the LCD?

B. Application

1) Gerard has2

1 piece melon and another3

2 piece of melon. He has 4 friends and

himself to share the melon equally. How would Gerard do it, so he will be fair?

2) Luz has2

1 kg of meat in the 1stbag,3

2 kg in the 2ndbag, and9

7 kg in the 3rdbag.

She wants to put equal amounts in the bags. What must she do first? Help her findthe least common denominator.

IV. EvaluationFind the LCD.

1)9

5 ,2

1 6)8

7 ,3

2 ,24

11

2)4

3 ,8

7 7)5

3 ,2

1 ,4

1

3)4

3 ,3

2 8)8

3 ,3

1 ,6

2

4)9

4 ,6

1 9)5

4 ,2

1 ,10

3

5)3

2 ,7

1 10)10

9 ,3

2 ,15

3

V. AssignmentFind the LCD.

1)6

3 ,18

5 ,3

2 6)15

9 ,10

5

2)9

4 ,6

2 ,3

2 7)9

3 ,6

4

3)6

2 ,3

1 ,4

3 8)5

4 ,10

9

4)3

2 ,15

1 ,6

5 9)9

4 ,7

6

5)5

4 ,2

1 ,4

3 10)10

3 ,4

1

Ordering Fractions

I. Learning ObjectivesCognitive: Order fractions in simple and mixed forms in ascending or descending

order using different methodsPsychomotor: Write in ascending or descending order fractions in simple and mixed

formsAffective: Prepare a budget


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Skill: Ordering fractions in simple and mixed forms in ascending or descendingorder using different methods

Reference: BEC PELC G.10Materials: strips of paper, activity cards, flash cards, drawingsValues: Money and time budgeting



1. Mental Computation

Change the following fractions to lowest terms:

a)4

2 b)15

6 c)18

10 d)36

21 e)24

18

2. ReviewActivity 1 - Game: Compare Mea) Any number of players may join the game.b) The teacher puts the signs , and = on the board. He/she prepares on flash

cards pairs of fractions to be compared.c) Teacher raises a flash card with a pair of fractions to be compared.d) Players get the correct sign on the board. The player with a wrong answer is

eliminated.e) The player who is not eliminated at the end of the game wins.

3. MotivationHow do you usually arrange names of pupils in a record? Why do we usually do it?How about numbers, how do we usually write them? Why? Can we also write thereverse way?


1. Presentation

Activity 1A Problem OpenerWhole Class Activity

Rita budgets her home activities as follows:

6

1 of the day gardening and cleaning the yard

6

2 of the day cleaning the house and doing laundry work

6

3of the day marketing, cooking, and sleeping

In what activities does she spend more time?Ask the children to make a diagram to find the answer.


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The diagram will look like this:

6

1 62 6

3 a) What kind of fraction are they?b) Compare the numerators.c) How will you order the fractions from least to greatest?d) How will you order the fractions from greatest to least?e) How do you order similar fractions?f) In what activities does Rita spend more time?

What does Rita do with her time?Do you think she can finish all her work?What must we do with our time so we can also finish our work?

Activity 2Whole Class Activity

There are other ways to order fractions. How do we order these fractions:

9

4 , 65 , 5

1 .1) Using Fraction Sense

Close to 0 21 1

5

1 94 6

5 Think of what the given fractions are close to. Order the fractions from least to

greatest: 51 , 94 , 65

.2) Visual Reasoning (Using equal length of strips of paper)

Ask pupils to show three paper foldings for the given fractions.

5

1 is shaded while 54 is not shaded. 5

4 is the largest part of the whole.

9

4 is shaded. 95

is not shaded and is larger than 94 .

6

5is shaded while 6

1 is not shaded. The unshaded is the smallest part of thewhole.Discuss:If you are to arrange the fraction from greatest to least, which is the first fraction?

3) Renaming to Like Fractions


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Find the LCM or LCD.

5

1 = 9018

9

4 = 9040

6

5 = 9075

Compare the numerators.

4) Using PatternsGiven:Order the fractions from least to greatest.

3

2 , 92 , 7

2 , 52 9

2 , 72 , 5

2 , 32

Discussion:a) Make some observations about the given fractions.b) How would you order fractions from least to greatest?c) What was your guide in saying which is the smallest/the largest?(For fractions with the same numerators, the bigger the denominator, the smallerthe value of that fraction.)

5) Using Cross-ProductsDetermine the cross-product of the fraction. Compare the products.

a) 24 45 b) 9 20 c) 6 25

9

4

65

51

94

51

65

24 < 45 9 < 20 6 < 25

6

5

94

94

51

51

65

The numerator that yields the bigger product is greater.

e.g.6

5 >9

4 , since 5 x 9 > 4 x 6.

Order from greatest to least: 65 , 9

4 , 51

6) Mixed Numbers

Order 655 , 4

35 , 875 from greatest to least and vice versa.

Compare the whole numbers.Find the LCD and change them to similar fractions.

6

5 = 2420

4

3= 24

18

87 = 2421

The fraction that yields the greatest numerator is the greatest.

Activity 3Small Group Activity

a) Give each group activity cards.Sample activity cards:

Order from greatest to least: 875 , 6

55 , 435 .

> > >


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Exercise 1: Order the fractions from least to greatest.

1) 32 , 9

2 , 72 , 5

2

2) 41 , 8

1 , 21 , 3

1

3) 75 , 6

5 , 125 , 9

5

4) 123 , 7

3 , 53 , 6

3

5) 94 , 8

4 , 54 , 12

4

6) 94 , 9

5 , 92 , 9

8

7) 75 , 7

1 , 73 , 7

4

8) 97 , 9

3 , 98 , 9

5

9) 52 , 5

1 , 54 , 5

5

10) 83 , 8

6 , 85 , 8

4

Exercise 2: Order the fractions from greatest to least.

1) 91 , 14

13 , 94

2) 21 , 8

5 , 52

3) 54 , 7

4 , 21

4) 92 , 5

3 , 94

5) 125 , 6

4 , 43

6) 66 , 7

6 , 106

7) 65 , 8

3 , 62

8) 21 , 6

5 , 43

b) Make a report on the work of each group.c) Discuss.d) Guide the pupils for some learning insights.

2. Fixing Skills

Exercise 3: Order the fractions in descending order:

1) 436 , 3

26 , 101

7 , 325

2) 117

12 , 43

12 , 111

13

3) 62

1 , 63

1 , 64

1

4) 724 , 7

34 , 754

5) 42

1 , 63

1 , 21

1

Exercise 4: Order the fractions in ascending order:

1) 21

, 124

, 31

2) 4

33 , 853 , 2

13

3) 62

1 , 63

1 , 64

1

4) 107

, 65

, 32

5) 9

8 , 92 , 9

7

3. GeneralizationWhat are the different ways of ordering fractions? What should be the basis inordering fractions in ascending order? Descending order?

C. Application

Read and solve.

1) Perry helped his father do repair work in the yard for 41

1 hours, 21

1 hours in the

house, and 61

1 hours in the garage. What activity does Perry spend the most time?least time?

2) Eric budgets his money as follows:5

1 of his money to buy food,3

1 for his fare,10

1 for

school supplies, and15

1 for his savings. If you are to order Eric expenses, what item

does he spend the most? What is his second least expense?


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3) Carol spends her working time as follows:

2

1 of it for caring the baby

4

1 of it for washing clothes

8

2 of it for doing other things

On what activity does Carol spend less time?On what activity does she spend the most time?What value do the persons in problems 1, 2, and 3 show? Would you be like one ofthem? Who of them would you like to imitate? Why?

IV. Evaluation

Arrange the fractions in ascending order.

1) 52 , 3

1 , 84

2) 85 , 4

3 , 32

3) 43 , 3

2 , 95

4) 418 , 5

25 , 217

5) 818 , 8

12 , 816

V. Assignment

Arrange the fractions in descending order.

1) 124 , 9

4 , 104 , 7

4

2) 21 , 5

1 , 101

3) 32 , 6

5 , 94

4) 54 , 4

3 , 107

5) 65 , 8

7 , 613

6) 213 , 8

72 , 513

7) 432 , 8

72 , 532

8) 433 , 3

22 , 125

3

9) 21 , 8

5 , 115

10) 65 , 3

2 , 127

Solving Word Problems Mentally


Cognitive: Solve mentally word problems involving fractionsPsychomotor: Reduce final answer to lowest termsAffective: Spend time profitably


Skill: 1. Solving mentally word problems involving fractions

2. Reducing final answer to lowest termsReference: BEC PELC II.I.1.1Materials: math textbookValue: Wise use of time


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A. Preparatory Activities1. Mental Computation

GameWho Are We?a) Form 4 teams with equal members.b) Teacher flashes cards for pupils to answer.

Sample flash cards:Name 12as a sum. (Sample answers 2 + 10, 4 + 8, 6 + 6, 1 + 3 + 8,)You can also name me

4

3 . (8

6 ,16

12 ,32

24 ).

I am 2. Give me a fraction name. (2

4 ,3

6 ,4

8 ).

c) The first pupil tries to answer the question or condition flashed. Each membertake turns to satisfy the condition. When all members of the team haveanswered at the given time, answers are checked after 2 or 3 rounds. The teamwith the most correct answers is declared the winner?

2. Reviewa) Check up of assignment.b) Reduce the following to lowest terms:

1)4

2 2)8

6 3)15

10 4)6

10 5)30

15

6)24

12 7)10

6 8)22

11 9)9

6 10)45

15

3. MotivationHow do you spend your Saturday and Sunday? (Wait for some response.) Lets

talk about Lito and find out what he does? Listen carefully and find the good trait ofLito. Do you possess the same trait. Give some activities that you do at home.


1. Presentation

Activity 1A Problem Opener

Lito spends4

11 hours gardening and4

11 hours cleaning the yard on Saturday

and Sunday. How many hours of the day does he spend profitably?1) What are the things you must look for in a problem before solving it?2) What is asked in the problem?3) What facts are given?4) What operation are you going to use to solve the problem?5) Can you solve the problem mentally?6) Reduce your answer to lowest terms.7) What profitable things does Lito do on weekends?

What profitable things do you do on weekends?

What profitable hobby can you do on weekends?Activity 2

Can you solve problems mentally? How many of these problems can you solvecorrectly without paper and pencil. Reduce your answer to lowest terms.

1) Mother prepared a pitcher of juice for our merienda. She used4

3 litre of water

and4

1 litre of juice concentrate. How much more water did she use than juice

concentrate?


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2) Lina ate8

2 of a cake while Vic ate8

4 of the same cake. How much cake did

both of them eat together?3) How much cake was left in Problem 2?4) Maya studied for 45 minutes. What fraction of an hour is this?

5) Bobby measured a piece of rod to be 80 centimetres long. What fraction of a

metre is this?(Use 1 m = 100 cm)

Activity 3Game: How Many Can You Answer?

Students answer on a piece of paper. At the teachers signal, they raise theiranswer. They record their correct answers. The student with the highest point gets asmall reward.

1) Bernie spends8

3 of the day studying in school and8

2 of the day sleeping at

home. What fraction of the day does he spend studying and sleeping.

2) Mother had 43

of a dozen eggs in the refrigerator. She used 41

of a dozen eggfor breakfast. What fraction of a dozen eggs was left?3) Long is

4

21 m tall. Ling is4

1 m shorter than Long. How tall is Ling?

4) A lobster weighs4

21 kg. A crab weighs4

1 kg less than the lobster. What is their

combined weight?

5) Pedro bought8

4 kg of lanzones. Jose bought8

6 kg. Who bought more

lanzones?6) Nena bought

5

42 kilograms of pork. Rosa5

13 kg. How many kilograms did they

buy in all?7) Mother bought

6

18 metres of red lace. Ana bought6

58 metres of white lace.

Who bought the longer length of lace? By how many?

8) Mario can hike 835 km a day. Pedro can hike 8

12 km. How much more canMario hike than Pedro?

9) Liza uses2

12 litres of water for watering her ampalaya seedlings in the morning

and4

11 litres in the afternoon. How many litres of water does she use daily?

10) Ali has a small plot in the garden. He planted6

3 of it to radishes and6

1 to

carrots. What part of the plot did he use?

2. Fixing SkillsIndividual Work: Write your answer on your Show Me Board.

1) My sum is6

5 . What fractions could we be?

2) I am a whole number and a fraction. What kind of fraction am I?3) I am divided into 12 equal parts. You take 9 parts out of me. What names canyou give me?

4) What is the total of4

3 and8

6 . Simplify my name?

5) I am the number 1. Name me as a fraction. How many names can you give me?


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3. Generalization

How do you solve problems mentally?

C. Application

Solve the problems mentally. Write the answer on your paper. Reduce your answer tolowest terms.

1) Mother bought2

1 kg of pork and4

2 kg of beef. How many kilograms of meat did she

buy?2) Mr. Cruz bought

5

4 metre of white cloth and5

2 metre of red cloth. How many metres

of cloth did he buy in all?3) Jason and Jeff are brothers. Jason uses

4

11 metres for pants while Jeff uses8

21

metres. Who between the two is bigger?

4) Mercy has4

3 metre of lace for a blouse. She needs2

1 metre lace for the collar.

What part of the lace was used for the blouse?

5) Rosa bought 86

metre lace. She used 84

metre of it for her handkerchief. How muchlace was left?

IV. Evaluation

1. Father had8

440 metres of wire. He used

8

210 metres to fence his rectangular garden.

How much wire was left?

2. The first swimmer to reach the finish line was timed10

458 seconds while the last

swimmer was10

864 seconds. What was the difference in time?

3. The first set of a volleyball game was finished in 107

45 minutes. The second set was

finished in10

535 minutes. How much longer did it take to finish the first set than the

second set?

4. Mr. Miranda bought a roll of wire 30 metres long. He used2

110 metres. How many

metres of wire were not used?

5. Mother bought 20 metres of certain material. She used4

15 metres for the bedroom.

How many metres were left?

V. AssignmentMake 5 word problems involving fractions that can be solved mentally.

Documents

Lesson Guides Book 7 v0.2