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This lesson plan is about Congruence and Similarity.
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LESSON PLAN
Level : Junior High School
Subject : Mathematics
Class : IX
Semester : I
Topic : Similarity and Congruence
Standard Competence : Understanding the similarity of
figures and the use of it in
problem solving
Time Allocation : 2 x 40 minutes
Standard Competence
Understanding the similarity of figures and the use of it in problem solving
Basic Competence
Identifying similar and congruent figures
Indicators
1. Cognitive
a. Determining whether or not two figures are similar
b. Mentioning the pairs of similar figures
c. Solving problems dealing with similar figures
2. Psychomotor
a. Drawing two similar figures
b. Drawing two figures which are not similar
3. Affective
a. Characterized Behaviors
Responsibility, willingness to help others, and the feel of never
surrender.
b. Social Skills
Team working, be active in discussion, be brave to deliver ideas, be
open to criticisms, and be able to give others the opportunity to speak
up.
Learning Objectives
1. Cognitive
a. Given two figures, students are supposed to be able to determine
whether or not the figures are similar
b. Given some problems dealing with the concept of similarity, students
are supposed to be able to solve them.
2. Psychomotor
a. After learning about similar figures, students are supposed to be able
to draw a pair of similar figures.
b. After learning about similar figure, students are supposed to be able to
draw a pair of figures which are not similar.
3. Affective
a. Characterized Behaviors
Being involved in a student-centered learning activities, students are
supposed to be able to show responsibility, wilingness to help others,
and the feel of never surrender at least be judged as “Starts to appear”.
b. Social Skills
Being involved in a student-centered learning activities, students are
supposed to be able to work in teams, be active in discussion, be open
to criticisms, and be able to give others the opportunity to speak up at
least be judged as “In Progress”.
Learning Model
Learning Model : Problem-Based Instruction
Learning Activities
Introduction (± 10 minutes)
1. Phase 1. Students on the issue orientation
o Teacher leads the students to recall what they have learned from
the previous meeting. These questions may help: “What did you
learn in the last meeting? Is it about similarity? What are the
properties of two similar figures? When are two figures said to be
similar?”
o Motivation: Teacher gives an illustration of an event taken from
daily life related to the concept of similarity. Here is one of the
possible illustrations.
All of you must have allowance or
pocket money. Your parents most
likely give you the money at the
beginning of the week. Now, take a
look at the money that you have in
your pocket right now! Do you have
any coins with you? Last meeting
we had studied about similarity and
the properties of two similar figures. Now, what do you think about the coins? Are
they similar? Why are they or why are not they? And now, do you have cash? In
what shape are they? Are they similar? Why are they or why are not they?
o Teacher communicates the outlines of basic competence and
indicator that will be learnt.
o Teacher leads students to recall the lesson that had been learnt in
the previous meeting e.g. “when are two figures said to be similar?
What are the requirements for two figures to be congruent?”.
o Teacher may ‘gradually’ lead students to deal with the topic which
is going to be delivered in the meeting.
Main Activities (± 70 minutes)
2. Phase 2. Organize students to learn
o In this stage, teacher can divide students into several learning
groups containing three to four students.
o Further, teacher can pose a problem dealing with similarity (the
problems are available in the worksheet).
3. Phase 3. Guide the investigation of individual and group
o Teacher guides and assists students to work in groups to solve the
problems.
4. Phase 4. Develop and present the work
o Teacher helps students to present the work (the result of the
discussion) in front of the class.
5. Phase 5. Analyze and evaluate the problem solving process
o In this phase, teacher may ask several groups to present their work.
o Teacher emphasizes that the other student who do not get the
chance to present their work shoul give their opinion regarding to
the presenting teams’ works. Here, teacher leads the discussion and
helps students to settle the problem by getting closer to the right
answer.
Note: Teacher can also modify the learning activities by posing more than one
problem. In modifying this, teacher may provide more than one worksheet. Then,
the learning activities will be going back to the second step until the fifth step.
This can be repeated until all the problems have been settled. Here, I suggest to
use two or three problems in two or three worksheets.
Closure (± 10 minutes)
o Teacher leads students to conclude what they have learned that day.
o Teacher might ask the students to write a reflection regarding to the
lesson and the learning activities that they have experienced that
day.
o Teacher may also gives homework for students to practice.
o Teacher closes the lesson that day.
Assessment
The assessment can be done by assessing the student performance during the
project presentation, the content of the work presented, and also the activities
within the groups. The students who do not present their work are assessed by the
worksheet/s that have/s been completed.
ATTACHMENTS
1. Are all rectangles similar? Why or why not? (to answer this question, you’d
better refer to the properties of similar figures)
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2. Are all isosceles right-angled triangle similar? (to answer this question,
you’d better refer to the properties of similar figures)
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3. Mention at least three pairs of planes that are always similar!
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4. Take a look at the figure below! The triangle ABC is an isosceles right-
angled triangle. If AD=BD and CE=EB, segment CD is the altitude of
ΔACB as well as the bisector, and segment DE is the altitude of ΔBCD as
well as the bisector, which triangles are similar to ΔEBD? Explain!
5. Draw a pair of similar quadrilaterals, and explain why they are said to be
similar!
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6. Draw a pair of quadrilaterals of the same kind which are not similar, and
explain why they are said not to be similar!
P
Q R
A
CB
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7. Take a look at the two figures below!
If the magnitude of angle A is equal to the magnitude of angle P, are the two
triangles similar? Why? Explain your answer! (Note that the two triangles
are right-angled triangle!)
If PQ:AB=1:8, how many ΔPQR is needed to cover all the surface of
ΔABC?
ANSWER KEY OF WORKSHEET
1. Are all rectangles similar? Why or why not? (to answer this question, you’d
better refer to the properties of similar figures)
No, because not all rectangles have the corresponding sides in the same
ratio, which fails them to be always similar.
2. Are all isosceles right-angled triangle similar? (to answer this question,
you’d better refer to the properties of similar figures)
Yes, because all isosceles right-angled triangle have the corresponding
angles equal in magnitude and the corresponding sides in the same ratio.
3. Mention at least three pairs of planes that are always similar!
Squares, circles, isosceles right-angles triangle, equilateral triangle.
4. Take a look at the figure below! The triangle ABC is an isosceles right-
angled triangle. If AD=BD and CE=EB, segment CD is the altitude of
ΔACB as well as the bisector, and segment DE is the altitude of ΔBCD as
well as the bisector, which triangles are similar to ΔEBD?
A B
CD
P
S R
Q
A
D C
B
P
S R
Q
From the given informations, it is obviously seen that the five triangles
formed in the picture are isosceles right-angled triangle. We know that all
isosceles right-angles triangle are always similar. Thus, we have four
different triangles which are similar to ΔEBD, they are ΔACB, ΔECD,
ΔDCB, and ΔDCA.
5. Draw a pair of similar quadrilaterals, and explain why they are said to be
similar!
They are said to be similar because the corresponding angles are equal in
magnitude and the corresponding sides are in the same ratio.
6. Draw a pair of quadrilaterals of the same kind which are not similar, and
explain why they are said not to be similar!
They are said not to be similar because even though the corresponding
angles are equal in magnitude, but the corresponding sides are not in the
same ratio.
7. Yes, the two triangles are similar. Since the two triangles are right-angles
triangle, then if the magnitude of angle A is equal to the magnitude of angle
P, the magnitude of angle C must be equal to the magnitude of angle R.
Since the three corresponding angles are equal in magnitude, then the two
triangles are similar.
Since PQ:AB=1:8, then there needed 64 pieces of ΔPQR to cover all the
surface of ΔABC.
Name :
Class :
1. Is there any quadrilaterals that are dissimilar but the corresponding sides are
proportional? Explain your answer! (Give an example if any)
2. Is there any quadrilaterals that are dissimilar but the corresponding angles
are equal in magnitude? Explain your answer! (Give an example if any)
3. A rectangular frame of photograph is 40 cm x 60 cm, and a rectangular
photograph is 30 cm x 40 cm. Are the frame and the photograph similar?
Suppose we modify the size of the frame so that the frame and the
photograph are similar. What is the size?
ANSWER KEY OF QUIZ
1. Yes, there is. The example is rhombus. We know that all the four sides of a
rhombus are equal in length. Thus, all rhombuses must have proportional
corresponding sides. However, it doesn’t guarantee that all rhombuses are
similar since the corresponding angles are not always equal in magnitude.
(The maximum score is 30)
2. Yes, there is. The example is rectangle. We know that all the four angles of
a rectangle are right angle which are always equal. Thus, all rectangles must
have the corresponding angles equal in magnitude. However, it doesn’t
guarantee that all rectangles are similar since the corresponding sides are not
always proportional.
(The maximum score is 30)
3. One of the alternatives is:
No, they are not similar since the corresponding sides are not proportional
(compulsory answer)
If we modify the length of the sides, I would like to change the size of the
frame to be 45 cm x 60 cm.
(The maximum score is 40)
CHARACTERIZED BEHAVIORS OBSERVATION
Name :
Class :
Date :
For each and every characterized behavior below, assess students by using this
table.
No. Aspect AssessedNot yet
seen
Started to
appear
Started to
developHabitual
1. Responsibility
2.Willingness to help
others
3.Feeling of never
surrender
SOCIAL SKILLS OBSERVATION
Group :
Class :
Date :
For each and every social skill below, assess students by using this scale.
D : Poor
C : In Progress/ Acceptable
B : Good
A : Excellent
No. Aspect Assessed Poor (D)In Progress/
Acceptable (C)Good (B) Excellent (A)
1. Team-working
2.Activeness in
discussion
3.Bravery in
delivering ideas
4. Be open to
criticisms
Note:
Team-working
A group gets an A if all the members of the group get involved actively in
working within the team, gets a B if at most a member of the group does not
contribute actively in working within the team, gets a C if at most 2 members
of the group do not take part in working within the team, and gets a D if only 1
member of the group who works for the team.
Activeness in discussion
A group gets an A if all members of the group are actively involved in the
discussion, a B if 1 member of the group does not get involved actively in the
discussion, a C if 2 members do not give any contributions to the discussion,
and a D if most of the members do not get in the discussion.
Bravery in delivering ideas
A group gets an A if most of the members contribute actively in the discussion
by delivering supporting ideas, a B if some members do not give any ideas, a C
if only 1 member of the group who always presents ideas, and a D if none of
the members deliver ideas in the discussion within the class.
Be open to criticisms
A group gets an A if they are open to criticisms, showed by getting
improvements based on the critiques suggested, a B if the improvement is not
really significant, a C if the improvement is not essential, and a D id there is no
improvement in the work after getting some critiques.
P.S. : This criteria is supposed to be used for groups of 3 to 5.
SCORING CARD FOR GROUP PERFORMANCE
Group :
Class :
Date :
For each and every social skill below, assess students by using this scale.
1 : Poor
2 : Acceptable
3 : Good
4 : Excellent
No. PerformanceScoring
4 3 2 1
1.Showing comprehension dealing with
similarity.
2.The skill to solve problems dealing with the
concept of similarity.
3.The skill to comprehend the problems dealing
with similarity.
4. The skill to provide ideas in the discussion.
5. Assignment is satisfied.
Achieved Score
Maximum Score 20
Note:
Showing comprehension dealing with similarity.
A group gets a 4 if all six numbers of the worksheet are completed with right
answers, a 3 at most 1 number is wrongly answered, a 2 if at most 3 numbers
are wrongly answered, and a 1 if only 1 or 2 number/s completed with right
answer/s.
The skill to solve problems dealing with the concept of similarity.
A group gets a 4 if all numbers in the worksheet from 1 to 4 are well answered,
a 3 if only 3 numbers are right, a 2 if only 2 numbers are right, and a 1 if only 1
number is right.
The skill to comprehend the problems dealing with similarity.
A group gets a 4 if the numbers 1, 2, and 4 in the worksheet are righteously
answered, a 3 if only 2 numbers are right, a 2 if only 1 number is right, and a 1
if none of the numbers required is right.
The skill to provide ideas in the discussion.
A group gets a 4 if most of the members contribute actively in the discussion
by delivering supporting ideas, a 3 if some members do not give any ideas, a 2
if only 1 member of the group who always presents ideas, and a 1 if none of the
members deliver ideas in the discussion within the class.
Assignment is satisfied.
Observed from the completeness of th worksheet.
Criteria:
5 - 8 : Failed
9 - 12 : Needs Improvement
13 - 16 : Satisfactory
17 - 20 : Outstanding
SCORING RUBRIC FOR WORKSHEET NUMBER 5 AND NUMBER 6
Group :
Class :
Date :
For each and every social skill below, assess students by using this scale.
1 : Poor
2 : Acceptable
3 : Good
4 : Excellent
No. PerformanceScoring
4 3 2 1
1.Accuracy, including the length of the sides
and the magnitude of the angles.
2.The comprehension regarding to the concept
of similarity.
3. The skill to explain ideas and reasoning.
Achieved Score
Maximum Score 12
Note:
Accuracy, including the length of the sides and the magnitude of the angles.
A group gets a 4 if the measurement of the lengths and the angles are perfectly
accurate, a 3 if most of the measurement is accurate, a 2 if only a half of the
measurement is accurate, and a 1 if most of the measurement is wrong.
The comprehension regarding to the concept of similarity.
A group gets a 4 if the two numbers are righteously answered, a 3 if there is a
mistake in one of the numbers, a 2 if one number is wrongly answered, and a 1
if only a slight part of the two numbers is righteously answered.
The skill to explain ideas and reasoning.
A group gets a 4 if the reasons provided in the two numbers are correct, a 3 if
there is a slight mistake in the reasoning, a 2 if most of the reasoning is wrong
and a 1 if the reasonings are completely wrong.
Criteria:
3 - 5 : Failed
6 - 7 : Needs Improvement
8 - 9 : Satisfactory
10 - 12 : Outstanding
