This is the Grade 5 Mathematics Quarter 2 Module 6 self-learning module, Solving Routine or Non-routine Problems Involving Addition and Subtraction of Decimal Numbers Including Money Using Appropriate Problem-Solving Strategies and Tools. It is an Alternative Delivery Mode module (First Edition, 2020) from DepEd Region VIII, written by Editha T. Montermoso. Learners practice solving word problems about money, savings, purchases, change, lengths, and liters by adding and subtracting decimals step by step.
What learners will learn
After going through this module, learners are expected to:
- Solve routine or non-routine problems involving addition and subtraction of decimal numbers including money using appropriate problem-solving strategies and tools (M5NS-IIc-108.1).
Before starting, learners should already know how to add and subtract decimal numbers. The module reviews both skills first.
Routine and non-routine problems
The module’s lesson, “Solving Routine and Non-Routine Problems,” begins by explaining two kinds of word problems:
- Routine problems have an immediate solution. You solve them with at least one of the four operations (addition, subtraction, multiplication, division).
- Non-routine problems need some creativity. They usually do not have an obvious strategy. The module says they prepare learners for real life, because real problems do not come with prescribed steps.
Review: adding and subtracting decimals
The module uses the same four steps for both operations, with the example 546.34 and 8.9:
- Write the numbers vertically and line up the decimal points, so digits with the same place value are in the same column.
- Add zeros after the last digit so all numbers have the same number of decimal places (8.9 becomes 8.90).
- Add or subtract, regrouping if necessary.
- Put the decimal point in the answer, aligned with the decimal points above it.
| Operation | Problem | Answer |
|---|---|---|
| Addition | 546.34 + 8.90 | 555.24 |
| Subtraction | 546.34 − 8.90 | 537.44 |
Steps for solving routine word problems
The “What I Have Learned” part lists six steps:
- Identify what is asked.
- List down what are given.
- Identify the hidden question, if there is any.
- Identify the operation needed.
- Write the mathematical sentence.
- Solve the problem.
Example from the module: Pedro spent ₱120.50 for food in the morning and ₱150.25 at lunchtime. What is asked is the total he spent. There is no hidden question, the operation is addition, and the number sentence is N = 120.50 + 150.25. Pedro spent ₱270.75.
Another example compares two electric bills of a car wash shop: ₱5,391.50 last month and ₱3,150.25 this month. Subtracting gives ₱2,241.25, which is how much more they paid last month.
Strategies for non-routine problems
The module lists these strategies:
- Look for a pattern
- Guess and check
- Work backward
- Make a model or visualize the problem
- Break up the problem into smaller parts and solve each
For example, one problem says the prices of three tubs of peanut butter add up to ₱496.28, and two tubs cost ₱238.94 and ₱110.09. Working backward, you subtract the known prices from the total: 496.28 − 238.94 − 110.09 = 147.25. The third tub costs ₱147.25.
How to use this module
The module is arranged in this order:
- What I Need to Know: the learning goal.
- What I Know: a 10-item multiple-choice pretest on money problems such as deposits, change, and purchases.
- What’s In: a review of adding and subtracting decimals.
- Lesson and What’s More: the discussion and independent activities.
- What I Have Learned: the six steps and the non-routine strategies.
- What I Can Do: two word problems answered step by step.
- Assessment: a 10-item multiple-choice post-test.
- Additional Activities: three extra problems on lengths, liters, and prices.
- Answer Key: answers for the activities and tests.
For learners: Write your answers and solutions on a separate sheet of paper, not on the module. Read each direction carefully, and use the answer key honestly to check your work only after you answer.
For parents: Help your child read each problem slowly and ask, “What is asked? What are given?” Real situations at home, like counting change after buying something, make good extra practice.
For teachers: Use the pretest to see who needs more help with decimal operations before the lesson. Ask learners to show their six-step solutions, not just the letter of the answer. Check the answer key against your own computations before using it for grading.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 5 Mathematics, Quarter 2, Module 6. It was produced by DepEd Region VIII as an Alternative Delivery Mode module, First Edition, 2020.
What is the difference between a routine and a non-routine problem?
A routine problem has an immediate solution using at least one of the four operations. A non-routine problem needs creativity and has no obvious strategy, so you may look for a pattern, guess and check, work backward, make a model, or break the problem into parts.
What are the steps for solving a routine word problem?
Identify what is asked, list what are given, find any hidden question, choose the operation, write the mathematical sentence, and solve. The module shows these steps with problems about food expenses and electric bills.
Does the module have an answer key?
Yes. It has answers for the pretest, the independent activities, What I Can Do, the assessment, and the additional activities. Teachers may want to check the answers against their own computations.
How do you add or subtract decimals with different numbers of decimal places?
Line up the decimal points, then add zeros at the end so all numbers have the same number of decimal places. For example, 8.9 becomes 8.90 before adding it to or subtracting it from 546.34.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 2 – Module 6: Solving Routine or Non-routine Problems Involving Addition and Subtraction of Decimal Numbers Including Money Using Appropriate Problem-Solving Strategies and Tools
5
[illustration: students and a teacher studying outdoors and at a desk, a globe, and a child writing by a lamp]
CO_Q2_Math5_Module6
Mathematics– Grade 5 Alternative Delivery Mode
Quarter 2 – Module 6: Solving Routine or Non-routine Problems Involving Addition and Subtraction of Decimal Numbers Including Money Using Appropriate Problem Solving Strategies and Tools 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 the exploitation of such work for a 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 book 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: Editha T. Montermoso Editor: Maria Niann L. Atis, Merlinda F. Mirales, Reviewers: Renato S. Cagomoc, Rolando Lacbo, Joshua Sherwin T. Lim, Ramil A. Tan, Ronaldo M. Eco, Jr. Layout Artist: Joey Sustitudo Management Team: Ramir B. Uytico Arnulfo R. Balane Rosemarie M. Guino Joy B. Bihag Ryan R. Tiu Sarah S. Cabaluna Thelma Cabadsan-Quitalig Elena S. De Luna Renato S. Cagomoc Noel E. Sagayap Geraldine P. Sumbise Joshua Sherwin T. Lim
Printed in the Philippines by Department of Education – Region VIII Office Address: DepEd Regional Office No. 8 Candahug, Palo, Leyte Telefax: 053 – 832-2997 E-mail Address: region8@deped.gov.ph
5
Mathematics
Quarter 2 – Module 6: Solving Routine or Non-routine Problems Involving Addition and Subtraction of Decimal Numbers Including Money Using Appropriate Problem-Solving Strategies and Tools
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.
Good luck and happy learning!
[illustration: target with an arrow]
What I Need to Know
In this module, you are going to test your ability in solving routine or non-routine problems involving addition and subtraction of decimal numbers including money. Following the steps and using different strategies will help you solve the problems.
After going through this module, you are expected to:
Solve routine or non-routine problems involving addition and subtraction of decimal numbers including money using appropriate problem-solving strategies and tools. M5NS-Ilc-108.1
[illustration: pencil]
What I Know
Directions: Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper.
Leon has ₱4,522.08 savings in his bank account. He deposits another ₱875.50, and then deposits another ₱300.75 the following month. How much savings he got in his account?
- A. ₱3,588.03
- B. ₱4,658.50
- C. ₱5,658.30
- D. ₱5,658.33
Rodolfo had ₱368.29 money. His mother gave him ₱253.46 and his sister gave him ₱57.39. How much money does he have now?
- A. ₱675.50
- B. ₱678.15
- C. ₱679.14
- D. ₱778.14
Maria had saved ₱469.38 from her Christmas presents last December. She gave ₱99.37 to Mario and ₱124.93 to Martha. How much money is left with her?
- A. ₱99.37
- B. ₱124.93
- C. ₱224.30
- D. ₱245.080
Tanya bought a book for ₱152.75, a pen for ₱45.25 and a bar of chocolate for ₱28.75. How much amount did she spend for the items she bought?
- A. ₱225.75
- B. ₱226.75
- C. ₱226.76
- D. ₱227
Nancy sold a pencil case to her classmate for ₱51.25. She was given a ₱100.00 bill. How much did Nancy give to her classmate for her change?
- A. ₱48.75
- B. ₱48.80
- C. ₱49.70
- D. ₱51.00
CO_Q2_Math5_Module6
Wilma had ₱305.80 money in her bank. She deposited ₱250.25 more and then withdrew ₱317.50 from her account. What is the balance now in her account?
- A. ₱235.50
- B. ₱238.55
- C. ₱556.00
- D. ₱556.05
Lando wants to buy a chess book guide costing ₱600.00. He has ₱475.25 only in his purse. How much more money does he need to purchase the book?
- A. ₱124.75
- B. ₱125.05
- C. ₱238.50
- D. ₱238.55
Mrs. Santos is trying to bake cookies for her daughter’s birthday party. She needs to buy one-fourth kilogram of white flour for ₱20.75, one-fourth kilogram of oatmeal flour for ₱55.25, and one-half cup of almond flour for ₱87.05. How much will she pay for all the types of flour she needed?
- A. ₱164.00
- B. ₱163.10
- C. ₱163.05
- D. ₱165.50
Cristina and her mother ate in a carenderia and ordered one serving of beef bulalo for ₱45.50, chopseuy for ₱42.50, and a platter of rice for ₱35.75. Her mother gave the cashier ₱1,000.00 bill. How much is their change?
- A. ₱876.20
- B. ₱876.25
- C. ₱875.50
- D. ₱900.25
Rolando deposited ₱8,780.00 into a savings account. After six months, his money earned an interest of ₱105.36. How much was in the account then?
- A. ₱8,885.36
- B. ₱8,885.30
- C. ₱8,885.00
- D. ₱8,880.36
CO_Q2_Math5_Module6
Lesson 1
Solving Routine and Non-Routine Problems
The Routine word problem is a type of problem in which there is an immediate solution, it involves using at least one of the four arithmetic operations.
The Non-routine problem solving is a creative problem solving that requires some degree of creativity, it typically does not have an immediately apparent strategy for solving them. It prepares the learners for real-life problem-solving. Real-life problems do not come with prescribed steps on how to solve them.
[illustration: puzzle pieces icon]
What’s In
Before you start with this lesson, you should have mastery in addition and subtraction of decimal numbers.
Addition of Decimals
Step 1: Write the decimal numbers vertically. Align the decimal points so that all the whole numbers are aligned on the left side of the decimal point and all the decimal numbers are aligned on the right side of the decimal point. The digits with the same place values should be aligned.
546.34
+ 8.9
Step 2: Add zeros after the last digit at the right of the decimal point so that all of the numbers have the same number of decimal places.
546.34
+ 8.90
Step 3: Add the decimal numbers. Starting on the left most part numbers going to the right. Regroup if necessary.
1 1
546.34
+ 8.90
555 24
Step 4: Put the decimal point on the answer. It should be aligned with the decimal point of the given numbers.
546.34
+ 8.90
555.24
Subtraction of Decimals
Step 1: Write the decimal numbers vertically. Align the decimal points so that all the whole numbers are aligned on the left side of the decimal point and all the decimal numbers are aligned on the right side of the decimal point. The digits with the same place values should be aligned.
546.34
- 8.9
Step 2: Add zeros after the last digit at the right of the decimal point so that all of the numbers have the same number of decimal places.
546.34
- 8.90
Step 3: Subtract the decimal numbers. Starting on the left most part numbers going to the right. Regroup if necessary.
315 1
546.34
- 8.90
537 44
Step 4: Put the decimal point on the answer. It should be aligned with the decimal point of the given numbers.
546.34
- 8.90
537.44
4) Robin's bank account has Php 1,200.57. He earned Php 590.00 by working at an ice cream shop and Php 460.93 by tutoring his classmates. If he deposits all his earnings, how much money would his bank account has in total?
5) Katherine wants to buy a present for his best friend's birthday. The present Katherine wants to buy is worth Php 394.75. Katherine's mother already gave her Php 125.25. Her piggy bank contains Php 214.80. If she adds all the money she has, how much more does she need to be able to buy the present?
## What I Have Learned
To solve routine word problems, the following steps are used:
**Step 1:** Identify what is asked.
**Step 2:** List down what are given.
**Step 3:** Identify the hidden question, if there is any.
**Step 4:** Identify the operation needed to solve the problem.
**Step 5:** Write the mathematical sentence that will be used to solve the problem
**Step 6:** Solve the problem.
Different strategies are used in solving non-routine word problems.
- Look for a pattern
- Guess and check
- Work backward
- Make a model/ visualize the problem
- Break up the problem into smaller parts and solve each
## What I Can Do
### A. Solve the problem below
1) Pedro lives in far flung barangay of Calbayog City. Sometimes he went to school early with an empty stomach. Upon arriving at school, that's the time that he will look for something to eat before the classes start. Today, he spent ₱120.50 for his food in the morning and ₱150.25 during lunchtime. How much did Pedro spend in total for his food?
**Step 1:** What is asked? _____
**Step 2:** What are given? _____
_____
**Step 3:** What is the hidden question, if there is any?
_____
**Step 4:** What operation is needed to solve the problem?
_____
**Step 5:** What is the mathematical sentence that will be used to solve the problem?
_____
**Step 6:** Solution of the problem.
2) Joanna's Car Wash Shop operates daily before the Enhanced Community Quarantine (ECQ) took place. But during the quarantine period the owners closed the shop as part of the protocol for small establishments and businesses. But when they received the electric bill last month, it declared an amount of ₱5,391.50. This month's electric bill is ₱3,150.25. How much more did they pay last month than this month's electric bill?
## Assessment
**Directions:** Solve the following word problems. Choose the letter of the best answer. Write the chosen letter and your solutions on a separate sheet of paper.
1) Roy recorded the number of liters of gasoline that he used for three days. He recorded 11.2 liters, 10.8 liters, and 14.2 liters. How many liters of gasoline did he use in all?
- A. 30.2 liters
- B. 36.2 liters
- C. 36.2 liters
- D. 38.2 liters
2) Talahib rice company produced 2000 kilograms of rice. How many kilograms of rice was left after selling 1475.5 kilograms?
- A. 500.5 kilos
- B. 522.5 kilos
- C. 524.5 kilos
- D. 528.5
3) Benjie spent ₱878.50 for the spare parts that were needed for the repair of his motorcycle. How much of his money was left if he originally had ₱950.00?
- A. ₱70.50
- B. ₱71.50
- C. ₱71.55
- D. ₱75.50
4) The sum of three decimal numbers is 496.28. Two decimal numbers are 238.94 and 110.09. Find the third decimal.
- A. 147.25
- B. 148.35
- C. 606.37
- D. 735.25
5) Cagbayang Central Elementary School needs additional funds for the renovation of their computer laboratory. To answer their problem, they conducted a fund raising activity for a week. They earned ₱1,820.75 on the first day, ₱2,947.50 on the second day, and ₱1,932.25 on the third day. How much did they earn for the first three days of the fund raising activities?
- A. ₱6700.20
- B. ₱6700.50
- C. ₱6900.50
- D. ₱7700.50
6) Anthony bought a ticket for the roller coaster ride for ₱47.50 discounted price.He paid at the ticket booth ₱100 bill. While he was counting his change, he dropped a few coins and counted that he only got ₱40.25 left. How much did Anthony drops?
- A. ₱52.50
- B. ₱40.25
- C. ₱15.00
- D. ₱12.25
7) Joey has Php545.95 savings. He gave Php290.80 to his brother. From the remaining money, he gave Php95.50 to his sister, how much money was left to Joey?
- A. ₱79.50
- B. ₱386.30
- C. ₱836.75
- D. ₱159.65
8) Rodrigo, Esmael, and Romy have a combined height of 8.7 meters. If Rodrigo is 2.31 meters tall and Esmael is 2.6 meters tall, how tall is Romy?
- A. 5.79 meters
- B. 4.91 meters
- C. 3.79 meters
- D. 2.79 meter
9) Ricky and Samuel had dinner at Bay Park Restaurant. Ricky's ordered meal cost Php 240.27, and Samuel's cost Php215.40. How much did the two meals cost altogether?
- A. ₱450.67
- B. ₱455.65
- C. ₱455.67
- D. ₱550.67
10) Bobby's house is 3.5 meters taller than Ted's house and Bonnie's house is 1.2 meters shorter than Ted's house. How tall is Bobby's house than Ted's house?
- A. 1.3 meters
- B. 2.3 meters
- C. 4.7 meters
- D. 5.8 meters
## Additional Activities
**Directions:** Read and analyze the problems. Solve what is being asked.
1) The length of the ribbon is 1.28 meters. The length of the rope is 2.74 meters longer than the ribbon. What is the length of the rope?
2) A pail holds 5.2 liters of water. A bottle holds 3.0 liters less water than the pail. What is the volume of the water in the bottle?
3) Helen bought three tubs of peanut butter in different sizes. The sum of the prices of the three tubs of peanut is Php496.28. Two tubs are Php238.94 and the other is Php110.09. Find the price of the third tub.
## Answer Key
### Additional Activities
The length of the rope is 4.02 meters
The volume of the water in the bottle is 1.3 liters
The price of the third tub of peanut butter is Php147.25
### What I Can Do
A.
1.
Step 1: The amount of money Pedro spent for food.
Step 2: Money spent in the morning – Php 120.50
Money spent at lunch time – Php 150.25
Step 3: No hidden question
Step 4: Addition
Step 5: N = 120.50 + 150.25
Step 6: Pedro spent Php 270.75 for food
2.
Step 1: The amount of more than what Joanna's Car Wash Shop pay last month than this month's electric bill?
Step 2: Last month's bill – ₱ 5,391.50
This month's bill – ₱ 3,150.25
Step 3: No hidden question
Step 4: Subtraction
Step 5: N = 5,391.50 + 3,150.25 [?]
Step 6: They paid Php 2,241.25 more for last month's bill
*[transcriber's note: the Step 1 and Step 5 lines are printed in a jumbled order on this page; the operator in Step 5 is hard to read in the image, so it is given as best read.]*
### Assessment
1. A 6. D
2. C 7. A
3. C 8. D
4. A 9. B
5. B 10. B
### What I Know
1. C 6. B
2. A 7. C
3. D 8. C
4. B 9. D
5. A 10. A
### What's More
#### Independent Activity 1
Step 1: The amount of money Cristina still needed to buy the shoes
Step 2: Shoe cost – Cristina's savings
Php 1,464.75 – Php 542.68
Step 3: No hidden question
Step 4: Subtraction
Step 5: N = 1,464.75 – 542.68
Step 6: Cristina still needs Php 922.07 to buy the shoes
#### Independent Activity 2
1. Php 430.8
2. Php 76.36
3. Php 62,059.73
4. Php 2251.5
5. Php 54.7
## References
Camarista, G., and S. G. Gabinete. 2016. *The Art of Problem Solving.* Philippines: Lorimar Publishing, Inc.
Ghosh, Priyanka. 2021. *Math Only Math.* Accessed August 2021. https://www.math-only-math.com.
OnlineMathLearning.com. 2020. *Online Math Learning.* Accessed August 2021. https://www.onlinemathlearning.com.
Quipper. 2021. *Quipper Philippines.* Accessed August 2021. https://link.quipper.com/en/organizations/547fe96ad11ff00002005c53/curriculum#curriculum.
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