mathematics 9 proportional segments

BASIC EDUCATION ASSISTANCE FOR MINDANAOLEARNING GUIDE

THIRD YEAR - MATHEMATICSSIMILARITY

Module 15: Proportional Segments

COPYRIGHT NOTICE

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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.

Basic Education Assistance for MindanaoLearning Guide, May 2009 3



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• 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"


• Visual/Spatial


Skills

• Knowledge of major ideas





SIMILARITY


Activity 3: "Look for Me"


• Body/Kinaesthetic


Skills


• Mastery of subject matter

• Solve problems using required skills or knowledge

Activity 4: "Segmented"


• Visual/Spatial


Skills


• Mastery of subject matter

• Solve problems using required skills or knowledge

Activity 5: "Hand Me Your Proportional Arm"


• Interpersonal


Skills

• Translate knowledge into new context


• Generalize from given facts

Activity 6: "My Journal on Proportional Segments"


• Intrapersonal

• Verbal/Linguistic

Skills

• Translate knowledge into new context

• Recognize subjectivity




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Text Types

• Discussion

Key Assessment Strategies• Observing students

• Games

• Performance test

• Checking of outputs




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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)




SIMILARITY


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.


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.




SIMILARITY


3. Set a time allotment for them to perform the activity.

4. Ask volunteers to present their outputs to the class for comparison.


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.


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?




SIMILARITY


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.


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



SIMILARITY


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




SIMILARITY


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


A B C

P Q R



SIMILARITY


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.


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.


D

E

F M

L

K



SIMILARITY


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.


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 4: “Segmented”

Instructions:

1. Organize the class into groups of 6

2. Distribute to each group the activity sheets.


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.


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.


Students will apply their learning on proportional segments in solving problem related to real-life experiences.




SIMILARITY


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


• tape measure

Activity 5: “Hand Me You Proportional Arm”

Instructions:

1. Divide the class into groups of 6.

2. Distribute the needed materials.


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.


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.


In this stage, students will consolidate their learning about proportional segments by writing a journal.




SIMILARITY


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.


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.




SIMILARITY


STUDENT ACTIVITY 1“What's the Ratio?”


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



SIMILARITY


TEACHER RESOURCE SHEET 1“What's the Ratio?”

Answer Key


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



SIMILARITY


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.


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



SIMILARITY


STUDENT ACTIVITY 2“Who Am I”Worksheet 2




SIMILARITY


TEACHER RESOURCE SHEET 2“Who Am I”Answer Key


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



SIMILARITY


TEACHER RESOURCE SHEET 3“Look for Me”




SIMILARITY



Directions:1. Reproduce and cut each strip.2. Post one set of answer strips on the board for each group.


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



SIMILARITY



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



SIMILARITY



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


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



SIMILARITY


.

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


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



SIMILARITY


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.


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



SIMILARITY


Line Segment

Solution/Reason Line Segment

Solution/Reason

1. DJ 4. AB

2. KJ 5. OK

3. HK 6. BC


Color Code4 → Green 6.4 → Black7 → Red 8 → Orange10 → Yellow 11.5 → White12.5 → Blue 17.5 → Violet



SIMILARITY


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




SIMILARITY


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


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



SIMILARITY


`


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.



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TEACHER RESOURCE SHEET 7My Journal on Proportional Segments




SIMILARITY


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SIMILARITY


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




SIMILARITY


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
