Download NJDOE MODEL CURRICULUM PROJECT CONTENT AREA

NJDOE MODEL CURRICULUM PROJECT
CONTENT AREA: Mathematics
Course:
Geometry
UNIT #: 3
UNIT NAME: Trigonometry
#
STUDENT LEARNING OBJECTIVES
1
Find the point on a directed line segment between two given points that partitions the segment in
a given ratio.
Prove theorems about triangles. *
2
3
4
5
6
7
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in
geometric figures.
Derive the definitions for trigonometric ratios using similarity of right triangles.
Explain and use the relationship between the sine and cosine of complementary angles.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.★
Derive and use the formula for the area of an oblique triangle (A = 1/2 ab sin (C)).
CORRESPONDING
CCSS
G.GPE.6
G.SRT.4
G.SRT.5
G.SRT.6
G.SRT.7
G.SRT.8
G.SRT.9
Prove and apply the Laws of Sines and Cosines to solve problems involving both right and oblique
G.SRT.10, G.SRT.11
triangles.
* G.SRT.4 (Triangles) Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the
Pythagorean Theorem proved using triangle similarity.
Major Content Supporting Content Additional Content (Identified by PARCC Model Content Frameworks).
Bold type indicates grade level fluency requirements. (Identified by PARCC Model Content Frameworks).
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NJDOE MODEL CURRICULUM PROJECT
CONTENT AREA: Mathematics
Course:
Geometry
UNIT #: 3
UNIT NAME: Trigonometry
Selected opportunities for connection to mathematical practices
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.
SLOs 3 Justify solutions to problems involving side lengths and angle measures using triangle congruence and similarity criteria.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
SLO 4 Demonstrate the need for precision when deriving definitions.
7. Look for and make use of structure.
SLO 8 Look for hidden structures to prove and apply the law of Sines and Cosines.
8. Look for and express regularity in repeated reasoning.
*All of the content presented in this course has connections to the standards for mathematical practices.
Code #
Common Core State Standards
G.GPE.6
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
G.SRT.4
G.SRT.5
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally,
and conversely; the Pythagorean Theorem proved using triangle similarity.
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
NJDOE MODEL CURRICULUM PROJECT
CONTENT AREA: Mathematics
G.SRT.6
G.SRT.7
G.SRT.8
G.SRT.9
G.SRT.10
G.SRT.11
Course:
Geometry
UNIT #: 3
UNIT NAME: Trigonometry
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of
trigonometric ratios for acute angles.
Explain and use the relationship between the sine and cosine of complementary angles.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★
(+) 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.
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
(+) 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).
Major Content Supporting Content Additional Content (Identified by PARCC Model Content Frameworks).
Bold type indicates grade level fluency requirements. (Identified by PARCC Model Content Frameworks).