Grade 11:
Unit: 7 Trigonometry
Approximate Time Frame:
Connections to Previous Learning:
●
●
Students have understanding of trigonometric functions and their inverse.
Students have understanding of the relationship of side lengths of 30-60-90 and 45-45-90 triangles.
Focus of the Unit:
●
●
●
●
●
Students understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
Students can explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers,
interpreted as radian measures of angles traversed counterclockwise around the unit circle.
Students can identify trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Students understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its
inverse to be constructed.
Students can prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ)
and the quadrant of the angle.
1
Grade 11:
Unit: 7 Trigonometry
Connections to Subsequent Learning:
●
●
Students comprehension of the unit circle will be applied in a fourth year math course.
Students understanding of trigonometric functions will be applied in a fourth year math course.
Desired Outcomes
Standard(s):
F.TF.1 - Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
F.TF.2 - Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as
radian measures of angles traversed counterclockwise around the unit circle.
F.TF.5* - Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
F.TF.6 - Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to
be constructed.
F.TF.8 - Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the
quadrant of the angle.
Priority Standards
Supporting Standards
Additional Standards
Transfer: Students will apply…
2
Grade 11:
Unit: 7 Trigonometry
Understandings: Students will understand that…
Essential Questions:
3
Grade 11:
Unit: 7 Trigonometry
Highlighted Mathematical Practices: (Practices to be explicitly emphasized are indicated with an *.)
1. Make sense of problems and persevere in solving them. Students demonstrate their ability to persevere by selecting a modality to
begin representing their understanding (i.e manipulatives, pictures). They can work collaboratively to represent their measurements or
quantities and discuss their representations.
2. Reason abstractly and quantitatively. Students will demonstrate their abstract and quantitative reasoning by estimating lengths
and then refining their estimates based upon new information. They also demonstrate reasoning by explaining indirect
measurements. They need to use measurement units correctly – understanding that the smaller the unit, the more units you need to
measure a given object.
3. Construct viable arguments and critique the reasoning of others. Students will explain why they chose to represent a quantity or
measurement in a particular way. They will also listen to each other and explain what their peers have said.
4. Model with mathematics. In this unit, students are asked to transfer between manipulative, number line, drawings and other visual
representations. They are asked to explain in words how their visuals are representing measurements or quantities.
5. Use appropriate tools strategically. Students demonstrate their ability to use non-standard measurement units to measure lengths of
objects. Hey need to select the correct tools and know when a number line is an appropriate representation.
6. Attend to precision. Students demonstrate precision by using comparison language appropriately to describe their measurements and
quantities. They count precisely to measure accurately.
7. Look for and make use of structure. Students demonstrate the ability to use structure in their graphs, ten frames and on the 120 chart.
Students can use these structures to explain the patterns and answer questions about measurements and quantities.
8. Look for express regularity in repeated reasoning. When students note patterns on, and can use the 10 frames, 120 chart and graphs
to solve problems or create new representations, they are using their repeated reasoning.
4
Grade 11:
Unit: 7 Trigonometry
Prerequisite Skills/Concepts:
Advanced Skills/Concepts:
Students should already be able to…
Some students may be ready to…
5
Grade 11:
Knowledge:
Students will know…
Unit: 7 Trigonometry
Skills:
Students will be able to…
WIDA Standard: English Language Learners
English language learners communicate information, ideas and concepts necessary for academic success in the content area of
Mathematics.
English language learners would benefit from:
6
Grade 11:
Unit: 7 Trigonometry
Academic Vocabulary:
Critical Terms:
Supplemental Terms:
Assessment
Pre-Assessments
Formative Assessments
Summative Assessments
Self-Assessments
7
Grade 11:
Unit: 7 Trigonometry
Sample Lesson
Sequence
8