Download GEOMETRY E08

GEOMETRY
(SECONDARY)
ESSENTIAL UNIT 8 (E08)
(Trigonometry)
(July 2013)
Unit Statement: In this unit the concept of similarity is extended to right triangles.
Trigonometric ratios are developed and applied. Also the method for calculating areas of
polygons is presented with the addition of vectors and geometric probability.
Essential Outcomes: (must be assessed for mastery)
Problem solving and higher order thinking components are essential for A level mastery.
Each outcome can contain problem solving and higher order thinking components (as
found in suggested text).
1. The Student Will use geometric mean and similarity to find segment lengths and
solve problems in right triangles (8.1 pp 534 - 539).
2. TSW use the sine, cosine, and tangent ratios to find side lengths in right triangles
(8.2 pp.541 - 548).
3. TSW use trigonometric ratios to find angles measures in right triangles (8.3 pp.
552 - 559).
4. TSW solve problems involving angles of elevation and angles of depression (8.4
pp. 562 - 567).
5. TSW use the Law of Sines and the Law of Cosines to solve triangles (8.5 pp. 569 576).
6. TSW find the direction and magnitude of vectors and use vector addition to solve
problems (8.6 pp. 577 - 585).
Introduced and Practiced Outcomes: (taught not assessed)
1. The Student Will make a clinometer to find indirect measurements using
trigonometry (8.4 p. 568).
Key Terms and Concepts:
angle of depression
equal vectors
geometric mean
sine
angle of elevation
cosine
equal vectors
tangent
component form
magnitude
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QSI GEOMETRY SEC E08
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parallel vectors
vector
resultant vector
direction
Suggested Assessment Tools and Strategies:
Attached Rubric or teacher generated rubric that assesses ALL essential outcomes
(TSWs).
Suggested Resources:
Holt McDougal Geometry, Chapter 8, Sections 1 - 6.
Holt McDougal Geometry, Problem Solving Workbook
Holt McDougal Geometry, Practice Worksheets
Holt McDougal Geometry, Reading Strategies
Holt McDougal Geometry, Reteach Worksheets
Holt McDougal Geometry, Challenge Worksheets
Holt McDougal Geometry, Assessment Resources
Technology Links:
Holt McDougal Geometry, Online Edition, 6-year subscription
Holt McDougal Geometry, Interactive Answers and Solutions CD-ROM
Holt McDougal Geometry, Lesson Tutorial Videos DVD-ROM
Holt McDougal Geometry, Teacher One-Stop DVD
On Core Mathematics Deluxe Eamview Grades 6-12 CD-ROM
On Core Mathematics High School Activity Generator CD-ROM
Follett Destiny WebPath Express (found on school’s automated library system)
Tenmarks www.tenmarks.com/
Khan Academy https://www.khanacademy.org/
PhET Simulations http://phet.colorado.edu/en/simulations/category/math
EVALUATION RUBRIC FOUND ON FOLLOWING PAGE…………
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QSI GEOMETRY SEC E08
Copyright © 1988-2013
UNIT EVALUATION RUBRIC


Geometry
Essential Unit 8 (E08)
To receive a ‘B’, the student must show ‘B’ level mastery on all six TSW’s.
To receive an ‘A’, the student must show ‘A’ level mastery in at least 4 of the 6
available TSW’s and ‘B’ level mastery on all of the remaining TSW’s.
TSW
1- use geometric mean
and similarity to find
segment lengths and
solve problems in
right triangles.
‘A’ LEVEL
The student is able to
apply the geometric mean
when completing a proof.
‘B’ LEVEL
The student is able to use
geometric mean and
similarity to find segment
lengths and solve
problems in right
triangles.
2- use the sine, cosine,
and tangent ratios to
find side lengths in
right triangles.
The student can prove
basic trigonometric
identities using the sine,
cosine, and tangent ratios.
The student is able to use
the sine, cosine, and
tangent ratios to find side
lengths in right triangles.
3- use trigonometric
ratios to find angles
measures in right
triangles.
The students can analyze
trigonometric functions
(ex. sin 235° and sin 240°)
to determine which is
greater without the use of
a calculator.
The student is able to use
trigonometric ratios to
find angles measures in
right triangles.
4- solve problems
involving angles of
elevation and angles
of depression.
The student is able to find
the height of an object
given two different angles
of elevations from two
different vantage points.
The student can solve
problems involving angles
of elevation and angles of
depression.
5- use the Law of Sines
and the Law of
Cosines to solve
triangles.
The student is able to use
the Law of Sines and the
Law of Cosines to solve
complex, multiple-step
story problems.
The student is able to use
the Law of Sines and the
Law of Cosines to solve
triangles.
6. find the direction and
magnitude of vectors
and use vector
addition to solve
problems.
The student is able to
draw and assess vector
story problems involving
airplane velocity and
changing crosswind
velocities.
The student can find the
direction and magnitude
of vectors and use vector
addition to solve
problems.
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QSI GEOMETRY SEC E08
Copyright © 1988-2013
Notes