![Secondary Lesson Plan Template
Lesson Duration: 44 mins Lesson Number: 3 of 3
Subject / Content area: Algebra 2 Grade Level: 11th
grade
Learning Segment: Trigonometric Functions and Right Triangles
Lesson Title: The Six Trigonometric Functions
Central Focus for the Learning Segment:
Students will be able to apply trigonometric functions to find side lengths and angle measures of
right triangles in theoretical and world problems.
Content Standard(s) (List the number and text of the standard. If only a portion of a standard is
being addressed, then only list the relevant part[s].):
CCSS.MATH.CONTENT.HSG.SRT.C.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
CCSS.MATH.CONTENT.HSF.TF.B.7
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate
the solutions using technology, and interpret them in terms of the context.*
CCSS.MATH.PRACTICE.MP6 - Attend to precision.
Mathematically proficient students try to communicate precisely to others. They try to use clear
definitions in discussion with others and in their own reasoning. They state the meaning of the
symbols they choose, including using the equal sign consistently and appropriately.
Learning Objectives associated with the content standards:
Students will be able to:
1. Use the definition of angles of elevation/depression to solve right triangle problems
2. Construct and integrate several different strategies to solve a mathematical word problem
using trigonometric functions and right triangles.
3. Explain how to find and use the different trigonometric functions for right triangle problems
Student Assessments (Assessments should vary in kind and purpose):
Assessments:
Students ability to use the definition of angles of elevation/depression to solve right triangle
problems will be assessed by:
Whiteboard Review: This will serve as a formative assessment during class.
Balaam’s Donkey: This will serve as a summative assessment
Analyze the Error: This will serve as an informal assessment
To Be Continued: This will serve as a summative assessment
Students ability to construct and integrate several different strategies to solve a mathematical word
problem using trigonometric functions and right triangles will be assessed by:
Whiteboard Review
Balaam’s Donkey
To Be Continued
Students ability to explain how to find and use the different trigonometric functions for a right triangle
problems will be assessed by:
Whiteboard Review
Animation Investigation
Analyze the Error
To Be Continued
Modifications to the Assessments:
Student groups will intentionally be given Animation Investigation problems of varying difficulty.
Instructional Resources and Materials to engage all learners:
Pens & pencils, worksheet/graphic organizer, document camera, Smartboard, paper, SMART
Notebook and board, masking tape, notecards
Student Cultural Background and Experience (including those outside of school)
Considerations (Identify how knowledge of students informed instructional planning):](https://image.slidesharecdn.com/lesson3-200429231112/85/Balaam-Trigonometry-1-320.jpg)
![Differentiation and Planned Universal Supports (Supports are listed below and described in the
Planning Commentary. Supports given with specific attention to groups within the class and
individuals[IEPs, 504s, ELL, achievement gaps, gifted/talented] i.e. Whole class, groups within the
class, specific needs of individuals):
Before Learning Whiteboard Review
During Learning Angles of Elevation/Depression graphic organizer,
Balaam’s Donkey worksheet
After Learning Analyze the Error worksheet
To Be Continued take home quiz
Academic Language (Specifically address how these language demands and supports are used in
respect to the language function):
Language Function:
The language function is “explain.” Students will be able to explain how to find and use the different
trigonometric functions for a right triangle” (Learning Objective 2)
Language Demands of the Lesson (vocabulary, syntax, discourse) :
o The vocabulary terms that are review consist of: hypotenuse, right triangle, vertex, and the
Pythagorean Theorem.
The vocabulary terms that are unfamiliar to students are sine, cosine, tangent, cotangent,
cosecant, and secant.
The vocabulary terms that may have been encountered by students before but need review
are opposite side to angle theta and adjacent side to angle theta.
In addition, the symbols associated with the language function are: θ representing the
unknown measure of an acute angle in the right triangle.
o The syntax demand of this language function would be how the students describe the
Pythagorean Theorem. This includes the organization of the symbols and abbreviation that
represent each of the sides of the triangle, and how they relate to one another.
o The discourse demand of this language function would be how the students represent the
different trigonometric functions and sides of a right triangle. This could include labeling the
opposite and adjacent sides of triangle with respect to angle θ. It could also include the form
of an equation with trigonometric function, written like sin θ =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
. With an equation such
this, the opposite and adjacent sides could also be abbreviated as opp and adj, or simply O
and A respectively. Another discourse demand of this language function would be how the
students represent the Pythagorean Theorem. This could be in the form of an equation
a2
+b2
=c2
or by labeling the sides and hypotenuse of a right triangle.
Language Supports
The following will support students in meeting the academic language demands of the lesson and
accomplish the language function:
o Angles of Elevation/Depression
o Balaam’s Donkey
Instructional Procedure: (These must connect to the central focus of the learning segment and
learning objectives while meeting the needs of students):
Prior Knowledge Activation:
Whiteboard Review (5 mins)
1. Walk through a warm-up problem as a class.
2. It will involve using the inverse trig. function
3. After the class has walked through it, instruct them to take out their basketball worksheets
from yesterday
Learning Task(s)/Learning Activity(ies):
Angles of Elevation/Depression (10 mins)
1. Instruct students to turn their handout to the back side](https://image.slidesharecdn.com/lesson3-200429231112/85/Balaam-Trigonometry-2-320.jpg)
Balaam & Trigonometry
- 1. Secondary Lesson Plan Template Lesson Duration: 44 mins Lesson Number: 3 of 3 Subject / Content area: Algebra 2 Grade Level: 11th grade Learning Segment: Trigonometric Functions and Right Triangles Lesson Title: The Six Trigonometric Functions Central Focus for the Learning Segment: Students will be able to apply trigonometric functions to find side lengths and angle measures of right triangles in theoretical and world problems. Content Standard(s) (List the number and text of the standard. If only a portion of a standard is being addressed, then only list the relevant part[s].): CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. CCSS.MATH.CONTENT.HSF.TF.B.7 (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.* CCSS.MATH.PRACTICE.MP6 - Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. Learning Objectives associated with the content standards: Students will be able to: 1. Use the definition of angles of elevation/depression to solve right triangle problems 2. Construct and integrate several different strategies to solve a mathematical word problem using trigonometric functions and right triangles. 3. Explain how to find and use the different trigonometric functions for right triangle problems Student Assessments (Assessments should vary in kind and purpose): Assessments: Students ability to use the definition of angles of elevation/depression to solve right triangle problems will be assessed by: Whiteboard Review: This will serve as a formative assessment during class. Balaam’s Donkey: This will serve as a summative assessment Analyze the Error: This will serve as an informal assessment To Be Continued: This will serve as a summative assessment Students ability to construct and integrate several different strategies to solve a mathematical word problem using trigonometric functions and right triangles will be assessed by: Whiteboard Review Balaam’s Donkey To Be Continued Students ability to explain how to find and use the different trigonometric functions for a right triangle problems will be assessed by: Whiteboard Review Animation Investigation Analyze the Error To Be Continued Modifications to the Assessments: Student groups will intentionally be given Animation Investigation problems of varying difficulty. Instructional Resources and Materials to engage all learners: Pens & pencils, worksheet/graphic organizer, document camera, Smartboard, paper, SMART Notebook and board, masking tape, notecards Student Cultural Background and Experience (including those outside of school) Considerations (Identify how knowledge of students informed instructional planning):
- 2. Differentiation and Planned Universal Supports (Supports are listed below and described in the Planning Commentary. Supports given with specific attention to groups within the class and individuals[IEPs, 504s, ELL, achievement gaps, gifted/talented] i.e. Whole class, groups within the class, specific needs of individuals): Before Learning Whiteboard Review During Learning Angles of Elevation/Depression graphic organizer, Balaam’s Donkey worksheet After Learning Analyze the Error worksheet To Be Continued take home quiz Academic Language (Specifically address how these language demands and supports are used in respect to the language function): Language Function: The language function is “explain.” Students will be able to explain how to find and use the different trigonometric functions for a right triangle” (Learning Objective 2) Language Demands of the Lesson (vocabulary, syntax, discourse) : o The vocabulary terms that are review consist of: hypotenuse, right triangle, vertex, and the Pythagorean Theorem. The vocabulary terms that are unfamiliar to students are sine, cosine, tangent, cotangent, cosecant, and secant. The vocabulary terms that may have been encountered by students before but need review are opposite side to angle theta and adjacent side to angle theta. In addition, the symbols associated with the language function are: θ representing the unknown measure of an acute angle in the right triangle. o The syntax demand of this language function would be how the students describe the Pythagorean Theorem. This includes the organization of the symbols and abbreviation that represent each of the sides of the triangle, and how they relate to one another. o The discourse demand of this language function would be how the students represent the different trigonometric functions and sides of a right triangle. This could include labeling the opposite and adjacent sides of triangle with respect to angle θ. It could also include the form of an equation with trigonometric function, written like sin θ = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 . With an equation such this, the opposite and adjacent sides could also be abbreviated as opp and adj, or simply O and A respectively. Another discourse demand of this language function would be how the students represent the Pythagorean Theorem. This could be in the form of an equation a2 +b2 =c2 or by labeling the sides and hypotenuse of a right triangle. Language Supports The following will support students in meeting the academic language demands of the lesson and accomplish the language function: o Angles of Elevation/Depression o Balaam’s Donkey Instructional Procedure: (These must connect to the central focus of the learning segment and learning objectives while meeting the needs of students): Prior Knowledge Activation: Whiteboard Review (5 mins) 1. Walk through a warm-up problem as a class. 2. It will involve using the inverse trig. function 3. After the class has walked through it, instruct them to take out their basketball worksheets from yesterday Learning Task(s)/Learning Activity(ies): Angles of Elevation/Depression (10 mins) 1. Instruct students to turn their handout to the back side
- 3. 2. Tell students we want to define the terms angle of elevation and angle of depression 3. Tell students to think of words that remind them of elevation and depressions 4. Define it mathematically as a class, and then find one of the angles of elevation/depression in the problem 5. Then have students work on the bottom half of the page for a couple of minutes 6. Circulate throughout the room to make sure students are understanding the material. 7. If all groups are understanding, then go on to the next activity 8. If a third or more of students are confused, stop the class and walk through the questions together Balaam’s Donkey – Trig. Problem (20-25 mins) 1. Explain that we will be bringing together everything we’ve learned this week 2. Hand each student the first worksheet with the account of Balaam and the map 3. Pick a volunteer to be Balaam and another volunteer to be the angel. 4. There will be tape on the floor marking Balaam’s travel route. 5. Explain that our goal is to figure out the distance from the angel to Balaam’s starting point 6. Have students take turns reading the story of Balaam on their sheet. 7. While the students are reading aloud the story, walk the Balaam volunteer along the travel route. 8. Then tell student there are notecards on their desks that corresponds to measurements in the story 9. They need to figure out where to put the measurements on our larger version of the travel route on the classroom floor. 10. Then have them fill out their corresponding individual travel routes with the info. From the floor 11. If students have made an error in placing the measurements on the map, bring the class together and tell them that # of measurements are misplaced. Can you spot the incorrect angle or side measure? 12. Next hand students a worksheet of question that correspond to the activity. 13. Tell them they must complete these in their groups and hand for a grade 14. Circulate throughout the room to make sure students are understanding the concepts 15. If there is a major misconception/error, bring the class together and address it 16. Also, if there are any really good student questions/insights, bring the class together and have the student explain her/his question or insight to the class 17. Talk through the answers as a class. Make sure to have students explain their reasoning using the vocabulary words 18. If students have not completed the activity before the last 5 minutes of class, they will have to complete the rest for homework. 19. If students complete the activity early, ask them to explain their reasoning on the last question. Then let them begin the Homework Quiz Closure to Lesson: Analyze the Error (5 mins) 1. Hand each student a half-sheet for this activity To Be Continued 1. Give each student a To Be Continued Worksheet 2. This will be there homework for the weekend to be finished by Monday Relevant Theories and/or Research Best Practices: (Identify how these theories and research served as a foundation for instructional choices within your lesson) (Dickmann and Stanford-Blair 2009); (Marzano 2009); (Zweirs 2014); (Tsuei 2012), (Posamentier, Germain-Williams, Jaye 2013); (Smith and Stein 2011); (Boaler 2012); (Boaler 2015).
- 4. Trigonometry & Balaam’s Donkey - Numbers 22:21-29 (Queen Hahn’s Math International Version) A. “Balaam got up in the morning, saddled his donkey and went with the Moabite officials. But God was very angry when he went, and the angel of the LORD stood directly north of Balaam in the road to oppose him. B. Balaam was riding on his donkey... When the donkey and Balaam travelled 40 feet north, the donkey saw the angel of the LORD standing in the road with a drawn sword in his hand… C. The donkey turned off the road going 90 ft. northeast into a field. D. Balaam beat it to get it back on the road…and they moved directly west 62 ft. back towards the road. E. As soon as they were back in the road, the donkey saw the angel of the LORD. It took off Northwest at a 67 o angle of elevation and then ran into a wall, crushing Balaam’s foot against it. F. So Balaam beat the donkey again and it travelled 35 ft. back into the road. G. Then the angel of the LORD stood in a narrow place due north and Balaam and the donkey travelled north 70 ft. towards it. H. When the donkey saw the angel of the LORD again, it lay down under Balaam, and he was angry and beat it with his staff. The donkey was 15 ft. away from the angel. (G.)Balaam’s journey ended here (A.)Balaam’sjourney started here
- 6. Balaam’s Donkey Goal: By the end of this activity, we will answer… HOW FAR AWAY WAS THE ANGLE FROM BALAAM WHEN HE STARTED HIS JOURNEY? 1. Look back in the story. Circle all degree measurements given, and underline all distance measurements given. 2. Label the given measurements from Balaam’s route on the attached page. (Hint: See the floor for help) Parts A-D 3. What is the definition of an angle of elevation? (in your own words or from worksheet yesterday) 4. What type of angle is angle Ѳ ? Angle of ________________ 5. Which trig. function can we use to solve for angle theta Ѳ with the info. given? ___________ or ___________ 6. Solve for angle Ѳ below. (Show at least one thinking step) 7. How did we solve for angle Ѳ ? By using an _________________ trigonometric function 8. Solve for distance X below to the nearest foot (Show at least one thinking step) 9. Did you use angle Ѳ when solving for distance X? ____ 10. How did you solve for distance X ? (Explain using vocab words: hypotenuse, opposite, adjacent, angle Ѳ)
- 7. Parts E-H 11. How can we find angle Beta β? 12. What is the measure of angle beta β ? _________ 13. Which trig. function can we use to solve for distance Y with the info. given? ___________ or _______________ 14. Below solve for angle the distance Y to the nearest foot. (Show at thinking step) GOAL: HOW FAR AWAY WAS THE ANGLE FROM BALAAM WHEN HE STARTED HIS JOURNEY? 15. How did you find that distance?