Lesson plan Congruence and Similarity

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Lesson plan Congruence and Similarity

  1. 1. LESSON PLANLevel : Junior High SchoolSubject : MathematicsClass : IXSemester : ITopic : Similarity and CongruenceStandard Competence : Understanding the similarity offigures and the use of it inproblem solvingTime Allocation : 2 x 40 minutesStandard CompetenceUnderstanding the similarity of figures and the use of it in problem solvingBasic CompetenceIdentifying similar and congruent figuresIndicators1. Cognitivea. Determining whether or not two figures are similarb. Mentioning the pairs of similar figuresc. Solving problems dealing with similar figures2. Psychomotora. Drawing two similar figuresb. Drawing two figures which are not similar
  2. 2. 3. Affectivea. Characterized BehaviorsResponsibility, willingness to help others, and the feel of neversurrender.b. Social SkillsTeam working, be active in discussion, be brave to deliver ideas, beopen to criticisms, and be able to give others the opportunity to speakup.Learning Objectives1. Cognitivea. Given two figures, students are supposed to be able to determinewhether or not the figures are similarb. Given some problems dealing with the concept of similarity, studentsare supposed to be able to solve them.2. Psychomotora. After learning about similar figures, students are supposed to be ableto draw a pair of similar figures.b. After learning about similar figure, students are supposed to be able todraw a pair of figures which are not similar.3. Affectivea. Characterized BehaviorsBeing involved in a student-centered learning activities, students aresupposed 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 SkillsBeing involved in a student-centered learning activities, students aresupposed to be able to work in teams, be active in discussion, be open
  3. 3. to criticisms, and be able to give others the opportunity to speak up atleast be judged as “In Progress”.Learning ModelLearning Model : Problem-Based InstructionLearning Activities Introduction (± 10 minutes)1. Phase 1. Students on the issue orientationo Teacher leads the students to recall what they have learned fromthe previous meeting. These questions may help: “What did youlearn in the last meeting? Is it about similarity? What are theproperties of two similar figures? When are two figures said to besimilar?”o Motivation: Teacher gives an illustration of an event taken fromdaily life related to the concept of similarity. Here is one of thepossible illustrations.All of you must have allowance orpocket money. Your parents mostlikely give you the money at thebeginning of the week. Now, take alook at the money that you have inyour pocket right now! Do you haveany coins with you? Last meetingwe had studied about similarity andthe properties of two similar figures. Now, what do you think about the coins? Arethey similar? Why are they or why are not they? And now, do you have cash? Inwhat shape are they? Are they similar? Why are they or why are not they?o Teacher communicates the outlines of basic competence andindicator that will be learnt.
  4. 4. o Teacher leads students to recall the lesson that had been learnt inthe 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 whichis going to be delivered in the meeting. Main Activities (± 70 minutes)2. Phase 2. Organize students to learno In this stage, teacher can divide students into several learninggroups containing three to four students.o Further, teacher can pose a problem dealing with similarity (theproblems are available in the worksheet).3. Phase 3. Guide the investigation of individual and groupo Teacher guides and assists students to work in groups to solve theproblems.4. Phase 4. Develop and present the worko Teacher helps students to present the work (the result of thediscussion) in front of the class.5. Phase 5. Analyze and evaluate the problem solving processo In this phase, teacher may ask several groups to present their work.o Teacher emphasizes that the other student who do not get thechance to present their work shoul give their opinion regarding tothe presenting teams‟ works. Here, teacher leads the discussion andhelps students to settle the problem by getting closer to the rightanswer.Note: Teacher can also modify the learning activities by posing more than oneproblem. 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 touse two or three problems in two or three worksheets. Closure (± 10 minutes)o Teacher leads students to conclude what they have learned that day.
  5. 5. o Teacher might ask the students to write a reflection regarding to thelesson and the learning activities that they have experienced thatday.o Teacher may also gives homework for students to practice.o Teacher closes the lesson that day.AssessmentThe assessment can be done by assessing the student performance during theproject presentation, the content of the work presented, and also the activitieswithin the groups. The students who do not present their work are assessed by theworksheet/s that have/s been completed.
  6. 6. ATTACHMENTS
  7. 7. 1. Are all rectangles similar? Why or why not? (to answer this question, you‟dbetter refer to the properties of similar figures)..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................2. Are all isosceles right-angled triangle similar? (to answer this question,you‟d better refer to the properties of similar figures)..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
  8. 8. 3. Mention at least three pairs of planes that are always similar!........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................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 ofΔACB as well as the bisector, and segment DE is the altitude of ΔBCD aswell as the bisector, which triangles are similar to ΔEBD? Explain!5. Draw a pair of similar quadrilaterals, and explain why they are said to besimilar!
  9. 9. ..............................................................................................................................................................................................................................................................................................................................................................................6. Draw a pair of quadrilaterals of the same kind which are not similar, andexplain why they are said not to be similar!..............................................................................................................................................................................................................................................................................................................................................................................7. Take a look at the two figures below!ACBPQ R
  10. 10. If the magnitude of angle A is equal to the magnitude of angle P, are the twotriangles similar? Why? Explain your answer! (Note that the two trianglesare right-angled triangle!)If PQ:AB=1:8, how many ΔPQR is needed to cover all the surface ofΔABC?
  11. 11. ANSWER KEY OF WORKSHEET1. Are all rectangles similar? Why or why not? (to answer this question, you‟dbetter refer to the properties of similar figures)No, because not all rectangles have the corresponding sides in the sameratio, 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 correspondingangles 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 ofΔACB as well as the bisector, and segment DE is the altitude of ΔBCD aswell as the bisector, which triangles are similar to ΔEBD?
  12. 12. From the given informations, it is obviously seen that the five trianglesformed in the picture are isosceles right-angled triangle. We know that allisosceles right-angles triangle are always similar. Thus, we have fourdifferent 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 besimilar!They are said to be similar because the corresponding angles are equal inmagnitude and the corresponding sides are in the same ratio.6. Draw a pair of quadrilaterals of the same kind which are not similar, andexplain why they are said not to be similar!A BCDPS RQAD CBPS RQ
  13. 13. They are said not to be similar because even though the correspondingangles are equal in magnitude, but the corresponding sides are not in thesame ratio.7. Yes, the two triangles are similar. Since the two triangles are right-anglestriangle, then if the magnitude of angle A is equal to the magnitude of angleP, 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 twotriangles are similar.Since PQ:AB=1:8, then there needed 64 pieces of ΔPQR to cover all thesurface of ΔABC.
  14. 14. Name :Class :1. Is there any quadrilaterals that are dissimilar but the corresponding sides areproportional? Explain your answer! (Give an example if any)2. Is there any quadrilaterals that are dissimilar but the corresponding anglesare 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 rectangularphotograph 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 thephotograph are similar. What is the size?
  15. 15. ANSWER KEY OF QUIZ1. Yes, there is. The example is rhombus. We know that all the four sides of arhombus are equal in length. Thus, all rhombuses must have proportionalcorresponding sides. However, it doesn‟t guarantee that all rhombuses aresimilar 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 ofa rectangle are right angle which are always equal. Thus, all rectangles musthave the corresponding angles equal in magnitude. However, it doesn‟tguarantee that all rectangles are similar since the corresponding sides are notalways 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 theframe to be 45 cm x 60 cm.(The maximum score is 40)
  16. 16. CHARACTERIZED BEHAVIORS OBSERVATIONName :Class :Date :For each and every characterized behavior below, assess students by using thistable.No. Aspect AssessedNot yetseenStarted toappearStarted todevelopHabitual1. Responsibility2.Willingness to helpothers3.Feeling of neversurrender
  17. 17. SOCIAL SKILLS OBSERVATIONGroup :Class :Date :For each and every social skill below, assess students by using this scale.D : PoorC : In Progress/ AcceptableB : GoodA : ExcellentNo. Aspect Assessed Poor (D)In Progress/Acceptable (C)Good (B) Excellent (A)1. Team-working2.Activeness indiscussion3.Bravery indelivering ideas4.Be open tocriticismsNote: Team-workingA group gets an A if all the members of the group get involved actively inworking within the team, gets a B if at most a member of the group does not
  18. 18. contribute actively in working within the team, gets a C if at most 2 membersof the group do not take part in working within the team, and gets a D if only 1member of the group who works for the team. Activeness in discussionA group gets an A if all members of the group are actively involved in thediscussion, a B if 1 member of the group does not get involved actively in thediscussion, 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 ideasA group gets an A if most of the members contribute actively in the discussionby delivering supporting ideas, a B if some members do not give any ideas, a Cif only 1 member of the group who always presents ideas, and a D if none ofthe members deliver ideas in the discussion within the class. Be open to criticismsA group gets an A if they are open to criticisms, showed by gettingimprovements based on the critiques suggested, a B if the improvement is notreally significant, a C if the improvement is not essential, and a D id there is noimprovement in the work after getting some critiques.P.S. : This criteria is supposed to be used for groups of 3 to 5.
  19. 19. SCORING CARD FOR GROUP PERFORMANCEGroup :Class :Date :For each and every social skill below, assess students by using this scale.1 : Poor2 : Acceptable3 : Good4 : ExcellentNo. PerformanceScoring4 3 2 11.Showing comprehension dealing withsimilarity.2.The skill to solve problems dealing with theconcept of similarity.3.The skill to comprehend the problems dealingwith similarity.4. The skill to provide ideas in the discussion.5. Assignment is satisfied.Achieved ScoreMaximum Score20
  20. 20. Note: Showing comprehension dealing with similarity.A group gets a 4 if all six numbers of the worksheet are completed with rightanswers, a 3 at most 1 number is wrongly answered, a 2 if at most 3 numbersare wrongly answered, and a 1 if only 1 or 2 number/s completed with rightanswer/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 1number 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 righteouslyanswered, a 3 if only 2 numbers are right, a 2 if only 1 number is right, and a 1if 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 discussionby delivering supporting ideas, a 3 if some members do not give any ideas, a 2if only 1 member of the group who always presents ideas, and a 1 if none of themembers deliver ideas in the discussion within the class. Assignment is satisfied.Observed from the completeness of th worksheet.Criteria:5 - 8 : Failed9 - 12 : Needs Improvement13 - 16 : Satisfactory17 - 20 : Outstanding
  21. 21. SCORING RUBRIC FOR WORKSHEET NUMBER 5 AND NUMBER 6Group :Class :Date :For each and every social skill below, assess students by using this scale.1 : Poor2 : Acceptable3 : Good4 : ExcellentNo. PerformanceScoring4 3 2 11.Accuracy, including the length of the sidesand the magnitude of the angles.2.The comprehension regarding to the conceptof similarity.3. The skill to explain ideas and reasoning.Achieved ScoreMaximum Score12
  22. 22. 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 perfectlyaccurate, a 3 if most of the measurement is accurate, a 2 if only a half of themeasurement 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 amistake in one of the numbers, a 2 if one number is wrongly answered, and a 1if 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 ifthere is a slight mistake in the reasoning, a 2 if most of the reasoning is wrongand a 1 if the reasonings are completely wrong.Criteria:3 - 5 : Failed6 - 7 : Needs Improvement8 - 9 : Satisfactory10 - 12 : Outstanding

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