Ateneo de Zamboanga University
Grade School
PAASCU Level III Accredited
ALTERNATIVE ACADEMIC ACTIVITIES IN MATHEMATICS
Grade Six
I- OBJECTIVES
At the end of the lessons, the students are expected to:
a. add and subtract dissimilar fractions;
b. multiply a whole number by a fraction, and a fraction by another
fraction;
c. divide a whole number by a fraction, and a fraction by another
fraction; and
d. solve word problems involving fractions.
II- TIME FRAME
October 16 – 18, 2013
III- LESSON
Four Fundamental Operations on Fractions
Application of Fractions
References
Aguilar,I, and Hipolito, S,( 2009), Integrative Mathematics 6, Quezon
City, Sibs Publishing House, Inc,
Yusingco, J, and Ledesma, L,(2007), Today’s Math 6, Quezon City,
Sibs Publishing House, Inc.
Charles, R, Crown, W, Fennel,F, Caldwell,J, Cavanagh, M,
Chancellor, D, Ramirez, A, Ramos, J, Sammons, K, Schielack, J,
Tate, W, Thompson, M, Van de Walle, J, (2006), Louisiana
Mathematics , Glenview, Illinois, Pearson Education, Inc.
Retrieved- October 11, 2013 - www.swisd.net/hip/Hip_Units/6thGradeMAth/6MathMod5.pdf
III- LEARNING EXPERIENCE
DAY 1
1. ADDITION AND SUBTRACTION OF FRACTIONS
1.1 Analyze the given problem.
Mrs. Gonzales walked 1/3 kilometer in the morning and
5/9 kilometer in the afternoon.
a. How far did she walk in all?
b. How many more kilometers did she walk in the
afternoon than in the morning?




How many km did Mrs. Gonzales walk in the morning?
How far did she walk in the afternoon?
What are you asked to find?
How would you get the answer?
a. How far did she walk in all?
Add the fractions.
1
5
3
9
b. How many more km did she walk in the afternoon than in the
morning?
Subtract the Fractions
5
1
9
3
c. Illustrations
1/3
5/9
1.2 How to add or subtract dissimilar fractions:
 First, find a common denominator
Least Common Multiple
To find a common denominator, find the Least Common Multiple
(LCM) of the denominators.
There are different methods on how to find the LCM.
Listing method 3: 3, 6, 9, 12
9: 9, 18, 27
Division by primes
3
3
9
1
3
= 9
LCM
 Second, write the equivalent fractions
After finding a common denominator, you must write equivalent
fractions.
1x 3 = 3
5 x 1= 5
3x 3 = 9
9 x 1= 9
We chose to multiply
by 3 to get to the common
denominator of 9 on the
bottom.
We chose to multiply
by 1 because the
denominator is already
9.
Points to ponder:
 Why is it necessary for fractions to have common
denominators before you add or subtract?
 Third, add or subtract the numerators
a. How many kilometers did she walk in all?
1
5
3
5
3
9
9
9
8
9
b. How many more km did she walk in the afternoon than
in the morning?
5
1
5
3
2
9
9
9
9
9
 Fourth, check to see if your answer can be simplified.
a. 8/9 km – mother walked
b. 2/9 km – mother walked 2/9 more km in the afternoon
than in the morning.
1.3 LET’S PRACTICE
Try to solve the following :
a. What is the sum of 5/12 and 1/3 ?
b. What is the difference between 5/9 and 2/5?
c. Suppose Wanda studied ¾ hour for the math quiz and Shirley
studied 5/6 hour. Who studied longer? How much longer?
2. MULTIPLICATION OF FRACTIONS
21. Analyze the given problem.
Our table at home has a length of 5/8 meter
and a width of 2/3 meter. What is the area of
the table at home?




What is the length of the table at home?
What is its width?
What is being asked in the problem?
What operation should you use to solve the problem?
a. What is the area of the table at home?
Multiply the given fraction by the other fraction
5
2
8
3
2.2 How to multiply a fraction by another fraction
 First, multiply the numerator by the other numerator.
5
2
10
8
3
 Second, multiply the denominator by the other
denominator.
5
2
10
8
3
24
 Third, simplify the answer if needed
10 or 5
24
12 square meter is the area of the table
How to simplify a fraction?
You may use the division by primes
method to get the simplified fraction.
Divide the numerator and denominator by
primes
2 10 24
5
12
= 5/12
2.3 How to multiply a whole number by a fraction
Ex.
4
3
4
 First, rewrite the whole number as a fraction by using 1 as
the denominator.
Hhhhhhhh
4
3
1
4
 Second, multiply the numerator by the other numerator.
Then multiply the denominator by the other denominator.
4
1
3
4
12
4
 Third, simplify the answer.
12 or 3 or 3
4
1
2.4 Practice Activity
Try to solve the following:
a. What is the product of 1/9 and 6/7 ?
b. What is 7/9 of 81?
c. Celine read 8 books. Three-fourths of them were mysteries.
How many mystery books did Celine read?
3. DIVISION OF FRACTIONS
3.1 Analyze the problem.
Mrs. Tan packed 3 kilograms of peanuts in plastic
bags that hold ¼ kilogram each. How many plastic bags
did she fill?


How many kilograms of peanuts did Mrs. Tan have?
How many kilograms of peanuts did she put in each plastic
bag?
 What is the best operation to use to find the answer?
a. How many plastic bags did she fill?
Divide the whole number by the fraction
3
1
4
b. Illustrations
3.2 How to divide a whole number by a fraction?
 First, find the reciprocal of the divisor.
3
¼=n
¼ is the divisor
4/1 is the reciprocal of ¼
3
4
1
 Second, rewrite the whole number as a fraction by using 1
as the denominator.
3 x 4
1
1
 Third, multiply the dividend by the reciprocal of the
divisor.
3
1
4
1
12
1
 Simplify the answer if necessary.
12
1
or 12 plastic bags
3.3 Practice Activity
Try to solve the following. Simplify the answer if necessary.
a. Divide 8/9 by 12.
b. Find 3/8 ÷ ¼
c. Mr. Warren makes use of peg markers for his wooden games. He
cuts the pegs from the dowel rod. How many ¾ inch pegs can he
cut from a 16 – inch dowel rod?
Ateneo de Zamboanga University
Grade School
PAASCU LEVEL III Accredited
Day 2 - Addition and Subtraction of Fractions
Name: _________________________________________________ HPS: 25 pts.
Section: _______________________________________________
A. COMPUTATION
Directions: Perform the indicated operations. Show the solution and simplify your answer
if needed.( 1 pt. each )
1. 2/5 + 3/8 =
2. 7/12 + 2/3 =
3. 7/8 – 5/12=
4. 10 – 2/5 =
B. PROBLEM SOLVING
Directions: Solve each word problem . Show the solution below. (3 pts.each)
1. The basketball team practiced ¾ hour in the morning and 7/9 hour in the
afternoon. How long did the team practice in a day?
2. You have to walk 8/10 km to school. If you already walked 3/7 km, how
much farther would you have to go?
3. Mother has 2 liters (L) of milk. She used 1/8 L to make leche flan and
1/3 L to make a cake. How much milk did she use? What fractional part of
the milk was left?
4. Jess is making 3 recipes that each requires a mixture of flour. One recipe calls for 2/3
cup flour, another calls for 7/8 cup, and the third requires ¾ cup. How much flour will
Jess need?
5. Liza ran ½ km on Monday, 3/4 km on Wednesday, and 7/8 km on Friday.
a. How long did Liza run for three days?
b. How much farther did Liza run on Wednesday than on Monday?
c. About how much farther did Liza run on Friday than on Wednesday?
Ateneo de Zamboanga University
Grade School
PAASCU LEVEL III Accredited
Day 3 - Multiplication and Division of Fractions
Name: _________________________________________________ HPS: 25 pts.
Section: _______________________________________________
A. Directions: Perform the indicated operation. Simplify the answer if possible.( 1pt each )
1. 2/3 x 12 =
2. 28 x 5/7 =
3.10 ÷ 5/9 =
4.6/7 ÷ 1/3 =
B. Directions: Analyze and solve each word problem .Show the solution below.
Simplify the answer if necessary.( 3 pts. each )
1. Ella bought a 12 m of ribbon from which she wants to cut ¾ m pieces. How
many pieces can she cut from her 12 m of ribbon?
2. Mandy has a garden in which 3/5 of the plants are tomato plants. Of the
tomato plants, 1/3 are cherry tomato plants. What fraction of the plants in
Mandy’s garden are cherry tomato plants?
3. Carol is 1/3 times as tall as her younger brother. Her younger brother is 48
inches tall. How tall is Carrol?
4. Find the perimeter of a rectangle whose length is 3 meters and whose width is
12/15 m.
5. A developer plans to divide 18 acres of land into ¾ - acre building sites.
How many building sites will there be?
6. Jamie decorates picture frames with lace. How many meters of lace does
she need to decorate 15 frames if each frame requires 3/9 m ?
7. Ester used 1/10 kilogram of ground beef for each hamburger patty. How
many hamburger patties did she make from 2 kilograms of ground beef?