TTLCOL_Temperament+Style+Lesson

Hank Buckingham
 * Temperament Style Lesson**

Title of lesson: Practice with proofs

Time: 2 periods

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

Procedures: - 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) - The results will be discussed, as some examples are debatable and have multiple correct answers (appealing to NF with an open-class discussion) - I will show the students two triangles and give them 2 facts that are true. - As a class, we discuss what other facts can be discerned by analyzing the triangles (appealing to NT with Socratic questioning and debates). - 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). - The finished product is an example of a 2-column proof. - Demonstrate the same proof using other two styles. - Have students practice in groups to prove 4 other examples (appealing to NF with peer tutoring and SJ with repetition exercises) - Each group presents one of the proofs that I assign for them (appealing to SP with a performance for the class) - Additional practice is given by having each student work with laptops to complete an interactive acitivy. - 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. - 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) - 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) - Students complete proofs for homework and class is opened the following period with solutions as a review

Homework: - Students complete the "peer proofs"


 * **The 5cs** || **Your Lesson Information** ||
 * 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? ||
 * 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? ||
 * Conceptualize || What would these steps look like when placed in order? ||
 * Comprehend || Practice proving the triangles congruent given a variety of different information. ||
 * 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**