Bank+On+It


 * Bank on it **

**Introduction: ** During this lesson students will review SOHCAHTOA and what it means. Also, students will learn how to apply and find lengths of right triangles using the sine, cosine, and tangent ratios. Finally, we will briefly talk about Pythagorean's Theorem, and special properties of 45-45-right triangles, but students will not be tested on this. This lesson is strictly for sine, cosine, and tangent. Teachers can use this as their actual lesson plan in teaching this subject or a teacher can take parts of this lesson in assisting them to teach sine, cosine, and tangent.


 * Teacher Candidates **: Joey Tivnan, Nate Nielsen, Kevin Cullen, Eric Hull

**DATE:** March 11, 2011

**GRADE LEVEL & SUBJECT:** ﻿11th Grade Trigonometry Class

**LEARNING TARGETS: **
G.3.C Use properties of special right triangles (30-60-90 degree and 45-45-90 degree) to solve problems.

G.3.D. Know, prove, and apply the Pythagorean Theorem and its converse.

G.3.E Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent.

__Learning Outcomes: __
Students will be able to: 1. Know the acronym SOHCAHTOA and what it means. 2. Define what sine, cosine, and tangent are equal to in terms of ratios. 3. Apply/ use sine, cosine, and tangent to find the lengths of sides of right triangles.

**ASSESSMENT STRATEGIES: **
**Formative**: Active participation with students paying attention and following directions. Also, asking questions to check for student understanding before moving on. ** Summative ** : Worksheet (provided below). Use grading rubric to determine full or partial credit (also provided below).

**GROUPING OF STUDENTS FOR INSTRUCTION: **
The class will be in a computer lab and activities will be explained in detail below.

**<span style="font-family: 'Times New Roman',Times,serif;">INSTRUCTIONAL MATERIALS, EQUIPMENT, AND TECHNOLOGY NEEDED: **
<span style="font-family: 'Times New Roman',Times,serif;">Computer lab, pencil, and calculator (TI -83 or above)

**<span style="font-family: 'Cambria','serif';">PRIOR KNOWLEDGE AND SKILLS: **

 * Basic understanding of trig ratios
 * <span style="font-family: 'Cambria','serif'; margin: 0in 0in 0pt; text-indent: 0.5in;">Algebra skills/ being able to solve for variables.
 * <span style="font-family: 'Cambria','serif'; margin: 0in 0in 0pt; text-indent: 0.5in;">Use TI-83 calculators.
 * <span style="font-family: 'Cambria','serif'; margin: 0in 0in 0pt; text-indent: 0.5in;">Pythagorean's theorem

**New Material**:
 * Applying the trigonometric ratios of sine, cosine, and tangent to find lengths of the sides of triangles


 * <span style="font-family: 'Cambria','serif'; font-size: 12pt; text-transform: uppercase;">LEARNING EXPERIENCES: **

<span style="font-family: 'Times New Roman',Times,serif;">Exploratory/ Engaging Activity:
 * <span style="font-family: 'Times New Roman',Times,serif;">Have all students open the Illuminations Billiards Applet.
 * <span style="font-family: 'Times New Roman',Times,serif;">Go through login steps specific to your network.
 * <span style="font-family: 'Times New Roman',Times,serif;">Open Firefox or whatever browser you prefer.
 * <span style="font-family: 'Times New Roman',Times,serif;">Type in [] (written on board) or you can do a Google search for “Illuminations Paper Pool.”
 * <span style="font-family: 'Times New Roman',Times,serif;">Once all students have the applet running on screen. Show and explain how to use the applet. Have the applet on the class overhead screen and walk around to ensure student understanding.
 * <span style="font-family: 'Times New Roman',Times,serif;">First, have the students adjust the slider to change the width/height.
 * <span style="font-family: 'Times New Roman',Times,serif;">Second, have the students adjust the slider to change the speed to highest.
 * <span style="font-family: 'Times New Roman',Times,serif;">Once all students are set, tell them to click on ball in the lower left corner to shoot it.
 * <span style="font-family: 'Times New Roman',Times,serif;">Ask the students about what they saw.
 * <span style="font-family: 'Times New Roman',Times,serif;">Quick Competition- “Who can get the most hits?”
 * <span style="font-family: 'Times New Roman',Times,serif;">Approximately 2 minutes
 * <span style="font-family: 'Times New Roman',Times,serif;">Tell the students to manipulate the dimensions of the table to see how many hits you can get.
 * <span style="font-family: 'Times New Roman',Times,serif;">At this point they should experiment with different dimensions to increase their number of hits. Write up totals on the board as students call out their number of hits.
 * <span style="font-family: 'Times New Roman',Times,serif;">The maximum number of hits possible is 41.
 * <span style="font-family: 'Times New Roman',Times,serif;">Hand out a small prize to the winner.
 * <span style="font-family: 'Times New Roman',Times,serif;">Quick Competition 2- “Which pocket will it go in?”
 * <span style="font-family: 'Times New Roman',Times,serif;">Have all students set the dimensions of the applet to 9x7, but tell them not to shoot!
 * <span style="font-family: 'Times New Roman',Times,serif;">Have the students guess which pocket the ball will go into. Record the number of A, B, C, and D guesses on the board. After guesses are tallied, have all students shoot the ball. The ball will go in (C). Congratulate the winning guessers.
 * <span style="font-family: 'Times New Roman',Times,serif;">Next have the students set dimensions to 12x7, but tell them not to shoot!
 * <span style="font-family: 'Times New Roman',Times,serif;">Have the students guess which pocket the ball will go into. Record the number of A, B, C, and D guesses on the board. After guesses are tallied, have all students shoot the ball. The ball will go in (B). Congratulate the winning guessers.
 * <span style="font-family: 'Times New Roman',Times,serif;">Exploratory Question – Did anyone try dimensions that were square?
 * <span style="font-family: 'Times New Roman',Times,serif;">What happened? (It went straight into the opposite corner.)
 * <span style="font-family: 'Times New Roman',Times,serif;">Why? (All shots are 45 degrees, cuts 90 degree angle in half.)

<span style="font-family: 'Times New Roman',Times,serif;">Transition to Trigonometry Material:

<span style="font-family: 'Times New Roman',Times,serif;">
 * <span style="font-family: 'Times New Roman',Times,serif;">Transition Question: Using this example of the pool applet (4x4 pool table with 45 ° shot from one corner to the other) how could we find how far the ball is traveling? Put 4x4 applet back on screen.
 * <span style="font-family: 'Times New Roman',Times,serif;">Expect answers involving Pythagorean’s Theorem
 * <span style="font-family: 'Times New Roman',Times,serif;">If some students come up with the property of all 45-45-right triangles that the hypotenuse (length of shot) is the length of one leg multiplied by √2, continue to remind all students of that property associated with the Pythagorean Theorem. Additionally, a 45-45-90 triangle will be constructed on whiteboard.
 * <span style="font-family: 'Times New Roman',Times,serif;">Remind students that the hypotenuse (length of shot) of the triangle created by the shot and the walls of the pool table can be easily found by a formula they should already know: that for any 45-45-right triangle, the hypotenuse equals the length of one leg multiplied by √2.
 * <span style="font-family: 'Times New Roman',Times,serif;">Proposition Question: What if we tried using trigonometry to solve this?
 * <span style="font-family: 'Times New Roman',Times,serif;">Review what was learned last week about trig functions (informal assessment of student’s knowledge). Does anyone remember the acronym for sin, cos, and tan? Students hopefully remember SOHCAHTOA. Write acronym on the board. Have students help you with what the acronym means and write the definitions on a space on the board and you can leave them there throughout the lesson as well.
 * <span style="font-family: 'Times New Roman',Times,serif;">sinθ = opp/hyp
 * <span style="font-family: 'Times New Roman',Times,serif;">cosθ = adj/hyp
 * <span style="font-family: 'Times New Roman',Times,serif;">tanθ = opp/adj
 * <span style="font-family: 'Times New Roman',Times,serif;">Talk to students about how to apply trig function to finding lengths of the sides of triangles. Meaning that if you know an angle and at least one side of a triangle then you can find another length of a right triangle. Refer to the applet still on the screen and explain how each trig. function applies
 * <span style="font-family: 'Times New Roman',Times,serif;">Our example: sin45° = 4/x therefore x= 4/sin45°
 * <span style="font-family: 'Times New Roman',Times,serif;">Solve the equation with students
 * <span style="font-family: 'Times New Roman',Times,serif;">Show them how to plug it into their calculators.
 * <span style="font-family: 'Times New Roman',Times,serif;">Tell students- “Let’s try some examples when we don’t have a special triangle like a 45-45-right triangle where we can find the length of the hypotenuse (or how far the ball is traveling) very easily.”
 * <span style="font-family: 'Times New Roman',Times,serif;">“What if the given angle is 53° and the length of the opposite side is 7? How would we find the length of the hypotenuse?”(Draw diagram on the board)
 * <span style="font-family: 'Times New Roman',Times,serif;">“We’re kind of forced to use trigonometry to solve this because we have a given angle that doesn’t have any special properties we can use to find the length of the hypotenuse and we also are only given the length of one side of the triangle so we can’t use Pythagorean’s Theorem either. So from our definitions of the trig ratios, which one best fits the scenario we have here?”
 * <span style="font-family: 'Times New Roman',Times,serif;">Guide students to discover we need the sine ratio referring to the definitions on the board: “Which trig ratio uses the information we are given? We have an angle, a side opposite the angle, and we are trying to find the length of the hypotenuse.”
 * <span style="font-family: 'Times New Roman',Times,serif;">“Ok, so now that we know what ratio to use, tell me how we are going to write it out.”
 * <span style="font-family: 'Times New Roman',Times,serif;">Have students verbally explain that sin53° = 7/x
 * <span style="font-family: 'Times New Roman',Times,serif;">“Our x variable in this case represents what? The hypotenuse right? So how are we going to solve for x?”
 * <span style="font-family: 'Times New Roman',Times,serif;">Have students verbally walk you through the steps of using basic algebra to solve that x= 7/sin53°
 * <span style="font-family: 'Times New Roman',Times,serif;">Have students plug this into their calculators to find the exact length and have them repeat it back making sure that all students agree on the answer.
 * <span style="font-family: 'Times New Roman',Times,serif;">“Ok, let’s try something a little bit different now. What if the given angle is 25° this time but now we are only given that the adjacent side has a length of 5? How would we find the length of the hypotenuse?”(Draw diagram on board)
 * <span style="font-family: 'Times New Roman',Times,serif;">Guide students to discover we need the cosine ratio referring to the definitions on the board: “Which trig ratio uses the information we are given now? We have an angle, a side adjacent the angle for this situation, and we are trying to find the length of the hypotenuse.”
 * <span style="font-family: 'Times New Roman',Times,serif;">“Ok, so now that we know we need the cosine ratio, tell me how we are going to write it out.”
 * <span style="font-family: 'Times New Roman',Times,serif;">Have students verbally explain that cos25° = 5/x
 * <span style="font-family: 'Times New Roman',Times,serif;">“Since we know that our x variable is what we are looking for, how are we going to solve for it?”
 * <span style="font-family: 'Times New Roman',Times,serif;">Have students verbally walk you through the steps of using basic algebra to solve that x= 5/cos25°
 * <span style="font-family: 'Times New Roman',Times,serif;">Have students plug this into their calculators to find the exact length and have them repeat it back making sure that all students agree on the answer.
 * <span style="font-family: 'Times New Roman',Times,serif;">“Let’s look at one more scenario. What if we wanted to find the horizontal distance that the ball was traveling across the table instead of the total distance the ball was traveling like we have been looking at?”
 * <span style="font-family: 'Times New Roman',Times,serif;">“Given an angle of 40° and a length of 6 for the hypotenuse, how far does the ball travel horizontally (or what is the length of the adjacent side)?” (Draw diagram on board)
 * <span style="font-family: 'Times New Roman',Times,serif;">“By our other examples, can you tell me which trig ratio we will need to solve this? We still need to use the cosine function right? Let’s try it out.”
 * <span style="font-family: 'Times New Roman',Times,serif;">“Help me write this out.” Have students work through writing the equation with you to find that this time cos40° = x/6.
 * <span style="font-family: 'Times New Roman',Times,serif;">“So now how do we solve for x?” Have students explain that 6cos40°= x
 * <span style="font-family: 'Times New Roman',Times,serif;">Have students plug this into their calculators to find the exact length and have them repeat it back making sure that all students agree on the answer.
 * <span style="font-family: 'Times New Roman',Times,serif;">Ask students if they have any questions or need any clarification on the material
 * <span style="font-family: 'Times New Roman',Times,serif;">Hand out the worksheet that will be graded (formal assessment of student knowledge).

Extension:
This lesson can be altered to also apply the inverses of sin, cos, and tan to find angles of triangles. Also, one can bring into this lesson cot, csc, and sec and their inverses as well.

Teacher Reflection:
Using the pool applet really engaged our students and got them excited and on task. Also, our transition from the applet to trigonometry was very smooth and the kids understood where we were heading. Looking back I probably should have walked around the class more to give individual attention to students who needed it. Overall the lesson I believe went well.