This is the Mathematics 6 Quarter 2 Module 8 self-learning module, “Describing the Set of Integers,” from DepEd Region VI’s Alternative Delivery Mode series (First Edition, 2020). It is for Grade 6 learners studying at home or in class, and for the teachers and parents who guide them. After this module, learners can tell positive integers, negative integers, and zero apart, place them on a number line, and write an integer for everyday situations such as deposits, withdrawals, temperatures, and weight gain or loss.
What learners will learn
After going through this module, learners are expected to:
- identify and describe the set of integers using real-life situations through a number line; and
- illustrate real-life situations involving integers using number lines.
The module has one lesson: Lesson 1 – Describing and Identifying the Set of Integers.
Key ideas: positive, negative, and zero
The lesson starts with temperatures. In the What’s New part, Vienne watches a weather report that shows temperatures around the world, such as Japan at -4 °C, Mongolia at -1 °C, Saskatoon at +2 °C, and Baguio at +12 °C. The module explains that a thermometer is like a vertical number line. You can also turn it sideways into a horizontal number line, with zero in the middle.
On the number line:
- Positive integers are to the right of zero. Their value is greater than zero. They are written with a plus sign, for example +6 (positive six).
- Negative integers are to the left of zero. Their value is less than zero. They are written with a minus sign, for example -6 (negative six).
- Zero has no sign. It is neutral, neither positive nor negative.
- Positive numbers, zero, and negative numbers together make up the set of integers.
Because the plus and minus signs are also used for adding and subtracting, the module suggests raising the sign slightly when writing integers, especially when working on integer operations, to avoid confusion.
Opposites
If you fold the number line at zero, -6 lands exactly on +6. These are called mirror images, or opposites. Opposites are on different sides of zero but are the same distance from it. Every integer has an opposite.
Moving along the number line
The module shows how to count units from a point:
- The integer 7 units to the left of 0 is -7.
- The integer 4 units to the right of +6 is +10.
Key ideas: integers in real life
The module teaches learners to look for clue words. Words like “above” and “northward” suggest an increasing value, so they point to positive integers. Words like “loss,” “down,” and “spent” suggest a decreasing value, so they point to negative integers.
| Situation from the module | Integer |
|---|---|
| The pole stands 25 feet above the ground. | +25 |
| Glenn has a weight loss of 2 kilograms. | -2 |
| The car slid 100 meters down the hill. | -100 |
| Eden drives 60 kilometers northward. | +60 |
| I spent ₱220.00 for fruits. | -220 |
The activities use the same idea with money (deposits and withdrawals), distance (east, upstream, below sea level), temperature, weight, and quiz points.
Parts of the module
- What I Need to Know: the objectives.
- What I Know: a 10-item pretest on describing sets of integers and writing integers for situations.
- What’s In: drawing thermometers to show the freezing point, boiling point, and normal body temperature, plus temperatures below them.
- What’s New and What is It: the weather report story and the discussion of integers, opposites, and clue words.
- What’s More: writing the integer that matches labeled points on a number line.
- What I Have Learned: a summary of the main ideas.
- What I Can Do: finding integers by counting units on a number line, including the integer halfway between +14 and -2.
- Assessment: a 10-item post-test.
- Additional Activities: plotting 10 real-life situations on a number line.
- Answer Key: answers for all tests and activities.
How to use this module
- Learners: Start with the What I Know pretest to see what you already know. Then go through the parts in order and finish with the Assessment. Write all your answers on a separate sheet of paper and do not mark the module. Check your work with the answer key only after answering, and be honest when you use it.
- Parents: Help your child connect the lesson to home life, such as reading a thermometer or talking about money saved and spent. Encourage your child to ask the teacher or facilitator when a task is hard.
- Teachers: Use the pretest to decide who needs extra help. The Assessment and Additional Activities give ready material for checking whether learners can describe integers and show them on a number line.
Frequently asked questions
What grade and quarter is this integers module for?
It is for Grade 6 Mathematics, Quarter 2, Module 8. Its title is Describing the Set of Integers.
What is the set of integers?
The set of integers is made up of positive numbers, zero, and negative numbers. Positive integers are to the right of zero on a number line, and negative integers are to the left.
Is zero positive or negative?
Neither. The module explains that zero has no sign, so it is neutral.
What are opposite integers?
Opposites are two integers that are the same distance from zero but on different sides of it, such as -6 and +6. Every integer has an opposite.
Does the module have an answer key?
Yes. The answer key covers the pretest, What’s In, What’s More, What I Can Do, the Assessment, and the Additional Activities.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 2 – Module 8 : Describing the Set of Integers
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[illustration: students learning in a classroom, outdoors, and at home, with a globe and a lantern]
CO_Q2_Mathematics6_Module8
Mathematics– Grade 6 Alternative Delivery Mode Quarter 2 – Module 8: Describing Set of Integers First Edition, 2020
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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
Printed in the Philippines by ________________________
Department of Education – Region VI
Office Address: Duran Street, Iloilo City_________________________
Telefax: (033)336-2816, (033)509-7653___________________ E-mail Address: region6@deped.gov.ph_________________________
Development Team of the Module
Author: Lalyn Galon Lumandog
Editors: Rebecca Billones and Collin G. Sales
Reviewers: Elleda Ebreo De la Cruz, Rosemarie Dicen Aclan and Collin G. Sales
Illustrator: Lalyn Galon Lumandog
Layout Artist: Felizardo S. Valdez III
Management Team: Ramir B.Uytico Pedro T. Escobarte, Jr. Elena P. Gonzaga Donald T. Genine Ma. Roselyn J. Palcat Nordy D. Siason, Jr. Rowena S. Carillo Rosemarie D. Aclan Arthur J. Cotimo Felizardo S. Valdez III Marve E. Gelera
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Mathematics
Quarter 2 – Module 8 : Describing the Set of Integers
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CO_Q2_Mathematics6_Module8
What I Need to Know
This module was designed and written with you in mind. It is here to help you understand the concept of integers. The scope of this module allows you to use it in many different learning situations. The language used recognizes your diverse vocabulary level.
The module contains a lesson on describing the set of integers and identifying real-life situations that make use of it.
After going through this module, you are expected to:
- identify and describe the set of integers using real-life situations through a number line; and,
- illustrate real-life situations involving integers using number lines.
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CO_Q2_Mathematics6_Module8
What I Know
A. Choose which one best describes the given set of integers. Write the letter of the correct answer on your answer sheet.
{ -1, -5, -3, -28, -7 }
A. set of negative integers
B. set of positive integers
C. set of positive and negative integers
D. set of odd negative integers{ +16, +14, +12, +10, +8 }
A. set of positive integers in increasing order
B. set of positive integers decreased by 2
C. set of negative integers
D. set of positive odd integers{ -24, -6, -18, -2, -20}
A. set of even numbers
B. set of even positive integers
C. set of even negative integers
D. set of decreasing even positive integers{ -15, -5, -3, -7, -13)
A. set of odd positive integers
B. set of even positive numbers
C. set of odd negative integers
D. set of even negative integers{ -3, +3, -2, +2, -1, +1, }
A. set of negative integers
B. set of positive integers
C. set of equal integers
D. set of opposite integers
B. Write an integer to describe each situation. Do this on your answer sheet.
- Prince deposited ₱186.00 in his Aflatoun account.
- The delegates are moving 3 kilometers east.
- Evelyn is gaining 9-kilogram weight.
- A withdrawal of ₱1 500.00 was made by Darnelle from her bank account.
- Loren has a fever. His body temperature is 39◦C.
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CO_Q2_Mathematics6_Module8
Lesson 1 – Describing and Identifying the Set of Integers
Being one of the essentials in our lives, we need to get a deeper understanding of numbers. A number can be a whole number, a fraction, or a decimal. But there are quantities that can be best represented by the kind of numbers other than what we have already known. These numbers are what we call integers.
What’s In
Draw a thermometer for each item on your answer sheet. Then show the given temperature on each thermometer.
[illustration: five blank thermometer scales, each marked in °C from -20 to 100]
_______ 2) _______ 3) _______ 4) _______ 5) _______
Freezing point of water
Boiling point of water
Normal body temperature
41 degrees below normal body temperature
8 degrees below freezing point
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What’s New
Vienne is watching international news on TV. At the end of the weather report, the atmospheric temperatures of various places around the world are shown as follows:
| Place | Temperature |
|---|---|
| Japan | -4 °C |
| Saskatoon | +2 °C |
| New York | +7 °C |
| China | -3 °C |
| Mongolia | -1 °C |
| Afghanistan | +6 °C |
| Korea | -6 °C |
| Baguio | +12 °C |
Now, Vienne is thinking about what these numbers mean. Can you help her?
What is It
These temperatures, when plotted in a thermometer, can be seen as follows.
[chart: thermometer diagram; temperatures plotted on a vertical thermometer scale from -20 to 100 °C]
| Label | Temperature |
|---|---|
| New York | +7 °C |
| Saskatoon | +2 °C |
| China | -3 °C |
| Japan | -4 °C |
| Baguio | +12 °C |
| Afganistan | +6 °C |
| Mongolia | -1 °C |
| South Korea | -6 °C |
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We can think of a thermometer as a vertical number line. We can also represent this number line horizontally.
(-4, +2, +7, -3, -1, +6, -6, +12)
[chart: horizontal number line; integers from -12 to +12 marked, with 0 labeled Neutral, negative numbers to the left and positive numbers to the right]
Negative Numbers | Neutral | Positive Numbers
Numbers found on the right of zero are called positive numbers. Their value is greater than zero. Positive numbers are also called positive integers. Positive integers are written with a plus sign just like in addition. So, in order to avoid confusion between the two uses of this symbol, raise the plus sign to indicate positive integers especially when working on integer operations.
Example:
+6 → positive six
+1 → negative oneNotice that numbers found on the left of zero are called negative numbers. It means that their value is less than zero. Negative numbers are also called negative integers. Negative integers are written with a minus sign just like in subtraction. So, in order to avoid confusion between the two uses of this symbol, raise the minus sign to indicate negative integers especially when working on integer operations.
Example:
-6 → negative six
-1 → negative oneNotice also that zero has no sign. So the integer zero is neutral. It is neither positive nor negative.
Positive numbers together with zero and negative numbers are called set of integers
- What integer is 7 units to the left of 0? (Ans. -7)
- Name the integer that is 4 units to the right of +6. (Ans. +10)
[transcriber’s note: the heading for this page’s content appears on page 8, which is transcribed separately.]
[chart: number line; labels “opposites” (arrows pointing to -6 and +6), “-6”, “-4”, “-3”, “-1”, “0”, “+2”, “+6”, “+7”, “+12”, “Negative Integers” (bracket under the left side), “Positive Integers” (bracket under the right side), “Neutral” (arrow pointing down to 0)]
Now, consider folding the number line at point zero.
• You will notice that -6 will fall exactly from the reference point as with +6. They are called mirror images or opposites. They are found on the opposite sides of the number line, and having equal distance from zero. Any integer has its opposite.
Here are more examples for you to study:
Use a number line to identify integers being described in the following situations.
- The pole stands 25 feet above the ground. (Ans. +25)
- Glenn has a weight loss of 2 kilograms. (Ans. -2)
- The car slid 100 meters down the hill. (Ans. -100)
- Eden drives 60 kilometers northward. (Ans. +60)
- I spent ₱220.00 for fruits. (Ans. -220)
Remember:
- The words “above” and “northward” suggest an increasing value of a number. Hence, referring to positive value or what we call positive integers.
- The words “loss”, “down”, and “spent” suggest a decreasing value of a number. Hence, referring to negative value or what we call negative integers.
What’s More
A. Write the integer that matches each point.
[chart: number line; points labeled A, B, C, D, E, with 0 marked at the center; no values are printed on the chart]
- A
- B
- C
- D
- E
What I Have Learned
- Positive and negative numbers and zero are called integers.
- Zero is neutral. It is neither positive nor negative.
- Positive integers are found to the right of zero in a number line. It means that their value are greater than zero.
- Negative integers are found to the left of zero in a number line. It means that their value are less than zero.
- Two integers are opposites of each other if each has the same distance from zero. One is positive while the other is negative.
What I Can Do
Use a number line to identify the integers being described.
- An integer that is 8 units to the right of -5.
- What integer is 10 units to the left of +4?
- 15 units to the right of 0
- 7 units to the right of -19
- An integer that is halfway between +14 and -2 on a number line.
Assessment
A. Identify what is referred to in the following items. Write the letter of the correct answer on your answer sheet.
These numbers are found on the right of zero and whose values are greater than zero.
- A. integers
- B. positive integers
- C. negative integers
- D. neutral
These integers are written with a minus sign just like in subtraction.
- A. integers
- B. positive integers
- C. negative integers
- D. neutral
They are called mirror images and having equal distance from zero.
- A. plus sign
- B. neutral
- C. integers
- D. opposites
It is neither positive nor negative.
- A. zero
- B. integers
- C. opposites
- D. number line
They are the positive and negative numbers and zero.
- A. plus sign
- B. neutral
- C. integers
- D. opposites
B. Write an integer to describe each situation. Do this on your answer sheet.
- withdrew ₱20 000.00 from her savings account
- absent from school for 15 days
- received ₱50 000.00
- spent a total of ₱10 000.00 for medicine
- a gain of 7 kg
Additional Activities
Plot on the number line the integer described in each of the following situations. Do it on your answer sheet.
- a temperature decreased by 6°C
- lost 4 kilograms after getting sick
- going 18-kilometer elevation upstream
- move 3 steps backward
- consumed 30 liters of fuel
- temperature reading of 99°C
- an additional of 15 points in Math quiz
- walk 7 kilometers down the valley
- 42 feet below sea level
- stands at approximately 35 meters east
[transcriber’s note: this page is printed upside down (rotated 180 degrees). The text below is transcribed in reading order after rotation.]
Answer Key
[illustration: thermometer diagram with arrows labeling readings; labels “1) 0°C”, “2) 100°C”, “3) 37°C”, “4) -4°C”, “5) -8°C”]
[chart: number line; labels from -12 to +15 with points marked; printed values: “-12”, “-6”, “+3”, “+6”, “+15”]
[chart: number line; scale labeled with values from -100 to 100 and marked points; the labels on the scale are small and not fully legible]
What I Know
A.
- a
- b
- c
- c
- d
- +186
- +3
- +9
- -1 500
- +39
What’s In
- 0°C
- 100°C
- 37°C
- -4°C
- -8°C
What’s More
- -9
- -4
- +1
- +7
- +11
Assessment
A.
- b
- c
- d
- a
- c
B. 6) -20 000 7) -15 8) +50 000 9) -10 000 10) +7
What I Can Do
- +3
- -6
- +15
- -12
- +6
Additional Activities
- -6
- -4
- +18
- -3
- -30
- +99
- +15
- -7
- -42
- +35
References
- Bureau of Elementary Education, Department of Education 2010, Lesson Guide in Elementary Mathematics 6, Book Media Press, Inc., 353-356
- Department of Education 2016, 21st Century MATHletes 6, Book Media Press Inc., 144-151
- DepEd Most Essential Learning Competencies (MELC) in Mathematics 6
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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