TTLCOL_Final+Project

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 * Part 1 - Overview of Lesson**
 * Summary of the Lesson: Once students have learned the five triangle congruence theorems, we practice using logic and proofs to explain how those triangles are congruent in a variety of forms.
 * My audience is: 9th grade students
 * The subject/content is: Geometry/working with proofs
 * Learning Objectives or Essential Questions are:
 * Goal:
 * Students will be able to prove two triangles congruent
 * Objectives:
 * Students will use the five triangle congruence properties
 * Students will employ definitions of types of angles
 * Students will format proofs in one of three acceptable ways (two-column, paragraph, flow-chart)
 * Students will order steps according to a logical sequence
 * State or District Standards Addressed in this lesson are:
 * CYMAGE.3.1.01 - Use deduction to make and test conjectures.
 * CYMAGE.3.1.06 - Identify and use properties of triangles. (medians, altitudes, angle bisectors, perpendicular bisector, angle sum, sides/angles)
 * CYMAGE.3.1.05 - Classify triangles by their sides and angles
 * CYMAGE.3.1.11 -Explore, develop, and use methods for proving segments, angles, and triangles congruent.


 * Part 2 - Learning Channels Lesson Template**

Procedures: 1. Class will start with a review of the 5 congruence theorems (SSS, SAS, ASA, AAS, HL) by completing a worksheet with examples (appealing to SJ with step-by-step activities, workbook assignments, and memorization; appealing to Sequential for step-by-step instruction) 2 . The results will be discussed, as some examples are debatable and have multiple correct answers (appealing to NF with an open-class discussion; appealing to Global for inductive reasoning and synthesizing solutions; appealing to Auditory by talking about options and discussing in large group; appealing to CW of Power by allowing students to debate with one another) 3 . I will show the students two triangles and give them 2 facts that are true. 4 . As a class, we discuss what other facts can be discerned by analyzing the triangles (appealing to NT with Socratic questioning and debates; appealing to Abstract by speaking words and labeling items; appealing to Visual by ). 5 . Listing these facts on the board, we analyze the order of them and change it around to follow a logical sequence (appealing to SJ with a factual presentation). 6 . The finished product is an example of a 2-column proof. 7 . Demonstrate the same proof using other two styles (appealing to Visual by using flow-charts). 8 . Have students practice in small groups to prove 4 other examples in the style of their choice (appealing to NF with peer tutoring and SJ with repetition exercises; appealing to Kinesthetic with a small group discussion; appealing to CW of Freedom by giving them options from which to choose and Belonging by working with others) 9 . Each group presents one of the proofs that I assign for them (appealing to SP with a performance for the class) 10 . Additional practice is given by having each student work with laptops to complete an interactive activity (appealing to CW of Fun by removing the "kill" from "drill and kill") 11 . This activity gives a diagram and 2 given facts as well as a conclusion. It also lists the other necessary steps, but without a reason and not in the correct order (appealing to CW of Survival by promoting decision-making and confidence-building) 12 . Students must mix and match these steps while supplying a reason to complete the proof (appealing to SP with a virtual hands-on activity and NT with a puzzle challenge; appealing to Concrete for manipulating objects; appealing to Tactual by working with things he can handle while progressing at own pace ) 13 . Provide closure by having each student create a proof situation and solution (separately) and then randomly distribute them throughout the class (appealing to SP with a fast-paced activity, NT with intellectual pursuits, and NF as an assignment with personal choice; appealing to CW of Belonging by having everyone participate in shared activity together) 14 . Students complete proofs for homework and class is opened the following period with solutions as a review. These solutions are done by the students in a way similar to the laptop activity, but with "bricks" that students must put in correct order to "build" the solution (appealing to Kinesthetic by using the physical environment in learning; appealing to CW of Fun by making an activity enjoyable and Power because students see their products dictating instruction)

Homework: - Students complete the "peer proofs"


 * **The 5cs** || **Your Lesson Information** ||
 * 15. Compare || What do the 5 congruence theorems all share? How are they related to one another? Although the proof formats are different, what are the common threads that run between them? ||
 * 16. Contrast || Although each theorem proves triangles identical, how does each differ from one another? What makes each of the proof formats different from one another? ||
 * 17. Conceptualize || What would these steps look like when placed in order? ||
 * 18. Comprehend || Practice proving the triangles congruent given a variety of different information. ||
 * 19. Combine || How can a two-column proof be adjusted into a flow-chart proof, or vice-versa? When can this pattern of logic be employed outside of a math classroom? How can it be applied to situations that do not use triangles? ||

This can be a difficult lesson for different students depending on their needs. It is very verbal and linguistic and uses many terms; ESL/ELL students struggle with this terminology. In order to help with this, I have a "cheat-sheet" made that lists the 5 theorems and their names. This can be used a reference as we go through the unit. This is also very beneficial to students with processing deficiencies and helps them focus on the logic instead of the definitions. If students have trouble using the language, they can write phrases rather than complete sentences without taking away from the proving process.
 * Accommodations for special populations**