Ch.5 Cartoonproof

Ch. 5 Cartoon & Proof

ch5 project

Proofs

Trigonometric Proof

Prove sinu + sinv = 2sin (u+v/2) cos (u-v/2)

1. 2sin (u+v/2) cos (u-v/2)	1. Given
2. sinu cosv = ½ (sin (u+v) + sin (u-v))	2. This is the product-to-sum formula, ½ (sin (u+v) + sin (u-v)) that was also given.
3. 2 x ½ (sin (u+v – (u-v)/s) + sin (u+v+u-v)/2)	3. Plug in the equation 2sin (u+v/2) cos (u-v/2)
4. 1 (sin (2v/2) + sin (2u/2))	4. Distributive property of multiplication and combine like terms.
5. 1 (sinv + sinu) = sinv + sinu	5. Simplify!

Paragraph Proofs: I would like to prove that sinu + sinv = 2sin (u+v/2) cos (u-v/2). I was given that sinu cosv = ½ (sin (u+v) + sin (u-v)) so I plugged 2sin (u+v/2) cos (u-v/2) into ½ (sin (u+v) + sin (u-v)) and I got 2 x ½ (sin (u+v – (u-v)/s) + sin (u+v+u-v)/2). Then I used the distributive property of multiplication and combined like terms to get 1 (sin (2v/2) + sin (2u/2)) and lastly, I simplified the equation to get sinv + sinu.

Ch 5 Project Proofs and Cartoons

Ch 5 Cartoon & Proof

Ch 5 Project

Chapter 5 Project- Proof & Cartoon.

Ch 5 Project

Ch 5 Cartoon & Proof

CH 5 Cartoon & Proof

Ch 5 Cartoon

 

Instructions For Investors

Dear Investors,

Thank you for taking time from your busy schedules to help us with our math project.

Background:

I am a math teacher at at Oakland High. I am currently working on my National Boards Certification via a support group at Stanford. For one of the portfolio entries, I needed to create project involving the community.

The project I created is for my Precalculus class. The students in this class are the best and brightest Oakland has to offer. Most of the students are 11th graders, but there are a few 10th graders and one senior.


Significance:

We currently working on exponential and logistic functions. This project focuses on a section called The Mathematics of Finance. In the past, students haven't fully understood how powerful mathematics can be when applied to the world of finance. Also my students come from poor backgrounds and don't have access to people in the finance industry.


Description:

My students will create presentations on formulas and concepts commonly used in finance.

Each presentation will include:

• The derivation of the formula
• A numerical example
• A graphical example
• An algebraic example
• A real world example

The presentations will be on one of the following 6 topics:

1. Interest Compounded Annually

A = P(1 + r)ⁿ

2. Interest Compounded k Times per Year

A = P( 1 +( r/k) )^kt

3. Interest Compounded Continuously

A = Peⁿ

4. Annual Percentage Yield
The percentage rate that, compounded annually would yield the same returns at the given interest rate with the given compounding interest.

5. Annuities - Future Value

FV = R  (1+ i)ⁿ  - 1

                     i

6. Annuities - Present Value (Loans and Mortgages)

PV = R  1 – (1 + i ) ^–n

                      i

How we would like you to help:

1. There will be six presentations in total. We would like each volunteer to choose one of the six topics listed above.
2. The students will need one example of how these formulas or concepts are used in investing. We are looking for a general example, not specifics of course : ).
3. The students will also be asking you background questions.
For example: Where did you go to school? How did you become involved in finance? Do you have any advice? etc.


You can respond in one of the following 3 ways.

1. Respond directly on the Voice Thread presentation via webcab, audio or by typing.
Please see http://voicethread.com/ for instructions.
2. Respond in the comment section of the blog entry.
3. Email a response to abernethy.ohs@gmail.com

The presentations will be available online on Friday March 23rd, and we would like you comment by Tuesday, March 27th.

Thank you very much for your time and consideration. It is greatly appreciated!

Rori Abernethy
Math Teacher
Oakland High

3 How to do a Voice Thread

Students must post one individual voice thread to prepare for the CH 3 Project.

Go to http://voicethread.com/ for detailed instructions.

Each voice thread must include:

1. A voice comment
2. A written comment
3. A video comment
4. A scribble

You may use the laptops in class if you do not have a web cam or microphone on your computer at home.

Chapter 3 Project- VoiceThread.

5 How To Do a Trigonometric Cartoon Proof

Each student will write the same trigonometric proof in the following 3 ways:

• A a 2 column proof
• A paragraph proof
• A cartoon proof

Step 1   Choose a proof from the list
Step 2   Write a two column proof and have your proof checked by Abernethy.
Step 3   Write a paragraph proof and have your proof check by Abernethy.
Step 3   Choose cartoon template and a character and write your cartoon proof. Use the proofs that geometry students have completed as examples. These are posted on the bulletin boards outside the classroom, inside the classroom and upstairs outside of vice principal Mr. Rodgers office.

How To Make up a Word Problem using Trigonometry and Indirect Measurement.

Each student will make up a word problem using trigonometry and indirect measurement.

1. Use page 426 examples 2, 3, 4, and 5 as a guideline to make up a word problem.
2. Sketch a picture to illustrate your problem
3. Include 4 questions (labeled a, b, c and d)
4. Solve your problem
5. Have your problem check by Abernethy
6. Write your problem on white paper WITHOUT an picture and WITHOUT the solution. Make sure your problem is descriptive enough so that another student can sketch a picture and solve your problem.
7. Write the solution on white paper with illustrations for each set.
8. Trade problems with you assigned partner.
9. Solve you partners problem. If you find mistakes, PLEASE CORRECT THEM. You will receive full credit this way. Your partner will have points taken off if they have not caught their own mistakes.