NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE. SUBJECT: Math Trigonometry TIMELINE: 4 th quarter

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1 Expressing Geometric Properties with Equations:Translate between the geometric description and the equation for a conic section Standards: G-GPE.1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. I can complete the square to find the center and radius of a circle given by an equation.m I can derive the equation of a circle given center and radius applying the Pythagorean Theorem. M Practices] Section 4.5 Complete the Square Center Radius Expressing Geometric Properties with Equations:Translate between the geometric description and the equation for a conic section Niobrara County School District #1, Fall 2012 Page 1

2 Standards: G-GPE.2. Derive the equation of a parabola given a focus and directrix. I can derive the equation of a parabola given a focus and directrix. M Practices] Section 4.5 Focus Directrix Expressing Geometric Properties with Equations:Translate between the geometric description and the equation for a conic section Standards: G-GPE.3. Derive the equations of ellipses and hyperbola given the foci, using the fact that the sum or difference of distances from the foci is constant. I can derive the equations of ellipses and hyperbola given the foci, using the fact that the sum or differences of distances from the foci is constant. M Sythesis Section 4.5 Ellipses Hyperbola Foci Expressing Geometric Properties with Equations: Apply Niobrara County School District #1, Fall 2012 Page 2

3 trigonometry to general triangles. Standards: 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 = 1/2 ab sin(c) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.m Practices] Section 6.3, 6.4 & 6.7 A = 1/2 ab sin(c) Auxiliary Line Vertex Perpendicular Expressing Geometric Properties with Equations: Apply trigonometry to general triangles. Standards: G-SRT.10. Prove the Laws of Sine and Cosines and use them to solve problems. I can prove the Laws of Sine and Cosines and apply them to solve problems.m Chapter 4 Law of Sine Law of Cosine Test (Textbook Assessment s Test 16 Form B) Expressing Geometric Properties with Equations: Apply trigonometry to general triangles. Standards: G-SRT.11. Understand I can apply the Law of Sines Applications Law of Sine Law of Cosine Niobrara County School District #1, Fall 2012 Page 3

4 and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non right triangles. and Law of Cosines to find unknown measurements in right and non-right triangles. M Practices] Chapter 4 Vector and Matrix Quantities: Represent and model with vector quantities. Standards: N-VM.1. Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes. Vector and Matrix Quantities: Represent and model with vector quantities. I recognize that vector quanities have both magnitude and direction and can represent them by directed line segements and appropriate applying symbols for vectors and their magnitudes. M Application Application --Section 6-6 Vector Quantities Magnitude Direction Directed Line Segments Vector Symbols Vector Components Initial Point Niobrara County School District #1, Fall 2012 Page 4

5 Standards: N-VM.2. Find the components of a vector by subtracting the coordinates of initial point from the coordinates of a terminal point. I can determine vector components by subtracting the coordinates of initial point from the coordinates of a terminal point. M Practices] --Section 10-2 NCTM Illuminations Vector Investigation Activity-- Move the boat around the water by changing the magnitude and direction of the boat's speed (blue vector) or the magnitude and direction of the water current (red vector). Try to land the boat on the island but be careful not to hit the walls! g/activitydetail.aspx?id=4 2 Terminial Point Vector and Matrix Quantities: Represent and model with vector quantities. Standards: N-VM.3.Solve problems involving velocity and other quantities that can be represented by vectors. I can solve problems involving velocity and other quantities that can be represented by vectors.m Velocity Niobrara County School District #1, Fall 2012 Page 5

6 Practices] Vector and Matrix Quantities: Standards: N-VM.4a. Add and subtract vectors. a) Add vectors endto-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. I can add and subtract vectors end-to-end, component-wise, and by the parallelogram rule. M I can demonstrate that the maginitude of a sum of two vectors is typically not the sum of the magnitudes. M Applications End-to-End Component- Wise Parallelogram Rule Vector and Matrix Quantities: Standards: N-VM.4b. Add and subtract vectors. b) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. Given two vectors in magnitude and direction form, I can determine the magnitude and direction of their sum. M Analysis Niobrara County School District #1, Fall 2012 Page 6

7 Practices] Vector and Matrix Quantities: Standards: N-VM.4c. Add and subtract vectors. c) Understand vector subtraction v w as v + ( w), where w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. I can apply properties of vector subtraction and can represent vector subtraction graphically. M Comprehension Vector and Matrix Quantities: Standards: N-VM.5a. Multiply a vector by a scalar. a)represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar mulitiplication component-wise. I can multiply a vector by a scalar and then represent the product graphically and possibly reversing their direction. M I can perform scalar Application Vector Scalar Component- Wise Niobrara County School District #1, Fall 2012 Page 7

8 N-VM. Vector and Matrix Quantities: Standards: N-VM.5b. Compute the magnitude of a scalar multiple cv using cv = c v. Compute the direction of cv knowing that when c v 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). multiplication componentwise. M I can compute the magnitude and direction of scalar multiplication. M Evaluation Practices] Niobrara County School District #1, Fall 2012 Page 8