This document provides a lesson on solving problems involving percentages, rates, and bases. The objective is for students to learn to solve such problems. The lesson includes examples of percentage problems where students must find the percentage, rate, or base given various amounts of information. It also includes exercises for students to practice these skills and assessments to check their understanding.
5. Reading
drill
THE ENCHANTED DEER
Once there were two warring tribes whose
kingdoms were divided only by a wide river.
The king on the land north of the river had a
beautiful daughter named Mayumi; while the
king on the land south of the river had a
brave handsome son named Bayani.
6. Both kings hated each other so much
that they even wanted their children to hate
each other, too.
But fate played a trick on them. Mayumi
and Bayani felt so madly in love with each
other that they defied their parents wish.
They often met secretly in the nearby
forest.
7. One early morning, Mayumi went to meet Bayani
in the forest. She had some enchanted power, so
she changed herself into a deer. She did not want
anybody to see her.
Bayani waited for her. When he saw the deer, he
was attracted to it. He quickly shot an arrow not
knowing it was Mayumi.
The deer fell bleeding. Bayani ran to see his prize,
but he saw Mayumi instead. He wept and, in his
grief, he stabbed himself to death.
9. Whats your target score in a 20-
item test? What is the passing
score?
10. Pablo listens very well to the teacher
during the discussion of the lesson.
When they were given a 5-item test
his grade was 80%. How many
correct answers did Pablo get?
PROBLEM OPENER
11. Processing Questions:
a. Who listens very well to the teacher?
b. How many items was their test?
c. What was his grade in the test?
d. If you were Pablo, will you also be listening
intently to the teacher? Why?
e. Do you think you can get a higher grade than
Pablo? Why do you think that you can get a
higher grade than Pablo?
14. Solve for the percentage.
a. 36% of 95 is N.
b. 48% of 290 is what number?
c. N is 20% of 8?
d. What is 20% of 8?
e. 60% of 80 is _____.
EXERCISE 1
15. a.There are 40 pupils in a class.
Seventy-five percent of them are
present. How many are present?
How many are absent?
PAIR-SHARE
16. PAIR-SHARE
b. Rhodas allowance for the day is P250. She
spends 80% of it and saves the rest. How
much does she spend? How much does she
save?
17. What have you learned?
How do you find the percentage
when the rate and base are
given?
18. A S S E S S M E N T
Answer the following:
1.What is 25% of 4?
2. _____ is 10% of P1,000,000.
3. N is 50% of 2.
4. What number is 1% of P1,000.
5. 200% of 3 is what number?
19. A S S I G N M E N T
Complete the table.
BASE RATE PERCENTAGE
1. 30 10%
2. 50 60%
3. 60 30%
4. 180 150%
5. 200 75%
23. Reading
drill
THE ENCHANTED DEER
Once there were two warring tribes whose
kingdoms were divided only by a wide river.
The king on the land north of the river had a
beautiful daughter named Mayumi; while the
king on the land south of the river had a
brave handsome son named Bayani.
24. Both kings hated each other so much
that they even wanted their children to hate
each other, too.
But fate played a trick on them. Mayumi
and Bayani felt so madly in love with each
other that they defied their parents wish.
They often met secretly in the nearby
forest.
25. One early morning, Mayumi went to meet Bayani
in the forest. She had some enchanted power, so
she changed herself into a deer. She did not want
anybody to see her.
Bayani waited for her. When he saw the deer, he
was attracted to it. He quickly shot an arrow not
knowing it was Mayumi.
The deer fell bleeding. Bayani ran to see his prize,
but he saw Mayumi instead. He wept and, in his
grief, he stabbed himself to death.
26. KING BACK
L
Activity
Naming the Baby
Using your show-me-board, write the answer to
the following:
a. 2:8 in percent is _____.
b. 0.35 in percent is ______.
c. 遜 in decimal is ______.
27. Do you use the front and back
pages of your notebook? Why?
28. Sixto, a grade six pupil, has 24 sheets
of art paper for his project in Math. If
6 sheets of art paper were used by
Sixto, what percent of the sheets of
art paper did he use?
PROBLEM OPENER
29. Processing Questions:
a) Who uses art paper for Math project?
b) How many sheets of art paper does he have?
c)How many sheets of art paper did he use?
d)If you were Sixto, will you be using all the sheets of
art paper and ask some more? Why?
e) Will you do what Sixto has done if you were him?
Why?
30. Analyze the problem.
a) What does the problem want you to solve
for?
b) What are the given data?
c) What are the needed data?
d) Determine the base and percentage in the
Techans Triangle.
e)What will you do to find the answer?
32. Solve for the percentage.
a. 24 is what percent of 120?
b. What percent of 120 is 24?
c. 24 is ____% of 120.
d. 24 is N% of 120.
e. ___% of 120 = 24.
EXERCISE 1
33. 1.)What percent of 105 is 35?
2.)72 is what percent of 144?
3.)N% of 56 is 7
4.)24 is N% of 120
5.)2.5 is what percent of 75?
Brother and sister technique:
34. b. Read, analyze and solve.
1.In a class of 50 pupils, 24 are boys. What
percent of the class are boys? What
percent are girls?
2.A vendor had 200 balloons for sale. If he
sold 125 of them, what percent remains
unsold?
35. Solve the ff. problem.
a) Ricardo got 90% of a 20-item test in Math. How
many items did he answer correctly?
b) In a school of 680 Grade 6 pupils, 646 graduated.
What percent of the Grade 6 pupils graduated? How
many did not graduate?
c) One stormy day, 12 pupils of Mrs. Loyola were
absent. If there are 50 pupils in the class, what
percent of the class is absent? present?
36. What have you learned?
How do you find the rate or percent when
the base and percentage are given?
37. A S S E S S M E N T
Answer the following:
1) ___% of 10 = 2.
2) N% of 28 is 14.
3) What percent of 20 is 5?
4) 4 is what percent of 20?
5) 18 is N% of 30.
38. A S S I G N M E N T
Solve.
1)What percent of 8 is 64?
2)7 is what percent of 35?
3)63 is N% of 252.
4)___% of 9 = 45.
5)N% of 875 is 210.
42. Reading
drill
THE ENCHANTED DEER
Once there were two warring tribes whose
kingdoms were divided only by a wide river.
The king on the land north of the river had a
beautiful daughter named Mayumi; while the
king on the land south of the river had a
brave handsome son named Bayani.
43. Both kings hated each other so much
that they even wanted their children to hate
each other, too.
But fate played a trick on them. Mayumi
and Bayani felt so madly in love with each
other that they defied their parents wish.
They often met secretly in the nearby
forest.
44. One early morning, Mayumi went to meet Bayani
in the forest. She had some enchanted power, so
she changed herself into a deer. She did not want
anybody to see her.
Bayani waited for her. When he saw the deer, he
was attracted to it. He quickly shot an arrow not
knowing it was Mayumi.
The deer fell bleeding. Bayani ran to see his prize,
but he saw Mayumi instead. He wept and, in his
grief, he stabbed himself to death.
45. KING BACK
L
Do what is asked for:
1) ___% of 80 = 20.
2) N% of 180 is 35
3) what percent of 800 is 400?
4) 7.5 is what percent of 30?
5) 18 is N% of 24.
46. How much is your daily
allowance?
Are you contended with it?
47. PROBLEM OPENER
Manuel, a son of a school janitor, does not
ask for more. He has a daily allowance of
P10 a day which is 20% of his classmates
daily allowance. How much is his
classmates daily allowance?
48. Processing Questions:
a) Who is the son of a school janitor?
b) How much is his daily allowance?
c)Does he ask for more allowance like his other
classmates? Why?
d)Do you think Manuel spends his money wisely?
How do you know?
e)If you were in his shoes, what will you do? Why?
49. Analyze the problem.
a) What does the problem require you to
look for?
b) What facts are given?
c)What are the needed data?
d)What will you do to solve the problem?
e) What equation best transforms the
problem?
51. 1. 75% of N is 15.
2. 15 is 25% of what number?
3. 25 is 75% of N.
4. 45% of N = 15.
5. 65% of what number is 15?
EXERCISE 1
52. EXERCISE 2
Solve for the base.
1) 50% of ____ is 3.
2) 20% of what number is 14.
3) 14 is 35% of N.
4) 10.5 is 30% of what number?
5) 65% of N = 58.5.
53. Read, analyze and solve.
1.In a math class, 8 pupils received a grade
of 90. If 16% of the class got 90, how
many pupils are there in a class?
2.In a Grade 6 outing, 240 pupils
participated. If 80% joined the outing, how
many grade 6 pupils are there in the
school?
54. Solve the following problems.
1.A grade six class went on a field trip. Only
98% or 49 pupils joined the activity. What
was the class enrolment?
2.Chito has 20 in his pocket which is only
5% of the money of her sister. How much is
the money of her sister?
55. What have you learned?
How do you find the base when the
percentage and rate are given?
56. A S S E S S M E N T
Solve for n.
1) 20% of n is 2.
2) 7 is 35% of n.
3) 40% of n = 8.
4) 10 is 40% of what number?
5) 25% of what number is 2?
57. A S S I G N M E N T
Solve.
1) 6% of n = 4.5.
2) 6.72 is 7% of what number?
3) 12% of n is 14.4.
4) 117 is 65% of n.
5) 88% of what number is 660?
61. Reading
drill
THE ENCHANTED DEER
Once there were two warring tribes whose
kingdoms were divided only by a wide river.
The king on the land north of the river had a
beautiful daughter named Mayumi; while the
king on the land south of the river had a
brave handsome son named Bayani.
62. Both kings hated each other so much
that they even wanted their children to hate
each other, too.
But fate played a trick on them. Mayumi
and Bayani felt so madly in love with each
other that they defied their parents wish.
They often met secretly in the nearby
forest.
63. One early morning, Mayumi went to meet Bayani
in the forest. She had some enchanted power, so
she changed herself into a deer. She did not want
anybody to see her.
Bayani waited for her. When he saw the deer, he
was attracted to it. He quickly shot an arrow not
knowing it was Mayumi.
The deer fell bleeding. Bayani ran to see his prize,
but he saw Mayumi instead. He wept and, in his
grief, he stabbed himself to death.
64. KING BACK
L
Do what is asked for:
1)What is 25% of 30? _______
2)Forty is what percent of 200?_______
3)18 is 30% of what number? _______
65. How much money do you
spend in school every day? Do
you save some of it for future
use? Why did you do it?
66. PROBLEM OPENER
Reyes family has a monthly income of P 15, 850. They
allotted 40% for food, 25% for education, 15% for
water and electricity bills, 8% for transportation, 7%
for miscellaneous expenses and 5% for savings. How
much money is allotted for their savings?
67. Answer the following questions:
What is asked in the problem?
What are the given facts?
What is the operation to be used?
Why does Reyes family allotted a certain
amount as savings?
Is it a good thing to save money?
68. 1.A pair of leather shoes was on
sale and was given a discount of P
600 at 30%. What was the original
price of the shoes?
EXERCISE 1
69. 2. There are 24 carabaos in the
farm and 6 of them are male.
What percent of the 24 carabaos
are male? Think: What percent of
24 is 6?
EXERCISE 1
70. 3. Joselito got 80% of 60 items
correct in a mathematics test. How
many correct items did he get?
EXERCISE 1
71. EXERCISE 2
Solve.
1.Elena has 12 hours working at
home daily as a full time wife and
mother. She spends 12.5% of the
time washing clothes. How many
hours does she wash the clothes?
72. 2. Among the 50 pupils in a Grade 6
class, 6% are left-handed. How many
are left-handed?
3. Marias allowance is P50 daily. She
saves 8% of it. How much does she
save?
73. Solve the following problems.
1.Rosa got 20% of an 80-item test incorrectly. How
many items did she get correctly.
2.Lilia has an error of 20% in a 60-item test. How
many mistakes does Lilia have in the test?
3.Ruby has 170 in her pocket. She gives 50% of the
money to her youngest brother. How much does
Ruby give to her brother?
74. 4.The money of Mr. Manipis is not enough to
buy a wristwatch at P3,000. His wife gave him
80% of the cost. How much money did he
receive from his wife?
5.There were 50 pupils in Grade III. If 28% of
the pupils were absent, how many pupils were
present?
75. What have you learned?
How do you solve problems
involving percentage, rate and
base ?
76. A S S E S S M E N T
Answer the following:
1.Joy got 70% of the 50 words in the spelling
contest. How many words did he spell correctly?
2. A bag that costs P450 is marked 15% discount.
How much would you pay for the bag?
77. 3. Of the 120 Grade 6 pupils, 30 prefer apples, 44
want oranges and the rest want bananas. What
percent of the Grade 6 pupils prefer bananas?
4. The newly elected President of SPG got 35 out
of 70 votes from his classmates. What percent of
the votes did he get?
5. Out of 50 pupils, only 48 joined the educational
trip. What percent joined the trip?
78. A S S I G N M E N T
1.Of 40 pupils only 30 pupils passed their project on
time. What percent passed their project on time?
2. Rhod gets 95% of the Math test correctly which is
38. How many test items are there in all?
3. In a Grade 6 class of 40 pupils, 36 pupils attended
the meeting of the Math Club. What percent of the
class attended the meeting?