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ATENEO DE MANILA HIGH SCHOOL | TULONG-DUNONG TUTORING
MATH 6
LESSON GUIDE NO. 8
Introduction to Fractions
LEARNING OBJECTIVES
At the end of the session, the TD Kids should be able to
1. Compare and arrange fractions in a particular order
2. Express fractions in lowest terms
3. Convert improper fractions to mixed numbers (and vice versa)
REVIEW OF PREVIOUS LESSON / MOTIVATIONAL ACTIVITY FOR NEW LESSON
This part will be prepared by the TD tutors.
LESSON PROPER
A. Present the following word problem to the kids:
Kuya Marius brought one big chocolate bar for his four TD kids as a prize for the
fastest Math problem-solver among them. Toto solved the Math problem first, and
Kuya Marius gave him 14 of the chocolate bar. Krysta solved the Math problem next,
and Kuya Marius gave him 13 of the chocolate bar. Annalissa solved the problem after
Krysta and received 123 of the chocolate. Bibo finished last and received the remaining
1
of the chocolate.
6
Of Kuya Marius's four kids, who got the biggest piece of chocolate? Who got the
smallest piece of the chocolate?
1. Ask the students to read the word problem out loud. Then instruct them to answer the
problem in their own notebooks.
2. After 3-4 minutes, ask the kids to show their solutions and answers. (The following are the
correct answers: Krysta got the biggest piece while Bibo got the smallest piece.) Check if
the students were able to answer the problem correctly.
3. Demonstrate how to solve the above problem by drawing a model of the fractions and
using the following steps:
a) First, THINK about what is being asked: In the given word problem, you are being
asked to compare the different portions of chocolate that each kid received and to
determine two things – the kid who got the biggest piece and the kid who got the
smallest piece. Think about what is already given: Each kid was a given a fraction of
the whole chocolate, but the fractions cannot be easily compared because they have
different denominators.
b) Next, PLAN how you can obtain the unknown: The simplest way to find out is to draw
the fractions and compare them visually.
c) SOLVE the problem by drawing each fraction on your whiteboard:
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Toto got
1
4
Krysta got
of the chocolate.
1
3
of the chocolate.
Annalissa got
Bibo got
1
6
3
12
of the chocolate.
of the chocolate.
Based on the drawings, it appears that Krysta got the biggest piece while Bibo got
the smallest.
d) Lastly, LOOK BACK and check if the answer is correct. (Is there any other way to arrive
at the answer?)
B. Briefly go through the key concepts of this lesson focusing more on the topics that you notice
the kids find more difficult or confusing:
1. Review the definition of a fraction:
a) Definition from Essential Math Connections & Communication: "a fraction is any number
in the form ab when a and b are whole numbers, and that b cannot be equal to zero."
(The portions received by each kid -- 13 , 14 , 123 , and 16 -- are all examples of fractions.)
b) In a fraction, the denominator b tells us into how many parts 1 whole unit is divided,
while the numerator a tells us how many of these parts there are to be considered.
2. Comparing two fractions:
(1) If two fractions have the same denominators (i.e. like fractions), simply compare
the numerators.
(2) If two fractions have different denominators (i.e. unlike fractions), rename them to
have the same denominators (by getting the least common denominator or LCD)
and then compare the numerators. (Another method is to simply cross multiply
and compare the resulting products.)
Note: The LCD of two or more denominators is similar to the LCM of the numbers
represented by the denominators.
3. Arranging several fractions in ascending order (from smallest to biggest) or descending
order (from biggest to smallest):
a) For like fractions, simply compare their numerators. Arrange them accordingly.
(Provide an example.)
b) For unlike fractions, rename them to have the same denominator (by getting their LCD)
and then comparing the numerators. Arrange the fractions accordingly. (Provide an
example.)
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c) If fractions have the same numerators but different denominators, the fraction with the
smallest denominator is the greatest/biggest fraction while the fraction with the
biggest denominator is the smallest/least fraction. (Provide an example.)
4. Equivalent fractions are fractions that are equal to each other when expressed in lowest
terms. (Ask the kids to identify two equivalent fractions in the given word problem.)
5. A fraction is in lowest terms if the numerator and denominator are relatively prime. This
means that the numerator and denominator can no longer be divided by a common number
other than 1. The following are the steps to get the lowest terms of a fraction:
a) Get the GCF of the numerator and the denominator.
If the fraction is
3
,
12
the GCF of 3 and 12 is 3.
b) Divide both the numerator and the denominator by the GCF.
3 ÷ 3 = 1 and 12 ÷ 3 = 4
Therefore, the lowest terms of 123 is 14 . (In the above problem, both Toto and
Annalissa received a same-sized piece of chocolate.)
6. Working with improper fractions and mixed numbers:
a) A fraction greater than 1 can be written either as an improper fraction or a mixed
number. An improper fraction is a fraction of the form ab where a is equal to or greater
than b. (That is, the numerator is equal to or greater than the denominator.) A mixed
number, on the other hand, is a number with a whole number and a fraction part.
Example:
If there is one whole pizza pie and one-fourth of another pizza left, we can express
this either as 45 (an improper fraction) or 1 14 (a mixed number).
b) An improper fraction may be renamed as a mixed number by dividing the numerator by
the denominator. The quotient becomes the whole number of the mixed number, while
the remainder over the divisor forms the fraction part. (Provide an example.)
c) A mixed number may be renamed as an improper fraction by multiplying the
denominator by the whole number and adding the numerator to the result. This gives
the numerator of the improper fraction. The denominator of the fraction part of the
mixed number is also used as the denominator of the improper fraction.
C. Depending on the strengths and weaknesses of your kids on these topics, ask them to answer
the related exercises.
EXERCISES
A. Translate each expression into a fraction:
1. ate 2 of 5 slices of pie
2. read 4 of 6 chapters of a book
3. slept for 6 of 24 hours in a day
4. walked 7 half-mile distances
5. prepared 9 apple quarters
6. To be provided by the TD Tutor
7. To be provided by the TD Tutor
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B. Use any method to write each set of fractions in:
ASCENDING ORDER
4 3 2
10 6 5
2 2 2
2.
3 5 9
1.
2
3
2
7
3.
3 5 7 3
2 6 12 4
4. To be provided by the TD Tutor
DESCENDING ORDER
5
12
8
6.
12
5.
3
12
3
9
8 1
12 12
7 11
4 6
7.
4 3 5 4
5 4 2 3
8. To be provided by the TD Tutor
C. Decide whether each fraction is in lowest terms or not. If it is, encircle the fraction. If it is not,
reduce it to lowest terms.
25
12
35
2.
25
123
3.
321
810
720
100
5.
101
350
6.
560
1.
4.
D. Solve for n in each of the following equations:
3 n
=
4 4
1 n
2. 5 =
5 5
n 19
3. 2 =
7 7
1.
n 23
=
4 4
2
n
5. 3 = 2
3
3
4.
2
5
6. To be provided by the TD Tutor
E. Solve the following problems. Label your answers.
1. Toto and Krysta walked with Kuya Marius during their home visit. If Toto walked
4
of the
6
3
of the way, who walked farther?
5
1
2. For the party, Annalissa brought 4 gallons of chocolate ice cream while Bibo brought 11
2
way and Krysta walked
quarts (a quart is one-fourth of a gallon) of vanilla ice cream. Who brought more ice cream
to the party?
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ENRICHMENT
Use the following True or False questions to assess the students' understanding of the concepts
discussed. On the space before each statement, indicate whether the statement is TRUE or FALSE.
______ 1.
In a fraction, the numerator is always less than the denominator.
______ 2.
All fractions are less than 1.
______ 3.
In the fraction
______ 4.
3
4
7
,
4
7 is called the numerator and 4 is called the denominator.
is greater than 12 .
______ 5.
0 can be used as a denominator.
______ 6.
An equivalent fraction is a fraction that is equal to the same fraction.
______ 7.
If a fraction is in lowest terms, then the numerator is less than the denominator.
______ 8.
When expressing a fraction in lowest terms, we cancel the LCM of both the numerator
and the denominator.
______ 9.
4
5
and
80
100
are equivalent fractions.
______ 10. All like fractions are equivalent fractions.
EVALUATION
A. Arrange the following fractions in the order described:
1. Ascending Order
5 4 3 7
8 2 5 20
2. Descending Order
2 10 1 11
5 15 3 15
B. For each set of fractions, cross out the fraction that is not equivalent to the other three
fractions. In the space provided, write the fraction in lowest terms to which the three
remaining fractions are equivalent.
______ 1.
______ 2.
______ 3.
8
28
40
50
28
12
10
45
20
15
56
24
12
42
80
60
35
15
18
63
60
45
70
20
C. Find the value of n in each of the following:
50 n
=
15 3
4 22 + n
2. n =
7
3
1.
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D. Solve the following problem. Label your answers and answer in complete sentences.
Annalissa and Toto met at the store. They each bought a box of eggs. Annalissa's egg tray
was
39
26
full while Toto's was
full. Who bought more eggs?
45
30
ASSIGNMENT
This part will be prepared by the TD tutors.
SOURCES
Sanchez et al. Essential Math Connections & Communication. QC: Dane Publishing House,
Inc. 2004.
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