BASIC EDUCATION ASSISTANCE FOR MINDANAOLEARNING GUIDE
THIRD YEAR - MATHEMATICSSIMILARITY
Module 15: Proportional Segments
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Written, edited and produced by Basic Education Assistance for Mindanao, May 2009
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
Information about this Learning Guide
Recommended number of lessons for this Learning Guide: 6
Basic Education Curriculum CompetenciesThird Year Mathematics: Proportional Segments
• Demonstrate knowledge and skills in verifying and applying ratio and proportion, proportionality theorems, similarity between triangles and similarities in a right triangle
• Apply the fundamental law of proportion
• Product of the means is equal to the product of the extremes
• Apply the definition of proportional segments to find unknown lengths.
Objectives• Determine the ratio of objects.
• Find the equivalent of a ratio.
• Apply the fundamental law of proportion.
• Apply the definition of proportional segments to find unknown lengths.
Essential concepts, knowledge and understandings targeted• In a proportion, the product of the means is equal to the product of the extremes. In
symbols, if a:b = x:y, then bx = ay.
• Corresponding segments are proportional if the segments of one figure have the same ratio as the segments of the other.
Specific vocabulary introduced• ratio - is a comparison of two quantities expressed as the quotient of one divided by the
other
• proportion - is a statement of equality between two ratios
• means of a proportion - are the two inner quantities in a proportion
• extremes of a proportion - are the two outer quantities in a proportion
• segment or line segment - is a part of a line having two endpoints
• proportional segments - are segments that are divided proportionally
• length of line segments - is a real number which represents the distance between the endpoints of a line segment
• database - a collection of related records or information stored on a computer and organized to make any part of it accessible
Suggested organizational strategies• Have a classroom ready to accommodate groups of students to learn and explore the
activities where they will feel at ease and comfortable to move and explore.
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THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
• Assign roles to students within the group.
• Be prepared with the materials to be used by the student in the different activities.
• Prepare enough and clear copies of the activity sheets prior to the lesson.
Opportunities for IntegrationSCIENCE
• Student Activity 5, "Hand Me Your Proportional Arm", under Stage 5 provides opportunity for students to identify some parts of the body and discover interesting facts about them.
ENGLISH
• The activities in this Learning Guide tap students' communication skills by letting them express their ideas.
• Student Activity 6, "My Journal on Proportional Segments", allows students to freely express their thoughts through writing.
PEACE EDUCATION
• The activities in this Learning Guide develop a sense of unity, cooperation, sharing and understanding of each individual.
MULTICULTURALISM
• The activities in this Learning Guide are suited to different cultures and tribes.
GENDER INCLUSIVITY
• All the activities emphasize mutual responsibility and conscious participation of both gender, boys and girls.
Activities in this Learning GuideActivity 1: "What's the Ratio?"
Multiple Intelligences
• Visual/Spatial
• Logical/Mathematical
Skills
• Interpret facts, compare, contrast
• Understanding information
Activity 2: "Who Am I"
Multiple Intelligences
• Visual/Spatial
• Logical/Mathematical
Skills
• Knowledge of major ideas
• Understanding information
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BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
Activity 3: "Look for Me"
Multiple Intelligences
• Body/Kinaesthetic
• Logical/Mathematical
Skills
• Understanding information
• Mastery of subject matter
• Solve problems using required skills or knowledge
Activity 4: "Segmented"
Multiple Intelligences
• Visual/Spatial
• Logical/Mathematical
Skills
• Understanding information
• Mastery of subject matter
• Solve problems using required skills or knowledge
Activity 5: "Hand Me Your Proportional Arm"
Multiple Intelligences
• Interpersonal
• Logical/Mathematical
Skills
• Translate knowledge into new context
• Understanding information
• Generalize from given facts
Activity 6: "My Journal on Proportional Segments"
Multiple Intelligences
• Intrapersonal
• Verbal/Linguistic
Skills
• Translate knowledge into new context
• Recognize subjectivity
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BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
Text Types
• Discussion
Key Assessment Strategies• Observing students
• Games
• Performance test
• Checking of outputs
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THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
Mind Map
The Mind Map displays the organization and relationship between the concepts and activities in this Learning Guide in a visual form. It is included to provide visual clues on the structure of the guide and to provide an opportunity for you, the teacher, to reorganize the guide to suit your particular context.
Stages of Learning
The following stages have been identified as optimal in this unit. It should be noted that the stages do not represent individual lessons. Rather, they are a series of stages over one or more lessons and indicate the suggested steps in the development of the targeted competencies and in the achievement of the stated objectives.
Assessment
All six Stages of Learning in this Learning Guide may include some advice on possible formative assessment ideas to assist you in determining the effectiveness of that stage on student learning. It can also provide information about whether the learning goals set for that stage have been achieved. Where possible, and if needed, teachers can use the formative assessment tasks for summative assessment purposes i.e as measures of student performance. It is important that your students know what they will be assessed on.
1. Activating Prior LearningThis stage aims to engage or focus the learners by asking them to call to mind what they know about the topic and connect it with their past learning. Activities could involve making personal connections.
Background or purpose
Students will determine the ratio of objects.
Strategy
THINK INK PAIR SHARE. This strategy allows students to think individually about an issue, question or problem and record response. Discuss ideas with a partner and record what they have shared. Share with the whole group or join another pair to reach consensus.
Material
• activity sheet (refer to Student Activity 1 on page 17)
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BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
Activity 1: “What's the Ratio?”
Instructions:
1. Pair the students and provide them the activity sheet on page 17.
2. Let each student work individually then share and discuss the answers with his/her partner to reach a consensus.
3. Then, let them compare outputs with another pair.
4. Ask at least two volunteers to present their outputs to the class.
5. Process the activity through an interactive discussion by asking the following questions.
• What is a ratio?
• How are ratios expressed?
A ratio is a comparison of two quantities expressed as the quotient of one divided by the other. It can be expressed using a colon, :, as in 2:3; a
division/fraction bar, ---, as in23
, or obelus, ÷, as in 2 ÷ 3.
Formative Assessment
Monitor the performance of the students as they perform the activity.
Check their outputs. Refer to the answer key on page 18.
Roundup
Students would have determined the ratio of objects.
2. Setting the ContextThis stage introduces the students to what will happen in the lessons. The teacher sets the objectives/expectations for the learning experience and an overview how the learning experience will fit into the larger scheme.
Background or purpose
In this stage, students will find the equivalent of a ratio.
Strategy
DECODING. A strategy used to translate data or message from a code into the original language or form. In the context of this activity, the students will find the equivalent of a ratio. After which, they will look for the corresponding answers on the decoder that will answer the given problems.
Material
• activity sheets (refer to Student Activity 2 on pages 19-20)
Activity 2: “Who Am I?”
Instructions:
1. Organize the class into groups of 6 or as desired.
2. Distribute to each group the activity sheets.
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BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
3. Set a time allotment for them to perform the activity.
4. Ask volunteers to present their outputs to the class for comparison.
Formative Assessment
Ensure that each student works cooperatively with his/her group.
Check the groups' outputs using the answer key on page 21.
Roundup
Students would have found the equivalent of a ratio.
3. Learning Activity SequenceThis stage provides the information about the topic and the activities for the students. Students should be encouraged to discover their own information.
Background or purpose
In this stage, students will apply the:
☑ fundamental law of proportion; and
☑ definition of proportional segments to find unknown lengths.
Strategies
INTERACTIVE LECTURE. This strategy provides the students with the general outline to give them the framework for thinking about a subject and to structure their note-taking. This type of lecture involves students by focusing their attention on key words. It emphasizes information transfer at the knowledge, recall and comprehension levels of learning.
GAME. This strategy enables the students to learn and develop their mathematical skills in a fun and interesting way. It caters students whose comprehensions are activated using visuals. This enhances their logical/mathematical, kinesthetic, and spatial intelligences.
Materials
• problem and answer strips (refer to Teacher Resource Sheet 4 on pages 23-24)
• mechanics
• manila paper
• pentel pen
• pasteTeacher's Input
Begin this stage by telling students to list down all the equivalent ratios in Student Activity 2.
1: 2, 1734
and 3 :6
1256
, 3 :4 and628
4 :7, 2442
and 1628
44
, 1 :1 and 5:5
2:7, and 16 :5649
, 20: 45 and 818
6052
, and 15:13
3:1, 21 :7 and279
Ask the following questions.
1. When can you say that two or more ratios are equal (Say
1: 2 and 1734
or 1734
and 3 :6 )?
2. What do you call these ratios?
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BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
3. In the proportion, 1:2 = 3:6, what are the outer quantities? inner quantities? What have you noticed with their products? Is it true to all proportion? Support your answer.
Solving Proportions
Solve for x.
1. 5:4 = x:12
Solution:
4x = 512
4x = 60
Case 1
Steps for solving a proportion involving colon.
Equate the product of the means and the product of the extremes.
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Proportion is a statement of equality between two ratios.
KEY CONCEPTS
Examples : 4:7 = 24 :42, 3:1= 21:7, 49=
818
,27=
1656
REMEMBERIn a proportion, the product of the means is equal
to the product of the extremes
3 : 1 = 21 : 7
Means
Extremes
4 : 7 = 24 : 42Means
ExtremesProduct of Means = Product of Extremes
(7)(24) = (4)(42) 168 = 168
Product of Means = Product of Extremes(1)(21) = (3)(7)
21 = 21
49
=818
49
=818
MeansExtremes MeansExtremes
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
x = 604
x = 15
To check:
Substitute x = 15 to the proportion.
5:4 = x:12
5:4 = 15:12
(4)(15) = (5)(12)
60 = 60
Solve for the the value of the variable.
The product of the means is equal to the product of the extremes.
2.54= x
12
Solution:
54= x
12
4x = 512
4x = 60
x = 604
x = 15
Case 2
Steps for solving a proportion involving division bar.
Cross multiply as indicated.
Solve for the value of the variable.
3.5
x2= 4
x−7
Solution:
5x2
= 4x−7
5x−7 = 4x2
5x−35 = 4x8
5x−4x = 835
x = 43
Let the students solve the following problems and check their solutions.
1. 3:7 = 21:x + 1
2.x4= 16
x
Answers: 1. x = 48
2. x = ±8
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BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
Finding the Unknown Lengths of Proportional Segments
Proportional Segments
Corresponding segments are proportional if the segments of one figure have the same ratio as the segments of the other.
Consider the two line segments below.
Both AC and PR are divided equally into four equal line segments. Though the two
segments are not equal in lengths, it can be seen thatABAC
= 14
andPQPR
= 14
hence
ABAC
= PQPR
. The segments are said to be divided proportionally by points B and Q
respectively. Therefore, the following proportions are true.
BCAC
= QRPR
ABBC
= PQQR
ABAC
= PQPR
ABPQ
= BCQR
Suppose BC = 9, PQ = 6 and QR = 18, find the length of AB.
Solution 1:
ABBC
= PQQR
AB9
= 618
18AB = 96
AB = 5418
AB = 3
Solution 2:
ABPQ
= BCQR
AB6
= 918
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A B C
P Q R
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
18AB = 69
AB = 5418
AB = 3
Challenge the students to answer the next exercise.
In the figure shown below, EL proportionally divides DF and KM . If DE = 25, EF = 15 and KL = 28, find the length of KM .
Solution:
KMKL
= DFDE
KM28
= 4025
, whereDF = DEEF = 2515 = 40
25KM = 2840
KM = 112025
KM = 2245
KM = 44.8
Activity 3: “Look for Me”Instructions:
1. Prior to the activity, prepare the materials. Write the mechanics on a manila paper to be posted on the board. Refer to page 22.
2. Organize the class into groups of 12 and ask the members to pair up. Instruct them to line up by pair.
3. Distribute to each group the needed materials.
4. Read and explain the mechanics of the game.
5. When all groups are ready, start the game.
Formative Assessment
Monitor students as they perform the activity to come up with the expected output.
Check students' outputs using the answer key on pages 25-26.
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D
E
F M
L
K
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
Roundup
Students would have applied the fundamental law of proportion and the definition of proportional segments to find unknown lengths.
4. Check for Understanding of the Topic or SkillThis stage is for teachers to find out how much students have understood before they apply it to other learning experiences.
Background or purpose
Students will apply the fundamental law of proportion and definition of proportional segments to find the unknown lengths.
Strategy
BUZZ SESSIONS. This strategy aims to maximize students' engagement and to tap their verbal/linguistic and mathematical intelligences through answering questions or solving problems and come up to some kind of conclusion.
Material
• activity sheets (refer to Student Activity 4 on pages 27-28)
Activity 4: “Segmented”
Instructions:
1. Organize the class into groups of 6
2. Distribute to each group the activity sheets.
3. Set a time allotment for them to perform the activity.
4. When they are done, let them exchange their outputs with other groups for comparison.
5. Ask volunteers to present their outputs to the class for discussion.
Formative Assessment
Ensure that each student works cooperatively with his/her group.
Check the groups' outputs using the answer key on page 29.
Roundup
Students would have applied the fundamental law of proportion and definition of proportional segments to find the unknown lengths.
5. Practice and ApplicationIn this stage, students consolidate their learning through independent or guided practice and transfer their learning to new or different situations.
Background or purpose
Students will apply their learning on proportional segments in solving problem related to real-life experiences.
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SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
Strategy
MODELLING. A strategy which explicitly demonstrates the cognitive processes and skills required of a learner for a particular task. The activity in this stage, “Hand Me Your Proportional Arm”, aims to develop awareness and appreciation among students on the real-life application of proportional segments as well as tap their mathematical/logical and interpersonal intelligences.
Materials
• activity sheets (refer to Student Activity 5 on pages 30-31)
• tape measure
Activity 5: “Hand Me You Proportional Arm”
Instructions:
1. Divide the class into groups of 6.
2. Distribute the needed materials.
3. Set a time allotment for them to perform the activity.
4. Then, instruct them to compare their outputs.
5. After which, ask at least 2 volunteers to present their outputs for discussion.
Note:
The ratio of of the forearm length (f) to hand length (h) is written asfh
and
equal to1.61804 ...
1. There might be slight differences in the ratio obtained by
the students/groups and in order to produce a value closer to 1.61804 ...
1, get
their average. The length of the forearm can be determined using the proportionfh= 1.62
1where f is the forehand length and h is the hand length.
Formative Assessment
Monitor students' involvement in the activity.
Check the groups' outputs.
Roundup
Students would have applied their learning on proportional segments in solving problem related to real-life experiences.
6. ClosureThis stage brings the series of lessons to a formal conclusion. Teachers may refocus the objectives and summarize the learning gained. Teachers can also foreshadow the next set of learning experiences and make the relevant links.
Background or purpose
In this stage, students will consolidate their learning about proportional segments by writing a journal.
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SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
Strategy
JOURNAL. This provides a good opportunity for students to demonstrate and reflect on their learning. It is a good source of assessment for teachers.
Material
• journal (refer to Teacher Resource Sheet 7 on pages 32-33)
Activity 6: “My Journal on Proportional Segments”
Instructions:
1. Post an enlarged copy of the journal on the board.
2. Instruct students to complete the journal individually.
3. Set a time allotment.
4. Ask them to compare their journals.
5. Call volunteers to read their journals in front of the class.
6. Collect their outputs.
Formative Assessment
Assess their outputs using the rubric on page 34.
Roundup
The students would have consolidated their learning about proportional segments by writing a journal.
Teacher Evaluation
(To be completed by the teacher using this Teacher’s Guide)
The ways I will evaluate the success of my teaching this unit are:
1.
2.
3.
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MODULE 15: PROPORTIONAL SEGMENTS
STUDENT ACTIVITY 1“What's the Ratio?”
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DirectionsObjective: Give the ratio of objects.
1. Give the ratio of the following animals.2. Write your answer inside the box and simplify it.
rabbits to chicken1
two-legged animals to four-legged animals2
birds to all animals3
cattle to winged animals4
chicks to horses5
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
TEACHER RESOURCE SHEET 1“What's the Ratio?”
Answer Key
Basic Education Assistance for MindanaoLearning Guide, May 2009 18
rabbits to chicken 4:71
two-legged animals to four-legged animals 1:12
birds to all animals 1:23
cattle to winged animals 3:144
chicks to horses 3:15
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
STUDENT ACTIVITY 2“Who Am I”Worksheet 1
Objective: Find the the equivalent of a ratio.Directions:
1. Find the equivalent of each given ratio inside the code box.2. Then, write the corresponding letter of your answer on top of it to
determine the term defined by each statement.
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16:56
5:5
312
628
415
3:63:6
20:35279
818
16:10
15
15:13
105 5:20
155
9:24
9:24
3:1 6:30 21:7 20:45 1:13
126052
1:2 4:7 3:14 2:7 16:281256
1734
44
2442
49
“proper relation between things or parts”
“a unit of data in a database”
CODE BOX
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
STUDENT ACTIVITY 2“Who Am I”Worksheet 2
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BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
TEACHER RESOURCE SHEET 2“Who Am I”Answer Key
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S
3:1
E
6:30
G M
21:7
E
20:45
N
1:1
T3
126052
1:2
P R
4:7
O P O
3:14
R T
2:7
I
16:28
O N1256
1734
44
2442
49
“proper relation between things or parts”
“a unit of data in a database”
Source: http://dictionary.reference.com/browse/proportion
Source: http://dictionary.reference.com/browse/segment
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
TEACHER RESOURCE SHEET 3“Look for Me”
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MODULE 15: PROPORTIONAL SEGMENTS
TEACHER RESOURCE SHEET 4“Look for Me”
Directions:1. Reproduce and cut each strip.2. Post one set of answer strips on the board for each group.
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1
2
3
3:8 = x :561x=
18x−34
x−7:3 = 2x :73x
6x2−8=
12x−4
4−3x :19= 2:5−12x−6
=x6
3
PROBLEM STRIPS
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MODULE 15: PROPORTIONAL SEGMENTS
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ANSWER STRIPS
A B C
Given: AB = 2, BC = 8, AC = 10
D E F
Given: EF = 8
M N O
Given: MN = 9, NO = 10, MO = 19
G H I
Given: HG = 12
PP Q R
Given: PQ = 18, QR = 4, QR = 22
T US
Given: ST = 8
Given: JL = 5
J K L
21
−2
49
23
0
−65
−12
x = 21
x = 49
x = -2
x = 0
PP Q R x=−65
x=−12
x=23
PP Q R
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
TEACHER RESOURCE SHEET 5“Look for Me”
Answer Key
3:8 = x :568x = 356
8x = 168
x = 1688
x = 21
1x= 18
x−341x−34= 18x
x−34 = 18x18x−x =−34
17x =−34
x =−3417
x =−2
x−7 :3 = 2x:7x−77= 32x
7x−49 = 6x7x−6x = 49
x = 49
3x6x 2−8
= 12x−4
3x 2x−4 = 16x2−86x2−12x = 6x 2−8
−12x =−8
x = −8−12
x = 23
4−3x: 19 = 2 :54−3x 5 = 192
20−15x = 38−15x = 38−20−15x = 18
x = 18−15
x =−65
−12x−6
= x63
x6x−6 = −123x2−36 =−36x2 =−3636
x2 = 0x = 0
JKJL
= ABAC
JK5
= 210
JK = 5 210
JK = 1
KLJL
= BCAC
KL5
= 810
KL = 5 810
KL = 4
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1 2
3
ANSWER STRIPS
A B C
Given: AB = 2, BC = 8, AC = 10
D E F
Given: EF = 8
M N O
Given: MN = 9, NO = 10, MO = 19
G H I
Given: HG= 12
PP Q R
Given: PQ = 18, QR = 4, QR = 22
T US
Given: ST = 8
Given: JL = 5
J K L
21
−2
49
23
0
−65
−12
x = 21
x = 49
x = -2
x = 0
PP Q R x=−65
x=−12
x=23
ANSWER STRIPS
A B C
Given: AB = 2, BC = 8, AC = 10
D E F
Given: EF = 8
M N O
Given: MN = 9, NO = 10, MO = 19
G H I
Given: HG= 12
PP Q R
Given: PQ = 18, QR = 4, QR = 22
T US
Given: ST = 8
Given: JL = 5
J K L
21
−2
49
23
0
−65
−12
x = 21
x = 49
x = -2
x = 0
PP Q R x=−65
x=−12
x=23
BASIC EDUCATION ASSISTANCE FOR MINDANAO
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SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
.
DEMN
= EFNO
DE9
= 810
DE = 9 810
DE = 7210
DE = 7.2
DFEF
= MONO
DF8
= 1910
DF = 8 1910
DF = 15210
DF = 15.2
HIQR
= HGPQ
HI4
= 1218
HI = 4 1218
HI = 489
GI = HGHI
GI = 12 489
GI = 523
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ANSWER STRIPS
A B C
Given: AB = 2, BC = 8, AC = 10
D E F
Given: EF = 8
M N O
Given: MN = 9, NO = 10, MO = 19
G H I
Given: HG = 12
PP Q R
Given: PQ = 18, QR = 4, QR = 22
T US
Given: ST = 8
Given: JL = 5
J K L
21
−2
49
23
0
−65
−12
x = 21
x = 49
x = -2
x = 0
PP Q R x=−65
x=−12
x=23
ANSWER STRIPS
A B C
Given: AB = 2, BC = 8, AC = 10
D E F
Given: EF = 8
M N O
Given: MN = 9, NO = 10, MO = 19
G H I
Given: HG = 12
PP Q R
Given: PQ = 18, QR = 4, QR = 22
T US
Given: ST = 8
Given: JL = 5
J K L
21
−2
49
23
0
−65
−12
x = 21
x = 49
x = -2
x = 0
PP Q R x=−65
x=−12
x=23
PP Q R
ANSWER STRIPS
A B C
Given: AB = 2, BC = 8, AC = 10
D E F
Given: EF = 8
M N O
Given: MN = 9, NO = 10, MO = 19
G H I
Given: HG = 12
PP Q R
Given: PQ = 18, QR = 4, QR = 22
T US
Given: ST = 8
Given: JL = 5
J K L
21
−2
49
23
0
−65
−12
x = 21
x = 49
x = -2
x = 0
PP Q R x=−65
x=−12
x=23
ANSWER STRIPS
A B C
Given: AB = 2, BC = 8, AC = 10
D E F
Given: EF = 8
M N O
Given: MN = 9, NO = 10, MO = 19
G H I
Given: HG= 12
PP Q R
Given: PQ = 18, QR = 4, QR = 22
T US
Given: ST = 8
Given: JL = 5
J K L
21
−2
49
23
0
−65
−12
x = 21
x = 49
x = -2
x = 0
PP Q R x=−65
x=−12
x=23
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
STUDENT ACTIVITY 4“Segmented”
Objectives: Students will apply the fundamental law of proportion and definition of proportional segments to find the unknown lengths.
Directions:1. Find the length of each line segment in the figure to complete the table.2. Look for the corresponding color of the answer in the color code box.3. Then, color the area in the figure with the indicated segment.
Basic Education Assistance for MindanaoLearning Guide, May 2009 27
J G = 1 0D E = 2A K = 1 4B J = 1 6K L = 6
E F H J i s a s q u a r eM L O N i s a p a r a l l e l o g r a mS e g m e n t s A K , D J a n d H K a r e d i v i d e d p r o p o r t i o n a l l yS e g m e n t s O K a n d B J a r e d i v i d e d p r o p o r t i o n a l l yH I = H G = H FM N = A B
G i v e n / A s s u m p t i o n
J G = 1 0D E = 2A K = 1 4B J = 1 6K L = 6
E F H J i s a s q u a r eM L O N i s a p a r a l l e l o g r a mS e g m e n t s A K , D J a n d H K a r e d i v i d e d p r o p o r t i o n a l l yS e g m e n t s O K a n d B J a r e d i v i d e d p r o p o r t i o n a l l yH I = H G = H FM N = A B
G i v e n / A s s u m p t i o nGiven
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
Line Segment
Solution/Reason Line Segment
Solution/Reason
1. DJ 4. AB
2. KJ 5. OK
3. HK 6. BC
Basic Education Assistance for MindanaoLearning Guide, May 2009 28
Color Code4 → Green 6.4 → Black7 → Red 8 → Orange10 → Yellow 11.5 → White12.5 → Blue 17.5 → Violet
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
TEACHER RESOURCE SHEET 6“Segmented”
Answer Key
Line Segment Solution/Reason Line
Segment Solution/Reason
1. DJDJ= JEDE = 52 = 7JG= 10 and JH =HG = 5
SinceEFHGisa square,hence JE= 5.4. AB
Since AK andDJaredividedproportionally ,therefore
ABAK
= EDDJ
AB14
= 27
AB= 4
2. KJ
SinceHK andDJaredividedproportionally ,therefore
KJHJ
= JEDE
KJ5
= 52
KJ = 252
= 12.5
5. OK
OK = OLKL = 46= 10AB = MN = 4OL = MN = 4
Notethat MLONisaparallelogram.
3. HK HK = KJJH= 2525 = 35
2= 17.5 6. BC
Since OKandBJ aredividedproportionally ,therefore
BCBJ
= OLOK
BC16
= 410
BC= 6410
= 6.4
Basic Education Assistance for MindanaoLearning Guide, May 2009 29
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
STUDENT ACTIVITY 5“Hand Me Your Proportional Arm”
Apply the fundamental law of proportion and definition of proportional segments to find unknown lengths.
Name of Group Members
Average
Length of forearm
Length of hand
Ratio of forearm length to hand length
Basic Education Assistance for MindanaoLearning Guide, May 2009 30
Objective
1. Measure the length of the forearm and hand of each group member.2. Then, complete the table and answer the questions below.
Length of the handLength of the hand
Length of the forearm
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
`
Basic Education Assistance for MindanaoLearning Guide, May 2009 31
What have you noticed with the ratio of your forearm length to hand length?
While looking at the pages of her family photo album, Arley found her
great-grandfather's handprint on one of the pages. She measured it
and found out that it was 8 inches long. How long was his great-
grandfather's forearm? Use your average ratio of the forearm length to
hand length to solve this problem. Show your solution.
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
TEACHER RESOURCE SHEET 7My Journal on Proportional Segments
Basic Education Assistance for MindanaoLearning Guide, May 2009 32
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
:
Basic Education Assistance for MindanaoLearning Guide, May 2009 33
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
TEACHER RESOURCE SHEET 8
RUBRIC FOR JOURNAL WRITING
CRITERIAPOINTS
Score4 3 2 1
Organization
The information is logical, interesting sequence which reader can easily follow.
Student presents information in logical sequence which reader can follow.
Reader has difficulty in following work because student jumps around.
Sequence of information is difficult to follow.
Content/Knowledge
Student demonstrates full knowledge more than what is required.
Student shows at ease with the information about the subject and is able to demonstrate basic concepts.
Student shows a grasp of information about the topic but fails to elaborate basic concepts.
Students does not show grasp of information; it does not demonstrate concepts about the subject.
Grammar and Spelling
Presentation has no misspelled words or grammatical errors.
Presentation has no more than two misspelled words and/or grammatical errors.
Presentation has three misspelled words and/or grammatical errors
Work has four or more misspelled words and/or grammatical errors.
NeatnessWork is neatly done. Work has one or two areas
that are dirty.Work has three or four areas that are dirty.
Work is illegible.
Originality Work displays no duplication at all.
Work displays few duplication.
Work displays many duplication.
Work displays total duplication.
Total
Basic Education Assistance for MindanaoLearning Guide, May 2009 34
BASIC EDUCATION ASSISTANCE FOR MINDANAO
THIRD YEAR - MATHEMATICS
SIMILARITY
MODULE 15: PROPORTIONAL SEGMENTS
For the Teacher: Translate the information in this Learning Guide into the following matrix to help you prepare your lesson plans.
Stage 1. Activating Prior Learning
2. Setting the Context
3. Learning Activity Sequence
4. Check for Understanding
5. Practice and Application
6. Closure
Strategies
Activities from the Learning Guide
Extra activities you may wish to include
Materials and planning needed
Estimated time for this Stage
Total time for the Learning Guide Total number of lessons needed for this Learning Guide
Basic Education Assistance for MindanaoLearning Guide, May 2009 35