Pasig Catholic College Grade School Department PCC @ 103

Pasig Catholic College Grade School Department

PCC @ 103: Be with Jesus, Be with the Poor S.Y. 2015 – 2016

MATH 5 SECOND QUARTER

DLA No. 1 TYPES OF ACTIVITY: Concept Development

TOPIC : Concept of Fractions LEARNING OBJECTIVES : 1. Identify the kinds of Fractions 2. Illustrate the given fractions Reference : Experiencing Math Author/s : Manuel Mallari CONCEPT NOTES :

KINDS of FRACTIONS Proper Fraction is a fraction less than 1 and whose Numerator is smaller than the denominator.

Example: !!

0 1 2 3 4 5 6 7 8 Improper Fraction is a fraction equal to or more than 1 and whose numerator is bigger than the denominator.

Example: !!

Mixed Number is a combination of whole number and a fraction and sometimes called mixed fraction.

Example: 1 !!

Similar Fractions – fractions whose denominators are the same. Example: 3 , 4 , 6 7 7 7 Dissimilar Fractions – Fractions whose denominators are different. Example: 5 , 7 , 9 6 5 10



Math 5 SECOND QUARTER


TOPIC : Changing an Improper Fraction into a mixed number and vice versa. LEARNING OBJECTIVES : Change an Improper Fraction into a mixed number and vice versa. Reference : Soaring 21st Century Mathematics Author/s : Eduardo O. Dela Cruz Jr., Ed.D. CONCEPT NOTES :

To convert mixed number to an improper , multiply the denominator by the whole number and add the numerator. Write the numerator over the same denominator. Example:

3 !! = (5 x 3 + 2 ) = 17

5 5

Mixed Number 3 !! =

!"!

Improper Fraction

To convert improper fraction to a mixed number, divide the numerator by its denominator. Write the quotient as a whole number and the remainder as he numerator then copy the same denominator.

Example: !!! means 11 ÷ 2.

!!!

= ___5___ = 5 𝟏𝟐

2 / 11 10_ 1

Improper Fraction !!! = 5

!! Mixed Number





TOPIC : Recognizing Equivalent Fractions LEARNING OBJECTIVES : 1. Identify equivalent fractions 2. Form equivalent fractions Reference : Simplifying Mathematics 5 Author/s : Erminda E. De Leon CONCEPT NOTES : a. Equivalent Fractions name the same parts of a fraction. They name the same value. !

!

Equivalent Fractions

!!

b. Fractions can be change to higher terms by multiplying the numerator and denominator by the same number. Example:

• Multiply to make higher equivalent fractions. !

! x !

! = !

! , !

! x !

! = !"

!"

!

! is equivalent to !

! , !"

!" ,..

c. Fractions can be changed to lower terms by dividing the numerator and denominator by the same number. Example:

• Divide to make lower equivalent fractions. !"

!" ÷ !

! = !

! , !"

!" ÷ !

! = !

!

!"

!" is equivalent !

! , !

! ,..

d. Fractions are equivalent if their cross- products are equal. Example: (25 x 3) 75 = 75 ( 5 x 15)

!! !"

!"



Math 5

SECOND QUARTER DLA No. 4

TYPES OF ACTIVITY: Concept Development TOPIC : Changing Dissimilar Fractions to Similar Fractions LEARNING OBJECTIVES : 1. Find the LCD of two or more fractions 2. Change dissimilar fractions to similar fractions Reference : Transformative Mathematics 5 Author/s : Debbie Y. Grafil CONCEPT NOTES : To change dissimilar fractions to similar fractions, follow the steps below: Step 1. Find the least common denominator (LCD) of the fractions. LCD= 30 Write 30 as the new denominator for the two fractions.

!! =

𝟑𝟎

!! =

𝟑𝟎

Step 2. Divide the LCD by the denominator of each fraction.

!! =

!" 30 ÷ 6 = 5

!! =

!" 30 ÷ 5 = 6

Step 3. Multiply the quotient by the numerator. The answer becomes the new Numerator.

!! =

!"!"

30 ÷ 6 = 5 x 3 = 15

!! =

!"!"

30 ÷ 5 = 6 x 4 = 24

Dissimilar fractions !! and !

! changed to similar fractions

!"!" and

!"!"





TOPIC : Comparing Fractions LEARNING OBJECTIVES : 1. Compare fractions by using >,< and = 2. Order or arrange fractions from least to greatest or vice versa Reference : Experiencing Math 5 Author/s : Manuel M . Mallari CONCEPT NOTES : * To compare fractions using cross – multiplication, get the cross product of the two fractions. Compare the products. Example:

Compare !! and !

!"

1 x 12 = 12 6 x 5 = 30

!! !

!"

Since 12 < 30, then !! <

!!"

. * To compare three or more dissimilar fractions, get the least common denominator or LCD of the given fractions. Rename dissimilar to similar fractions. Compare the numerators, the greater the numerator the greater the value of the fraction. Example: Compare then arrange the following fractions from least to greatest.

!!"

, !! , !

!

Step 1. Find the LCD of 10, 6 and 5 LCD = 30 Step 2. Change dissimilar to similar fractions.

!!"

= !"!"

( 30 ÷ 10 x 7 = 21)

!

! =

!"!"

( 30 ÷ 6 x 5 = 25 )

!

! =

!"!"

( 30 ÷ 5 x 3 = 18 )

Since !"!"

< !"!" < !"

!" , then ordering the fractions from least to

greatest we have !! , !

!" , !

!



Math 5

SECOND QUARTER Activity Sheet No. 6

TYPES OF ACTIVITY: Concept Development TOPIC : Simplifying Fractions LEARNING OBJECTIVES : 1. Reduce fraction to its lowest 2. Answer Word Problem Involving Simplifying Terms Reference : Math for Life 5 Author/s : Amelia Celeridad- Wright, Adela C. Villamayor

CONCEPT NOTES : * To simplify a fraction means to reduce it to lowest terms. * A fraction is said to be in lowest terms if the GCF of its numerator and denominator is 1. * To reduce a fraction to lowest terms, divide its numerator and denominator by its GCF. Example:

𝟗𝟏𝟓

The GCF of 9 and 15 is 3.

!!"

= !!"

÷ 𝟑𝟑 =

!!

Therefore, !!"

when reduce to lowest terms is !!



Math 5


TYPES OF ACTIVITY: Computational Skills TOPIC : Adding Similar Fractions LEARNING OBJECTIVES : 1. Add similar fractions and mixed number with the same denominators. 2. Solve word problems involving similar fractions Reference : Experiencing Math 5 Author/s : Manuel M . Mallari

C ONCEPT NOTES : Ø Similar fractions have the same denominators. Ø To add similar fractions: • Add the numerators. • Use the same denominator. • Simplify the sum, if possible. Example:

!! + !

! + !

! = !

! or 1

!!

Ø To add fraction and a whole number: • Add or combine the two and simplify the sum if possible. Example:

12 !!"

+ !!" = 12 410 or 12

!!




DLA No. 9 TYPES OF ACTIVITY: Computational Skills

TOPIC : Adding Dissimilar Fractions LEARNING OBJECTIVES : 1. Change Dissimilar to similar fractions 2. Add Dissimilar Fractions Reference : Using Math in This Millennium 5 Author/s : Adele C. Villamayor CONCEPT NOTES :

To add dissimilar fractions: a. Find the least common denominator of the given Fractions. b. Change the fraction to similar fractions • Divide the LCD by the denominator. • Multiply the quotient and the numerator. • Write the product as the new numerator. c. Add the numerators and write the sum over the common denominator/ LCD. d. Express the sum in its simplest form, if possible.

Example: a. Get the LCD. b. Change to similar fraction

!! =

𝟏𝟐 !

! = 𝟗

𝟏𝟐 (12 ÷ 4 x 3 = 9)

+ +

!! =

𝟏𝟐 !

! = 𝟖

𝟏𝟐 (12 ÷ 3 x 2 = 8)

____________________ __________________ c. Add.

!! =

!!"

+

!! = !

!"

______________________ d. simplify.

!"!"

or 1 !!"



Math 5


TYPES OF ACTIVITY: Concept/ Skill Development TOPIC : Adding Dissimilar Fractions and Mixed Numbers LEARNING OBJECTIVES : 1. Add dissimilar fraction and mixed numbers 2. Solve word problems involving dissimilar fractions. Reference : Using Math in This Millennium 5 Author/s : Adele C. Villamayor

CONCEPT NOTES : To add mixed number with different denominators: a. Find the least common denominator of the given fractions. b. Change the fraction to similar fractions

• Divide the LCD by the denominator. • Multiply the quotient and the numerator. • Write the product as the new numerator.

c. Copy the whole number. d. Add the numerators and write the sum over the common denominator/ LCD. Then add the whole numbers. e. Express the sum in its simplest form, if possible. Example: a. Get the LCD. b. Change to similar fraction. c. Copy the whole number.

1 !! =

𝟏𝟐 1 !

! = 1 𝟏𝟎

𝟏𝟐

+ +

3 !! =

𝟏𝟐 3

!! = 3 𝟑

𝟏𝟐

____________________ __________________ d. Add.

1 !! = 1

!"!"

+ +

3 !! = 3

!!"

_____________________________ d. simplify.

4 !"!"

or 5 !!"



Math 5


TYPES OF ACTIVITY: Problem Solving Name______________________________________________Score___________Grade & Section______________________________________Date___________ TOPIC : Word Problems LEARNING OBJECTIVES : 1. Solve word problems involving fractions. Reference : Realistic Math Author/s : Paulino T. Gureng CONCEPT NOTES :

Ø When solving word problem, follow these four steps: • THINK - Identify the given facts and what is asked in

the problem. • PLAN - Determine the unknown data if there is any;

Specify the operation and the equation to be used to solve the problem.

• SOLVE - Carry out the plan. Solve the equation. • LOOK BACK – Check and label the answer.


PCC @ 103: Be with Jesus , Be with the Poor S.Y. 2015 – 2016

Math 5


TYPES OF ACTIVITY: Skill Development TOPIC : Subtraction of Similar Fractions LEARNING OBJECTIVES : 1. Subtract fractions with like denominators. 2. Solve word problems involving subtraction of fraction. Reference : Conceptual Math Author/s : Roy Aarlo L. Advincula CONCEPT NOTES :

Ø To subtract similar fraction, Subtract the numerators and copy the common denominator. Reduce the answer to simplest form if possible. Example: Subtract

!! — !

! =

( ! !! )!

=

!! — !

! =

( ! !! )!

= !!

Reduce to simplest term !!



Math 5

SECOND QUARTER Activity No. 13

TYPES OF ACTIVITY: Skill Development TOPIC : Subtraction of Proper and Improper Fraction from a Whole Number LEARNING OBJECTIVES : 1. Subtract proper and improper fraction from a whole number. 2. Solve word problems involving subtraction of fraction. Reference : Conceptual Math Author/s : Roy Arlo L. Advincula CONCEPT NOTES :

To subtract proper fraction from a whole number. Borrow 1 from the whole number, then change it to a fraction equal to one whole using the same number as the given denominator.

• Subtract and simplify the answer, if possible Example: Step 1. Step 2.

2 = 1 !"!"

2 = 1 !"!"

— !!"

= !!"

— !! =

!!"

_______________________ ___________________

1 !!"

= 1 𝟑𝟒

Ø To subtract improper fraction from a whole number: Method A.

• Borrow 1 from a whole number and rename it as fraction using the number in the number in the denominator of the subtrahend.

• Change the subtrahend to mixed number. • Proceed to subtraction and simplify the answer, if possible.

Example: Method A. Making both terms mixed number. Step 1. Step 2.

4 = 3 𝟒𝟒 3

!! = 3

!!

— !! =

!! —

!! = 1

𝟐𝟒

_______________________ ___________________

Step 3.

3 !!

— 1 !!

______________

2 !! = 2

𝟏𝟐

Method B.

• Borrow 1 from a whole number and rename it as fraction using the number in the denominator of the subtrahend.

• Change minuend to improper form. • Proceed to subtraction and simplify the answer.

Example Method B. Making both terms improper fractions. Step 1. Step 2.

4 = 3 𝟒𝟒 3

!! =

𝟏𝟔𝟒

— !! =

!! —

!! =

!!

_______________________ ___________________ Step 3.

!"!

— !!

______________

!"! = 2

𝟏𝟐



Math 5

SECONDD QUARTER DLA No. 14

TYPES OF ACTIVITY: Skill Development TOPIC : Subtraction of Dissimilar Fraction LEARNING OBJECTIVES : 1. Change dissimilar fractions to similar fraction 2. Subtract dissimilar fraction. 3. Solve word problems involving subtraction of dissimilar fractions. Reference : Math for Life Author/s : Roy Arlo L. Advincula

CONCEPT NOTES : To subtract dissimilar fractions: Find the least common denominator (LCD) of the given denominators. • Change dissimilar fractions to similar fractions. § Divide the LCD by the denominator § Multiply the quotient and the numerator. § Write the product as the new numerator. • Subtract the numerators and write the difference over the common

denominators. • Express the answer in simplest form. Example:

Step 1. Step 2.

!! =

𝟏𝟓 !

! =

𝟗𝟏𝟓

— —

!!"

= 𝟏𝟓

!!"

= 𝟔𝟏𝟓

_____________ _______________ Step 3. Step 4

!! =

!!"

!! =

!!"

— —

!!"

= !!"

!!"

= !!"

________________ _______________

𝟑𝟏𝟓

!!"

= 𝟏𝟓

Pasig Catholic College

Grade School Department PCC @ 103: Be with Jesus, Be with the Poor

S.Y. 2015 – 2016


Activity No. 15 TYPES OF ACTIVITY: Problem Solving

TOPIC : Problem Solving involving Addition and Subtraction of Dissimilar Fraction LEARNING OBJECTIVES : 1. Solve word problems involving addition and subtraction of dissimilar fractions. Reference : Math for Life /Using Math in this Millennium Author/s : Roy Arlo L. Advincula/ Adela Villamayor CONCEPT NOTES :

Ø When solving word problem, follow these four steps: • THINK - Identify the given facts and what is asked in the problem. • PLAN - Determine the unknown data if there is any; Specify the operation and the equation to be used to solve the problem. • SOLVE - Carry out the plan. Solve the equation. • LOOK BACK – Check and label the answer.




Activity Sheet No. 17 TYPES OF ACTIVITY: Concept Development/ Computational Skill

TOPIC : Multiplication of Fractions. LEARNING OBJECTIVES : 1. Multiply Fraction by another fraction . 2.Find Fractional part of a whole . Reference : Experiencing Math 5 , Math for Life Author/s : Manuel M . Mallari, Amelia Wright CONCEPT NOTES :

Ø To multiply two fractions, multiply the numerator and the denominator. Ø When multiplying a whole number by a fraction, remember that the denominator of any

whole number is one. Example:

!!

1.

!!

!! of !

! =

!! x !

! =

𝟏𝟔

!!

2.

!! x 4 =

!! = 1

!!



S.Y. 2015 – 2016 Math 5


TYPES OF ACTIVITY: Concept Development/ Computational Skill TOPIC : Multiplication of Fraction to a Mixed Number and vice versa. LEARNING OBJECTIVES : 1. Multiply fraction to a mixed number. 2.Multiply Mixed number by another mixed number. Reference : Experiencing Math 5 , Math for Life Author/s : Manuel M . Mallari, Amelia Wright CONCEPT NOTES : To multiply fraction and a mixed number:

• Change the mixed number to improper fraction. • Multiply the fractions, then simplify your answer. Ø To multiply mixed number by another mixed number: • Change the mixed numbers to improper fractions, then multiply. • Simplify your answer, if possible.

To simplify multiplication of fraction, cancellation can be used. Cancellation is similar to reducing a fraction. However, when you cancel, you simplify the fraction first before you multiply. Example: Multiplying a Mixed Number by a fraction. Step 1. Step 2. 2 !

! x !

! !

! x !

! = 𝟒𝟖

𝟏𝟐

𝟖

𝟑 = ( 3 x 2 + 2) simplify !"

!" = 4

𝟖

𝟑 x !

!

Ø Multiplying Mixed Number by another Mixed Number. Step 1. Step 2.

3 !! x 2

!! !"

! x !"

! =

𝟐𝟔𝟎𝟑𝟎

change to improper fractions

𝟐𝟎𝟔 x

𝟏𝟑𝟓

simplify !"#!"

= 8 𝟐𝟑

v Simplifying multiplication of fraction using cancellation.

Step 1 Find the GCF of the opposite terms. Divide the numerator and the denominator by the GCF. 20 ÷ 5 = 4 13 = 13 ÷ 1

!"! x !"

!

6 ÷ 1 = 6 1 = 5 ÷ 5 The GCF of 20 and 5 = 5 The GCF of 13 and 6 = 1 Step 2. Multiply the new numerator and denominator then simplify the answer if Possible.

!! x !"

! =

!"! = 8

!! = 8

!!



Math 5


TYPES OF ACTIVITY: Problem Solving TOPIC : Problem Solving Involving Multiplication of Fraction LEARNING OBJECTIVES : 1. Solve word problems involving multiplication of fractions. Reference : Math for Life /Using Math in this Millennium Author/s : Roy Arlo L. Advincula/ Adela Villamayor CONCEPT NOTES : When solving word problem, follow these four steps: • THINK - Identify the given facts and what is asked in the problem. • PLAN - Determine the unknown data if there is any; Specify the operation and the equation to be used to solve the problem. • SOLVE - Carry out the plan. Solve the equation. • LOOK BACK – Check and label the answer.


PCC @ 10Be with Jesus , Be with the Poor S.Y. 2015 – 2016

Math 5


TYPES OF ACTIVITY: Performance Task Name_____________________________________________Score___________ Grade & Section_____________________________________Date___________ TOPIC : Project Making LEARNING OBJECTIVES : 1. Follow the given directions accurately. 2. Mix colours using fractional parts . Reference : Experiencing Math 5 , Math for Life Author/s : Manuel M . Mallari, Amelia Wright CONCEPT NOTES : Students will be guided how to mix colors using fractional parts of it and should come up with the perfect blend of color. Materials: Food coloring Water Stirring rod Vials/small bottles Activity: Mixing of Colors 1. Distribute the activity sheets to the pupils. 2. Group the pupils into 8’s. 3. They need to follow directions accurately to achieve the perfect blend of colors and to solve the corresponding problem .




DLA No. 21 TYPES OF ACTIVITY: Concept/Skills Development

TOPIC : Division of Fraction LEARNING OBJECTIVES : 1. Get the reciprocal of the divisor. 2. Divide fraction by another fractions. Reference : Experiencing Math 5 , Math for Life Author/s : Manuel M . Mallari, Amelia Wright CONCEPT NOTES : In dividing fraction by another fraction, get first the reciprocal of the divisor, then multiply the fractions. Reduce the fraction in its lowest term if necessary. Reciprocal the reciprocal of a fraction is its invented form. When a number is multiplied by its reciprocal, the product is 1. Example:

!!

!

! !

! !

!

0 !! !

! !

! !

! or 1 whole

The reciprocal of !! is 𝟒

𝟏 since !

! x 𝟒

𝟏 = 1

Reciprocal of the divisor

!! ÷ !

! =

!! x 𝟒

𝟏 =

!"! or 3



Math 5

SECOND QUARTER Activity Sheet No. 22

TYPES OF ACTIVITY: Conceptual Development/Computational Skill TOPIC : Divide Whole Number by a Fraction and a Fraction by a Whole Number LEARNING OBJECTIVES : 1. Get the reciprocal of the divisor. 2. Divide whole number by a fraction. 3. Divide fraction by a whole number. Reference : Experiencing Math 5 , Math for Life Author/s : Manuel M . Mallari, Amelia Wright CONCEPT NOTES : In dividing a whole number by a fraction, get first reciprocal of the divisor, then then multiply the whole number by the reciprocal of the divisor. Reduce the fractions in lowest term if necessary.

Example: 2 ÷ !! = N

2

15

15

15

15

15

5 ( !! s) + 5 (

!! s) = 10 (

!! s)

reciprocal

2 ÷ !! = 2 x

𝟓𝟏 =

!"! = 10

In dividing a fraction by a whole number, the divisor which is the whole number must be change to an improper fraction by using 1 as the denominator. Then multiply the dividend by the reciprocal of the divisor.

Example: !! ÷ 2 = N

= 𝟏𝟔

!! ÷ 2

!! ÷ 2 =

!! ÷

!! =

!! x

!! =

𝟏𝟔

15

15

15

15

15



S.Y. 2014 – 2015


DLA No. 23 TYPES OF ACTIVITY: Conceptual Development/Computational Skill

TOPIC : Dividing Mixed Numbers LEARNING OBJECTIVES : 1. Get the reciprocal of the divisor. 2. Divide mixed number by a fraction. 3. Divide mixed number by another mixed number. Reference : Experiencing Math 5 , Math for Life Author/s : Manuel M . Mallari, Amelia Wright CONCEPT NOTES : To divide mixed number by a fraction:

• Change the mixed number to improper fractions. • Multiply the dividend by the reciprocal of the divisor. • Express the answer in simplest form if needed.

reciprocal

Example:

2 !! ÷

!! =

!! ÷

!! =

!! x

!! =

!"!"

= 3 𝟑𝟒

change to improper fraction

Ø To divide mixed number by another mixed number. Change first all mixed numbers to improper fractions. Then get the reciprocal of the divisor. Multiply the dividend by the reciprocal and reduce the answer in its lowest term if possible. Example: 10 1

5 !! ÷ 1

!! =

!"! ÷

!! =

!"! x

!! =

!"! = 3

𝟏𝟑

3 1



Math 5


TYPES OF ACTIVITY: Problem Solving TOPIC : Problem Solving involving Division of Fraction LEARNING OBJECTIVES : 1. Solve word problems involving division of fractions. Reference : Math for Life /Using Math in this Millennium Author/s : Roy Arlo L. Advincula/ Adela Villamayor CONCEPT NOTES : When solving word problem, follow these four steps:

• THINK - Identify the given facts and what is asked in the problem.

• PLAN - Determine the unknown data if there is any; Specify the operation and the equation to be used to solve the problem.

• SOLVE - Carry out the plan. Solve the equation. • LOOK BACK – Check and label the answer.



Math 5


TYPES OF ACTIVITY: Problem Solving TOPIC : Problem Solving involving Division of Fraction LEARNING OBJECTIVES : 1. Solve word problems involving division of fractions. Reference : Math for Life /Using Math in this Millennium Author/s : Roy Arlo L. Advincula/ Adela Villamayor CONCEPT NOTES :

When solving word problem, follow these four steps:

• THINK - Identify the given facts and what is asked in the problem.

• PLAN - Determine the unknown data if there is any; ( ( Answering the unknown data first will lead to the solution of the problem) Specify the operation and the equation to be used to solve the problem.

• SOLVE - Carry out the plan. Solve the equation.

• LOOK BACK – Check and label the answer.

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Pasig Catholic College Grade School Department PCC @ 103