Created on: January 8, 2011

Website Address: https://library.curriki.org/oer/Algebra-in-the-End-Zone-Project--Reflections-on-Fall-2009-version

TABLE OF CONTENTS

**Algebra in the End Zone: The First Attempt**

Introduction

After the success of Writing in the End Zone which greatly increased the success of traditionally at-risk football players in their writing courses, we decided to attempt a similar approach in algebra. The inaugural class began with 13 student-athletes and had a traditional curriculum with an infusion of the algebra and analysis of football statistics. And the results were mixed at best, weak at the worst. I can say without any doubt that this was easily my worst class of the three classes I had this past semester. I can further say that while we did make progress, in terms of college level work habits and learning mathematics we did not make enough progress. But given that this was the first attempt, it will provide a good baseline. So while I can say that we did achieve well enough for the students to be successful in mathematics at the college level, without more information and more data for comparison I cannot tell you whether as a class we underachieved or overachieved. My gut tells me with confidence that we did not overachieve. Having said that, it also occurs to me that it is possible, given the make-up of the class, that we made decent progress, and that the Algebra in the End Zone must be viewed as progress made over more than one semester. With more experience and data we will know more. What follows is a summary of semester.

The end zone course

As noted above, the course took relatively traditional algebra content and into that infused the statistics of football. I have included copies of most of the football-related assignments and quizzes that we worked on throughout the semester. The class met for an extra hour per week. We met the standard Monday, Wednesday and Friday from 12-1 and then every Monday and Wednesday the players were scheduled for study hall with Coach Pollack. Coach Pollack and I agreed that Wednesday the players would spend the 1-2 hour with me. Initially I used this time to work on the football content of the curriculum. As the semester progressed we began to use the time more fluidly as needed. I used the extra hour to spend additional time on topics with which we were struggling, conferences with the players, and computer time. On a few occasions I also used the Monday 1-2 hour.

The semester viewed from afar

Viewed from afar, I see three distinct periods. The first period felt like a settling in period. Some days felt good and others absolutely horrible. On the good days I felt like the focus and attention to learning was strong, while the bad days could be absolutely disastrous. On my part I treated the students as I do most college students in that I give them considerable freedom and trust in their commitment to learning to keep each class focused on learning. For most classes at the college level this works well. For others more strict enforcement of rules of behavior is necessary. I adjust as needed. In the case of football players stricter enforcement was necessary. I began regularly counseling them, discussing their performance in algebra and their behavior. Finally, roughly 5 weeks into the semester, I took the Wednesday 1-2 hour to sit down with each student to discuss their grade and their behavior. I explained what was working and on what they needed to improve. That Friday went well, but the following Monday was another disaster. For some reason the players tended to be particularly unfocused on Mondays. We had discussed this and given that we had just talked one-on-one the past Wednesday I was ... well I was surprised at Monday going so poorly and ultimately I very pissed off. By the end of class I was furious and without going into detail I will just say I told them how I felt. It was not pretty but I definitely had their attention. On Wednesday I announced new rules (I have never had to do this in a college class before). The rules were as follows: (1) you must sit in the first three rows, (2) no cell phones or MP3 players should be visible during class and (3) no one talks unless I call on them. I told them I hate stupid sets of rules and that these were stupid rules but that I would do whatever it takes to make this a good class.

This brings us to the second period of the semester. Not sure what they thought but for some reason they followed the new rules. I told them how crazy it was that they followed the stupid rules but chose not to follow the rules that might help them to learn. In any event, we had quiet, not very interactive classes for a few days and gradually we got more interactive, the players raising their hands to talk. Occasionally I would ease off on the rules a bit, trying to get to a comfortable and more casual learning environment and away from a strict unbending environment, and they would get a bit out of control. And I would crack down, going back to the strict rules. This period lasted maybe 3 weeks.

Finally the third period brought a better balance to the classes. The players talked more freely but understood when it was time to stop. We were able to joke (which I love to do with all my classes) and still focus quickly back on the mathematics. We definitely found a better place and rhythm. I am not sure that we were necessarily doing that much better mathematics but we were at least behaving better and giving the impression of doing better mathematics. This period lasted to the end of the semester.

The semester viewed close up

While there certainly were successes, I cannot even remotely say that the semester was a success. If I were to summarize the results I would consider three groups of students. The first group would be comprised of those students who did well in the end zone course. I would suggest that these students would have done well in a traditional class. The second group would be comprised of those who did not do well in the end zone class. Clearly the end zone approach in some very critical ways did not help them or help them enough. And then there are those who lie in between these two groups, not doing particularly well and not really failing either. Here again it is hard for me to say that the end zone approach succeeded to any significant degree.

Some reflections and observations:

1. The students have their best focus when working actively on tasks in class.

2. The students do the minimal amount of homework and it is hard to move them to committing more time and effort to doing more thorough and thoughtful homework.

3. The students have a very short attention span when I am lecturing.

4. They can at times take great pride in the quality of their work, particularly on quizzes.

5. The students do not come to office hours except on very rare occasions.

6. I never got the class to really gel and, as a group, sincerely care about learning algebra.

To more clearly explain and to provide greater detail I thought it might be helpful to write a little profile of each of the students in the course.

I will begin first with the four who started the course but did not finish.

**Ashanti **

During the very first week of the semester, Ashanti announced that he was going to be the top student in the class. I told him that I hoped that would be the case. In short time Ashanti proved to be the worst by most any measure. He rarely did homework, had to be constantly reminded and monitored to do class work, and not surprisingly struggled on quizzes. After several weeks of poor, no make that dismal, performance and many warnings I told Ashanti he was not welcome in class until he showed some commitment to learning, and that he needed to come see me in office hours. After a couple of unsuccessful attempts to talk his way back in to the class he came to see me in office hours. We went over what he needed to do in order to earn his way back into class. We shook hands and I never saw him again. I dropped Ashanti about half way into the semester.

**Kyle**

Kyle showed two things during the time he participated in the class: first that he was capable of doing extremely well in the class if he chose to and second that he chose not to do more than the very minimum. Actually he gave the minimum for about half the semester. He then got sick apparently, gradually came to class less and less and then just disappeared. Rumor has it that he still occasionally attended his English class, but he stopped coming to algebra and I eventually dropped him. I wish I had more to tell you about Kyle but he would not engage substantively me at any level or on any topic. I never got anything to work with out of Kyle. So chalk Kyle up as a rather definite failure.

**Nate**

Nate would have to be classified as one of the failures of the semester, at least in the short-term. For the first 10 weeks of the semester Nate did a good job 80% of the time and a poor job 20%. During the good times Nate did all his work and mostly attempted to do it well, although often his goal seemed more to be to finish his work as fast as possible first and to do it well second. But when he missed a class he checked in to see what work he needed to make up. This is rare for these guys. Mostly when they miss a class they let that day go and move on as if they had not missed a thing. Suffice to say Nate was one of the brighter spots of this group and all in all I could have lived with that had it continued. But then Nate got sick, missed most of about two weeks and ... well he just checked out. No more making material up. He missed classes even on days that he was on campus. He seemed to stop caring. If fact on the last day to drop classes he showed up to ask if could stay in the class and in our conversation conveyed to me that he had in fact checked out for the past month. I told him it was too late and that you just cannot quit on a class for a whole month and realistically expect to or be able to make it up. So I dropped him.

This highlights something that I have struggled with. I have treated these guys differently because ... they are different. I treat all students differently based on them as individuals. But I came into the end zone experience expecting that this would be a particularly problematic population. Coming in with this tilt, if you will, I have been a bit tilted, off-balance, myself and feel that I have not held the standards that I normally do. Had I, I would have dropped well over half the class by mid-semester. And yet the guys need to learn to rise to higher standards. Of course if I drop them, I cannot help them, unless dropping them conveys a statement of minimum acceptable standards, which I am hoping will be the long-term story with Nate. But in the end ("the love you take is equal to the love you make" - sorry just a quick Beatles interlude) I need to find my bearings with this group. In time I will, but experience will be the vehicle.

** **

**Kevin**

Oh wow, what a disaster. Kevin never had a chance. Never believed he had a chance, never worked hard enough to give himself a chance, and just never was even close to being in the game. There were times he claimed to be trying, and he might have been, but the work he generated was so poor that it was hard to tell. I cannot even tell you what Kevin is capable of. I think the most salient issue with Kevin is that he is a space cadet. And I mean that quite literally. I watched day after day, week after week, a hard and impenetrable glaze come over Kevin's face in class almost immediately after I would begin to talk to the class, sometimes even when I talked directly to him. I talked to him about it, tried to have him focus on it and describe it, fight it, or even just recognize it. But there was no there there. Kevin just spaced (Kevin Spacey?). He did it in math and according to Bret he did it in football practice.

About mid-semester Kevin told me he wanted to try to improve, to do better in algebra. I said go for it. Nothing changed. His frequency and quality of work never improved. He came to class less and less. I dropped Kevin several weeks later after he stopped coming to class completely. The goal I have for all my students is growth and I can with confidence say in terms of growth this class failed with Kevin. Even worse is that I have no idea how to reach Kevin or how to help him.

So with that I leave the realm of complete failure to the realm of ... incomplete failure? Some degrees of success? Sure why not.

**Kasey and Doug **

Both Kasey and Doug received A grades for the semester and were the two most consistent and dedicated students in the class. I have a saying that goes like this: I assign it, you do it, not negotiable. Well except for Kasey and Doug, the guys pretty much ignored that. Kasey and Doug did do everything I assigned though and I am thankful for their commitment. And on that level one would have to view these two as a success of the course. But I still must take a bit of a negative angle here in that I believe if Kasey and Doug had been in a regular class of mine they would have done better. I believe that all the crap with which we had to deal prevented Kasey and Doug from achieving at a higher level.

To shed some light on this consider an assessment I give all my algebra classes somewhere towards the end of the semester. For all problems in the course I have my students follow a 3-step process that involves an explanation of the problem, doing the problem and checking all solutions. More specifically I have them do the following:

1. identify the type of problem,

2. state the goal of the problem,

3. describe the process required to achieve the goal,

4. do the problem and

5. check all solutions.

One of the outcomes that I hope to achieve from this is the ability to recognize how to do problems with which they are not completely familiar. For example we learn how to solve two variable linear equations (equations of the form *y* = *mx* + *b*) and why the approach we take (graphing) is necessary (because there are infinitely many solutions). If we do this correctly then it should be a natural step to be able to solve any two variable equation since the process is essentially the same. So without having discussed two variable quadratic equations I give them one (e.g., *y* = *x*^{2}) to identify, state the goal, describe the process and do. While they do not know the word quadratic they should be able to see that they are being asked to solve a two variable equation and that graphing is required.

The results of this short quiz I found interesting. Kasey struggled with the problem but did a decent job. Doug failed the quiz. Both Kasey and Doug finished in the bottom half of the class on this quiz. Four other students aced the quiz and showed very good grasp of the general concept of solving two variable equations. Some things I take away from this assessment are:

1. These guys are intelligent and if I can even get them to care about learning they will do well.

2. I found that Kasey and Doug are well-trained at the schooling game but not as good at the thinking game.

3. I could have helped Kasey and Doug more if I have not been so focused on the off-task issues brought on by the other students.

I any event, Kasey and Doug will do well because they care and are capable. I just am not so sure that the end zone class is the best place for them to learn.

**Saia **

I got the most satisfaction out of working with Saia. Saia started out pretty lukewarm on the class, began to slip away towards the middle of the semester but then came around over the second half. He is the one student who said he wanted to turn things around and actually did. Over the last 7-8 weeks Saia was the strongest student in the class. When he slacked off a bit several weeks from the end of the semester I called him on it and the very next class he turned in the two assignments he had missed plus two extra assignments that I had not assigned. Just as important, all the work was excellent. This last point is important. While most of the guys did manage to consistently do the homework much of it was not done well. For most all students at this level they need to learn the difference between doing homework and doing it well. Saia did the best homework in the class. Ultimately Saia also wrote the best paper in the class. The paper assignment was for the students to write a manual for solving equations. Saia used his own words and his explanations read very well. Again without any extra information I cannot know for sure but I think maybe that Saia might have done better in this class than in a traditional class. Regardless Saia did a good job, he knows the course material well, and received a B for the semester.

**Cory**

Cory just never cared much about the course. Every couple of weeks he would make some kind of an attempt at making a good contribution to the class and to his learning. But none of these attempts ever lasted more than a day or two. Then Cory would just kind of fade away, sometimes physically in that he would not even come to class and other times mentally, often both.

I had a couple of lengthy conversations with Cory about school, football and his life. But I never really felt I got through to him. I always felt like Cory did not trust me or maybe he did but just really did not care about algebra and sought only to do as little as possible and hope he would pass. It would take a monumentally optimistic person to call Cory a success to any degree. That is a euphemistic way of saying I believe that the program did not work for Cory. He received a D for the semester and never really was close to passing the course.

**Mike **

When I first began working with Mike I was very concerned that he was not ready for the class. Boy first impressions can be so wrong. Mike is one of the most intelligent students in the class, maybe the most intelligent when it comes to algebra. Whatever I saw that worried me at the beginning of the semester just flat out missed the mark with Mike. He is very good at algebra, when he tries. The key of course is getting him to try on a consistent basis (tell me if you have heard this before). When he does try Mike is fun to work with. He really grapples with the material and I can see that he really understands what he is doing. Recall the quiz I gave the students on *y* = *x*^{2} described in the Doug and Kasey section. Mike did great on this and additionally on a similar problem on the final exam when I asked them to identify, state the goal of, describe the process for, and do *y* = *x*^{3} + 1. Where others memorize, Mike thinks. This is rare in students at the algebra level.

Mike could be such a strong student if he applied himself over an entire semester. He even professes to like math. And when he is into learning, Mike rocks as a student. And when he is not into learning, he can be a pain in the butt. Overall if I had a class full of Mikes I think it would be an inconsistent but ultimately good class. Mike received a C for the semester. While he is surely capable of A work it is not clear to me whether this class or any other class would make much of a difference to him. He goes his own way.

**Solomon**

Solomon began the semester well, had a few minor bumps and the middle and then faded seriously at the end. Throughout all his ups and downs he really was a pleasure to have in class. He had generally good focus when I lectured and he worked great in small groups, talking problems through, seeking help when he needed it and helping others when he could. He ultimately just missed too many classes and too much homework. He always had good reasons for missing class but never made up what he missed. This is a common thread with most all of the guys. With few exceptions (Kasey, Doug and Saia), when they miss a class it never occurs to them to ask about what assignments, class work or quizzes they missed, let alone to make it up. They go on as if nothing had happened at all. And so it was with Solomon. As he got further and further behind, we had brief conversations about what he needed to do the catch up but in the end he never made the work up. Solomon did not show up for the final exam (although he did email me during finals week - really this is an amazingly rare act for these guys) and ultimately failed the course. Hard to see much success here but I can say it was good getting to know Solomon and I am hopeful about next semester.

**Mark**

Mark has been are hard nut to crack. He did not offer much in the way of interaction with me certainly when talking algebra but even when talking football. But he never missed class and most always did his homework (but again his quality standards were not as high as I would have preferred). On the dark side he constantly forgot to bring his calculator, which helped to do many problems including problems involving fractions, and then complained about not being able to do fractions. He also tended to confine his work to the traditional textbook assignments which I spent much of the semester trying to convince them that doing those assignments is necessary but not sufficient to high quality learning of algebra. But in the end it felt like Mark was just playing the game called math class. While he was not disruptive he also did not contribute much to a better class, a better focus on learning. If I reached Mark in any significant way I have seen no indication of it. While he passed with a C grade I am not confident in his algebra abilities. But mostly I just hope to get to know Mark better next semester so that I can hopefully be more successful in reaching him.

**Nikko**

I had Nikko for Math 811 last spring semester. Nikko so pissed me off with his poor work ethic that I began the semester ready to drop him. He had survived Math 811 because the structure of the course allows one to pass the course by passing three exams and Nikko knew enough arithmetic to cram for and pass the three exams. But in algebra Nikko struggled and his poor work ethic prevented him from learning much. He ultimately did not even show up for the final exam and failed the class.

I did however make some progress with Nikko. While he did not work nearly hard enough to succeed in the course he did show signs of hard work. Again his effort was far too inconsistent to have much positive effect but nevertheless I saw Nikko take some pride in his performance. It is a little thing but it is better than nothing. Outside of academics, I was able to help Nikko as he worked through some financial issues. Between helping him secure a student loan and attending games, I believe that Nikko believes that I really am there for him, to help him, anyway I can. Whether this will "pay-off" academically who knows. In spite of Nikko's grade in the course I do feel a sense of success with him and do believe that the end zone program helped in his case.

** **

**Alex**

Alex is a kick. He is just a big offensive lineman with a pleasant and happy personality. I very much enjoyed having him throughout the semester. While he still fell into the "I do homework but not quality homework" category too often, he did at times do good homework and by the end of the semester he would talk trash about how good his quizzes were, which many were, and about all the extra credit he would be receiving because of the excellent work he did. He honestly cared about doing well in the class and overall I would have to say he represents a success of the semester.

One of the coolest things Alex did was take the final exam, an exam from which he was exempt. Briefly one of my main goals for any class in any semester is to keep the focus on learning and growth rather than on test taking. Towards that end I gave the students a chance to be exempt from the final exam. To be exempt I ask that they (a) do well in the course in terms of grade and (b) work hard for 17 weeks. The point here is that I value 17 weeks of good, hard, consistent training in algebra over the results of one 2.5 hour written exam. In this class Kasey, Doug, Saia and Alex received exemptions. So Alex had a B for the semester guaranteed without taking the final but came to take it anyway. That was cool. He did a good job on the exam and received a B for the semester. But more importantly he showed that he cared about the course and learning. Yeah, I think Alex should be considered a success of Algebra in the End Zone.

So there it is. For me personally in terms of effort, I gave it my best shot and I feel good about that. In terms of achievement, I cannot say there is all that much to feel good about. But hey you give your best shot, get knocked on your ass, drag yourself back up and try again. What the hell, that is what makes life interesting. I think perhaps I might go grab a beer. Blue Moon anyone?

**Appendix**

What follows is a collection of assignments I wrote for the course. While there were many variations of each assignment and quiz actually used in the class, these represent the spirit and content of the "infused algebra and analysis of football statistics." One key adaptation involved using the game statistics from the most recent game and the cumulative statistics from the whole season.

**A. "Algebra in the End Zone" - A Summary of Important Equations**

Equations with which we should be very familiar:

Average Yards Per Event

Average yards per event =

Specifically we have the following equations which are all specific cases of the general equation stated above.

Average yards per carry =

Average yards per reception =

Average yards per return =

Average yards per completion =

Average yards per attempt =

Percent

Percent = Amount out of 100 =

Specifically we have the following equations which are all specific cases of the general equation stated above.

Completion percentage =

Touchdown percentage =

Interception percentage =

Quarterback Ratings

College rating equation: QB Rating = Completion % + 3.3(TD%) - 2(Int%) + 8.4(

Professional rating equation: QB rating =

**B. "Algebra in the End Zone" - ****Assignment #1: **One of each type of formula minimum to set the scene.

You may use a calculator but must show me what you entered into your calculator to arrive at each answer.

1. Leading rusher Daniel Porter rushed 183 times for 823 yards in 10 games. How many rushing yards did Daniel average per game? What was his average gain per rush?

2. Leading receiver Eric Robertson caught 26 passes for 384 yards in 10 games. How many receiving yards did Eric average per game? What was his average gain per reception?

3. Leading punt returner Eric Robertson returned 12 punts for 185 yards in 10 games. How many punt return yards did Eric average per game? What was the average length of each return?

4. Quarterback Matt Pelesasa completed 22 of his 40 attempted passes for 293 yards. He threw 3 touchdown pass and had 3 intercepted.

(a) How many yards per attempt did Matt average?

(b) How many yards per completion did Matt average?

(c) What percent of his passes did Matt complete?

(d) What percent of Matt's passes were for a touchdown?

(e) What percent of Matt's passes were intercepted?

** **

** **

** **

** **

** **

**C. "Algebra in the Endzone" - Assignment #2: **Focus on comparison. Who is better? Why?

You may use a calculator but must show me what you entered into your calculator to arrive at each answer.

1. Recall the following statistics:

- Eric Robertson returned 19 kicks for 492 yards and no touchdowns.
- Jarret Gooden returned 6 kicks for 188 yards including one for a 95 yard touchdown.

Who was the better kick returner? Explain your reasoning.

2. Recall the following statistics:

- Quarterback JT Ramos completed 55 of his 104 attempted passes for 611 yards. He threw 3 touchdown passes and had 10 intercepted.
- Quarterback Wes Price completed 28 of his 62 attempted passes for 354 yards. He threw 1 touchdown pass and had 3 intercepted.
- Quarterback Matt Pelesasa completed 22 of his 40 attempted passes for 293 yards. He threw 3 touchdown pass and had 3 intercepted.
- Quarterback Justin Montes completed his only pass for 21 yards for a touchdown.

Who was the better quarterback? Explain your reasoning.

** **

**D. "Algebra in the Endzone" - Assignment #3: **Practice with all the relevant equations.

All the statistics cited below are totals from College of San Mateo Bulldogs 2008 football season.

1. Leading rusher Daniel Porter rushed 183 times for 823 yards in 10 games. How many rushing yards did Daniel average per game? What was his average gain per rush?

2. Leading receiver Eric Robertson caught 26 passes for 384 yards in 10 games. How many receiving yards did Eric average per game? What was his average gain per reception?

3. Leading punt returner Eric Robertson returned 12 punts for 185 yards in 10 games. How many punt return yards did Eric average per game? What was the average length of each return?

4. Eric Robertson returned 19 kicks for 492 yards. How many kick return yards did Eric average per game? How yards per return did he average?

5. Jarret Gooden returned 6 kicks for 188 yards including one for a 95 yard touchdown. How many kick return yards did Eric average per game? How yards per return did he average?

6. Eddie Elder led CSM in interceptions with 6. Eddie returned the interceptions for a total of 121 yards. How many return yard did Eddie average per game? How many yards did Eddie average per interception return?

7. Quarterback JT Ramos completed 55 of his 104 attempted passes for 611 yards. He threw 3 touchdown passes and had 10 intercepted.

(a) How many yards per attempt did JT average?

(b) How many yards per completion did JT average?

(c) What percent of his passes did JT complete?

(d) What percent of JT's passes were for a touchdown?

(e) What percent of JT's passes were intercepted?

8. Quarterback Wes Price completed 28 of his 62 attempted passes for 354 yards. He threw 1 touchdown pass and had 3 intercepted.

(a) How many yards per attempt did Wes average?

(b) How many yards per completion did Wes average?

(c) What percent of his passes did Wes complete?

(d) What percent of Wes's passes were for a touchdown?

(e) What percent of Wes's passes were intercepted?

9. Quarterback Matt Pelesasa completed 22 of his 40 attempted passes for 293 yards. He threw 3 touchdown pass and had 3 intercepted.

(a) How many yards per attempt did Matt average?

(b) How many yards per completion did Matt average?

(c) What percent of his passes did Matt complete?

(d) What percent of Matt's passes were for a touchdown?

(e) What percent of Matt's passes were intercepted?

10. Quarterback Justin Montes completed his only pass for 21 yards for a touchdown.

(a) How many yards per attempt did Justin average?

(b) How many yards per completion did Justin average?

(c) What percent of his passes did Justin complete?

(d) What percent of Justin's passes were for a touchdown?

(e) What percent of Justin's passes were intercepted?

**E. "Algebra in the Endzone" - Assignment #4: **Practice with the QB rating equations.

For each quarterback find their QB rating using (a) the college rating equations and (b) the professional rating equation.

1. Quarterback JT Ramos completed 55 of his 104 attempted passes for 611 yards. He threw 3 touchdown passes and had 10 intercepted.

(a) How many yards per attempt did JT average?

(b) How many yards per completion did JT average?

(c) What percent of his passes did JT complete?

(d) What percent of JT's passes were for a touchdown?

(e) What percent of JT's passes were intercepted?

2. Quarterback Wes Price completed 28 of his 62 attempted passes for 354 yards. He threw 1 touchdown pass and had 3 intercepted.

(a) How many yards per attempt did Wes average?

(b) How many yards per completion did Wes average?

(c) What percent of his passes did Wes complete?

(d) What percent of Wes's passes were for a touchdown?

(e) What percent of Wes's passes were intercepted?

3. Quarterback Matt Pelesasa completed 22 of his 40 attempted passes for 293 yards. He threw 3 touchdown pass and had 3 intercepted.

(a) How many yards per attempt did Matt average?

(b) How many yards per completion did Matt average?

(c) What percent of his passes did Matt complete?

(d) What percent of Matt's passes were for a touchdown?

(e) What percent of Matt's passes were intercepted?

4. Quarterback Justin Montes completed his only pass for 21 yards for a touchdown.

(a) How many yards per attempt did Justin average?

(b) How many yards per completion did Justin average?

(c) What percent of his passes did Justin complete?

(d) What percent of Justin's passes were for a touchdown?

(e) What percent of Justin's passes were intercepted?

**F. "Algebra in the End Zone" - Assignment 5** - The QB rating formula - college versus professional. What is different? Which is best?

**G. "Algebra in the End Zone" - Assignment 6** - Develop formulas for defensive players, non-QB offensive players, kickers, ...