MYP Geometry Unit 2: Similarity And Congruence In

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MYP Geometry Unit 2: Similarity and Congruence in ArchitectureSimilar/Congruent Triangles Unit Project – Geogebra constructions to determine congruent/similar triangles & quadrilaterals.AOI: Human Ingenuity, Approaches to LearningCriteria: B – Application and Reasoning; C – Communication; D-ReflectionLink to Geogebra installer: http://www.geogebra.org/cms/en/installersProject: Each student gets a database/pool of examples of similar and congruent figures in architecture (international examples). Students need tomatch the quadrilaterals and triangles to pictures they have selected of architecture and explain where they see similar triangles/quadrilaterals;congruent triangles/quadrilaterals, and justify their conclusions using geometry properties learned in class. (ASA, AAS, SSS, SAS, HL). Students select or are assigned a minimum of two pictures to analyze. They should cite the building/structure, architect if possible.Paste the picture into Sketchpad/Geogebra and superimpose triangles and quadrilaterals onto the architecture. Measure the sides andangles. Find potential similar and congruent triangles and quadrilaterals and measure angles and sides using superimposed figures. (Willneed intensive modeling – Netbooks).Students will classify triangles and quadrilaterals accurately. They should identify as many different shapes as possible.Students summarize their findings in a conclusion as to why congruent shapes and the concept of similarity.Students must provide at least one independent example to achieve Advanced (not from the pool of pictures.) The pool of pictures will beposted on a web page off the teacher page.Report Template: Picture with superimposed quadrilaterals & trianglesTriangle/Quadrilateral 1 Comparison withCongruent/Similar? Why? (WhatTriangle/Quadrilateral 1principles apply).Triangle/Quadrilateral 2 Comparison withTriangle/Quadrilateral 2Triangle/Quadrilateral 3 Comparison withTriangle/Quadrilateral 3Triangle/Quadrilateral 4 Comparison withTriangle/Quadrilateral 4Triangle/Quadrilateral 5 Comparison withTriangle/Quadrilateral 5Classification of triangle/quadrilateral and why.

MYP Geometry Unit 2: Similarity and Congruence in ArchitectureExample:Assigned Picture will be pasted into Geogebra File.Label and Identify Basic Geometry Figures (point, line segment,angle)Draw and label polygons to compare; Measure angles/sidesSummarize findings: Classify all polygons (and reasons why). ABC GIH through AA postulate.Quad JKLM is a trapezoid since –J –K 180 (two linesw/transversal and same side interior angles sum to 180 meansparallel lines).There are multiple instances of congruent triangles and similartriangles in this example. Congruent triangles aid in the aestheticsas well as useful architecture. Multiple instances of parallel lines,trapezoids also exist.Guiding questions: Why do builders/architects use congruentshapes? Similar shapes? Symmetry?

MYP Geometry Unit 2: Similarity and Congruence in ArchitectureTeacher Name: Mr. EiflerStudent Name:CATEGORYMatchingShapes OverArchitecture4Student superimposes appropriateshapes over the architectureconsistently and correctly.3Student superimposesreasonable shapes over thearchitecture most of the time.Concepts ofSimilarity andCongruenceExplanation shows completeunderstanding of how similarityand congruence are applied inarchitecture with clear calculationsand examples.Explanation showsunderstanding of how similarityand congruence are applied inarchitecture with minor gaps.Calculations and examples mayhave minor errors.Mathematical Correct terminology and notationTerminologyare always used, making it easy toand Notation understand what was done.Correct terminology andnotation are usually used,making it fairly easy tounderstand what was done.CompletionThree or more pictures of differentarchitecture are superimposed andanalyzed correctly for congruenceand similarity.At least two pictures of differentarchitecture are superimposedand analyzed for congruence andsimilarity with minor errors.History andSummaryThe history and location of eachexample is clear and engaging. Thesummary of the importance ofcongruence and similarity inarchitecture is clear and logical.The history and location is clearand engaging for only one or twoexamples. The summary hasminor errors or omissions.Criterion B: Investigating Patterns2Student sometimessuperimposes reasonable shapesover the architecture. Correctuse can be achieved with limitedassistance.Explanation shows someunderstanding of how similarityand congruence are applied inarchitecture. Significant gaps incalculations and examples. Aproficient explanation can beachieved with limited assistance.Correct terminology and notationare used, but it is sometimes noteasy to understand what wasdone.1Student rarely superimposesreasonable shapes over thearchitecture. Requires significant reteaching.One or more pictures of differentarchitecture are superimposedand analyzed for congruence andsimilarity. Significant errors existin one or more examples.The history and location is givenfor only one example, or hassignificant omissions. Thesummary has significantomissions or errors that could becorrected with additionalinstruction.One picture is are superimposed andanalyzed for congruence andsimilarity, or incomplete examples aresubmitted. Significant re-teaching oranalysis is required.The history and location for theexamples are mostly missing ordifficult to follow. The summaryrequires major revision or is missing.Explanation shows limitedunderstanding of how similarity andcongruence are applied inarchitecture.There is little use, or a lot ofinappropriate use, of terminology andnotation.

MYP Geometry Unit 2: Similarity and Congruence in ArchitectureAchievementlevel01-23-45-67-8Level descriptorThe student does not reach a standard described by any of the descriptors given below.The student applies, with some guidance, mathematical problem-solving techniques to recognize simple patterns.The student selects and applies mathematical problem-solving techniques to recognize patterns, and suggests relationships orgeneral rules.The student selects and applies mathematical problem-solving techniques to recognize patterns, and suggests relationships orgeneral rules.The student selects and applies mathematical problem-solving techniques to recognize patterns, describes them asrelationships or general rules, draws conclusions consistent with findings, and provides justifications or proofs.Criterion C: Communication in MathematicsAchievementlevel01-23-45-6Level descriptorThe student does not reach a standard described by any of the descriptors given below.The student shows basic use of mathematical language and/or forms of mathematical representation. The lines of reasoning aredifficult to follow.The student shows sufficient use of mathematical language and forms of mathematical representation. The lines of reasoning areclear though not always logical or complete. The student moves between different forms of representation with some success.The student shows good use of mathematical language and forms of mathematical representation. The lines of reasoning areconcise, logical and complete. The student moves effectively between different forms of representation.Criterion D: Reflection in MathematicsAchievementlevel01-23-45-6Level descriptorThe student does not reach a standard described by any of the descriptors given below.The student attempts to explain whether his or her results make sense in the context of the problem. The student attempts todescribe the importance of his or her findings in connection to real life.The student attempts to explain whether his or her results make sense in the context of the problem. The student attempts todescribe the importance of his or her findings in connection to real life. The student attempts to justify the degree of accuracy ofhis or her results where appropriate.The student critically explains whether his or her results make sense in the context of the problem and provides a detailedexplanation of the importance of his or her findings in connection to real life. The student justifies the degree of accuracy of his orher results where appropriate. The student suggests improvements to the method when necessary.

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Project: Each student gets a database/pool of examples of similar and congruent figures in architecture (international examples). Students need to match the quadrilaterals and triangles to pictures they have selected of architecture and explain where they see similar triangles/quadrilaterals;

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