The carnival has arrived in Newport and now is the perfect time to show what you know about applying Sine and Cosine Functions to model periodic behavior.
Who wants to just ride a Ferris Wheel when you now know enough to write and graph a function to model the motion. You can also describe to your friends when and how often they will be at certain height by just knowing how long it takes to go around once.
That is hands down better. PERIOD.
There is a wealth of demonstrations of the connections between Ferris Wheels and Trig. class by a simple google search trigonometry ferris wheel video.
The only thing you have not learned is how to interpret or use phase shifts to create different types of models. We will learn that this week and then complete a task.
The visuals displays should really help you put it all together. I like the second short 60 second video that popped up with my google search.
Sunday, May 10, 2015
Friday, April 3, 2015
Tips for El Segundo Task
Your responses to the Arrive at Five task are due Monday. What you hand in and one final in class summative assessment will be your final opportunties to show what you know for Quarter 3.
I checked my calculations for finding the direct distance between Newport, RI and El Segundo, CA. I used latitude/longitude coordinates, arc length, and the Pythagorean Theorem. The right triangle and arc length based calculations will not the same as what you get using an online distance calculator (and they shouldn't be). Do some further reading if you want to know why.
You are still expected to find the calculations by hand.
Give it a shot and hand in Monday.
I checked my calculations for finding the direct distance between Newport, RI and El Segundo, CA. I used latitude/longitude coordinates, arc length, and the Pythagorean Theorem. The right triangle and arc length based calculations will not the same as what you get using an online distance calculator (and they shouldn't be). Do some further reading if you want to know why.
You are still expected to find the calculations by hand.
I wrote the El Segundo problem to give you an
opportunity to do three things:
- Show that you know how to convert
coordinates (both Latitude and Longitude) from degree minutes seconds to
decimal degrees and vice-versa.
- Make the
connection that you can use the difference between any two latitudes (an
angle) and the radius of the earth to calculate a curved distance over the surface of the Earth. You can do a similar set of calculations for the Longitudes.
-
THEN APPLY THE
PYTHAGOREAN THEOREM.
Kind of
like the diagram above. Basically, get
the red and blue then
a^2 + b^2 = c^2 to get green
a^2 + b^2 = c^2 to get green
Give it a shot and hand in Monday.
Source:
http://derickrethans.nl/spatial-indexes-calculating-distance.html
BUT:
because of the curvature of the earth and other factors the diagonal
distance Between
cities will not be precise. A full
explanation is pretty complicated but is explained in more detail using the link above.
New addition to the Trig. playlist: A Tribe Called Quest
Sunday, March 29, 2015
FourFive and Knowing Two of Three
FourFive Addition to Trigonometry Playlist
It still doesn't feel like spring! In response to a student request to add FourFive Seconds to the Trig. playlist, consider it added. However, I originally thought I heard "Forty-Five" which connected to 45 seconds per minute loosely relating the lyrics to Trig. Forty-Five clock seconds representing 3pi/2 radians of a turn of course. But since Paul McCartney is involved we can add it to the playlist.
Two of Three
If I had to choose one number theme to relate FourFive to what we learned last week to what we will learn this week it is two of three. In simplest terms, if you can identify Two of Three math facts in a word problem, you typically can connect to the elationship (Formula) you need to apply.
Typical Problems from Last Week:
Know: Angle in Radians and Radius Want: Arc Length
Know: Rotations and Time Want: Angular Speed
Know: Angular Speed and Radius Want: Linear Velocity
Two of Three Examples you will see this week:
Given a Triangle:
Know: An OPPOSITE and HYPOTENUSE
Want: The SINE of the Angle
SOH CAH TOA. There is even a two of three mnemonic
to help you make decisions for basic trigonometry.
Note: SOH CAH TOA should be familiar from previous classes. If it is not, I strongly recommend you visit Khan Academy (or another site) for basic trigonometry review. https://www.khanacademy.org/math/trigonometry/basic-trigonometry view first video and example.
More Additions to the Playlist
"So What'cha Want" to inspire you to show your work
https://www.youtube.com/watch?v=RWfqPIyU9Zw
"My Shirona" because it sounds like the mnemonic SOH CAH TOA
https://www.youtube.com/watch?v=g1T71PGd-J0
"The Logical Song" because you need to know radical form
https://www.youtube.com/watch?v=fBoYZqmcZuc
and because classic music videos are a lost art form.
It still doesn't feel like spring! In response to a student request to add FourFive Seconds to the Trig. playlist, consider it added. However, I originally thought I heard "Forty-Five" which connected to 45 seconds per minute loosely relating the lyrics to Trig. Forty-Five clock seconds representing 3pi/2 radians of a turn of course. But since Paul McCartney is involved we can add it to the playlist.
Two of Three
If I had to choose one number theme to relate FourFive to what we learned last week to what we will learn this week it is two of three. In simplest terms, if you can identify Two of Three math facts in a word problem, you typically can connect to the elationship (Formula) you need to apply.
Typical Problems from Last Week:
Know: Angle in Radians and Radius Want: Arc Length
Know: Rotations and Time Want: Angular Speed
Know: Angular Speed and Radius Want: Linear Velocity
Two of Three Examples you will see this week:
Given a Triangle:
Know: An OPPOSITE and HYPOTENUSE
Want: The SINE of the Angle
SOH CAH TOA. There is even a two of three mnemonic
to help you make decisions for basic trigonometry.
Note: SOH CAH TOA should be familiar from previous classes. If it is not, I strongly recommend you visit Khan Academy (or another site) for basic trigonometry review. https://www.khanacademy.org/math/trigonometry/basic-trigonometry view first video and example.
More Additions to the Playlist
"So What'cha Want" to inspire you to show your work
https://www.youtube.com/watch?v=RWfqPIyU9Zw
"My Shirona" because it sounds like the mnemonic SOH CAH TOA
https://www.youtube.com/watch?v=g1T71PGd-J0
"The Logical Song" because you need to know radical form
https://www.youtube.com/watch?v=fBoYZqmcZuc
and because classic music videos are a lost art form.
Sunday, March 22, 2015
What Time is it! Time for My Three Songs.
Happy Spring!
Before Pandora, Spotify, and itunes, some radio stations used to play “My
Three Songs” and listeners had to guess what they had in common. These three songs have circles in
common! Here are your three Trig. Songs for
the week and 6 extra credit opportunities.
Note: You may respond for extra credit
one time and be the
first commenter/not duplicate someone else’s response to earn credit (read
blog comments section before responding).
To clarify who you are and get credit, write your response in the comments section.
e.g. The Artist is Sade! and note that is sounds like “Gaudet” - grs
Note the 6.1d has not been assigned as of Sunday and
E-Period has not received the ASMT2 Handouts yet.
It has been a while since we made musical connections to our class
content
(see Missy Elliot in February or of Course Sade’s Smooth Operator in
Quarter2).To clarify who you are and get credit, write your response in the comments section.
e.g. The Artist is Sade! and note that is sounds like “Gaudet” - grs
|
Unit 6 Trig. Tune
|
Extra Credit Task
|
|
You Spin me Round (Like a
Record) https://www.youtube.com/watch?v=PGNiXGX2nLU
|
+5% to this week’s quiz.
(name this artist in comments below)
+10% to this week’s quiz State 3 unique “circle facts” that relate to
learning target 1.
|
|
The Spin Doctors What time is it?
https://www.youtube.com/watch?v=eqS5pJDX5j4
|
+5% State the time/name the album.
+10% State the angle measurement between the hands in radians. Exact
|
|
BHTM Circle
|
+ 5% Name the Band and state where the lead singer is from.
+10% Explain what co-terminal
means and provide an example of two coterminal angles
|
This is unconventional way to earn credit, but the time is now Spring
and we have to mix things up. Plus, we
need more two-way communication and this is one way to implement a blog. Also, recall that I did ask you to follow
this blog earlier in the year. I may
reward the followers. My Seniors, hang
in there we are not done yet.
I created a google document that will be updated as new material is
assigned. The document can be view here:
Sunday, February 22, 2015
The big thaw...
After our cold week off, I want you to assemble and bring in the text homework you have completed so far to show what you know about exponentials. Next class you will be handed a highlighter and need to choose and highlight about 10 problems that show you know the learning targets listed below. An even better plan is to highlight (I mean just draw a yellow box around significant problems to draw attention to important problems) before you come to the next class.
The problems you highlight should demonstrate that you know the learning targets described below:
(1) I understand all the parameters of an exponential function y = Cax . Given a table, I can determine initial values and growth/decay factors to write an exponential function. Given a graph or situation, I can identify and interpret the appropriate equation using my understanding of exponentials.
(3) I recognize a logarithm function as the
inverse of an exponential function. I
can solve exponential equations by applying
log base 10 and the natural log functions to “undo” exponential functions.
There will also be a survey you need to complete next class that rates your understanding of the targets above more specifically. Be sure you have your work to look at so you can back up what you see about your understanding.
The problems you highlight should demonstrate that you know the learning targets described below:
Learning
Targets By
the end of this unit you should be able to say and demonstrate that:..
(1) I understand all the parameters of an exponential function y = Cax . Given a table, I can determine initial values and growth/decay factors to write an exponential function. Given a graph or situation, I can identify and interpret the appropriate equation using my understanding of exponentials.
(2) Given a real-life scenario, I can create and evaluate exponential (and
later logarithmic) functions to solve
problems. I can interpret different
types of compounded interest formulas and y = ex and use technology to identify
solutions to problems.
Sunday, February 8, 2015
Second week of Exponentials and Missy Elliot
Last Week
We learned exponential growth and decay function key features and end behavior.
- The y-intercept (0,a) is always a good feature to inspect and
the end behavior either grows rapidly towards infinity or approaches the x-axis asymptotically. [Unless the function is transformed of course]
- We learned the basic structure of exponential equations: y=ab^x and y = a (1+r)^x
and it is all about the base (if "it" means determining growth versus this decay.
Next Step(s): Apply and interpret more sophisticated exponential models, like models for compounded interest and models to display scientific phenomenon.
- We learned how to interpret patterns (mainly from tables) and determine if it represents an exponential or linear function. Then, actually write the formula using the appropriate structure of an equation.
Next Step(s): Contrast exponential functions with Quadratic Functions, and learn about the Exponential Function's Evil Twin Function which can undo it. If we can undo an operation, we can solve equations.
Mathematician's call it the Inverse Function, and Missy Elliot refers to it in one of her songs, Work it. If it is worth it, we can work it and then something about flipping it and reversing it.
Expect a paper pencil quiz this week and one more tenmarks track that will also count as a quiz.
We learned exponential growth and decay function key features and end behavior.
- The y-intercept (0,a) is always a good feature to inspect and
the end behavior either grows rapidly towards infinity or approaches the x-axis asymptotically. [Unless the function is transformed of course]
- We learned the basic structure of exponential equations: y=ab^x and y = a (1+r)^x
and it is all about the base (if "it" means determining growth versus this decay.
Next Step(s): Apply and interpret more sophisticated exponential models, like models for compounded interest and models to display scientific phenomenon.
- We learned how to interpret patterns (mainly from tables) and determine if it represents an exponential or linear function. Then, actually write the formula using the appropriate structure of an equation.
Next Step(s): Contrast exponential functions with Quadratic Functions, and learn about the Exponential Function's Evil Twin Function which can undo it. If we can undo an operation, we can solve equations.
Mathematician's call it the Inverse Function, and Missy Elliot refers to it in one of her songs, Work it. If it is worth it, we can work it and then something about flipping it and reversing it.
Expect a paper pencil quiz this week and one more tenmarks track that will also count as a quiz.
Sunday, February 1, 2015
Transitioning from Polynomial Functions to Exponential Functions begins Groundhog's Day!
Monday Task
Last week we did a couple of open-ended practice task problems. Monday (if we don't get another foot of snow!), you will complete an open response problem that is probably less difficult than the practice problems we did together, but will still challenge you to make sense of a problem and apply what we have learned to solve problems pertaining to volume in a different context. This will count as the first test grade of the new quarter. I don't think most of us really need to do a whole lot of studying for this task, but if you want to spend 10 minutes preparing, it would be a good idea to organize your unit 4 polynomial notes and perhaps log on to www.khanacademy.org and search "Dimensions from volume of box". There is a short 5-minute video that shows a simpler problem than what you will need to complete, but the core problem solving elements are pretty similar and it should build your confidence.
Guiding Questions for Tenmarks Problems
Last week we did a couple of open-ended practice task problems. Monday (if we don't get another foot of snow!), you will complete an open response problem that is probably less difficult than the practice problems we did together, but will still challenge you to make sense of a problem and apply what we have learned to solve problems pertaining to volume in a different context. This will count as the first test grade of the new quarter. I don't think most of us really need to do a whole lot of studying for this task, but if you want to spend 10 minutes preparing, it would be a good idea to organize your unit 4 polynomial notes and perhaps log on to www.khanacademy.org and search "Dimensions from volume of box". There is a short 5-minute video that shows a simpler problem than what you will need to complete, but the core problem solving elements are pretty similar and it should build your confidence.
Guiding Questions for Tenmarks Problems
To prepare for upcoming material, your weekend homework was to complete 4 www.tenmarks.com tracks to refresh your memory about the key features and behavior of exponential graphs, structure of exponential equations, and patterns to interpret tables of values modeling exponential functions.
Your first homework grade will be your TM scores for the four assigned tracks. One student finished all four last Monday in about 30 minutes. I recommend your complete the tracks and as you are working, answer the following guiding questions:
Your first homework grade will be your TM scores for the four assigned tracks. One student finished all four last Monday in about 30 minutes. I recommend your complete the tracks and as you are working, answer the following guiding questions:
- Representing and Interpreting Exponential Functions [FIF7e] . For polynomial functions we learned about key features and behavior of that family of function. Given a simple exponential function y = b^x, what key features do we need to recognize? What is different about the behavior and rates of change of an exponential function compered to other functions we have studied.
- Understanding Exponential Growth and Decay [F-IF.8b] For polynomial functions, we learned what how each of the parameters in y = a (x-h)^3 +k affects the graph of a polynomial. What can you recognize about the roles of the a and b for a polynomial function y = ab^x? What happens if b>1? What happens when 0<b<1?
- Calculating Exponential Growth and Decay Algebraically [F-LE.1c] For linear functions, we know all about positive and negative slope and the y-intercept for any y = mx+b. Exponentials are not characterized by slope and the y-intercept is not a "b". What can you generalize about the y-intercept of exponential functions? What is generally true about the x-intercept(s)?
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