This is the Grade 5 Mathematics self-learning module for Quarter 1, Module 4: “Solving Problems Involving Factors, Multiples and Divisibility Rules.” It is an Alternative Delivery Mode module (First Edition, 2020) from DepEd Region VIII, written by Christine G. Velasco. After working through it, learners can solve routine and non-routine word problems using factors, multiples, and the divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12.
What learners will learn
When they finish the module, learners will be able to:
- solve routine and non-routine problems involving factors, multiples, and divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12.
The module explains that these rules help you find the factors of a big number just by looking at its digits.
Lesson in this module
The module has one lesson: Lesson 1: Solving Routine and Non-routine Problems Involving Factors, Multiples, and Divisibility Rules for 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12. It reviews the divisibility rules from the previous module, then shows how to use them with Polya’s four-step plan to solve word problems.
Divisibility rules to remember
A divisibility rule is a quick way to tell whether a number can be divided by another number with no remainder. The module reviews these rules with examples:
| A number is divisible by | If | Module’s example |
|---|---|---|
| 2 | it is even and ends in 0, 2, 4, 6, or 8 | 106 ends in 6 |
| 3 | the sum of its digits is divisible by 3 | 315: 3 + 1 + 5 = 9 |
| 4 | the number formed by its last two digits is divisible by 4 | 612: 12 is divisible by 4 |
| 5 | its ones digit is 0 or 5 | 487 580 ends in 0 |
| 6 | it is divisible by both 2 and 3 | 5 652 is even; 5 + 6 + 5 + 2 = 18 |
| 8 | the number formed by its last three digits is divisible by 8 | 913 824: 824 is divisible by 8 |
| 9 | the sum of its digits is divisible by 9 | 9 684: 9 + 6 + 8 + 4 = 27 |
| 10 | its ones digit is 0 | 850 ends in 0 |
| 11 | the difference between the sums of the odd-positioned and even-positioned digits (from the left) is 0 or a multiple of 11 | 2 376: (2 + 7) – (3 + 6) = 0 |
| 12 | the sum of its digits is divisible by 3 and its last two digits form a number divisible by 4 | 324: 3 + 2 + 4 = 9, and 24 is divisible by 4 |
Solving word problems with the four-step plan
The module describes two kinds of word problems:
- Routine problems are useful in daily life and can be solved with a standard procedure.
- Non-routine problems build mathematical reasoning. They can be solved without a standard procedure, for example by drawing a picture, using a number line, acting it out, or making a table.
To solve them, learners use Polya’s four-step plan:
- Understand: know what is asked and what is given.
- Plan: decide on the operation, method, or procedure.
- Solve: use the method to find the answer.
- Check and Look Back: test the answer against the facts of the problem.
Worked examples from the module
- Tree planting: Grade 5 boys plant 50 seedlings and girls plant 30, with equal numbers of trees per row. The module finds the common factors of 50 and 30 in three ways: a factor tree, listing the factors (50 = 1, 2, 5, 10, 25, 50 and 30 = 1, 2, 3, 5, 10, 15, 30), and a table that checks each divisibility rule. The possible common numbers of trees per row are 2, 5, and 10.
- Delfin’s age: His age is divisible by 12, is a multiple of 9, and is less than 51. Listing the multiples of 12 below 51 (12, 24, 36, 48) and eliminating those that are not multiples of 9 leaves 36.
- Clean-up drive: 125 registered youths must be divided into equal groups. Testing the rules shows 125 is divisible by 5 but not by 2, 3, 4, 6, 8, 9, 10, 11, or 12, so the module’s answer is 5 groups of 25 members.
What is inside the module
- What I Know: a pretest problem about dividing 36 mongo seeds and 33 corn seeds equally into pots, solved with the four-step plan.
- What’s In: a review of the divisibility rules and a checklist table for five numbers.
- What’s New and What Is It: the tree planting problem and the worked examples above.
- What’s More: four multiple-choice problems (tiles, blocks, volleyball players, stacks of blocks) and three non-routine problems.
- What I Have Learned: a summary of the four-step process and exercises on divisibility by 4, 8, and 9.
- What I Can Do: problems on onions in rows, marbles in jars, a mystery number N, and a six-digit number puzzle.
- Assessment: five multiple-choice word problems.
- Additional Activities: a seat plan problem, a remainder puzzle, and finding pairs that sum to a multiple of 11.
- Answer Key: answers for the activities and the assessment.
How to use this module
- Learners: Start with the pretest in What I Know, then go through the parts in order. Write your answers on a separate sheet of paper or in your Math Activity Notebook, not on the module. Use the four-step plan for every word problem, and check your work with the answer key honestly after answering.
- Parents and facilitators: Help your child read each problem slowly and name what is asked and what is given before solving. Encourage them to check answers by actually dividing, as the module does in the Check and Look Back step.
- Teachers: The module includes routine and non-routine items, so it can serve as practice and enrichment. Review the answer key before using it, since a few entries in the printed key appear to have errors.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 5 Mathematics, Quarter 1. It is Module 4 of the quarter.
What does the module teach?
It teaches learners to solve routine and non-routine word problems using factors, multiples, and the divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12, following Polya’s four-step plan.
What is the difference between routine and non-routine problems?
Routine problems are useful in daily life and follow a standard procedure. Non-routine problems develop mathematical reasoning and can be solved in creative ways, such as drawing a picture, using a number line, or making a table.
What are the four steps for solving word problems?
Understand (know what is asked and what is given), Plan (choose the operation or method), Solve (use the method), and Check and Look Back (make sure the answer fits the problem).
Does the module have an answer key?
Yes. The answer key covers the pretest, the What’s In table, What’s More, What I Have Learned, What I Can Do, and the Assessment.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 1 – Module 4: Solving Problems Involving Factors, Multiples and Divisibility Rules
CO_Q1_Math5_Module4
Mathematics – Grade 5 Alternative Delivery Mode Quarter 1 – Module 4: Solving Problems Involving Factors, Multiples and Divisibility Rules 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: Christine G. Velasco Editors: Zosimo M. Miñozo Jr., Cristian L. Senolos, Mhe Shaila D. Olin, Harold Naputo, Ramil R. Magdua, Joseph Randolp Palattao, Lilia Martinez, Bernadeth Daran, and Lilia L. Lagrimas, Lido C. Manicane Reviewers: Renato S. Cagomoc, Rolando Lacbo, Joshua Sherwin T. Lim, and Christopher Salino, Hazel L. Maravelis, Miguel V. Dumas, Jr. Layout Artist: Angel T. Porlares, Ryan R. Tiu Management Team: Ramir B. Uytico, Arnulfo M. 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: Government Center, Candahug, Palo, Leyte Telefax: 053 – 832-2997 E-mail Address: region8@deped.gov.ph
Mathematics Quarter 1 – Module 4: Solving Problems on Divisibility Rules
5
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 SLMS 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 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.
CO_Q1_Math5_Module4
What I Need to Know
Hi, Mathletes!
In this module, you will learn how to solve routine and non-routine problems involving factors, multiples and divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12. This will help you find easier the factors of a big number by just looking at its digits.
When you are done with this module, you will be able to:
- solve routine and non-routine problems involving factors, multiples, and divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12.
What I Know
Directions: Solve the problem below by using the four-step plan. Use a separate sheet of paper or your Math Activity Notebook.
The pupils of Grade 5-Slate are having an experiment on the germination of seeds on different types of soil. One group received 36 mongo seeds and 33 corn seeds. They placed both the mongo and corn seeds into small pots such that seeds of the same types were divided equally into the small pots. How many small pots will they use for each kind of seed?
- Understand
a. Know what is asked:
b. Know what is/are given: - Plan
c. Determine the operation/ method/ procedure to be used. - Solve
d. Use the method to solve the problem - Check and Look Back
e. Check your answer
CO_Q1_Math5_Module4
Lesson 1: Solving Routine and Non-routine Problems Involving Factors, Multiples, and Divisibility Rules for 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12
A divisibility rule is a simple way of determining whether a given number is divisible by another number. It can be used to quickly find the factors of given numbers. “Divisible by another number” means a number can be divided by another number without any remainder.
What’s In
In the previous module, you have learned how to find common factors by understanding the divisibility rules.
By looking at the digits of a large number or by doing simple calculations, you can easily tell whether a number is a factor of a given number or not. Remember that a number is divisible by:
➢ 2 – if it is even and ends in 0, 2, 4, 6, or 8 Example: 106 is divisible by 2 because it ends in 6.
➢ 3 – if the sum of the digits of the number is divisible by 3 Example: 315 is divisible by 3 because 3 + 1 + 5 = 9 and 9 is divisible by 3.
➢ 4 – if the number formed by its last two digits is divisible by 4. Example: 612 is divisible by 4 because the number formed by its last two digits are 12, which is divisible by 4.
➢ 5 – if its ones digit is either 0 or 5 Example: 487 580 is divisible by 5 because it ends in 0.
➢ 6 – if it is divisible by 2 and 3 Example: 5 652 is even. The sum of its digits is 5 + 6 + 5 + 2 = 18, which is divisible by 3. So, 5 652 is divisible by 6 because it is divisible by both 2 and 3.
[transcriber’s note: the digits that are underlined in the examples above are not marked in this transcription]
CO_Q1_Math5_Module4
➢ 8 – if the number formed by its last three digits is divisible by 8. Example: 913 824 is divisible by 8, because the number formed by its last three digits is 824, which is divisible by 8.
➢ 9 – if the sum of its digits is divisible by 9. Example: 9 684 is divisible by 9 because the sum of all its digits is 9 + 6 + 8 + 4 = 27, and 27 is divisible by 9.
➢ 10 – if its ones digit is zero Example: 850 is divisible by 10 because 850 ends in 0.
➢ 11 – if the difference of the sum of the odd-positioned digits (starting from the left) and the sum of the even-positioned digits (starting from the left) is zero or if it is a multiple of eleven. Examples: 2 376 is divisible by 11, because (2 + 7) – (3 + 6) = 0. 76 813 is divisible by 11, because (7 + 8 + 3) – (6 + 1) = 11, which is a multiple of 11.
➢ 12 – if the sum of its digits is divisible by 3 and the number formed by its last two digits is divisible by 4. Example: 324 is divisible by 12 because the sum of all its digits is 3 + 2 + 4 = 9, which is divisible by 3. Also, the number formed by its last two digits is 24, which is divisible by 4.
Do the activity below:
Directions: Determine whether the given numbers are divisible by the number in each column or not. Put a check (✓) on the appropriate column. Number 1 is already done for you. Use your Math Activity notebook in answering this.
| Number | Divisible by 2 | Divisible by 3 | Divisible by 4 | Divisible by 5 | Divisible by 6 | Divisible by 8 | Divisible by 9 | Divisible by 10 | Divisible by 11 | Divisible by 12 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1) 5 814 | ✓ | ✓ | ✓ | ✓ | ||||||
| 2) 81 235 | ||||||||||
| 3) 3 285 | ||||||||||
| 4) 34 281 | ||||||||||
| 5) 11 255 |
CO_Q1_Math5_Module4
What’s New
Study the problem below
Malopalo Elementary School is set to conduct a tree planting activity on September 1, 2020. All Grade 5 boys are expected to plant 50 seedlings, and the Grade 5 girls are to plant 30 seedlings. They will plant the seedlings in such a way that the trees will grow in equal numbers per row. What is the possible common number of trees in each row?
What Is It
There are two types of word problems you may encounter. It could be:
❖ Routine problems that are useful for daily living; or
❖ Non-routine problems which are mostly concerned with developing mathematical reasoning and fostering an understanding that mathematics is a creative endeavor.
To answer the problem above, we can apply the Polya’s technique in solving word problem:
Using POLYA’S four-step plan
a. Understand: ➢ Know what is asked The common number of trees in each row ➢ Know what are given 50 seedlings of boys 30 seedlings of girls
b. Plan: ➢ Determine the operation/method/procedure to be used Find the common factors by factor tree method
c. Solve:
➢ Use any method to solve the problem Find the common factors of 50 and 30
1) By using Factor Tree technique
[chart: factor trees; unlabeled tree diagrams as printed]
- Tree for 50: 50 → 5 x 10; 10 → 2 x 5
- Tree for 30: 30 → 3 x 10; 10 → 2 x 5
So, the common factors of 50 and 30 are 2, 5, and 10
50 = 2 x 5 x 5 25 x 2 10 x 5 50 x 1
30 = 2 x 3 x 5 15 x 2 5 x 6 10 x 3 30 x 1
2) By listing the factors
50 = 1, 2, 5, 10, 25, 50 30 = 1, 2, 3, 5, 10, 15, 30
[transcriber’s note: in the printed listing, the entries 2, 5, and 10 are enclosed in boxes]
Therefore, the listing method can be used also in getting the common factors of 50 and 30 which are divisible by 2, 5, and 10.
3) The Table Method
[transcriber’s note: the printed table has a spanning header “Can trees be planted equally in a row by” above the columns 2? through 10?]
| Number of Seedlings | 2? | 3? | 4? | 5? | 6? | 8? | 10? |
|---|---|---|---|---|---|---|---|
| 50 for boys | / | x | x | / | X | X | / |
| 30 for girls | / | x | x | / | X | X | / |
Answer: The possible common numbers of trees in each row are 2, 5, and 10.
d. Check and Lookback:
Check if 50 and 30 are divisible by 2, 5, and 10
- 50 ÷ 2 = 25 | 30 ÷ 2 = 15
- 50 ÷ 5 = 10 | 30 ÷ 5 = 6
- 50 ÷ 10 = 5 | 30 ÷ 10 = 3
Let’s have another example.
Delfin is willing to give a reward to whoever guesses his age this year. His clues state that his age is divisible by 12 and is multiple of 9, and that he is less than 51 years old. How old is Delfin?
a. Understand
- What is asked?
The age of Delfin this year - What are given?
Age is divisible by 12
Age is multiple of 9
Age is less than 51
b. Plan
- What strategy can we use to solve this problem?
Since there are just a few numbers less than 51 which are divisible by 12 and 9, we will use Listing Method and Elimination.
c. Solve
Delfin’s age is less than 51, so our range is from 1-50. Listing all numbers divisible by 12 within that range, we have:
12, 24, 36, 48.
Another clue is that, his age is a multiple of 9. Among the four numbers, we can eliminate 12, 24, and 48 because the only number that is multiple of 9 is 36.
Answer: Therefore, Delfin’s age is 36.
d. Check and look back
We will check if our answer satisfies the clues provided by Delfin.
- 36 is divisible by 12
- 36 is a multiple of 9
- 36 is less than 51
Let us have another problem.
The Barangay Youth Officials of Purok SONA are planning to conduct clean-up drive and tree planting in their costal area. There are 125 youths who are officially registered and are requested to participate the said activity. How many groups could there be with equal number of members in a group?
Given: 125 registered youth
Asked: number of group and equal number in each group.
Solution:
125 is divisible by what number? By 2, 3, 4, 5, 6, 8, 9 and 10?
By 2: even and number ending in 0, 2, 4, 6, or 8 ➢ 125 is not divisible by 2.
By 3: if the sum of the digits is divisible by 3. ➢ 1 + 2 + 5 = 8 is not divisible by 3.
By 4: if the last two digits are divisible by 4. ➢ 125 = 25 is not divisible by 4.
By 5: if its ones digit is either 0 or 5. ➢ 125, ones digit is 5, so, 125 is divisible by 5.
Trying 6, 8, 9, 10, 11 and 12 divisibility rules, 125 is only divisible by 5.
Therefore, to answer the problem above:
There will be 5 groups and each group will have 25 youths members to do the tree planting and clean-up drive.
What’s More
Directions: Solve the following problems involving factors, multiples, and divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12.
- Ruben is arranging 648 tiles fitted a bathroom. He wants to put the same number of tiles on each row. How many tiles can Ruben put on each row?
- A. 5
- B. 11
- C. 10
- D. 12
- Tessa is organizing 990 blocks into boxes at the toy store. She needs to put the same number of blocks in each box without any leftover blocks. How many boxes would Tessa use for the blocks?
- A. 4
- B. 10
- C. 12
- D. 8
- Around 420 players joined in the volleyball tournament. Each team should have the same number of players. How many players could there be on a team?
- A. 8
- B. 9
- C. 11
- D. 12
- David’s little sister is playing with blocks. She wants to put all 63 of her blocks into stacks with the same number of blocks in each stack. How many blocks could David’s sister put into a stack?
- A. 4
- B. 6
- C. 9
- D. 10
Non-routine problems can be done without using a standard procedure. They can be solved by drawing a picture, using a number line, acting-out, making a table, and many others.
How many whole numbers among the given numbers are divisible by 2? by 5? by 10?
a. Numbers between 86 236 and 87 000
b. Numbers between 2366 and 8080What is the biggest three-digit multiple of 2 that you can think of that uses the digits 5 and 8? Show your answer using any method.
What is the largest possible five-digit number divisible by 12 that you can make from the digits 1, 2, 3, 5 and one more digit?
What I Have Learned
After going through this module, I have learned that:
Solving word problems involving factors, multiples, and divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12 is done using the 4-step process.
Understand:
- Know what is asked.
- Know the given facts.
- If any, determine the question.
Plan:
- Determine the operation to be used.
- Write the number sentence.
Solve:
- Use the operation in solving
Check and Look Back:
- Write the correct answer.
A. Find out without actual division if the given numbers are divisible by 4 and by 8. Why? Answer using your activity notebook.
Given number:
a) 356 232 b) 541 644 c) 759 326
B. When is a number divisible by 9? Find out if the given numbers below are divisible by 9.
Given:
a) 135 b) 326 c) 7893 d) 346 752
What I Can Do
Directions: Solve the following problems. Use a separate sheet of paper.
- Joseph planted 600 onions equally in 20 rows. How many onions were planted in each row? If Joseph decided to plant at least 10 onions in each row, will it still be distributed equally?
Understand:
Plan:
Solve:
Check and look back:
- Jerry and Henry love playing marbles. Jerry has 60 marbles while Henry has 80 marbles. They plan to keep their marbles in a clay jar. How many possible groups will there be if they are going to put them equally inside the clay jar respectively? Put a star [illustration: star outline placed over the text “clay jar”] if the number is divisible of the given number.
[transcriber’s note: the printed table has a spanning header “Can marbles be put in a clay jar equally by” above the columns 2? through 20?]
| Number of Marbles | 2? | 3? | 4? | 5? | 6? | 8? | 9? | 10? | 11? | 12? | 20? |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Jerry has 60 | |||||||||||
| Henry has 80 |
A number N is less than 100. N is multiple of 3, 4, 5 and 6. N is a factor of 120, and if divided by 7, N leaves a remainder of 4. What is N? You may present your answers using a model or any method.
Arrange the digits 1, 2, 3, 4, 5 and 6 to form a number that is divisible by 6 and satisfies the following conditions:
- When the last digit is removed, it becomes a five-digit number which is divisible by 5.
- When the last digit is removed, it becomes a four-digit number which is divisible by 4.
- When the last digit is removed again, it becomes a three-digit number divisible by 3.
- When the last digit is removed again, it becomes a two-digit number divisible by 2.
Finally, when the last digit is removed, it is a one-digit number divisible by 1. What is the number? Explain your strategy in solving this problem.
Assessment
Directions: Solve the following problems involving factors, multiples, and divisibility rules for 2,3,4,5,6,8,9,10,11, and 12. Write the letter of the correct answers on your answer sheet.
- Ralph needs to set up 20 chairs for a mini concert. He wants to put the same number of chairs in each row with no chairs left. How many chairs could he put in a row?
- A. 9
- B. 3
- C. 6
- D. 5
- Editha wants to arrange 124 roses into vases. How many roses could she put in each vase without having any leftover roses?
- A. 10
- B. 4
- C. 5
- D. 6
- There are 632 guavas in the jars in a pantry. If each jar contains the same number of guavas, how many jars would there be?
- A. 4
- B. 10
- c. 3
- D. 9
- A slipper factory needs to ship an order of 620 pairs. The factory will ship the slippers in several boxes. Each box must contain the same number of pairs of slippers. How many boxes could the factory use for the order?
- A. 6
- B. 9
- C. 10
- D. 3
- A warehouse contains 6 432 boxes of milk, and each row has the same number of boxes. How many rows could there be?
- A. 9
- B. 3
- C. 5
- D. 10
Additional Activities
Direction: Solve the problem below.
Mrs. Velasco plans to arrange 27 boys and 18 girls in rows for her seat plan. She wishes to arrange them in such a way that only boys or girls will be there in a row. Find the common number of students that could be arranged in a row.
Solution to the problem:
Using the four-step plan (Routine)
- a. Understand:
- Know what is asked _____
- Know what is/are given _____
- b. Plan:
- Determine the operation/ method/ procedures to be used
- c. Solve:
- Use the method to solve the problems_____
- d. Check and look back: _____
- a. Understand:
A number n is less than 50. If n is divided by 9, the remainder is 6, and if I divide it by 4, the remainder is 1. Also, if I divide it by 10, the remainder is 3. What is n?
Agatha is trying to find pairs of number that will sum up to a multiple of 11. From the numbers in the grid below, help Agatha find these pairs of numbers.
| 3 | 8 | 14 |
|---|---|---|
| 52 | 36 | 20 |
| 69 | 74 | 47 |
- a) How many pairs of number did you find? What are these? Explain your strategy.
- b) Did you find any number that has no partner?
- c) Did you find any number that could have more than one partner?
- d) What do you think is special about these pairs of numbers? Did you find any pattern? Explain your answer.
Answer Key
What I Know
Using the 4-step plan
Understand:
a. Know what is asked: Common number of small pots.
b. Know what are given: 36 mongo seeds, 33 corn seeds
Plan:
c. Determine the operation/method/procedure to be used: Find the common factors by listing
Solve:
d. Use the method to solve the problem: By listing the factors
33 = 1,3,11,33
36= 1,3,4,6,9,12,36
The common factor of 33 and 36 is 3
Check and Look back
e. Check if the solution is correct
33÷3 = 11 36÷3 = 12
What’s In
5, 814= 2,3,6,9
81,235= 5,11
3,285=3,5,9
34,281=3,9
11,255=5
What I Can Do
Problem 1
Asked: Number of onions planted in a row
Given: 600 onions, 20 rows
Plan: Division
Solution: 600÷ 20= 30
Check: 20 x 30 = 600, therefore, there are 30 onions planted in a row.
Problem 2
Jerry (60) =2,3,4,5,6,10,12,20
Henry (80) =2,4,58[?], 10, 20
Problem 3
Ans. N= 60
Problem 4
Ans. 321654
What I Have Learned
Answer:
A. Divisible by 4 and by 8
a) 356 232 is divisible by 4 and 8
“32, last 2 digits, is divisible by 4
“232, last 3 digits, is divisible by 8
b) 541 644 is divisible by 4 but NOT by 8
c) 759 326 is not divisible both by 4 and by 8.
B. Divisible by 9
The number is divisible by 9 if the sum of its digits is divisible by 9.
a) 135 is divisible by 9
b) 326 is NOT divisible 9
c) 7893 is divisible by 9
d) 346752 is divisible by 9
What’s More
D
B
D
C
Non-routine :
Divisible by 2, 5, 10
- a) Numbers between 2366 and 8080
- Divisible by 2: 2556
- Divisible by 5: 1142
- Divisible by 10: 571
- b) Numbers between 86236 and 87000
- Divisible by 2: 381
- Divisible by 5: 152
- Divisible by 10: 76
- a) Numbers between 2366 and 8080
958
75312
Assessment
D
B
A
C
B
References
University of Cambridge. 2021. Dozens. Accessed July 5, 2021. https://nrich.maths.org/dozens/solution-Non-Routine.
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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