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2016.17, Geometry, Quarter 3 The following practice standards will be used throughout the quarter: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Ongoing Standards Note to Teachers: The following ongoing and fluency standards will be practiced all year long and embedded into your instruction instead of being taught in isolation. G.WCE.1 I can use correct notation to describe and name all geometric figures. G.WCE.2 Correctly interprets geometric diagrams and determines what can and cannot be assumed. G.WCE.3 I can explain the meaning of the symbols in the formulas. G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. *Unless otherwise noted, all resources are from the HMH Geometry 2015 edition. Standards Student Friendly “I Can” Statements Unit 5 Trigonometry G.SRT.6 Understand that by similarity, side ratios in right I can use properties of similar right triangles to form the definitions of triangles are properties of the angles in the triangle, leading to trigonometric ratios for acute angles. definitions of trigonometric ratios for acute angles. Page 1 of 4 G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. I can calculate sine and cosine ratios for acute angles in a right triangle when two side lengths are given. I can explain and use the relationship between the sine of an acute angle and the cosine of its complement. G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. I can use the Pythagorean Theorem to solve for unknown side length of a right triangle. I can draw right triangles that describe real world problems and label the sides and angles with their given measures. WCE.G.16 Apply the geometric mean to right triangles. WCE.G.17 Prove the Pythagorean Theorem using triangle similarity WCE.G.18 Make use of the converse of the Pythagorean Theorem, Pythagorean triples and special right triangles and use them to solve problems. I can solve application problems involving right triangles, including angle of elevation and depression, navigation and surveying, using the Pythagorean Theorem and trigonometry. I can use the geometric mean to find parts of a right triangle with an altitude drawn to the hypotenuse. I can prove the Pythagorean Theorem using triangle similarity. I can use the converse of the Pythagorean Theorem to determine if a triangle is acute, obtuse, or right. I can list the common Pythagorean triples. I can solve right triangles including special right triangles (such as 30-60-90 and 45-45-90) by finding the measures of all sides and angles in the triangles. Unit 7- Measurement and Modeling in Two and Three Dimensions G.GMD.1 Give an informal argument for the formulas for the I can define 𝜋 as the ratio of a circle’s circumference to its diameter. circumference of a circle, area of a circle, volume of a cylinder, I can use algebra to demonstrate that because 𝜋 is the ratio of a circle’s pyramid, and cone. Use dissection arguments, Cavalieri’s circumference to its diameter that the formula for a circle’s circumference principle, and informal limit arguments. must be C = 𝜋 ∙ d. Page 2 of 4 G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. I can develop formulas to calculate the volumes of 3-D figures including spheres, cones, prisms, and pyramids. WCE.G.21 Use the similarity ratio between two solids to find the volume. I can use the similarity ratio between two solids to find the volume. G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). I can use geometric shapes, their measures and their properties to describe objects. G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). I can apply the concept of density when referring to situations involving area and volume. G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). I can apply geometric methods to solve design problems. WCE.G. 8 Find the lateral area and surface area of threedimensional figures. I can find the surface area of prisms, cylinders, pyramids, spheres and cones. I can describe the difference between lateral and surface area. Honors Addendum Note for Teachers of Honors: Do not teach this Honors Addendum at the end of the quarter. Embed the Honors Addendum within the regular Scope & Sequence. G.SRT.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. I can derive the formula, A = ½ absin(C), for the area of a triangle. I can calculate the area of a triangle using the formula A=1/2absin(C) Page 3 of 4 G.SRT.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems. I can derive the Law of Sines. I can use the Law of Sines to solve real world problems. I can derive the Law of Cosines. G.SRT.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). I can use the Law of Cosines to solve real world problems. I can distinguish between situations that require the Law of Sines or the Law of Cosines. I can represent real world problems with diagrams of right and non-right triangles and use them to solve for unknown side lengths and angle measures. Page 4 of 4