Long Form Lesson Plan – Real Life Application of Trigonometric Ratios Grade: 9/10 Content Area/Class Title: Accelerated Geometry School/MT: Fountain Valley High/Jane Springer Group Size: 31 Lesson Length: 48 minutes Language Proficiency Level (# of students at each level): Emerging: 0

Expanding: 0

Bridging: 2

RFEP: 14

Student Context: This course is for honor students that were placed here due to their proficient performance in Algebra 1. The majority of the students are motivated and active students of the class. They complete most of their homework and they can persevere in challenging problems. Students with Specific Learning Needs IEP/504 Plans: Number of Students Classifications/Needs N/A N/A Other Learning Needs

Number of Students

Low reading level

2

Supports, Accommodations, Modifications, Pertinent IEP Goals N/A Supports, Accommodations, Modifications Read directions slowly and loudly as the students follow along reading the directions on the hand out All students to read the directions and discuss the directions with a part Make real world and/or relative references to connect the math terms in a given world problem or direction

Practices/Habits of Mind: Make sense of problems and persevere in solving them Use appropriate tools strategically

Model with mathematics

Key Content Standards: G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems Key ELD Standards (if you have English language learners in your class): CCSS.ELA-LITERACY.SL.9-10.6 - Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate Collaborative: 1. Exchanging information and ideas with others through oral collaborative discussions on a range of social and academic topics 2. Interacting with others in written English in various communicative forms

Learning Objective A. Cognitive Task: Students will be able to explore real world scenarios of angles of elevation and depression right outside their classroom by using a hand-made inclinometer and their knowledge of trigonometry ratios to find the distance between two objects that are not on the same level as each other. B. Understanding or Skill to be Enhanced: Students will enhance their understanding of trigonometry ratios by being able to form right triangles using the horizontal line formed with the angle of elevation/depression as well as the line of sight. In forming these right triangles students can model a given scenario to extend their knowledge of trigonometry ratios. C. Transfer Goal: (How will the student use this?): The students will be able to transfer this skill in setting up right triangles to a scenario with angles of elevation/depression to solve for other real world applications. Formative and Summative Assessments: During: Think-Pair-Share during the engage portion to have students guess the angle of elevation and depression of the scenarios that is posed in class. Circulation/Monitoring as students are discussing how to go about solving the scenarios during class. Also, I will circulate and monitors students thinking as they are doing the experiment outside. Thumbs Up, Thumbs Sideways, Thumbs Down to gauge how students are grasping the directions of the outdoor experiment before going outside. Also, this assessment would be use during the closure part of the lesson to see if students understood the meaning behind the experiment. Closure: I will bring the class together after the experiment to have the students explain their calculations and result of the height of the flagpole. I will view the results to see if any are far off from the actual and clear up any misconceptions during this time. Questions at different depths of knowledge: Facts/Memorization Skills/Procedure What is the definition of angle of elevation and angle of depression?

What trigonometry ratio would you need to use to solve for the missing side length?

Conceptual What do the segments of the similar triangle represent in regards to the real world problem in the experiment? What two rays form the angle of elevation/depression for the given scenario?

Application or Relational Knowledge In forming the right triangle for the scenario, what other factors should you consider to find the true height of the object? Would the angle of elevation/depression be greater if the distance between the objects gets shorter? Gets greater?

Prerequisite Skills and Knowledge: How was the standard addressed in previous lessons? In previous lessons, students used similar triangles to measure distances indirectly using the geometric mean proportion. Now, with students’ knowledge of trigonometry, they will use this with angles of elevations and depressions to find the distance between two objects. They will be using their procedural fluency of trigonometry ratios and apply it to real world problems to solidify their mathematical reasoning and problem solving skills.

Describe common mathematical or scientific preconceptions, errors or misunderstandings with your lesson and how you will address them. Some common preconceptions that students might have are that they will not consider the initial height of the angle of elevation when solving for the height of the object. Students will be cleared of this preconception during the beginning part of my lessons as I draw a diagram with the given picture to explain how the angle of elevation starts from the individual’s eyes. Thus, the students need to take in consideration the height of the individual to find the height of a certain object. Lesson Resources/Materials: - Handmade Inclinometer - Experiment Record Sheet - Scientific Calculator - 3 Measuring Tape INSTRUCTIONAL SEQUENCE: ENGAGING STUDENTS IN THE LEARNING PROCESS Introduction: (How will you engage students, connect to prior knowledge and review necessary academic language?) Highlight student discourse strategies in blue. Teacher Student Universal Design for Learning - The teacher will show 2 pictures of - Students will discuss Guideline 3: scenes within the school (flagpole, how with a partner Provide Options for and bowl area). Then, the teacher will how they would solve Comprehension have the students Think-Pair-Share for the height or on how they can find out the distance of the object - Maximize transfer height/distance of the each object in - Students can be and generalization each scene. guided to see that - The teacher will draw a diagram of they can form a right right triangles within the pictures to triangle in this have the students see that they can situation and use apply the right triangles trigonometry trigonometry ratios to ratios to the scenario find the height of the - The teacher will then introduce the objects hand-made inclinometer and how to - Students will practice use it for the students using the inclinometer in class Body of the Lesson: Describe step-by-step what the teacher and the students will be doing during the lesson. Include questions you will use to help make thinking visible, and code questions as to higher level (HL) and lower level (LL). Highlight student discourse strategies in blue. Teacher Student Universal Design for Learning - The teacher will pass out the Record Sheet for - Students will Guideline 5: the experiment and explains how the students work together Provide Options will record their findings within their for Expression and - The teachers will give the breakdown of the groups to solve Communication experiment: each station There will be 2 stations outside of class. - Each students - Students will be Each station will have one of the objects will be using multiple where the students must find the height of assigned a job: tools for it. The distance from each object will be Recorder, construction and marked on the ground with chalk. Measurer, composition There will be 4 groups at each station and Reporter, the groups will be rotated every 10 minutes. Performer - Students will use The students must find the distance from - Students will rulers and the chalk to the base/top of the object using work together calculators during

a measuring tape, estimate the angle of elevation/depression using the inclinometer, and use the trigonometry ratios to solve for the height of the object Students can have two trials of using the inclinometer with two different students so they can have two different heights for the start of the angle and see if the height of the object is still the same. - Once outside the teacher will walk around to check up on each group and ask the following questions to help guide them through the activity: What trigonometry ratio would you need to use to solve for the missing side length? (LL) In forming the right triangle for the scenario, what other factor should you consider to find the true height of the object? (HL)

on the problem once they find their measurements

the investigation activity Guideline 1: Provide Options for Perception - Offering ways of customizing display of information. Color use and lay out of visuals

Closure: Summarize how you will bring the lesson to a close allowing students to reflect or summarize what they learned in regards to the lesson objective. Highlight any student discourse strategies in blue. Teacher Student Universal Design for Learning - The teacher will bring the class back Academic Language Guideline 3: together in class to debrief the - Students will share out Provide Options for findings of the experiment: their findings for each Comprehension - Each group will share out their height and engage in a average height/distance of the 2 class discussion to - Maximize transfer objects that they solved for explain the process of and generalization - The teacher will bring up the pictures solving the problem of the two objects and draw the right triangles that are used to solve for the heights. - The teacher will facilitate a discussion with the class on how they approach each scenario to solve the problem Academic Language 1. Describe the cognitive task related to the content learning objective: a. Students will be able to explore real world scenarios of angles of elevation and depression right outside their classroom by using a hand-made inclinometer and their knowledge of trigonometry ratios to find the distance between two objects that are not on the same level as each other. 2. Language Demands: Describe how students will be communicating in relation to the content in the cognitive task? Identify the communicative mode. o Collaborative (engagement in oral or written dialogue with others) Students will be in groups of four as they experiment on how to find the height of objects using their knowledge of angle elevation/depression and trigonometry ratios. Each student will have a role within the group: Recorder, Measurer, Performer, and Reporter.

Interpretive (comprehension and analysis of written and spoken texts) Students will interpret the real life scenario from the experiment to make connections to the trigonometry ratios that they learned from the previous lessons. They must be able to comprehend how to relate the triangle to the real world experiment. 3. Language Function: Choose one language function essential for student learning. Highlight the language function of the lesson. o

Math

Compare/Contrast

Conjecture

Describe

Explain

Prove

4. What language demand (written or oral) will you help the students develop during the lesson? • Vocabulary and/or symbols: Angle of elevation and angle of depression • Mathematical precision (e.g., using clear definitions, labeling axes, specifying units of measure, stating the meaning of symbols), appropriate to your students’ mathematical and language development: Students will be using a measuring tape and a handmade inclinometer during the experiment. Students must use the proper unites of degrees. • Plus at least one of the following: o Discourse: Students will be using Think-Pair-Share during the engaging portion to share and build upon each other ideas in finding methods to finding the height of an object. 5. List the instructional strategies you will use to support the development of academic language skills (related to the identified language demand above). a. I will facilitate the class discussion to push students thinking and understanding by asking “Why?” and “How?” on the process of solving the real world problem b. I would invite other students to join in on the conversation with talk moves – Who got a different answer? Who agrees and disagrees? What do group __ think of this process? 6. Describe additional strategies you will use to meet the needs of students with varying levels of language proficiency. o Bridging: Allow for more student interaction in explaining problems orally and in writing. Provide multi representation to real world examples that they are familiar with. Have more opportunities for students to write down their thoughts with provided sentence frames. Provide rephrasing and repeating of directions and problem questions