K TO 12 GRADE 5 LEARNER’S MATERIAL IN MATHEMATICS (Q1-Q4)

Lesson 1: Visualizing Numbers up to 10 000 000 with emphasis on
numbers 100 001 – 10 000 000
A group of doctors donated a total of 234 534 kilograms of rice to the
earthquake victims. Can you imagine how big the number 234 534 is? One way
you can imagine is to think of discs to represent the number shown below.
Two 100 000 Three 10 000 Four 1 000 Five 100 Three 10 Four 1
200 000 30 000 4 000 500 30 4
234 534
What number is represented by these number discs? Write your answer in your
notebook.
100 000
100 000
10 000
10 000
10 000 1 000
1 000
1 000
1 000
100
100
100
100
100
10
10
10
1
1
1
1
100 000
100 000
10 000
10 000
100 000
1 000
1 000
1 000
1 000
100
100
100
1 000
10 000
10
10
100
1
1
10
10
Get Moving!
Explore and Discover!

Use number discs to show the following numbers.
1. 10 345 789
2. 389 456
3. 4 234 789
4. 123 098
5. 4 456 678
Read the following items. Then, write your answer to each item in your notebook.
1. There were 345 895 children and adults who watched the football game. Draw number
discs to show the given number.
2. How will you show the number 2 345 789 using number discs?
3. There were 1 234 897 tree seedlings distributed to the barangays by the Department of
Environment and Natural Resources. Draw number discs to show the given number.
4. Mrs. Angeles bought some appliances worth Php 156 907. Represent this amount using
number disc.
5. Which number is 100 000 smaller than 234 456?
a. 134 456
b. 334 456
c. 34 456
d. 434 456
Keep Moving!
Apply Your Skills!

Lesson 2 : Reading and Writing Numbers up to 10 000 000 in Symbols
and in Words
EXPLORE AND DISCOVER!
The Department of Agriculture distributed 1 456 897 eggplant seedlings in some farmers
in Region IVA.
How do you read and write the number 1 456 897 in words and in symbol?
The number 1 456 897 is read as “ one million four hundred fifty-six thousand eight
hundred ninety-seven”. In symbol it is 1 456 897.
GET MOVING!
A. Write the following numbers in words.
1. 10 345 897
2. 7 456 902
3. 234 713
4. 678 345
5. 1 097 234
B. Rewrite the numbers correctly by putting a space in the correct places in column A. In
column B, write the numbers in words.
Number Column A Column B
1234678
6578234
10234123
123987
23908

KEEP MOVING!
Write the numbers in symbols.
1. Three million seven hundred eighty-six thousand four hundred 10
2. Five hundred ten thousand twenty- six
3. Ten million two hundred seven thousand one hundred seven
4. Six million eighty-three
5. Four million seven hundred twenty thousand three hundred eight
APPLY YOUR SKILLS!
A. 1. What is largest 7- digit number having different digits?
Write it in symbols and in words ___________________________________
2. What is the number next to 234 456?
Write it in symbol and in words ___________________________________
3. What is the smallest 6-digit number having different digits?
4. What is the number before 1 567 678?
5.What is the number between 890 789 and 890 791?
Write it in symbol and in words ____________________________________

1
Lesson 3 : Rounding Numbers to the Nearest Hundred Thousands and Millions
The circumference of the earth is 40 053 840 meters.
About how many million meters is the circumference of the earth?
You can find the answer by rounding 40 053 840 to the nearest millions.
Study these examples.
Number
Rounded to
Millions Hundred thousands
3 456 789 3 000 000 3 500 000
14 578 907 15 000 000 14 600 000
2 389 897 2 000 000 2 400 000
1 345 890 1 000 000 1 300 000
7 567 079 8 000 000 7 600 000
GET MOVING!
A. Round each number to the place value of the underlined digit.
1. 12 234 556 ______________________
2. 3 456 871 ______________________
3. 5 098 678 ______________________
4. 9 789 123 ______________________
5. 6 234 189 ______________________
B. Complete the table.
Number
Round to the nearest
Millions Hundred thousands
4 496 709
13 508 807
5 889 897
6 045 890
7 527 099

2
KEEP MOVING!
A. Encircle the numbers that can be rounded to the given number.
1. 8 900 000
8 923 567 8 984 456 8 908 671 8 938 123 8 971 109
2. 7 000 000
6 821 507 7 284 471 7 578 653 6 968 123 7 771 178
3. 4 500 000
4 493 517 4 381 426 4 508 671 4 561 126 4 478 120
4. 3 200 000
3 194 100 3 283 401 3 221 611 3 138 170 3 201 156
5. 6 000 000
5 622 160 6 904 431 5 998 601 6 868 173 6 001 101
B. Round to the highest place value.
1. 345 789 ______________________________
2. 1 563 890 ______________________________
3. 3 213 456 ______________________________
4. 9 912 123 ______________________________
5. 312 465 ______________________________

3
APPLY YOUR SKILLS!
A. Complete the table.
Greatest Number Rounded Number Least Number
3 000 000
2 400 000
10 200 000
6 300 000
1 000 000
B. Read the problem and complete the table below.
Mrs. Angeles bought the following cars for her 5 children.
Honda Civic – Php 1 289 980
Limousine - Php 5 561 003
Ferrari - Php 8 123 315
Jaguar - Php 4 123 980
BMW - Php 3 901 312
Copy the price of each item. Then, round each to the nearest hundred thousand and
millions.
Item Price Hundred Thousands Millions
Honda Civic Php 1 289 980
Limousine Php 5 561 003
Ferrari Php 8 123 315
Jaguar Php 4 123 980
BMW Php 3 901 312

Lesson 4: Using Divisibility rules for 2, 5 and 10 to find common
factors
Jaira has 70 collected stamps. Can she shared that equally to 2 friends? 5 Friends? 10
friends?
To solve the problem, you need to know if 2 5 and 10 are factors of 70 or if 70 is divisible
by 2 5 and 10.
To see if the number is divisible by 2, 5 or 10 ,test by checking the ones digit
DIVISIBILITY TEST 70
By 2: Is the ones digit 0,2,4,6 or 8? YES
By 5: Is the ones digit 0 or 5? YES
By 10: Is the ones digit 0? YES
Get Moving!
A. Put a check under each column to identify whether each number is divisible by 3, 6 or 9.
2 5 10
54180
912
2700
5605
568
3765
233
80

B. Determine whether the first number listed is divisible by the second number. Write Yes
or No on the blank.
Yes or No
1. 45 ; 2 ____________
2. 5080 ; 5 ____________
3. 90 ; 5 ____________
4. 1180 ; 10 ____________
5. 6998 2 ____________
Keep Moving!
Underline the answer that makes each sentence correct.
1. Twenty is (divisible/not divisible) by ten.
2. Three hundred is (divisible/not divisible) by five.
3. Nine hundred ninety is (divisible/not divisible) by two.
4. One hundred six is (divisible/not divisible) by five.
5. Ten thousand four hundred two is (divisible/not divisible) by two.
Apply Your Skills!
Use divisibility rules to help you solve the following problems.
1. Frances has a collection of 672 stamps. She wants to place the stamps in 2 envelopes
.Can she place the same number of stamps in each envelope?
2. The number of books in Karla’s collection is divisible by 2,5 and 10. She has more than
11 books and fewer than 25 books. How many books does Karla have?

Lesson 5: Using Divisibility rules for 3, 6 or 9 to find common factors
Nena’s garden has 414 bougainvillea plants. She wants to arrange them in either rows
of 3, 6 or 9. Which are the possible arrangements of the plants?
To solve the problem, you need to know if 3 6 or 9 are factors of 414 or if 414 is divisible
by 3, 6 or 9.
Recall the rules:
 Divisible by 3: sum of digits of the number is divisible by 3
414= 4+1+4=9, 9 is divisible by 3,therefore 414 is divisible by 3
 Divisible by 6: number is divisible by both 2 and 3
414 is divisible by 2 and 3, therefore 414 is divisible by 6
 Divisible by 9: sum of the digits of the number is divisible by 9
414= 4+1+4=9, 9 is divisible by 9, therefore 414 is divisible by 9
Get Moving!
A. Put a check under each column to identify whether each number is divisible by 3, 6 or 9.
3 6 9
528
1242
3456
624
852
2547
324
120
B. Write the letter of the correct answer on your notebook.
1. Which of the following is divisible by 3?
a.11 b.36 c.23
a. 108 b.100 c.124
a. 71 b.134 c.234
4. 3 is a factor of
a.272 b.153 c.92
5. 6 is a factor of
a.84 b.75 c.53

Keep Moving!
A . Tell whether each number is divisible by 6 or not.
1.906
2.1322
3.4714
4.5166
5.84510
B. Tell whether each number is divisible by 9 or not.
1.89019
2.4617
3.48753
4.1404
5.75834
Apply Your Skills!
Answer the following questions and write the answers on your notebook.
1. Are all numbers divisible by 9 also divisible by 3?
2. How many numbers between 50 to 100 are divisible by 3?
3. Marjorie wants to arrange her 186 books in three rows. Would it be possible?

Lesson 5: Using Divisibility rules for 4, 8, 12 and 11 to find common factors
The school auditorium has 372 chairs. Mrs.Cruz, the principal wants to align them in
either rows of 4,8,12 or 11. Which are the possible alignments of the chairs?
To solve the problem, you need to know if 4, 8,12 or 11 are factors of 372 or if 372 is
divisible by 4, 8, 12 or 11.
Recall the rules:
 Divisible by 4: if the last two digits form a number that is divisible by 4.Also, numbers
ending in two zeros are divisible by 4
372→ 72 ÷ 4 = 18, therefore 372 is divisible by 4,chairs can be aligned by 4
 Divisible by 8: if the number formed by the last 3 digits is divisible by 8.Also, a number
ending in three zeros are also divisible by 8
372 ÷4 = 93,therefore 372 is divisible by 8,chairs can be aligned by 8
 Divisible by 12: if the sum of the digits of the number is divisible by 2 and 3
372= 3+7+2=12, 12 is divisible by 2 and 3, therefore 372 is divisible by 12
 Divisible by 11:if the sum of the digits in the odd places and the sum of the digits in the
even places are equal or their difference is a multiple of 11.
372→(3+2)-7= -2,therefore 372 is not divisible by 11,chairs CANNOT be aligned by 11
Get Moving!
A. Encircle 4,8,11 and 12 if these are factors by these numbers.
1. 1572 - 4 8 11 12
2. 88 - 4 8 11 12
3. 160 - 4 8 11 12
4. 642 - 4 8 11 12
5. 2400 - 4 8 11 12
B. Write on the blank before each number whether it is divisible by 4,8,11 or 12.
_____1. 500
_____2. 3000

_____3. 121
_____4. 492
_____5. 648
Keep Moving!
Supply the missing number to make the number divisible by the number opposite it.
1.273_ - 4
2.216_ - 8
3.91_ - 12
4.26_ - 11
5.38_ - 12
Apply Your Skills!
Answer the following questions and write the answers on your notebook.
1. Can 88 stamps be shared equally by 4 friends? 8 friends? 11 friends? 12 friends?
2. Annie wants to distribute his 276 marbles to 12 children. Will each child receive the
same number of marbles?

Lesson 7: Solving Routine and Non – Routine Problems Involving Factors, Multiples and
i
Divisibility Rules for 2,3,4,5,6,7,8,9,10,11 and 12
Read the problems below.
Can you solve the problem?
Here are the steps in analyzing and solving word problems.
Study the solution below.
Problem 1:
Michael has to split 60 students in
his class into different groups with
equal number of students each .Not
all students can be in one group and
each group has to have more than
one student. In how many ways can
he form these groups?
Mila baked cookies for her 3 sons
and 2 daughters. If she baked 45
cookies only. How many cookies did
her 3 sons have and 2 daughters
have?
 Understand
Know what is asked: In how many ways can he form these groups?
Know the given facts: 60 students, different groups with equal number of students
each
 Plan
Determine the way/s to be used: factoring, finding the multiples and divisibility rules
 Solve
Show your solution:
A. Find the factors of 60.
60= 4X15= 2X2X3X5
B. Get the numbers(once) on the given factors. Then find the multiples of each
number till you reach 60.
 Multiples of 2 = 2, 4, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40,
42, 44, 46, 48, 50, 52, 54, 56, 58, 60
 Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60
 Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
Members 2 3 4 5 6 10 12 15 20 30
Groups 30 20 15 12 10 6 5 4 3 2
Ways 10 ways
C. Identify the number that can divide 24 equally.
Answer: There are 10 ways to form a group.

Problem 2:
Which of the problems do you think is easier to solve? Why?
Can you try solving this problem?
Do this with your partner.
1. A farmer in Calauan gathered 96 pineapples. If he would want to distribute those 96
pineapples in baskets, how many ways can he distribute when each basket has the
same number of pineapples?
Get Moving!
Solve the following problems:
1. Josephine planted 600 onions equally in 20 rows. How many onions were planted in
each row?
Understand:____________________________________________________________
Plan:__________________________________________________________________
Solve:_________________________________________________________________
Check and Look back:____________________________________________________
2. The product of numbers is 138.If one factor is 2, hat is the other factor?
Understand:____________________________________________________________
Plan:__________________________________________________________________
Solve:_________________________________________________________________
 Understand
Know what is asked: How many cookies did her 2 sons have? How many cookies
did they have individually?
Know the given facts: 3 sons and 12 daughters ,30 cookies
 Plan
Determine the way/s to be used: Finding Multiples
 Solve
Find the multiples of 2 and 1 till you get the sum of 30.
3 sons 3 6 9 12 15 18
2 daughters 2 4 6 8 10 12
sum 5 10 15 20 25 30
Answer: There are 18 cookies for her 3 sons and 12 cookies for her 3 daughters.
Show your solution:
 Check and Look back
Review and recheck your answer:

3. How many 5,00 are there in 50,000?
Understand:____________________________________________________________
Plan:__________________________________________________________________
Solve:_________________________________________________________________
Keep Moving!
Solve the following word problems
1. Joel and Harry love playing marbles. Joel has 60 marbles while Harry has 80 marbles .
They plan to keep their marbles in a clay jar. How many clays are there?
2. What is the smallest number of avocados that can be placed in baskets with 50 and 75
pieces ?
3. Joseph has some chocolates. If he shares them equally among 4 friends or 5 friends,
there are always 2 exrta chocolates left. What is the possible number of chocolates
Joseph Could have?
Apply Your Skills!
Try solving more problems.
Read and analyze more problems. Then write your solutions and answers in your
notebook.
1. Lorna earns Php 10,000 a month. How much does she earn in 2 years?
2. A farmer planted 180 monggo seeds equally in 3 big bowls. How many monggo were
planted each row?

Lesson 8: Creates Problem (with Reasonable Answers) Factors, Multiples and Divisibility
Rules
Arrange the sentences to form a word problem
Get Moving!
Use the data inside the box to complete the problems below. Solve the problem in your
notebook.
1. The average of five consecutive odd numbers is 155.
What are the five odd numbers?
2. I am thinking of a number . Twice the number plus . What is my number?
3. How many are there on a n 8-by-8 checkerboard?
4. The average of consecutive numbers is 112. What is the largest number?
and the total payment of T-shirts
Ronald paid P155.00 each T-shirts for his indigent students for the to use as a
uniform and the total payment of T-shirts he bought is P1,240.00. How many T-
shirts did he buy?
How many T-shirts did he buy?
P
he bought is P1,240.00.
Ronald paid P155.00 each T-shirts
Answer:
for his indigent students for the to use as a uniform
115 equals 52 squares 5 even

Keep Moving!
Study the story problems given below. Complete each problem by creating a question for what
is asked. Then, solve the problem.
1. Karen collected 28 recipes of salad. She devided them equally into different categories.
Fruit salad is her favourite category.
Question:_____________________________________________________________?
Solution and Answer:
2. Mike 42 seashells. He places an equal number of seashells in different boxes.
Question:_____________________________________________________________?
3. Sarah wants to invite her cousins to see a volleyball game with her. She has
Php500.Each ticket costs Php85
Question:_____________________________________________________________?
Apply Your Skills!
Create a problem using the given data. Then solve the problem.
1. Given : 31 sachet of shampoos / month
1 year
Asked: total number of sachet of shampoos in 1year
Problem:_____________________________________________________
Solution and answer:
2. Given : 12 apples / day
3 months
Asked: total number of apples in 3 months
Problem:_____________________________________________________
3. Given : 36 red mangoes for Anny
40 green mangoes for Sonia
4 mangoes a day
Asked: total number of mangoes mangoes last individually.
Problem:_____________________________________________________

Lesson 9: Stating, Explaining, and Interpreting Parenthesis, Multiplication, Division,
Addition, Subtraction (PMDAS) or Grouping, Multiplication, Division, Addition,
Subtraction (GMDAS) rule.
Study the rules in the order of operations.
Examples:
1. 12 ÷ 6 × 2 + 4 – 5
2. 6 ÷ 3 × 2 + 5 – 1
3. 3 ×[4 - 2 × (10 -8) + 12 ÷ 6 × 1]
How will you solve the order of operations?
To solve the order of operations, follow the rules listed above.
Solutions:
1. 12 ÷ 6 × 2 + 4 – 5
2 × 2 + 4 – 5
1. Perform the operations within each pair of grouping symbols
(parenthesis, brackets, and braces) beginning with the innermost pair.
2. Simplify the expression with exponents.
3. Perform multiplication and division as they occur from left to right.
4. Perform addition and subtraction as they occur from left to right.
4 + 4 -5
8 - 5
3
Rule 3
Rule 3
Rule 4

2. 6 ÷ 3 × 2 + 5 – 1
3. 3 ×[4 - 2 × (10 -8) + 12 ÷ 6 × 1]
2× 2 + 5 – 1
4+ 5 – 1
9– 1
8
Rule 3
Rule 3
Rule 4
3 × 2
3 × [4 - 2 × 2 + 12 ÷ 6 × 1]
3 × [4 – 4 + 12 ÷ 6 × 1]
3 × [4 – 4 + 2 × 1]
3 × [4 – 4 + 2]
3 × [o + 2]
3 × 2
6
Rule 1
Rule 3
Rule 3
Rule 4
Rule 1
Rule 3

Get Moving
Solve the expression below by following the rules.
1. 32 ÷ 2 × 2
2. 6 ÷ 2 +1 × 4
3. (15 – 6) + (4 – 1) × 23
4. 3 × [3 + 2 × (10 -3)]
5. 12 + 3 × 3 {3 × [4 +(9 – 8) – 2] – 3}
Keep Moving
Perform the indicated operations.
1. (12 + 3) – 7 = N
2. 4 (6 + 8) = N
3. 25 ÷ 5 + 9 = N
4. (18 – 4) + (5 + 3) = N
5. (6 ÷ 3) + (10 × 3) = N
Apply Your Skills!
A. Place parenthesis in the equation so that each equation will be a true statement.
1. 16 – 7 + 8 = 1
2. 3 × 5 – 4 = 3
3. 18 ÷ 6 × 3 = 1
4. 16 – 7 + 8 = 17
5. 12 ÷ 2 + 4 = 2
B. Use the numbers 3, 4, 6, and 8 once in each exercise to make a true statement.
( ______ × _______ ) ÷ ( _____ + ______ ) = 2
______ × _______ ÷ ( ______ × _______ ) = 1
______ × ( ______ × ______ ) ÷ _______ = 18
______ ÷ ( _______ - _______ ) + _______ = 14

Lesson 10 : Simplifies a series of operations on whole numbers
involving more than two operations using the PMDAS or GMDAS rule.
A lot of problems in mathematics involve more than one operation. Some may contain a
series of operations and different grouping symbols such as parenthesis ( ),
brackets[ ], and braces { }
 Simplify 4 + 32
.
You need to simplify the term with the exponent before trying to add in the 4:
4 + 32
= 4 + 9 = 13
 Simplify 4 + (2 + 1)2
.
You have to simplify inside the parentheses before I can take the exponent through.
Only then can I do the addition of the 4.
4 + (2 + 1)2
= 4 + (3)2
= 4 + 9 = 13
 Simplify 4 + [–1(–2 – 1)]2
.
You shouldn't try to do these nested parentheses from left to right; that method is simply
too error-prone. Instead, you will try to work from the inside out. First you will simplify
inside the curvy parentheses, then simplify inside the square brackets, and only then
take care of the squaring. After that is done, then you can finally add in the 4:
4 + [–1(–2 – 1)]2
= 4 + [–1(–3)]2
= 4 + [3]2
= 4 + 9
= 13

Get Moving!
A. Simplify the following expressions in your notebook following the PEMDAS or
GEMDAS rule.
1. 3 + 52
– 2
2. (2 – 5 ) + 42
– 10 ÷ 5
3. ( 4 – 1 )2
+ 15 ÷ 3 – 1
4. 10 – ( 3 + 4 ÷ 2 )2
+ 15
5. (3 + 2 ) + 8 ÷ 2 x 4
B. Complete the table. Write the order of operations to simplify the given
expression.
Expression Operation first to perform Answer
6) 6 + 5 x 3 – 7
7 ) 6 + 15 - 7
8) 14 – 7 + 18 ÷ 3
To simplify series of operations on whole numbers involving more than two
operations using PEMDAS or GEMDAs rule.
 First, perform operations inside the innermost grouping symbols,
if any.
 Next, evaluate powers.
 Then, perform multiplication/division from left to right.
 Finally, perform addition/subtraction from left to right.

9) 7 + (15 - 6 x 2)
10) 2 ( 2 + 5 ) 2
Keep Moving!
A. Simplify the following expressions in your notebook following the PEMDAS or
GEMDAS rule.
1. (25 + 5) x 3 – 13
2. 19 + 12 x 3 – 5
3. 54 + 23 ÷ 2
4. 21 + 34 x 3 ÷ 2
5. (5 + 3) x (3 + 8)
6. 2 + 16 x 7 – 3
7. 11 + 5 x 5 – 10
8. 31 – 24 ÷ 1 -7
9. 21 + 16 – 8 ÷ 9
10.(19 – 3 ) x 3
Apply Your Skills!
A. Write the expression and solve the given problems.
1. Peter has 450 pesos. He spends 210 pesos on food. Later he divides all the
money into four parts out of which three parts were distributed and one part he

keeps for himself. Then he found 50 pesos on the road. Write the final
expression and find the money he has left?
2. You pay 10.00 pesos to buy a package of paper napkins costing 640 pesos. How
much change will you get back? Give the expression also.
3. Liza has 1,000 pesos to be distributed among two groups equally. Later, the first
part is divided among five children and second part is divided among two
brothers. Give the expression that represents how the money distribution
between two groups was dispersed?
Challenge yourself with this problem!
Read the problem and then write the answers to the questions in your notebook.
1) Flora bought 3 notebooks for 10 pesos each, a box of pencils for 21.00
pesos, and a box of pens for 35.00 pesos.
2) Darwin had 35 500 pesos and withdrew 5200 pesos from his bank account.
He bought a pair of trousers for 340 pesos, 2 shirts for 360 pesos each, and 2
pairs of shoes for 540 each. Give the final expression, and determine how
much money Darwin had at the end of the shopping day.

1
Lesson 11: Finding the common factors and the GCF of two - four
numbers using continuous division
You find the common factors and Greatest Common Factor or (GCF) of 24, 30 and 42.
Using Continuous Division
2 24 30 42
3 12 15 21
3 5 7
A. Find the common factors and GCF of the following numbers.
1) 24 32 4) 4 6 20
2) 12, 30 42 5) 8 56 84 112
3) 28 32 40
Mrs. Ragas bought 24 mangoes, 30 apples and 42
bananas. If she is going to group these equally, what is
the greatest number of mangoes, apples and bananas in
each group?
GCF: 2 x 3 = 6
The greatest number of mangoes, apples and
bananas is 6.
Get Moving!

2
B. Find the GCF of the following problems using continuous division.
1) Miss Dela Cueva has to prepare number of exercises for her lesson for the
day. She has three classes. One class has 48 pupils, another class has 50,
and another has 46. What must be the largest number of exercises she
should prepare so that each class will have the same number of pupils
working on different problems?
2) There are 10 green, 14 blue, 20 red and 24 yellow bulbs to be used for a
birthday party. They are to be placed in plastic bags so that each bag
contains the same number of green, blue, red and yellow bulbs. What is the
largest number of plastic bags that will be needed?
A. Determine the GCF.
1) 3 72 99 126 GCF = ________
3 24 33 42
8 11 14
2) 5 90 135 180 195 GCF = ________
8 17 36 39
3) 2 42 56 70 98 GCF = ________
7 21 28 35 49
3 4 5 7
A. Find the common factors and GCF the following word problems.
4) The mathematics teacher in a certain elementary school is planning to have
an educational tour for four grade levels with 800 pupils in Grade II, 560
Keep Moving!

3
pupils in Grade III, 480 pupils in Grade IV and 400 pupils in Grade V. What is
the largest number of pupils in a group in each grade level so that each group
has the same number of pupils?
5) A group of 45 dancers will march behind a group of 30 clowns in a parade.
You want to arrange the two groups in rows with the same number of people
in each row, but without mixing the group. What is the greatest number of
people you can have in each row?
6) A group of 45 dancers will march behind a group of 30 clowns in a parade.
You want to arrange the two groups in rows with the same number of people
in each row, but without mixing the group. What is the greatest number of
people you can have in each row?
Read and solve the common factors and GCF the following word problems.
1) The mathematics teacher in a certain elementary school is planning to have
an educational tour for four grade levels with 800 pupils in Grade II, 560
pupils in Grade III, 480 pupils in Grade IV and 400 pupils in Grade V. What is
the largest number of pupils in a group in each grade level so that each group
has the same number of pupils?
2) The parents are making sandwiches for the class picnic. They have 72 ham
slices, 48 cheese slices, and 96 tomato slices. What is the greatest number of
sandwiches they can make if each sandwich has the same filling?
Apply Your Skills!

4
1) Gina has two pieces of cloth. One piece is 72 inches wide and the other piece
is 90 inches wide. She wants to cut both pieces into strips of equal width that
are as wide as possible. How wide should she cut the strips?
2) The GCF of 40 and a number 8. What is the number if it lies between 70 and
80?
3) Two numbers have a GCF of 6. If their difference is also equal to their GCF,
what are the numbers?
4) Find three consecutive even numbers such that their GCF is the lowest of the
three even numbers.

Lesson 12: Finds the common multiples and LCM of two - four
numbers using continuous division
To solve the problem, you need to find the least common multiple or LCM of 6
and 9 using continuous division.
Here’s how you do it.
3 6 9
2 3
LCM = 2 x 3 x 3 = 18
 Notice that 18 is the least common multiple or LCM of 6 and 9. Therefore, the
smallest number of roses and daisies that she will need for her bouquets is 18.
 You do not include when dealing with common multiples.
Get Moving!
A. Write the letter of the correct answer in your notebook.
1) The common multiples of 6 and 4 are
a. 2, 3, 4 b. 4, 6, 8 c. 8, 12, 16 d. 12, 24, 36
2) The common multiples of 4, 5 and 8 are
a. 8, 10, 16 b. 16, 20, 24 c. 40, 80, 120 d. 50, 90, 100
Lovelyn and Zerma are going to
prepare bouquets with 6 roses to a bouquets
and with 8 daisies to a bouquet. What will be
the smallest number of roses and daisies that
she will need for their bouquets?

3) The LCM of 15 and 9 is
a. 3 b. 15 c. 45 d. 135
4) The LCM of 2, 3, 4 and 5 is
a. 20 b. 30 c. 50 d. 60
5) A common multiple of 3, 5, 9 and 10 is
a. 30 b. 50 c. 90 d. 100
B. Determine the LCM.
1) 3 9 12 LCM = ________
3 4
2) 5 5 10 30 45 LCM = ________
1 2 6 9
3) 2 12 16 20 28 LCM = ________
2 6 8 10 14
3 4 5 7
Keep Moving!
A. Find the Least Common Multiple (LCM) of the given sets of numbers use
continuous division.
1) 3 15 21 LCM = ________
2) 4, 8, 16, 20 LCM = ________
3) 5, 10, 25, 30 LCM = ________
4) 6, 12, 15, 60 LCM = ________
5) 2, 6, 10, 14, LCM = ________

B. Find the Least Common Multiple (LCM) the following word problems using
continuous division.
1. What is the least number of candies that can be divided equally among 8, 9,
and 12 children?
2. You bring the drinks for your basketball team every sixth game. Every third
game is a home game. When will you first bring the drinks to a home game?
If there are 20 games in an annual sportsfest, how many times will you bring
the drinks to a home game?
Apply Your Skills!
Read and solve the common factors and GCF the following word problems.
1. Chill water her petchay every 2 days, and her cabbage every 3 days. Not
counting the first day, when is the first time both plants are waters on the same
day? When is the next time?
2. Efren goes home every other day. His wife Fely goes home every 4 days. His
daughter Edlin goes home every 6 days. If they see each other today, when will
they see each other again at home?
A. Mr. Placido, a security guard, has 3 successive night duties a week? His wife
who is a nurse has 2 successive night duties. When will they see again if they
are together now?

B. Two films were played at the same time. But the length of time of each film is
different from each other. Film A took 120 minutes while Film B took minutes.
After how many minutes will the two films be played at the same time again?
C. Find the LCM of each pair of number.
a. 33
and 23
b. 23
and 42
c. 8, 16, 24 and 48
d. 12, 30, 42, and 66

Lesson 13: Solves real life problems involving GCF and LCM of 2-3 given numbers.
Elmer wants to cut as many pieces of wood of equal lengths from three pieces with
lengths 35dm, 49dm, and 56 dm. What is the longest that he could cut each piece? How will you
solve for the answer to the problem?
You can use the 4 - step plan in solving for the answer.
Understand:
What does the problem? The longest that he could cut each piece.
What facts are given? 35 dm, 49 dm, 56 dm of wood.
Plan
How will you solve the problem? By finding the Greatest Common Factor (GCF) and Least
Common Multiple (LCM)
Solve:
How is the solution done? By listing the factors
35: 1, 5, 7, 35
49: 1, 7, 49
56: 1, 2, 4, 7, 8, 14, 28, 56
GCF: 7
By Prime Factorization
35: 5 x 7
49: 7 x 7
56: 7 x 2 x 2 x 2
GCF: 7
Check and Look Back:
What is the answer to the
problem?
7 dm is the longest cut can be done in the wood.
Can you think of other ways to solve the problem?
Get Moving!
Read each problem and answer the questions that follow. Write your answers in your notebook.
1. Mr Ramos has to prepare a number of exercises for his lesson for the day. He has three
classes. One class has 48 students, another class has 50, and another has 46. What
must be the largest number of exercises he should prepare so that each class will have
the same number of students working on different problems?
a. What is asked in the problem? __________________________________________
b. What facts are given? _________________________________________________
c. How will you solve the problem? _________________________________________
d. What is the answer to the problem? ______________________________________

2. Yesterday Tony bought 4 “Monay Bae” for Php. 5.00. He sold 3 “Monay Bae” for Php.
5.00. How many “Monay Bae” did he have to sell in order to make a profit of Php. 5.00.?
a. How will you solve the problem? ______________________________________
b. What is the answer to the problem? ___________________________________
Keep Moving!
Read and solve each problem. Write the solution in your notebook.
1. There are 14 blue and 20 red bulbs to be used for a birthday party. They are to be
placed in the plastic bags so that each bag contains the same number of blue and red
bulbs. What is the largest number of plastic bags that will be needed?
2. Liza has bought eight hair clips for Php. 10.00 and has sold them at 6 clips for
Php.10.00. How many hair clips have to be sold to make a profit of Php. 10.00?
Apply Your Skills!
Challenge yourself by solving these problems. Write your answers in your notebook.
1. Serena wants to create snack bags for a trip she is going on. She has 6 granola bars
and 10 pieces of dried fruit. If the snack bags should be identical without any food left
over, what is the greatest number of snack bags Serena can make?
2. Evelyn is packing equal numbers of apple slices and grapes for snacks. Evelyn bags the
apple slices in groups of 18 and the grapes in groups of 9. What is the smallest number
of grapes that she can pack?

Lesson 14: Create problems (with reasonable answers) involving GCF and LCM of 2-3
given numbers.
How will you create a problem involving Greatest Common Factor (GCF) or Least Common
Factor (LCM) given the following information?
You can create a problem by following this guide:
 Familiarize yourself with the concepts of GCF and LCM and their application to real life
situations.
 Think of the type of problem you want to create.
 Read some problems and study their solutions.
Problem 1:
Arielle is making flower arrangements. She has 7 roses and 14 daisies. She wants to
make all the arrangements identical and have no flowers left over.
Problem 2:
Tayli wishes to advertise her business, so she gives packs of 13 red flyers to
each restaurant owner and sets of 20 blue flyers to each clothing store owner. Tayli
realizes that she gave out the same number of red and blue flyers.
Study the following problems as examples for the above information.
Problem 1 involves finding the Greatest Common Factor (GCF)
Arielle is making flower arrangements. She has 7 roses and 14 daisies. She
wants to make all the arrangements identical and have no flowers left over.
What is the greatest possible number of flower arrangements she can make?
Problem 2 involves finding the Least Common Multiple (LCM)
Tayli wishes to advertise her business, so she gives packs of 13 red flyers to each
restaurant owner and sets of 20 blue flyers to each clothing store owner. Tayli realizes that she
gave out the same number of red and blue flyers.
What is the minimum number of flyers of each color she distributed?
Can you make another problem similar to these examples?

Get Moving!
A. Write a question to complete each item. Then, solve each problem.
1. Nathan is stocking bathrooms at the hotel where he works. He has 18 rolls of toilet paper and
9 bars of soap. If he wants all bathrooms to be stocked identically, with the same combination of
supplies in each one and nothing left over, what is the greatest combination of bathrooms
Nathan can stock?
2. Sarah’s Shipping and Ryan’s Mail Services both ship packages. Sarah’s trucks will only carry
loads of 18 packages. In contrast, Ryan’s trucks will only carry loads of 11 packages. If both
businesses ended up shipping the same number of packages this morning, what is the
minimum number of packages each must have shipped?
B. Create some problems involving GCF and LCM.
Keep Moving!
Write a problem for the numbers and phrases in the box.
1.
2.
3.
4.
Apply Your Skills!
Create problems involving GCF and LCM based on the following situations:
1. Alaiza arranged the fruits in a box.
2. Luisa shared her toys with her playmates.
3. Anthony is selling newspaper every morning.
4. Volunteers gives clothes in the orphanage.
5. Joey is preparing cake for her friends.
30 and 48 cookies Biggest numberPut inside the
identical container
32, 24, 16 balloons Arranged in a table Greatest number
5, 10 and 15
pictures
Smallest numberCollected
photographs
5, 6, 30 books Least numberNumber of books in
a shelve

Lesson 15: Adds fraction and mixed fraction without and with regrouping
A. Musician practiced very well for the concert. He practiced hours yesterday and hours
today. How many hours did he practice in two days?
The mathematical sentence is: + = n
Step 1 Step 2 Step 3
Find the LCD of the add the fractional Add the whole numbers
Given fractions and rename parts reduce in lowest term
These to similar fraction if needed
= = = 5 + 5 +
= = = = =
______ ______
= 5
Will become
While
Will become the answer will be

And will become in lowest term.
Get Moving!
Find the sum. Express your answer in lowest terms if possible.
1. 2. 18 3. 4. 5.
+ + + + +
_________ _________ _________ _________ _________
Keep Moving!
Add. Rename the sum in lowest terms if possible.
1. 2. 3. 4. 5.
+ 216 + + + +
_________ _________ _________ _________ _________
Apply Your Skills!
Read each Problem then, answer the question that follow.
1. Joshua picked 2½ buckets of strawberries. Joe picked 3½ buckets of strawberries. How
many buckets of strawberries did the two boys pick?
a. What is asked?
b. What are given?
c. What is the operation to be used?
d. What is the number sentence?
e. How is the solution done? Show your solution?
f. What is the complete answer?

2. Mrs. Gonzales used 2¼ cups of flour to make a plain cake, 3 ½ cups to make brownies and
2 ¾ cups to make doughnuts. How many cups of flour did she use?
a. What is asked?
b. What are given?
3. Three hogs weigh respectively kilograms, kilograms and kilograms. What
is the total weight?
a. What is asked?
b. What are given?

Lesson 16: Subtracting Fractions and Mixed fractions without and with Regrouping
Karen bought kilogram of lanzones and kilograms of banana.
How many more kilograms of lanzones than banana did she buy?
How will you answer the question in the problem?
To answer the question, subtract .
The number sentence is
= Change and to similar fractions by first finding
= the LCD OF 2 and 4.
Subtract the numerators.
Write the sum over the least common denominator
So, Karen bought kilogram more lanzones than banana.
Get Moving
Subtract the following fractions
1.
2.
3.
4.
5.
6.
7.
8.
LCD
LCD

Keep Moving
Subtract. Reduce the difference to lowest terms whenever possible.
1. 2. 3. 4. 5.
Apply Your Skills!
A. Read and solve each problem.
1. Jerrie can repair her car in hours. A mechanic can do the same job in 8/12 hour.
How much longer does it take Jerrie to do the job?
2. Pia spent hours in her grandparents’ house. This was of an hour more than
the time she spent at the mall. How much time did she spend at the mall?
3. Ana bought kg of grapes for her younger sister. They ate kg of it. How many
kilograms of grapes were left?
B. Read and solve each problem
1. Lailani has meters of yarn on a ball. After meters were unwound, how many
meters of yarn remained on the ball?
2. There are 5 pitchers of fruit juiced arranged in a row. The first pitcher contains
cups of juice. If each pitcher has cups less juice than the one before it, find the
amount of juice in each of the other pitchers.
3. Alvin weeded the garden in hours and watered the plants in hours. How
much longer did he spend weeding the garden than watering the plants?

First Quarter- Week 6
Lesson 17:Solving Routine and non routine problems involving addition and/ or subtraction of
fraction using appropriate problem solving strategies and tools.
EXPLORE AND DISCOVER
Darwin painted his room using 5/6 liter of blue paint and 2/3 liter of white paint.
What color of paint was used more than the other? How much more of it was used than
the other?
You can solve the problem using the following steps.
Understand:
 Know what is asked : The paint color that was used more and by
by how much more
 Know the given facts: 4/6 liter of blue paint; 4/5 liter of white paint
Plan:
 Draw a picture :
5/6
2/3 = 4/6 1/6
 Identify the operation to be use: Subtraction
 Write the number sentence : 5/6 – 2/3 = n
5/6 – 2/3= 5/6 – 4/6 = 1/6
Solve:
 Solution:
Check and Look back:
 Answer: a. more blue paint was used
b. by 1/6 liter
Get Moving

Read each problem carefully and then solve.
1. Mark wash his car in 4/5 of an hour, cleaned the garage in 2/6 of an hour, and painted
the garden fence in 2 hours. How long did it take him to do all the tasks?
2. Anthony walked ¼ of a kilometer to Jane’s house and 7/8 of a km to the park. How
far did he walk?
3. Jenny spends ¼ of her daily allowance for snacks, ½ for lunch, 1/8 for transportation,
and saves the rest. What part of her daily allowance does she save?
Keep Moving
Read and solve each problem.
1. Liza spent ¾ hour preparing the soil and 2/3 hour planting. How much time did she
spend in the garden?
2. In a fruit basket, 4/5 of the fruits are bananas and 3/8 are mangoes, which are more-
the bananas or the mangoes?
3. Ronnie had 7/8 gallon of paint. He used 4/5 of it. What fraction of a gallon of paint was
used? How much paint remained?
Apply Your Skills
1. Four fifths of a group of rallyists were students, If 3/8 of the students were female,
what part of the rallyists were male students?
2. Angie covered ¾ of a bulletin board with white paper. Then, she made a Math poster
on 2/3 of the white paper. What part of the board was covered by the poster?
3. A water tank was 20/21 full. If 3/5 of it was used to water the plants, what fraction of
the tank was used in watering the plants?

Lesson 18: Creating problems (with reasonable answers) involving addition and/or subtraction
Fraction using appropriate problem strategies
Explore and Discover
How do you create a word problem involving addition, subtraction, or addition and
subtraction of fractions?
You can create a word problem by observing the following guide:
 Familiarize yourselves with the concept of addition and subtraction of fractions
and their application to real- life situations
 Think of the problem you want to write.
You also consider the following when creating a problem:
a. Characters
b. Situation/ setting
c. Data
d. Key question
Study the table below:
Name Ribbons used/ left Quantity Unit
Liza White ribbon 2/8 meter
yellow 2/4 meter
Ribbons left 3/6 meter
Study the problem as an example for the given data.
Liza bought 2/8 m of white ribbon and 2/4 m of yellow ribbon to make flowers.
After making 5 flowers, she found out she had 3/6 m of ribbons left. How many
meters of ribbon did she use for the flowers?
Get Moving!
Use the data below to create a one-step word problem involving subtraction of
fractions.
Name Color of Paint used in the
classroom
Quantity Unit
James Blue 4/5 liter
Harold Green 3/6 liter

Keep Moving!
Use the data below to create a two- step word problem involving addition and
subtraction of fractions.
Name Quantity Unit Color of cloth
needed in science
project
Carmen 3/5 Meter White
Rowena 2/8 Meter Red
Aileen 5/6 Meter yellow
Apply Your Skills!
Using the table below, create a problem for each of the following.
1. One- step word problem involving addition of fractions (Group 1)
2. One-step word problem involving subtraction of fractions (Group 2)
3. Two-step word problem involving addition and subtraction of fractions (Group 3)
Name Quantity Quantity ( in kilograms)
Sharon Grapes 1/2
Vilma Papaya 3/4
Nora Lansones 4/8

1 x 1 = 1
5 2 10
LESSON 19 Visualizes Multiplication Of Fractions Using Models
Darwin had a piece of plastic cover ½ meter long. He used 1/5 of it to cover his book. What fractional
part of the plastic cover did he use?
To find the answer, get 1of 1.
5 2
The diagram below will help you find the answer.
If the rectangle represents 1 metre, the shaded part represents the plastic cover of Darwin.
To find 1 of 1 , we have to divide the shaded
parts into 5 equal parts and take 1 of the equal
parts 5 2
The part of the whole representing the product of 1/5 x 1/2 is the region that has been shaded twice.
Notice that the rectangle has been divided into 10 equal parts and 1 part is shaded twice so 1/5 x 1/2
must be 1/10, Darwin used 1/10 metre of plastic cover.
STUDY THESE EXAMPLE
Let us use a region to find 1/3 of 2/5 or 1/3 x 2/5.
The region at the left has been divided vertically into 5 parts of
the same size. Therefore each parts is 1/5 of the whole region.
Ask. How many fifths are shaded? What part of the region is
shaded?

Thus: 1 2122
3 of 5 equals 3 x 5 = 15
Get Moving
1. Write a multiplication equation for each visualization and find the answer
a
X = =
_________
b.
X =
= _________
c.
x = =
____
Next picture 2 horizontal lines have been drawn to divide
each 1/5 into 3 equal parts.
Into how many equal parts is the region now divided?
How many small regions are shaded?
Next , 1/3 of the shaded part has been shaded in
another direction. How many of the small regions are
now shaded twice ? What part of the whole region is
shaded twice?

Keep Moving !
Match the picture in Column A with the multiplication sentence in Column B. Write your answer
in your notebook.
A B
Apply Your Skills:
Write the multiplication equation for each and find the answer.
a. 11
2 of 4
b. 13
3 of 4
c. 11
5 of 2

x =
=
A. Illustrate and Find the Product
1 323 5. 31
3 45 4 5 4
x =
x
=
x
= x =
=
3.
4.
1.
2.

LESSON 20: MULTIPLIES A FRACTION AND A WHOLE NUMBER AND
ANOTHER FRACTION
First Quarter : Week 7
A. Michelle bought kg of carrots for her pet rabbit. Her
pet ate of this how many carrots did her pet
eat?
To know the amount of carrots the rabbit ate, let us compute of . How do we right of
in a number sentence ? x = N
Let’s solve this in two ways
First let us use an illustration to get the product.
3
4
133 1
3 4 12 4
The double shaded parts show the parts of the carrot eaten by the rabbit. .When reduced to
lowest terms is
So, Michelle’s pet ate ¼ of the carrots.
1
3
1
3
1
3
3
4
3
4
x = =
3
12
1
4
1
3
3
4

3
12
Let’s solve x again, this time through computations.
Multiply the numerators x =
Multiply the denominators x =
Reduce the product to lowest terms ÷ =
Study these other examples:
of == or x 8
If we have a whole number like 8 we can also write it as a fraction with a denominator of 1.
1
4 because 0r 2
GET MOVING
Direction : Cut each strip. You may paste them in a chipboard or cartolina to make them harder.
STEP 1
1
3 3
4
3
STEP 2
1
3
3
4
3
12
STEP 3
3
3
1
4
1
4 8
1
4
1
4
1 8
so4 x 8 = 4 = 2
X 8 = 2,
1
4
x 8
1
= 8
4

KEEP MOVING !
Read the problem:
A. Ramona has yard of a beautiful lace. She gave of it to her friend for their project.
If 2/3 of the apples above are green, then how many are green apples ? Color them to
show your answer ?
If 6/7 of the socks are black,
then how many pieces are
not black ? Color them to
show
ofof the pizza shown will be
given to my classmate. Draw line/s on it to
show the part to be given.
1
2
3
4
4
6
2
3

What part of the lace did Ramona give to her friend ?
B. Bon bought 8 kilos of mango in the market. He shared of it with his relatives for their
outing. How many kilos of mango did he share?
C. One fifth of the 40 pupils of Miss Ramos are Math Club members. How many pupils are
Math Club members ?
APPLY YOUR SKILLS !
Find the product. Always express answers in lowest terms.
1. What is 2,andof ? __________________
2. What is the product of 3/4 ,4 and ½ ? __________
3. What is the value of N ? 5 x ¾ x = N
4. Multiply, and 4.The answer is ________.
5. What is the product of 5 , ½ and? _________
2
3
5
6
3
4
2
4
3
4
2
6
3
6

Lesson 21: Multiplying Mentally Proper Fractions with the Denominators Up to 10.
Nelia has ½ piece of a cartolina. She shares 1/3 of it to Joe who needs it very badly for his
Science project. What part of the cartolina did Nelia Share?
How will you solve for the product of the fractions mentally?
Here’s how to do it.
Do these steps in your mind.
11 1x1 =1
2 x 3 = 2x3 =6 Step 1: Multiply the numerators.
1x1 = 1
Step 2: Multiply the denominators.
2x3 = 6
Step 3: Express the answer in lowest terms if needed.
Get Moving!
Solve the following mentally.
13318541 2 1
5 × 4 = 7 × 3 = 10 × 6= 9× 2 = 8×3 =
A. Find the product mentally.
7461256379
9 x 5 = 10x6 = 3x9 = 8x 5 = 8x 10 =
B. Find the value of N.
1237548134
2 x 3 =N 5 x 8 =N 6 x 9 =N 9 x 3 =N 7 x 5 =N
Apply Your Skills!
A. Read the problems, then solve them mentally.
1. Roy harvested 5/6 crates of mangoes. He sold 4/5 of them. What part of the crate of
mangoes was sold?
2. Dino bought ½ L of white paint. He used ½ of this to paint the doghouse that he
made. How many litres of paint did he use?
B. Understand the equations carefully, then answer it.

1. In the equation 2/3 x ½ =N, what is the value of N?
2. If you multiply ¼ and 2/3, what will be the product?
3. Multiply 2/5, 3/4 and 4/5. It will give a product of_____.
4. What is the product of 2/7,3/8, and ½ ? _______
5. Multiply 2/3, 5/6 and ¾. The answer is _______

1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
Lesson 22: Solving Routine or Non-routine Problems Involving
Multiplication Without or With
 Addition or Subtraction of Fractions and Whole Numbers
Using Appropriate Problem Solving Strategies or Tools.
Problem 1: Lucy’s mother worked in her boutique for 2 ½ hours each day for 2 weeks.
How many hours did she work in all?
You can solve the problem using the steps below:
 Understand
Know what is asked: No. of hours she worked in all.
Know the given facts: 2 ½ hours and 14 days = 2 weeks
 Plan
Determine the operation to be used: Multiplication
Write the number sentence: 2 ½ × 14 = N
 Solve: Show your solution:
2 ½ × 14 = N
2 ½ × 14/1 = N
5/2 × 14/1 = N
1 7
5/1 × 7/1 = 35/1 or 35 hours
Lucy’s mother worked 35 hours in 2 weeks or 14 days.
 Check and look back: Did I do the operation correctly?
Is my answer reasonable? Did I write my answer in a complete sentence?
Problem 2: Jose harvested 15 kilograms of guavas from the orchard. He gave 2/5 of them to
his neighbors. How many kilograms of guavas did he share to his neighbors?
 Understand
Know what is asked: No. of kilograms he shared to his neighbors.
Know the given facts: 15 kilograms of guava and 2/5 part shared to his
neighbors
 Plan: Make a diagram or drawing.
 Draw 15 kilograms of guavas

1kilo
o
1kilo 1kilo
1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
Divide 15 kilograms of guavas into group of 5.
There will be 3 kilograms per group.
Circle 2 parts of it to show 2/5.
Each group shows 1/5 or 3 kilograms of guavas. There are 2 groups of 1/5 and
this shows 2/5.
So, 2 × 3 = 6 kilograms of guavas he shared to his neighbors.
 Look back: To check 15 × 2/5 = 6 kilograms.
15 × 2/5 = 3 15 × 2 =6 or 6 kilograms of guavas
1 5 1 1
Answer: He shared 6 kilograms of guavas to his neighbors.
Can you try solving the following problems?
1. One – fourth meter of the cloth was left from Evelyn’s uniform. Her friend asked
3/5 of it to her Science project. What part of the cloth did her friend get?
2. Mrs. Albano gathered 50 eggs from her poultry. She gave 4/8 of these to her co-
teachers. How many eggs were given to her co-teachers?
Get Moving!
Solve the following problems.
1. A recipe for doughnuts needs 1 ¼ cups of flour. Mother will prepare 1 1/3 times the
recipe. How much flour will she need?
2. On Jenny’s birthday, her mother prepared 48 cupcakes. If ¾ of the cupcakes were
served, how many cupcakes were served?
1kilo
3 kilo
1kilo1kilo1kilo
o
1kilo 1kilo
3 kilo 3 kilo
3 kilo 3 kilo
3 kilo
1kilo 1kilo 1kilo 1kilo 1kilo 1kilo 1kilo 1kilo1kilo

3. Nelson had 3 ½ liters of paint. He used 2/3 of it to paint their fence. What part of the
paint did he used?
4. Remy had ¾ meter long of lace. She gave 1/3 of it to her classmate to decorate her
Science project. What part of the lace was given to her classmate?
5. Everyday Alvin spends 3 ½ hours reading books. How many hours does he spend in a
week reading books?
Keep Moving!
Solve the following problems. Write your solutions and answers in your notebook.
1. Anselmo spent 6/8 of his time in morning studying Math and Science. He spent ¼ of this
time studying Science. What fraction of the total time did he spend studying Science?
2. What is the area of a rectangle whose length is 8/10 m and width is 2/3 m?
3. Aling Aning planted vegetables on 4/7 of her vacant lot. Two thirds of it was planted with
pechay. What fraction of the vacant lot had pechay?
4. Lorna had 2 ½ liters of beef broth. She used 3/5 of it to make soup. How much beef
broth did she use to make soup?
5. A recipe calls for 1 1/3 litres of milk. How many litres of milk do you need to make 2
recipes?
Apply Your Skills!
Try solving more problems!
1. Joanne signed up for 24 dancing lessons. She took ¾ of them by April. How many
dancing lessons did she take by April?
2. Father’s monthly salary amounts to ₱ 20,500. Every time he receives his salary, he
deposits 1/5 of it. How much is father’s monthly savings? How much is his annual
savings?
3. How far can father go in 8 ½ hours if he travels at an average speed of 15 kilometers an
hour?
4. Six pitchers each filled with ¾ liter of juice were served to Luisa’s visitors. Find the total
amount of juice served.
5. The school Home Economics Club had a buko pie sale. The member sold 2/3 of their
pies in the morning and 1/6 of their pies in the afternoon. If 150 pies were left, how many
pies had been sold?

Alice used ¼ teaspoon of salt on her cake recipe. How much salt is needed if
she will make 8 recipes of it?
Lesson 23: Creating Problems (with reasonable answer) Involving
Multiplication of Fractions
How do you create a word problem involving multiplication of fractions?
Observe the guide below in creating a word problem:
 Familiarize yourselves with the different Mathematical concepts
especially multiplication of fractions.
 Analyse the data and think of the type of problems you
want to create.
 Read and study some sample problems and be familiar with
the organization of data on the problem.
 Learn about the basic terms or word clues often used in mathematical problems.
The following data is important to be considered in creating a problem:
 Name/Character
 Situation/Setting
 Data
 Unit
 Key question
Study the given data below:
teaspoon of salt for cake recipe
8 recipes to make
Study the problem as an example for the data given.

Get Moving!
Create a one-step word problem involving multiplication of fractions using the
data given.
1. – part of Mrs. Marco’s class who joined the field trip
30 - total number of pupils
2. kg- mixed nuts bought by Ana
of it given to Alma
3. 12 km- distance of Elmo’s house to school
of total distance is being travelled by jeepney
4. Php 24,000- amount raised by PTA of Del Mundo Elementary School
spend for completing the school’s fence
5. 5 kg of rice bought by mother
cooked for dinner
Keep Moving
Create a one-step word problem involving multiplication of fractions using the data given.
1. kg meat bought by Mr. Guanson
kg cooked
2. Php 420 earnings of Gab every day in working at a printing house
for transportation allowance
3. 5 m ribbon bought by Kim for gift wrapping
used in wrapping square boxes
used in wrapping rectangular boxes

Apply Your Skills!
Create a word problem involving multiplication of fractions for each of the following. Use the
data below.
1. One-step word problem involving multiplication of fractions.
2. Two or more step word problem involving multiplication of fractions.
Name Monthly Salary Monthly Savings
Randy Php 12,000
Ryan Php 15, 000

4 x
𝟏
𝟒
=
𝟒
𝟏
x
𝟏
𝟒
=
𝟒
𝟒
= 1
𝟏
𝟐
𝟑
x
𝟑
𝟓
=
𝟓
𝟑
x
𝟑
𝟓
=
𝟏𝟓
𝟏𝟓
= 1
𝟑
𝟕
x 𝟐
𝟏
𝟑
=
𝟑
𝟕
x
𝟕
𝟑
=
𝟐𝟏
𝟐𝟏
= 1
Lesson 24: Show that multiplying a fraction by its
reciprocal is equal to 1
Janice shared the pizza she made among her 5 friends.
Each one received of the pizza. Nothing was left for her.
How much pizza did she make?
Find: 5 x
Solution:
5 x = x = = 1
Answer: Janice made 1 whole pizza divided among her five friends.
Study some more examples:
 Two numbers whose product is 1 are reciprocals of each other.
 To find the reciprocal of a fraction make the numerator of the
fraction the denominator of the reciprocal and the denominator of
the fraction the numerator of the reciprocal.
 Mixed fractions must first be converted to improper fractions
before the method can be applied.
 Write the reciprocal of a whole number as fraction.

Get Moving!
Give the reciprocal of each number.
1. 51 6. 11. 2
2. 3 7. 12. 35
3. 8. 13. 5
4. 9. 14. 12
5. 24 10.5 15.
Keep Moving!
Write the missing factor.
1. x = 1 6. x = 1
2. x = 1 7. x = 1
3. x = 1 8. 5 x = 1
4. 15 x = 1 9. x = 1
5. x = 1 10. x = 1
Apply Your Skills!
1. The reciprocal of a number is , and their product is 1. What is the number?
2. Two numbers are reciprocals of each other. One number is 36 times as large as the other. What
are the numbers?
X = 1
3. What is the reciprocal of a number whose numerator is 8 times as great as 3 and the
denominator is half the numerator?

Lesson 25: Visualizing Division of fraction
Janella helps her mother cut meter long ribbon from meter ribbon. How many strips can she
cut? Study the illustration and solution below.
Number sentence :
÷ = __________
From the figure we can see that there are twenty-eight in . Therefore, the answer is 28.
Get Moving!
Use illustrations to answer each question.
1. How many are there in 9?
2. How many s are there in ?
3. How many are there in 24?
4. How many are there in ?
5.
6. How many are there in ?
Keep Moving!
Illustrate to find the quotient.
1. ÷ = 2. ÷ = 3. ÷ = 4. ÷ = 5. ÷ =

Apply your Skills!
Use a model to solve the problem.
1. Camille needs m of cloth for a banner. If she has m of cloth, how many banner can
she make?
2. Mrs. Dator needs4 liters of fresh milk. The store has liter packs of fresh milk. How
many packs does she need to buy?
3. Mario has 8 logs to be cut in fourths to make fence posts. How many fence post can he
make?
4. Mother bought 5 apples. She divided them into halves. How many pieces of apple
were there?

Lesson 26: Dividing Simple Fractions and Whole Number and a Fraction
Nathan wants to share his buko pie with his friends. He has of the buko pie, and he wants to
give each friend of the buko pie. How many friends can Nathan feed?
Solution:
Without any illustration we can solve the problem following the steps in dividing simple fraction.
Solution:
÷ = n
÷ = n Write the reciprocal of the divisor
x = n Change the division sign into multiplication sign
x = Multiply the numerators then the denominators
÷ = 4 Express in lowest term if necessary
Therefore ÷ = 4
Nathan can feed 4 of his friends.
Problem 2.
Jane received 3 guavas from her friend. She cut it into pieces. How many halves did she
have?
Use real guava to solve the problem
Problem 3
Lina has of a chocolate bar. It will be divided equally among 4 persons, what part of the
chocolate bar will each one get?
We can solve the problem following these steps:
Step 1. Write thee number sentence. ÷ 4 = ___
Step 2. Rename the whole number in fraction form ÷ = ___
Step 3. Get the reciprocal of the divisor then proceed to
Multiplication of fractions. ÷ =

Step 4. Write the product of the numerators over the product
of the denominators; and reduce the fractions if needed
Get Moving!
Read and analyze each question then solve.
1. What is the quotient of and ?
2. If you divide by times, what is the answer?
3. What is the quotient of divided by ?
4. ÷ =
5. ÷ = n
Find the quotient. Show your solution.
1) 6  = n
2) 16  = n
3) 14  = n
4) 8 = n
5) 30 = n
Keep Moving!
Find each quotient.
1. ÷ = n 2. ÷ = n 3. ÷ = n 4. ÷ = n 5. ÷ = n
Find the quotient.
1. 10 = n 2. 15 = n 3. 45 = n 4. 36 = n 5. 28 =
Apply your Skills!
1. Find the number of eights ( ) in
2. AlingNarda repacked kg of pepper into kg bags . How many bags of pepper can she
make?
6
5
4
3
7
2
8
1
4
3

3. There are 4 kilograms of rice. Each girl scout can consume kg of rice per meal. For
how many girl scouts is the rice enough for a meal?
5
1

Lesson 27 : Solving Routine or Non-Routine Problems Involving Division Without or With
Any of the Other Operations of Fractions and Whole Numbers Using
Appropriate Problem Solving Strategies and Tools.
Read the problems below.
Can you solve the problem?
Here are the steps in analyzing and solving the problems.
Problem 1
A 4-meter piece of wood is to be
divided into pieces, each 2/3 m long.
How many pieces can be cut from it?
Nicole has 42 meters of ribbon. She
uses meters for every box she
makes. How many boxes can she
make from the ribbon?
 Understand
Know what is asked: Number of pieces that can be cut
Know the given facts: 4 meter piece of wood
m each long
 Plan
Determine the operation to be used: Division
Write the number sentence: 4 = n
 Solve
Show your solution:
4 = n x = or 6
Review and check your answer
Answer: There were 6 pieces of wood
 Check and look back
Did I do the operations correctly?
Is my answer reasonable?

Problem 2
1. If a skirt requires 1 ¼ meters of cloth, how many skirts can be made from 21
meters of cloth?
2. Linda made a trip of 112 kilometers in 2 ½ hours. What was her average
speed?
Get Moving!
1. A log 5 ¾ meters long will be cut into 6 equal pieces. How long will each piece
be?
 Understand: _____________________________________________
 Plan:___________________________________________________
 Solve: __________________________________________________
 Look back: ______________________________________________
2. Andrea has 35 meters of cloth. How many aprons can she make if each
apron requires meters?
 Understand: _____________________________________________
 Plan:___________________________________________________
 Solve: __________________________________________________
 Look back: ______________________________________________
 Understand
Know what is asked: The number of boxes that can be make from the ribbon
Know the given facts: 42 meters of ribbon
meters for each box
 Plan
Write the number sentence: 42 = n
Solve
Show your solution:
42 = n = = = 18
Using cancellation
= x = or 18
Review and recheck your answer:
Answer: Nicole can make 18 boxes from the ribbon.
Review and check your answer
Answer: There were 6 pieces of wood

3. Calix needs to divide cups of flour among 3 recipes. How many cups
of flour does each recipe need?
 Understand: _____________________________________________
 Plan:___________________________________________________
 Solve: __________________________________________________
 Look back: ______________________________________________
4. The class of Lora is repacking goods for the outreach. How many kg
packs of sugar can they make out of a bag that contains 15 kg of sugar?
 Understand: _____________________________________________
 Plan:___________________________________________________
 Solve: __________________________________________________
 Look back: ______________________________________________
5. Nikki has 8 meters of fabric to make shirts. If each shirt requires m of
fabric, how many shorts can she make?
 Understand: _____________________________________________
 Plan: ___________________________________________________
 Solve: __________________________________________________
 Look back: ______________________________________________
Keep Moving!
1. Jeff has meters of rope. He wants to make 3 pieces of clothes hanger
out of it. How long will each clothes hanger be?
2. A farmer bought kilograms of fertilizer for his rice, camote, and potato
crops. If the fertilizer will be used equally on the three crops, how much
will be used for each crop?
3. Mr. Reyes has a coconut plantation that measures hectares. If the
entire plantation is to be subdivided among 36 tenants, how much would
be each tenant’s share ?
4. Donald was able to harvest 2 ¼ kg of tomatoes from each of 4 plots.
Then he divided them equally into 6 piles. How many kilograms of
tomatoes did each pile have?
5. Lucy equally poured 4/5 liter of lemonade into 6 cups. How much
lemonade did each cup have?
Apply Your Skills!
Try solving more problems!
Read and analyze the following problems. Solve them in any method you like
1. Mrs. Gibe has to pack 50 kg of rice. How many plastic bags are needed if
each bag can contain kg of rice?
2. Merllie makes hand towels for sale. How many hand towels can she make
from 6 meters of cloth if meter is used for 1 hand towel?
3. How many meter of cloth can be cut from 40 meters of ribbon?

4. On their trip to Laguna, Mr. Santos’ family bought 4 baskets of lanzones.
Each basket contained kg of lanzones. The family shared the 4 baskets of
lanzones among 8 persons. How many kilograms of lanzones did each one
receive?
5. How many m pieces of ribbon can be cut from a 50 m of ribbon?

Lesson 28 : Creating Problems (with reasonable answers) Involving Division or With Any
of Other Operations of Fractions and Whole Numbers
How do you create a word problem involving division or with any of other operations of
fractions and whole number?
 Familiarized yourselves with the concepts division with other operation of
fractions and whole number and their application to real-life situations.
 Think of the problem you want to write.
You also consider the following when creating a problem:
a. Characters
b. Situation/Setting
c. Data
d. Key Question
Look at the given data below.
 60 kilograms of rice
 kg of rice in each plastic bag
 Number of plastic bags needed for repacking
Can you now complete the word problem below and solve for the correct answer, too?
Do this in your notebook.
Mrs. Ana has to pack _____________. How many plastic bags are needed if each bag
can contain______________?
Get Moving!
Create a word problem from the given data below.
Solve the problem in your notebook.
1. 12 kilograms of flour
¾ kilograms in each plastic bag
Number of plastic bags used
Problem:______________________________________________________________
Solution and Answer:____________________________________________________
2. 30 meters long of wood
1 ½ meters long for each piece
The pieces of woods that can be cut
Problem:______________________________________________________________

3. meters long of electric wire
6 equal pieces
The length of each wire
Problem:______________________________________________________________
4. of a pie
4 persons
The part of the pie each one gets
Problem:______________________________________________________________
5. 5 meters of cloth
2/3 meters for each scarf
The number of scarves that can be make
Problem:______________________________________________________________
Keep Moving!
Complete each problem by creating a question for what is asked. Then, solve the problem.
1. Ella has 15 kilograms of rice for sale. She placed these in plastic bags. Each bag
contains kilograms.
Question:________________________________________________________
Solution and Answer: ______________________________________________
2. A log meters long will be cut into 7 equal pieces.
Question:________________________________________________________
3. Nene has cake. She divided it among her 6 friends.
Question:________________________________________________________
4. Michelle needs to divide cups of flour among 3 recipes.
Question:________________________________________________________
5. A tailor has a bolt of cloth 20 meters long. Each uniform needs meters of cloth.
Question:________________________________________________________

Apply You Skills!
Create a problem using the given data. Then, solve the problem.
1. Given: 50 kilograms of cholcolate
kilograms packed in each box
Asked: Number of boxes used
Problem: _____________________________________________________
Solution and Answer: ___________________________________________
2. Given: 12 meters of fabric
meters for each shirt
Asked: Number of shirts that can make
Problem: _____________________________________________________
3. Given: 15 meters of cloth
meters for each cloth
Asked: Number of blouses that can make
Problem: _____________________________________________________
4. Given: 24 kilograms of rice
kilograms in each bag
Asked: Number of bags used
Problem: _____________________________________________________
5. Given: 8 meters piece of wood
meters long for each piece of wood
Asked: Pieces of woods that can be cut
Problem: _____________________________________________________

Lesson 29: Giving the Place Value and the Value of a Digit of a Given Decimal Number
through Ten Thousandths
Study the chart below.
PlaceValue
Tens
Ones
Decimal
point
Tenths
Hundredths
Thousandths
Ten
thousandths
Digits 0  5 9 8 7
Value 0  .5 .09 .008 .0007
In 0.5987 the digit 0 is a place holder of ones place. The digit 5 is in tenths place. Its
value is .5. The digit 9 is in the hundredths place. Its value is 0.09. The digit 8 is in the
thousandths place. Its value is 0.008 and digit 7 is in the ten thousandths place, its value is
.0007. Hence, 0.5987 means five thousand nine hundred eighty-seven ten thousandths.
Here are other examples:
1.3984
Digit Place Value Value
1 Ones 1
3 tenths 0.3
9 hundredths 0.09
8 Thousandths 0.008
4 Ten thousandths 0.0004

Get Moving!
Write each in symbols, then give the value and place value of the underlined digit.
Symbol Value Place Value
1. Five and three hundred ten thousandths
2. Twenty-five and two hundred ten
thousands
3. Fifteen hundredths
4. One hundred one and one tenths
5. Five hundred and three ten thousandths
6. Ten and ten hundredths
7. Ninety-nine ten thousandths
8. One and fifteen ten thousandths
9. Fifty-nine and four hundred ninety-eight
ten thousandths
10. Eight ten thousandths

Keep Moving!
A. Give the place value of the underlined digit.
1. 6.28 6. 4.3763
2. 0.0028 7. 0.7659
3. 0.827 8. 2.7854
4. 21.843 9. 3.9681
5. 9.375 10. 19.0365
B. Write the place value of the digit 8 in each number.
1. 29.378 6. 86. 047
2. 908.176 7. 45.801
3. 471.081 8. 567.3278
4. 57.8012 9. 67.8703
5. 870.2194 10. 0.2358
C. In 50 678.39241, identify the digit in the ….
a. Hundreds place _________
b. Thousandths place _______
c. Tenths place ________
d. Ten thousands place ______
e. Hundredths place _________

Apply Your Skills!
Read and answer the questions that follows:
1. Men’s gymnastics is divided into compulsory and optional events. In 1984, the United
States team members won the gold medal. Their score in the optional events was
296.0391. in the compulsory events they scored 259.3127.
a. Read 296.0391 259.3127
b. Identify the place value of each decimal numbers.
2. Copy all decimals that have 2 in ten thousandths place. Give the place value and
value of the digit before the digit in the ten thousandths place.
a. 6.28 d. 8.2902
b. 0.0028 e. 9.0092
c. 4.4689
3. Copy the decimals that have 5 in the ten thousandths place. Give the value and place
value of the digit after the decimal point.
a. 5.5543 d. 5555
b. 19.5555 e. 3.4835
c. 6.4625

Lesson 30: Reading and Writing Decimal Numbers through Ten Thousandths
What are the numbers in the situation? 45.8 and 43.75
What kind of number is that? Decimals
How do you read and write decimal numbers?
The decimal 45.8 is read as forty-five and eight tenths
The decimal 43.75 is read as forty-three and seventy-five hundredths
Decimals are just another way of writing fractions whose denominators are powers of ten
and the proper way to read them is the same as reading the corresponding fractions which they
are represent.
Here are other examples:
Decimal Fraction Read as:
0.6
10
6
Six tenths
0.12
100
12
Twelve hundredths
0.2568
10000
2568 Two thousand five hundred
sixty-eight ten thousandths
In the examples “zero” and the decimal point are not read nor write in words anymore.
Carl and his brother take good care of their bodies. They eat the
right kinds of foods to maintain their proper weights at their age. Carl
weighs 45.8 kilograms while his brother weighs 43.75 kilograms.

Get Moving!
A. Read each decimal number correctly.
1. 0.059 4. 0.0007
2. 20.7034 5. 7. 8254
3. 46. 340
B. Write a decimal number for each.
1. two hundred forty-six ten thousandths ______________
2. six and forty-eight thousandths ______________
3. twenty-six and eight tenths ______________
4. two hundred and forty-seven thousandths ______________
5. Seven hundred twelve and eleven ten thousandths ______________
6. thirty-one ten thousandths ______________
7. nine and nine tenths ______________
8. six hundredths ______________
9. three hundred seventy and four tenths ______________
10. ten and two thousand fifty-one ten thousandths ______________
Keep Moving!
A. Write in words.
1. 3.06 _________________________________________________________
2. 0.8009 _________________________________________________________
3. 0.014 _________________________________________________________
4. 15.300 _________________________________________________________
5. 18.009 _________________________________________________________
B. Write down as decimals.
1.
10
8
6.
10000
164

2.
1000
4
7.
10000
237
3.
100
45
8.
1000
258
4.
1000
17
9.
10000
10
5.
10000
69
10.
100
12
Apply Your Skills!
Read and answer the following:
1. The distance between the town church and the market is one and eighty-nine
thousandths kilometres. Write the distance as a decimal number.
2. How many decimal places does “one and three hundred sixteen ten-
thousandths”
have?
3. How many decimal places does thirty-three thousandths have?
4. I am a decimal number. My thousandths digit is three more than my tenths
digit.
My ones digit is 3 and so my tenths digits. All the other digits are 0 and I
have
four decimal places. What number I am?
5. How many hundredths are equal to 1.3?

Lesson 31. Rounding Decimal Numbers to the Nearest Hundredths and Thousandths
James climb a 483 meter hill. If there are 1000 meters in 1 kilometer,
what part of the hill and did Luis climb? Round to the nearest hundredths.
To know the part of the hill Luis climb.
1. Change meter to kilometre. (1000 m=1 km)
1000
483
= .483
Rounding off number using number line
.480 .481 .482 .483 .484 .485 .486 .487 .488 .489 .490
From the diagram, it is easy to see that .483 is nearer to .480 than .490. So .483 is rounded to
.480.
Now, let us try to round .483 to the nearest hundredths.
Study the illustration below.
.483
Rounding place
The digit to the right is smaller
than 5, so it rounds down.
.483 rounded to the nearest
thousandths is .480
 To round decimals
1. Identify the digit to be rounded-off.
2. Inspect the digit to the right of the required place.
a. If the digit is greater than 5, add 1 to the digit at the required place.
b. If the digit is less than 5, retain the digit at the required place. Then drop all
the digits to the right of the required place.
c. Copy all the digits to the left of the required place if there are any.

Get Moving!
A Round to the nearest hundredths.
1. 48.019 _____________________ 6. 0.925 ___________________
2. 16.975 ______________________ 7. 4.018 ___________________
3. 15.614 ______________________ 8. 12.3057 ___________________
4. 12.089 ______________________ 9. 8.1749 ____________________
5. 4.613 ______________________ 10. 1.001 ____________________
B. Round to the nearest thousandths.
1. 8.0079 ______________________ 6. 8.3056 ____________________
2. 1.4067 ______________________ 7. 1.6149 ____________________
3. 2.5974 ______________________ 8. 12.0192 ____________________
4. 0.1549 ______________________ 9. 3.8315 ____________________
5. 2.5973 ______________________ 10. 2.5615 _____________________
Keep Moving!
Decimal Round to nearest hundredths Round to the nearest
thousandths
1. 2. 3842
2. 0.56893
3. 2.96425
4. 5.2358
5. 0.86302

B. Write the letter of the number that rounds off to the given number.
1. 3.65 a. 3.624 b. 3.580 c. 3.672 d. 3.647
2. 15.27 a. 15.225 b. 15.278 c. 15.278 d. 15. 273
3. 10.85 a. 10.859 b. 10.857 c. 10.851 d. 10.856
4. 32.548 a. 32.5476 b. 32.5488 c. 23.534 d.32.6437
5. 211.78 a. 211.789 b.211.784 c. 211.786 d. 211.7865
C. Get the quotient up to the nearest thousandths plce. Then round the decimal to the nearest
thousandths. Number 1 is done for you.
1. 36 ÷7 = 5.1425.14 4. 73÷ 8 = ______ ________
2. 47 ÷ 8 = ____ ____ 5. 78 ÷ 9 = ______ ________
3. 71 ÷ 8 = ____ _____ 6. 34 ÷ 9 = ______ ________
Apply Your Skills!
Answer the following:
1. a. What are the smallest and largest decimals in hundredths that rounds to 0.5?
b. What is the largest decimal in hundreths round to 0.5?
2. One centimeter is equivalent to about 0.3937 inch. Round off the given equivqlent to the
nearest hunderdths.
3. Mrs. Edlagan has a total deposit of 50 766.25. The annual interest at 3% simple interest
is 1 522.9875. Round off interest to the nearest hundredths and thousandths.
4. The decimal rounds to 3.2. The digit in the thousandths place is 4 times that in the
hundredths place. The sum of the digits is 15. What decimal is it?

Lesson 32: Comparing and Arranging Decimal Numbers
How do you compare decimal numbers?
There are three ways to compare decimal numbers. The first one is by using a number
line for small scale or difference between numbers and place value chart for numbers that
cannot be represented in a number line. The third way is by adding zero to make the digits of
decimal numbers the evenly.
Study the example below.
Start at the left side.
The number line starts with 12.326. It is the smallest value in the set which is located at
the leftmost part of the number line.
The number line ends with 12.346. It is the greatest value in the set which is located at
the rightmost part of the number line.
In the number line we can clearly locate that 12.329 is at the left side while 12.341 is
located at the right side.
So, 12.341 is greater than 12.329. We can write it in symbol as 12.341 > 12.329.
Let’s try another example using different strategy. We can add 0 to make the number of
digits equally. Which is greater 0.2 or 0.198? Let’s compare it using the table below.
Original Number
0 2
0 1 9 8
New Number Formed
by Adding 0
0 2 0 0
0 1 9 8
Which is less 12.341
or 12.329?
12.326 12.327 12.328 12.329 12.330 12.331 12.332 12.333 12.334 12.335 12.336 12.337 12.338 12.339 12.340 12.341 12.342 12.343 12.344 12.345 12.346

Which is greater,
12.789 or 12.765?
Now, let’s take another look. The given decimals have the same number of digits. Which
is greater 0.200 or 0.198? In this example, 0.200 is greater than 0.198. In symbol, we can write
this as 0.200 > 0.198.
Study another set of example using the place value chart.
A. Compare the following. Write >, <, or = in to make the sentence true.
1. 1.396 0.95 9. 2.35 2.53
2. 0.29 0.3 10. 0.1 0.99
3. 6.5 6.500 11. 4.07 4.017
4. 7.4 7.049 12. 10.07 10.067
5. 27.5 27.492 13. 1.0 1.01
6. 2.098 2.904 14. 2 2.00
7. 0.30 0.300 15. 3.607 3.670
8. 8.10 8.1
B. Order the following decimals from least to greatest.
1. 3.21, 3.021, 3.12, 3.121
2. 1.3, 1.309, 1.03, 1.39
3. 0.09, 0.012, 0.0089, 0.0189
4. 4.01, 4.0011, 4.011, 4.101
PlaceValue
Tens
Ones
Decimal
Point
Tenths
Hundredths
Thousandths
Value 10 1 
Digits 1 2  7 8 9
Digits 1 2  7 6 5
Get Moving!

5. 5.5, 5.059, 5.0090, 5.05
6. 1.7, 0.9, 1.07, 1.9, 0.7
7. 2.0342, 2.3042, 2.3104, 2.4
8. 5, 5.012, 5.1, 0.502
9. 0.6, 0.6065, 0.6059, 0.6061
10. 12.9, 12.09, 12.9100, 12.9150
A. Write <, >, or = on the blank to make the sentence true.
1. 0.1114 ____ 0.2202 9. 0.0120 _____ 0.012
2. 0.1090 ____ 0.1009 10. 16.8930 _____ 16.893
3. 0.999 ____ 0.1000 11. 0.7985 _____ 0.7895
4. 4.8934 ____ 4.8943 12. 12.1 _____ 12.0100
5. 0.6390 ____ 0.639 13. 40.04 _____ 40.041
6. 0.55 _____ 0.055 14. 8.627 _____ 8.649
7. 0.7894 _____ 0.7658 15. 0.213 _____ 0.0213
8. 0.3937 _____ 0.3198
B. Order numbers from greatest to least.
1. 3.756 37.56 375.6 0.3756
2. 0.2468 0.2486 0.2648 0.2846
3. 11.010 11.011 11.0110 1.1101
4. 2313.2 23.132 2.3132 231.32
5. 555.555 55.5555 5.5555 5555.55
6. 0.481 0.38 0.256 0.7349
7. 2.461 2.3392 2.6789 2.7666
8. 0.93 6.87 5.241 6.786
9. 62.1254 26.2351 262.351 26.5321
10. 905.928 95.7654 5.8642 5.6248
Keep Moving!

A. Read and solve the following.
1. Jeremiah and Catherine are both honor pupils in their school. For the first quarter,
Jeremiah’s average is 93.1 while Catherine’s average is 93.095. Who topped the
first quarter?
2. Team Narra and Team Mahogany undergo a water challenge. Their task is to transfer the
water in a cup from the first player to the tenth player without spilling within the allotted
time. After the task, the team captain measure the water collected using a measuring cup.
Team Narra collected 1. 402 liters while Team Mahogany collected 1. 045 liter of water,
which team got more water?
3. Robert was asked to arrange the following numbers from least to greatest. Which number
comes last?
4. In a bazaar, different items are sale for big discounts. Irene is looking for a school bag. She
visited three stalls to buy one for his younger brother. The stall offered the school bag of the
same quality but differs in price. The first stall offered if for P 749. 25, the second stall sold it
for P 792.45 and third stall gave it P 724. 95. If she wanted to save, from which stall will she
buy school bag?
5. Aling Mila bought 0.82 m of red fabric, 0.79 m of yellow fabric, 0.805 m of blue fabric and
0.782 m of white fabric. Which ribbon is the longest? the shortest? Arrange the lengths of
the fabric form longest to shortest?
Apply Your Skills
2.099 2.9 2.99 2.109 2.5

Lesson 33: Visualizing Addition and Subtraction of Decimals
Gab and Sassa goes to school together by walking. The school is 2 km from their house. For first five
minutes Sassa and Gab has walked and reached 0.28 kilometer, after the next 8 minutes they recorded 0. 59
km. How far are they from school?
How can we solve the problem?
First identify the given. We have the following.
2 km – distance of school from Gab and Sassa’s house
0.28 km – the distance they have walked and reached for the first 5 minutes
0. 59 km – the distance covered by them for the next 8 minutes
What is asked in the problem?
The problem is looking for the distance from the school that they need to cover after driving for 13
minutes. So, let’s add the distance they have walked for 5 minutes and the distance covered by them for the
next 8 minutes.
Use the model below. Each square represents 0.001.
A. Add or subtract the following. Use drawing or illustration if possible.
0.028 0.087
0.059
+ =
Get Moving!

1. 0.27 + 0.61 6. 0.8 – 0.3
2. 0.13 + 0.22 + 0.45 7. 0.57 – 0.4
3. 0.261 + 0.003 8. 0.095 – 0.002
4. 0.005 + 0.024+ 0.314 9. 0.631 – 0.385
5. 0.421 + 0.06 + 0.104 10. 0.457 – 0.104
B. Find the sum or difference.
1. 0.549 – 0.014 6. 0.31 + 0.42+ 0.16
2. 0.653 – 0.128 7. 0.473 – 0. 251
3. 0.56 + 0.23 + 0.2 8. 0.927 – 0.302
4. 0. 783 – 0.53 9. 0.07 + 0.009 + 0.4
5. 0.205 + 0.612 10. 0.365 + 0.13 + 0.283
C. Find the sum or difference.
1. 0.684 2. 0.83 3. 0.73 4. 0.9002
+ 0.295 + 0.567 + 0.3073 + 0.8634
5. 0.84 6. 0.84 7. 0.540 8. 0.3
+ 0.8056 - 0.6358 - 0.2365 - 0.076
9. 0.6 10. 0.9702
- 0.1858 - 0.1694
A. Add or subtract the following.
1. 2.198 – 1.439 6. 2.67 + 8.94 + 6.43
2. 38.026 – 49.183 7. 12.652 – 9.758
3. 5.072 – 3.861 8. 45.006 – 39. 248
4. 45.349 – 29. 465 9. 6.89 + 23. 574 + 16.045
5. 18.860 + 34. 257 10. 7.14 + 8.432 + 9.77
B. Find the sum or difference of the following.
1. 37.813 – 27.654 6. 9.87 + 10.163 + 19.054
2. 12.095 + 9.389 7. 98.764 – 87.365
3. 43.702 + 18. 419 8. 63.007 – 48.642
4. 16.206 – 13.076 9. 9.71 + 52.075
5. 89.652 + 17. 378 10. 84.349 – 49.182
C. Add or subtract.
1. 0.38 + 0.47 = n 6. 0.23 – 0.16 = n
Keep Moving!

2. 0.412 + 0.638 = n 7. 0.97 – 0.178 = n
3. 0.529 + 0.646 = n 8. 0.232 – 0.046 = n
4. 0.412 + 0.473 = n 9. 0.76 – 0.057 = n
5. 0.284 + 0.325 = n 10. 0. 200 – 0.099 =
A. Read, analyze and solve the following.
1. During a vacation, Ben’s records showed gasoline purchases of 19.75 gallons, 15.4
gallons, 13.85 gallons and 21.06 gallons. How many gallons of gasoline did he buy?
2. The perimeter of a triangle is equal to the sum of the length of its sides. Find the
perimeter of a triangle whose sides are 8.75 cm, 9.6 cm and 10.375 cm.
3. Rachel has P 3 316.40 in her savings account. If she made withdrawals of P 285.00,
P 472.46 and P 1 042.25, how much money is left in her account?
4. One week a jogger ran the following distances : 15.3 km , 18.75 km , 19 km , 21.5 km,
25.375 km and 30.25 km. If his weekly average is 150 km, did he run less or more?
5. Romeo has P 20 000 in available credit on his Visa charge card. If she purchases a
portable CD player for P 8 139.55, a boom box for P 399.95 and two way speakers
for P 3 425.05, how much available credit does she have left ?
Apply Your Skills!

Lesson 34: Adding and Subtracting Decimal Numbers through Thousandths
Without and With Regrouping
Mr.Acapulco acquired a lot in a remote area in
Batangas to be planted by different kinds of fruit bearing trees. He
already acquired 105.652 square meters in Barangay Masikap and
91.246 square meters of lands in Brgy. Matamis. If Mr.
Acapulco needs 398.166 square meters, what part of land area
does he need to acquire?
Step 1:
How do we solve the problem? To solve the problem, we must
need to add the first two given data, 105.692 square meters of land in
Barangay Masikap and 91.246 square meters of land in
Barangay Matamis. The number sentence is 105.652 sq. m + 98.276
sq. m = N.
Without Regrouping
Step 2: After
getting the sum.
We must now
answer the
question raised in
the problem.
To know the part of land Mr. Acapulco still needs to acquire. We may now subtract the sum that we get to the
land area intended to plant with different fruit bearing trees. Here’s the number sentence to use: 398.166 sq. m
– 196.898 sq. m = N.
With Regrouping
Hundreds Tens Ones Decimal
Points
Tenths Hundredths Thousandths
9 1  2 4 6
1 0 5  6 5 2
1 9 6  8 9 8
Hundreds Tens Ones Decimal
Points
Tenths Hundredths Thousandths
2 18 7 10 15 16
3 9 8  1 6 6
1 9 6  8 9 8
1 9 5  2 6 8
+ Sum
Difference-
Get Mo

A. Find the sum of the following.
1. 3.76 2. 23. 347 3. 37.786
+ 4.356 + 8.92 + 2. 632
4. 4. 762 5. 5. 703 6. 87.652
+ 1.69 + 17.74 + 51.764
7. 0.9154 8. 92.65 7 9. 15.421
+ 0.2515 + 24.57 3 + 37.88
10. 0.3276
+ 0.1178
B. Find the difference.
A. Solve for the sum or difference.
1. 75.267 2. 59.246 3. 43.823 4. 86. 576
- 63.122 - 28.132 - 21.51 + 53.123
5. 98.364 6. 21. 924 7. 85.376 8. 58.148
- 72. 225 - 17. 379 - 49. 528 + 67.251
1. 93. 152
- 29. 184
2. 61.41
- 37.532
3. 57.31
- 46. 653
4. 154. 76
- 85.493
5. 380.205
- 278.398
Keep Moving!

9. 70.542 10. 59. 647
- 53.891 - 27.958
A. Read, analyze and solve.
1. Alex traveled 41.3 kilometers on Monday and 53.75 kilometers on Tuesday. How many
kilometers did he travel in two days?
2. In a midnight sale, a radio cassette player was sold at P 1 449.95. If it’s regular price was
P 1 950.50, how much less was the sale price?
3. Anna bought a bunch of flowers for P 125.50. If she gave a P 100 bill and P 50 bill, how
much was her change?
4. The rainfall on four consecutive days during a typhoon was 10.31 cm, 12.72 cm, 18.39 cm
and 9.84 cm. Find the total rainfall during the typhoon.
5. Mother bought 2.35 kg of pork, 3.75 kg of chicken, 1.1 kg of beef, and 1 kg of liver. How
many kilograms of meat did Mother buy in all?
Apply Your Skills!

Lesson 35: Estimating the Sum or Difference of Decimal Numbers with Reasonable Results
A.
Nancy wants to buy a blouse for Php.118.50, a t-shirt for Php.99.75 and a pair of shoes for Php.215.50.
If she has Php.500-bill, does she have enough money to pay for them?
To answer the question, we need to estimate. We can use the rounding method.
Php.118.50Php.120
Php.99.75 Php.100
Php.215.50Php.220
Php.440
Yes, Nancy has enough money to buy the three items.
B.
A salesman drove 17.65 km to one town and 15.86 km to a second town. How much farther is the first
town than the second town?
17.6518 km
15.8616 km
2 km
The first town is less than 2 km farther than the second town.
Get Moving!
A. Using the rounding off technique, find the estimated sum of the given decimals.
1. 23.45 + 8.63 + 2.75
2. 8.05 + 7.93 + 1.62
3. 112.56 + 23.63 + 12.45
4. 0.91 + 0.86 + 8.75
5. 2.843 + 15.624 + 13.56

B. Using the rounding off technique, find the rough estimated difference of the given decimals.
1. 634.58 – 436.79
2. 37.86 – 19.92
3. 14.39 – 8.59
4. 7.45 – 2.93
5. 15.63 – 8.79
Keep Moving!
A. Round to the greatest place value and estimate each sum.
1. 2347.081 + 5834.501
2. 9452.8 + 4671.2
3. 23.5 + 15.03 + 9.54
4. 7.45 + 8.83 + 6.55
5. 12.4 + 14.8 + 21.53
B. Round to the greatest place value and estimate each difference.
1. 678.23 – 451.2
2. 818.9 – 489.06
3. 951.4 – 568.19
4. 7512.2 – 3725.9
5. 9301.67 – 4878.8
Apply Your Skills!
Estimate the answer to each problem.
1. Gloria bought a t-shirt for Php.95.75 and a book for Php.175.60. how much more did the book cost
than the t-shirt?
2. A salesman traveled 78.45 km in the morning and 25.24 km in the afternoon. Did he cover at least
100 km?
3. A household consumes 222.5 liters of water a day. One faucet leaks 12.25 liters of water a day.
Estimate how many liters of water a day a household consumes when the faucet is fixed?
4. The Math Club raised Php 1 225.00 during their fund raising campaign. The club will be buying 3
items worth Php495.00, Php347.50 and Php862.90. How much more money does the club need to
buy the items?
5. A rectangular garden measures 22.7 meters by 16.6 meters. Estimate how many meters of fencing
material are needed to enclose it.

Lesson 36- Solving Routine or Non-routine Problems Involving Addition and Subtraction of
Decimal Numbers Including Money Using Appropriate Problem Solving Strategies
and Tools
Problem 1 Problem 2
Which of the two problems is easier to solve? Why?
Get Moving
1. The perimeter of a quadrilateral is 412.95 cm. If the three known sides measures
85.56cm, 112.77 cm, and 85.26 cm, how long is the fourth side?
2. I bought 4 items worth P39.90, P68.60, P 58.75 and P120.25. How much change will I
get from P 500-bill?
3. A rectangle is 13.8cm. long and and 9.7 cm wide. Find its perimeter.
4. Obed and Dario hiked 15.1 km. In one day and 13.75 km in the next day. How many
kilometres did they hiked in all?
Mang Isko has 18.48 pesos . If she has
to devide it into her 6 children, How
much will each one receive?
Marlene opened her math book and
found that the sum of the pages
facing her was 243. What pages did
she open to?
Understand
Know what is asked? The amount of money
each child receive?
Know the given facts: 18.48 pesos, 6 children
Plan
Write the number sentence: 18.48÷6=n
Solve
Show your solution: 18.48÷6=3.08
Check and look back
Review and re check your answer: you can
use calculator to divide 18.46 by 6 or multiply
3.08 by 6
Understand
Know what is asked: The pages of the book
Know the given facts: The sum of two pages was 243
Plan
Determine the operation to be used: Addition
Write the number sentence: n+(n+1)= 243
Solve
Show your solution: Trial and error method
If n=121, then 121+(121+1)= 243
121+122 =243
243 = 243
Review and check your answer: you cannot have a page
that is 121 r. 1

5. Mr. De Guzman and the boys spent P 567.75 for food and P 175.50 for transportation
during the Science Fair Camp. If they had P 800.00 to spend, how much money was
left?
Keep Moving
Analyze and sole the ff. Problems.
1) The diameter of the earth is 12 763.29 kilometers. If Mercury’s diameter is about
7 913.04 kilometers shorter than that of the earth, what is the diameter of Mercury?
2) Luz wants to buy a bag that costs 375.95. If she has saved 148.50 for it, how much
more does she need?
3) Martha bought 2.5 m of yellow ribbon, 3.4 m of red, 8.75 m of white, and 3.70 m of blue.
How many metres of ribbon did she buy altogether?
Apply Your Skills
Write the number sentence and solve.
1. Delia filled the container with 3.5 litres of water. Her mother used 0.75 litres of water for cooking
and 1.25 litres for palamig. How much water was left in the container?
2. Mang Caloy cut four pieces of bamboo. The first piece was 0.75 metre; the second was 2.278
metres, the third was 6.11 metres, and the fourth was 6.72 metres. How much longer were the
third and fourth pieces put together than the first and second pieces put together?

Lesson 37- Creating Problems (with reasonable answers)Involving Addition and Subtraction of
Decimal Numbers Including Money
Second Grading Period, Week 3
How do you create a word problem involving addition and subtraction of decimals including
money?
a. Familiarize yourself with the concept and their application to real life situation.
b. Think of the problem you want to create.
c. Read some problems and study their solutions
You also consider the following when creating a problem.
1. Characters
2. Situation/Setting
3. Data
4. Key Questions
Study the table below
Name Things bought Price
Shane T-shirt 250.75 kg.
Lito Shoes 1,999.99 kg.
Study the problem as an example for the data given.
Get Moving
Use the data below to create a two-step word problem involving addition and subtraction of
decimals.
Name Items bought Price
Carlo 10 note books P80.65
Lolit Bag P617.35
Jane Shoes P1,250.08
Shane and Lito went to the Department Store. Shane bought a T-shirt cost P 250.75. Lito bought a
shoes cost 1,999.99kg. How much more does Lito spend than Shane?

Keep Moving
Use the data below to create a two-step word problem involving addition and subtraction of
decimals.
Name Foods Ordered Price
Amie Spaghetti P50.75
Zet Palabok P48.25
Precy Regular Yum P30.75
Apply Your Skills
Use the data below to create a problem for each of the ff.
1. One- step word problem involving addition of fraction
2. One -step word problem involving subtraction of fraction
3. Two- step word problem involving addition and subtraction of fraction
Name Amount Deposited in the Bank
Allan P 2,978.88
Amiel P 4, 656.75
Raquel P 7, 665.50

Lesson 10: Visualizing Multiplication of Decimal Numbers Using Pictorial Models
Sophia’s rides the bus to and from school each day. A one-way trip is 8.12 kilometers.
How many kilometers does he travels in 5 days?
Can you visualize how far Sophia travels?
One way of visualizing how far Sophia travels is through number line.
Get Moving!
Show the following multiplication equations by using number lines.
1.) 0.3 x 0.6 =
2.) 0.5 x 0.8 =
3.) 0.7 x 0.4 =
4.) 0.2 x 0.9 =
5.) 0.8 x 0.3 =

Keep Moving!
Directions: Illustrate the given equation in a grid.
1. 0.7 x 0.6 = n 4. 0.2 x 0.3 = n
2. 0.4 x 0.8 = n 5. 0.3 x 0.5 = n
3. 0.6 x 0.6 = n
Use number lines to find the answer.
1.) Nichole needs 0.95 m of ribbon to trim a shirt. If the ribbon costs ₱ 0.75 per meter. How
much did she has to pay?
2.) JR can swim 12 meters in one minute. How far can he swim in 30 minutes?
Apply Your Skills!
Read and solve the following. Use your own pictorial model to answer the following.
1.) Looking after my baby cousins after classes, my Aunt Abing gives me ₱ 45.00 a day.
How can I save a week if I spend ₱ 100.00 for my snacks in school?
2.) Realyn bought 2.5 kg of meat at ₱ 100.00 per kg. she gave the seller a ₱ 500.00 bill.
How much change did she get?
3.) Each potted plant in a nursery costs ₱ 25.50. How much will be left on of my ₱ 400.00 if
I buy 10 potted plants.

Lesson 11: Multiplying decimals up to 2 decimal places by 1 to 2 digit whole numbers.
Look at this square.
What is its perimeter?
3.5 cm
How can you find the perimeter?
How many sides has a square?
What can you say about its side?
Because there are 4 equal sides and each measures 3.5 cm, we can compute this as 4 x 3.5 =
N. Here’s how this is done.
 Multiply as with whole numbers. Regroup if necessary.
3.5
X 4
140
 Count the number of decimal places in the factors.
3.5
X 4
140
 Place the decimal point in the product. The decimal place in the product is equal to the
total number of decimal places in the factors.
3.5
X 4
1.40 1 decimal place

Get Moving!
Multiply. Choose your answer from the choices given inside the parenthesis.
1.) 4 x 7.28 = ( a. 29.19 b. 291.2 c. 2.912 )
2.) 7 x 3.14 = ( a. 20.98 b. 21.98 c. 22.98 )
3.) 3 x 6.25 = ( a. 18.25 b. 18.5 c. 18.75 )
4.) 2 x 12.25 = ( a. 25.1 b. 25.12 c. 25.13 )
5.) 6 x 5.75 ( a. 34.5 b. 3.45 c. 0.345 )
Keep Moving!
A. Find the product in each of the following:
1.) 4.29 2.) 12.47 3.) 8.4
x 12 x 3 x 14
4.) 26.43 5.) 10.78
x 5 x 13
B. Solve
1.) What is 3.65 multiplied by 12?
2.) What is the product of 4 and 8.79?
3.) What is 24.5 times 6?
Apply Your Skills!
Solve the following problem.
1.) If a notebook is ₱ 5.25, how much is the cost of 6 notebooks?
2.) A working student earns ₱ 25.50 an hour. How much does he earn in 4 hours? If
he works 3 days a week, how much does she earn a week?
3.) Mrs. De Guzman’s class rode is 3.8 mile to the observatory. The next closest
observatory is 13 times as far. How many miles is the second observatory?

Lesson 13: Multiplying decimals with factors up to 2 decimal places
Arnold had a plot garden. What is its area if the length is 0.85 m and the width is 0.4 ?
To find the area of the plot garden, we multiply 0.85 by 0.4.
To solve for the 0.85 x 0.4 follow the steps:
1. Multiply the number as you would multiply whole numbers. Regroup if necessary.
0.85
X 0.4
0.340
2. Count the number of decimal places in the factors.
0.85 ------- 2 decimal places
X 0.4 ------- 1 decimal place
0.340 ------- 3 decimal places in all
3. Place the decimal point in the product according to the number of decimal places in
the factors.
0.85
X 0.4
0.340 ------- 3 decimal places in all
Get Moving!
Find the product in each case
0.25 x 0.5 0.27 x 0.16 0.25 x 0.31
0.64 x 0.8 0.85 x 0.34

Apply Your Skills!
Find the product.
1.) 0.06 x 0.72
2.) 0.85 x 0.3
3.) 0.37 x 0.40
4.) 0.64 x 0.42
5.) 0.53 x 0.15
6.) 0.79
x 0.06
7.) 0.55
x 0.23
8.) 0.63
x 0.21
9.) 0.87
x 0.75
10.) 0.19
x 0.73

Lesson: 41 Estimating the products of decimal numbers with reasonable results.
The class got about ₱ 2400.00.
To estimate the product round each factor to the greatest/highest place value, then multiply the
rounded factors.
Round each factor to the greatest place value and estimate each product.
1. 42.6 x 37.2= 2. 68.54 x 24.4= 3. 99.2 x 48.5= 4.123.86 x 31.5= 5.246.3 x 9.67
The following are some items that you need to buy from a store.
a pair of socks -₱20.95 handkerchief - ₱24.25 t-shirt - ₱119.50
shorts - ₱52.30 face towel - ₱8.75
* About how much money must you have to be able to buy:
1. a pair of socks?
2. two t-shirts?
3. five face towels?
4. seven handkerchiefs?
5. three shorts?
For their fund-raising, a Grade 5 class sold
packages of cookies at ₱ 11.75 a package. If
they sold 210 packages, about how much did
they get?
We use rounding to estimate products.
Study the solution
By rounding,
₱ 11.75 → ₱ 12.00
x 210 → x 200
₱ 2 400
Get Moving
Keep Moving

Read the problem then answer the questions that follow:
1. About how many kilograms of tomatoes were harvested for the Tiangge Day?
2. If they will sell the tomatoes for ₱24.25 a kilo,
a) By how much will they get for one kaing?
b) By how much will they get for all the tomatoes?
3. A businessman will buy all the tomatoes, but will be given 1.5 kilograms free for each kaing. About how much will he
pay?
4. Do you think that much of tomatoes will be ready to be sold for Tiangge Day if only Father picked the tomatoes?Why?
Apply Your Skills
Father and other farmers harvested tomatoes for the town's Tiangge
Day. They were able to fill 56.5 kaings each weighing 18.75 kilograms.

Lesson 42 : Solving routine and non-routine problems involving multiplication without or with addition or
subtraction of decimals and whole numbers including money using appropriate problem solving strategies and
tools.
B. Plan
1. Determine the operations to be used. Multiplication, Addition and Subtraction
2. Write the number sentences for the hidden questions.
4 x ₱ 350=n 4 x ₱ 350= ₱ 1,400
C. Solve: Show your solution:
(2 x 1000) - { (4x 350) +( 200+ 225)} = n
2000 - {1400 +425)= n
2000- 1825 = n
₱ 175 = n
So, the total change for ₱ 2000 of her mother is ₱ 175
D. Check and Look back:
Did I do the operation correctly? Is my answer reasonable? Did I write my answer in a complete
sentence?
Routine = Problem 1
To analyze and solve the problem, you can do this steps.
A. Understand
1. Read and understand the problem
2. Know what is asked for in the problem. How much
was left of her money?
3. Know the hidden information.
The total amount of 4 gallons of ice cream.
4. Find the necessary information
The given facts are: ₱ 200 a cake, 4 gallons of ice cream for ₱ 350 each, ₱ 225 cookies and 2
₱ 1000 bills.
Problem 2
Alvin bought 6 wattpad at ₱ 165 each
and 5 sports magazines at ₱ 85 for
his friends. How much change did he
get from his three 500- peso bills?
Problem 1
For Rina’s birthday, Mother bought a cake
at 200, 4 gallons of ice cream at 350
each and cookies worth 225. She
brought with her 2 1,000 bills. How
much was left of her money?

Non Routine = Problem 2
* Understand
Know what is asked: The total change did he get from his three 500- peso bills?
Know the given facts: 6 wattpad at ₱ 165, 5 sports magazines at ₱ 85 three 500- peso bills
Plan: Make a diagram or drawing.
--- + − + = n
Solve:
₱ 1500.00 - ( 6 x ₱ 165) + ( 5 x ₱ 85) = n
a). So we multiply (3 x ₱ 500), (6 x ₱ 165) and (5 x ₱85)
b) Get the product of the 3. (1500, 990, 425)
c) Get the sum of 990 + 425 (1415)
d) Minus ₱1500 to the sum of the two (1500- 1415)
e) The answer is 85
f.) So the final answer, ₱85 left with 3- ₱500 of Alvin.
Note:
The first problem is an example of a routine problem. Routine problem solving concerns
solving problems that are useful for daily living(in the present future)
The second problem is an example of a non routine problem. Non routine problem solving
is mostly concerned with developing pupil's mathematical reasoning power and fostering the
understanding that mathematics is a creative endeavour. This kind of problem helps the teachers to
motivate and challenge their pupils. Some strategies used in these kinds of problem are Acting,
Drawing, Using Patterns, Working Backwards,etc.
Give the hidden question, write the number sentence, and solve.
a. Mr. Salonga is paid 110.85 per hour of work. He worked six hours each day for four days. On
the fifth day, he worked 3.25 hours. How much did he receive for 5 days of work?
b. At a benefit show, special tickets cost 35.00 each while regular tickets cost 15.00. What was
the total sales if 275 regular tickets and 120 special tickets were sold?
Get Moving
3- ₱ 500
6 wattpad at
₱ 165,
5 sports
magazines at ₱85

c. Car A and Car B are running in opposite directions. Car A runs 65.5 kph while Car B runs 57.32
kph. How far apart will they be after 2.25 hours?
Write the number sentence for each problem then solve.
1) Barangay Maligaya is 28.5 km from the town proper. In going there, Jay traveled 15.75 km by jeep
and 3.5 km by tricycle and the rest by walking. How many km did he travel by walking?
2) The Butal family went to a carnival. They bought 2 tickets for adults at 80.00 each and 3 tickets
for children at 60.00 each. How much change did she receive from a 500 given to the ticket
seller?
3) For Rina’s birthday, Mother bought a cake at 200, 4 gallons of ice cream at 350 each and
cookies worth 225. She brought with her 2 1,000 bills. How much was left of her money?
A. Read, analyze, and solve for the answer.
Rhea and Cecil shared ₱ 500 each to buy the following for their brother's birthday: 12 pies at ₱ 20.50
each, 6 watermelons at ₱ 45.50 each, 4 cans of juice at ₱ 23.50 each. They spent the rest of the money
for ice cream and cookies. How much did they spend for the ice cream and cookies?
B.The table below shows the fare for a journey by taxi. Solve
First 500 m 30
Every subsequent 500 m or part thereof 2.50
Mrs. Ruiz took a taxi from her home to her office, which was 4.25 km away. How much taxi fare did she
have to pay?
Keep Moving
Apply Your Skills

Lesson 43: Visualizing Division of Decimals
Week 6
Let us use a number line.
The number line shows that there are four 0.2s in 0.8. So, 0.8 ÷ 0.2 = 4.
Answer: There were 4 pieces of bamboo.
MORE EXAMPLES
Use a number line to find each quotient.
1. 0.9 ÷ 0.3
There are three 0.3s in 0.9.
So, 0.9 ÷ 0.3 = 3.
2. 1.2 ÷ 0.4
A bamboo pole 0.8 of a metre
long was cut into pieces, each 0.2 of a
metre long. How many pieces of bamboo
were there?
Find: 0.8 ÷ 0.2
Get Moving!
0 0.2 0.4 0.6 0.8
0.2 0.2 0.2 0.2
0.8
0 0.2 0.4 0.6 0.9
0.3 0.3 0.3
0.9
0.1 0.3 0.5 0.7 0.8
0 0.4
0.4 0.4 0.4
1.2
1.20.8

There are three 0.4s in 1.2.
So, 1.2 ÷ 0.4 = 3.
How does the quotient compare with the dividend and divisor if both are decimals?
Write the division sentence shown in each number line.
1.
2.
3.
4.
Draw a number line. Use it to find each quotient.
5. 0.6 ÷ 0.3 6. 1.2 ÷ 0.3 7. 3.6 ÷ 0.9
8. 1.5 ÷ 0.5 9. 1.8 ÷ 0.2 10. 4.5 ÷ 0.5
Keep Moving!
0 0.2 0.4 0.6 0.7
0.2 0.2 0.2
0.6
0.1 0.3 0.5
0 0.2 0.4 0.6 0.8 1.0
0.4 0.4
0.8
0
1.2
1.2
0.3 0.3 0.3 0.3
0.6 0.90.3
0
1.4
1.2 1.40.2 0.4 0.6 0.8 1.0
0.2 0.2 0.2 0.2 0.2 0.2 0.2

Copy the grid at the right.
Find each quotient by using the grid.
1. 0.8 ÷ 0.2
2. 0.6 ÷ 0.1
3. 0.9 ÷ 0.3
Apply Your Skills!

18
4
24
24
0
Miss Reyes can prepare 18 certificates with a
ribbon of that size.
Lesson 44 : Dividing Decimals With Up to 2 Decimal Places
Miss Reyes has 0.64 dm of ribbon. She need 0.04 dm to prepare one certificate. How many
certificates can she prepare with the ribbon that she has?
The number of certificates she can prepare is 0.64 ÷ 0.04. But, how do we divide decimal by a
decimal?
Since we already know how to divide a whole number, we can make the divisor and the
dividend a whole number by multiplying it by a power of 10. As we have learned, the shortcut for this is
to move the decimal point as many places to the right as there are zeroes in the power of 10. We show
this by means of an arrow.
0.0 4 .6 4 4 64
 Multiply both the divisor and the dividend by 100 or power of 10. Using shortcut, shows
by means of an arrows.
 Divide as in dividing whole numbers.
Get Moving!
Divide. Show how the decimal point is moved in the divisor and the dividend. Check by
multiplication.
1. 0.02 .40
2. 0.02 .40
3. 0.02 .40
4. 0.02 .40
5. 0.02 .40

Keep Moving!
Solve for n. You can use a calculator to check if your answers are correct.
1. 7.26 ÷ 0.22 = n
2. 17.92 ÷ 0.64 = n
3. 7.65 ÷ 0.85 = n
4. 36.20 ÷ 0.05 = n
5. 31.85 ÷ 0.91 = n
Apply Your Skills!
Read, analyze and solve the following problems.
1. A nutritionist poured 0.70 liter of honey into 0.14 liter plastic cups filled.
2. A rectangular rice field is 0.04 kilometer wide and has an area of 0.80 square kilometer. Find the
length of the field.
3. A city government plans to put streetlights along its 8.40 km main road. The streetlights are to be
placed 0.20 km apart. How many streetlights will the city government need?
4. Mother paid Php198.45 for 0.81 kg of rice. How much did a kilogram of rice cost her?
5. A hiker walked 5.75 kilometers in 1.25 hours. What was his average speed?

0.8
120
0
Lesson 45: Dividing Whole Numbers with Quotients in Decimal Form
Clarissa helps in sari-sari store after her classes. If she works 12 hours in 15 days, what is the
average number of hours she works there in a day?
Find : 12 ÷ 15 = n
15 12.0
Check :
15
X .8
12
Answer : Clarissa works an average of 0.8 hours a day in the store.
Get Moving!
Divide. Round off your answer to the nearest hundredths.
1. 16 13
2. 26 19
3. 30 25
4. 65 57
5. 82 78
Follow these steps :
1. Add decimal point and zero in the dividend since it is smaller than its
denominator
2. Write the decimal point in the quotient directly above the decimal
point in the dividend.
3. Divide like you do with whole numbers.

Keep Moving!
Solve for n. You can use a calculator to check if your answers are correct.
1. 4 ÷ 80 = n
2. 7 ÷ 14 = n
3. 11 ÷ 19 = n
4. 31 ÷ 83 = n
5. 42 ÷ 52 = n
Apply Your Skills!
1. What is the quotient if 24 is divided by 48?
2. Jean has 35 m of wire for hanging pictures. She wants to divide it into 50 pieces for her frames.
How long did she used for each frame?
3. Father left Php5.00 for his 7 children. How much did each child received?
4. Mang Ricky is a hardworking man who owns 6 hectares of land. In his will, he divided his lot equally
Among his 7 sons. How much land each of his son received?
5. Troy and Raffy went to the market to buy 15 kilos of pork. When they came home, they divided the
meat into 16 parts and put it in plastic bags for future use. How many kilos of pork does each bag
contains?

Second Grading
Lesson 46. Estimating the Quotients of Decimal Numbers with
Reasonable Results
What is asked in the problem? The estimated number of pencils Mario can buy.
What are given? ₱200 and ₱4.75
How are you going to solve it? Estimate and divide.
To find an estimate, we round the divisor.
₱200 ÷ ₱4.75 = n
200 ÷ 5 = 40
So, ₱200 can buy at least 40 pencils.
To estimate a quotient, we can round the divisor and/or the dividend to a whole
Number or to a multiple of 10. We may also round one of them and use compatible numbers.
Compatible numbers that can be computed easily.
In the above example, we estimate the quotient by rounding off the divisor. In the next
example, you are going to learn how to estimate the quotient using other ways.
1. Estimate the quotient by rounding off the dividend.
144.3 ÷ 6 = n → 144 ÷ 6 = 24
2. Estimate the quotient by rounding off the dividend and the divisor.
482 ÷ 3.2 = n → 480 ÷ 3 = 160
3. Estimate the quotient by using compatible numbers.
19.12 ÷ 1.9 = n → 20 ÷ 2 = 10
Mario has a ₱200– peso bill. He wants to
buy a pencil which costs ₱4.75 each. About how
may pencils can he buy?

Get Moving !
A. In your notebook, estimate the quotient using compatible method.
1. 6.44 ÷ .89 = __________________
2. 62.4 ÷ 7.4 = __________________
3. 211.69 ÷ 38.7 = _______________
4. 16.621 ÷ 4.43 = _______________
5. 81.347 ÷ 9.53 = _______________
B. Estimate the quotient using the rounding method.
1. 24.1 ÷ 6.43 = _________________
2. 26.9 ÷ 3 = ____________________
3. 48.29 ÷ 12.107 = ______________
4. 300 ÷ 24.75 = _________________
5. 631.92 ÷ 31.84 = ______________
Keep Moving!
Estimate the following: a) use rounding off; b) use compatible numbers.
a. 87.5 ÷ 7.3 =
b. 72.6 ÷ 0.8 =
c. 98.8 ÷ 8.8 =
d. 88.5 ÷ 4.42 =
e. 63.8 ÷7.8 =

Apply Your Skills!
A. Round off then estimate. Write ˂ if the answer is less than or ˃ if greater than the actual
quotient.
_____ 1. 18.4 ÷ 9
_____ 2. 63.92 ÷ 7.84
_____ 3. 320 ÷ 12.5
_____ 4. 311.93 ÷ 3.08
_____ 5. 500 ÷ 24.62
B. Solve the problem.
1. Leonila bought 7 meters of plastic cover for ₱69.75. About how much did each meter
cost?
2. Celia earned ₱174.75 in 5 days from selling sampaguita, About how much was her
average earnings?

Second Grading
Lesson 47. Solving Routine and Non-Routine Problems Involving Division
Without or With Any of the Other Operations of Decimals and
Whole Numbers Including Money
While watching television, Mat recorded that the
5 commercials in the program he was watching took 6.15
minutes to be aired. What was the average length of each
commercial?
You can solve the problem using the following
steps.
1. Dessa, Anne, and Dy bought materials for their project worth ₱276.45. The girls divided the
amount equally among themselves. How much is each share?
2. Rico wants to buy a battery-operated toy car which costs ₱587.50. He already saved
₱150.00 and his ninong gave him ₱200.00. If he saves ₱12.50 a day from his allowance,
how long will it take him to save the rest of the moneyto buy the toy car?
Steps Answer
Understand:
1. Know what is asked in the problem Average length of the commercial.
2. Know the given facts. 5 commercials ; 6.15 minutes
Plan :
3. Determine the operation or formula to
use.
Division
Solve:
4. Show the solution. 6.15 ÷ 5 = 1.23
Check and look back:
 Check your answer.
● State your answer
The average length of each commercial is
1.23 minutes.

Get Moving !
1. Mr. Villa bought 91.25 inches of plastic labeling tape. He will make labels 1.25
inches long each. How many labels can he make?
● Understand : __________________________________________________
● Plan : ________________________________________________________
● Solve : _______________________________________________________
● Look Back : ___________________________________________________
2. Roman’s allowance a week is ₱250.75. If he will save ₱50.00 and equally divided
The rest into 5, how much will he spend a day?
● Understand : __________________________________________________
● Plan : ________________________________________________________
● Solve : _______________________________________________________
● Look Back : ___________________________________________________
3. How many pieces of ribbon 3.2 m each can cut from a spool of ribbon 25m long?
● Understand : __________________________________________________
● Plan : ________________________________________________________
● Solve : _______________________________________________________
● Look Back : ___________________________________________________
4. Glen was able to save ₱92.50 in five days, spending only ₱10.50 of the allowance given
to him him a day. How much allowance was given to him a day?
● Understand : __________________________________________________
● Plan : ________________________________________________________
● Solve : _______________________________________________________
● Look Back : ___________________________________________________
Keep Moving!
Solve the following problems. Write your solutions and answers in you notebook.
1. If a man works 8 hours a day he can finish a job in 12 days. How many hours per
day must he work to complete it in 10 days.
2. Mariella compared 9 different brands of ice cream and found that the average price of
the 9 brands is equal to ₱254. As she was going through another store she found two
other brands that cost ₱282.00 and ₱292.00 respectively. What will be the resulting
average of the 11 brands?

3. Mr. Macapagal covered 175.45 kilometers in his trip to the province. If his car consumed 12.5
liters of gasoline, how many kilometers did his car cover on a liter of gasoline?
4. Mr. Lopez will pay 12 monthly installments for a washing machine costs ₱6 775.20. He
deposited ₱1 200. How much will be his monthly payment?
5. Several civic organizations donated a total of 5 412.6 kg of rice to be equally divided among
the flood victims from six barrios. How many kilograms of rice will each barrio received?
Apply Your Skills!
Try solving more problems.
Read and analyze the following problems. Solve them in any method you like.
1. In a ballroom competition, Loui and Lyka scored 92.6, 94.8 and 91.75 on the first three
dances they performed. To qualify for the finals, they need an average score of 93. What
score do they need on their last dance to qualify for the finals?
2. When a greater number is divided by a lower number, the quotient is 20. If the lower
number is tenths of 2.5, find the greater number.
3. A boy bicycles 7.5 km in 40 minutes.. Find his average speed in kilometer per hour.
4. How many pieces of wire each 2.4 dm long can be cut from a roll of wire 15 m long?
5. Before Mr. Ignacio drove for a trip next town, the gasoline tank of his car was 0.75 full.
After the trip, he found out that the tank was 0.25 full and he had used 30 liters of gasoline.
How many liters of gasoline can the tank hold when full?

Second Grading
Lesson 48. Creating Problems ( with reasonable answers) Involving
Multiplication and/or Division or With Any Other Operations of Decimals and
Whole Numbers Including Money
Can you make a word problem out of the picture?
Is the given picture enough to make a word problem?
What are the things/data you see for you to create a word problem?
Look at the given data below.
● Mr. Sinsuat
● round trip
● distance he travel
What other data do you need? You can consider the following data in creating a word problem.
● 6.4 km → 6 trips
Can you now complete the word problem be and solve for the correct answer, too. Do this in
your notebook.
is a farmer. He made round trips hauling
sacks of palay from his farm
to the NFA. A is How far did he travel?

Get Moving !
Use the data inside the box to complete the problems below. Solve the problem in your
notebook.
1. A kilogram of rice cost _______. How much change will I get if I buy ______________
and give the seller a ________________.
2. Aling Mercy bought __________________ at _______ each. She sold them at ________
each. How much was her profit?
3. A plastic pipe ________ will be divide into pieces of _____ each piece. How many pieces
there be?
4. Mang Andy caught _____________________________ and ______________________
which he will equally sell among his _____________. How many kilograms of fish will
each buyer get?
5. A hiker walked _______________________ in _______________. What was his average
speed?
5.75 kilometers 1.25 hours
4 buyers 585 bananas
₱2.00 36.25 of bangus
34.75 kg of tilapia 24ft long
₱1.75 0.3 ft
₱17.50 5 kilos

Keep Moving!
Study the story problems given below. Complete each problem by creating a question for what
is asked. Then, solve the problem.
1. My 3 sisters and I contributed ₱175.00 each to buy a new water meter. A plumber charged
us ₱250.00 for replacing the old one.
Question : _________________________________________
Solution and Answer :
2 . Mila was able to sell 4 boxes of roses at ₱150.00 a box and half a dozen tulips at ₱45.00
per tulip.
Question : _________________________________________
3. Mother repacked a 50-kg of sugar into 2.5 kg smaller packs..
Question : _________________________________________
4. An iron pipe 24.36 ft long was divided into shorter pieces of 0.6 ft each.
Question : _________________________________________
5. Father subdivided his 72.9 hectares of land into lots of 0.9 hectares each.
Question : _________________________________________

Apply Your Skills!
Create a problem using the given data. Then solve the problem.
1. Given : ₱2 900.00 - cost of mountain bike.
₱1 575.00 - down payment
5 - equal installment
Asked : pay for each installment
Problem : ___________________________________________
2. Given : 14.4 m² - area of rectangular table
4 m - length
Asked : width of the table
Problem : ___________________________________________
3. Given : 46.15 kg- weight of each sack of palay
21 - number of sacks
Asked : total load of the trailer
Problem : ___________________________________________
4. Given : 152 - number of eggs
₱0.75 - earnings for each egg
Asked : earnings for a day
Problem : ___________________________________________
5. Given : 3.5 hours - length of work per week
₱528.50 - earnings per hour
3 - number of weeks
Asked : total earnings
Problem : ___________________________________________

Lesson 49: Visualizing the Ratio of 2 Given Numbers
Week 8
Doris cuts 2 squares for
every 3 circles to make a design.
The ratio 2 to 3 compares the
number of squares to the number of
circles Doris cuts.
There are 2 squares for
every 3 circles
The ratio of the number of
boys to girls is 2 to 2.
What is the ratio of
the number of:
1. Triangle to stars?
2. Stars to triangles?
3. Triangles to all shapes
What is the ratio of the number of boys to girls in your class?

What does each ratio compare?
6 to 6
3 to 1
6 to 3
3 to 4
Get Moving!

Use the sets of pictures. What is the ratio of the number of:
1. to 6. dogs to cats
2. to 7. kangaroos to dogs
3. to 8. chicken to all animals
4. to 9. cats to all animals
5. to 10. horse to dogs
Draw a picture to show:
11. a ratio of 3 to 4 12. a ratio of 5 to 6
13. a ratio of 10 to 2 13. a ratio of 2 to 24
15. a ratio of 20 to 5
Keep Moving!

1. What is the ratio of the number of vowels to the number of consonants in the English
Alphabet?
2. What is the ratio of the number of boys to the number of girls in your family member?
3. What is the ratio of the number of days to a week?
4. What is the ratio of a minute to seconds?
5. What is the ratio of the number of years to a decade?
Apply Your Skills!

Lesson 50- Visualizing ratio using the colon (:) or fraction
Look at the illustration below. Observe that there are 4 apples and 18 bananas.
To
______________ : ______________
Apples to Bananas
This can be written colon form 4: 18 or fraction form 4_
18
Get Moving
Color the figure and give the ratio in fraction and in colon form.
a. Triangle to square
b. Circle to square
c. Circle to triangle
d. Triangle to total number of figures
e. Square to total number of figures
Keep Moving
Write the following ratio in fraction form and in colon form.
1. A Football team 5 out of 9 games played. There were no tie games.
a. Ratio of wins to games played
b. Ratio of wins to losses
c. Ratio of losses to wins
d. Ratio of games played to wins
e. Ratio of losses to games played.
Apply your skills.
Give the answer

1. What is the ratio of vowels to consonant in the Alphabeth?
2. What is the ratio of vowels to all the letters of the Alphabeth?
3. What is the ratio of even numbers less than 50 to odd numbers less than 50?
4. What is the ratio of multiples of 3 between 1 to 100 to all the numbers between 1 to
100?
5. A car travels 120 km. In 2 hours. What is the ratio of the distance to the time?

=
means
extremes
Lesson 51: Identifying and Writing Equivalent Ratios
Study the pictures at the left. The
following ratios can be formed using
the pictures:
6 : 8 and 3 : 4
or 6 and 3
8 4
What is the relation between the two ratios?
Let us reduce the ratios to lowest terms by dividing the both terms of each ratio by
their GCF.
6 6 ÷ 2 3 3 is already in lowest terms. So 6 3 ,
8 8 ÷ 2 4 4 8 4
In the equality of ratios , a and d are called extremes while
b and c are called the means.
Note that can be written as a : b = c : d .
In equal ratios, the product of the means is equal to the product of the extremes.
Using the equal ratios above, we can see that the product of the means, 8 x 3 = 24, is
equal to the product of the extremes, 6 x 4 = 24.
= =
a c
b d
=
a c
b d
=

Get Moving!
Put a check ( √ ) if the ratios are equal and a cross ( X ) if they are not.
____ 1) 4 , 16 ____ 6) 16 : 20 , 4 : 5
5 20
____ 2) 3 , 6 ____ 7) 6 : 9 , 2 : 3
4 8
____ 3) 9 , 1 ____ 8) 4 : 5 , 2 : 5
10 5
____ 4) 1 , 7 ____ 9) 2 : 3 , 1 : 5
5 10
____ 5) 1 , 3 ___ 10) 18 : 9 , 2 : 1
10 30
Keep Moving!
A. Write = in the circle if the given pair of ratios are equal and ≠ if not.
1) 64 : 12 80 : 15 6) 8 : 12 10 : 15
2) 3/7 24/56 7) 16/32 2/6
3) 6/7 75/100 8) 10 : 13 20 : 23
4) 15 : 12 35 : 28 9) 15 : 6 20 : 8
5) 14 : 40 9 : 24 10) 60/100 9/15

B. Fill in each box with the correct number that will make equivalent ratios.
1) : 7 = 24 : 56 6) 11 : = 330 : 450
2) 8 : 3 = : 15 7) 35 : = 20 : 8
3) 12 : = 15 : 5 8) 12 : 15 = : 10
4) 4 : 16 = : 8 9) 5 : = 30 : 18
5) 27 : = 9 : 15 10) 20 : 12 = 15 :
Apply Your Skills!
1) Two numbers are in the ratio 2 : 3. If the bigger number is 6, what is the smaller
number?
2) What number compared with 8 is the same as 6 compared with 24?
3) There are 18 roses for every 6 roses. How many roses are there if there are 3 roses?
4) There are 7 children for every 2 adults in a plaza. How many adults are there, if there
are 21 children?
5) Two numbers are in the ratio 3 : 5. If their difference is 12, what are the numbers?

Lesson 52 : Expressing Ratios in their Simplest Forms
In Miss Lakandula’s class, there are 3 books for every 6 pupils.
Can 3 : 6 or 3/6 be reduced to lowest terms?
Let us draw a picture.
There are 3 books for every 6 pupils. It is
also true to say 1 book for every 2 pupils.
The ratio 3 : 6 or 3 can be
6
expressed as 1 : 2 or 1
2
1 : 2 or 1 is a ratio in lowest terms
2
for the ratio 3 : 6.
Study this table.
Ratio Terms
Greatest
Common
Factor (GCF)
between the
Terms
Divide the
Terms by Their
GCF
Values of the
Ratio in
Lowest Terms
8 : 12 8, 12 4 8 ÷ 4, 12 ÷4 2 : 3
5 : 15 5, 15 5 5 ÷ 5, 15 ÷5 1 : 3
24
6
24, 6 6 24 ÷ 6, 6 ÷ 6 4
1
15
9
15, 9 3 15 ÷ 3, 9 ÷3 5
3

Get Moving!
A. Express the ratio of the first quantity to the second quantity and reduce to simplest
form.
1) 2 teachers to 46 pupils
2) 4 books to 10 students
3) 12 flowers to 4 vases
4) 21 garbage cans to 14 classroom
5) 36 glasses of juice to 30 sandwiches
B. Reduce these ratios to lowest terms.
1) 10 : 5 4) 15
2) 3 : 12 30
3) 20 : 4 5) 6
8
Keep Moving!
A. Write a ratio for each of the following. Give each lowest terms.
1) 15 boys to 30 girls _____________
2) 5 boxes to 60 oranges _____________
3) 2 jeep for 44 passengers _____________
4) 7 days to 3 weeks _____________
5) 6 decades to 1 century _____________

B. Find the ratio of the time spent for the different activities.
AJ’s Daily Activities No. of Hours
Sleep 7
School 6
Exercise 1
Studying/Doing Assignments 2
Recreation 1
Meals and Personal Hygiene 2
Other Activities 3
1) sleeping to a whole day _____________
2) studying to the time in recreation _____________
3) in a school to a whole day _____________
4) in other activities to the time for meals and personal hygiene ____________
5) in exercise to sleeping _____________
Apply Your Skills!
Write the following ratios to lowest terms:
1) 25 wins in 30 games
2) 8 red balls to 12 blue balls
3) 25 dm to 2 m
4) What is the ratio of the letter O to all the letters in the word COLOR?
5) What is the ratio of Saturday and Sunday to the days in a week?

Lesson 53: Finding the Missing Term in a Pair of Equivalent Ratios
Marie can make 3 small mango pies for
every 5 mangoes. How many pies can she make
with 25 mangoes?
The ratio in the problem is 3 : 5. This means that
for every 3 pies, Marie needs 5 mangoes.
But how do we solve the problem?
We use equivalent ratios to find how many pies Marie can make with 25 mangoes.
To find the missing term in a pair of equivalent ratios, solve for equivalent fractions.
3 = pies
5 25 mangoes
3 x 5 = 15 Think: To get 25, you multiplied the denominator by
5 x 5 = 25 5, so we multiply the numerator by 5 also.
Marie can make 15 pies.

Get Moving!
A. Tell whether the following given ratios are proportions. Write YES if they are and NO if
not, change one term to make them proportions.
1) 4 and 28 4) 3 : 21 and 6 : 40
5 35
2) 18 : 45 and 4 : 12 5) 9 : 12 and 27 : 32
3) 20 and 15
48 36
B. Solve for the missing term in each proportion.
1) 6 : n = 8 : 12 4) y : 6 = 28 : 84
2) m : 7 = 6 : 21 5) 14 : 21 = 2 : n
3) 20 : 24 = x : 6
Keep Moving!
A. Tell whether n = 22 is a reasonable answer to complete each proportion. Write YES or
NO on the blank before each number.
__________ 1) n = 11 __________ 4) 45 = 15
24 12 60 n
__________ 2) 44 = n __________ 5) n = 110
72 36 33 165
__________ 3) 10 = 30
n 33

B. Solve for the missing term and check.
1) a = 3 6) 3 = 24
32 4 10 n
2) 90 = a 7) n = 32
54 3 4 24
3) x = 49 8) 5 = 23
9 63 n 69
4) 2 = n 9) 1 = 28
5 30 7 x
5) n = 9 10) 3 = 21
17 51 7 y
Apply Your Skills!
Solve for the missing term.
1) What number compared to 10 is the same as 28 compared to 5?
2) Lisa saves Php 60.00 in 4 weeks. At this rate, how long will it take her to save
Php 300.00?
3) Six compared to 11 is the same as 84 compared to what number?
4) A motorist travelled 240 km is 3 hours. At the same rate, how long will take to
travel 400 km?
5) A scale 3.5 cm on a map represents an actual distance of 175 km. What actual
distance does a scale distance of 5.7 cm represent?
6) There are 24 students in a Grade V class. During a tree planting day, they
planted a total of 24 mahogany and narra seedlings. Each girl planted 3
mahogany seedlings and every three boys planted 1 narra seedling. Find how
many mahogany and narra seedlings each are planted by the students?

Lesson 54: Defining and Describing a Proportion
SECOND QUARTER, WEEK 10
Day 1
Cassandra uses 3 kilos of sampaloc to make 24 dozens of
sampaloc candy. What is the ratio of the number of sampaloc
candy to the number of sampaloc used?
The ratio of sampaloc candy to sampaloc is 24 to 3 or 24:3.
We can form another ratio from 24:3 by reducing this to lowest terms.
24:3=8:1
How did we do this?
24÷3=8 or 24:3= 8:1
3 ÷3= 1
How do we check if the second ratio is proportional to the given ratio?
There are two parts in a proportion – the means and the extremes
24 : 3 = 8 : 1
means
extremes
Means refer to the inner terms in a proportion.
Extremes refer to the outer terms in a proportion.
The two ratios are proportional if the product of the extremes is equal to the product of
the means. Thus, proportion means that two ratios are equal. To find proportion, we can
use cross multiplication.
Example:
24 : 3 = 8 : 1
3x8=24
24x1=24

Get Moving!
Draw a if the given show proportion and draw a if it doesn’t show proportion.
_____ a. 3:9 = 9:27
_____ b. 7:1= 5:3
_____ c.15:5 = 5:15
_____ d.8:2 = 4:1
_____ e. 6:20 = 12:40
Keep Moving!
Read and analyze the problem.
A bag of N & N sweets contain just yellow and orange sweets. For
every 2 yellow sweets, there are 6 orange sweets. Complete the table below,
then answer the questions that follow.
Yellow 4 6
Orange 6 12
Total Sweets 24 40
a. What is the ratio of orange to yellow sweets?
b. If you have 8 yellow sweets, how many orange sweets will you have?
c. There are 32 sweets in the medium sized bag. How many will be yellow?
d. In the extra large bag there are 40 sweets. How many are orange?
e. You look in the sweet and count out 16 yellow sweets. How many sweets are in the bowl?
Apply Your Skills!
Form proportions out of the following problems then solve for the answer.
a. Three boiled camotes sell for P17.00. How much do 9 pieces cost?
b. Two boys can paint 5 desks in 1 day. How many desks can 10 boys paint?
c. What number compared to 10 is the same as 25 compared to 5?
d. Juliana saves P60.00 in 4 weeks. At this rate, how long will it take her P300.00?
e. A motorist travelled 240 km in 3 hours. At the same rate, how long will it take to travel
400km?

Lesson 55: Recognizing when two quantities are in direct proportion
SECOND QUARTER, WEEK 10
Day 2
Amanda and Cass sell newspapers on weekends to earn extra
money. For every 3 newspapers that Amanda sells, Cass sells 5. If
Amanda sold 15 newspapers, how many does Cass sell?
Solution 1:
Illustrate the problem.
Amanda
Cass
Through illustration, it is clear that for every 15 newspapers that Amanda sold, Cass was
able to sell 25 newspapers.
Solution 2:
Set up a proportion
Amanda 3 = 15 or Amanda: Cass= Amanda:Cass
Cass 5 N 3:5 = 15:N
Computing for the proportion: 3:5=15:N
3N=15x5
3N= 75
3
N= 25 newspapers
For every 15 newspapers that Amanda sells, Cass sells 25 newspapers.
This kind of proportion is called a direct proportion. The quantity changes in the same
direction. As the number of newspapers that Amanda sells increases, the number of
newspapers that Al sells also increases.

Get Moving!
Put check (/) on the box if the proportion shows direct proportion and put a cross (x) if it
doesn’t.
30:18 = 36:15
9:2 = 3:1
5:3 = 25:15
4:15 = 12:45
5:4 = 2:8
Keep Moving!
Check whether the following statements show direct proportion. Draw a happy face if it shows
direct proportion and a sad face if not.
_____ a. Three pieces of pad paper cost P1.00 while 21 pieces of pad paper cost P7.00.
_____ b. Four colored pencils cost P25.00 while 5 colored pencils P20.00.
_____ c. Two boiled bananas cost P7.00 while 6 boiled bananas cost P21.00.
_____ d. Three teachers for every 125 pupils:5 teachers for every 100 pupils
_____ e. A motorist travels 275km in 5 hours and continue traveling at 140km for 2 hours.
Apply Your Skills!
1. Write a proportion for each problem, then find the missing term.
a. The ratio of 2 numbers is 3:5. The larger number is 30. What is the smaller number?
b. There are 5 teachers to 125 pupils during the school program. How many teachers
were there if there were 2 500 pupils?
c. The ratio of male teachers to female teachers in a school is 2:9. If there are 108
female teachers, how many male teachers are there?
2. Dolor cooks for her family. Her recipe for ube jam is 4 cups of boiled and mashed ube, 1 cup
sugar and 3 cups of milk. If the recipe is good for 2 small bilao, how can Dolor modify it for 5
bilaos?

Lesson 56: Visualizing Percent and its Relationship to Fractions, Ratios, and Decimal
Numbers Using Models.
JianearnedP100 for selling junk. He gave hismother P 80 and
put P 20 in his coin bank. What percent of his earnings did he give to
his mother? What percent did he save?
Let us draw the model.
80%
There are 100 parts in al. the shaded part is 80 of 100 parts. Jian gave 80% of his earning to his
mother and saved 20% of it.
Let us study these;
The relation of percent to fraction
80% is equal to
100
80
or
100
80
÷
20
20
=
5
4
The relationship of fraction to decimal. Divide the numerator by the denominator.
.80
5 00.4
4 0
0
0
0

Another way:
80% =
100
80
÷
20
20
=
5
4
The relationship of percent to decimal. To change percent to decimal move the decimal point 2
places to the left and drop the % sign.
80% = 0.80
B. Compare the shaded part in each grid.
100
25
25:100 0.25 25%
Fraction Ratio Decimal Percent
Study these.
4
1
=
4
1
x
25
25
=
100
25
’ so
4
1
=
100
25
= 0.25 = 25%
5
2
=
5
2
x
20
20
=
100
40
, so
5
2
=
100
40
= 0.40 = 40%
To change from percent to fraction, change percent to fraction with 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 % to the number.

0.5 0.75
Get Moving!
A. Rearrange to link decimal, fraction and percent.
0.25
2
1
10
3
4
1
5
1
4
3
30% 20% 25% 75% 50%
B. Write the name for the shaded part of each figure as a fraction, ratio, decimal, and
Percent.
1. 2. 3. 4. 5.
Ratio ________ _______ _________ _________ ________
Fraction ________ _______ _________ _________ ________
Decimal ________ _______ _________ _________ ________
Percent ________ _______ _________ _________ ________
C. Write each as percent.
1.
100
5
2. 0.18 3.4: 100 4.
100
99
5. 0.89
0.20 0.30

Keep Moving!
A. Change the given fraction to decimal and to percent.
Fraction Decimal Percent
1.
2
1
2.
6
4
3.
8
1
4.
5
3
5.
100
13
B. Write the ratio, decimal and percent equivalent of each picture.

Fi
gu
re
R
at
io
De
ci
ma
l
Pe
rce
nt
1
2
3
4
5
C. Complete the
table to make the
statements true.
Decimal Fraction Percent
1 0.05
2
50
23
3 37.5%
4
18
15
5 0.87
6 50%
7
25
20
8 0.58
9 7%

Apply Your Skills!
Solve each problem.
1. 65 percent of the class are girls. Express 65% as a decimal.
2. Loraine spent 50 minutes in solving her Math assignment. What percent of an hour
was
that?
3. Out of 200 school days, Aaron was absent for 8 days. Express as a decimal the ratio
of
the number of absences of Aaron to the number of school days. _____. What percent
of the school days was he absent?_________
4. Arthur travelled 48 km in 3 hours. What is the ratio of km to hours?
5. Renan scored 32 out of a 100 item test in Math. What percent of the test did he
answer
correctly
10 1.25

Lesson 57: Defining Percentage, Rate or Percent and Base
Seventy-five percentof the the 40 pupils of Mrs. Gallardo like Mathematics. How many
pupils are Math lovers?
a. How many pupils does Mrs. Gallardo have in all?
40 is a whole number. It is called base.
b. How many percent of the pupils like Mathematics?
75% is the rate which can be expressed as a ratio or as fraction
c. How many pupils love mathematics?
30 is the percentage it is a part of the whole.
Study these example;
25% of 8 = 2
Rate
Base
Percentage
25% is the rate. It is given as a percent. It can be expressed as ratio or fraction
100
25
8 is called a base. It is a whole number of which you take the percent.
2 is called the percentage meaning a part of the whole. It is the resulting fractional part
of
the base.
Get Moving!
A. Write which is the rate, base, and percentage
1. 20% of 40 is 8 4. 40 is 10% of 400
Rate _______ Rate _______
Base _______ Base _______
Percentage ______ Percentage _________
2. 15 % of 200 is 30 5. 50 is 25% of 250
Rate_______ Rate ________
Base ______ Base ________
Percentage_______ Percentage _________

3. 70% of 50 is 35
Rate _______ Base __________ Percentage ________
B. Write “rate”, “base”, or “percentage” to identify what you need to solve for.
1. 30 is 15% of what number? _________
2. What is 78% of 100? __________
3. 8 is what percent of 16?_________
4. What percent of 35 is 5? _________
5. 22% of what number is 66?________
6. 24% of 300 is what number? _______
7. 12 is 40% of what number? ________
8. What is 90% of 30? _________
9. 7 is what percent of 14? _______
10. What percent of 45 is 9? ________
Keep Moving!
Write what is missing (base, rate, or percentage) and then solve.
1. 32 is what percent of 80? 6. 14 is what percent of 56?
What is missing?_____________ What is missing?_____________
Answer:____________ Answer:____________
2. 25% of what number is 12? 7. 200% of 10 is what number?
Answer:____________ Answer:____________
3. 30% of 70 is what number? 8. 9 is what percent of 180?
Answer:____________ Answer:____________
4. 100% of 11 is what number? 9. 2% of 250 is what number?
Answer:____________ Answer:____________
5. What percent of 28 is 14? 10. 6 is what percent 24?
Answer:____________ Answer:____________

Apply Your Skills!
A. Answer the following questions:
1. Which represent the whole?
2. Which represents part of the whole?
3. Which element has the symbol “%”?
B. Complete the following sentences to make them true:
1. In the statement 65% of 70 = N, 65% is called the rate because
_______________.
2. In 25% of 800 = 200, 200 is the percentage because
________________________.
3. In the statement in No. 2, 800 is the base. It tells __________________________

Lesson 58: Identify the Base, Percentage and Rate in the Problem
A survey conducted among 120 grade 5 pupils of Yukos
Elementary School showed that 45% like swimming. They found
that 54 out 120 pupils like swimming.
How can identify rate, base, and percentage?
We can identify the rate, base and percentage using the Techan’s Triangle.
P 54
R B 45% 120
We can also write:
45% of 120 = 54
Rate
Base
Percentage
Another examples:
1. 80% of P 9 475 = P 7 580
80% is the rate
P 9 475 is the base
P 7 580 is the percentage
We can say that:
Rate is the number written with the word “percent” or with the symbol “%”.
Base is the total or whole and it is the number that usually follows the phrase
“percent of” or “% of”.
Percentage is the part of the whole.
Techan’s Triangle is used to identify rate, base and percentage.

Get Moving!
A. Identify the rate, base, and percentage by completing the table.
Rate Base Percentage
1. 6 is 25% of 24
2. 20% of 15 is 3
3. 500 is
8
5
% of 800
4. 125% of 60 75
5. 1 400 is 275% P 3 850
6. 12 ½ % of 48 is 6
7. 17 is 33
3
1
% of 51
8. 30 is 50% of 60
9. 60 is 20% of 300
10. 0.5% of 2 000 is 10
B. Determine the rate, base and percentage.
1. 20% of 50 is 10
2. 80 is 125% of 64
3. 8% of 1 200 is 96
4. 48 is 40% of 120
5. Twenty-one is 25% of 84

Keep Moving!
Show the rate, base and percentage in the Techan’s Triangle about the following problem.
1. Jun deposited P 1 800 in a bank. After a year, his money earned P 90 which is 5% of
his initial deposit.
2. Althea gives 45% of her salary to her mother. She says she has P11 250 for her mother
because her income is P 25 000. Is she right?
3. Yanny has P5 000 in her pocket which is 25% of her father’s money. Her father must
haveP 20 000.
4. Jian bought a toy car with 15% discount or P150. The toy car must have a tag price of
P1,000.00.
5. An item is marked P6,010. This is 60% higher than the price. The original price must be
P3,756.25.
6. There are 40 students in the class 95% of them are present. There are 38 pupils
attended their class.
7. When we ate in the restaurant, our bill amounted P 450.00. to thank the the waiter for
his good service, Joan tipped him 10% of the amount . the waiter received P45.00 as
tip.
8. There are 160 families in our barangay, 40 families are engage in fishing. It means 25%
of them are fishermen.
9. During the basketball season, Alvin shot 175 free throws. He made 88% of them. He
make 154 free throws.
10. Among the 1 250 pupils who attend a school, 6% are left-handed. There are 75 left-
handed pipils.
Applying Your Skills!
Read and answer the following problems.
1. Mrs.Acorda opened an account in LandBank of the Philippines. She puts a principal
amount of P 15 000 that will earn an interest of P150 after a month at a rate of 1%
monthly.
a. What are given data in the problem?

b. Which of the data is the base? Rate?percentage?
2. She then updated her time deposit account. The amount typed at the back is P 30,900.
She asked for the rate given to her P30,000 deposit and was told that it is 3%.
a. What are the given data in the problem?
b. Which data is the rate? base? Percentage?

Third Quarter
Lesson 59: Finding the Percentage in a Given Problem
Read the problem below.
In the recent election held at Brgy. Masikap, it showed that the winning Brgy. Captain received 78% of
the total votes from 160, 000 population of the barangay. How many people voted the winning Brgy. Captain?
How will you solve for the answer for the problem?
A. Find the percentage of each by changing percent to fraction.
1. 16% of 10 = _____ 6. 90% of 100 = _____
2. 10% of 80 = _____ 7. 75% of 160 = _____
3. 40% of 50 = _____ 8. 12% of 200 = _____
4. 25% of 48 = _____ 9. 14% of 156 = _____
5. 5% of 40 = _____ 10. 80% of 650 = _____
B. Find the percentage of each by changing percent to decimal.
1. 12% of 40 = _____ 6. 11% of 90 = ______
2. 75% of 300 = _____ 7. 36% of 150 = _____
Get Moving!
 Rate- 78%
 Base – 160, 000
 Percentage - ?
Step 1: Identify the rate and the base in
the given problem.
 160, 000 x 78% = n Step 2: Transform the problem in equation form.
 P = B x R
= 160, 000 x 0.78
Step 3: Use the formula in finding the percentage.
Change the rate to a decimal then multiply
the base.
 160 000
x 0.78
1 280 000
+ 11 200 00_
12 480 0.00
Step 3: Solve. Follow the steps use in multiplication.
Put the decimal point on its corresponding
place.
124, 800 – number of people who voted the
winning Brgy. Captain

3. 12% of 120 = _____ 8. 42% of 500 = ______
4. 6% of 100 = ______ 9. 15% of 60 = ______
5. 48% of 35 = ______ 10. 88% of 120 = ______
A. Change percent to fraction then solve.
1. 4% of 25 = _____ 6. 10% of 20 = ______
2. 5% of 80 = _____ 7. 25% of 40 = _____
3. 5% of 90 = _____ 8. 120% of 50 = ______
4. 9% of 81 = ______ 9. 40% of 1206 = ______
5. 6% of 12 = ______ 10. 20% of 80 = ______
B. Change percent to decimal then solve.
1. 75% of 64 = _____ 6. 37.5% of 90 = ______
2. 16% of 80 = _____ 7. 12.8% of 60 = _____
3. 14% of 56 = _____ 8. 43.2% of 150 = ______
4. 60% of 30 = ______ 9. 67.5% of 120 = ______
5. 50% of 18 = ______ 10. 24.8% of 100 = ______
A. Solve each problem.
1. There are 40 students in a class. If 95% of them were present, how many students
attended their class?
2. Among the 1 400 students who attend school, 12% are left-handed. How many are
left-handed? How many are right-handed?
3. Jenny answered 95% of her test correctly. If there were 60 items in the test, how many
items did she answer correctly? How many mistakes did she make?
4. In a Math competition, 30 boys and 20 girls joined. At the awarding ceremony, 20% of
the boys and 15% of the girls were awarded prizes. How many received prizes?
5. Carlos sells an average of P 98 000 worth of goods in a month. The company gives him
16% of his sales. How much does he earn in a month? In 6 months?
6. The total enrolment for school this year is 1206. If 66 % are boys, how many are girls?
Keep Moving!
Apply Your Skills!

7. A talk show hosts has done 3 225 shows, 20% of which were shot on tape (not live).
How many of the shows were taped? How many were live?
8. The country’s biggest coliseum sold 20 million tickets for different events during one
year. Of these tickets 77.5 % were for sporting events. How many tickets were sold for
sporting events?
9. During the basketball season, George shot 175 free throws. He made 88% of them.
How many free throws did George make?
10. 120 points are given to each of two tests. If a boy gets 63 points in one test, how many
points must he get in the second test to get 60% for both tests?

Lesson 60: Solving Routine and Non-routine Problems Involving Percentage
Using Appropriate Strategies and Tools
Read the problem below.
Can you solve the problems?
Problem 1
Problem 2
In an 80-item Math Test, Carla
got 92% of correct answers. How many
items did she answer correctly?
 Understand
Know what is asked: The number of items she failed to answer correctly.
Know the given facts: 80-item test; 92% of correct answer
 Plan
Determine the operation to be used: Multiplication
Write the number sentence: 80 x 0.92 = n
 Solve
Show your solution:
 Check and Look Back.
See if your answer makes sense.
State the complete answer.
Carla got 72 correct answer in an 80-item test.
0.90
x 80
000
720__
72.00
7
Romeo celebrated his 11th
birthday. He counted the person who
attended the party and found out that
40% of the 200 visitors were male.
How many attendees are male?

You can solve by drawing an illustration first.
In the given problem, 40% can also be represented in fractional form which is . Since there are 200
visitors in the party, we can simple simply divide it into 10. So, each region represents 20 persons. Now, we
can easily solve the problem. If one shaded region represents 20 persons then 4 shaded regions represents 80
persons. It means that there are 80 male attendees in the birthday party.
Solve the following problems. Show your solutions. Use drawings, illustrations or number line if possible.
1. Ninety percent of the 50 members of Clean and Green Movement voted for the new
president. How many did not vote for the new president?
2. Of the 10 on-going projects of the movements 60% are fully implemented. How many projects
were fully implemented?
3. In a resort, the entrance fee per person is P 80.00 but in a group of 10 people it is fixed at
P 70.00 per head. If the resort gave an additional 5% discount for every person that
exceeds 10, how much is entrance fee paid by 21 persons?
4. Among 60 women in a slum area, 40% earn a living peddling plants and the rest earn their
living as live out domestic helpers. How many are live out domestic helpers?
5. Brgy. Masayahin has conducted a General Assembly, 120 people attended. Among them
60% were female. How many among them were male?
6. Marion has a certain amount of money on his pocket. He spent 10% of it on buying
chocolates and candies on the first store. Then he went to the next store and spent
15% of it for school supplies. If Marion had P 90.00 left on his pocket, how much
money does he have at first?
7. 10% of our class of 40 was unable to join the field trip. How many in our class joined the field
trip?
8. For every purchase of rubber shoes worth P 700.00, you will receive a 5% discount. If Dan
received P 280.00 as discounted price, how many shoes did he buy?
9. In a parent-teachers’ meeting, 80 people attended. 70% attendees were parents. How many
20 20 20 20 20 20 20 20 20 20
Get Moving!

were teachers?
10. In an organization with 10 members, each our required to save 5% from their daily
allowance of P 50.00. How long would it take them to save P 150.00?
Solve the following percentage problems.
1. Forty-six percent of people surveyed said that they exercised on a fairly regular basis. If 12
100 people were surveyed, how many of them exercise?
2. The price of gasoline decreased by 18%. If a liter of gasoline sold P 21.15 before the
decrease, what was the amount of the decrease ?
3. In a certain city, about 25% of the people are between the ages of 20 and 40 years. If the city
population is 1 430 000, how many people are between those ages?
4. Mike and his friends will watch a concert this weekend. A concert ticket cost P 750.00 but for
every 10 tickets you buy you will have a 15% discount. If they will buy 10 concert tickets, how
much will they pay?
5. Peter is asked to guess a number. Here’s the clue, it is 75% of 40% of 600 ?
1. The Jimenez family planned to save at least 7.5% of their monthly income of P 12 500. How
much did they plan to save?
2. Gerald saves 18% from his P 300.00 weekly allowance while Mirasol saves 25% from his
P 250.00 weekly allowance. Who saves more Gerald or Mirasol? By how much?
3. Marvin, a basketball player, usually scores 80% of his field shots. If he attempted 40 field
shots during a game, how many did he score ?
4. A fruit vendor was able to sell 85% of his 56 kilos of mangoes. How many kilos of mangoes
were sold?
5. Mark has 14 paper bills of different denominations on his pocket. He gave 45% of it to his
Keep Moving!
Apply Your Skills!

mother and 10% of it to his three younger sister. He has now P 864.00 left on his pocket.
How much money Mark had at first?

Lesson 61: Creating Problems Involving Percentage with Reasonable Answers
How will you create a problem given the information above?
You can create a problem using the following guide.
1. Familiarize yourself with the concept of rate, base and percentage.
2. Think of the problem you want to create and the operations to be used in
solving the problem.
3. Read other examples of problems. Study them and their solutions.
Study the following problem created with the information above.
Henry has already collected 500 different kinds of stamps. From these stamps,
85% are Philippine stamps and the rest are foreign stamps. How many are Philippine
stamps? How many are foreign stamps?
Can you create a word problem for the given information below?
A. Create a word problem based on each situation below. Write your answers in your notebook.
1.
Get Moving!
Henry has already collected 500 different kinds of
stamps. From these stamps, 85% are Philippine stamps and
the rest are foreign stamps.
240 intermediate students
80% present
1 500 people
48% -aged 0-14
36% - aged 15-64
16% - aged 65- above

2.
3.
4.
A. Create a word problem using the following information.
1.
2.
3.
Keep Moving!
48 marbles in a box
60% are red
15% are blue
125 Grade Six students
5% were absent
48% of P 5,000.00 spent for clothes
36% of P 5, 000.00 spent for shoes
1 000 square meters of field planted with corn
85% of corn are harvested
P 11, 200.00 monthly income
35% spent for education
12% spent for transportation
45% spent for food
8% savings
3 500 people visited the museum every week
38% visited on the third day
each passes cost P 50.00

4.
A. Create a word problem using the following information.
1.
2.
3.
4.
.
Apply Your Skills!
120 kilograms of mangoes
72% are ripe mangoes sold
Each kilo cost P 70.00
4 200 packs of noodles per day
45% are delivered to Laguna
38% are delivered to Batangas
the rest are delivered to Cavite
420 Grade Six pupils
70 % are Math lovers
600 pets in the shop
15% are birds
30% are fishes
45 % are dogs
the rest are cats
360 square meter lot with vegetables
40% were planted with pechay

Third Grading
Lesson 62. Visualizing, Naming and Describing Polygons with 5 or
More Sided Polygons
Week 3
Objective: Visualizes, names and describes polygons with 5 or more sides.
Prerequisite Concepts / Skills
► Identifying Geometric figures
► Kinds of angles
Materials : cut-outs, geoboard
References: K to 12 Grade 5 Curriculum Guide, p 61
Lesson Guide in Elementary Mathematics 5, p. 350-357
A. Preliminary Activities
1. Drill
Korek ka ba dyan?
Mechanics:
a. Group the pupils into 4’s.
b. Distribute envelopes with geometric figure to each group such as drawings of parallel
lines, intersecting lines, ray, line segment, perpendicular lines.
c. As the teacher flashes the words, the pupils will get from the envelope the geometric
figures and put it on the board assigned for the groups.
2. Review
“What am I” – kinds of angles
The teacher flashes a card with the following questions. Let it be answered by the
pupils.
a. I measure less than 90°.
b. I measure 110°
c. I measure 18°
d. I measure 90°
e. I measure more than 90° but less than 180°
3. Motivation
The teacher shows different cutouts and real objects.
What do you see class?
How many sides are there in the picture?
Value focus : cooperation

B. Developmental Activities
1. Presentation
Present these figures using a geoboard.
How many sides are there in the polygon shown in the geoboard?
What do you call a polygon with 5 sides? 6 sides? 7 sides? Etc?
Let the pupils show 5, 6, 7, etc. sided polygon using the geoboard and identify it.
2. Performing the Activities
Material : cut-outs of 5-12 sided polygons.
Mechanics :
a. Group the pupils into four.
b. She or he distributes cutouts placed in an envelope.
c. Let the pupils paste the cutouts intended for the different column as shown below.
Cutout Number of sides Name of polygon
5 sides
3. Processing the Activities
Call a leader to report for the group.
Ask. What are the different kinds of polygon?
How are they identified?
Present the chart of the different kinds of polygon

4. Reinforcing the Concept and Skill
Discuss the presentation under Explore and Discover on page ___, LM Math Grade 5.
Let the pupils do the activity under Get Moving on page ___, LM Grade 5. Check the pupil’s
work.
For more practice, let them answer Keep Moving on page _____, LM Grade 5.
5. Summarizing the Lesson
Ask: What are polygons?
How are they classified?
6. Applying the New and Other Situations
Name the figure below.
Let the pupils do items under Apply Your Skills on page ___, LM Math Grade 5.
C. Assessment
Match column A with column B.
A B
1. a polygon with 5 sides a. pentagon
2. a polygon with 10 sides b. octagon
3. a polygon with 8 sides c. nonagon
4. a polygon with 6 sides d. hexagon
5. a polygon with 9 sides e. decagon
D. Home Activity
Remediation
Complete each statement.
a. Dodecagon has ____ angles
b. a nonagon has _____ vertices
c. an octagon has _____ angles
d. A decagon has _____ vertices
e. A heptagon has _____ sides
Polygons are closed plane figure that formed
by the line segments that meet only at their
endpoints. The line segments are the sides and the
endpoints where sides meet are the vertices.
Polygons are classified according to the
number of their sides and angles.

Enrichment
Encircle the polygons. Explain why the others are not polygons.
a. b. c.
d. e.

Third Grading
Lesson 63. Describes and Compares Properties of Polygons
( Regular and Irregular Polygons)
When you travel on streets, you see road signs. Most of these have the shape of a
polygon.
A polygon is a closed figure formed by line segments that meet only at their endpoints.
The line segments are the sides and the points were the sides meet are the vertices. The
angles formed by the adjacent sides are the angles of the polygon.
Polygons are classified according to the number of
their sides and angles. A polygon
has as many sides as angles.

Get Moving !
Name each polygon. Tell whether it is regular or irregular.
1. 3. 5.
2. 4.
Keep Moving!
A. Count the number of sides then name each polygon. Identify whether it is
regular or irregular.
1. 2. 3.
4. 5 6.
B. Answer the following questions.
1. What are polygons?
2. Is a rectangle a regular polygon? Why?

Apply Your Skills!
A. Name each polygon described.
_____ 1. a polygon with 6 sides
B. Identify each polygon in the figure below.

Third Grading
Lesson 64. Drawing Polygons with 5 or more Sides
Get five strips of paper. Join the strips as
Shown in the picture. Mark points at the corner.
Remove the strips and connect the points. What
figure did you draw?
Another way to draw polygons with five or more sides is to use a square dot paper.
.
More Examples
A triangular dot paper can also be used to draw polygons.

Get Moving !
Copy and complete each polygon.
Hexagon Heptagon Decagon
Keep Moving!
A. Use a square dot paper to draw the following:
1. a polygon with 6 sides
B. Use a triangular dot paper to draw the following:

Apply Your Skills!
Copy these triangles and cut them. Use the triangles to form another polygon.

Lesson 65: Visualizing congruent polygons.
Are these polygons similar? Why or why not?
 Yes, they are. These polygons are regular, and all regular polygons are
similar.
Get Moving!
Arlene’s grandmother made a sash for her. The pattern of the sash is show below.

a. What type of triangles are shown in the pattern? Classify each type by their sides and their
angles. ______________________
b. Are the 2 triangles in the pattern congruent? ________
c. Are the 2 squares similar? ________
Keep Moving!
Circle the figure has same shape and size as the first picture.

Apply Your Skills!
Draw a congruent shape as the first one.

Lesson 65: Visualizing and describing a circle.

Get Moving!
Identify each element.

Keep Moving!
Find the circumference of the following.
Circumference = 2 r = 3.14

Apply Your Skills!
Draw a circle and label its part.

Lesson 67: Identifying terms related to a circle.
Using circular cutouts of different sizes, identify the center, radius, diameter of a circle.
Get Moving!
Use a compass or a cardboard strip to draw circles with the given radii.
1. radius = 7 cm
2. radius = 12 cm
3. radius = 20 cm
4. radius = 10 cm
5. radius = 15 cm
Keep Moving!
Draw as many circular objects as you can using the nine circles below.

Apply Your Skills!
Follow the directions.
1. Draw two circles with two common points and with radii equal to 3 cm.
2. Draw two circles with common point and with diameters equal to 12 cm.
3. Draw two with no common point. The first has a radius of 2 cm and another has a
diameter of 4 cm. What did you notice about the sizes of the two circles? Why is this so?
4. Draw two circles having the same center such that the radius of the bigger circle is twice
that of smaller circle.

Third Grading Period
Lesson: 68 Drawing of circles with different radii using a compass
Compass :
Use a compass to draw a circle of radius 4 cm.
Solution:
Step 1: Use a ruler to set the distance from the point of the compass to the pencil's lead at 4 cm.
Step 2: Place the point of the compass at the centre of the circle.
Step 3: Draw the circle by turning the compass through 360º.
To draw a circle (or arc) with a compass:

 make sure that the hinge at the top of the compass is tightened so that it does not slip
 tighten the hold for the pencil so it also does not slip
 align the pencil lead with the compass's needle
 press down the needle and turn the knob at the top of the compass to draw a circle
(or arc)
1. Use a compass to draw a circle of radius 6.5 cm.
2. Draw a diameter and label it PQ.
3. Draw a triangle PQR where R is on the semicircle.
4. Use a protractor to measure the size of angle
1. Use a compass 7.5 cm. to draw a circle of radius
2. Draw a diameter and label it PQ.
3. Draw a triangle PQR where R is on the semicircle.
4. Use a protractor to measure the size of angle PRQ.
1. Draw a radius or a diameter from the given point. Use a ruler. Look at the example.
Here, a radius is drawn
from the given point.
a. Draw a radius
b. Draw a radius from
each of the given points.
Get Moving
Keep Moving
Apply Your Skills

c. Draw a diameter
d. Draw a diameter for
the smaller circle and
a diameter for the bigger
circle from the given points.
e. Draw a radius from the
point A and a diameter
from the point B.
2. Learn to use a compass to draw circles.
a. Draw many circles with the compass.
b. Now, set the radius on the compass to be 3 cm, and draw a circle.
You can do that by placing the compass next to a ruler, and adjusting the radius of the
compass until it is
3 cm as measured by the ruler.Some compasses show the radius for you, so you won't
need a ruler.
c. Draw a circle with a radius of 5 cm.
d. Draw a circle with a radius of 1 ½ in.
3. a. Draw two diagonals into this square. Draw a point
where they cross (the center point of the square).
Now, erase the lines you drew, leaving the point.
b. Draw a circle around the square so that it touches
the vertices of the square. Use the point you drew
in (a) as the centerpoint.
c. Fill in: The _____________________ of the circle
has the same length as the diagonal of the square.

Lesson: 69 Visualizing and describing solid figures
Study the illustration below:
Name the objects that resemble to the following Spatial Figures shown on the picture:
Identify the spatial figure represented by the following:
1) ball ______ 3) funnel ______ 5) tent ______
2) globe _______ 4) test tube _______ 6) dice ______
Get Moving
What is Spatial Figure?
Spatial figure is a three
dimensional figure. It is
made up of plane figure
whose all sides are
joined together to form
a close figure . Some
examples of spatial
figures include cubes,
cylinders, cones,
prisms, pyramids,
spheres and rectangular
prisms.

Give 5 objects that are models of the following spatial figures:
1) cone 3) cube 5) sphere
2) cylinder 4) prism
Match Column A with Column B.
A
1) The base is a polygon and its faces are
triangles
2. A spatial figure with a polygonal base
whose edges meet at a common vertex.
edges meet at a common vertex.
edges meet at a common vertex.
3. A spatial figure having a circular base
and one vertex.
4) A spatial figure with 2 parallel congruent
faces called bases and the other faces
are parallelograms.
5) A spatial figure with 2 circular bases, no
edge and no vertex.
Keep Moving
Apply Your Skills
B
a) rectangular prism
b) cone
c) pyramid
d) cylinder
e) triangular prism

Lesson: Making models of different solid figures: cube, prism, pyramid, cylinder, cone, and
sphere using
plane figure.
For each 3d shape, find the
correct net..
Identify the following nets as cube, rectangular prism, cylinder, or a pyramid.
Ex.
= rectangular prism
Get Moving

1. = _________________________
2. = ________________________
3. = ___________________________
4. =
____________________________
5. =
____________________________

Make models of each spatial figure using used folder:
1) cone 3) cube 5)
sphere
2) cylinder 4) prism
A. Matching Game : Using your models:
1) Blindfold a volunteer member in your group.
2) Let him/her hold a spatial figure.
3) Let him/her identify and describe it.
B. Complete the table.
Spatial Figure No. of Faces No. of Edges No. of Vertices
1. cube
2. rectangular prism
3. sphere
4. cylinder
5. triangular pyramid
6. rectangular pyramid
7. cone
Keep Moving
Apply Your Skills

Look for the pattern in the
sequence of encircled
numbers
Lesson 71 : Formulating the Rule in Finding the Next Term in a Sequence
A.
1, 3, 6, 10, 15, 21, 28, 36, 45
The encircled numbers form a number sequence. A number sequence is a list of
numbers in which successive terms follow a rule or pattern. Each number in s sequence is
called a term.
Looking at the pattern of the encircled number, to find the 2nd
term add 2, for the 3rd
term
add 3, for the 4th
term add 4, for the 5th
term add 7,
for the 8th
term add 8, and for the 9th
term add 9. Therefore. the rule in the sequence is ( +2, +3,
+4, +5, +6, +7, +8, +9 ).
By studying the sequence of numbers, we can find the rule governing the terms. The
rule can tell us what number will come next in the sequence.
B. Find the missing terms in the following situations below:
3 2 9 4 45 16 315 96
Can you find the pattern or sequence used?
The numbers inside the pentagon are multiplied by consecutive odd numbers 3, 5, 7.
Starting with 3 x 3 = 9, then 9 x 5 = 45, then 45 x 7 = 315, so the missing number in the last
pentagon is 2 835 ( 315 x 9 = 2 835 ).
The series of numbers inside the hexagon uses even numbers as factors. So, the
missing number inside the last hexagon is 768 ( 96 x 8 = 768 ).
1 2 3 4 5 6 7 8 9 10
11 12 13 14
15
16 17 18 19 20
21
22 23 24 25 26 27
28
29 30
31 32 33 34 35
36
37 38 39 40
41 42 43 44
45
46 47 48 49 50

Get Moving!
A. Find the rule, then, write the missing terms.
1. 12, 17, 22, ____, 32, ____
2. ____, ____, 67, 70, 73
3. 56, ____, 42, 35, 28, ____
4. 3, ____, 27, 81, ____
5. 78, 70, 62, ____, ____
B. Study the rule/pattern. Supply the missing terms.
6. 9, 16, 25, 36, ____
7. 16, ____, 36, 49, ____, 81
8. 10, 38, 150, ____, 2 390
9. 8, 16, 64, _____, _____
10. 6, 6, 18, _____, 630, _____
Keep Moving!
Find the missing terms and write the rules
.
1. 5, 6, 8, ____, 15, ____
2. 18, 20, 24, ____, 38, ____
3. 55, 54, 51, 46, ____, ____, 19
4. 25, 28, 3, ____, ____, 70
5. 82, 81, 78, ____, 66, ____
Apply Your Skills!
Formulates 5 rule or pattern of your own. Write one number sequence for each rule.

Lesson 72 : Using Different Strategies ( Looking for a Pattern, Working Backwards, etc )
to Solve for the Unknown in Simple Equations Involving One or More Operations on
Whole Numbers and Fraction
How will you solve this problem?
You can work backwards. Subtract the tax from the final cost of the bicycle to find the
original price of the bicycle without the tax.
Php195.00 – Php12.25 = Php181.75
The original price of the bicycle was Php181.75.
Remember that the answer is found by starting with the end result and working back to
the beginning.
Get Moving!
1. Brian gave 10 stamps from his collection to both Sam and Rob. Then he gave 14
stamps to Kathy and 6 stamps to Grace. He still had 275 stamps. How many stamps
were in Brian’s collection to begin with?
2. Brady was trying to decide when to get up in the morning. He needs 45 minutes to
get ready for school. It takes him 25 minutes to drive to school. He wanted to get to
school 20 minutes early to use the library. If school starts at 7:30, what time should
he get up?
The final cost of Bob's bicycle was Php194.
This included a tax of Php12.25. What was the original price
of the bicycle without the tax?

Keep Moving!
Work backward to solve each problem.
.
1. Mrs. Allen baked some cookies for the school bake sale. Franco bought 3 of the
cookies and Chandra bought 2. Mr. Walker bought 1 dozen of the cookies. William
and Starr each bought 6 cookies. Then Ms. Porter bought 4 of the cookies. That left
only 3 cookies for Scott to buy. How many cookies did Mrs. Allen bake for the sale?
2. Paula went shopping at a department store. She bought 2 CDs on sale for $8.95
each, a notebook for $4.29, and a bottle of shampoo for $2.58. When Paula paid for
her purchases, the cashier gave her $5.23 in change. How much money did Paula
give the cashier?
Apply Your Skills!
Read and solve the following problems carefully.
1. You save $3 on Monday. Each day after that you save twice as much as you saved
the day before. If this pattern continues, how much would you save on Friday?
2. Amy and Judy sold 12 show tickets altogether. Amy sold 2 more tickets than Judy.
How many tickets did each girl sell?
3. Carol has written a number pattern that begins with 1, 3, 6, 10, 15. If she continues
this pattern, what are the next four numbers in her pattern?

LESSON 73 MEASURES TIME USING A 12-HOUR AND 24-HOUR CLOCK
Third Quarter
WEEK 7
Explore and discover!
Claire and her friend meet at the SM mall movie theater to see Harry Potter. Claire arrive at
5:40 .Her friend arrives at 6:12. How long did Claire wait for her friend to arrive ?
What time is Claire’s friend arrived ?
What time did Claire arrive in movie theater ?
What is 5:40 and 6:12 on the 24 hours clock?
Claire arrived at 5:40 at the movie theater, and her friend arrived at 6:12.
If 5:40 convert to 24 hours system, it will be 17:40 ( seventeen and 40 hours ) and 6:12 will be
18:12 ( eighteen and twelve hours )
Therefore in changing 12 hours time to 24 hour time, add 12 to the hours and keep the minutes
same.
12:00 12:00
+ 5:40 + 6:12
17:40 18:12
Get Moving!
Write down all the possible times using the 12 and 24 hours clock. ( First is done for you )
12 Hours Clock 24 Hours Clock
___10:05 A.M.__ __10.05 A.M.__
___10:05 A.M.__ __22:05 A.M.__
_____________ _____________
_____________ _____________
_____________ _____________
_____________ _____________
_____________ _____________
_____________ _____________

Read and answer.
Challenge 1
 I am between 6 o’clock and 10 o’clock.
 I am not a half-past time.
 My hour is an odd number.
 What time am I? _______
Challenge 2
 I am earlier than 10 o’clock.
 I am later than 7 o’clock
 My big hand points to 6
 My hour is an even number.
 What time am I ? ___________
Keep Moving!
Converting 24 hours clock times
1 1:24 pm = 2 2:56 pm = 3 7:45 pm =
4 5:16 pm = 5 3:56 pm = 6 12:25 pm =
7 11:27pm = 8 8:13 pm = 9 12:42 am =
1 13:41 = 2 17:50 = 3 04:32 =
4 12:36 = 5 23:25 = 6 08:53 =
7 00:51 = 8 19:08 = 9 15:39 =
Apply your skills!
Distribute a set of cards with time/hours written and another sets of cards with the equivalent
number hours. Tell the pupils to find their match. The first pair to match wins. Post the number
pairs on the board.
Ex.00:00 zero hour’
1. 1:00
2. 12:00
1200 ( twelve hundred hours )
0100 ( one hundred hours )

3. 2:00
4. 4:00
5. 3:35
Read and answer the problem.
1. What is 2:40 a.m. on the 24 hour clock?
2. What is 4:47 a.m. on the 24 hours clock?
3. What is 11:28 a.m. on the 24 hours clock?
4. What is 5:00 on the a.m./p.m. clock?
5. What is 2:58 on the a.m./p.m. clock ?
All the clocks below show the time in the afternoon or evening. Write the times below the clocks
using 24 hour time.
0400 ( four hundred hours )
0200 ( two hundred hours )
0335 ( three and thirty five hours )
Time is :
_________
Time is :
_________
Time is :
_________
Time is :
_________
Time is :
_________

Time Arrival
Third Quarter
Lesson 74: Calculating Time in the Different World Time Zones in Relation to the
Philippines
Week 7
Mr. Reyes is going to Dubai to meet his wife who is working in a hospital as a nurse. He
will leave the Philippines at 4:30 pm. If the duration of his flight is 4 hours and 15 mins. What
time he will arrive at Dubai? And what time is it in the Philippines? How many hours is their time
difference?
Refer to the world time zone map.
4:30 – Departure Time
+ 4:15 - Travel Time
8:45 pm. - Philippine Time
4:45 pm - Dubai Time
If Mr. Reyes leave the Philippines at 4:30 pm. He will arrive in Dubai at 8:45 pm
( Philippines Time ). While in Dubai time is 4:45 pm. So therefore Dubai is behind 4 hours from
the Philippines.
To calculate time in the different world time zones in relation to the Philippines, we need
to use the world time zone map for as to easily understand their time differences.
Get Moving !
A. Tell the time of the following countries base on the Philippines time.
If the Philippines time is 2:30 pm, what is the time in;
Malaysia - _________
France- _________
Brazil - _________
India- _________
USA - _________

Keep Moving!
A. Give the time differences of the following countries.
How many times each country different to another country.
Philippines to Australia __________
France to Montreal __________
Nepal to Paris __________
Israel to Singapore __________
Ireland to Mexico __________
Apply your Skills!
( Refer to the world time zone map )
Country Time Philippines Time Time Difference
Ex. Cape Town 5:03 am ( UTC +2 ) 11:03 am ( UTC + 8 ) 6 hours
1.Tokyo
2.Hawaii
3.Greenland
4.Sydney
5. Los Angeles ( USA)
B. Use the time zone map to find out the times in these major cities.
Fill in the missing time in the clocks.
( Hint: You may find it easier to work out the time in Philippines first )
Philippines Paris Tokyo Nairobi
: :

LESSON 75 SOLVES PROBLEMS INVOLVING TIME
THIRD QUARTER
WEEK 7
The Reyes family will visit their cousin, who lives 3 hours
and 10 minutes away. They want to get there at 11:30 am.
What time should they leave ?
How will you solve the problem ?
Use these steps to solve for the problem ?
Steps Answer
Understand:
1. What is asked in the problem ? The time the Reyes family leave
2. What are given ? 3:10 ( time started )
11: 30 am ( time ended
Plan
3. What operation will be used ? Subtraction
4. What is the number sentence ? 11:30 – 3:10 = N
Solve
5. How is the solution done 11:30 8:20
-3: 10 3:10
Check and Look Back
6. What will you do to check if your
answer is correct ?
Add the difference to the subtrahend.
8:20
+3:10
11:30
11:30 = 8:20
7. What is the number to the problem ? They need to leave at 8:20 am
Get Moving!
1. Alex scored a touchdown at 7:48 pm. Steve intercepted a pass and scored a touchdown
11 minutes later. What time did Steve score the second touchdown ?
What is asked? _________________________________________________________
What are the given facts ? ________________________________________________

What operation is needed ? ________________________________________________
What is the number sentence ? _____________________________________________
How is the solution done ? _________________________________________________
What is the answer ? _____________________________________________________
2. Clara had an appointment at Dr. Calayan’s office yesterday at 11:30 am . the doctor
called her into his office right on time. She was out of there 25 minutes later. What time
did Clara leave the doctor’s office ?
What is asked? _________________________________________________________
3. Jessie and Melchor are going to watch in the big city parade on Monday. They have to
be at the parade an hour before it starts. The parade kicks off at 11:am. If it takes 25
minutes to walk to the starting point of the parade, what time will Jessie and Melchor
have to leave home in order to be there right on time ?
What is asked? _________________________________________________________
4. Nichole stopped at Shaira’s Soup and Salad for lunch. She stayed there until she had to
leave to met her cousin, Emanuel, at the library. They were meeting at 1:30 pm. The
school library is a 20 minute walk from Shaira. What time did Nichole have to leave the
restaurant in order to get to the library right on time ?
What is asked? _________________________________________________________
5. Mario has a busy day planned today. He will meet his friend Alexander , at the archade.
That is a 15 minute walk from home. They will stay at the arcade for an hour. Then they
will take a 10 minute walk over to the park. The first thing they will do there is to grab a
hot dog from Ephrame’s Dogs hot dog truck. If Mario left home at 10:00 am, what time
did he and Alexander get in line for a hot dog ?
What is asked? _________________________________________________________

Keep Moving!
A. Read the problem. Then write the letter of the correct answer.
1. Greg wakes up at 5:20 a.m. so that he will have time to prepare himself for
school. At 6:00 a.m. he is ready to go to school. How long does it take him to
prepare for school ?
What is asked in the problem?
a. The time Greg wakes up
b. The time he is ready to go to school
c. The length of time it takes Greg to prepare
d. The activity he does every morning
What operation will be needed to solve the problem ?
a. Addition
b. Subtraction
c. Multiplication
d. Division
What is the number sentence ?
a. 5:20 – 6:00 = N
b. 6:00 x 5:20 = N
c. 6:00 + 5:20 = N
d. 6:00 - 5:20 = N
What is the answer to the problem ?
a. It takes 40 mins. for Greg to prepare
b. It takes 20 mins. for Greg to prepare
c. John wakes up at 5:30
d. John prepares for school from 5:20 to 6:00
Apply your Skills!
1. Jethro went to the cinema to watch a film at quarter past 3. The film lasted for an hour,
what time did he leave ?
2. Cristy started walking to school at half past 9. She arrived at school 15 minutes later,
What time did Cristy get to school ?
3. You are watching a program at 5:05p.m. It finished 30 minutes later. What time does it
finish ?
4. A cake takes an hour to bake. It needs to be ready by 7:00 p.m. What time does it need
to go in the oven ?
5. I start playing on the xbox at 6:00 a.m. I play for two and half hours. What time do I finish
playing ?

Lesson 76: Visualizing the Circumference of a Circle
Week 8
Visualize the circumference of the following to answer the questions:
1. Would a circle with a diameter of 7 cm have a circumference of about 22 cm?
2. Would a circle with a diameter of 25 cm have a circumference of about 90 cm?
3. Would a circle with a diameter of 8.2 cm have a circumference of less than 20
cm?
Mrs Alejandro planted santan around her
circular garden which has a diameter of 2 meters.
How many meters did she plant with santan?
The distance around a circle is called
circumference. Is there a relationship between
the circumference and the length of a diameter of
a circle?
Get Moving!

Visualize the circumference of the following circles by drawing markings
on it.
a. b. c. d. e.
1 cm 2 cm 3 cm 4 cm 5cm
Copy this table and record the results in it.
Circle Diameter Circumference
A
B
C
D
E
a. Does the circumference of the circle increase as the diameter
increases?
1. Use other circular objects. Check if what you found in the previous activity
holds true.
2. State the relationship between the circumference and the diameter of a
circle based on the information you recorded in the table above.
Using something circle in your bag, try to visualize the circumference of it.
Keep Moving!
Apply Your Skills!

Lesson 77: Measuring Circumference of a Circle Using Appropriate Tools
Week 8
Look at the length of a diameter of each circle below. Each circle has been rolled once to find its
circumference. Study the table.
4 cm
1 cm 2 cm
Circle Length of Diameter (d) Estimated Circumference(C)
A 1 cm about 3 1/6 or about 3.16
B 2 cm about 6 1/3 or about 6.33
C 4 cm about 12 ½ or about 12.5
Ask: What is the average ratio of the circumference to the length of diameter?
Get an empty milk can. (The top of the can
represents a circle.) Wind a strip of paper once
around the can. The length of the strip is the distance
around a circle. Measure the length of the strip of
paper in your ruler or meter stick.
circumference. Is there a relationship between the
circumference and the length of a diameter of a
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Start A
B
C

From this point on, we will use the words “diameter” and “radius” to mean not only the
line segments but also the length of the line segments.
Use a ruler, meter stick or tape measure in finding the circumference of these
circles to answer the following:
1. Would a circle with a diameter of 5 dm have a circumference of about 16 dm?
2. Would a circle with a diameter of 2.5 dm have a circumference of about 8 dm?
3. Would a circle with a diameter of 6.2 dm have a circumference of less than 20
dm?
Answer the Following:
1. Get a 25¢ coin, a 1 peso coin, a 5 peso coin and a 10 peso coin. Use a
ruler to find the diameter and a string to find the circumference of each
coin to the nearest millimeter.
Copy this table and record the results in it.
Coin Diameter(d) Circumference(C) C÷d
25¢ coin
1 peso coin
5 peso coin
10 peso coin
Answer the following questions:
a. Are the ratios of the circumference to the diameter of the circles about
the same?
Get Moving!
Keep Moving!

b. Does the circumference of the circle increase as the diameter
increases?
2. Use other circular objects. Check if what you found in the previous activity
holds true.
3. State the relationship between the circumference and the diameter of a
circle based on the information you recorded in the table above.
About how far is the distance you will walk on a circular path with a diameter of 4 m?
Apply Your Skills!

Lesson 78: Deriving a Formula in Finding the Circumference of a Circle
Get an empty milk can. (The top of
the can represents a circle.) Wind a strip
of paper once around the can. The length
of the strip is the distance around the
circle.
circumference. Is there a relationship
between the circumference and the length
of a diameter of a circle?
Look at the length of a diameter of each circle below. Each circle has been rolled
once to find its circumference. Study the table.
Start
A
B
C
1 cm
2 cm
4 cm

Circle
Length of
Diameter (d)
Estimated
Circumference (C)
Ratio of C to d 





d
C
A 1 cm about 3
6
1
or about 3.16
1
16.3
= 3.16
B 2 cm about 6
3
1
or about 6.33
2
33.6
= 3.165
C 4 cm about 12
2
1
or about 12.5
4
5.12
= 3.125
What is the average ratio of the circumference to the length of the diameter?
From this point on, we will use the words “diameter” and “radius” to mean not only the
line segments but also the length of the line segments.
Get Moving!
A. Do what is asked.
Get a 25 ₡ coin, a ₱ 1 coin, and a ₱ 5 coin. Use a ruler to find the diameter and a
string to find the circumference of each coin to the nearest millimetre.
Copy this table and record the result in it.
Coin Diameter (d) Circumference (C) C ÷ d
25 ₡
₱ 1
₱ 5
Answer the following questions:
1. Are the ratios of the circumference to the diameter of the circles about the same?
2. Does the circumference of the circle increase as the diameter increases?
B. Using 3.14 for π , find the circumference of a circle with.
1) d = 15 cm 4) r = 2.5 cm
2) d = 6 cm 5) r = 4.5 cm
3) d = 8 m

10 cm
13 cm
7 cm
9 m 25 cm
Keep Moving!
1) About how many times as great is the diameter with the circumference?
2) Using
7
22
for , find the circumference of:
a. r = 2 dm
b. d = 42 cm
c. r = 5 cm
Apply Your Skills!
Find the circumference of these circles using π = 3.14.
1) 2) 3)
4) 5)

Lesson 79 : Finding the Circumference of a Circle
For any circle, the ratio of the circumference to the diameter is about 3.14 or
7
22
.
This number is represented by the Greek letter π (Read: pi).
Since circumference ÷ diameter =π, C ÷ d = π
then we can find the circumference (C)
by multiplying π and diameter (d). C = π x d
For any circle, the radius (r) is
one - half the diameter, so
C = π x 2 x r or
r =
2
1
x d or d = 2 x r. C = 2 x π x r or C= 2πr
We replaced d with 2r to find C.
For example, to find the circumference of a circle of diameter 4 cm, we compute as
follows:
C = π x d C = 2 x π x r
= 3.14 x 4 cm = 2 x 3.14 x 2 cm
= 12.56 cm = 12.56 cm
We can find the circumference of a circle if its diameter or radius is given.
For convenience, we will now use π = 3.14 unless otherwise specified.
Multiplication
is the inverse
of division

8 m
5 dm
7 cm 7 m3 dm
Get Moving!
A. Find the circumference of each circle. Use 3.14 for π.
1. 2. 3.
4. 5. 6.
B. Using π = 3.14, find the circumference.
1) r = 2.5 m 4) r = 0.5 m
2) d = 8 cm 5) r = 1.25 cm
3) d = 11 cm
Keep Moving!
Complete each table.
1.
Radius Diameter Circumference
52 cm
38.5 m
15.084 dm
2 cm

2.
5.28 dm
14 cm
32.656 m
3.
14 cm
22 m
75.36 dm
Apply Your Skills!
1. Find the error. Your friend is finding the circumference of a circle with a radius of 3
millimetres. Describe and correct the error.
2. Find the circumference of the circle described. Tell what value you used for π . Explain
your choice.
C = πd
= (314) (3)
= 9.42 mm

Lesson 80: Solving Routine and Non- Routine Problems
Involving Circumference of a Circle
THIRD QUARTER, WEEK 10
A goat is tied to a mango tree in the backyard. The stretched rope is 3 meters long. Up
to how many meters around the tree can the goat walk?
Using an illustration
Looking at the illustration, 3 meters is the radius of the circle and the distance around the
tree where the goat can walk is the circumference of the circle.
Using the formula, , we can solve for the distance around the circle where
the goat can walk.
Substituting the value = 2 x 3.14 x 3m
= 18.84 meters
The goat can walk up to 18.84 meters around the tree.
Use the four- step plan to solve the problem.
Understand
 Identify the question
 identify the relevant
facts
 The distance around the tree the goat can walk
 3 meters of rope
Plan
 Choose a strategy  Using a formula
Solve
 Perform the strategy 
= (2 x 3.14) x 3 m
= 6.28 x 3 m
C= 18.84 m

Answer: The goat can walk up to 18.84 meters around
the tree.
Check
 Verify if the answer is
correct
 Use the formula for the circumference when the
diameter is given.
d= 2 x 3 m = 6 m
= 3.14 x 6m
= 18.84 m
Let us have another example.
The circular wading pool of little Bettina has a radius of 1.5 meters. If Bettina walks
around it, how many meters will that be?
1.5 meters
Given the radius, use the formula,
r = 1.5 m and
C= 2 x 3.14 x 1.5 m
= 9.42 meters
Bettina walks 9.42 meters around the pool.
Get Moving!
A. Read each problem. Then, answer the questions that follow.
1. A circular plate has a radius of 6 inches. What is the circumference of the plate?
a. What is asked? ____________________________
b. What are the given facts? ____________________
c. What is the process needed? _________________
d. What is the number sentence? ________________
e. What is the answer? ________________________
2. A wheel has a diameter of 0.4 meters. Find the circumference of the wheel.
a. What is asked? ____________________________
b. What are the given facts? ____________________
c. What is the process needed? _________________
d. What is the number sentence? ________________
e. What is the answer? ________________________

B. Illustrate the following. Solve for the answer.
1. Mr. Castro had a circular lagoon built. The distance across the lagoon is 20 meters. What is
the distance around it?
2. A flagpole stands in the middle of a circular platform. The distance from the flagpole to the
edge of the platform is 2 meters. What is the circumference of the platform?
Keep Moving!
Read, analyze and solve.
1. A circular garden has a radius of 4.5 meters. What is its circumference?
2. A telescope has a lens with a diameter of 102 cm. What is the distance around the lens?
3. Find the radius of a circular lagoon whose circumference is 37.68 meters.
4. JB wants to fence his circular bamboo field with cyclone wire. How much cyclone wire must
he use if the field has a radius of 15 meters?
5. A wheel has a radius of 20 cm. What is the circumference of the wheel?
Apply Your Skills!
Challenge yourself with more problems!
Solve each problem.
1. A car tire has radius of 18 cm. How far will it go in 120 turns?
2. Benz has a circular flower garden with a radius of 5 meters. He wants to put up a chicken
wire fence around it. How many meters of chicken wire will he need?
3. A circular garden has a radius of 30 decimeters. Santan bushes 3 decimeters apart are to be
planted along its edges. How many bushes are needed?
4. A man jogs around a circular track 4 times and completes 4 710 meters. What is the diameter
of the track?

S OK
Lesson 81: Visualizes Area of a Circle
Study the situation:
Alicia and Megan observed circle in the chart and they wanted to visualize the area of a circle.
M J
R Q
This tips will help you visualize the area of a circle.
 A circle is a set of all points in a plane that are at fixed distance from a point called
center.
 A radius is a line segment from the center to a point on the circle.
 A diameter is a line segment which passes through the center of a circle whose
endpoints are on the circle.
 The length of radius is one half the length of a diameter of a circle.
 A compass is an instrument used to draw a circles.
Get Moving!
By looking in the circle answer the following questions:
1. What is the center of the given circle?
2. How many radius can you see? Name them.
3. How many diameter did you see? Name them.
Keep Moving!
Identify the parts of the circle referred to.
1. A segment that passes through the center of a circle and has both end points on the
circle. ______________________

2. A segment that has one end point on the circle and the other endpoint at the center
of the circle.
3. The length of the radius is always half of the ________________________.
Apply Your Skills!
Make or draw your own circle and form your own radius and diameter.

Lesson 82: Derives a Formula in Finding the Area of a Circle
Study the situation:
Anthony and Marlon cut the circle into pieces to derive a formula in finding the area of a circle.
They observed circle and try to form new shape.
This tips will help you visualize the area of a circle.
 Now we can use the area formula for a parallelogram to help us find the area of
the circle.
 The original circle’s outside perimeter was the distance around, or the
circumference of the circle
 Half of this distance around goes on the top of the parallelogram and the other
half of the circle goes on the bottom. This is known as the base of the
parallelogram.
 The height of the parallelogram is just the radius of the original circle.
 Now let’s substitute the information into the formula for the parallelogram.
Get Moving!
By looking in the circle above, form a parallelogram and derive the area of a circle.
Having a radius of 10cm try to find out the area.
Keep Moving!
Write true or false.
____________ 1. The formula in finding the area of a circle can be derived using the perimeter
of a rectangle.
____________ 2. The formula of a parallelogram can help to derive in finding the area of a
circle.
____________ 3. The formula of area of a circle is A = pi x r x r.

__________ 4. The formula of the triangle can help to derive the area of a circle.
__________ 5. Is a circle a polygon?
Apply Your Skills!
Make a circle and cut it into form of a parallelogram or triangle to derive the area of a
given circle. Be ready to present in the class.

Lesson 83: Finds the Area of a Given Circle
A dog is tied to a wooden stake in a backyard. His leash is 3 meters long and he runs
around in circles pulling the leash as far as it can go. How much area does the dog have to run
around it?
This tips will help you find the area of a given circle.
1. Draw a circle
2. Find the radius or diameter
3. Always remember that radius is half of the measurement of a diameter
4. Use the formula:
A = 3.14 x 3 x 3
= 3.14 x 9
= 28.26 m2
Get Moving!
Read each problem and find the area of a circle.
1. A lawn sprinkler sprays water 5 feet in every directions as it rotates. What is the area of
the sprinkled lawn?
2. A storm is expected to hit 7 miles in every direction from a small town. What is the area
that the storm will affect?
3. A semi –circle shaped rug has a diameter of 2 feet. What is the area of the rug?
Keep Moving!
Find the area of each circle
1.
9 meter
2.
15cm
3m

3.
6.25 m
4. 17cm
5. 14mm
Apply Your Skills!
Complete the table. Use the formula for the area of a circle.
Circle Radius Diameter Area
1 5.6 m
2 16 mm
3 25.6 cm
4 78.5 mm2
5 20 dm

Lesson 84 : Solving Routine or Non-Routine Problems Involving the Area of a Circle
Go around your classroom and identify all the circular objects that you can find.
Write the names of the actual objects you found in your room.
Complete the information for that object by making appropriate units of
measurement of the parts and getting the actual measurements using an appropriate
measuring instrument.
Actual Circular Objects
Found in the Room
Your Estimate Actual Area
π = 3.14
r =
A =
π = 3.14
r =
A =
π = 3.14
r =
A =
π = 3.14
r =
A =
π = 3.14
r =
A =
π = 3.14
r =
A =
π = 3.14
r =
A =
π = 3.14
r =
A =
π = 3.14
r =
A =
π = 3.14
r =
A =
Get Moving!
Do the following.
1. What is the shape of the cover of the pail in your school?
Draw the cover of the pail in your notebook. Using a meter stick, measure the
diameter and the radius. Indicate these measures on the drawing. Then, compute
the area of the cover.
2. Do you have a circular wall clock in your classroom? Or any circular objects? Draw it
in your notebook. Using a ruler or meter stick measure the diameter and the radius
and indicate these on your drawing. Using an appropriate formula, find the area.
Solve the following problems. Use the 4-Step Plan.
1. If the diameter of a circular wall clock is 30 cm, what is the area of the clock?
2. Find the area of a circular pool whose radius is 2 meters.

3. Father will fence a circular newly planted garden whose radius is 3.5 m. How
many meters of fencing material will he use?
Keep Moving!
1. A circular mirror has a radius of 28 cm. Find its area.
2. The wheel of a motorcycle has a diameter of 1 m. What is its area?
3. What is the area of a circle if the radius is 13 cm?
4. A dinner plate has a radius of 6 cm. What is its area?
5. The diameter of a circle is 11cm. Find the area.
Apply Your Skills!
A. Write the data required to complete the chart. Use π = 3.14.
Diameter Radius Area
1. 13 cm
2. 18 m
3. 20 cm
B. Solve the following problems.
4. The circle has a radius of 14 m. Find its area.
5. A circular clock has a diameter of 40 cm. What is the area of the clock?

Lesson 85 : Creating Problems Involving the Area of a Circle
Study the problem.
Aling Mila helps Mang Elpie water their circular flower garden whose diameter is 4
meters.
Can you create a problem about the garden?
You can create a problem by using the steps below:
1. Familiarized yourself with the concepts. Think of the application to everyday life
situations.
Think of the type of problem you want to create and the formula to be used. Relate the problem to a
real-life situation.
2. Read more on Math problem solving. Study the solution in solving the problems.
3. Make your own styles/strategies to justify the solutions.
Below is an example of problem that you can create:
1. Aling Mila helps Mang Elpie water their circular flower garden whose diameter is 8
meters. What area of their lot is the flower bed?
Solution to the problem created.
Formula =
diameter – 8 meters
radius – half of the diameter = 4 meters
A= 3.14 x (4 x 4)
A= 3.14 x 16
A= 50.24 square meters
Get Moving!
Create/Make a problem involving the area of a circle based on the given situation. Write
the answer in your notebook.
1. The diameter of a circular swimming pool is 18 meters.
Problem:____________________________________________________________

Answer:_____________________________________________________________
2. The area of a circle is 254.34 square meters.
Problem:____________________________________________________________
Answer:_____________________________________________________________
3. A circular doormat has a radius of 15 cm.
Problem:____________________________________________________________
Answer:_____________________________________________________________
Keep Moving!
Create/Make a problem involving the area of a circle.
1. The radius of a circle is 7 centimeters.
2. A circular plate has an area of 615.44 square centimeters.
3. Lety’s circular bed cover has a diameter or 3 meters.
Apply Your Skills!
Create problem involving area of a circle using the given data below.
1. circular saucer 2. circular table 3. circular garden
radius – 8 cm radius - ? radius – 6.5 m
A - ? A – 19.625 square meters A - ?
4. circular tablecloth 5. circular placemat
diameter – 1 m diameter – 36 cm
Area - ? Area - ?
Problem:
Answer:
Problem:
Answer:
Problem:
Answer:

A box is 10 cm long, 5 cm wide and 3 cm tall. What is its volume?
Let us visualize the problem.
The figure above is a box whose dimensions are 10 cm long, 5 cm wide and 3 cm high.
To find the volume, we need to know the number of cubes in the whole figure.
To find the total centimetre cubes,
 Multiply to find the number of cubes on the bottom layer.
 Then multiply by the number of layers
Multiply 10 by 5 by 3.
10 x 5 x 3 = 150 centimetre cubes the volume of the box is 150 cm3
Lesson 86: Visualizes the Volume of a Cube and Rectangular Prism
cubic centimetre
1 cm
A cube has 3 dimensions: length,
width and height.
It is the unit used for measuring
volume. Volume is expressed in
cubic units. The number of cubic
units needed to make or fill a solid
figure is called the volume. We
write cubic units: unit3
.
This is 1 cubic cm box.
1 cm
The figure at the right contains 27 cubes.
Its volume is 27 cubic or 27 cm3
.

Get Moving!
Count the cubic units to find the volume of each.
Keep Moving!
Read, analyze and solve.
1. How many jewelry boxes 10 cm by 6 cm by 4 cm can be packed into a box 50 dm lon, 4
dm wide and 3 dm high?
2. The diagram below shows a large cube made from 1 cubic cm.
a. How many small cubes are there in each
layer?
b. What is the volume of the rectangular prism?
Apply Your Skills!
Determine how many purple packages and green packages will fit into the white storage bin

Any unit of length gives a corresponding unit of volume, namely the volume of
a cube whose side has the given length. For example, a cubic centimetre (cm3
) would be the
volume of a cube whose sides are one centimetre (1 cm) in length.
In the International System of Units (SI), the standard unit of volume is the cubic
metre (m3
). Metric System also includes,
cubic meter (m3
) used to measure large amount of space occupied
cubic decimetre (dm3
)
cubic centimeter (cm3
)
cubic millimeter (mm3
) used to measure the small amount of space occupied
Lesson 87: Names the Appropriate Unit of Measure Used for Measuring the Volume of a
Cube and a Rectangular Prism.
Get Moving!
A. Tell the cubic unit of measure to be used in the following illustrations:
(in words and in exponential form)

Keep Moving!
Use m3
, dm3
, cm3
and mm3
to tell which cubic unit of measure is appropriate to be used.
1. match box
2. book
3. door
4. classroom
5. sofa
6. garden plot
7. closet
8. table
9. swimming pool
10. car
Apply Your Skills!
Write the best unit of measure for the following:
1. water in an aquarium
2. a bag of cement
3. a box of milk
4. wooden alphabet block
5. gasoline in a container

A cube is a solid whose length, width and height are equal. The formula for finding its
volume is: V = S x S x S or V = S3
Example:
S = 3 cm
S = 3 cm
S = 3 cm
If the length, width and height of a room are 8 m, 7 m and 4 m, then its volume is 8 m
X 7 m X 4 m = 224 m3
.
Example:
w = 7m
Lesson 88: Derives the Formula in Finding the Volume of a Cube and A Rectangular
Prism Using Cubic Centimeter and Cubic Meter.
Get Moving!
Find the volume of the following:
1. A rectangular prism whose dimensions are 12 cm. by 8 cm by 3 cm.
2. The length of an edge of a cube is 4 m. What is its volume?
3. Grade 5 – Earth made four garden plots. Each plot had the following measurements,
2.1m by 3m by 3m. How many cubic meters of garden soil did they use?
4. The dimensions of a tank are 5 m and 3m and 16m. Find the volume in cubic meter.
Keep Moving!
Find the volume, given the following:
Formula: V = S x S x S or V = S3
Solution: V = 3 x 3 x 3 V = 33
Answer: V = 27 cm3
V = 27 cm3
h = 4m
L = 8m
Formula: V = L x W x H
Solution: V = 8 x 7 x 4
Answer: V = 224 m3

1. S = 9 cm
2. l = 6cm, w = 3.1cm, h = 4cm
3. s = 1.2 m
4. l = 4.75cm, w = 1.8cm, h = 2.7cm
5. s = 8 m
Apply Your Skills!
Solve the following problems:
1. The sides of a cube is 1.2 cm. What is its volume?
2. A box is 162 cm long, 12 cm wide and 5.3 cm high. Find its volume.
3. How many centimetres of wood will be needed to completely surround a square whose
side is 2.3 metres?

Lesson 89: Converting cu.cm to cu.m and vice versa; cu.cm to L and vice versa
Cooperative Learning
Convert 438 cm3
to dm3
1dm3
438cm3
x 1000cm3
= o.438 dm3
Which is bigger cm3
of dm3
? When we change cm3
to dm3
,is it from a smaller unit
to a larger unit or larger unit to smaller unit? What process will you use?
Get Moving!
Change to smaller units.
1.25 cm3
=______mm3
2.89 dm3
= ______cm3
3.57 cm3
= ______mm3
4.126 dm3
= _____ cm3
5.32 dm3
= ______cm3
Keep Moving!
Fill in the blanks to complete the equivalent measures.
1.198cm3
= ______dm3
2. 1286dm3
= _____m3
3. ____cm3 =
35m3
4._____cm3
= 25dm3
5. 89m3
= ______dm3

Apply Your Skills!
Answer the following word problems.
1. A truck delivers sand weighing 85000 cm3
, what is the weight of the sand in cubic
decimeters?
2. A water tank holds 90000 dm3
of water, what is its weight in cm3
?

Lesson 90: Finding the volume of a given cube and rectangular prism using
cu.cm and cu.m
Read and study the problem below.
A storage box is 60 cm by 40 cm by 30 cm. What is the volume of the box?
The volume of a rectangular prism is equal to the product of its length,width and height.
V= LXWXH
60cm x 40 cm x 30 cm = 72000cm3
Get Moving!
Find the volume of each prism.
1. l=4m w=2.5m h=-3.5m V= _____
2. l=8cm w=4cm h=5cm V= _____
3. l=16.5cm w=12cm h=8cm V=_____
4. l=7m w=2m h=4m V=_____
5. l=16cm w=7cm h=12cm V=_____
Keep Moving!
Find the volume of the following figures.
1.
2.
8cm
5cm
12cm
10m

3.
Apply Your Skills!
Solve the following word problems.
1. A trailer is 15m long and 3m wide. If it can hold a cargo of 180 cubic meters, what is the
length of the trailer?
2. The volume of a rectangular prism is 240 cm3
.Its length is 4cm and its height is 6 cm.
How wide is it?
14m
20m
8m

Lesson 91: Estimating and using appropriate units of measure for volume
Read and study the problem.
Andrew has a rectangular box with sand inside it, he wants to know the
capacity of the box,what shall he do? What unit of measure will he use?
Get Moving!
Give the appropriate unit of measure for the following:
1. a wooden rectangular chop board
2. a container van
3. a room air-conditioner
4. brick of butter
5. a thick book
Keep Moving!
What unit of measure will you use to find the volume of these objects?
1. a hollow block filled with cement
2. a soap box
3. match box
4. wall cabinet
5. a rectangular lunch box

Apply Your Skills!
Answer the following word problems.
1. Mr. Gonzales has a front yard. What unit of measure will he use to find the volume?
2. How will you estimate the volume of your classroom?

Lesson 92: Solving Routine and Non-routine Problems Involving Volume of a Cube and
Rectangular Prism in Real-Life Situations Using Appropriate Strategies and Tools
A swimming pool has a length of 12 meters,
a width of 6 meters, and a height of 10 meters.
How much water is needed to fill the swimming
pool?
How will you solve the problem?
You can solve the problem following these steps.
Steps Answer
 Understand
1. Know what is asked in the problem.
2. Know the given facts.
- The amount of water needed to fill
the aquarium.
-
 Plan
3. Determine the operation or formula
to use.
- Multiplication:
 Solve
4. Show the solution using the
formula.
-
So, ; substitute 12 for
, 6 for w, 10 for h
=
=
 Check and Look Back
- Check your answer.
- State your answer.
- You need of water to fill the
swimming pool.

Get Moving!
A. Read the each problem, then solve by following the steps in solving problem.
1. Alice has a paperweight in the shape of pyramid. Its height is 6 cm, length is 5.2 cm and
width is 4.9 cm. What is its volume?
2. A juice has a base area of and a height of 12.2 cm. What is its volume?
3. A cone has a radius of 1.2 dm and a height of 3.4 dm. What is its volume?
B. Use any strategy to solve each problem.
1. How much space in a room will a cabinet occupy if it is 1.9 m long, 0.61 m wide, and 2.74 m
high?
2. A box is 3.5 dm long and 6 dm high. Its volume is . How wide is it?
3. A rectangular container is 0.4 m long, 0.3 m wide, and 1 m high. What is its volume in cubic
centimeters?
Keep Moving!
1. A pit is 7 dm long, 5 dm wide, and 8 dm deep. How many cubic meters of sand will fill the
pit?
2. A water tank is 0.8 m long, 0.6 m wide, and 1 m high. If the tank is half-full, how many cubic
centimeters of water does it hold?
3. A container box measures 5 dm on each edge. How much space can hold?
4. A is half-filled with salt. How much salt is still needed to completely fill
the container?
Apply Your Skills!
Challenge yourself with more problems.
1. An open box is 50 cm long, 25 cm wide, and 15 cm high. Find the volume.
50 cm
15 cm
25 cm
2. The width, height, and the volume of a rectangular prism are 5 cm, 3 cm, and ,
respectively. Find the length of the prism.

Lesson 93: Creating Problems (with reasonable answers) Involving Volume of a
Cube and Rectangular Prism in Real-Life Situations
Study the problem.
Karen has a rectangular prism with the dimensions shown in the diagram below.
5 cm
3 cm
8 cm
Can you create a problem about Karen’s rectangular prism?
You can create a problem by using the steps below:
1. Familiarize yourself with the concept. Think of an application to everyday life situations.
2. Think of the type of problem you want to create and the formula to be used. Relate the
problem to a real-life situation.
3. Read some problems and study their situations.
4. Make your own styles/strategies to justify your solutions.
Below are the examples of problem that you can create:
a. What is the volume in cubic cm of Karen’s rectangular prism?
b. Karen’s rectangular prism measure 3 cm long, 5 cm wide, and 8 cm high. What is its
volume?

Below is the solution to the problem.
Thus, the volume of the rectangular prism is 120 cubic cm.
Get Moving!
Make a problem involving the volume of a rectangular prism with the corresponding answer
based on the given situation.
1. An antique wooden chest is in the form of a cube. Its edge measures 5 cm.
2. A closet measures 4 m long, 5 m wide, and 3 m high.
3. A flower box is 7 m long, 3 m wide, and 20 cm high.
4. Robles family made a fish pond in their backyard measuring 5 meters long, 4 meters wide,
and 5 meters deep. They sold the soil for Php50 per cubic meter.
Problem:
Answer:
Problem:
Answer:
Problem:
Answer:
Problem:
Answer:

Keep Moving!
Make a problem involving the volume of a rectangular prism.
1. A rectangular seed box which measures 30 dm long, 15 dm wide, and high is to be
filled with soil.
2. The Reyes family dug a compost pit which measures 5 m long, 2 m wide, and 3 m deep.
3. An aquarium which is to be filled with water, measures 55 cm long, 40 cm wide, and 25 cm
high.
Apply Your Skills!
Make a three (3) problem involving volume. Write the answer to each problem on your
answer sheet. You may use an aquarium, shoebox, swimming pool, and other rectangular
prisms for the problem.

FOURTH QUARTER- Week 6
Lesson 94: Reading and Measuring Temperature Using thermometer (alcohol and/ or digital)
in degree Celsius.
A Thermometer is an instrument for measuring temperature, a unit for measuring
temperature if the degree Celsius (◦C).
A thermometer consists of a glass attached to a glass tube with a number
a scale. The liquid in the bulb rises or drops with change the temperature.
Each space in the number scale represents 1◦C. The numbers below 0 are
written with a minus (-) sign.
To read a thermometer, find the level of the liquid or the mercury.
Get Moving
What is the temperature for each?
1. Boiling point of water - _____________________________
2. Freezing point of water - ____________________________
3. Normal body temperature- __________________________
4. 3.5 ◦C higher than the normal body temperature _ ________
5. Between 30◦C to 40◦C - ____________________________
Keep Moving

A. Read the temperature shown in each thermometer.
B, Circle what you think is the temperature of the following:
1. Hot water a. -10◦C b. 30◦C c, 70◦C
2. A person with fever a. 30◦C b. 35◦C c. 40◦C
3. Ice cold tea a. 10◦C b. 20◦C c. 40◦C
4. Bread in oven a. 50◦C b. 150◦C c. 290◦C
5. Ice candy a. 100◦C b. 35◦C c. 0◦C
Apply Your Skills
The level of liquid in a thermometer is 22◦C lower than the boiling point of water.
What is the thermometer reading?

Lesson 95 : Estimating Temperature
The conference room received the afternoon sun. The room temperature was
found to be 35.6◦C. The janitor turned on the air-conditioner unit. After a few minutes
the thermometer recorded it to be 25.3◦C. What was the estimated change in
temperature?
Round each of the temperature to its highest place value; then subtract the
rounded numbers.
35.6◦C 36◦C
- 25.3◦C - 25◦C
11◦C
Answer: There are about 11◦C change in temperature.
You can find the actual difference to check if the estimated difference is
reasonable.
35,6◦C
-25.5◦C
10.1◦C actual difference
Notice that the estimated difference is close to the actual difference.
Get Moving
Answer the following problem.
1. Inside an air- conditioned room, the temperature is 14◦C. After sometime, the
temperature changes to 55.4◦C. How many ◦C is the estimated temperature
difference?
2. The temperatures on 3 different days were 29.6◦C, 28◦C, 29.5◦C.What was
their estimated average?
3. Find the estimated sum 11.4◦C, 23,2◦C and 25.5◦C.

Keep Moving
Choose the more sensible temperature.
1. Warm shower 90◦C 23◦C
2. Grilled barbeque 95◦C 35◦C
3. Cold water 20◦C 45◦C
4. Warm cup of coffee 78◦C 22◦C
5. Early morning 22◦C 42◦C
Apply Your Skills
Write the estimate temperature, then do the actual measuring of each using
liquid or digital thermometer.
Estimated Temperature Actual Temperature
1.Hot chocolate
2. frozen ice candy
3. a glass of iced tea

FOUTH QUARTER- Week 6
Lesson 96: Solving routine and non- routine problems involving temperature in real-life
situations.
From 6;00 a.m. to 11:00 a.m. the temperature went up steadily at 40◦C. at a rate
of 0.75◦C each hour, How many degree Celsius did it increase? What was the
temperature at 6:00 a.m.
How will you solve the problem? You can solve the problem following these
steps
Steps Answers
Understand:
1. Know what is asked in the problem. The temperature at 6:00 a.m.
2. Know the given facts 40◦C, 0.75◦C each hour
Plan
3. Determine the operation of formula to
use.
Multiplication and Subtraction
Solve
4. Show the solution using the formula 40◦C – ( 5x 0.75◦C)= n
Check and Look back
 Check your answer 40◦C-3.75◦C= 36.5◦C
 State your answer 36.5◦C was the temperature at
6:00 a.m
Get Moving
A. Use the facts in the table to solve each problem.
Element Melting point
Gold 1064.43◦C
Lead 327,5◦C
How much hotter is the temperature needed to melt gold than the temperature
needed to melt lead?
1. What is asked in the problem?
2. What facts are given?
3. What operation will be used?
4. How is the solution done?
5. What is the answer?
Keep Moving

1. If the temperature at 11:00 in the morning is 28.5◦C and became 32.7◦C, what was
the average temperature?
2. Lino’s temperature this morning was 38,2◦C. after 2 hours his temperature was 39.5◦C
Did he get better or worse?? How many degrees did his temperature rise?
Apply Your Skills
Solve the problem.
The temperature is 12◦C when the altitude is 3000 meters above sea level. At a
higher altitude the temperature reads 4◦C.Was there an increase or decrease in the
temperature?

Lesson 100: Interpreting Data Presented in Different Kinds of
Line Graphs (Single to Double-Line Graph)
A line graph is a visual comparison of how two variables-shown on the x- and y-axes-are related
or varies with each other. It is useful in displaying data or information that changes continuously
overtime. The points on a line graph are connected by a line.
Five parts of the line graph must be present for the graph to be complete.
a. Title
b. Scale
c. Labels
d. Points
e. Line
Below is an example of a line graph. Study its parts and answer some of the questions below.
1. What is the title of the line graph?
2. What information is placed along the vertical axis? On the horizontal axis?
3. What is the distance covered by the car after 45 seconds?
4. At what time did the car reach 80 meters?
5. What is the speed of the car after 15 seconds?
0
10
20
30
40
50
60
70
80
90
5 10 15 20 25 30 35 40 45 50
Distance vs. Time
Distance (meters)
Time ( sec)

Get Moving!
Study the line graph below. Then, answer the questions that follow.
1. What is the graph about?
2. How many houses were constructed in 2012?
3. How many more houses were constructed in 2013 than in 2011?
4. How many houses were constructed from 2011 to 2015?
5. On what year/years was there the same number of houses constructed?
Keep Moving!
Study this graph carefully, and then answer the questions that follow.
0
50
100
150
200
250
2011 2012 2013 2014 2015
0
100
200
300
400
500
600
700
800
900
1000
Sun Mon Tues Wed Thurs Fri Sat
NUMBER OF HOUSES CONSTRUCTED FOR FIVE YEARS
Numbe
r of
Houses
Year
Daily Sales at AlingTaling’s Store
Pesos
Days

1. What is the title of the graph?
2. How much was the sale on Wednesday?
3. On what day was the highest sale?
4. On what day was the sale lowest?
5. How much was the total sales for the week?
Apply Your Skills!
Use the graph below to answer the questions below.
1. What is the title of the graph?
2. What is the height of both plants at day 2?
3. Which plant shows great increase in height? Why?
4. What happen to the plant near the window?
0
1
2
3
4
5
6
7
8
Day 1 Day 2 Day 3 Day 4 Day 5
plant outside
plant near the window
COMPARISON OF PLANT GROWTH
Height (centimeters)

Lesson 101:Solving Routine and Non-routine Problems Using Data
Presented in a Line Graph
A. What is the difference between the lowest and highest temperature in Metro Manila?
Use the four-step plan to solve the problem.
Steps Answer
Understand:
What does the problem ask for? The difference between highest and lowest
temperature
What are the given data? 40⁰ C and 37⁰ C
Plan
What operation is/are to be used? Subtraction
What is the mathematical sentence? 40-37= N
Show how the solution is done using the
operation. 40-37= 3
Check
Check if the answer is correct.
State the final answer. The difference between the highest and lowest
temperature is 3⁰ C.
35
36
37
38
39
40
41
Day 1 Day 2 Day3 Day 4 Day 5
Temperature in Metro Manila
Temperature (Celsius)

B. What is the average temperature in Metro Manila for five days?
Steps Answer
Understand:
What does the problem ask for? The average temperature in Metro Manila for
five days
What are the given data? 39⁰ C, 37⁰ C, 40 ⁰ C, 38⁰ C and 40⁰ C
Plan
What operation is/are to be used? Addition and Division
What is the mathematical sentence? (39+ 37 + 40 +38 +40)÷ 5= N
Show how the solution is done using the
operation.
39+ 37 + 40 +38 +40=194
194 ÷5=38.8
Check
Check if the answer is correct.
State the final answer. The average temperature in Metro Manila for
five days is 38.8⁰ C.
Get Moving!
Study the table then answer the questions that follow.
1. What is the change in height after three days?
a. What is asked?
b. What facts are needed to solve the problem?
c. What operation will you use?
0
0.5
1
1.5
2
2.5
3
3.5
Day 1 Day 2 Day 3 Day 4 Day 5
Height of Seedlings
Heigh (cm)

e. What is the complete answer?
2. What is the difference in height at day five as compared to day 1?
a. What is asked?
Keep Moving!
Use the data in the line graph to answer the questions below.
1. What is the total number of customers at the first three months?
a. What is asked?
2. What was the average number of customers from February to April?
a. What is asked?
3. About how many more customers came into the saloon during the fifth month than during the fourth
month?
a. What is asked?
600
650
700
750
800
850
900
Jan Feb Mar Apr May
Customer in a Saloon
Number of Customers

Apply Your Skills!
Use the graph below to answer the questions below.
1. What was the increase in Joel’s height from six-year old up to eight-year old?
2. What is the change in his height from seven to eleven-year old?
100
105
110
115
120
125
130
6 7 8 9 10 11
Joel's Height
Height in centimeters
Age

Lesson 102:Drawing Inferences Based on Data Presented in
a Line Graph
Make a graph out of the given data below. Use the gridline to plot
the points.
HEIGHT OF MONGO PLANT
Number of Weeks Height in centimeter
1 3.5 cm
2 6.5 cm
3 9.5 cm
4 12.5 cm
5 15.5 cm
1. What is the height of the plant on the first week?
2. How do you describe the height of the mongo plant from first to fifth
week?
3. What could be its height on week 6? Why did you say so?

Get Moving!
Study the graph below and then answer the questions that follow.
1. How many grade five pupils were dewormed on the first three years?
2. What is the average number of pupils dewormed from 2010 to 2015?
3. If there is a total of 300 pupils in grade V, how many pupils were not
dewormed in 2013?
4. What is the difference in the number of grade five pupils dewormed in
2015 than 2014?
5. Why do you think there is a sudden increased in the number of pupils
dewormed in 2015?
100
150
200
250
300
350
2010 2011 2012 2013 2014 2015
Deworming of Grade V Pupils
Number of Pupils
Dewormed

Apply Your Skills!
Study the relationship of data on the graph below. Answer the questions that
follow.
1. What was the heat index in Metro Manila on April 15 in 2010? 2011?
2. Did the temperature increase on April 8 in 2010 and 2011?
3. What date in April was the highest heat index for the year 2010? What about in 2011?
4. How do you compare the average heat index in 2010 as compared to 2011?
5. Do you think the heat index in 2012 or 2013 will increase or decrease? Why do you say so?
30
31
32
33
34
35
36
37
38
39
40
1 8 15 22 29
2011
2010
Metro Manila’s Heat Index in April
Temperature (Celsius)
Date in April

Lesson 103 :DESCRIBING EXPERIMENTAL PROBABILITY
Andre and Emma are rolling a 0-5 number cube. When the cube shows 0,1 or 2, Andre wins.
When it shows 3,4,or 5 Emma wins
1. What is the probability that Emma will win?
2. What is the probability that Andre will win?
3. Suppose they play game 120 times.
a. About how many times would you expect Emma to win?
b. About how many times would you expect Andre to win?
c. Would you be surprised if Emma did not win exactly 60 times?
GET MOVING!
Skyler and Mackenzie flip a coin. Skyler will win if it lands heads up. Mackenzie will win if it
lands tails up.
4. What is the probability that Skyler will win?
5. If they play 120 times, about how many games would you expect Skyler to win?
6. Compare your answers from problem 3 and 5. ( Compare 3/6 of 120 and ½ of 120) Are they
the same or different?
7. Explain which probability is greater, 3/6 or ½?
KEEP MOVING!
A die is tossed. What is the probability of getting
1. 3 _________
2. An even number _________
3. 7 _________
4. An odd number _________
5. A prime number _________
Apply your skills
Think about rolling a red 0-5 number cube and a blue 5-10 number cube. In the table below, the
column on the left shows the number that could be rolled on the red 0-5 cube, while the row at
the top shows the possibilities for the blue 5 – 10 cube. The numbers on the two cubes can be
added to get a sum as small as 5 ( 0 red, 5 blue)or as great as 15 ( 5 red, 10 blue). The spaces
in the table represents the sums for every combination of the two cubes.

TABLE OF SUMS
5 6 7 9 9 10
0 5
1 7
2 9
3 11
4 13
5 15
1. Copy the table and fill in the missing sums.
2. When rolling blue and red cube, how many different sums are possible?
3. How many different cube combinations are possible?
4. How many different ways can you roll a sum of
a. 5
b. 6
c. 7
d. 8
e. 9
f. 10
g. 11
h. 12
i. 13
j. 14
k. 15
l. 16
5. What is the probability of rolling each of the following sums?
a. 10
b. 15
c. 5

Lesson 104 :PERFORMING AN EXPERIMENTAL PROBABILITY AND RECORDS RESULT
BY LISTING
Our class is having a contest. Each of us will answer a question concerning different
subjects. We have to spin a wheel to find out what category our question will be. The wheel
looks like this
What is the probability of the wheel stopping at:
a. SCIENCE ____________________
b. MATH ____________________
c. HISTORY ____________________
d. GEOGRAPHY ____________________
GET MOVING!
Refer to the exercise in Explore and Discover
1. Based on the number line of probability, between the given 2 subjects, in which subject
is the wheel more likely to stop?
a. Science or Math _______________________
b. History or Geography _______________________
c. Math or History _______________________
d. Geography or Science _______________________
e. Geography or Math _______________________
2. What is the probability of landing on a Music subject? Explain your answer.
KEEP MOVING!
In a bag there are 10 blocks numbered 1 to 10. I will draw a block from the bag. What is
the probability of my drawing a block with :
SCIENCE
MATH
SCIENCE
MATH
GEOGRAPHY
MATH
SCIENCE

a. Number 5 _______________
b. Number 9 _______________
c. Number less than 6 _______________
d. An odd number _______________
e. An even number _______________
f. Number more than 3 _______________
Which is more likely to happen, drawing an even numbered block or drawing an odd numbered
block? Explain your answer.
APPLY YOUR SKILLS
Kristine has 5 blouses – 1 with flower prints, 1 plain white, 1 with polka dots, a
checkered one and a plain yellow blouse. She also has 3 skirts – 1 black , 1 brown and 1 navy
blue. How many possible different combinations of skirt and blouse can she have?

Lesson 105 :ANALYZING DATA OBTAINED FROM CHANCE USING EXPERIMENTS
INVOLVING LETTER CARDS (A TO Z) AND NUMBER CARDS ( 0 – 20)
Study the situation and give the answer to the questions that follow.
Randy, Manny and Jan put 3 As, 4 Bs and 5 Cs in the box. They will take turns in getting
a letter from the box. They are trying to test the probability of getting their favourite letter.
Randy – A Manny – B Jan – C
1. What is the probability of getting each boy’s favourite letter?
a. Randy _____________
b. Manny _____________
c. Jan _____________
2. If you are next to Jan to pick up a letter and your favourite letter is A , What is the
probability of getting your favourite letter?
3. Who is most unlikely to get his favourite letter.
GET MOVING!
Make a list of all possible combinations of numbers 1 to 20 and letters A to Z.
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Tell how many possible outcomes there are.

KEEP MOVING!
Maybel put candies in a bag. 8 of the candies are red, 4 are yellow, 2 blue, and 7 brown.
She gave the bag of candies to Patti and Paul.
Patti’s favourite color is red and Paul’s is blue.
1. What is the probability of getting a:
a. Blue candy?
b. Yellow candy?
c. Brown candy?
d. Red candy?
e. Green candy?
f. Red or brown candy?
Assuming only the more likely outcome would happen, answer the following:
2. If Patti and Paul will take turns to get 1 candy each time, with Patti first and followed Paul,
what is the probability of?
a. Patti getting her favourite color? ________
b. Paul getting his favourite color? ________
APPLY YOUR SKILLS
Inside a bag are lollipops in wrappers of different colors. There are 5 lollipops in red
wrappers, 8 in green wrappers, 2 in blue wrappers, and 3 in yellow wrappers.
1. What is the probability of picking a lollipop in green wrapper?
2. What is the probability of picking a lollipop in red wrapper?
3. What color of lollipop is most unlikely to be picked?

Lesson 106: Solving Routine and Non-routine Problems Involving Experimental
Probability
Week 10
Trial1 Trial2 Trial3 Trial4 Trial5 Trial6
Coin H H T T H T
Dice 2 5 3 1 5 3
A coin is tossed and a dice is rolled simultaneously for 6 times. The outcomes are given in the
table above.
Find the experimental probability of getting a tail and a three together.
Understand:
 Know what is asked: The probability of getting a tail and a three.
 Know the given facts: 2 tail and a three out of 6 trials
Plan: There are 6 trials. Two of the trials are tail and three
Use the formula, and then substitute.
 P(E) = number of times the event occurs
Total number of Trials
Where E refers to the event
Solve:
 The probability of getting a tail and a three is= =
Check and Look Back:
 Since there are 6 trials and the tail and a three occurs 2 times, the
probability of getting tail and a three is = =

Get Moving!
Read each problem and then solve.
1. There are 10 books in the shelf, 3 Mathematics books, 2 Filipino books, 4 Science books
and 1 English book.
What is the probability of picking:
a. Mathematics books? ____________________
b. Science books? _______________________
c. Filipino books? _________________________
2. Jenny has given an entrance exam thrice and has not qualified even once. Find the
experimental probability of her qualifying the exam next time.
Keep Moving!
1. A bag contains 3 blue, 4 red, 2 white and 1 green marbles. You draw out a marble
without looking in the bag. What is the probability that you will not draw a red marble?
2. A spinner numbered 1 to 8 is spun.
What is the probability of spinning:
a) an odd number?
b) a factor of 9?
c) a multiple of 2?
d) a composite number?
e) a factor 18?
f) smallest even number?
g) a multiple of 10?
h) the greatest common factor of 24 and 32?
i) 10?
Apply your Skills!
1. What is the probability of drawing at random on the first draw?
a) a red ball from a bag containing 9 balls of which are red?
b) a black bean from a bag containing 24 beans of which 18 are black?
c) a marked card from a box containing 12 cards of which 4 are marked?
d) a green marble from a hat containing 30 marbles of which 18 are green?
2. Thirty-five students in Grade V class took a test, 9 received Very Good, 18 Good, and 8
received Fair. What is the probability that the student did not receive a Fair?
1
6
4
82
5
3
7

Lesson 107: Creating Routine and Non- Routine Problems Involving Experimental
Probability
Week 10
Create a problem on probability based on this information.
Study the cards with letters.
Can you create a problem given the above information?
You can create a problem by using the following as guides.
 Familiarize yourself with the concept and its application to real- life situation
 Think of the type of problem you will create.
Study the following examples of problems created for the situation.
 What is the probability of drawing a card having the following letters:
a. L,O,V,E
b. M, A,T,H
c. H,A,V,E
Get Moving!
Each item contains information for you to create a problem
1. 10 candies in a basket. 2 yellow, 3 violet, 2 red and 3 green.
2. A spinner with 5 colors, red , blue, purple , orange and green
Keep Moving!
Create a problem from the following information.
I L O V E M A T H

1.
2.
Apply your Skills!
Create two problems with the given information below.
Results from rolling a six- sided die.
1.

K TO 12 GRADE 5 LEARNER’S MATERIAL IN MATHEMATICS (Q1-Q4)

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K TO 12 GRADE 5 LEARNER’S MATERIAL IN MATHEMATICS (Q1-Q4)