Mathematics Curriculum Document for Pre-Calculus Curriculum

Mathematics
Curriculum Document for Pre-Calculus
Unit Title: Vectors
Six Weeks: 5th
Time Frame: 5 blocks
Unit Number: 8
Curriculum
Enduring Understandings (Big Ideas):
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Mathematics is a universal language that allows us to
communicate in a precise and effective manner.
Real-world phenomena can be modeled mathematically in
multiple ways.
The student will know:
• Vectors have both direction and magnitude
• Definition of a vector in standard position with respect to a
coordinate plane
The student will be able to:
• Use vectors to model situations involving magnitude and
direction
• Represent the addition of vectors geometrically and
symbolically
• Represent the multiplication of a vector by a scalar
geometrically and symbolically
• Find the magnitude of vector quantities
• Compose vectors from right angle components
• Decompose vectors into right angle components
• Find and apply unit vectors
• Find the dot product (scalar product) of two vectors
• Find the direction angle of a vector
• Find the angle between two vectors
• Test whether vectors are orthogonal
• Solve speed and direction problems using vectors
• Solve mathematical and real-world problems involving vectors
using the Law of Sines, Law of Cosines, and right triangle trig
• Find trig form of complex numbers (EXTENSION)
Unit Title: Vectors
Unit Number 8
Revised Summer 2013
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Mathematics
Curriculum Document for Pre-Calculus
Essential Questions:
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Why is it important to model real-world phenomena mathematically in multiple ways?
In what ways does the language of mathematics allow us to simplify problem solving?
How do the various topics of mathematics interact?
Student Understanding (student friendly TEKS):
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I can use trigonometry to solve vector problems. (taken from PC.4.E and PC.4.F)
I can apply the Law of Sines and the Law of Cosines to solve vector problems. (taken from PC.4.G and PC.4.H)
I can use vectors to solve problems involving magnitude and direction. (taken from PC.4.I)
I can perform operations with vectors both algebraically and geometrically to solve problems. (taken from PC.4.J and PC.4.K)
I can apply math in everyday life. (taken from PC.1.A)
I can develop a problem solving model and justify my solutions. (taken from PC.1.B)
I can select appropriate tools and techniques to solve problems. (taken from PC.1.C)
I can communicate using appropriate mathematical language. (taken from PC.1.D)
I can use various representations to communicate mathematical concepts. (taken from PC.1.E)
I can analyze relationships to connect and communicate mathematical ideas. (taken from PC.1.F)
I can use precise mathematical language in both written and oral communication. (taken from PC.1.G)
TEKS:
(PC.4) Number and measure. The student uses process standards in mathematics to apply appropriate techniques, tools, and formulas to
calculate measures in mathematical and real-world problems. The student is expected to:
(E) determine the value of trigonometric ratios of angles and solve problems involving trigonometric ratios in mathematical
and real-world problems;
(F) use trigonometry in mathematical and real-world problems, including directional bearing;
(G) use the Law of Sines in mathematical and real-world problems;
(H) use the Law of Cosines in mathematical and real-world problems;
(I) use vectors to model situations involving magnitude and direction;
(J) represent the addition of vectors and the multiplication of a vector by a scalar geometrically and symbolically; and
(K) apply vector addition and multiplication of a vector by a scalar in mathematical and real-world problems.
(PC.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
Unit Title: Vectors
Unit Number 8
Revised Summer 2013
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Mathematics
Curriculum Document for Pre-Calculus
solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
(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.
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols,
diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral
communication.
Targeted College Readiness Standards:
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IA1-2, IB1, IC1, IIA1, IIB1, IID1, IIIA3, VIIIA1-5, VIIIB1-2, VIIIC2, IXA1-3, XB1-2
Targeted ELPs:
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1A, 1C, 1D, 1E, 1F, 1H, 2C, 2D, 2E, 2G, 2I, 3D, 3E, 3F, 3G, 3H, 3I, 3J, 4C, 4D, 4F, 4G
Academic Vocabulary:
• Vector
• Scalar
• Magnitude
Unit Title: Vectors
Language of Instruction:
Directed distance
Resultant vector
Unit vector
Component vector
Decomposition
Composition
Modulus
Orthogonal
Normal
Perpendicular
Dot product
Parallelogram
Linear combination form
Trigonometric form of complex numbers
Unit Number 8
Revised Summer 2013
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Mathematics
Curriculum Document for Pre-Calculus
Instruction
Instructional Resources:
Textbook:
Chapter 6.3-6.5
(will need to use additional resources for navigation problems)
Technology:
Career Connections/Real Life Application:
Exemplar Lessons:
Research Based Instructional Strategies:
Assessment
Student self-assessment & reflection:
Unit Title: Vectors
Acceptable evidence or artifacts:
Performance Task Unit 8
Unit Number 8
Revised Summer 2013
Page 4 of 4