7
MATHEMATICS
First Quarter-Week 8:
Illustrates the Different Subsets of Real Numbers.
Arranges Real Numbers in Increasing or Decreasing
Order and on the Number Line
Project CLEAR
Division of Oriental Mindoro
QUARTER 1
WEEK 8
Subsets of Real Numbers
7
LEARNING COMPETENCIES:
1. Illustrates the different subsets of real numbers
2. Arranges real numbers in increasing and decreasing order
Lesson 1
Quarter 1 – Module 8:
Estimating the Square Roots
of Whole Numbers and
In this lesson, you will learn how to describe and illustrate the real number system; classify
the number by naming set or sets to which it of they belong using Venn diagram.
Plotting Irrational Numbers
Pretest
Directions: Read the statement very carefully. Find the correct answer.
Write the letter on the space provided before each number.
For Questions 1-3, classify the subset of real numbers to which each number belongs.
A.
B.
C.
D.
Rational
Rational, Integer, Whole, Natural
Irrational
Irrational, Whole
____________1. 12
____________ 2.√2
____________ 3.
1
3
____________ 4. Which statement is NOT true?
A. Every counting number is a whole number.
B. Every integer is a rational number
C. Every decimal is an irrational number.
D. Every natural number is a real number.
____________5. Which statement is TRUE?
A. The set of real numbers is a subset of rational numbers.
B. The set of decimal numbers are subset of irrational numbers.
C. The set of whole numbers is subset of integers.
D. The set of irrational numbers are subset of rational numbers.
___________ 6. Which of the following is not a rational number?
A.π
21
B. 7
C.3.14
D.2.15
MATH 7 ORIENTAL MINDORO DIVISION
___________ 7. Which of the following is not an integer?
A. -11
9
C. √49
B. 3
D.-
13
5
___________8. Which of the following is a rational number but not an integer?
A.√16
3
B. - 6
C. -
15
D.-6
3
__________9. Which of the following number is an integer but not a whole number?
A. -7
B. 8
C. -π
D.
16
4
__________10. Which is not an irrational number?
A.√18
B. √121
C. √156
D. √223
Activity 1. Let’s Recall. Complete the table. Round each number to the nearest hundredths.
Square root
√48
√87
√121
√150
√225
Illustrative Examples
Value
Rational or Irrational
Subsets of Real Number
MATH 7 ORIENTAL MINDORO DIVISION
Subsets of the Set of Real Numbers
Natural Numbers - Numbers being use in counting
Whole Numbers – natural numbers along with zero
Integers- natural numbers, their negative numbers and zero make the set of integers
Rational – A number of the form p/q, where p and q are both integers and is not equal to zero.
Irrational Number – Number which cannot be written in the form p/q, where p and q are both integers and q is
not equal to zero.
NUMBER
1. Natural Number
1,5,7
2.
3.
4.
5.
0,10,53
-7, 11
1.3, ½, 1/4
5√23
√23
Whole Number
Integer
Rational
Irrational
Sample
Activity 2. Where do I belong?
Directions: Analyze and classify the real numbers to which subset it belongs.
Use a tick mark (
Number
) to answer.
Whole
Number
Integer
Rational
Irrational
-3
0
𝟒
𝟕
√𝟔𝟒
13
-0.125
√𝟐
e
MATH 7 ORIENTAL MINDORO DIVISION
.50
Directions: Fill in the missing word in the blank. Choose the correct answer from the pool words
in the box below.
Counting
Integers
Rational
1.
2.
3.
4.
5.
Irrational
Whole
___________ is a subset of real numbers that can be positive, negative or zero.
Counting numbers and zero are called ________________numbers.
The set of ___________numbers are cannot be expressed as fraction,
Natural Numbers are also called ______________ numbers.
The subset of _____________numbers include integers, whole and counting numbers.
Write the following numbers below
on the figure at the left. Write each
one of these numbers to its specific
classification.
Assessment
Subsets of a Real Number
1. √2
2. 5.645123874
3.
1
3
3
4. - -4
5. -8
6. -1000
7. √6
8. 2
9. √9
10. 10
11.
12.
4
4
9
2
13. -2
14. 0.2222
15. 0
MATH 7 ORIENTAL MINDORO DIVISION
Additional Activities
A. Classify the different sets of numbers below.
1. -3, -2, -1, 0, 1,2,3
2. √5 ,π
3. 0
4. 0,1,2,3…
5. 1,2,3…
References:
http://www.khanacademy.org/math/pre-algebra/pre-algebra-radicals-square-roots/v/approximating-square-roots
Amid and Tibulan, (2017) Math Time Grade 7, Educational Resources Corporation, Quezon City, Philippines.
Oronce and Mendoza, (2015) E-Math 7, Rex Bookstore, Inc. manila Philippines.
https://www.storyofmathematics.com/types-of-numbers
Answer
Key
Week 8 Lesson 1
Square
root
√48
√87
√121
√150
√225
6.93
9.33
11
12.25
15
Value
Rational or
Irrational
Irrational
Irrational
Rational
Irrational
Rational
Activity 1
What’s in
MATH 7 ORIENTAL MINDORO DIVISION
Activity 2
QUARTER 1
WEEK 8
Subsets of Real Numbers
7
LEARNING COMPETENCIES:
Lesson 2
3. Illustrates the different subsets of real numbers
4. Arranges real numbers in increasing and decreasing order
Quarter 1 – Module 8:
Estimating the Square Roots
of Whole Numbers and
In this lesson, you will learn how arrange real numbers in increasing and decreasing order.
This is a continuation of the concepts on the subsets of real numbers.
Plotting Irrational Numbers
Pretest
Directions: Read the statement very carefully. Find the correct answer.
Write the letter on the space provided before each number.
____________1. Which number is the smallest?
B. 0.33…
A. 2.5
C.√9
D. -3
C.√9
D. -3
____________2. Which number is the greatest?
B. 0.33…
A. 2.5
____________ 3. Which is in order from least to greatest?
1
A. √25 ,4.20, 3 ,-0.66…, -7
1
B. -7, -0.66…, 3 ,4.20, √25
1
C. -0.66…,3 ,-7,4.20, √25
1
D. √25 ,-0.66…,4.20, -7,3
_____________4. Which list shows the numbers in decreasing order.
A.
1
√25 ,4.20, 3 ,-0.66…, -7
1
B. -7,0.66…, ,4.20, √25
3
1
C. -0.66…,3 ,-7,4.20, √25
1
D. √25 ,-0.66…,4.20, -7,
3
____________ 5. Which of the following best represents the arrangement 0f -2.25, -1, 1, 3/2, on
the number line?
MATH 7 ORIENTAL MINDORO DIVISION
Lesson Proper
Review
Activity 1. Let’s Recall. Write T in the blank if the statement is true and write F if the statement is
False.
_________1. All rational numbers are real numbers.
_________2. An irrational Number is always a real number.
_________3. Every whole number is an integer.
_________4. There are no natural number between -5 and 0.
_________5. All repeating decimals are irrational numbers.
_________6. Zero is an integer.
_________7. Every decimal number is an integer.
1
_________8.3 is an irrational number.
_________9. All natural numbers are sometimes positive.
_________10. All real numbers are integers.
In this lesson, your previous knowledge about rational numbers from one part to
another, particularly changing rational numbers to decimal from. Exercises will help the learners
to master how to arrange real numbers from least to greatest and vice versa.
Activity 2. Let’s Travel.
Ben travelled 4 km from their school to the left (0 being the place of origin) and Chad
did the same but travelled 2 km longer than Ben. On the other hand, Kent travelled to the right
starting from the same origin with the distance of 3 km. Place those people on the number line
to find their position from the place of origin.
MATH 7 ORIENTAL MINDORO DIVISION
Arranging real numbers in increasing and
decreasing order.
Illustrative Examples
1. Arrange 2.55…,√9,
15
11
4
5
,-
in ascending order and plot the numbers on a number
line.
Solution:
Step 1. Change the following numbers to decimals:
2.555= 2.56 (Round off to the nearest hundredths)
√9
= 3
𝟏𝟓
=
𝟒
-
𝟏𝟏
𝟓
3.75
= -2.2
Step 2. Arrange from least to greatest
-
𝟏𝟏
𝟓
, 𝟐. 𝟓𝟓 … , √𝟗,
𝟏𝟓
𝟒
Step 3. Plot the points on the number line.
5
2. Which is the largest:√4, − 2 , ¾, - 0.30?
Solution:
Step 1. Change the following numbers to decimals:
= 2
√4
-
𝟓
𝟐
= -2.5
¾ = 0.75
MATH 7 ORIENTAL MINDORO DIVISION
-0.30
Step 2. Arrange from greatest to least
𝟓
√4 , ¾, -0.30, - 𝟐,
Step 3. Therefore, the largest value is √4 .
Activity 3. Least or Greatest?
Directions. Compare the following real numbers. Write the right symbol <, > or =
in the blanks to make the statement true. Use your activity notebook, show your
solution.
1. 7/3 _________9/2.
2. -1.23 _______-5/2
3. √121 ________18
4. 0.57
_________7/9
5. −11/4___________ − 2
Directions: Fill in the blanks to make the statement TRUE.
1. The figure
is called _____________.
2. When ordering set of real number from _____________ to ____________, follow the
order on the number line from left to right.
3. When ordering set of real number from _____________ to ____________, follow the
order on the number line from right to left.
4. To arrange real numbers in ascending or descending order, the first step it to change
the number to _______ form.
Arranging real numbers in ascending and descending order.
Assessment
Directions: Arrange the following sets of real numbers in descending order and plot them on the number line.
2
1. -3.45, 0.98,√16, -5/2
3. -2/5,
, 5.72, -1.23
2. 4.26, -√9, 0.15, -1.11
4. 5/2, 3,11/5, 2.8, 13/4
√4
Additional Activities
MATH 7 ORIENTAL MINDORO DIVISION
Applying the learnings in arranging sets of real numbers in ascending and descending order in the
actual context is exciting. Let us try this in real world.
Four people have tried to find the length of burb wire used by the owner to surround his farm in Nagiba 1, Naujan. Since these four people used different ways to determine its lengths, their findings are also different.
Among the four, who got the longest lengths? Show your solution in your activity notebook.
Name
Findings (has)
Nathan
√16
Clod
4.10
Bjay
15/4
Walter
21/5
References:
http://www.khanacademy.org/math/pre-algebra/pre-algebra-radicals-square-roots/v/approximating-square-roots
Amid and Tibulan, (2017) Math Time Grade 7, Educational Resources Corporation, Quezon City, Philippines.
Oronce and Mendoza, (2015) E-Math 7, Rex Bookstore, Inc. Manila Philippines.
https://www.storyofmathematics.com/types-of-numbers
Prepared by : EMELYN M. ARANAS
HT-IV Naujan Municipal High School
Answer
Key
5.
Walter – 4.2 has.
Answer:
Additional Activities:
Week 8 Lesson 2
6. D
7. C
8. B
9. A
10.
Pre -test
4. 11/5, 5/2, 2.8, 3,
13/4
D
√
Activity
What’s in
MATH 7 ORIENTAL MINDORO DIVISION
1. -3.45, -5/2, 0.98,√16
2. -√9 ,-1.11,0.15,4.26
2
3. -1.23, -2.5, 4 , 5.72
Assessment