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)

D.E.V. - Andy

https://docs.google.com/viewer?a=v&pid=explorer&srcid=0BzVy65zMaBWeQkRjd3dmRTJjX0k

Question 1:

Solve the following quadratic equation:

5x² + 20x – 466 = 119

The General Form of a quadratic is y = ax² + bx + c

Step 1: Set the equation equal to zero. So in this case, subtract 119 from each side.

            5x² + 20x – 466 = 119

                              -119   -119

5x² + 20x – 585 = 0

Step 2: Factor out the greatest common factor, or the largest number that goes into each term. For this equation, it is 5.

            5x² + 20x – 585 = 0

            5        5        5

            5(x² + 4x – 117) = 0

If you didn’t realize it factored, follow this link: http://www.youtube.com/watch?v=1lmO0Np1Jbw

Note: After factoring out the GCF, it always stays with the equation outside the parenthesis.

Step 3: Determine what factors multiply to get -117 that also add up to 4.

            Factors that multiply to get -117: 3*-39, -3*39, -13*9 and 13*-9

            Of these, only 13*-9 add up to get 4.

Step 4: Convert the equation to factored form.

            5(x + 13)(x – 9) = 0

            You know this works because if you expand it, you get the equation set equal to zero which was: 5x² + 20x – 585 = 0.

Step 5: Solve for x. To solve for x, you must set both (x + 13) and (x – 9) equal to zero then get x all by its self for both.

            (x + 13) = 0                 (x – 9) = 0

                  -13     -13                    +9     +9

             x = -13                        x = 9

            Now that we have factored the equation and solved for x, all we have left to do is find the vertex of the equation.

Find the vertex:

5x² + 20x – 585 = 0

Step 1: Find the “x” of the vertex. The “x” of the vertex equals –b

                                                                                                  (2 * a)

            x = -20             x = -20             x = -2

                (2 * 5)                 10

            So the x of the vertex = -2

            Note: In this case the “-b” means opposite b. If the b value was negative, the number would become positive and vice versa.

Step 2: Plug -2 back into the original equation to get the “y” of the vertex.

            y = 5(-2)² + 20(-2) – 585         y = 20 – 40 – 585        y = -605

            Vertex: (-2, -605)

Graph the equation

5x² + 20x – 585 = 0

Step 1: The only value we don’t have is the y – intercept. The y – intercept is the constant number, or the number that doesn’t change, in each equation. The only number that will not change is -585.

            The x – intercepts we found when solving the original equation for x.

            X – Intercepts: (-13, 0) (9, 0)

            Y – Intercept: (0, -585)

            Vertex: (-2, -605)

A link to the equation graphed: http://www.youtube.com/watch?v=qBSQCYSWH38
Question 2:

Solve the following equation:

Log₂₁(4) + Log₂₁(3x+2) = Log₂₁(4x+1) - Log₂₁(9x+2) + 2

Step 1: Get all the logs on onto one side.

            Log₂₁(4) + Log₂₁(3x+2) = Log₂₁(4x+1) - Log₂₁(9x+2) + 2

            -Log21(4x+1)                 - Log₂₁(4x+1) + Log₂₁(9x+2)

            The equation now looks like:

            Log21(4) + Log21(3x+2)) + Log21(9x+2) - Log21(4x+1 = 2

           

Step 2: There are 8 rules of logarithms, two of which apply here.

            The product rule of logarithms: Log_aM + Log_aN = Log_aMN

            The quotient rule of logarithms: Log_aM - Log_aN = LogM

                                                                                                    N

            Applying these rules, the new equation is:

            Log₂₁(4)(3x+2)(9x+2) = 2

                              (4x+1)

Step 3: Turn the equation into an exponential.

            21² = (4)(3x+2)(9x+2)             441 = (4)(3x+2)(9x+2)

                            (4x+1)                                        (4x+1)

Step 4: Multiply both sides by the denominator.

            (4x+1) * 441 = (4)(3x+2)(9x+2) * (4x+1)      =          1764x + 441 = 108x² + 96x + 16

                                            (4x+1) 

Step 5: Set the equation equal to zero.

            1764x + 441 = 108x² + 96x + 16

           -1764x -441                  -1764x  -441

            108x² – 1168x – 380 = 0

Step 6: Complete the square. Add the constant to the other side.

            108x² – 1168x – 380 = 0

                                    + 380    + 380

            108x² – 1168x = 380

Step 7: Factor out the “a” value.

            108(x² – 1168x) = 380

                            108

Step 8: Find the perfect “c” value using (b²) and then add a * (b²) to the other side.

                                                                                      2                                 2

            108(x² – 1168x + 21316) = 380 + (108 * 21316 )

                            108         729                               729

Step 9: Factor into the perfect square binomial.

            108(x – 1168)² = 1768962963

                          216           500000

Step 10: Divide each side by the “a” value.

            108(x – 1168)² = 1768962963

                          216           500000

                          108              108

Step 11: Take the square root of each side.

            √(x – 1168)² = √3275857337

                                       100000000

Step 12: Isolate the variable.

            x – 1168 = +-5723510581 + 1168

              + 1168         1000000000

Step 13: Solve for x.

            x = 5723510581 + 1168 = 1173723511         x = -5723510581 + 1168 = 1162276489

                  1000000000                  1000000                     1000000000                    1000000

Question 3

Factor the following polynomial and solve:

7x⁴ + 35x³ – 84x² – 420x = 0

Step 1: Factor out the greatest common factor.

            7x(x³ + 5x² – 12x – 60) = 0

Step 2: Put the equation into two sets of parenthesis. In order to do this, two things must be true:

1: The four terms in each equation must be increasing by the same increment. In this case, 5.

2: All numbers must have the same sign.

            7x(x³ + 5x²) – (12x + 60) = 0

            Note: In the second set of parenthesis, it becomes positive 60 instead of negative 60. This is because subtracting a negative is the same thing as adding a positive value. So we change the sign to accommodate rule #2.

Step 3: Factor out the greatest common factor from each parenthesis.

            7x[x²(x + 5) – 12(x + 5) = 0

Step 4: Combine the greatest common factor from both parenthesis into one.

            7x(x² – 12)(x + 5) = 0

Step 5: Solve for x.

            7x = 0              x = 0                x + 5 = 0                      x = -5

            7      7                                         - 5   - 5  

            x² – 12 = 0                   √x² = √12                    x = +-√12                   

                + 12   + 12

Question 4

Find the domain of the following equation:

√3x² +21x + 36 = 0

                                                          72x + 9327

Note: The entire numerator of the equation is under the radical. My computer just doesn’t allow me to do that.

Step 1: Let’s just start with the numerator to begin with. Factor out the greatest common factor.

            3(x² + 7x + 12) = 0

Step 2: Factor the numerator.

            3(x + 4)(x + 3)

Step 3: Determine the range for the numerator by solving for x. Because the numerator is under a radical, the equation cannot be a negative number. So we must set the terms greater than or equal to zero.

            x + 4 ≥ 0                                  x + 3 ≥ 0

                - 4   - 4                                     - 3   - 3

            x ≥ -4                                       x ≥ -3

Step 4: Now let’s find the range for the denominator by solving for x. However, because this is in the denominator, the term cannot equal zero because dividing by zero is undefinable. So x cannot equal zero.

            72x + 9327 ≠ 0

                    - 9327    - 9327

            72x ≠ -9327

            72         72

            x ≠ -129.542

Step 5: Combine both domains into one.

            (-∞, -129.542) U [-4, -3] U [-3, ∞)

You may notice there are parentheses around certain numbers and brackets around others. Because (-)∞ is not reachable and cannot be plugged into an equation, a parenthesis is used. One is also used on -129.542 because the number cannot be plugged into the denominator or else it would equal zero, which isn’t allowed. Brackets are used on the other numbers because they can be plugged into the equations. This is because under a radical, the number cannot be negative. Plugging the numbers in would not make any negative. The U means union which just combines the domains together.


Reflection:


This project wasn't fun for me like I thought it would be. It turned out to just be a whole lot of stress. I thought I was going to be able to do something really creative and fun, but, because of how crappy my computer is and my lack of internet, I had to do a crappy extended blog post. I picked the problems that I did because they were what I struggled with from the respective units. I thought that creating problems and solving them would help me get a better grasp on the material, which it did. Making the problems was a struggle in its self. I hated having to be able to come up with equations that were not only challenging but solvable. Running through everything step by step for the post made things seem to make a lot more sense. That’s why I chose the problems that I did. These problems provide my best mathematical understanding because I tried to make them very challenging. For me, each problem took about an hour to two hours to create to make them complicated.  These are all hard question for me so to be able to create them and solve them is a great way to prove my understanding of what I’ve learned thus far. This was somewhat valuable to me. I don’t think it helped as much as it could. I still need to use my notes to complete some types of problems such as completing the square. However, it did make me have a better overview of the subjects that I covered. I learned that hard-work pays off for projects like this. Spreading my time out more wisely would have benefitted me more for this project. I didn’t like how broad this project was. If the questions had designated topics, it would have been easier for me to come up with the problems. Leaving it as broad as it was freaked me out and put me in a “deer in headlights” type trance that made me get lost trying to figure out what to do.

D.E.V.

hey Mr. Jackson this is our project
http://thegeniusesprecalcfunctions.weebly.com/
Branden and Emma were in my group

DEV - Tyler

I chose the problems that i did because they where some of the more difficult ones for me, i had some real problems earlyer on in this class, and that is why some of mine are from earlier units. i attempted to add a more to problems that we were already used to doing, by adding something we had never seen before in order to add to the complexity. In the beginning i didn't believe this project would help at all. Once i began working i remembered stuff i had forgotten weeks ago. It helped me have a review in some areas of the class that i had forgotten. Overall a not bad project that helped with for the exam.


-Tyler Fassezke

Kristi's DEV Project

https://www.dropbox.com/s/5l39e2h38ud3vm0/DEV%20Project.docx?m

Summary is included in file. Enjoy :)

Patrick and Quincie's :) DEV Project

D.E.V.-Katelynn

D.E.V.-Katelynn from KatelynnNoel

This project really helped me understand the problems more in depth. When you have to think about creating a problem that will work, you think about it on a different level than just solving it, that different level increased my comprehension. I chose these concepts because I felt I had a good understanding of them and I could teach them to another person. Overall this project went well, my only problem was time management because I am a habitual procrastinator.

DEV Project

For the DEV project the most difficult thing was coming up with problems. I felt like I couldn'
t make the problems hard enough or long enough, which made me feel frusterated.  It was also hard to get what I wanted to say on a slide, I had a lot of trouble wording what I wanted to say. Otherwise than  that I didn't think that it was too bad.
 

Dev project from Annikawp

Dannica and Taylor's DEV!

DEV from dannicahoskins

http://www.slideshare.net/dannicahoskins/dev-15331554

D.E.V. - Doug

Jackson d.e.v. from Dougfield32

http://www.slideshare.net/Dougfield32/jackson-dev

DEV NICOLE AND DYLAN

Pc functions final project D.E.V. from NICCIROSE

http://www.slideshare.net/NICCIROSE/pc-functions-final-project-dev#btnNext

The D.E.V. is in SlideShare

D.E.V. Sarah.

D.E.V. Sarah. on Prezi

Not only did the concepts I chose help me review for the final exam, but I learned to develop solvable problems and now understand the process it takes to form these questions.  I chose to incorporate difficult concepts to grasp at first, but improve with repetition.  I feel the problems I formed show vital mathematical knowledge that helped me to expand on the basic concepts.  I wanted to create challenging problems, but not problems that one would spend hours working on.  Honestly, I believed this project would be much easier than it actually was.  Like a lot of things I thought I could spend a couple hours and have solid work however it took over ten hours to form questions and put them online.  Through weeks of struggle, I formed questions that I can be proud of.  Working hard on a project makes me appreciate what I had to do in order to understand the different concepts.  With trial and error on each and every single problem I also learned that I don't work best frustrated, and if I start to get upset if a problem isn't perfect to take a break and come back to it.  I had to stop halfway through a problem numerous times just to calm down and collect my thoughts.  If I spent too much time on an unsolvable problem, then I was wasting time that I could use to create a new problem.  I was glad I managed to spread my work out over the course of a couple weeks rather than a single day because it would have been near impossible. Overall, this was a unique project that tested my knowledge over the span of the trimester.  I found this project to be useful to me because I gained responsibility with relying on myself to construct problems in an efficient manner, yet having beneficial information within the problems.  I hope to continue to expand on intriguing topics in mathematics.

"In three words I can sum up everything I've learned about life: it goes on"       -Robert Frost

Sarah.

Paige's DEV

Paige's DEV from ps114

For this project, I tried to look at the types of problems that people (including myself) found impossible or hopeless.  I wanted to capture the idea that in order to move forward, we have to look back at mistakes, regardless of how humiliating or time consuming or upsetting it may be.  I tried to use content from more than one unit in each problem, which is specifically why I used a logarithm for the farmer ted type problem.  Although it’s not exactly “necessary”, I wanted to incorporate the relationship between logs and exponentials in some way.  I focused a lot on domain and long division because they require a complex understanding of small details.  Also, I included rational functions because I had the most problems with that unit, and wanted to improve on those.  I used a farmer ted type problem because I have found that concept of finding the maximum or minimum x value to be very useful.  I look at this project as a glimpse of a journey, which is where I got the idea for my theme.  My goal when working on this project was to portray pre-calc functions as entirely possible, while also displaying the knowledge I have gained throughout the trimester.  Overall, I gained knowledge as I put these problems together because I had to work backwards.  Though it was very stressful at times, this project made me think about the content we’ve learned in new ways and helped me review for the exam.


- Paige

DEV Struggles

So, I am sitting here, trying to think of ways to make my project the most creative and complicated thing ever and I'm drawing blanks. Can someone help me please? I cannot, for the life of me, think of a way to make a math problem "creative."

DEV-Math Wars by Libbey and Greg

Please watch the video clip before clicking on the link below to view our project. 

Here's the link: http://www.authorstream.com/Presentation/LibJones-1599104-dev/

DEV

More PowerPoint presentations from Libbey

Libbey,

I have always enjoyed a good challenge, and when Mr. Jackson introduced this project, I knew that I wanted to create a project that would not only challenge myself, but challenge others.  My partner and I chose the concepts that we did because they were some ideas that we struggled to grasp at first but wanted to improve our understanding on.  Also, we chose ideas such as long division or graphing because even though the problems take a long time, for my partner and I they are fun to work through and rewarding when they are finally solved.  When creating the problems, my partner and I tried to demonstrate a complete understanding of the concepts by making the problems challenging and tough to work through.  My partner and I created 5 problems that included concepts from almost every single unit of study.  Creating the project was a great way to review information from all of the units and touch back on concepts that we found challenging at first. 

Overall, I learned a lot from this project.  I was able to review a lot of the concepts that we studied throughout the trimester.  It was a perfect way to review for the exam because it required looking back through notes, and worksheets in order to create the problems.  Also, by doing this project, I learned new ways how to complete a project online, using different technology sources and tools.

I think that this project should definitely be used in the future because it is a really good way to study for finals and truly grasp all of the concepts that we learned in Pre-Calculus Functions.  It is a good way to get students to challenge themselves and think creatively.

Greg,

My partner and I created five problems that demonstrated our highest  understanding of the math concepts that we chose.  We did not necessarily pick concepts from the units that we understood the best, for we felt that in order to improve our mathematical skill we needed to work with concepts that we had both previously struggled with.  These five problems show our best mathematical understanding of the concepts that we chose because the problems we created are long and challenging, and each problem includes multiple concepts from multiple units.  In each problem we tried to make them complicated and cumulative; meaning that in order to find the final answer of each problem, one must solve for multiple solutions along the way.

This assignment was very valuable to me personally.  It not only allowed me to deepen my understanding in all of the concepts that my partner and I chose, especially the concepts that were fuzzy in my mind, but it also enabled me to demonstrate my (hopefully) expert understanding of the concepts.  This project should definitely be assigned in the future.  Not only was this project a great review for the final exam, but it also allowed me to actually (physically) show my understanding of the many concepts that are included in my problems.  The project let me actually teach the problems that my partner and I created.  There are many educational benefits for students in this project; therefore, I believe it should be assigned for future classes.

Thanks to all of my classmates, especially my lovely partner.

From both of us:

Thank you Mr. Jackson for a great learning experience and for always being there for all of us when we needed you.