____________ 1. The number we if multiply.

____________ 2. The numbers multiplied together.

____________ 3. The number that multiplies.

____________ 4. It is a short way of adding the same number of number times.

____________ 5. Multiplication is the inverse of _____________

III. Complete the following that corresponds to themissing answer.

1. 0.42 - ______ 6. 0.183 - ______ x 0.34 - ______ x 0.141 - ______ _____ - product _____ - product

2. 0.12 - ______ 7. 12.55 - ______ x ____ - multiplier x 21.45 - ______0.0132 - ______ _____ - product

3. ____ - multiplicand 8. ____ - multiplicand x 4.62 - _______ x 0.96 - _______ 0.1848 - _______ 0.1848 - _______

4. 56.08 - ______ 9. 1.45 - ______ x 31.901 - ______ x 6.56 - _____________ - product ______ - product

5. 8.08 - multiplicand 10. 8.145 - multiplicandx 8.14 - multiplier x 6.001 - multiplier _____ -________ _____ -________

Lesson 22MULTIPLYING DECIMALS

Lesson Objectives: After finishing the lesson, the students are expected to:1. Learn how to multiply decimal numbers.2. Follow the steps in multiplying decimal numbers.3. Know how to place the decimal point in the product.

Study these examples. Where do you place the decimal point in the product?

0.432 0.614 × 0.15 × 0.37

2160 4298 + 432 + 1842_ 0.06480 0.22718

Remember:In multiplying decimals, the

placement of the decimal point in the product is determined by the total number of decimal places in the factors. Count the number of decimal places from the right. To check, divide the product by either factors.

6480 four digits 22718 five digitsAdd a zero to make Additional zeros isfive decimal places in theproduct. not needed.0.06480 0.2271

AdditionalZero

Add the decimal places in the factors. Then see how many decimal places the product has.

0.432 × 0.15

Five decimal places

0.614 × 0.37

Five decimal places

PRACTICE:

Find the product by fill in the boxes for the correct answer.

0.3 0.2 0.4

0.1 0.5 0.6

0.4 0.7 0.3

0.5 0.4 0.3

0.7 0.6 0.8

0.4 0.2 0.10.5 0.4 0.3

0.7 0.6 0.8

0.4 0.2 0.1

1.9 1.5 1.8

2.5 3.5 2.0

3.5 3.8 3.1

0.1 0.44 0.87

0.54 0.53 0.09

0.9 0.76 0.36

1.90 1.2 2.9

1.8 2.2 2.99

1.66 0.8 1.52.2 1.4 1.9

1.4 1.7 1.9

1.7 2.0 2.7 1.6 1.8 1.7

1.89 1.89 1.7

2.7 2.6 2.9

I. Put the decimal point on the product for the correct places.

1. 0.192 x 0.428 1536

384 + 768__

82176

2. 0.342 x 0.153

1026 1710 + 342

52326

3. 0.208 x 0.274

832 1456 + 416 56992

4. 0.263 x 0.29

2367 + 526 7627

5. 0.1594 x 0.37

11158 + 47852 58978

III. Multiply the following decimal numbers and putthe decimal point.

1. 0.987 x 0. 270

2. 0.158x 0.258

3. 0.4789 x 0.1247

4. 0.2547 x 0.2479

5. 0.3647 x 0.1248

What did the big flower say about the little flower?

To find the answer, write each of the following productsin multiplying decimals.

__________ ___________ ___________ __________

0. 7537344 0.0132 0.0003 0.08537832

___________ ___________

0.001445 0.290523

_________ __________ _________ ________ ________

0.0000195 0.0044902 0.000492 0.05626725 0.0006

Lesson 23MULTIPLYING MIXED DECIMALS BY

WHOLE NUMBERS

Lesson Objectives: After finishing the lesson, the students are expected to:1. Multiply mixed decimals by whole numbers.

2. Find the partial products. 3.Understand the rules in multiplying mixed decimals by whole numbers.

Christopher can save Php. 18.65 in one month. How much money can he save in four months?

18.6 → two decimal placesx 474.60

Decimals are multiplied the same way as whole number.

Remember:In multiplying mixed decimals by

whole numbers, count the decimal places in the mixed decimal to determine the placement of the decimal point in the product. Start counting the number of decimal places from the right.

Study other examples.

23.729 → three decimal placesx 47

166103 + 94916 1115.263

↑

Partialproduct

6.3572 → four decimal placesx 158

508576 317860 + 63572 1004.4376

↑

Partialproduct

I. In the following problems, the final product is given. Find the partial products. Place the decimal points in the correct position.

1. 81.83 2. 62.872 3. 7.0194 × 57 × 34 × 271

+ + 466431 2137648 +

19022574

4. 17.59 5. 48.723 6. 8.0035 × 83 × 52 × 179

+ + 145997 2533596 +

14326265

II. Find the product.

7. 934.04 8. 282.5601 9. 37.5852 × 251 x 49 × 784

10. 51.207 11. 4672.397 12. 693.3521 × 490 × 268 × 922

13. 75.373 14. 149.1811 15. 10.1496 x 44 x 1012 x 189

Lesson 24MULTIPLICATION OF MIXED DECIMALS BY

MIXED DECIMALS

Lesson Objectives: After accomplishing this lesson, you are expected to:1. Multiplying mixed decimals by mixed decimals.

2. Perform the operation correctly. 3. Understand the rules in multiplying mixed

decimals by mixed decimals.

What is the area of Ariel’s backyard if it is 12.932 m long and 8.45 m wide? NOTE:

Area = length x width = 12.93m x 8.45m = 109.27540 sq.m² = m x m = m²

12.932 → three decimal places × 8.45 → two decimal places

64660 51728+ 103456 109.27540 → five decimal places

The backyard is 109.27540 square meters.

NOTE:Area = length x width = 12.93m x 8.45m = 109.27540 sq.m² = m x m = m²

When multiplying mixed decimals

by mixed decimals, the

decimal point of the product is determined in this manner.

Decimal Decimal DecimalPlaces of first Places of second Places of Factor Factor the product

I. Rewrite and arrange the partial products properly. Find the product and place the decimal points in the correct position.

1. 4.9526 2. 9.18234 × 3.215 × 75.68 247630 7345872

49526 5509404 99052 451170

+ 148578 + 6427638

3. 57.6012 4. 2.01938 × 4.765 × 36.24

2880060 8077523456072 4038764032084 1211628

+ 2304048 + 605814

Find the product.

5. 15.6027 6. 92.46355 7. 8.932682 × 8.306 × 1.728 × 9.1865

8. 743.9516 9. 268.924 10. 5.1367× 4.321 × 4.321 × 9.824

Lesson 25MULTIPLYING DECIMALS BY 10, 100 and 1000

Lesson Objectives: At the end of the lesson, you are expected to:1. Multiply decimals by 10, 100 and 1000.

2. Write the product correctly. 3. Observe the rules in multiplying decimals

by 10, 100 and 1000.

Take a decimal, 0.7568. Multiply it by 10, by 100 and by 1,000. What are the products?

Look at the following:

0.7568 0.7568 0.7568 × 10 × 100 × 1000

7.5680 75.6800 756.8000

You see that the number of zeros contained in the factors 10, 100 and 1,000 tells how many places the decimal point in the other factor must be moved to the right to get the product.

Examples:

10 × 0.75 = _______100 × 0.75 = _______1,000 × 0.75 = _______

Observe:

750.75.7.5

0. 7500. 750.75

0.7500.750.750.75

× 1,000× 100× 10Decimal

Move 1 place to the right.

Move 2 place to

the right.

Move 3 place to the

right.

Complete the following equations.

1.3.67 × 10 = ______2.100 × _____ = 45213.1000 × _____ = 0.00494._____ × 100 = 854.85.2.918 × _____ = 29186.35.66 × _____ = 356607.0.0074 × _____ = 7.48._____ × 10 = 0.1639.0.089 × 10 = _____10. _____ × 100 = 100.78

II. Complete the table by multiplying each factor by 10, 100 and 1,000.

III. Multiply the following. Write your answers in the blanks provided:

1. 0.386 × 10 = ________2. 0.86 × 100 = ________3. 0.36 × 1000 = ________4. 0.473 × 1000 = ________5. 0.496 × 10 = ________6. 0.85 × 1000 = ________7. 0.7 × 1000 = ________8. 0.512 × 100 = ________9. 0.93 × 100 = ________10. 0.603 × 10 = ________

Lesson 26ESTIMATING PRODUCTS OF DECIMAL

NUMBERS

Lesson Objectives: After understanding the lesson, you must able to:1. Learn how to estimate the products correctly.

2. Learn how to make an estimates product infastest way.

3. Follow the steps in estimating products.

The fastest way of solving problem is to estimate. In estimating the products:

Round the given decimal numbers to the highest place value.

Estimate and multiply. Compute the exact answer.

Products can be estimated in the same way as sum and difference.

1. Rounding Method

4.52 × 6 27.12

Actual Value Rounded Value

5.00× 6 30.00

2. Front End Method

4.56 4.00 4.52 .50 450 × 6 × 6 × 6 × 6 × 6 24.00 + 3.00 = 27.00

The front – end method with adjustment is usually closer to the actual value.

I.Estimate the product using rounding and front-end with adjustment.

1. 3.754 2. 48.263 3. 28.169 × 8 × 5 × 7

4. 38.721 5. 28.765 6. 75.814 × 3 × 9 × 13

7. 96.250 8. 18.263 9. 927.231 × 42 × 41 × 507

10. 36.287 11. 76.298 12. 28.183 × 206 × 304 × 543

Lesson 27PROBLEM SOLVING INVOLVING

MULTIPLICATION OF DECIMAL NUMBERS

Lesson Objectives: After understanding the lesson, you must

able to:1.Solve word problem involving multiplication of

decimals.2.Write the numbers sentence.3.Solve word problems correctly and accurately.

Example 1:

A cone of ice cream costs Php. 16.25, how much in all did the 6 children spend for ice cream?

Example 2:

What is the area of a rectangle with a length of 9.72 cm and width of 6.34 cm?

Read, analyze and translate these problems to number sentence then solve.

1. Mrs. Hernandez baked 1,000 pineapple pies for a party of her daughter Kiana. If each pie costs Php. 17.85, how much did the 1,000 pies cost?

2. If a car travels 55.6 km an hour, how far will it travel in 8 hours?

3. Mang Freddie sold 46 cotton candies at Php. 2.15 each. How much altogether is the cost of the cotton candies?

4. A rope measures 4.63 m. How long is it in centimeters?

5. If 1 meter of cloth costs Php. 72.95, how would 6.5 meters cost?

6. Mang John, a balot vendor bought 120 new duck eggs at Php. 3.85 each. How much did he pay all the eggs?

7. A can of powdered milk has a mass of 0.345 kilogram. What is the mass of 12 cans of milk?

8. Mr. Gelo Drona bought a residential lot with an area of 180.75 m at Php. 650.00 per square meter. How much did he pay for the lot?

9. Niña works 40 hours a week. If his hourly rate is Php. 640.25, how much is she paid a week?

10. The rental for a Tamaraw FX is Php. 3,500 a day. What will it cost you to rent it in 3.5 days?

OVERVIEW OF THE MODULAR WORKBOOK

This modular workbook provides you’re the language of division of decimal numbers and how to divide decimals in different ways.

OBJECTIVES OF THE MODULAR WORKBOOKAfter finishing this unit, you are expected to:

1. Understand the language of division of decimals.

2. Know how to divide decimal numbers.3. Follow the steps in division of decimal numbers.4. Participate actively in division of decimal numbers.5. Learn the different form of dividing decimal numbers.

Lesson 28MEANING OF DIVISION OF DECIMAL

NUMBERS

Lesson Objectives:After accomplishing this lesson, you are

expected to:1. Define division.2. Understand the language in division of decimals.3. Know the parts in dividing decimal numbers.

Division is the process of finding out how many times one number is contained in another number.

Division is the process of finding out how many times one number is contained in another number.

0.09 → quotient9 0.81 → dividend - 0 81 - 81 0

Divisor

The number that contains another number a number of times is called the dividend. The number that is contained in another number a number of times is called the divisor. The number that indicated how many times a number contained in another number is called the quotient.

Division may also be defined as the process of separating a number into as many equal parts as indicated by another number. The symbol for division ( ÷ ), which is read as “divided by”. Thus, 0.81 ÷ 9 = 0.09 is read as “eight-one hundredths divided by nine equals nine thousandths.”

Another symbol is a line written over and above the dividend and a slanting line connecting it at the left of the dividend and at the right of the divisor.

Another symbol is a line over which the dividend is written and the divisor below.

0.81 9

I. Give the meaning and explain the use of the following: 5points each.

What is division?What is

division?What is divisor?What is divisor?

What is dividend?What is

dividend? What is quotient

?

What is quotient

?

1. Division ____________________________________________________________________________________

2. Divisor____________________________________________________________________________________

3. Dividend ____________________________________________________________________________________

4. Quotient ____________________________________________________________________________________

II. Enumeration…

A. What are the parts of division?B. What symbols that can be used in dividing numbers?

A._____________________________________________________________________________________________________________________________

B._____________________________________________________________________________________________________________________________

Lesson 29DIVIDING DECIMAL BY WHOLE NUMBERS

Lesson Objectives:After accomplishing this lesson, you are

expected to:1. Divide decimals by whole numbers.2. Follow the rules in dividing decimals by whole numbers.3. Find the quotient correctly.4. Using two methods in dividing decimals.

Dividing decimals by a whole number is the same as dividing a whole number by another whole number.

Observe the following examples.

0.15 0.054 0.60 9 0.45 - 4 - 0 20 45 - 20 - 45 0 0

To check the answer, multiply the quotient by the divisor:

0.15 x 4

0.60

0.05 x 9

0.45

In dividing decimals by whole numbers, the number of decimal places in the quotient equals the number of decimal in the dividend.

Look at the other examples: Example 1: 0.6 ÷ 3 = _____

We used 2 methods in dividing decimals by whole numbers.

1. Using a region

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

0.2 0.2 0.2 0.2 0.2

0.6

A whole is divided into 10 equal parts. Each part is called 1/10 or 0.1. 6/10 or 0.6 are shaded.0.6 is divided into 3 groups.

How many tenths are in each group?

2. Using computations

6 ÷ 3 = 6 ÷ 3 = 210 1 10 ÷ 1 = 10

0.2 3 0.6 6 0

Let us check by using reciprocals.

Fractional Division:

6 ÷ 2 = 6 x 3 = 6 x 3 = 18 10 3 10 2 10 x 2 20

6 ÷ 3 = 6 × 1 = 6 = 1 = 0.2 and 110 10 3 30 5 5

is equivalent

to 0.2

Why? Explain. 6 ÷ 6 = 1 30 6 5

0.2 5 1.0 1.0 0

Let us divide hundredths by a whole number.

Example 2: 6 0.18

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 910

1. Using a region A whole is divided into 100 equal pairs. Each part is called 1/100. Eighteen parts are called 18/100 or 0.18. We divide 0.18 in 6 groups.

How many hundredths are in each group?

Using computation 18 ÷ 6 = 18 ÷ 6 = 3100 1 100 ÷ 1 100

to get the tenths place. 0.03 → Quotient

6 0.18 - 18

0

Check: 6× 0.03 0.18

I. Find the quotient by using region and computations.

1.3 0.12 2. 5 0.35 3. 7 0.14

4. 3 0.42 5. 8 0.64 6. 4 0.56

7. 2 0.6 8. 9 0.81 9. 4 0.424

I.Find the quotients. Answer the question that follows.

1. 6 0.732 2. 4 0.524 3. 2 0.236

4. 5 0.655 5. 4 0.435 6. 7 0.851

How many decimal places are in the dividends of 1 to 6?________________________________________________________________________________How many decimal places should there be in the quotient?________________________________________________________________________________How many we use zero in the quotient?________________________________________________________________________________

Lesson 30DIVIDING MIXED DECIMAL BY WHOLE

NUMBERS

Lesson Objectives:After accomplishing this lesson, you are expected to:1.Divide mixed decimals by whole numbers.2.Understand the rule in dividing mixed

decimals by whole numbers.3.Answer the operation correctly.

Divide mixed decimals in the same way as in dividing whole numbers. To check, multiply the quotient by the divisor.Long method of division:

1.5734 5 7.8670 - 5

28 - 25 36 - 35

17 - 15 20 - 20 0

To check, multiply the quotient by the divisor.

1.5734x 57.8670

Remember that zeros added to a number to the right of the decimal point does not affect the value of the number.

7.8670 = 7.867

When dividing mixed decimals by whole numbers. The number of decimal places in the quotient is equal to the number of decimal places in the dividend. Align the decimal points of the quotient with that of the dividend.

Do another division.

To check, multiply…

Answer (quotient by

division)

Answer (quotient by

division)

5.1268x 14 205072 51268 71.7752

5.1268 14 71.1152

- 70 17 - 14

37 - 28

95 - 85

112 - 112 0

I. Find the quotient. Check bymultiplication.

CHECKING:

1.48.102 ÷ 21 =

2.56.381 ÷ 87 =

3. 140.722 ÷ 9 =

4. 28.6134 ÷ 5 =

5. 189.526 ÷ 32=

II. Solve for the quotient and check by longmultiplication method.

CHECKING:

1. 83.7169 ÷ 21 =

2. 92.0314 ÷ 37 =

3. 152.51 ÷ 28 =

4. 293.763 ÷ 48 =

5. 451.306 ÷ 89 =

Lesson 31DIVIDING WHOLE NUMBERS BY DECIMALS

Lesson Objectives:After accomplishing the lesson, the students are expected to:1. Divide whole numbers by decimals.2. State the rule for dividing a whole number by a decimal.3. Find the quotient correctly.

Let us divide whole numbers by decimals in

tenths.

Example 1: 0.8 72

Here are the steps in dividing whole numbers by

decimals...

STEP 1 Before we divide, we must change the divisor to a whole number. We multiply 0.8 by 10. We have 8.

STEP 2 We multiply the dividends by 10 also. 10 x 72 = 720, we

have 720 as dividend.

STEP 3 Then we begin to divide.

90 → quotient8 720 - 72 0

We check: 90 × 0.8

72.0

STEP 4

How we divide a whole number by a decimal in the

hundredths?

Follow this step to find the quotient.

Example 2: 0.14 588

STEP 1 Make the divisor a whole number.Multiply it by 100.

0.14 x 100 = 14 0.14 588

STEP 2 Multiply the dividend by 100.

14 588.00

STEP 3 Then divide as if dividing whole numbers. 4200

14 58800 -56 28 - 28 0

STEP 4 We check: 4200x 0.14 16800 4200 58000

I. Find the quotient and check.

1. 0.3 ÷ 936 =

2. 0.8 ÷ 856 =

CHECKING:

3. 0.9 ÷ 756 =

4. 0.5 ÷ 485 =

5. 0.4 ÷ 348 =

6. 0.6 ÷ 911 =

7. 0.2 ÷ 613 =

8. 0.7 ÷ 518 =

9. 0.2 ÷ 434 =

10. 0.5 ÷ 775 =

11. 0.7 ÷ 434 =

12. 0.7 ÷ 714 =

13. 0.8 ÷ 872 =

14. 0.6 ÷ 846 =

15. 0.5 ÷ 305 =

Lesson 32DIVIDING WHOLE NUMBERS BY MIXED

DECIMALS

Lesson Objectives:At the end of the lesson, the students are expected to: 1. Divide whole numbers by mixed decimals 2. Follow the rule in dividing whole numbers by mixed decimals. 3. Study division where the quotient is found to the ten thousandths place.

Let us observe the rule in dividing whole numbers by mixed decimals.

Example 1:Move the decimal point in the divisor to make it a whole number. The number of places the decimal has been moved to the right in the divisor is the same as the number of places the decimal point is to be moved in the dividend. Add the appropriate zeros to the dividend. Align the decimal point of the dividend.

In dividing decimals always try to divide to the last digit. When there are too many digits to divide, you can stop at the division by multiplying the quotient by the divisor. Divide 84 by 1.25.

67.21.25 84.00.0 - 750 900 - 875 250 - 250 0

67.2 x 1.25 33.60 13.44+ 67.2 84.000

Check the divisor by multiplying the quotient by the divisor.

Study another division where the quotient is found to the ten thousandths place.

Example 2: 16.0516

5.42 87.00.0000

- 542 3280 - 3252 280 - 000 2800 - 2710 900 - 542 3580 - 3252 328

To check:

16.0516 × 5.42 0.321032 6.42064 80.2580 86.999672 + 0.000328 87.000000

I. Find the quotient to the ten thousandths place then check.

CHECKING:

1.15 ÷ 4.7 =

2. 9 ÷ 5.28 =

3. 86 ÷ 7.245 =

4. 16. ÷ 7.32 =

5. 23 ÷ 8.16 =

6. 43 ÷ 15.8 =

7. 8 ÷ 1.43 =

8. 15 ÷ 3.786 =

9. 74 ÷ 16.37 =

10. 22 ÷ 5.61 =

Lesson 33DIVIDING DECIMAL BY DECIMALS

Lesson Objectives:At the end of the lesson, the students are expected to:1. Divide decimals by decimals.2. Follow the step in dividing decimals by decimals3. Use fraction in checking the division of decimals.

How is division done with decimals? What do we do with the decimal points? Let’s observe the following example.

STEP 1 STEP 2 STEP 30.5 0.75 5 0.7.5 1.5

5 7.5 - 5 25 - 25 0

Multiply 0.5 by 10 to make it a whole number.

Multiply 0.75 by 10 also. What we do with the divisor, we do to the dividend.

Divide just like whole numbers. The quotient has the same number of decimal places as the dividend.

Example: 0.5 0.75

Let us check by using fractions.

75 ÷ 5 = 75 ÷ 5 = 15 or 1 5 or 1.5100 10 100 ÷ 10 10 10

I. Divide the following and check it by using fractions.

1.0.72 ÷ 0.3 =

2. 0.96 ÷ 0.4 =

3. 0.387 ÷ 0.09 =

CHECKING:

4. 0.516 ÷ 0.6 =

5. 0.81 ÷ 0.9 =

6. 0.96 ÷ 0.8 =

7. 0.441 ÷ 0.7 =

8. 0.558 ÷ 0.06 =

9. 0.36 ÷ 0.3 =

10. 0.72 ÷ 0.8 =

II. Try to analyze. Check your answer.

1. 0.56 ÷ 0.008 =

2. 0.90 ÷ 0.090 =

CHECKING:

3. 0.72 ÷ 0.4 =

4. 0.26 ÷ 0.2 =

5. 0.9015 ÷ 0.5 =

Lesson 34Dividing Mixed Decimals by Mixed Decimals

Lesson Objectives:At the end of the lesson, the students are

expected to:1.Divide mixed decimals by mixed decimals.

2. Observe the rule in dividing mixed decimals by mixed decimals.3. Perform the operation correctly.

A full-grown Philippine eagle can grow to length of 102.6 cm including its tail. The tail can reach 49. 8 cm. When one of its wings is spread out, it can reach 63.2 cm. The length of its tail is what part of its whole length?Divide 102.6 cm (total length) by 49.8 cm (tail) to the hundredthsplace.

Move the decimal point one place to the right. The number of decimal places point has been moved in the divisor determines the number of decimal places it is moved in the dividend.

2. 0649.8. 102. 6. 00

- 996 300 - 000 3000 - 2988 12

To check, multiply it.

49.8 x 2.06 2.9 88 0.00 99.6__102.5 88+ 0.0 12102.6 00

In the case like this, when the remainder is added, the sum is equal to the dividend.

Mixed Decimals are divided in the same way as whole numbers. In dividing mixed decimals by mixed decimals, remember that the decimal point in the divisor is moved to the right to make it a whole number.

I. Find the quotient to the tenths place. Check it through multiplication.

1.8.376 ÷ 1.942 =

2. 7.801 ÷ 2.334 =

3. 9.482 ÷ 4.7636 =

CHECKING:

4. 10.857 ÷ 6.135 =

5. 23.154 ÷ 5.719 =

6. 41.028 ÷ 12.149 =

7. 183.945 ÷ 20.132 =

8. 151.932 ÷ 46.741 =

9. 273.921 ÷ 87.553 =

10. 491.72 ÷ 78.521 =

PAMN FAYE HAZEL M. VALIN

Brgy Bagong Pook Sta. Maria, LagunaJanuary 8, 1991E-mail Address :

herzelle_0108@yahoo.com

EDUCATIONAL ATTAINMENTElementary

Santa Maria Elementary SchoolSecondary

Santa Maria National High SchoolTertiary

Laguna State Polytechnic University (Formerly LSPC) Siniloan Host Campus

CourseBachelor of Elementary Education

MajorGeneral Education

RON ANGELO A. DRONA

Patricio Street, Brgy. San Jose Pangil, LagunaJune 04, 1991

E-mail Address : ronangelo_drona@yahoo.com

EDUCATIONAL ATTAINMENTElementary

Pangil Elementary SchoolSecondary

Laguna State Polytechnic University (Formerly LSPC) Siniloan Host Campus

TertiaryLaguna State Polytechnic University (Formerly LSPC) Siniloan Host Campus

CourseBachelor of Elementary Education

MajorGeneral Education

BEATRIZ P. RAYMUNDO

Brgy Bagong Pook Sta. Maria, LagunaApril 21, 1951

E-mail Address : raymundobeatriz@yahoo.com

EDUCATIONAL ATTAINMENT

ElementarySanta Maria Elementary School

SecondarySanta Maria Academy

TertiaryImmaculate Conception College

CourseBachelor of Secondary Education

MajorMathematics

MinorEnglish

Master’s DegreeMA Teaching (National Teacher’s College,

Manila)Teacher in Values Education and Filipino

FOR-IAN V. SANDOVAL

Siniloan, LagunaApril 5, 1979

E-mail Address : fvsandoval@yahoo.com

EDUCATIONAL ATTAINMENT

ElementaryPalasan Elementary School

SecondaryUnion College of Laguna

TertiaryFar Eastern University

CourseBachelor of Science in MathematicsBachelor of Secondary Education

(Unit Earner)

MajorComputer Science

Master’s DegreeMaster of Arts in Education Major in

Educational Management (with units)

Benigno, Gloria D. Basic Mathematics for College Students. Manila: REX Bookstore. 1993.

Calderon, Jose F. Basic Mathematics I. Quezon City: Great Books Trading. 1994.

Del Fiero, Jong. Power in Numbers 6. Manila: Saint Mary’s Publishing Corporation. 1999.

Department of Education Culture and Sports. Mathematics in Everyday Life (textbook for Grade V) Revised edition. Manila: Cacho Hermanos Inc., 1993.

Department of Education. Lesson Guides in Elementary (Mathematics for Grade VI). Bureau of Elementary Education in coordination with Ateneo de Manila University., 2003

Ibe, Milagros D. et. al. Highschool Mathematics-Concept and Operation, 3rd edition, First Year. Manila: DIWA Learning Systems Inc., 1999.

Jovero, Natividad V. Power in Numbers IV (Teachers Manual, Mathematics 4). Manila: Saint Mary’s Publishing Corporation. 1999.

Llanes, Estrelita M. and Li, Bernardino Q. Living with Math VI. Revised Edition. Quezon City: FNB Educational Inc. 1988.

Lopez, Kelli L., The Self-replicating Gene. Tatsulok. Vol. 14 No. 2 1st year. Pp 4-6,15.

Mendoza, Marilyn O. Workbook in Mathematics. Manila: Gintong Aral Publication. 1997.

Roxas, Mia P. and Zara, Evelyn F. Elementary Algebra. High School Mathematics. (Worktext I). EFEREZA Pulbication House. 2003.

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http://photobucket.com/images