Pictures

Goodbye for now

For many of you this is the last time I will see you in my classroom for the remaining years of high school.  I wish you luck and happiness.  No matter what the problem, just remember that I am always here for you.  Good luck and may the Force be with you.

Link to D.E.V.

https://docs.google.com/open?id=0B5yoh0sJhhpYeDVvVGZnekdtZ2c
Link to my D.E.V.

Corbin's D.E.V.

Dev corbin from shuler145


Reflection
            I greatly enjoyed doing this project. I picked problems that would let me review/ reflect on past units. I struggled the most with the first unit, and factoring as a whole, therefore I decided it would be in my best interest to explain problems of that nature. I got a better grasp on the given material by doing these problems. I think the thing that help the most with this project was simply taking my time and keeping a positive outlook. Looking at it more as review instead of a "project" helped. I think that you should continue to give out this project to future classes. However, it might be more beneficial to the students if you gave them more time to complete it. Maybe give it out toward the beginning of the trimester so the students can keep certain ideas in mind. Another thing I think that was unique to this project was the amount it tested my media tool skill set. To be completely honest this was only the second time I had ever used power point. I liked how I had to basically learn how to use it from scratch, I think this project not only lets students review for the exam, but it also allows them to go outside of the box, and find different ways to present their ideas.

D.E.V-H[anna]H

Hi! We'll be talking about a variety of topics today and we will talk you through each problem! Our pictures are color coded and you can follow along easily with the colored text next to the picture! Enjoy learning!
-Hannah and Anna!

Our first problem:

Solve and find the domain for the equation in black.
The equation in blue represents the "difference of squares , which is the equation we will use to factor what is under the the radical.
In order to find the "A" and "B" values, you need to think of what you need to square to get your original term.Hence a=4x^2 and b=15
Just as any other formula, plug the terms into the blue equation to achieve what we have in purple.
In green you see there is no radical sign. This is because the radical is accounted for by using the greater than or equal to inequality. Remember, a radicals domain cannot be negative, but can be equal                      to  zero! 
 From there we than split the factors apart to find the x-intercepts(where the factors are equal to zero).
Using algebra, solve each inequality. In orange, you see there is a negative under the radical. This means it in not a real solution, therefore, this solution will not show up for the domain or on the graph. 
The answer in gray represents the real solutions, and will account for the domain and be visible on the graph.



In order to visualize the domain better, we graphed it. The part of the graph highlighted in yellow is where inputs produce negative values. Which is not possible in a radical function.
The final domain is in purple. Notice the square brackets, this is because it can be equal to those numbers. Notice the parenthesis, this means it cannot be equal to those numbers, but as close as possible. Negative and positive infinity are not numbers and can never be reached! Hence the parenthesis.You also might notice a funky "u" in between, this  means union. A union is the combining of two sets of information, and that information exists for the entire problem, or in this case, the Domain! 


Our next problem:

Solve the equation in black and find the domain. The pink highlighted equations are what you must use.
Start by find the domain of each equation, which is highlighted in yellow(find by solving for x)
From there,  put the f(x) equation into the g(x) equation every time you see an X. You should end with what is in green.
Set what is under the big radical greater than or equal to zero. (we told you why in the last problem!)

Now its time to use our algebra skills! Subtract three from both sides , than divide by -1 to get rid of the negative radical. Note:when you divide by a negative number, your inequality sign changes directions. Than square both sides.
Add four!
You should have the highlighted green part at this point!

Set this equal to zero because you cannot find the square root of an inequality because you cannot be +/- of a inequality. (Think about it, it makes sense!)
You than get, what is in orange!
Final domain should look like the highlighted yellow portion.Remember why we have square brackets? We already told ya!;)

To help visualize the final domain we put f(x) and g(f(x)) domains on a number line. Where they overlap is highlighted in yellow, and that is where x values are possible for both equations. The domain is written in black! (There are those tricky brackets again...don't forget what they mean!)





Our next problem:

Solve for X by completing the square! What's completing the square? Well... it's where you take a quadratic equation in standard form(ax^2+bx+c=0), and turn it into vertex form[a(x-h)^2+K]! Let us show ya how!
We subtracted 39 from both sides to get rid of the "C" value. 
What you see around the 16 in the red equation is reference how we get our new "C" value. We found "64" by using (b/2)^2. Remember to add that number to both sides because what you do to one side of the equation, you must do to the other.

Whoa! How'd we get that purple equation?! Well, you must use  B/2 to find you "h" value. Don't forget to square the factor!
Now it's time to solve for X. Take the square root of both sides to eliminate the square. Remember  the square root of a number is +/-. 
Next add 8 to the 5 & -5.
Your final answers should be X=3 and X=13.





Our next problem:
*Note:Watch in HD, it gives way better picture quality so you can see what we're writing!

Here's another way of looking at it!

Our final problem:


Reflections!
Anna
I think the main reason we chose these problems was because we felt like we were experts at this topic and that we could teach them/ explain them well. I also liked these problems because there was a variety of topics in each problem. In all five problems they spanned through many units so I felt we showed our understanding of the entire trimester as a whole and tried to incorporate as much of it as possible. I feel from this project I understand the problems even more so than when I began. It  forced me to given a good reason for why I did the things in the problem, not just because Mr.Jackson told me to.I feel  in the future this assignment should be given at the very beginning of the trimester because maybe it would be easier to keep certain subjects in mind and to brainstorm problems. Overall, it was a decent project and the freedom of it was a lot  different than other school projects.

Hannah
I liked the idea of this project but it was not my favorite to work on. I felt like in order for my group to get a good grade, we would have to go above and beyond and use programs that I didn't even know how to use. I felt that the requirements for media tools was a little high for what this project was trying to accomplish.
Like I said, before, I like the idea of this project. It was good review for me and I was able to touch up on some ideas that weren't so clear before. However, I found that we spent more time trying to figure out our different media tools than we did with other things.
Overall, this project was alright. Anna and I chose topics that we thought would challenge us the most, and wanted to go above and try to explain a wide variety of subjects. We did a lot of double checking when working and it was nice being able to talk through the problems with someone. I enjoyed working with Anna and was glad to have some confusion cleared up.

DEV (Mackenzie Seth and Callie)

Seth's Reflection:

The reason I chose the concepts that I did was because I felt comfortable explaining them step by step. Even though I had some struggles throughout the class, these are the points I knew the best. Having to explain what I was doing aloud forced me to understand exactly what I was doing instead of just repeating the process over and over again. I learned a lot in this assignment through asking my partners questions to clear up parts that I was foggy on. This project was educationally valuable to me because it taught me to actually learn the material instead of just repeat steps.

Callie's Reflection:

I chose the concepts I did because I felt like these were the ones I could explain best. Even though most of the class I found understandable, the concepts that I chose to explain (such as logarithms) were things that I understood inside and out. I knew that these were ones I could facilitate with ease on the video. The other concepts that we did as a group (such as simplifying rationals) helped to clear up any uncertainties I had.  I found this project beneficial to do because it helped to review concepts that we might not have visited for a while, or forgotten about. In addition to the review this was helpful because it cuts down on time we have to spend trying to "relearn" how to do things from the beginning of the trimester, and fine tunes our skills. The only thing I would change is maybe have set problems given that you have to explain. I feel like that might be easier to do when it comes to creating them and would cut down on time spent trying to figure out problems and help do the actual project. Overall though I found this educationally valuable.

Mackenzie's Reflection:

As a group, we chose the concepts that we did because we felt that they were some of the most important concepts to learn and know. We felt like they were also the concepts that we knew the best and were most familiar with so we could teach them to the best of our ability. Though, some of the concepts that were my group members strengths were some of my weaknesses. In a way, this was a good thing because it helped to clear up some misunderstandings and confusion for me. I feel that the problems we chose best represented our understanding and overview of what we've learned so far because they are very important concepts to know. We also tried to choose problems that spanned several units so it showed that we had a good grasp and understand on more than just one unit. I think that this assignment was very helpful, because it forced me to really look at the problems and how to do them. It made it so that we had to pick apart the problems and really understand them so that we could reteach them the right way. I enjoyed this project and I believe that it really improved my understanding of important points in the information we have learned this trimester.

D.E.V. Project Stephany and Zoe

Math Around Mason on Prezi

We chose to do problems that illustrated the concepts that we had had the most difficulty with so that we could better understand them.  We chose 2 logarithms, 2 rationals and 1 factor by grouping problem.  This was a slow process because it was sometimes difficult to generate problems that worked and were solveable.  Once we had our problems, we thought it would be fun to do something around the town where we could demonstrate our knowledge and mastery of the concepts to others.  So we decided to go around to local businesses in Mason and, with the permission of the stores, we wrote and then solved the problems we created on their store windows using window crayons.  We got more than a few strange looks from passersby.  (We then thoroughly cleaned the windows.)

We discovered that much of the learning process happened not in solving the problems but in creating them, working backwards.  We gained a greater understanding of not just how the problems and solutions work, but why.

-Zoe and Stephany


Stephany's Reflection

Looking back on some of the problems, I realized how much of an understatement it was when I said I didn't understand. Having to create my own problems was extremely educationally valuable to me because it forced me to make sure I understood the concept. I had fun going around Mason and solving the problems. There was alot of laughing and it was really cool. The part that took the longest was getting five problems created, and solved that worked. Having to do that was really benificial. I looked at some other people's projects as well and those are really helpful to study from. You should definatly continue to use this project. It is a good tool for everyone to use, working through the problems, and looking at each other's projects.

Zoe's Reflection

I really enjoyed this project because it made me think more about the problems I was doing. I chose to do the log problems because I really understood how to do them. But while I understood HOW to do them, I didn't really why they worked or even all the steps. When I do math problems, I usually do most of the problem in my head and don't really think them through. Doing this project I had to slow down and think of how the problem worked. Another good thing about this project is that I got to understand the mechanics of Prezi. I really liked the idea of the project and would hope that it continues for future classes (not just precalc)