This is the Mathematics Grade 4 Quarter 1 Module 8 self-learning module, Solving Routine and Non-routine Problems Involving Multiplication of Whole Numbers. It is an Alternative Delivery Mode (ADM) module from DepEd Region V (First Edition, 2020), written by Ireneo D. Dechavez. It builds on the previous module, where learners multiplied numbers up to 3 digits by up to 2-digit numbers. Here they use that skill to solve real-life word problems, many of them about money.
What learners will learn
By the end of the module, learners will be able to:
- solve routine and non-routine problems involving multiplication of whole numbers, including money, using appropriate problem-solving strategies and tools.
The module asks learners to “put yourself in each problem” so the situation is easier to picture and solve.
Routine problems: four steps to a solution
The module explains that a routine problem is one whose solution can be identified right away. Its main example is about Ruby. She gets ₱30 a day as her allowance and saves ₱5 of it. How much does she save in a month of 21 school days?
The module solves it in four steps:
- Understand. Read the problem. Find what is asked (Ruby’s savings in a month) and the given facts (₱5 daily savings, 21 school days). The ₱30 allowance is not needed, because the question is about savings, not allowance.
- Plan. Choose the operation (multiplication) and write the number sentence: 21 x ₱5 = □.
- Solve. Multiply: 21 x 5 = ₱105.
- Check and look back. See if the answer makes sense, and state it completely: Ruby saves ₱105 in a month. A calculator can also be used to check.
Non-routine problems: draw, list, and look for patterns
The module says that non-routine problems develop reasoning power. Useful strategies include listing, making a table, guess and check, drawing a picture or diagram, using patterns, and using a number line.
Its worked example is about a school canteen. Four students can sit at one square table. How many can sit at five square tables placed end to end? Drawing the tables shows:
- the 2 end tables seat 3 students each: 3 x 2 = 6
- the 3 inside tables seat 2 students each: 2 x 3 = 6
- so 12 students can sit in all.
The module then asks which arrangement seats more students while the tables stay connected. Its answer is to join the tables corner to corner, so 4 students can still sit at each table.
Another common type is the distance problem. Electric posts stand 25 meters apart, and there are 10 posts. What is the distance from the first post to the last? A number line shows that 10 posts have only 9 gaps between them, so the answer is 9 x 25 = 225 m. The same idea appears in problems about Christmas light bulbs and rows of roses.
Parts of the module
| Part | What learners do |
|---|---|
| What I Know | 10-item pretest: 5 multiple-choice items and 5 problems to solve |
| What’s In | Review puzzle: find 7 products to spell the word for money that is not spent |
| What’s New and What is It | The Ruby savings problem and the canteen table problem, worked step by step |
| What’s More | Activity 1 (2 problems) and Assessment 1 (5 problems, including tiling block letters) |
| What I Have Learned | Summary of the four steps and of the strategies for non-routine problems |
| What I Can Do | Problems using Neo’s Canteen menu (for example, spaghetti ₱25, pancit ₱20, puto ₱6) and two more problems |
| Assessment | 10-item post-test on income, savings, prices, distances, and patterns |
| Additional Activities | 5 harder problems, such as pairs of factors of 36 and coins earned in a mobile game |
How to use this module
The module asks learners to answer on a separate sheet of paper and to leave no marks on the module itself.
- Learners: Start with the pretest in What I Know, then go through the parts in order. After each activity, check your work with the answer key at the back and be honest when you use it. Each part has a “Score update” that tells you how you did and when to go over the lesson again.
- Parents and facilitators: Help your child read each problem slowly and say what is asked and what facts are given before multiplying. Ask the teacher if your child keeps scoring low.
- Teachers: The pretest and the post-test both have 10 items, so you can compare them to see progress. What I Can Do and the Additional Activities suit learners ready for more challenge. The module lists the K to 12 Mathematics Curriculum Guide (August 2016) and the Mathematics Learner’s Material (Tabilang et al., 2015) as references.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 4 Mathematics, Quarter 1. It is Module 8 of the Alternative Delivery Mode series from DepEd Region V.
What is the difference between a routine and a non-routine problem?
A routine problem has a solution you can identify right away, like multiplying daily savings by the number of school days. A non-routine problem needs more reasoning and strategies such as drawing a picture, making a table, listing, guess and check, or using patterns.
What steps does the module use to solve routine word problems?
Understand (know what is asked and the given facts), Plan (choose the operation and write the number sentence), Solve (use the operation), and Check and Look Back (make sure the answer makes sense and state it completely).
Does the module have an answer key?
Yes. The answer key covers the pretest, the review puzzle, the activities, the assessments, and the additional activities, and score guides tell learners how they did.
Why is the distance between 10 posts placed 25 meters apart only 225 meters?
Ten posts in a row have only 9 spaces between them, so the distance is 9 x 25 = 225 m. The module shows this with a number line.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 1 – Module 8: Solving Routine and Non-routine Problems Involving Multiplication of Whole Numbers
CO_Q1_Mathematics4_Module8
[illustration: students reading and studying outdoors and indoors, with a teacher, a globe, and a lamp]
Mathematics – Grade 4 Alternative Delivery Mode Quarter 1 – Module 8: Solving Routine and Non-routine Problems Involving Multiplication of Whole Numbers 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
Writer: Ireneo D. Dechavez Editor: Elena D. Hubilla, Reviewers: Annavi M. Maravilla, Marites D. Dicen Illustrator: Jason C. Borabo Layout Artist: Teresa Vissia B. Suñga Management Team: Regional Director: Gilbert T. Sadsad CLMD Chief: Francisco B. Bulalacao Jr. Regional EPS In Charge of LRMS: Grace U. Rabelas Regional EPS In Charge of Math: Loyd H. Botor Regional ADM Coordinator: Ma. Leilani R. Lorico CID Chief: Monserat D. Guemo Division EPS In Charge of LRMS: Florena M. Deuna
Printed in the Philippines by _____
Department of Education – Region V
Office Address: Regional Center Site, Rawis, Legazpi City 4500 Telefax: 0917-178-1288 E-mail Address: region5@deped.gov.ph
4
Mathematics Quarter 1 – Module 8: Solving Routine and Non-routine Problems Involving Multiplication of Whole Numbers
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 learner! You have learned from the previous module how to multiply numbers up to 3 digits by up to 2-digit numbers without or with regrouping. In this module, you will encounter different problems involving multiplication of whole numbers including money. You will solve these problems using appropriate problem solving strategies and tools. Always put yourself in each problem so that you can easily solve it. Enjoy and have fun solving.
At the end of this module, you will be able to solve routine and non-routine problems involving multiplication of whole numbers including money using appropriate problem solving strategies and tools.
What I Know
A. Solve each problem and choose the correct answer.
Supelana Trading can sell 212 kilograms of rice a day. If a kilogram of rice costs ₱42, how much is the sales of Supelana Trading in a day?
a. ₱ 8 904
b. ₱ 1 372
c. ₱ 8 804
d. ₱ 1 732Analyn saves ₱12 from her daily allowance. How much did she save in 22 days?
a. ₱ 624
b. ₱ 264
c. ₱ 244
d. ₱ 424
2 CO_Q1_Mathematics4_Module8
Mrs. Rosario cooks siopao and sells it online for an extra income. If she sells 25 boxes to customers at ₱225 per box, how much is her income?
a. ₱ 5 562
b. ₱ 5 226
c. ₱ 5 625
d. ₱ 5 626The canteen of San Roque Elementary School has an average daily sale of ₱ 842. What is the monthly sale if there are 21 school days in a month?
a. ₱ 17 862
b. ₱ 16 782
c. ₱ 17 682
d. ₱ 16 872The electric posts along a straight road are 23 m apart. If there are 12 electric posts, what is the distance from the first post to the last post?
a. 253 m
b. 276 m
c. 300 m
d. 288 m
B. Solve the following problems.
The Department of Health will distribute 1 255 medicine kits to every town in a certain province. How many medicine kits will be distributed if there are 16 towns in that province?
A sari-sari store can sell 1 525 bottles of mineral water in a month. If a bottle costs ₱15, how much is the sale of the sari-sari store in a month?
T-shirts are sold on a “Buy 1-Take 1” basis for ₱320. How much will you pay for 10 T-shirts?
In a Fun Run Activity, the registration fee is ₱20. If there are 340 participants who registered, how much is the total collection for registration?
3 CO_Q1_Mathematics4_Module8
- Two workers can make 210 hollow blocks in an hour. How many hollow blocks can they make in 4 hours?
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
What’s In
YOU MUST HAVE IT!
Direction. Find the product. Then, write the corresponding letter of each product to solve the puzzle.
| 1. | 121 | 2. | 342 | 3. | 453 | 4. | 312 |
|---|---|---|---|---|---|---|---|
| x 8 | x 6 | x 11 | x 3 |
| 5. | 112 | 6. | 244 | 7. | 242 |
|---|---|---|---|---|---|
| x 8 | x 5 | x 4 |
A – 2 052 N – 896 V – 4 983 G – 1 220 I – 936 S – 968
“What is the amount of money that is not spent or used?”
ANSWER:
| 1. | 2. | 3. | 4. | 5. | 6. | 7. |
|---|---|---|---|---|---|---|
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
What’s New
How much money does your mother give you every day for your allowance? Do you spend all or you save some amount? Why do you need to save?
Read the problem.
Ruby receives from her mother the amount of ₱30 as her daily allowance in school. She saves ₱5 for future expenses. How much does she save in a month if there are 21 school days?
[illustration: a girl holding a paper with a peso sign, shrugging]
This is an example of a routine problem. Routine problems are problems that have solutions which can be immediately identified.
Try answering the given problem.
What is It
Let us see if we have the same answer.
To analyze and solve the problem, you can use these steps:
A. UNDERSTAND
- Read and understand the problem.
- Know what is asked in the problem.
Ruby’s savings in a month if there are 21 school days. - Find the necessary information.
The given facts: ₱5 – daily savings
21 – school days in a month
₱30 is not a necessary given fact because the focus is savings not monthly allowance.
B. PLAN
- Determine the operation to be used. MULTIPLICATION
- Write the number sentence. 21 x ₱ 5 = □
C. SOLVE
Solve using the operation.
21 x 5 ₱105
D. CHECK AND LOOK BACK
See if your answer makes sense. State the complete answer.
You can also use a calculator to check.
Ruby saves ₱105 in a month.
This is how to solve routine problems. How about solving non-routine problems? Go on with the next example. Study the example and ask questions as necessary.
Study this problem.
In a school canteen, 4 students can sit in a square table. How many students can sit in five square tables placed end to end?
You can solve by drawing a picture.
[chart: diagram of five square tables placed end to end, with seats numbered around them; no number or title printed]
- Top row: 2, 3, 4, 5, 6
- Left: 1
- Right: 7
- Bottom row: 12, 11, 10, 9, 8
Solving non-routine problems develops your reasoning power. You can use the following strategies in solving non-routine problems: Listing, Making a Table, Guess and Check, Drawing/Diagram, Using patterns, etc.
Two end tables: 3 x 2 = 6 (3 students can sit) Three inside tables: 2 x 3 = 6 (2 students can sit)
So, 12 students can sit in five square tables placed end to end.
What do you think is the best arrangement of the square tables such that more students may be seated and the square tables are still connected to each other?
You can solve this problem by making an illustration.
[chart: diagram of square tables arranged corner to corner, with seats numbered 1 to 20; no number or title printed]
- Top: 2 (above left table), 6 (above right table)
- 1 (left of top-left table), 3, 5, 7 (right of top-right table)
- 9 (below 3 and 5), 4 (below top-left table), 8 (below top-right table)
- 10 (left of center table), 11 (right of center table), 18 (right of 11)
- 13 (below 10), 12 (below center table)
- 14 (left of bottom-left table), 15 (below… right of 14), 17 (right of 15), 19 (right of bottom-right table)
- Bottom: 16 (below bottom-left table), 20 (below bottom-right table)
You can arrange the tables by connecting a corner of a table (the vertex) to another corner in such a way that 4 students can be seated at each table as shown.
Therefore, the best arrangement of the square tables is corner to corner wherein 4 students can be seated.
Now, you learn solving non-routine problems. This time you are now ready for the activities. LET’S GO!
What’s More
Activity 1
Solve the following problems. Show your solutions.
- During weekends, Cedrick and his friends collect plastic bottles and sell them to a junkshop. They collected 36
kilograms of plastic bottles. How much will they receive if each kilogram costs ₱12?
- The electric posts are 25 meters apart. If there are 10 electric posts, what is the distance from the first electric post to the last electric post?
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
Assessment 1
Solve the following problems.
- A group of workers can make 830 pieces of siomai an hour. How many pieces of siomai can they make in 36 hours?
- T-shirts are sold on a “Buy 1 – Take 1” basis. If one shirt costs ₱ 120, how much will you pay for 10 T-shirts?
- The 13 divisions of DepEd Bicol will conduct a simultaneous earthquake drill. If each division is required to have 920 participants, how many will join the drill?
- A square tile costs ₱45 each. Find the cost to tile the word.
[illustration: three block letters made of square tiles, H, I and D]
- A raffle ticket costs ₱25. How much is the cost of 680 raffle tickets?
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
What I Have Learned
How do you solve routine and non-routine word problems involving multiplication of whole numbers including money using appropriate strategies and tools?
To solve routine problems involving multiplication of whole numbers including money using appropriate strategies and tools, follow these steps:
UNDERSTAND
- Know what is asked.
- Know the given facts.
PLAN
- Determine the operation to be used.
- Write the number sentence.
SOLVE
- Use the operation to solve.
CHECK AND LOOK BACK
- Write the correct answer.
Non-routine problems can be solved by drawing a picture, using a number line, making a table, and others.
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
What I Can Do
A. Use the Neo’s Canteen menu to answer the following questions.
- How much will two orders of spaghetti cost?
- How much will eight orders of egg sandwich cost?
- How much will Ruby pay for four orders of banana cue?
- How much will the Mercado Family pay for 4 pieces of puto, 4 orders of pancit, and 4 orders of calamansi juice?
| NEO’S CANTEEN MENU | |
|---|---|
| Spaghetti | ₱25 |
| Pancit | ₱20 |
| Banana Cue | ₱15 |
| Puto | ₱6 |
| Egg Sandwich | ₱24 |
| Calamansi Juice | ₱10 |
| Buko Juice | ₱12 |
[transcriber’s note: the menu’s column headings are not printed; the title is the first row]
B. Read, analyze, then solve.
- The distance between each bulb of a Christmas light is 6 cm. What is the distance from the first bulb to the last bulb if there are 100 bulbs?
- A sari-sari store sells pineapple juice at ₱15 per bottle. What is the monthly sales of the sari-sari store if it sells 215 bottles of pineapple juice?
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
Assessment
Read, analyze, then solve each problem.
- Mang Gusting earns ₱1 355 from his tricycle every week. How much will he earn in 10 weeks if the tricycle will be in good condition for the period given?
- The Diaz family conserves electricity everyday by turning off unused lights and appliances. Compared to their previous bill, they have saved ₱125. How much will they save if they continue conserving for 12 months?
- A box of corned beef containing 36 cans is sold with 3 cans free. Aling Belen bought 3 boxes for her sari-sari store. How many cans of corned beef will she have?
- A box of pencils costs ₱108. How much will you pay if you buy 12 boxes?
- Connecting four dots makes a square. If you add two more dots and connect them, you can make two squares. Given the condition, how many dots compose 10 such squares?
- A barber shop haircut service costs ₱50. If the shop has an average of 113 haircut services daily, how much is the income of the barber shop everyday?
- Kiko sells sampaguita garlands during weekends. Each sampaguita garland costs ₱8. How much will he earn if he sold 150 pieces?
- Roses are planted 3 meters apart. If there are 25 roses, what is the distance from the first rose to the last rose?
- Strawberries from Baguio are sold for ₱350 a kilo. How much will a tourist pay for 15 kilos?
- A printer can print 20 copies in a minute. How many copies can it print in 3 hours?
(Please go to page 12 for the Answer Key)
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
Additional Activities
Solve the following problems.
- On the first two days of the Palarong Pambansa, a vendor sold 310 T-shirts at ₱175. How much was the vendor’s sale for the first two days?
- A rectangle is composed of 15 squares. The three middle squares of the rectangle are painted. How many non-painted squares are there if there are 20 rectangles?
- Lance is a thrifty student. He opens a student savings account in a bank and deposits ₱110 weekly. How much will his total savings be after 48 weeks?
- Six is a product of the two pairs of factors: (6×1 or 1×6) and (2×3 or 3×2). How many pairs of factors does 36 have?
- In a mobile game, every level passed is rewarded with 50 coins. The game finishes at Level 50 with a reward of a winner’s trophy instead of 50 coins. If you happen to reach the last level and win the game, how many coins can you earn in all?
CONGRATULATIONS! You are doing very well. See you in the next module.
[transcriber’s note: this page is printed rotated 180 degrees; the answers are transcribed in their reading order]
Answer Key
What I Know
A.
- ₱8 904
- ₱264
- ₱5 625
- ₱17 682
- 253 m
B.
- 20 080 medicine kits
- ₱22 875
- ₱1 600
- ₱6 800
- 840 hollow blocks
What’s In
- 968
- 2 052
- 4 983
- 936
- 896
- 1 220
- 968
Answer: SAVINGS
What’s More
Activity 1
- Solution:
36 x 12 72 36 + ₱432
Answer: They will receive ₱432.
- Solutions:
[chart: number line; positions labeled 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th]
9 x 25 = 225 m
Answer: The distance from the first electric post and the last electric post is 225 m.
Assessment 1
- They can make 29 880 pieces in 36 siomai hours.
- ₱600
- There are 11 960 participants.
- The cost to tile the word is ₱765.
- The cost of 680 raffle tickets is ₱17 000.
What I Can Do
- ₱50
- ₱192
- ₱60
- ₱144
- The distance from the first bulb to the last bulb is 594 cm.
- The total sale of the sari-sari store is ₱3 225.
Assessment
- He will earn ₱13 550 in 10 weeks.
- He will save ₱1 500.
- Aling Belen took home 117 cans of corned beef for her sari-sari store.
- ₱1 296
- 22 dots
- ₱5 650
- ₱1 200
- 72 meters
- ₱5 250
- 3 600 copies
Additional Activities
- The vendor’s sale for the first two days is ₱54 250.
- There are 240 squares without paint.
- He deposited ₱5 280.
- There are 5 pairs of factors with a product of 36.
- You earned 2 450 coins in all.
[transcriber’s note: the file name refers to Solving Routine and Non-Routine Problems Involving Multiplication of Whole Numbers, but the printed footer on these pages reads CO_Q1_Mathematics4_Module8.]
Score update: Additional Activities
- 3 WOW! GREAT JOB!
- 2 NICE!
- 0-1 Don’t worry. Your teacher will be happy to help you. Do not be shy to ask questions. Have fun!
Score update: What I Know and Assessment
- 10 WOW! GREAT JOB!
- 7-9 VERY NICE!
- 5-6 NICE!
- 3-4 OOOPPPS! Let us review and go over with the test again.
- 0-2 Don’t worry. Take time to go over the lesson again. Do not be shy to ask help from your teacher or facilitator. Have fun!
Score update: What’s In
- 7 WOW! GREAT JOB!
- 6 VERY NICE!
- 5 NICE!
- 0-4 OOOPPPS! Don’t worry. Take time to study this module. Do not be shy to ask help from your teacher or facilitator. Have fun!
Score update: What’s More- Activity 1
- 2 WOW! GREAT JOB!
- 1 NICE!
- 0 Don’t worry. Your teacher will be happy to help you. Do not be shy to ask questions. Have fun!
Score update: What I Can Do
- 6 WOW! GREAT JOB!
- 4-5 NICE!
- 0-3 Don’t worry. Your teacher will be happy to help you. Do not be shy to ask questions. Have fun!
Score update: What’s More – Assessment 1
- 5 WOW! GREAT JOB!
- 3-4 NICE!
- 0-2 Don’t worry. Your teacher will be happy to help you. Do not be shy to ask questions. Have fun!
References
K to 12 Mathematics Curriculum Guide, August 2016.
Tabilang, A. et. al. (2015). Mathematics: Learner’s Material, Pasig City: Lexicon Press.
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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