ࡱ> FHEVq` =*bjbjqPqP .::=":!:!:!8tt9kr!L!!!!"""jjjjjjj$lh#ojB%""B%B%j!!j(((B%!!j(B%j((jcdg!7u ',:!%d2h k09kdro&oddgodgh"K#|(#d+$"""jj'd"""9kB%B%B%B%:!:! Focus Plan Texarkana Independent School District GRADING PERIOD:1st six weeksPLAN CODE:10M7 Pythagorean Theorem 10M8 Pythagorean Theorem Teacher: Dottie JohnsonCourse/subject:Math 10Grade(s):10Time allotted for instruction:1 class periods on block  Title: Modeling, Using, and Applying the Pythagorean TheoremLesson TOPIC: The student will use graph paper, scissors, and glue to create geometric models of the Pythagorean Theorem, use the converse of the Pythagorean Theorem, and practice finding missing sides of right triangles.TAKS Objective: Objective 7: The students will demonstrate an understanding of two- and three-dimensional representations of geometric relationships and shapes. Objective 8: The student will demonstrate an understanding of the concepts and uses of measurement and similarity.FoCUS TEKS and Student Expectation: 8.7 The student uses geometry to model and describe the physical world. The student is expected to use pictures or models to demonstrate the Pythagorean Theorem. 8.9 The student uses indirect measurement to solve problems. The student is expected use the Pythagorean Theorem to solve real-life problems.Supporting TEKS and Student Expectations: Geometry: (c) (3) The student identifies and applies patterns from right triangles to solve problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.aligned TEKS and Student Expectations for modifications:   ConceptsEnduring Understandings/Generalizations/Principles The student will understand thatModel the Pythagorean Theorem using squaresThe student will identify the hypotenuse and legs of a right triangle. The student will model visually the Pythagorean Theorem by cutting and attaching squares to a right triangle. The Pythagorean Theorem will be discussed as  EMBED Equation.3  Which will be shortened to  EMBED Equation.3 . Use the Pythagorean Theorem to find a missing side in a right triangle when two sides are knownThe student will solve the Pythagorean Theorem to find the hypotenuse when two sides are given and to find a leg when one side and the hypotenuse are given. Radicals will be given decimal approximations using the calculator. The student will correctly write the equation that solves this missing side.Use the converse of the Pythagorean Theorem to determine whether or not a triangle is a right triangle.The student will take three numbers and decide if these numbers satisfy the Pythagorean Theorem and therefore showing that the numbers can form a right triangle.Use the Pythagorean Theorem to solve simple real world problemsThe student will use the Pythagorean Theorem to solve simple real world problems where a side of a right triangle is missing. The student will correctly write the equation that solves the missing side.  I. Sequence of Activities (Instructional Strategies) A. Focus/connections The Pythagorean Theorem is a powerful mathematical idea that man has known for thousands of years. It is important to study this theorem in various perspectives. Just stating the theorem in words or in symbols does not give the power of the mathematics or the beauty and simplicity of the idea. This lesson begins with a statement of the Pythagorean Theorem which the students are already familiar with, and proceeds to model the theorem with the students actually cutting out squares, gluing squares, and relating the resulting pictures to the theorem in algebraic terms. B. Instructional activities (demonstrations, lectures, examples, hands-on experiences, role play, active learning experience, art, music, modeling, discussion, reading, listening, viewing, etc.) The students will complete the activity sheet where they will create a model for the Pythagorean Theorem. C. Guided activity or strategy The teacher will guide and help the students in the problems on the activities sheet. The students may not be familiar with solving equations involving a radical. They will need to be shown where the square root button is located on the calculator. The teacher will work the sample problems with the students on the assignment sheets. When using formulas the students will need guidance in using the calculators. Practice sheets one should be completed the first day. Sheet two includes Pythagorean triples and solving real world problems. Accommodations/modifications Students with modifications should be able to solve the problems where both legs are given and the hypotenuse is missing. Finding a missing leg when one leg and the hypotenuse is given may need to be deleted for these students. These students may be paired with a partner or given extra guidance from the instructor. . Enrichment Students can complete the enrichment page given with this lesson plan. II. STUDENT PERFORMANCE A. Description Students will complete the activity lesson individually or with a partner. They will follow the instructions of the teacher as they complete each part. Some students can work at their own pace after having completed the model of the little triangle. At the end of the activity students will have two models of the Pythagorean Theorem. Students should copy the examples worked by the teacher on the practice sheets. Students may then work individually or in pairs as they complete the problems on the practice sheets. Accommodations/modifications C. Enrichment Students may do the enrichment activity in class or at home. Many students will be able to complete this activity. . iii. Assessment of Activities A. Description The teacher should circulate among the students to make sure the discovery activity is correctly completed. The teacher should remind students to copy the examples as they are worked by the teacher. Assignment answers should be checked and discussed when completed. B. Rubrics/grading criteria Students should be given a daily completion grade for the activity. A class work / homework grade should be given for the individual assignment. C. Accommodations/modifications Students should complete modified discovery sheet and modified assignment. D. Enrichment Bonus points should be given to any students completing enrichment activity correctly. E. Sample discussion questions Discussion questions are listed on the discovery activity. F. Sample TAKS questions (attached) IV. TAKS Preparation A. Transition to TAKS context Students must know the Pythagorean Theorem is on the formula card in the traditional way:  EMBED Equation.3 . Students must either memorize  EMBED Equation.3 or understand what a, b, and c stand for in the traditional formula. B. Sample TAKS questions (attached) V. Key Vocabulary Pythagorean Theorem Right triangle Legs of a right triangle Hypotenuse of a right triangle Square root Pythagorean Triple VI. Resources A. Textbook Geometry by Glencoe Chapter 1 lesson 4 Chapter 8 lesson 1 B. Discovering Geometry by Serra Chapter 10 lessons 1, 2, 3 VII. follow up activities (reteaching, cross-curricular support, technology activities, next lesson in sequence, etc.) The next lesson will be on the distance formula which is a very basic application of the Pythagorean Theorem. A major will be given over the midpoint, the Pythagorean Theorem, and the distance formula. A review section on transformations will be included. VIII. Teacher Notes A. For a class of 10th grade Algebra II students, give the sample TAKS questions first. Students not scoring 3/4 should work through the activity and some of the practice problems. B. This lesson should be covered in one and one/half days on the block schedule. C. Do not become discouraged when students do not seem to understand the concepts or are slow in completing activities. Students need to see mathematics from various perspectives. Different learning styles will affect the students response to each different approach. Most students need lessons from all four learning styles, lots of practice, and weeks of spaced review before a concept if fully understood.     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