This is the Grade 4 Mathematics Self-Learning Module for Quarter 3, Module 11: Conversion of Square Units. DepEd Region V published it as a First Edition (2020) Alternative Delivery Mode module. It is for Grade 4 learners who already know the difference between perimeter and area. By the end, they should be able to change area measures from square centimeters to square meters and back.
On this page 6 sections
What learners will learn
After going through this module, learners are expected to:
- Convert square centimeters (cm²) to square meters (m²)
- Convert square meters (m²) to square centimeters (cm²)
The module also explains that square units such as cm², dm², m², in², and ft² are units of area. Bigger units are used for big areas and smaller units for small areas.
Key idea: 1 square meter = 10 000 square centimeters
The module starts from the length equivalence 1 m = 100 cm. A square meter is 1 m by 1 m, so:
- 1 sq. m = 100 cm × 100 cm = 10 000 sq. cm
The two amounts are equal, so dividing one by the other gives 1. This creates two conversion factors. Multiplying by 1 changes the form of a number but not its value.
| To convert | Multiply by | Shortcut |
|---|---|---|
| sq. cm to sq. m | 1 sq. m / 10 000 sq. cm | Move the decimal point 4 places to the left |
| sq. m to sq. cm | 10 000 sq. cm / 1 sq. m | Move the decimal point 4 places to the right |
Worked examples from the module
- Gabriel and Joseph’s classroom. The floor is 9 m long and 8 m wide, so its area is 72 sq. m. Multiplying by 10 000 sq. cm / 1 sq. m gives 720 000 sq. cm.
- Hannah and Jannah’s bathroom. The floor is 200 cm by 150 cm, so its area is 30 000 sq. cm. Multiplying by 1 sq. m / 10 000 sq. cm gives 3 sq. m.
More examples from the module:
- 60 000 sq. cm = 6 sq. m
- 47 000 sq. cm = 4.7 sq. m
- 4.2 m² = 42 000 cm²
- 56.1 sq. m = 561 000 sq. cm
Why cancellation and the decimal shortcut work
The module explains cancellation in two parts.
- Why units cancel. Dividing 2 sq. m by 1 sq. m asks “how many 1 sq. m are in 2 sq. m?” The answer is just 2, with no unit.
- Why the zeros work as a shortcut. Multiplying by 10, 100, 1 000, or 10 000 moves the decimal point 1, 2, 3, or 4 places to the right. For example, 1.234 × 10 000 = 12 340. Dividing moves it to the left. For example, 432.1 ÷ 10 000 = 0.04321. Count the zeros to know how many places to move.
The module also notes that area units can be written in different ways. For example, square centimeter, centimeter square, sq. cm, and cm² all mean the same unit.
Parts of the module
- What I Know: a 10-item pretest of equal or not equal items, conversions, and a word problem
- What’s In: a review of dividing and multiplying by 10 000 and converting cm to m, plus the meanings of milli, centi, and kilo
- What’s New: the classroom-floor problem
- What Is It: the lesson on conversion factors, cancellation, and decimal shortcuts
- What’s More: Activity 1 (six conversions) and Activity 2 (a table to complete)
- What I Have Learned: a step-by-step summary of both conversions
- What I Can Do: three real-life problems, such as painting a wall and tiling a floor
- Assessment: five conversion items
- Additional Activities: five word problems, such as a plywood door, chalkboards, wallpaper, and manila paper
- Answer Key
How to use this module
- Learners: Answer the pretest first. If you score 8 to 10, the lesson should be easy for you. If you score 7 or below, study the discussion and examples carefully. Write your answers on a separate sheet of paper, not on the module. Check each activity with the answer key honestly.
- Parents and facilitators: Help your child read the directions before each task. Encourage them to show the conversion factor or the decimal-point shift in their solutions.
- Teachers: Use the What I Can Do and Assessment items to check mastery. Use the Additional Activities for enrichment.
A note on the answer key: the key gives “Irregular – Octagon” and “Irregular sq. cm – Heptagon” for Additional Activities items 2 and 3. These do not match the questions, so check those answers by working them out. For example, 56 sq. m = 560 000 sq. cm, so 570 000 sq. cm of wallpaper would be enough.
Frequently asked questions
What grade and quarter is this module for?
It is Grade 4 Mathematics, Quarter 3, Module 11: Conversion of Square Units.
How many square centimeters are in one square meter?
One square meter equals 10 000 square centimeters, because 1 m = 100 cm and 100 cm × 100 cm = 10 000 sq. cm.
What is the quick way to convert square meters to square centimeters?
Move the decimal point four places to the right, adding zeros as needed. For example, 42 sq. m becomes 420 000 sq. cm.
How do I convert square centimeters to square meters?
Move the decimal point four places to the left, which is the same as dividing by 10 000. For example, 30 000 sq. cm becomes 3 sq. m.
Does the module have an answer key?
Yes, it has an answer key for the pretest, activities, and assessment. The answers given for Additional Activities items 2 and 3 do not match those questions, though.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 3 – Module 11: Conversion of Square Units
[illustration: learners studying outdoors and at home, with a teacher and a globe]
CO_Q3_Mathematics _ Module 11
Mathematics – Grade 4 Alternative Delivery Mode Quarter 3 – Module 11: Conversion of Square Units First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them.
Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Development Team of the Module
Writers: Ireneo D. Dechavez Editors: Elena D. Hubilla Reviewers: Loyd H. Botor Illustrator: Ireneo D. Dechavez Layout Artist: Maelyne L. Yambao Management Team: Gilbert T. Sadsad Francisco B. Bulalacao Jr. Grace U. Rabelas Ma Leilani R. Lorico Monserat D. Guemo Florena M. Deuna
Printed in the Philippines by _____________________
Department of Education – Region V
Office Address: Regional Center Site, Rawis, Legaspi City 4500 Telefax: 0917-178-1288 E-mail Address: region5@deped.gov.ph
5
Mathematics Quarter 3 – Module 11: Conversion of Square Units
Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.
What I Need to Know
Good day!
In the previous module, you learned about the difference between perimeter and area. Now, you will learn about square units. Square units like cm2, dm2, m2, in2 and ft2, which are read as square centimeters or centimeter square, square decimeters or decimeter square, and so on, are units of areas. Some of these units may be smaller or bigger than the others. You use bigger units to measure big areas and smaller units for small areas.
This module will also help you understand how area measures may be converted from one unit to another, in particular, measures in square centimeters to square meters, and vice versa. We know that you will not only find the lesson in this module useful but fun as well.
Good luck!
After going through this module, you are expected to be able to convert square centimeters (cm2) to square meters (m2) and vice versa.
What I Know
EQUAL or NOT EQUAL
A. Write = if the conversion is correct and ≠ if it is not.
- 20 000 sq. cm _____ 2 sq. m
- 500 000 sq. cm _____ 500 sq. m
- 41 sq. m _____ 410 000 sq. cm
- 7 sq. m _____ 7 000 sq. cm
- 34 000 sq. cm _____ 3.4 sq. m
B. Convert the following to square meters (m2).
- 28 000 sq. cm = ______ sq. m
- 420 000 sq. cm = ______ sq. m
C. Convert the following to square centimeters (cm2).
- 17 sq. m = __________ sq. cm
- 9 sq. m = __________ sq. cm
D. Solve the problem.
- The standard outer area of a house in a village is 54 m2. What is this in square centimeters (cm2)?
To check, go to page 17 for the Answer Key. If you got a score of 8 – 10, VERY GOOD! The lesson will be easy for you. If you got a score of 7 or below, study carefully the discussion and examples in this module.
What’s In
Look at the example below and do as directed in the exercises that follow.
Example: 40 000 / 10 000 = 4
A. Simplify the following.
- 70 000 / 10 000
- 230 000 / 10 000
- 100 000 / 10 000
- 4 550 000 / 10 000
B. Find the product.
- 12 x 10 000
- 51 x 10 000
- 721 x 10 000
C. Convert the following using the equivalence:
100 cm = 1 m
- 800 cm = __________ m
- 7 m = __________ cm
- 45 m = __________ cm
While there are other units in the metric system of measurement, millimeters (mm), centimeters (cm), meters (m), and kilometers (km) are the more common ones used for measuring lengths or distances. The meaning of the prefixes is shown below:
milli – 1/1 000 centi – 1/100 kilo – 1 000
You therefore have,
1 mm = 1 m / 1 000; 1 cm = 1 m / 100; and 1 km = 1 000 m
Please check your answers with the ANSWER KEY on page 17.
What’s New
How big is your classroom? How do you maintain the cleanliness of your classroom?
Read the problem below.
Gabriel and Joseph go to school early everyday. When they reach school, instead of playing, they sweep the floor of their classroom. One day, they measured the length and width of the floor and they found it to be 9 m long and 8 m wide. Using these, they computed for its area and got 72 sq. m. They wanted to find out the equivalent of 72 sq. m in sq. centimeters. Can you help them?
[illustration: two boys sweeping a classroom floor beside a blackboard showing A = L x W and a window]
What Is It
How do you get the equivalent of 72 square meters in square centimeters?
Remember, 1 m = 100 cm. Using this, you may now get the equivalent of 1 sq. m in sq. cm as follows,
1 sq. m = 1 m × 1 m = 100 cm × 100 cm
You therefore have this equivalence:
1 sq. m = 10 000 sq. cm
Since 1 sq. m is equal to 10 000 sq. cm, if you divide one by the other, you get 1 either way. And so, you have,
- (1 sq. m) / (10 000 sq. cm) = 1
- (10 000 sq. cm) / (1 sq. m) = 1
Remember that 1 is the identity element for multiplication. Multiplying a number by 1 does not change its value even if there may be a change in its form.
You can now then get the two conversion factors below:
| sq. cm → sq. m | sq. m → sq. cm |
|---|---|
| 1. (1 sq. m) / (10 000 sq. cm) | 2. (10 000 sq. cm) / (1 sq. m) |
Going back to the question: How do you get the equivalent of 72 sq. m in sq. cm?
Using conversion factor number 2, you have,
72 sq. m = 72 sq. m × (10 000 sq. cm) / (1 sq. m) = (72 sq. m × 10 000 sq. cm) / (1 sq. m)
72 sq. m = (72 sq. m) / (1 sq. m) × 10 000 sq. cm = 72 × 10 000 sq. cm = 720 000 sq. cm
You can get the same result using what is called cancellation. Using the same problem above, we have,
72 sq. m × (10 000 sq. cm) / (1 sq. m) = 72 sq. m × (10 000 sq. cm) / (1 sq. m) = 720 000 sq. cm
Therefore, Joseph and Gabriel’s classroom floor has an area of 720 000 sq. cm.
But let us look at why cancellation works. First, on why units get “cancelled”. Examine the fraction: (2 sq. m) / (1 sq. m).
You are dividing 2 sq. m by 1 sq. m. What do you understand by this?
When you are dividing, you are really asking yourself how many of the divisors there are in the dividend. For example, when you are dividing 10 by 2, you are really asking yourself how many 2s there are in 10. Your answer is of course 5 since there are five 2s in 10.
So, when you are dividing 2 sq. m by 1 sq. m, you really want to know how many 1 square meters there are in 2 square meters. Your answer is, of course, just 2, without units. Why?
It would be different if we were to divide, for example, 4 square meters by 2. Here, the answer would be 2 square meters, with units. Why?
Second, on why we can “cancel” the 0s.
Let us use the number 1.234 and see what happens when we multiply this by 10, 100, 1 000, 10 000, and so on.
1.234 x 10 = 12.34 1.234 x 100 = 123.4 1.234 x 1 000 = 1234 1.234 x 10 000 = 12340
You can see that when you multiply a number by 10, you can also get the product by just moving the decimal point of the other factor one place to the right, adding the 0 digit, when needed.
Multiplying by 100, 1 000, 10 000, and so on, is just like multiplying by 10 twice, three times, four times over, and so on. So, you just move the decimal point 2, 3, 4 and so on places to the right, again adding 0 digits when and as may be needed.
You just count the number of zeros to know how many places to move the decimal point to the right.
So, in converting square meters to square centimeters, instead of actually multiplying by the conversion factor (10 000 sq. cm) / (1 sq. m), we may just move the decimal point four places to the right, adding 0 digits when and as needed.
Examples: 42 sq. m = 420 000 sq. cm = 420 000 sq. cm 56.1 sq. m = 561 000 sq. cm = 561 000 sq. cm
This time, let us use the number 432.1 and see what happens when you divide this by 10, 100, 1 000, 10 000, and so on.
432.1 ÷ 10 = 43.21 = 43.21 432.1 ÷ 100 = 4.321 = 4.321 432.1 ÷ 1 000 = 0.4321 = 0.4321 432.1 ÷ 10 000 = 0.04321 = 0.04321
You can see that when you divide a number by 10, you can get the quotient by just moving the decimal point of the dividend one place to the left, and again also adding a 0 digit, when and as needed. Dividing by 100, 1 000, 10 000, and so on, is just like dividing by 10 twice, three times, four times, and so on. So, you just move the decimal point 2, 3, and so on places to the left, also adding 0 digits when and as may be needed.
Again you just count the number of zeros in the divisor to know how many places to move the decimal point to the left.
Therefore, in converting square centimeters to square meters, instead of using the conversion factor (1 sq. m) / (10 000 sq. cm), you may just move the decimal point four places to the left, adding 0 digits when and as needed.
Examples: 32 000 sq m = 32 000 sq. cm = 3.2 sq. m 374.2 sq. cm = 0.03742 sq. m = 0.03742 sq. m
Now, read the problem below.
Hannah and Jannah were cleaning their bathroom which had a rectangular floor. They measured the floor and found it to be 200 cm long and 150 cm wide. Using the formula for the area of a rectangle which is L x W, they got 30 000 sq. cm. What is the area of the bathroom floor in
[transcriber’s note: the text in the box ends at “in”; the remainder of the question does not appear on this page]
Using conversion factor no. 1, we have,
30 000 sq. cm = 30 000 sq. cm × (1 sq. m) / (10 000 sq. cm) = (30 000 sq. cm × 1 sq. m) / (10 000 sq. cm) = (30 000 sq. cm) / (10 000 sq. cm) × 1 sq. m = 3 × 1 sq. m = 3 sq. m
If you use cancellation, you get the same result as you can see below,
30 000 sq. cm = 30 000 sq. cm × (1 sq. m) / (10 000 sq. cm) = 3 sq. m
So, Hannah and Jannah’s bathroom had a floor area of 3 sq. m.
NOTE: Area units may be written in different ways.
square centimeter → centimeter square → sq. cm → cm² square meter → meter square → sq. m → m²
Study the following examples:
Converting sq. cm to sq. m
a. 60 000 square centimeters = 6 square meters b. 580 000 cm² = 58 m² c. 47 000 sq. cm = 4.7 sq. m
Converting sq. m to sq. cm
a. 3 square meters = 30 000 square centimeters b. 71 sq. m = 710 000 sq. cm c. 4.2 m² = 42 000 cm²
Now that you already know how to convert sq. m to sq. cm, and vice versa, you are now ready for some activities. LET’S GO!
What’s More
Activity 1
A. Convert the following to square meters.
- 590 000 sq. cm = __________ sq. m
- 20 000 sq. cm = __________ sq. m
- 850 000 sq. cm = __________ sq. m
B. Convert the following to square centimeters.
- 48 sq. m = _______________ sq. cm
- 5 sq. m = _______________ sq. cm
- 70 sq. m = _______________ sq. cm
Please check your answers for each activity with the ANSWER KEY on page 17. If you answered all of them correctly, Great job! Keep up the good work! If you have some mistakes, review the lesson and decide which of the two solutions presented is
Activity 2
Complete the table with the correct square units.
| Area in cm² | Area in m² |
|---|---|
| 320 000 cm² | 1. |
| 2. | 8 m² |
| 820 000 cm² | 3. |
| 4. | 12 m² |
| 60 000 cm² | 5. |
| 6. | 57 m² |
| 27 000 cm² | 7. |
| 8. | 2.4 m² |
Please check your answers with the ANSWER KEY on page 17. If you got 6-8, Excellent job! If you got below 6, it’s okay. You can always review the lessons and examples given.
What I Have Learned
How do you convert square centimeters to square meters and vice versa?
Recall the equivalence,
10 000 sq. cm = 1 sq. m
A. To convert sq. cm to sq. m:
- multiply by the conversion factor:
$\frac{1\ sq.,m}{10,000\ sq\ cm}$
- and, to simplify,
a. move the decimal point 4 places to the left,
b. cancel sq. cm, and
c. express the result in sq. m.
B. To convert sq. m to sq. cm:
- multiply by the conversion factor:
$\frac{10,000\ sq.,cm}{1\ sq.,m}$
- and, to simplify,
a. move the decimal point 4 places to the right,
b. cancel sq. m, and
c. express the result in sq. cm.
What I Can Do
Solve the following problems.
Mang Emong is painting his 420 000 sq. cm wall. What is its area in sq. m?
A bathroom floor has an area of 8 sq. m. What is the floor area in square centimeters?
An 81 sq. m floor of Dina’s house is to be tiled. What is this in square centimeters?
Please check your answers with the ANSWER KEY on page 17.
Assessment
Convert the following to sq. cm or to sq. m, as required.
- 920 000 sq. cm = _____ sq. m
- 15 sq. m = _____ sq. cm
- 760 000 sq. cm = _____ sq. m
- 100 000 sq. cm = _____ sq. m
- 37 sq. m = _____ sq. cm
Please check your answers with the ANSWER KEY on page 17.
To check, turn to page 17 for the Answer Key. Congratulations for reaching this part of the module.
You can always review the previous pages of this module if you need to.
Additional Activities
Solve the following problems.
Rye has a broken 30 000 cm2 – sliding door. He will temporarily replace it with plywood. How many m2 of plywood does he need?
Miguelito volunteers to clean their two chalkboards. Both chalkboards are of the same size. The two chalkboards have a total area of 4 sq. m. What is the area of each chalkboard in sq. cm?
A 56 sq. m – wall is to be covered with wall paper. Would 570 000 sq. cm of wall paper be enough to completely cover it? Why?
If 1.5 m2 = 15 000 cm2, how many m2 are there in 23 000 cm2?
One sheet of manila paper is given to each group for a group activity in Mathematics. One sheet is 1.08 m2. What is this in cm2?
Answer Key
[transcriber’s note: this page is printed upside down; it is transcribed below in reading order, with its two columns read top to bottom, left column first]
What I Know
A.
- =
- ≠
- =
- ≠
- =
B. 6. 2.8 7. 42
C. 8. 170 000 9. 90 000
D. 10. 540 000 sq. cm
What’s In
- 7
- 23
- 10
- 455
- 120 000
- 510 000
- 210 000
- 8
- 700
- 4 500
What’s More
Activity 1:
A.
- 59
- 2
- 85
B.
- 480 000
- 50 000
- 700 000
Activity 2:
- 32 m2
- 80 000 cm2
- 82 m2
- 120 000 cm2
- 6 m2
- 570 000 cm2
- 2.7 m2
- 24 000 cm2
What I Can Do
- 42 sq. m
- 80 000
- 810 000 sq. cm
Assessment
- 92
- 150 000
- 76
- 10
- 370 000
Additional Activities
- 3
- Irregular – Octagon
- Irregular sq. cm – Heptagon
- 2.3
- 10 800 cm2
References
Tabilang, Alma R., Ian Jay B. Arce, Rodrigo V. Pascua, Nelma P. Calayag, Lolita P. Dacuba, Dioleta B. Borais, Rafael B. Buemia, Myrna T Collao, Larry G. Morandante, Amado B. Danao, Laura N. Gonzaga, Isagani A. Briones, John Antonio D. Daganta, 2015, Mathematics 4 Learner’s Material, Department of Education
Tabilang, A., Arce, I., Pascua, R., Calayag, N., Dacubo, L., Borais, D., Buemia, R., Collao, M., Morandante, L., Danao, A., Gonzaga, L., Briones, I., and Daganta, J. 2015. Mathematics 4 Learner’s Material, Department of Education.
For inquiries or feedback, please write or call:
Department of Education – Bureau of Learning Resources (DepEd-BLR)
Ground Floor, Bonifacio Bldg., DepEd Complex Meralco Avenue, Pasig City, Philippines 1600
Telefax: (632) 8634-1072; 8634-1054; 8631-4985
Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph
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