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Title Trigonometry Suggested Time Frame 4th Six Weeks 10 Days Guiding Questions Big Ideas/Enduring Understandings Module 13 • Trigonometry can be used with right triangles to solve realworld problems. Geometry Unit 5 Module 13 • How do you find the tangent ratio for an acute angle? • How can you use the sine and cosine ratios, and their inverses, in calculations involving right triangles? • What do you know about the side lengths and the trigonometric ratios in special right triangles? • How can you solve a right triangle? Vertical Alignment Expectations TEA Vertical Alignment Chart Grades 5-8, Geometry Sample Assessment Question Coming Soon... The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material. A portion of the District Specificity and Examples are a product of the Austin Area Math Supervisors TEKS Clarifying Documents available on the Region XI Math website. Geometry Unit 5 Updated November 19, 2015 Page 1 of 7 Ongoing TEKS Math Processing Skills G.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: ● (A) apply mathematics to problems arising in everyday life, society, and the workplace; (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution; Focus is on application (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; ● Students should assess which tool to apply rather than trying only one or all (E) create and use representations to organize, record, and communicate mathematical ideas; ● Students should evaluate the effectiveness of representations to ensure they are communicating mathematical ideas clearly Students are expected to use appropriate mathematical vocabulary and phrasing when communicating ideas (F) analyze mathematical relationships to connect and communicate mathematical ideas; and ● Students are expected to form conjectures based on patterns or sets of examples and non-examples (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication ● Precise mathematical language is expected. (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; Geometry Unit 5 Updated November 19, 2015 ● Page 2 of 7 Knowledge and Skills with Student Expectations District Specificity/ Examples G.9 Similarity, Proof, and Trigonometry. The student uses the process skills to understand and apply relationships in right triangles. G.9(A) The student is expected to determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems; G.9A Teacher should: • Show how to set up a trig ratio • Explain vocabulary hypotenuse, opposite & adjacent • How to solve with the calculator • Explain inverse calculation for angles (on calculator) Students should be able to: • correctly identify the hypotenuse, adjacent and opposite sides of a triangle in relation to a given angle. • Use inverse operations to calculate a missing angle of a right triangle given two sides. Vocabulary ● ● ● ● ● ● ● ● ● ● ● ● ● 30-60-90 triangle 45-45-90 triangle adjacent side cosine ratio hypotenuse opposite side Pythagorean Theorem Pythagorean Triples right triangle sine ratio special right triangle tangent ratio trigonometric ratios Suggested Resources Resources listed and categorized to indicate suggested uses. Any additional resources must be aligned with the TEKS. Resources: HMH Geometry Unit 5 A&M Consolidated Fall 03-04 Unit 07 - Right Triangles Kagan Geometry Redbook Geometry Section 4 Web Resources Khan Academy - Basic Trigonometry Setting up the Trig Ratios - Kuta Example Problems—See next page Evaluating Trig Ratios - Kuta Finding the Missing Side Finding the Missing Angle Sin, Cos, Tan Practice Geometry Unit 5 Updated November 19, 2015 Special Right Triangles Page 3 of 7 Khan Academy - Special Right Triangles Special Right Triangle Word Problems Khan Academy - Pythagorean Theorem Practice with Pythagorean Theorem Example Word Problems A new rope must be ordered for the flagpole in front of the school. Before ordering the rope, the height of the pole must be determined. It is observed that the flagpole casts a shadow 10.5 meters long when the sun is at an angle of elevation of 33 degrees. How tall is the flagpole? A cat is trapped on a tree branch 18.5 feet above the ground. The ladder is only 20 feet long. If you place the ladder’s tip on the branch, what angle must the ladder make with the ground? Misconceptions: When to use the sine, cosine, and tangent keys versus the inverse keys. (Only use the inverse key if solving for an angle.) Geometry Unit 5 Updated November 19, 2015 Page 4 of 7 G.9(B) The student is expected to apply the relationships in special right triangles 30°- 60°- 90° and 45°45°- 90°and the Pythagorean theorem, including Pythagorean triples, to solve problems. G.9B Teacher should show: How to identify the sides of a special right triangle • Show how 30-60-90 is an equilateral cut in half • Derive side lengths of 30-60-90 & 45-45-90 using basic triangle starting with one as a side length • Use that triangle to create relationships • x; x; x√2 x; 2x; x√3 simplify the radical and rationalize the denominator How to use pythagorean triples and their multiples • -Focus on identifying triples such as 3,4,5 & 5, 12, 13 (as well as dilations) Also show 7, 24, 25 & 8, 15, 17 Students should: • Have previous knowledge of simplifying radicals, multiplying/dividing radicals and rationalizing denominators. • Use ratios, special relationships, Pythagorean theorem to solve for missing sides • Complete multi step problems for area and perimeter • Know the difference between the two types of special right triangles and their relationships • Investigate to find the ratios of SRT’s • Have previous knowledge of how to solve Pythagorean Theorem problems Geometry Unit 5 Updated November 19, 2015 Page 5 of 7 Misconception: Students should know that if given two congruent sides with included 90 degree angle, then it is a 45-4590. Simplifying radicals & rationalize denominator Examples How to Solve Missing Sides Geometry Unit 5 Updated November 19, 2015 Page 6 of 7 Example Problems The perimeter of a square is 36. What is the length of a side of the square? The length of the diagonal? Geometry Unit 5 Updated November 19, 2015 Page 7 of 7