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Instructor: Qian Bradley Subject: Properties of Isosceles Triangle (Geometry) Content Goal: 1. Review the definition and vocabularies of the isosceles triangle: a. an isosceles triangle is a triangle with at least two congruent sides b. a triangle with at least two congruent sides is an isosceles triangle 2. Isosceles triangle conjecture: if a triangle is an isosceles triangle, then the base angles are congruent 3. Converse of the isosceles triangle conjecture: if a triangle has 2 congruent angles, then it is an isosceles triangle. Literacy Focus: Mathematic vocabularies and responsive teaching in a Three-Part Learning Framework a. Pre-learning, review vocabularies with the students: i. isosceles triangle ii. equilateral triangle iii. congruent iv. conjecture v. converse b. During-learning, use the text book, visual helper and study guide, do group reading and assessment of new vocabularies: i. vertex angle ii. base iii. base angle iv. leg v. base triangle conjecture vi. converse of the base triangle conjecture c. After-learning, use the triangle-square-circle method, let the students write reflective notes AZ State Standards: 1. MHS-S4C1-06 Solve relationships and 2. MHS-S4C1-10 Solve including special problems using angle and side length attributes of polygons. problems using right triangles, triangles. 3. MHS-S5C2-02. Solve problems by formulating one or more strategies, applying the strategies, verifying the solution(s), and communicating the reasoning used to obtain the solution(s). Prerequisites: Understanding of the isosceles triangle definition (Chapter 1) Instructional Objectives: Objectives 1. Review the definition of the isosceles triangle and the related vocabularies. 2. Solve problems related to the conjecture of the isosceles triangle and its converse. Assessment In class activity Group activity: study guide questionnaire Individual work: worksheet Instructional Procedure: Warm up: Review the definition and vocabularies of isosceles triangle Questions to ask: Rhetorical: Anyone remember what is an isosceles triangle? Review i. ii. iii. iv. v. the following vocabulary with the students: isosceles triangle equilateral triangle congruent conjecture converse Question to ask: Rhetorical: Is equilateral triangle an isosceles triangle? Anticipatory hook: Euclid (Greek mathematician popularly considered as the He is believed to have been during the reign of Ptolemy from 300 BC.), is "Father of Geometry". active in Alexandria, I (323 BC–283 BC). Euclid’s Element Book I Proposition 5 stated a conjecture - In an isosceles triangle the angles at the base are equal. Pappus (Greek) who followed him gave a clever proof of this theorem. Transition: distribute the visual helper and study guide. Group students with 3 – 4 students per group. Ask the students to make sure work on the questions on the handout using their text books. Group work: Read text book (Geometry) chapter 4.2, using the visual helper and study guide handout. (-Handout: i. ii. iii. iv. v. vi. What is vertex angle of an isosceles triangle? What is the base of an isosceles triangle? What is the base angle of an isosceles triangle? What is the leg of an isosceles triangle? What is the isosceles triangle base triangle conjecture? What is the isosceles triangle converse of the base triangle conjecture? --) Discussion: Each group will take turns answer the questions in the study guide. Class as a whole, check the answers and make sure students correct the definition of the vocabularies. Transition: students return to their original seating. Distribute worksheet. Class Activity: Worksheet page 1 Ask the students to report on answers after each problem. Through the assessment, decide whether to move on or review part of the content. 1. Mark Mark Find Find Find the the the the the leg(s) on the diagram base on the diagram value of the vertex angle value of the base angle value of angle “x” 2. Fill in the blanks. Class Activity: Worksheet page 2 Ask the students to report on answers after each problem. Through the assessment, decide whether to move on or review part of the content. 1. Find mPQR Find mP Find the value of the vertex angle Find the value of the base angle 2. In class discussion. Closure: Introduction to Triangle-Square-Circle method: what are the 3 most important things that you learned today, what squares (clicks) with your interest in math, what question still circles around your head? Students do their own reflective writing: call out 2 students to read what they write and share.