MATH 5
QUARTER 3 Week 1
NAME: ____________________________________ GR & SEC: _____________________
Competency:
The learners are expected to:
1. Visualize percent and its relationship to fractions, ratios and decimal numbers using
models (M5NS-IIIa-136);
2. Define percentage, rate or percent and base (M5NS-IIIa-137); and
3. Identify the base, percentage and rate in a problem (M5NS-IIIa-138).
To the Learners:
Before starting the module, I want you to set aside other tasks that will disturb you while
enjoying the lessons. Read the simple instructions below to successfully enjoy the objectives of this
kit. Have fun!
1. Follow carefully all the contents and instructions indicated in every page of this module.
2. Writing enhances learning. Keep this in mind and take note of the important concepts in your
notebook.
3. Perform all the provided activities in the module.
4. Let your facilitator/guardian assess your answers using the answer key card.
5. Analyze the post-test and apply what you have learned.
6. Enjoy studying!
Expectations
This module was designed to help you master on how to visualize percent and its relationship
to fractions, ratios and decimal numbers using models, define percentage, rate or percent and base,
and identify the base, percentage and rate in a problem.
1.
2.
3.
4.
After going through this module, you are expected to:
Visualize percent and its relationship to fractions, ratios and decimal numbers using models;
Define percentage, rate or percent and base;
Identify the base, percentage and rate in a problem: and
Answer all the activities, pre-test and post- test that will enhance your understanding of the
concepts and ideas of the lessons.
MATH 5 QUARTER 3 WEEK 1
Page 1
Pre- Test
Direction: Write the letter of the correct answer before the number.
1.
Which of the following fractions shows the shaded part a 25%?
B.
A.
2.
Which of the fuel gas shows 4/5 full?
A.
B.
C.
D.
C.
D.
3.
Convert 72% into fraction and decimal number. Which of the following set of answer is
correct? Express your answer in lowest term.
A. 72/100 and 0.72
B. 72/100 and 72.0
4.
C. 18/25 and 0.72
D. 36/50 and 0.72
It is the fractional part of a whole or total and is usually followed by the word “is”.
A. Percentage
B. Rate
C. Base
D. Percent
5.
What is the original amount, usually the whole and is written after the word “of” or the
phrase “percent of”?
A. Percentage
6.
B. Rate
B. 60
C. Base
D. Percent
C.25%
D. 20
When one finds what percent one number is of another, we look for the______.
A. Percentage
9.
D. Percent
15 is 25% of 60. The percentage in the problem is __________.
A.15
8.
C. Base
In the equation 16 is 20% of 80, what do you call the part with a percent symbol?
A. Percentage
7.
B. Rate
B. Rate
C. Base
D. Ratio
Anna got 90% of a 50-item test in Math. She answers 45 items. What is the base?
A. 90%
B. %
C. 45
D. 50
10.
A 15% or PhP 3 375 is the down payment for a brand new refrigerator. The original price of the
refrigerator is PhP 22 500. The percentage in the problem is ___________.
A. %
B. 15%
C. PhP 3 375
D. PhP 22 500
Looking Back at Your Lesson
Let us have a little recap, before we proceed to the deepest part of the lesson. Percent means
parts PER HUNDRED. The word comes from the Latin phrase per centum, which means per hundred.
In mathematics, we use the symbol % for percent.
MATH 5 QUARTER 3 WEEK 1
Page 2
Given below are three grids. Each grid has 100 squares.
Problem: What fraction of each grid is shaded?
Answer:
Answer:
Answer:
So, 5% actually means 5 out of 100.
We can represent fractions as percent using the symbol %.
Comparing Shaded Boxes to Total Boxes
Grid
1
Ratio
96 to 100 or 96:100
Fraction
96/100
Percent
96%
2
3
9 to 100 or 9:100
77 to 100 or 77:100
9/100
77/100
9%
77%
Introduction of the Topic
Lesson 1: Visualizing Percent and its Relationship to Fractions, Ratios
and Decimal Numbers Using Models
Visualizing percent is seeing it in your mind as part of a whole. This can be shown in a number
of different ways.
When you’re filling a
glass with water, the
percentage tells you
how full the glass is.
This glass of water
shows 100% full
This glass of
shows 50% full
1 part
1 part to 2 parts
This glass of
shows 25% full
water
=
𝟏
𝟐
=
𝟓𝟎
𝟏𝟎𝟎
= 50%
1 part to 4 parts
=
𝟏
𝟒
=
𝟐𝟓
𝟏𝟎𝟎
𝟓𝟎
x 𝟓𝟎
1 part
𝟐𝟓
x 𝟐𝟓
= 25%
MATH 5 QUARTER 3 WEEK 1
water
Page 3
Example 1: Let us assume the picture below is a whole cake which is divided into 100 equal parts.
The shaded part is green. Let us try to
represent the shaded parts as:
Fraction
Decimal
Percent
Ratio
The whole square has 100 equal parts or has 100% whole.
The shaded part is 50 of 100 parts.
50
Fraction: 100 (50 shaded part out of 100 parts)
Decimal: 0.50 (read as 50 hundredths and place 50 in hundredths place)
Percent: 50% (50 shaded part per 100)
Ratio: 50:100 (50 shaded part to the total of 100 parts)
Example 2: Let us see in another example. This is a whole pizza.
100% represents a
whole pizza.
Hence, 100% = whole
Half of the
pizza was
eaten.
Therefore, since a whole is 100%, half of it is 50%.
50% is also 50/100 or ½
In fraction, 1 is a whole number while half of a whole is ½
In decimal numbers, ½ is equal to 0.50 or if you divide the numerator (1) by its denominator
(2) you will have a decimal number 0.50
( 1 ÷ 2 = 0.50 ).
Note: We can also change percent to decimal by simply drop the % symbol and move the
decimal point 2 places to the left.
( 50%
50.
0.50 )
In ratio, since we divided a whole pizza into 2 total parts, we wrote this as 1:2 or 1 to 2
Example 3: How about let us try to visualize and represent another example which is not exactly by
100 parts.
MATH 5 QUARTER 3 WEEK 1
Page 4
●
This is a whole square. The entire square represents a whole which is
divided by 10 parts. Try to represent the part that is in shaded blue as in
fraction, decimal, percent and ratio.
●
Percent means per 100, since 6 over 10 parts (6/10) is also same thing
with 60 per 100 or 60/100 is equal to 60%
●
There are 6 blue shaded parts out of the 10 equal sections which is
represented in fraction as 6/10 of a whole. (Fraction : 6/10 or 3/5 if you divide
both the numerator and denominator by two).
●
In decimal, we have to go to decimal place value first, 6/10 can also read as six tenths. So we will
put 6 in a tenths place (0.6).
●
In the entire square, the ratio of the shaded parts (6 shaded parts) to the total number of parts
(10 equal parts) is represented as 6 to 10 or 6:10.
Lesson 2 Defining Percentage, Rate or Percent and Base
All simple percent problems have three (3) parts:
The percentage (P) is the fractional part of a whole or total. It is usually followed by the word “is”.
Keyword: before or after the word “is”
Example No. 1
Example No. 2
Example No. 3
16 is 20% of 80.
30% of 70 is 21.
68% of 1 200 is 816.
The rate (R) is the percentage in relation to the whole or base. It is written in percent symbol (%).
Keyword: percent symbol (%)
Example No. 1
16 is 20% of 80.
Example No. 2
Example No. 3
30% of 70 is 21.
68% of 1 200 is 816.
The base (B) is the original amount, usually the whole. It is written after the word “of” or the phrase
“percent of”.
Keyword: after the word “of” or “percent of”
Example No. 1
Example No. 2
Example No. 3
MATH 5 QUARTER 3 WEEK 1
16 is 20% of 80.
30% of 70 is 21.
68% of 1 200 is 816.
Page 5
Lesson 3
Identifying Percentage, Rate, and Base in a Problem
We deal with the three elements: percentage, rate and base:
50% of 80 =
Rate
40
Base
Percentage
We can also use the Techan’s Triangle to identify the percentage, rate and base.
50% of 80 is 40.
Example No. 1 Identify the percentage, rate and base in the table below.
1.
2.
3.
4.
5.
60 is 20% of 300
20% of 50 is 10
39 is 50% of 78
21 is 25% of 84
One hundred twenty- five percent of 60 is 75
Example No. 2
60 is 20% of 300
Cover with your palm
Percentage
PERCENTAGE (P)
60
10
39
21
75
RATE (R)
20%
20%
50%
25%
125%
BASE (B)
300
50
78
84
60
what is NOT asked in the Techan’s Triangle.
Rate
Base
Example No. 3 Identify the rate, base and percentage in the problem.
Paolo listens very well to the teacher during the discussion of the lesson. When they were given
a 5-item test, he got 4 correct answers. He has a grade of 80%.
What is the percentage? ______4______
What is the rate?
______80%___
What is the base?
______5______
MATH 5 QUARTER 3 WEEK 1
Page 6
Activities
Activity 1 Are you ready for more exciting adventure in this module?
Imagine that you are riding in a flying car. You are now travelling in the world of shapes and
objects. There are different shapes being shaded. Now, you have to represent the shaded part in
percent, fraction, decimal and ratio.
START HERE:
2.
1.
3.
100
4.
5.
100
0
1. Grid
2. Pizza
2. Soil
100
3. Area
4. Gas
Percent
Fraction
Decimal
Ratio
MATH 5 QUARTER 3 WEEK 1
Page 7
Activity 2 Identify the percentage, rate, and base in the problem. Write your answer in its proper
place inside the Techan’s Triangle.
There are 200 mangoes harvested in Nonoy’s farm. Seventy percent are ripe.
There are 140 ripe mangoes.
Percentage
Rate
Base
Remember
Percent means parts per hundred. We use the symbol % to represent it.
To change from percent to fraction, we use a denominator of 100, and
then simplify it.
To change percent to decimal, drop the % symbol and move the
decimal point 2 places to the left.
To change decimal to percent, simply move the decimal point 2 places
to the right, then annex the symbol % after to the number.
To change percent to ratio, first convert the percentage into fraction
and then the fraction into ratio since ratio is a comparison of two
quantities.
The percentage (P) is the fractional part of a whole or total. It is
usually followed by the word “is”.
The rate (R) is the percentage in relation to the whole or base. It is
written in percent symbol (%).
The base (B) is the original amount, usually the whole. It is written
after the word “of” or the phrase “percent of”.
Techan’s Triangle is also used in identifying rate, base and
percentage.
Check Your Understanding
I. Pizza Puzzle Set
Directions:
1.
2.
3.
There are five pizza plates below.
Convert the given fraction, percent, ratio or decimal on the pizza plate.
Write your answer inside the box.
MATH 5 QUARTER 3 WEEK 1
Page 8
Pizza Puzzle Set
Yay! Let us help Steffie solve the pizza puzzle. The more
you get the correct answer, the more pizza she can eat!
Ready?
Convert the given fraction, percent, decimal and ratio to
percent, decimal, fraction and ratio.
Pizza Plate 1
Pizza Plate 2
Pizza Plate 3
Pizza Plate 4
Pizza Plate 5
II. Match three cards that are related to each other by coloring it with the same color. (rate yellow, base-red, percentage-blue)
III. Complete the table. Identify the percentage, rate, and base in each problem.
PERCENTAGE (P)
RATE (R)
1. 85% of 100 is 85
2. 13 is 2% of 650
3. PhP 195 is 50% of PhP 390
4. 50 items, 45 correct answers, 90% score
5. Kris has 24 pencils. 25% of the pencils are
yellow. There are 6 yellow pencils.
MATH 5 QUARTER 3 WEEK 1
Page 9
BASE (B)
Post- Test
Direction: Write the letter of the correct answer before the number.
1. Which of the following fractions show the shaded part a 25%?
A
B.
C.
D.
2. Which of the fuel gas shows 4/5 full?
A
B.
C.
D.
3. Convert 72% into fraction and decimal number. Which of the following set of answers is correct?
Express your answer in lowest term.
A. 72/100 and 0.72
B. 72/100 and 72.0
C. 18/25 and 0.72
D. 36/50 and 0.72
4. It is the fractional part of a whole or total and is usually followed by the word “is”.
A. Percentage
B. Rate
C. Base
D. Percent
5. What is the original amount, usually the whole and is written after the word “of” or the phrase
“percent of”?
A. Percentage
B. Rate
C. Base
D. Percent
6.In the equation 16 is 20% of 80, what do you call the part with a percent symbol?
A.Percentage
B. Rate
C. Base
D. Percent
7.
8.
15 is 25% of 60. The percentage in the problem is __________.
A.15
B. 60
C.25%
D. 20
When one finds what percent one number is of another, we look for the______.
a. Percentage
B. Rate
C. Base
D. Ratio
9. Anna got 90% of a 50-item test in Math. She answers 45 items. What is the base?
a. 90%
B. %
C. 45
D. 50
10. A 15% or PhP 3 375 is the down payment for a brand new Refrigerator. The original price of
the ref is PhP 22 500. The percentage in the problem is ___________.
a. %
B. 15%
C. PhP 3 375
D. PhP 22 500
MATH 5 QUARTER 3 WEEK 1
Page 10
Reflection
After studying the lessons and answering all the activities in this module, write an example for each
lesson how your learnings can help you in daily activities.
References and Additional Activities
You may visit the following sites for additional information:
https://www.slideshare.net/JunindMaeCamarillo/rate-base-percentage-80134206
https://www.mathsisfun.com/percentage.html
https://www.youtube.com/watch?v=NbmG7pwY6W0&t=163s
https://www.youtube.com/watch?v=NbmG7pwY6W0&t=163s
https://www.mathgoodies.com/lesson/vol4/meaning_percent
https://www.mathisfun.com/percentage.html
https://study.com/academy/lesson/how-to-visualize-percent-using-diagram.html
https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-intropercents/v/describing-the-meaning-of-percent
MATH 5 QUARTER 3 WEEK 1
Page 11