LG MATH Grade 5 - Ratl.nos.Mult.dec. v2.0

7/28/2019 LG MATH Grade 5 - Ratl.nos.Mult.dec. v2.0

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Lesson Guide

In

Elementary MathematicsGrade 5

Reformatted for distribution via

DepEd LEARNING RESOURCE MANAGEMENT and DEVELOPMENT SYSTEM PORTAL

DEPARTMENT OF EDUCATIONBUREAU OF ELEMENTARY EDUCATION

in coordination with

ATENEO DE MANILA UNIVERSITY

2010

Chapter II

Rational Numbers

Multiplication of Decimals

INSTRUCTIONAL MATERIALS COUNCIL SECRETARIAT, 2011


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Lesson Guides in Elementary MathematicsGrade 5

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 5

Region 3

Nelia D. Bamba PampangaMagdalena P. Garcia Angeles City

Region 4-A (CALABARZON)

Gundalina C. Gonzales Batangas

Gerlie Ilagan QuezonConsuelo Caringal Batangas

National Capital Region (NCR)

Teresita P. Tagulao Pasig CityAlyn G. Mendoza Mandaluyong CityEmma S. Makasiray Pasig/San JuanEster A. Santiago ValenzuelaMilagros Juakay Pasig/San JuanLucia Almazan ManilaJulie La Guardia Valenzuela

Bureau of Elementary Education (BEE)

Federico L. ReynoNoemi B. Aguilar

Ateneo de Manila University

Grace Uy

Support Staff

Ferdinand S. BergadoMa. Cristina C. Capellan

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

Consultants

Fr. Bienvenido F. Nebres, SJ President,Ateneo de Manila University

Carmela C. Oracion Principal,Ateneo de Manila University

Pacita E. HosakaAteneo de Manila University

Project Management

Yolanda S. Quijano Director IVAngelita M. Esdicul Director III

Simeona T. Ebol Chief, Curriculum Development DivisionIrene C. De Robles OIC, Asst. Chief, Curriculum Development Division

Virginia T. Fernandez Project Coordinator

EXECUTIVE COMMITTEE

Jesli A. Lapus Secretary, Department of EducationJesus G. Galvan OIC, Undersecretary for Finance and Administration

Vilma L. Labrador Undersecretary for Programs and ProjectsTeresita G. Inciong Assistant Secretary for Programs and Projects

Printed By:

ISBN 971-92775-4-8


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TABLE OF CONTENTS

Introduction .................................................................................................................................. ivMatrix ........................................................................................................................................ v

II. RATIONAL NUMBERS

Multiplication of Decimals

Visualizing Multiplication of Decimals ................................................................................... 1Multiplying:

Tenths by Tenths ..................................................................................................... 5 Hundredths by Tenths and Vice Versa .................................................................... 9 Mixed Decimals by Whole Numbers ....................................................................... 12 Mixed Decimals by Mixed Decimals ........................................................................ 15 Decimals by 10 and 100 .......................................................................................... 19

Decimals Mentally ................................................................................................... 22Solving Problems .................................................................................................................. 26


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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 V

COMPETENCIES VALUES INTEGRATED STRATEGIES USED MULTIPLE INTELLIGENCESTECHNIQUES

With HOTS

II. RATIONAL NUMBERS

Comprehension of Multiplication ofDecimals

1. Multiply mixed decimals and wholenumbers1.1 Visualize multiplication of decimalsusing models

Keep ones work andwork area neat and

clean

Modeling, Drawinggraphs

Cooperative groups,Graphs

1.2 Tenths by another tenths Appreciation of thebeauty of nature

Conceptdevelopment,

Modeling

Diagrams, Nature

1.3 Hundredths by tenths and viceversa

Sharing Acting out theproblem, Looking for

patterns

Diagrams

2. Generalize the step in multiplyingdecimals3. Multiply mixed decimals with tenthsand hundredths by whole numbers

Working well withothers

Games, Conceptdevelopment

Games, Hands-onactivities, Cooperative

groups

4. Multiply mixed decimals by mixeddecimals with tenths and hundredths

Healthconsciousness,

Accuracy

Game, Conceptdevelopment

Puzzles

5. Multiply decimals by 10 and 100 Awareness Looking for patterns,Acting out the

problem

Tables, Self-awarenessactivities

6. Multiply decimals mentally by 0.1,0.01, and 0.001

Helpfulness,Cooperation

Looking for patterns,Drawing tables

Tables, Cooperativegroups

7. Application of Multiplication ofDecimals7.1 Solve word problems involvingmultiplication of decimals includingmoney

Accuracy, Spendingmoney wisely

Acting out theproblem, Simplifying

the problem

Writing, Speaking, Simpleplay, Cooperative groups


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Visualizing Multiplication of Decimals

I. Learning Objectives

Cognitive: Visualize multiplication of decimals using modelsPsychomotor: Draw and color neatly the decimal models

Affective: Appreciate the value of clean work

II. Learning Content

Skill: Visualizing multiplication of decimalsReference: BEC-PELC II.H.1.1Materials: Flash cards, colored chalk, drawingsValue: Keep ones work and work area neat and clean

III. Learning Experiences

A. Preparatory Activities

1. Drill

Strategy: Draw me

Materials: Flash cards, colored chalk

Mechanics:

a. Divide the class into 4 groups.b. Teacher flashes a card with a fraction written on it.

Example:

c. The first pupil in each group will go to the board to make an illustration of the fraction.d. The one who drew the correct drawing gets the point.e. Continue this until everyone in the group has participated.f. The group with the most number of points wins.

2. Review or Mental Computation

1) Aling Rosa bought 0.8 kg of hotdog. She placed 0.25 kg of it in the refrigerator andcooked the rest. How much hotdog did she cook?

2) A Math book is 0.6 dm thick. A science book is 0.2 times as thick. How thick is thescience book?

B. Developmental Activities

1. Presentation

Strategy 1: Using a problem opener with transparent plastic

Mr. Dizons farm is 0.3 km long and 0.1 km wide. How big is his land?

4

3

5

2

8

7

6

7etc.


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0.1 or10

10.3 or

10

3

100

3

10

3x

10

1

Into how many parts is the whole divided?How is 0.3 shown in the grid?What about 0.1?How many squares are double shaded?

In fraction form write10

1of

100

3

10

3x

10

1

10

3 .

Another way of writing fraction is in decimal form.0.1 of 0.3 = 0.1 x 0.3 = 0.03How many decimal places are there in both factors? How about in the product?

Strategy 2: Coloring (Using paper grid)

(Group Work) [2 x 0.8 = N]

=

=

1 0.600.8 0.8 =

1.6

How many grid did we use to show 0.8? Why?

Strategy 3: Use of number line

2 x 0.8 = N

0.8

0.8

0 1 2 3 4 5 6 7 8 9 1.0


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0.8 0.8

The number line above shows that when we joined the two eight tenths, we completed oneline of 10 and up to 6 on the line of 10. Therefore, 2 x 0.8 = 1.6.

2. Fixing Skills

A. Use numberlines to show the product of the following.

1.

3 x 0.4

2.

4 x 0.6

B. Using paper grid, show the product of the numbers by shading it more darkly.

1. 0.5 x 0.4

2. 0.7 x 0.8

C. Give the factors of the illustration showing the products of the following.

_____ x _____ = _____

_____ x _____ = _____

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

0 1 2

0 1 2 3

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

0 21


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3. Generalization

How do we visualize multiplication of decimals? Multiplying decimals can be visualizedby representing each factor with the horizontal and vertical lines placed over the other.The double shaded part represents the answer to the equation.

C. Application

Using illustration, give the answer of the following situation.

1. Every morning Yvan goes jogging. He can jog a distance of .9 kilometer. How manykilometers can he jog in 6 days? (numberline)

2. A rectangular table is 0.8 m and 0.5 m. Find its area. (Paper grid)

IV. Evaluation

A. Write the correct multiplication equation for each of following numbers represented by theshaded region.

=

_____ x ______ = ______

=

_____ x ______ = ______

=

_____ x ______ = ______


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B. Shade the figures to represent each number sentence.

1) 0.8 2) 0.3 3) 0.9x 0.3 x 0.4 x 0.6

4) 0.7 5) 0.4x 0.7 x 0.9

C. Illustrate the following number sentence.

1) 2 x 0.5 = N2) 0.6 x 0.7 = N3) 4 x 0.3 = N4) 0.9 x 0.2 = N5) 0.8 x 0.4 = N

V. Assignment

Prepare paper grid divided into 100 equal parts and be ready to show your own multiplicationequation of decimals.

Show the following multiplication equations by using number lines.

1) 0.3 x 0.6 =2) 0.5 x 0.8 =3) 0.7 x 0.4 =4) 0.2 x 0.9 =

Multiplying Tenths by Tenths


Cognitive: Multiply tenths by another tenthsPsychomotor: Write decimal point in the product correctlyAffective: Appreciate the beauty of nature


Skill: Multiplying tenths by tenthsReference: BEC-PELC II.H.1.2Materials: Multiplication wheel, 10 by 10 grid (transparent plastic)Value: Appreciation of the beauty of nature


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III. Learning Experience


1. Drill

Basic Multiplication FactsMultiplication wheel

2. Mental computation

a. If you have three 500-peso bills, how much do you have in all? At 12.75 for eachripe mango, how much will 6 ripe mangoes cost?

b. Rene deposits 200 every month. How much is his deposit in one year?

3. Review

Illustrate the number sentence.

a. 3 x .5 = 1.5b. .6 x .3 = .18

4. Motivation

How many of you have gone to Luneta? Fort Santiago? What do you usually see in theseplaces?


1. Presentation

Strategy 1: Using a problem opener

The park is rectangular in shape and measures 0.3 km, long and 0.2 km wide. What isits area? What do you picture out in your mind when you read the problem? What are the signs that you usually see in parks?

As a good boy or girl what must you do with signs that you see in parks? What is asked in the problem? How shall we solve it?

4

10

2

8

5 3

6

9

1

7

9 x


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Use of Grid:

Strategy 2

To find the area, we multiply the length and the width.

Step 1: Multiply the digit as if you are multiplying whole numbers

2 2 x 3 = 6

Step 2: Count the number of decimal places in the multiplicand and multiplier. Thesum of the number of decimal places in the factors is equal to the number ofdecimal places in the product.

Step 3: Add zero if necessary.

Strategy 3

Using fractions:

10

3 x10

2 =100

6 so 0.3 x 0.2 = 0.06

Strategy 1: Use of Grid

Into how many equal parts is the whole divided?

How many parts are double-shaded?The double shaded part is the product of 0.2 and 0.3.

3 x 2

0.3 x 0.2 = 0.06

A = 0.06 km

w = 0.2 km

0.3 km

L = 0.3 km


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2. Fixing Skills

Find the product.

A. 1. 0.5 2. 0.9 3. 0.5x 0.2 x 0.4 x 0.6

B. Give the answer.

1. What is the product of 0.6 and 0.8?2. If 0.7 and 0.4 is multiplied, what is the answer?3. 0.5 time 0.9 equals _____.4. 0.2 x 0.2 x 0.2 = _____.

C. Solve.

What is the area of the illustration board with .6 dm and .8 dm dimensions?

3. Generalization

How do we multiply tenths by another tenths?In multiplying tenths by another tenths, multiply like multiplying whole numbers.

Place the decimal point in the product equal to the sum of the number of decimal placesin both factors.

C. Application

1. A lot has a length of 0.4 and 0.3 wide. What is its area?2. A painting having a dimension of 0.4 m and 0.8 m is to be wrapped with a cloth 0.4 m

larger than its dimensions. What is the area of the cloth?

IV. Evaluation

A. Copy and place the decimal point in the product.

B. Give the products mentally.

C. and complete each table.

x 0.3 0.4 0.51. 0.62. 0.73. 0.8

x 0.6 0.7 0.8

1. 3.42. 1.23. 0.6

1) 0.70.5

2) 0.80.6

3) 0.90.5

4) 0.60.3

5) 0.40.7

35 48 45 18 28

1) 0.40.5

2) 0.60.8

3) 0.70.3

4) 0.90.5

5) 0.90.8


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V. Assignment

Slow: Find the products. Write in column.

1) 6.5 x 0.7 = 2) 0.8 x 0.3 = 3) 9.3 x 0.8 =4) 0.9 x 0.9 = 5) 0.7 x 0.6 =

Fast: Write the following fractions to decimals then multiply.1)

10

8 x10

4 = N 2)10

6 x10

5 = N 3)10

8 x10

8 = N

4)10

7 x10

8 = N 5)10

9 x10

6= N 6)

10

3 x10

9 = N

Multiplying Hundredths by Tenths and Vice Versa


Cognitive: Multiply hundredths by tenths and vice versaPsychomotor: Apply the rule in multiplying decimalsAffective: Appreciate the value of helping one another


Skill: Multiplying Hundredths by Tenths and Vice VersaReference: BEC-PELC II.H.1.3Materials: Flash cards, pictures of a familyValue: Sharing



1. Drill

Basic Multiplication Facts

Relay (Flash cards)a. Let 3 pupils stand on the aisle of the room.b. Teacher flashes card on basic multiplication facts then the pupils answer.c. The pupil who gets the correct answer moves one step forward. (One step for every

right answer.)d. The pupil who reaches the place of the teacher first wins the game.

2. Review /Mental computation

a. Anne bought 7 apples. If each apple cost 15.00, how much did she pay for it?b. A bag of sugar weighs 3.5 kg. What is the weight of 3 bags of sugar?

3. Motivation

(Show a picture of a family)What can you say about the family in the picture? Why do you think the family lookshappy? How do help your younger brother or sister?


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1. Presentation

Strategy: Problem opener (Acting out the Problems)

Activity 1

A piece of chocolate bar is 0.16 dm long. James shared it with his sister. If Jamesgot 0.2 of the chocolate bar, how long was for her sister?

How do you find James and his sister in the story? In the school, how will you show your care for others? What are we going to find in the problem? What are given? What operation will we use? How will you state the number sentence?

Study the following solutions:

Multiply the decimals as if they are whole numbers: 16 2 = 32Count the number of decimal place in both factors. The number of decimal places in thefactors is equal to the number of decimal places in the product. 0.16 x 0.2 = 0. 0 3 2

Activity 2

Using fractions:

0.16 x 0.2 = 100

16

x 10

2

= 1000

32

= 0.032

What is the product of100

16x10

2in decimal?

How does the sum of the number of zeros in the denominators of the factors compare

with the number of decimals in the product?How does the number of decimal places in the product compare with the number ofdecimal places in the factors?

2. Fixing Skills

A. Tell how many decimal places each product will have without actually computing.

1. 0.6 x 0.05 ______2. 0.11 x 0.7 ______3. 0.58 x 0.9 ______4. 0.8 x 0.12 ______5. 0.95 x 0.6 ______

B. Do the following exercises.

1. 0.23 2. 0.09 3. 0.63x 0.4 x0.3 x 0.5

4. 0.51 x 0.7 = n5. 0.9 x 0.25 = n


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C. Give the answer.

1. What is the value of (0.2)2 - (0.2)?2. If 0.56 x 0.8 = 0.448, what is 0.56 x 0.80 equal to? Explain your answer.

3. Generalization

How do we multiply hundredths by tenths?To multiply hundredths by tenths, multiply like whole numbers and count as many

decimals places in the product as there are in the multiplicand and multiplier together.

C. Application

1. Multiply and place the decimal point correctly in the product.

2. Multiply then express your answer into decimals.

a) 0.14 0.3 =b) 0.22 0.4 =c) 0.35 0.2 =d) 0.41 0.5 =e) 0.62 0.6 =

3. Solve.

A book is to covered with a plastic cover 3 cm more than the dimensions of the book0.65 dm and 0.8 dm. How much plastic cover is needed to cover it?

IV. Evaluation

A. Place the decimal point in the product.

1) 0.6 0.32 = 01922) 0.09 0.45 = 004053) 0.2 0.45 = 00904) If 0.9 x 0.45 = 0405, what is 0.90 x 0.45 = N?5) 0.49 times 0.7 is 0.343, what is 4.9 times .07?

B. Multiply and place the decimal point in the product.

1) 0.34 0.4 =2) 0.6 0.47 =

3) 0.74 0.6 =4) What is the area of a rectangle with a length of .75 dm and a width of .5 dm?5) What is the area of a picture frame having a length of 0.95 dm and a width of 0.6 dm?

0.41 0.24 0.11 0.12 0.32x .2 x 0.3 x 0.6 x 0.4 x 0.3


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V. Assignment

A. Write in column and multiply.

1) 0.28 x 0.3 = ________2) 0.6 x 0.36 = ________3) 0.7 x 0.95 = ________4) 0.4 x 0.04 = ________5) 0.24 x 0.6 = ________

B. Think of your own decimal numbers in hundredths and in tenths, multiply them. Construct atleast three problems.

Multiplying Mixed Decimals by Whole Numbers


Cognitive: Multiply mixed decimals with tenths and hundredths by whole numbersPsychomotor: Act promptly on given workAffective: Work well with others


Skill: Multiply mixed decimals with tenths and hundredths by whole numbersReference: BEC-PELC II.H.1.4Materials: cards with whole and decimal numbers, charts, cubes with numbers, activity

sheetsValue: Working well with others



1. Drill: Flashcards of basic multiplication facts

2. Review

Strategy: Tossing Dice

Materials: Two dice with the following faces: 1.2, 3.5, 2.6, 4.1, 1.2 and 3.3Mechanics:a. Distribute 2 cubes to each group.b. One pupil rolls the cube and another records the face up digits.c. The group who gives the most number of correct answers wins the game.

3. Motivation

Which are mixed decimals?Which are whole numbers?

2 7.44 0.61 3.789 15 891

Whats the difference between a whole number and mixed decimal numbers? Can wemultiply the two numbers?


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1. Presentation

Get a card with a whole number and another one with a mixed decimal. Lets multiply.Example: 7.44 x 2 =

Strategy 1: Number Cards

The answer is 14.88. How many number of decimal places in the multiplicand?(Two) Then put the same number of decimal places in the answer.

Strategy 2: Problem opener

A faucet can fill a large drum in 1.15 hours. How many hours will it take to fil l 3drums?

a. What is the problem asking us to find?b. How can we solve for the answer?

Multiply 1.15 by 3.c. What kind of number is 1.15? What about 3?d. How many decimal places are there in 1.15?e. How many decimal places should there be in the product?

Therefore 1.15 x 3 = 3.45

Strategy 3: Use activity Sheets

Materials: Activity Sheets with the following problems.

a) 2.78 b) 50.04 c) 153.62x 46 x 93 x 21

d) 10.49 e) 5.68x 6 x 32

a. Divide the class into groups with 5 members each.b. They will work on the activity sheets.c. Remind the pupils to estimate first the products. Tell them that estimating the

products before performing actual multiplication will help them place the decimalpoint correctly in the final product. Remind them also to count the decimal places inthe product starting from the right. Emphasize that in multiplying decimal, there is noneed to line up the decimal points.

d. After doing the activity, the members of the group will exchange work for checking.

Strategy 4

Rudolf lives 2.4 km from school. How far does he ride in going to and from school?

Multiply like whole numbers:

Multiply each digit of the multiplicandwith the multiplier.Start from the hundredths to thetenths and whole number.

7.44x 214.88 2 x 4 = 8

2 x 4 = 82 x 7 = 14


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To find our answer we multiply 2.4 by 2.Solution:

2. Fixing Skills

A. Tell how many decimal places each product will have without actually computing.

1. 3.6 x 52. 14.35 x 123. 458.013 x 24. 15 x 5.7035. 78 x 16.9054

B. Find each product.

1. 2.3 2. 15.12 3. 26.936x .6 x 5 x 5

4. The product of 19.21 x 12 is _____.5. If a notebook is cost 5.25, how much is the cost of 6 notebook?

3. Generalization

How do we multiply mixed decimals by a whole number?To multiply mixed decimals by a whole number, multiply like whole numbers then countthe number of decimal places in the factors. The factors and the product must haveequal decimal places.

C. Application

1. Complete the table by giving each product.

2. Andrei bought apples at 15.50 each. How much did he pay for 5 apples?3. A working student earns 25.50 an hour. How much does he earn in 4 hours? If he

works 3 days a week, how much does she earn a week?

IV. Evaluation

A. Tell whether the decimal point is written on the proper place.Put a check mark () in the box to indicate correct answers.

1) 2.3x 2

2) 3.6x 4

3) 54.12x 7

.46 14.4 37.884

4) 29.14x 82

5) 3.42x 9

6) 18.6x 7

Steps:Multiply like whole numbers.Count the decimal places in thefactors.Do the same in the product.

2.4x 2

4.8 2 x 4

2 x 2

x 2.6 11.92412


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2389.48 30.78 16.74

B. Copy and give the product:

1) 0.76 2) 0.12 3) 16.57 4) 0.93 5) 38.2x 4 x 5 x 6 x 8 x 7

C. Give the missing numbers.

1. If 367 x 28 = 10276, what is 36.7 x 28 equal to?2. If 1238 x 36 = 44568, what is 12.38 x 36 equal to?3. If 3856 x 6 = 23136, what is 38.56 x 6 equal to?4. If 275 x 4 = 1100, what is 0.275 x 4 equal to?5. 1637 x 7 = 11459, what is 1.637 x 7 equal to?

V. Assignment

A. Write the product with the decimal point in the correct place. Then be ready to read youranswers aloud.

1) 6.48 2) 20.6 3) 7.644 4) 3.65 5) 348.1x 32 x 18 x 24 x 23 x 5

Multiplying Mixed Decimals by Mixed Decimals


Cognitive: Multiply mixed decimals by mixed decimals with tenths and hundredthsPsychomotor: Tell the rules in multiplying decimalsAffective: Appreciate the importance of exercise to stay fit


Skill: Multiplying mixed decimals by mixed decimals with tenths and hundredthsReference: BEC-PELC II.H.1.5Materials: pictures, flash cards, number cardsValue: Health consciousness, accuracy



1. Drill

Multiplication of Decimal Fractions

Procedure:a. Place number cards, face down on table.b. Pupils take turns selecting two cards.c. For each pair of cards, all in group writes the multiplication equation and gives the

answer.d. Pupils check each others answer.

Ex:

10

3

100

2=10

3x100

2= N

1000

6


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2. Review

3. Mental Computation

a. If 1 kg of onions cost 25.10, how much is 1.5 kg of onions?b. Anne uses 0.75 metre of cloth to make a pillowcase. If she finished 5 pillowcases,

how many metres of cloth did Anne use?

4. Motivation

What do you understand of the saying Health is Wealth?How do you keep yourself healthy?


1. Presentation

Strategy 1: Using a problem opener

Chet burns 7.5 calories of food energy per minute while jogging. How many caloriesdoes she burn if she jogs for 6.75 minutes? Why do you think Chet jogs every morning? What are the importance of exercise to our body?Lets find out the number of calories Chet burned in 6.75 minutes. How shall we do it?

Strategy 2: Short Way

6.75x 7.5

2 decimal places (multiplicand)1 decimal place (multiplier)

3375

472550.625 3 decimal places (product)

How many decimal places are there in the multiplicand? in the multiplier? How manydecimal places are there in the product? What did you do to find the number of decimalplaces in the product?

a) 4.3 1 decimal place b) 21.4 1 decimal place

2.6 1 decimal place .32 2 decimal places

25886

428642

11.18 2 decimal places 6.848 3 decimal places

Multiply: 2.3x 4

5.13x 2

16.2x 3

7.11x 5

8.6x 2


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Strategy 3: Using a Puzzle

In the problem, select the multiplication problem that is described by the clues.

[Puzzle 1]Clues:1. The first partial product is 57.2. The second partial product is 38.

After which clue helped you know the answer? Put a check ().Clue #1 ____Clue #2 ____What is the answer?[Puzzle 2]Clues:

1. The first partial product is 2128.2. The second partial product is 608.

After which clue helped you know the answer?Clue #1 ____Clue #2 ____What is the answer _____

2. Fixing Skills

A. Without actually multiplying, can you tell if the whole number part of each product willbe ones, tens, or hundreds? Can you explain your answer?

1. 2.465 x 6.0032. 54.002 x 4.0073. 0.8051 x 9.0054. 21.06 x 0.5075. 68.08 x 0.495

B. Try harder. Find each product.

1. 2.09 2. 7.47 3. 21.03

x 5.36 x 1.3 x 5.6

4. What is 45.7 times 4.06?

5. What is the cost of 15.25 kg of sugar if the price per kilo is 52.25?

3. Generalization

How do we multiply mixed decimals by mixed decimals?

1.92.3

2.41.6

3.21.8

A B C

2.582.6

4.612.8

3.042.7

A B C


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To multiply decimals, do the following:

1. Multiply as for whole numbers.2. Count the number of decimal places in the factors.3. Put the decimal point in the product so that there are as many decimal places as

there are in the factors.4. If there are not enough digits in the product obtained in (1), add the necessary

number of zeros to the left of the product before placing the decimal point.

C. Application

Get The Message

1) 7.02 2.5

2) 6.39 4.1

3) 12.6 35

4) 35.18 0.3

A = 27.675C = 13.078

D = 70.155) 11.07

2.56) 7.02

2.57) 6.25

1.58) 5.03

2.6E = 26.199I = 17.55

L = 10.5549) 11.5

6.1

10) 10.04

4.01

M = 40.2604

O = 17.550U = 44.1V = 9.375

Message:6

I

4

L

1

O

7

V

2

E

3

U

IV. Evaluation

A. Copy and place the decimal point in the product.

1) 2.3 4.09 = 94072) 3.6 5.28 = 19008

3) 4.8 6.79 = 325924) 5.6 8.95 = 50125) 1.2 2.46 = 2952

B. Encircle the letter of the best answer

1) 74.12 6.3 = a. 486.956 b. 476.855 c. 486.9562) 5.49 4.6 = a. 23.244 b. 24.254 c. 242.543) 13.7 .56 = a. 7.561 b. 76.72 c. 7.6724) 12.63 3.2 = a. 40.416 b. 41.416 c. 404.165) 4.26 2.5 = a. 11.650 b. 10.650 c. 10.550

C. Find the product.

1) Find the product of 3.3 and 7.15.2) What the product of 2.34 and 2.5?3) If 6.1 is multiplied with 9.28, what is the product?4) Find the cost of 1.5 kg of rice at 24.75 per kg?5) What is the area of a rectangle with the length of 10.75 cm and a width of 6.25 cm?


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V. Assignment

A. Locate the decimal point in the product.

1) 8.70 1.5 = 130502) 1.3 2.6 = 338

3) 4.28

1.3 = 55644) 6.05 5.2 = 314605) 8.65 x 7.6 = 65740

B. Multiply and locate the decimal point in the product.

a) 2.64

3.5b) 3.85

4.6c) 4.95

2.5d) 8.65

6.4

e) 3.50

1.8f) 24.64

2.5g) 86.75

3.6h) 98.47

4.7

C. Find the products.

1) 6.3 10.25 = N2) 18.4 35.15 = N3) 16.76 7.7 = N4) 22.12 4.8 = N5) 11.11 x 19.6 = N

Multiplying Decimals by 10 and 100


Cognitive: Multiply decimals by 10 and 100Psychomotor: Write the product of decimals by 10 and 100Affective: Recite with ease and confidence


Skill: Multiplying decimals by 10 and 100Reference: BEC-PELC II.H1.6Materials: Flash cards, chartsValue: Awareness



1. Drill

Multiplication of whole numbers by 10, 100 and 1000.

The Weakest Linka. Group the class into 4, each with 5 members.b. The teacher flashes a card, for example:

63 x 100


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c. The pupil is given 1 second to answer. If he or she cant give the right answer, he orshe is the weakest link and should be out of the line.

d. Continue the game until everybody in the group has participated.e. The pupil left in the line is called the strongest link. He is the winner.

2. Mental Computation

How much is 2 hankies at 5.25 each?How much is 3 pairs of socks at 32.00?


1. Presentation

Strategy 1: Problem Opener

The diameter of Earth is about 12.56 thousand kilometres. The diameter of Jupiter ismore than 10 times that of Earth. Estimate Jupiters diameter.

a. Teacher will discuss the lesson:

Multiply 12.56 and 10 to solve the problem.12.56 x 10 = 125.6Look at the multiplier and the product.

b. What happened to the decimal point in the product?c. The decimal point is moved 1 place to the right.d. Jupiters diameter is more than 125.6 thousand kilometres.

Strategy 2: Looking for the Pattern

Study each set of examples. Observe the pattern.

A0.8 x 10 = 82.5 x 10 = 2517.3 x 10 = 173

0.26 x 10 = 2.64.28 x 10 = 42.8

B64.8 x 100 = 6 48075.2 x 100 = 7 52018.5 x 100 = 1 850

2.87 x 100 = 2879.162 x 100 = 916.27.468 x 100 = 746.8

Look at box A.a. What is our multiplicand?b. Compare the multiplier and the product.c. In what direction did we move the decimal point?d. If the decimal point is after the number, is it necessary to use zero as a placeholder?

Look at box B.

The numbers are multiplied by 100. Why do you think zero is added to the product?

Strategy 3: Acting-out

Mila received a birthday gift of $ 10 from her daughter. How much would she get inpeso if the exchange rate is 45.40 to a dollar.

How much is the rate of $ 1? What can you say about it?


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What are the effects of the weakening of the peso against the dollar on oureconomy?

How will you find the value of $ 10 at 45.40 to dollar?

Pupils will act out using play money. One will act as Mila and one pupil as themoneychanger.

2. Fixing Skills

A. Place the decimal point in the correct place.

1. 10 x 9.34 = 9340 6. 100 x 98.65 = 9865002. 10 x 0.546 = 5460 7. 100 x 6.0042 = 60042003. 10 x 6.897 = 6897 8. 100 x 75.53 = 7553004. 10 x 95.93 = 95930 9. 100 x 3.0054 = 30054005. 10 x 5.0023 = 500230 10. 100 x 0.4312 = 431200

B. Place the decimal point in the correct place.

1. 10 x 5.46 6. 100 x 6.422. 10 x 87.5 7. 100 x 0.19523. 10 x 0.475 8. 100 x 3.654. 10 x 23.8 9. 100 x 435.85. 10 x 67.32 10. 100 x 9.8127

C. Solve.

A tailor needs 2.75 m of cloth from one uniform. How many meters will beneeded for every 100 uniforms?

3. Generalization

How will you write the product of 10, 100 and a decimal?

a. To write the product of 10 times a decimal, move the decimal point one (1) place tothe right.

b. To write the product of 100 times a decimal, move the decimal point two (2) places tothe right use zero as a placeholder if necessary.

C. Application

1. Tell the number of decimal places in the product then multiply. Use the pattern to helpyou.a) 2.147 x 10 = n b) 0.05 x 10 = n c) 0.003 x 10 = nd) 35.86 x 10 = n e) 0.418 x 10 = n f) 0.4 x 10 = ng) 0.7 x 100 = n h) 32.15 x 100 = n

2. Give the answer orally.a) 10 x .8 = b) 10 x 27.64 =c) 10 x 2.93 = d) 100 x 1.876 =e) 10 x 4.632 = f) 100 x 22.76 =

3. Solve the following:

a. Liza earns 250.00 for selling empty bottles every week. How much does she earnin 10 weeks?


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b. Rey and Joy picked 100 kg of mangoes from their mango trees. If they sold at75.00, how much did he get?

IV. Evaluation

A. Multiply.

B. Write 10 or 100 in the.

1) x 0.06 = 62) x 7.8 = 783) 3.7 x = 370

4) x 638 = 63.85) .125 x = 12.5

C. Find the product.

1) 73.8 x 10 = _____2) 16.73 x 101 = _____3) 94.6 x 10 = _____4) 276.7 x 101 = _____5) 5.948 x 10 = _____

V. Assignment

A. Copy the table and complete.

B. Multiply.

1) 4.36 x 10 = 2) .7132 x 103 =3) 37. 5 x 101 = 4) .0765 x 10 =5) 6.035 x 10

3= 6) 26.179 x 10

1=

7) 18.61 x 10 = 8) 1.76 x 101 =

Multiplying Decimals Mentally


Cognitive: Multiply decimals mentally by 0.1, 0.01 and 0.001Affective: Be a worthy member of a group

10 x

0.9 ___

10 x

75.46 ___

0.06 ___ 4.08 ___

0.75 ___ 56.79 ___

4.96 ___ 4.32 ___

.8317 ___

x 0.9 0.46 x 0.33 0.04 0.96 8.73

10 10100 100


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Skill: Multiplying decimals mentally by 0.1, 0.01 and 0.001Reference: BEC-PELC II.H 1.7Materials: Chart, straw, boxes and show-me-boardValue: Helpfulness/Cooperation



1. Drill

Multiply decimals mentally by 0.1, 0.01 and 0.001

Mechanics:a. Teacher prepares questions written on manila paper.

Example: 2.25 x 10 =b. Pupils in each group write their answers on their show-me-board. They are given 30

seconds to answer.

c. The group with the most number of correct answers wins the game.2. Mental Computation

a. Each of the 100 families in a certain community will share 12.50 for the cleaning oftheir drainage. How much will the community raise?

b. A barangay chairman bought 100 pieces of plastic chairs at 185.75 each. Howmuch was the total cost of all the plastic chairs?

c. If you are a member of this community, how will you react to the problem?d. What kind of community do you see?e. Are the members of the community helping one another? How will you prove it?


1. Presentation

Strategy 1: Looking for the Pattern

Activity 1

Study each set of examples. Observe the pattern.

A B C

0.7 x .1 = 0.07 0.4 x .01 = 0.004 0.9 x .001 = 0.00093.2 x .1 = 0.32 7.2 x .01 = 0.072 0.47 x .001 = 0.0004745.6 x .1 = 4.56 54.3 x .01 = 0.543 6.2 x .001 = 0.006217.19 x .1 = 1.719 69.87 x .01 = 0.6987 84.73 x .001 = 0.0847330.45 x .1 = 3.045 47.05 x .01 = 0.4705 65.08 x .001 = 0.06508

Look at box A.a. Compare the multiplier and the product.b. In what direction did we move the decimal point?c. Why do you think zero is added to the product?d. Do we always add zero? Why not?

Analyze box B.a. How many decimal places did we move the decimal point?b. To what direction? How about box C?


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Activity 2

Joeysaid

Joy answered Joey said Joy Answered Joy said JoeyAnswered

0.3 0.03 33.86 0.3386 548.3 0.54838.4 0.84 46.9 0.469 92.27 0.092279.7 ___ 58.47 ___ 48.63 ______ 0.42 ___ 0.032 ___ 0.9214___ 0.09 8.4 ___ 6.9 ___

Guess each rule. Then give the missing numbers.

Strategy 2: Tossing Dice

Mechanics:a. Each group is divided into 2 competing teams with 4 members each.b. Each team is to have a set of straws with accompanying holder.

(Green for 1 place decimal, red for 2 places and yellow for 3 places)c. The first team rolls the dice and multiplies the two decimal numbers.

Example:1) If the product is two decimal places the team will put the red straw in their strawholder.2) The teacher checks their answers and give the score of 5 for correct answersand 0 for wrong answer.

3) The activity goes on with the team taking turns in throwing the dice.

2. Fixing Skills

A. Use of flash cards (Orally)Multiply:0.12 x .01 = n 2.15 x .1 = n0.8 x .001 = n 65.75 x .01 = n0.748 x .1 = n 97.125 x .01 = n2.34 x .001 = n

B. Calculator (Printed on Manila Paper)

PRESS 0.1

2.215 =0.1 0.213 =

0.1 34.16 =

0.1 0.246 =

PRESS 0.01 0.781 =

0.01 7.9 =


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0.01 5.32 =

0.01 2.5 =

PRESS .001 3.82 =

.001 10.3 =

.001 2.7 =

.001 .86 =

C. Multiply the following mentally.

1) 2.8 x 0.1 2) 16.506 x 0.13) 197.64 x 0.1 4) 0.001 x 0.11845) 0.01 x 30.8 6) 0.01 x 0.897) 35.678 x 0.1 8) 6.5 x 0.001

3. Generalization

How do we multiply decimals by 0.1, 0.01 and 0.001 mentally?When multiplying decimals by:a. 0.1 simply move mentally the decimal point in the multiplicand one place to the leftb. 0.01 move 2 places to the leftc. 0.001 move 3 places to the left. Use zero as a place holder if necessary

C. Application

1. Give the product of the following.

a. 0.14 x 0.1 = nb. 2.13 x 0.1 = nc. 0.45 x 0.01 = n

d. 0.001 x 0.546 = ne. 0.001 x 11.205 = n

2. Use the symbol >, < or = to make the statement true.

a. 0.21 x 0.1 0.21 x 0.01b. 5.21 x 0.01 52.1 x 0.01c. 11.03 x 0.01 1.103 x 0.01d. 0.053 x 0.001 0.053 x 0.01e. 8.01 x 0.001 80.1 x 0.01

3. Solve

Every 0.1 grams of gold cost 450. How much is 0.8 grams of gold cost?

IV. Evaluation

A. Multiply mentally.

1. 7.32 2. 0.854 3. 4.048x 0.1 x 0.1 x 0.01


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4. 12.605 5. 16763x 0.001 x 0.001

B. Give the correct answer mentally.

1. The product of 6.35 multiplied by 0.1 is _____.

2. 0.478 times 0.01 is _____.

3. What is the number: x 0.001 = 6.7386?

4. What is the other factor? 94.09 x = 0.9409

5. Compare: 5.34 x 0.01 53.4 x 0.1. Use the symbol (>,


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Answer: enough

Luis is 2.6 cm taller than Lito. How tall is Luis?Three girls have the same weight. If one girl weighs 28.7 kilos, what is the total weight?Allan has 6 pieces of 10.00 bill. How much money does he have in all?


1. Presentation

Strategy 1: Acting Out the Problem

Mechanics:

a. Place objects like bananas, sandwiches, biscuits, juice, cup cakes with tag price onthe teachers table.

b. Group the pupils by five. Each group will be given play money. The group willdecide on what to buy for snacks. They will budget their money so that each one willhave a share.

c. Pupils will write their orders with their computation on a paper.

d. The teacher acts as storeowner. If the computation is correct, she will give the items.If incorrect, she will return the paper and let the group solve again.Bananas Sandwich Juice Biscuits

2.50 29.50 6.00 5.00

Strategy 2: Using a problem opener (Simplifying the problem)

Cherrys aunt has arrived from America. She gave Cherry a $10-bill and Cherrysmother a $100-bill. How much will Cherry get in pesos if the exchange rate of one USdollar is 53.217? How much will her mother get in pesos?

a. Ask the following questions:

What are given? What is asked? How will you solve the problem? What is the number sentence or equation? Write the number sentence. Solve for N. State the complete answer. Look back if the answer makes sense.

b. Copy and complete the chart below.The first and second column show the name and cost of each item.

COST OF ITEMS

1 2 3 4

Pencil 4.50 9.00

Ball pen 8.35

Notebook 23.40

Pad & Paper 12.50

Eraser 5.60


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c. Solve the following problems and state the complete answer.

1. If a car travels 55.6 kilometres an hour, how far will it travel in 8 hours?2. If 1 metre of cloth costs 72.95, how much would 6.4 metres cost?3. A cone of ice cream costs 16.25. How much will the 6 children spend on ice

cream?4. A kilo of rice is 21.50. What is the cost of a sack of rice containing 50 kilos?

d. Analyze and solve the problems. Remember to write an equation.Show your solution and label your answer.

1) During recess, Romeo bought 3 packages of toasted bread at 6.50 each. Howmuch did he pay for all the packages?

2) Mother bought 4 cans of evaporated milk at 16.50 each. How much did shepay in all?

3) Mrs. Moran bought a whole dressed chicken weighing 2.2 kilograms. If akilogram of chicken costs 72.50, how much did she pay for the chicken?

2. Fixing Skills

Solve the following problem.

1. A meter of ribbon cost 23.50. Jean needs 1.7 meters to make a sash. How manymeters of ribbon does she need to buy for the sashes of 20 contestants in a beautypageant? How much will she spend?

2. Gina works 35.5 hours per week as operation manager. She earns 528.50 anhour. How much does he earn in 3 weeks.

3. Malou uses 0.65 meter to make a pillow case. How many meters of cloth will sheuse to make a dozen of pillow case?

4. Joshua collects comic magazines of his favorite cartoon characters. He is going tobuy 2 new comic magazine that cost 450.00 each. He saves 35.50 a day fromMondays to Fridays. How many weeks does she need to save to buy themagazines?

3. Generalization

What must we follow in solving problems involving multiplication of decimals?

In solving word problem involving multiplication of decimals.

1. Analyze the word problem:a. Find out what is askedb. Note the given factsc. Decide the operation to be used

2. Write the operation.3. Solve and label the answer.

C. Application

Solve the following:

1. Arnel plays volleyball with his friends for 1.5 hours every practice day. How many hoursdoes he play in 5 days?

2. Father needs 25.6 metres of barbed wire to fence each of his chicken coops. If he has 10coops, how many metres of barbed wire does he need?


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IV. Evaluation

A. Write the mathematical sentence then solve.

1. Ms. Sison bought 5 bags of refined sugar each weighing 2.5 kilograms. What is the totalweight of 5 bags of sugar?

2. Lyn bought ribbons at 30.50 each. How much did she pay for 7 ribbons?3. Mr. and Mrs. Alan de Jesus have 4 children. One Sunday afternoon, they had snacks at

Jollibee. Each child ordered value meal worth 39.50. How much did Mr. and Mrs. DeJesus spend for the children?

4. Anne went to the market. She bought the following:

1.2 kg of onions at 35.45 a kg1.3 kg of tomatoes at 25.25 a kg1.5 kg of potatoes at 28.30 a kg

a. find the cost of onionsb. find the cost of tomatoesc. find the cost of the potatoes

B. Read and solve.1. Stephanie pays 2000 a month for her piano lessons. How much does she pay for one

year?Answer __________

2. Rommy bought 6 bags of apples. If each bag weighs 1.5 kg, how many kilograms ofapples did he buy?

Answer __________3. At 18.35 a litre, what is the cost of 7.5 litres of gasoline?

Answer __________

V. Assignment

Solve the following problems.

1. Elvie has 2.85 metres of ribbon. She used 0.75 of it to make her project in EPP. What part ofthe ribbon did she use?

2. Princess uses 0.85 metre of cloth to make a pillowcase. If she finished 75 pillowcases, howmany metres of cloth did she use?

LG MATH Grade 5 - Ratl.nos.Mult.dec. v2.0

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Transcript of LG MATH Grade 5 - Ratl.nos.Mult.dec. v2.0