Download Geometry Unit 5 - Cleburne Independent School District

Title
Trigonometry
Suggested Time Frame
4th Six Weeks
10 Days
Guiding Questions
Big Ideas/Enduring Understandings
Module 13
• Trigonometry can be used with right triangles to solve realworld problems.
Geometry
Unit 5
Module 13
• How do you find the tangent ratio for an acute angle?
• How can you use the sine and cosine ratios, and their inverses,
in calculations involving right triangles?
• What do you know about the side lengths and the trigonometric
ratios in special right triangles?
• How can you solve a right triangle?
Vertical Alignment Expectations
TEA Vertical Alignment Chart Grades 5-8, Geometry
Sample Assessment Question
Coming Soon...
The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper
depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the
suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the
district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material. A portion of the District Specificity and
Examples are a product of the Austin Area Math Supervisors TEKS Clarifying Documents available on the Region XI Math website.
Geometry Unit 5
Updated November 19, 2015
Page 1 of 7
Ongoing TEKS
Math Processing Skills
G.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 solution, justifying
the solution, and evaluating the problem-solving process and the
reasonableness of the solution;
Focus is on application
(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;
●
Students should assess which tool to apply rather than trying only one or all
(E) create and use representations to organize, record, and communicate
mathematical ideas;
●
Students should evaluate the effectiveness of representations to ensure they are
communicating mathematical ideas clearly
Students are expected to use appropriate mathematical vocabulary and phrasing
when communicating ideas
(F) analyze mathematical relationships to connect and communicate
mathematical ideas; and
●
Students are expected to form conjectures based on patterns or sets of examples
and non-examples
(G) display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication
●
Precise mathematical language is expected.
(D) communicate mathematical ideas, reasoning, and their implications using
multiple representations, including symbols, diagrams, graphs, and language
as appropriate;
Geometry Unit 5
Updated November 19, 2015
●
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Knowledge and Skills
with Student
Expectations
District Specificity/ Examples
G.9 Similarity, Proof, and
Trigonometry. The
student uses the process
skills to understand and
apply relationships in
right triangles.
G.9(A) The student is
expected to
determine the
lengths of sides and
measures of angles in
a right triangle by
applying the
trigonometric ratios
sine, cosine, and
tangent to solve
problems;
G.9A
Teacher should:
• Show how to set up a trig ratio
• Explain vocabulary hypotenuse, opposite & adjacent
• How to solve with the calculator
• Explain inverse calculation for angles (on calculator)
Students should be able to:
• correctly identify the hypotenuse, adjacent and opposite
sides of a triangle in relation to a given angle.
• Use inverse operations to calculate a missing angle of a
right triangle given two sides.
Vocabulary
●
●
●
●
●
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30-60-90 triangle
45-45-90 triangle
adjacent side
cosine ratio
hypotenuse
opposite side
Pythagorean
Theorem
Pythagorean
Triples
right triangle
sine ratio
special right
triangle
tangent ratio
trigonometric
ratios
Suggested Resources
Resources listed and categorized to indicate
suggested uses. Any additional resources must
be aligned with the TEKS.
Resources:
HMH Geometry
Unit 5
A&M Consolidated Fall 03-04
Unit 07 - Right Triangles
Kagan
Geometry
Redbook Geometry
Section 4
Web Resources
Khan Academy - Basic
Trigonometry
Setting up the Trig Ratios - Kuta
Example Problems—See next page
Evaluating Trig Ratios - Kuta
Finding the Missing Side
Finding the Missing Angle
Sin, Cos, Tan Practice
Geometry Unit 5
Updated November 19, 2015
Special Right Triangles
Page 3 of 7
Khan Academy - Special Right
Triangles
Special Right Triangle Word
Problems
Khan Academy - Pythagorean
Theorem
Practice with Pythagorean
Theorem
Example Word Problems
A new rope must be ordered for the flagpole in front of the
school. Before ordering the rope, the height of the pole must be
determined. It is observed that the flagpole casts a shadow 10.5
meters long when the sun is at an angle of elevation of 33
degrees. How tall is the flagpole?
A cat is trapped on a tree branch 18.5 feet above the ground.
The ladder is only 20 feet long. If you place the ladder’s tip on
the branch, what angle must the ladder make with the ground?
Misconceptions:
When to use the sine, cosine, and tangent keys versus
the inverse keys.
(Only use the inverse key if solving for an angle.)
Geometry Unit 5
Updated November 19, 2015
Page 4 of 7
G.9(B) The student is
expected to apply
the relationships in
special right triangles
30°- 60°- 90° and 45°45°- 90°and the
Pythagorean
theorem, including
Pythagorean triples,
to solve problems.
G.9B
Teacher should show:
How to identify the sides of a special right triangle
• Show how 30-60-90 is an equilateral cut in half
• Derive side lengths of 30-60-90 & 45-45-90 using
basic triangle starting with one as a side length
• Use that triangle to create relationships
•
x; x; x√2
x; 2x; x√3
simplify the radical and rationalize the denominator
How to use pythagorean triples and their multiples
• -Focus on identifying triples such as 3,4,5 & 5, 12,
13 (as well as dilations) Also show 7, 24, 25 & 8, 15,
17
Students should:
• Have previous knowledge of simplifying radicals,
multiplying/dividing radicals and rationalizing
denominators.
• Use ratios, special relationships, Pythagorean
theorem to solve for missing sides
• Complete multi step problems for area and
perimeter
• Know the difference between the two types of
special right triangles and their relationships
• Investigate to find the ratios of SRT’s
• Have previous knowledge of how to solve
Pythagorean Theorem problems
Geometry Unit 5
Updated November 19, 2015
Page 5 of 7
Misconception:
Students should know that if given two congruent
sides with included 90 degree angle, then it is a 45-4590.
Simplifying radicals & rationalize denominator
Examples How to Solve Missing Sides
Geometry Unit 5
Updated November 19, 2015
Page 6 of 7
Example Problems
The perimeter of a square is 36.
What is the length of a side of the square?
The length of the diagonal?
Geometry Unit 5
Updated November 19, 2015
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