This is the Grade 6 Mathematics Self-Learning Module (SLM) for Quarter 2, Module 9: Comparing Integers with Whole Numbers, Fractions, and Decimals. It was developed by DepEd Region VI under the Alternative Delivery Mode (First Edition, 2020). It helps learners study at home and use a number line to decide which of two numbers is greater or less.
What learners will learn
The module covers the competency comparing integers with whole numbers, fractions, and decimals (M6NS-IIg-152). After working through it, learners are expected to:
- identify positive and negative integers;
- compare integers with other numbers such as whole numbers, fractions, and decimals; and
- use a number line to compare integers with whole numbers, fractions, and decimals.
Key idea: the number to the right is greater
The module builds on the previous lesson, where learners described the set of integers and used integers for real-life situations. For example, “May gained 2 pounds” is +2, and “Jean withdrew P1 500.00” is -1 500.
The main rule is simple: when you compare an integer with a whole number, fraction, or decimal, the number farther to the right on the number line has the greater value.
The module introduces this through a Math Camp challenge. Gia and her team must compare -2 with the numbers 2, 0.5, and 1 1/4. When all four numbers are plotted on the number line, -2 sits to the left of each of the others, so:
| Comparison | Reason | Result |
|---|---|---|
| -2 and the whole number 2 | -2 is to the left of 2 | -2 < 2 |
| -2 and the decimal 0.5 | -2 is to the left of 0.5 | -2 < 0.5 |
| -2 and the mixed number 1 1/4 | -2 is to the left of 1 1/4 | -2 < 1 1/4 |
A second example plots -4, -3, -2.5, 1, and 1 3/4. It shows that 1 < 1 3/4 and that -3 < -2.5. Among negative numbers, the one closer to zero is greater.
Terms to remember
- Integers: positive whole numbers, their negatives, and zero. Negative integers are to the left of zero and positive integers are to the right.
- Whole numbers: the positive integers and 0. They have no fractional or decimal part and no negatives.
- Fractions and decimals: numbers found between integers, such as 0.5 between 0 and 1.
- Relation symbols: > (greater than), < (less than), and = (equal to).
The module also includes cases that are easy to get wrong. One asks how 15 compares with +15 (they are equal). Another compares 0.5 with 1/2 (also equal). Others compare -15 with -15.5, or -5 with -5.8.
How to use this module
The module follows the usual SLM parts, in this order:
- What I Know: a 10-item pretest. Part A compares pairs with <, >, or =. Part B uses a number line.
- What’s In: a review that asks you to write an integer for each real-life situation.
- What’s New and What is It: the Math Camp challenge and the worked examples on the number line.
- What’s More: five practice pairs to compare.
- What I Have Learned: a short summary of the rule.
- What I Can Do: ten items using symbols and short word questions.
- Assessment: a 10-item posttest. Part A asks you to plot pairs on a number line, and Part B is multiple choice.
- Additional Activities: plot eight numbers (-3.5, 9, -3 1/2, 0.5, -4, 2, 0, 7 1/4), then write and compare five pairs.
Learners: Write all answers on a separate answer sheet, not on the module. Draw a number line whenever you are unsure which number is farther to the right. Check your work with the answer key at the end only after you finish each part.
Parents: Ask your child to explain why one number is greater by pointing to its place on a number line.
Teachers: The answer key covers What’s In, What I Know, What’s More, What I Can Do, the Assessment, and possible answers for Additional Activities. Review it against the items before giving it to learners, because a few keyed answers do not appear to match the questions as printed.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 6 Mathematics, Quarter 2, Module 9. It was developed by DepEd Region VI as a First Edition, 2020 Alternative Delivery Mode module.
What competency does this module cover?
It covers comparing integers with whole numbers, fractions, and decimals, with the competency code M6NS-IIg-152.
How do you compare an integer with a fraction or decimal?
Plot both numbers on a number line. The number farther to the right has the greater value, so -2 < 0.5 because -2 is to the left of 0.5.
Does the module have an answer key?
Yes. The last pages have answers for What’s In, What I Know, What’s More, What I Can Do, the Assessment, and possible answers for the Additional Activities.
What are whole numbers according to the module?
Whole numbers are the positive integers and 0. They have no fractional or decimal part and no negatives.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 2 – Module 9: Comparing Integers with Whole Numbers, Fractions, and Decimals
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[illustration: students reading and working with a teacher under a tree, with a globe and a lamp]
CO_Q2_Mathematics6_Module9
Mathematics – Grade 6 Alternative Delivery Mode Quarter 2 – Module 9: Comparing Integers with Whole Numbers, Fractions, and Decimals First Edition, 2020
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Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Printed in the Philippines by _____________________
Development Team of the Module
Authors: Collin G. Sales, Marilou G. Dormis, and Arlie V. Ferraro Editors: Rebecca O. Billones, Ma. Portia G. Galanto and Collin G. Sales Reviewers: Rosemarie D. Aclan and Collin G. Sales Illustrator: Marilou G. Dormis 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
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
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Mathematics
Quarter 2 – Module : Comparing Integers with Whole Numbers, Fractions, and Decimals
What I Need to Know
This module was designed and written with you in mind. It is here to help you master comparing integers with whole numbers, fractions and decimals. The scope of this module permits it to be used in many different learning situations. The language used recognizes your vocabulary level. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using.
The module contains lesson on comparing integers with whole numbers, fractions, and decimals (M6NS-IIg-152)
After going through this module, you are expected to:
- identify positive and negative integers;
- compare integers with other numbers such as whole numbers, fractions, and decimals; and,
- use a number line to compare integers with whole numbers, fractions, and decimals.
What I Know
A. Below are pair of numbers to be compared. Use the following relational symbols <, >, or =. Write your answers on your answer sheet.
- 25 _____ 0.25
- 7 _____ 1.5
- -1 _____ 5/8
- +98 _____ 7 1/8
- 27 _____ -29.16
What I Know (continued)
B. Use the number line to compare the numbers below.
[chart: number line; labels from -8 to +8 on the axis, with plotted points labeled -6, -4, -3, -2, 1/2, +2, +3, 4.25, 5 1/2, and 7]
- Which is greater, -2 or 7? _____
- Which is greater, 1/2 or +3? _____
- Which is greater, -6 or 4.25? _____
- Which is lesser, 2 or -4? _____
- Which is lesser, 5 1/2 or -6? _____
Lesson 1: Comparing Integers with Whole Numbers, Fractions, and Decimals
You have learned how to describe the set of integers and identify real-life situations that make use of integers in the past lesson. Now, you will learn how to compare integers with other numbers such as whole numbers, fractions and decimals.
What’s In
Read the given situations below. Write an integer to represent each situation on your answer sheet.
- May gained 2 pounds after a month of taking food supplement.
- Ann moves 4 steps backward as she dances.
- Mr. Cruz deposited P2 000.00.
- Ray stretches his arms 10 cm. upward to reach the fruit of the guava tree.
- Jean withdrew the amount of P1 500.00 from her savings account.
What’s New
During the Math Camp, Gia and her team is going to solve a challenge. Their task is to compare -2 with the numbers given below:
{2, 0.5, 1 1/4}
If you are a member of the team, how would you compare the given numbers?
What is It
When comparing integers with whole numbers, fractions, and decimals, the one that is on the right direction of the number line has greater value.
Study the following.
Let us plot the numbers (-2, 2, 0.5, 1 1/4) on the number line.
[chart: number line; plot of -2, 2, 0.5, and 1 1/4. Labels: Negative Integers (left of zero), zero, Positive Integers (right of zero), Whole Numbers (zero and to the right). Axis labels: -4, -3, -2, -1, 0, +1, +2, +3, +4. Points labeled 0.5 and 1 1/4 lie between 0 and +2; the points -2 and 2 are plotted on the line.]
A. Compare the integer -2 and the whole number 2. Since -2 can be found to the left of 2; therefore, -2 is less than 2. Let us use a relation symbol to compare the two numbers. -2 < 2
B. Compare the integer -2 and the decimal number 0.5. Since -2 can be found to the left of 0.5; therefore, -2 is less than 0.5. Let us use a relation symbol to compare the two numbers. -2 < 0.5
C. Compare the integer -2 and the mixed number 1 1/4. Since -2 can be found to the left of 1 1/4; therefore, -2 is less than 1 1/4. Let us use a relation symbol to compare the two numbers. -2 < 1 1/4
What is It (continued)
Here is another example:
Plot the following numbers on the number line and study how the pair of numbers are compared. (-4, -2.5, 1, 1 3/4, -3)
[chart: number line; points plotted and labeled -4, -3, -2.5, 1, and 1 3/4. Axis labels: -4, -3, -2, -1, 0, 1, 2, 3, 4.]
A. 2.5 _____ -4 B. 1 _____ 1 3/4 C. 3 _____ -2.5
Answer: A. 2.5 > -4 B. 1 < 1 3/4 C. -3 < -2.5
What’s More
Below are pair of numbers for you to compare. Choose the appropriate relation symbol >, <, = to make the expression true.
- +9 _____ 1/2
- 0.36 _____ -6
- 1/3 _____ +2
- 0 _____ -9
- -5 _____ -5.8
What I Have Learned
You can use a number line to compare integers with whole numbers, fractions and decimals.
Whole numbers are set of positive integers and 0. Whole numbers have no fractional or decimal part, and no negatives.
Fractions and decimals are found between integers and whole numbers.
When comparing integers with whole numbers, fractions, and decimals, the one that is farther to the right on the number line has greater value.
What I Can Do
A. Write >, <, = on the blank to make each expression true. Write your answer on your answer sheet.
- -5 _____ 10
- +9 _____ 1/8
- -7 _____ 0.7
- -15 _____ -15.5
- 0.5 _____ 1/2
B. Read carefully each situation and write the correct answer on your answer sheet.
- In a number line, Jean plotted 0.15 and -15. Which is higher?
- Which is lower, -2 or 3/4?
- How would you compare 15 and +15?
- Which is greater, 0.7 or +1?
- Which is lesser, 1 or 0.25?
Assessment
A. Plot the following pair of numbers below on the number line. Write >, < or = to make each mathematical statement true. Write your answer on your answer sheet.
- -1.5 _____ +5
- -7 _____ -1.5
- 12/17 _____ -6
- +9 _____ -4.7
- +27 _____ 29.16
B. Read and answer the questions below. Write the letter of the correct answer on your answer sheet.
Which of the following statements is true?
a. -15 > 3/4
b. 1.4 < -24
c. -8 = 8
d. +15 > -12Mrs. Reyes wrote the integer -33 on the board. Which of the following is less than the given integer?
a. 0
b. 1/3
c. -35
d. 1.2Compare: -8 __ 10
a. greater than
b. neither
c. less than
d. equal toWhich of the mathematical statements below shows the correct comparison?
a. 4 < -3
b. 12 = +12
c. -6 > 1.2
d. -27 > 5/6The following mathematical statements are true except one. Which one is it?
a. -12 > 11
b. -2 < 1/4
c. 4.5 > +4
d. 9 > -9
Additional Activities
Plot the numbers (-3.5, 9, -3 1/2, 0.5, -4, 2, 0, 7 1/4) on the number line. Give five pairs of numbers and compare them using the relation symbols >, <, =.
[chart: number line; no labels printed]
Answer Key
Answer key, first table
| What’s In | What I Can Do | Additional Activities |
|---|---|---|
| 1) +2 2) -4 3) +2 000 4) -10 5) -1 500 | A. 1) < 2) > 3) < 4) > 5) = B. 6) 0.15 7) -2 8) equal 9) < 10) > | Possible Answers 1) -3.5 < 9 [transcriber’s note: symbols in this key were read from a rotated image; check against the original] 2) 0.5 > -4 3) 2 > 0 4) -3.5 = -3 1/2 5) -4 < -3 1/2 |
Answer key, second table
| What I Know | What’s More | Assessment |
|---|---|---|
| A. 1) B 2) A 3) B 4) A 5) C B. 6) -4 7) -1 8) +3 9) -5 10) +5 | 1) > 2) > 3) < 4) > 5) > | A. 1) < 2) < 3) > 4) > 5) < B. 6) D 7) C 8) C 9) B 10) A |
References
Most Essential Learning Competencies (MELCs) in Mathematics 6
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