Saturday, November 24, 2018

Small Business Saturday Post

Table of Contents

1. Pappas Question of the Day
2. Small Business State Meet Saturday
3. Starting Line: Freshman Year
4. Mile 1: Sophomore Year
5. Mile 2: Junior Year
6. Finish Line: Senior Year
7. Cross Country and Academics
8. McFarland USA
9. McFarland's XC Team -- and My Team -- Now
10. Conclusion

Pappas Question of the Day

Today on her Mathematics Calendar 2018, Theoni Pappas writes:

The area of ABCD = ?

(Here is the given info from the diagram: AB = 5', BC = 6', CD = 3', Angles C, D are right angles, AD unknown but it's clear that AD > BC.)

Notice that Quadrilateral ABCD is a (right) trapezoid. To find the area of a trapezoid, we need its height and two bases. The height is CD = 3 (the height because of the right angles) and one of its bases is BC = 6. But we don't know the length of the other base AD.

Let's drop a perpendicular from B to AD and label the foot of the perpendicular E. Then BCDE is a rectangle, with ED = BC = 6 and BE = CD = 3. So ABE is a right triangle with leg 3 and hypotenuse 5, and then it's easy to find AE, the other leg using the Pythagorean Theorem:

a^2 + b^2 = c^2
BE^2 + AE^2 = AB^2
3^2 + AE^2 = 5^2
9 + AE^2 = 25
AE^2 = 16
AE = 4

And AD = AE + ED = 4 + 6 = 10, so we finally have the length of the other base. Now we can use the trapezoid area formula:

A = (1/2)h(b_1 + b_2)
A = (1/2)(CD)(BC + AD)
A = (1/2)(3)(6 + 10)
A = 24

Therefore the area of Trapezoid ABCD is 24 square feet -- and of course, today's date is the 24th.

The trapezoid area formula appears in Lesson 8-6 of the U of Chicago text. But this problem can't be solved until after the following lesson, Lesson 8-7. This is because the Pythagorean Theorem is needed to find one base of the right trapezoid.

Small Business State Meet Saturday

Today is Small Business Saturday, the day after Black Friday and two days after Thanksgiving. It was created by American Express in order to encourage Christmas shopping at local stores. It can be shown that "Saturday after Thanksgiving" is equivalent to "last Saturday in November," which makes the date easy to find on a calendar.

But Small Business Saturday has only existed since the start of the decade. To me, the Saturday after Thanksgiving has had another meaning -- the day of the California State Cross Country Meet. This is a race of about three miles (actually five kilometers) in length.

I've mentioned my career as a high school distance runner several times on the blog (most recently on Halloween and All Saints Day, when I spoke to the XC runner in the class I subbed for). Therefore, I'll devote today's post to a full discussion of my cross country career. After all, it's still Thanksgiving break as well as State Meet Saturday.

But first, let me point out the significance of the date. The State Meet was always held the Saturday after Thanksgiving. In fact, the dates of all the races can be determined by counting backwards from State Meet Saturday (or Thanksgiving). On the other hand, the dates of the first day of school, the second semester, and the last day of school are determined at many schools by counting forward from Labor Day, not Thanksgiving.

For example, here were some key dates from my own days as a XC runner:

  • First race of the season: 12 Saturdays before State Meet (first Saturday in September)
  • Last dual meet of season: 4 Thursdays before Thanksgiving (last Thursday in October)
  • League Finals: 3 Thursdays before Thanksgiving (first Thursday in November)
  • Section Finals: Saturday before Thanksgiving (penultimate Saturday in November)
  • State Meet: Saturday after Thanksgiving (last Saturday in November)
Since then, some of these dates have changed. For example, there's now a tendency for dual meets in many leagues (including my own) to be held on Wednesdays, not Thursdays. The first race of the season is also now a week earlier (the last Saturday in August). But the State Meet hasn't changed.

In other high school sports, such as football, the dates have changed dramatically -- the season starts nearly a month earlier now than my own high school days. This is mainly so that there's enough time to hold the state finals comfortably before Christmas. (In my days, there were no state football finals.)

Football season now begins 14 weeks before Thanksgiving (in mid-August). The season itself is 11 weeks long (enough for ten games and a bye week). In November, four rounds of sectional playoffs take place (at least here in the Southern Section -- the state's largest section). The first round is three weeks before Thanksgiving and the last round is this weekend. Last night, a sectional finals game took place between arguably the top two teams in the nation -- Mater Dei and St. John Bosco. (In the end, Mater Dei upset Bosco 17-13.) Then there are two weeks for state semifinals and state finals.

I often wondered why the new football schedule would take effect this year, when Thanksgiving falls on its earliest possible date (November 22nd). It would have been less a shock for players and coaches had the transition occurred next year, when Turkey Day is as late as possible (the 28th).

But the extra week turns out to be beneficial this year -- due to the California wildfires, many playoff games were cancelled. The state finals were pushed back a week, to December 14th-15th. So starting the season early allows some leeway if a game needs to be cancelled (for wildfires or any other reason) and still allow the state finals to be played before Christmas.

That's enough about football -- let's get back to my sport, cross country. Actually, I've read that some cross country races were also cancelled, including the Los Angeles Section Prelims. (That's right -- the LAUSD, as well as charters within LAUSD, aren't part of the Southern Section but are placed in their own City Section.) Instead, all LA City teams proceeded directly to the section finals.

In today's post, I wish to tell you the story of how I became a high school cross country runner.

Starting Line: Freshman Year

I admit that growing up, I'd never thought of myself as an athlete, much less a distance runner. I've heard that I had a slender frame -- a runner's body. But still, running races wasn't something that I had an urge to do. For most sports, I was often the proverbial "last person picked."

I remember one day in seventh grade, when the P.E. teacher had all students compete in two races on the track -- 200 meters and 400 meters. After the races, she told the first few runners in each race to stand up and be acknowledged. I was one of the top runners in the 400, but not the 200. As I stood up, another student -- one of the top 200 runners -- remarked that we weren't the fastest runners. In a way, he was right -- the 200 is a pure sprint. The 400, while not exactly a distance race, nonetheless isn't a pure sprint either. Speed matters, but endurance starts to make a difference too. The other guy had the speed, but lacked the endurance to keep up with runners like me in the long sprint.

Throughout middle school P.E., we occasionally had to do a mile run on the track. I remember one such four-lap run in eighth grade. After the first lap I was ahead of all my classmates. After the second and third laps I was in second place. I finished the race in third place. If I recall correctly, my time was just under eight minutes, good enough for an "A" in the mile run. (Ten minutes was a "B," twelve minutes was a "C," and any time over twelve was a "D" provided a full mile was completed.)

Early the following summer, I received a letter. It was from the coach of a sport that I had never heard of -- cross-country running. He was inviting me to join the team. At first I was intimidated -- three miles sounded like such a long distance. But then I reminded myself that I had a runner's body, and I was unlikely to be successful in any other sport. And so I joined the team.

On the first day of practice, the coach told me to run three miles on the track. Then he led the rest of the team on a "short" distance run to the mall and back -- a round trip of just over four miles. I completed the dozen laps on the track, but I had to stop and rest several times.

Summer practices were held thrice a week. Mondays were for long road runs, while Wednesdays were for intervals on the track. Other types of workouts were held on Thursdays. At the end of each summer workout, the coach would give us all sodas.

One memorable workout occurred on Monday, August 14th. For the workout, the coach had planned an eight-mile road run -- four miles out, four miles back. For the first three miles, I tried to keep up with my more experienced teammates. We managed to catch every green light until we reached the three-mile mark. It was the first time that I'd ever run the length of a XC race without stopping -- though it took me about a half-hour.

I stopped to catch my breath, while the rest of the team continued to run. I decided that since I was still a novice runner, I wouldn't be able to complete the full eight-mile workout. Typically, the coach would have us run the return part of each workout along the side of the "river" (which here in Southern California really means something like "flood control channel"). This way, we'd be able to avoid red lights and run the distance without stopping.

And so I ran three miles along the river bike path back to school. But for some reason, the gate leading from the river back to the street was locked. I'd either have to run an extra mile to the next street (and yet another mile to get back) and hope the gate was unlocked, or try to climb the fence. I was too tired even to climb the fence. Instead, I decided to take a shortcut directly across the river. I remind you that this isn't a real river (like the Mississippi) -- it's only a few feet across and only a few inches deep.

But the force of this river was powerful -- once I stepped in, it's impossible even to stand up! The river swept me several miles away from the school (and in the opposite direction from where my teammates were running). I was saved only because one person driving on a bridge spotted me -- and she just happened to have a cell phone. (This was in 1995, so cell phones were rare.) A fireman was summoned, and he intercepted me one mile farther down the river.

What should I have done? Either I should have simply climbed over the gate, or perhaps waited for the teammates running the extra two miles to catch up. (I'd already run to a second gate hoping it would be open, and there was no guarantee the others would have run past the second gate if they were already climbing over the first one.)

A few weeks later, the season began. The early-season schedule had us racing twice a week -- on Thursdays there would be a non-league dual meet (that is, a race against one other school that isn't in our league) and on Saturdays there were weekend invitationals against many schools. In my first Thursday meet my time for three miles was around the mid-24's, and in my second invitational nine days later, my time was in the mid-21's. The coach joked that if I could keep this up, I could run it nine minutes by the end of the season! (Of course, that would be a world record by fat.)

In reality, by the time the league dual meets began I didn't keep improving by a minute every race (no one can). But in my third invitational -- the huge Dana Hills Invitational -- I broke 21 minutes. That is to say, I ran under 21 minutes for the first time (I believe my time was 20:50).

This was the year that I moved from one school to another. As it turned out, the week of the move was the same week as League Finals, and so I didn't actually complete my freshman season.

At my new school, Cross Country season was over, but many runners move on to track. The distance races that most XC runners participated in are 800, 1600, and 3200 meters. (For those who don't know the conversion, 1600 meters is almost one mile.)

Mile 1: Sophomore Year

At my new school, the season schedule was a little different. The first race of the season was always a time trial (that is, we ran against the clock, not another school). It also marked the main fundraiser of the season -- tickets to a pancake breakfast. Also, there were no non-league dual meets -- the five league dual meets fell on the five Thursdays in October, followed by League Finals. The time trial as well as three of the league meets took place on our home course.

But I always had trouble filling out the athletic clearance papers in time for the start of the season. So instead, my first race of the season was the third Saturday. This is another huge invitational -- the Woodbridge Invitational. Held on that high school's campus, the Woodbridge race regularly produces our fastest times of the year. That day, I broke 20 minutes for the first time.

Another major race that we prepared for was the Mt. SAC Invitational. This race regularly takes place in mid-October, on the second Saturday before League Finals. The name Mt. SAC refers to a community college, but that word "Mt."/"Mount" gives away what the course was like. It's the hilliest XC course that we run on. During the weeks leading up to Mt. SAC, we would have "hill repeats," which are like intervals except they're run on a nearby hill. These workouts were often led by our two senior captains.

I never looked forward to hill repeats, or any hill workouts. But they're very helpful -- after running six, seven, eight miles on hills in practice, the three-mile Mt. SAC course was a cinch! Of course, my times at Mt. SAC were never as good as Woodbridge -- that year, my Mt. SAC time was mid-20's.

The following Thursday was the last dual meet of the season -- Halloween. That year, Thanksgiving fell on its latest possible date (the 28th) and so the last dual meet was four weeks earlier. It marked the only time I've ever raced on Halloween. (Nowadays, with league meets on Wednesdays, this year's early Thanksgiving leads to League Finals on Halloween.) The final dual meet was held on our home course, and that day I ran a few seconds slower than Woodbridge.

A week later was my first League Finals, held at a local park. That day I capped off the season with my third (or maybe fourth) sub-20 performance.

Mile 2: Junior Year

Once again, I wasn't cleared to run in races until Woodbridge. Once again, I set another PR, or personal record, as I broke 19 that day.

That year, our school had many fast runners. Some of our top runners were hoping to advance all the way to the State Meet. But only Varsity runners were allowed at postseason races. The Varsity team consisted of seven runners plus two alternates -- and our top nine runners all had sub-17 times.

Since my PR was just barely under 19 minutes, I had to run Junior Varsity, not Varsity. All juniors and seniors not on Varsity were relegated to the JV team. As it turns out, not many members of the Classes of 1998 and '99 had joined the cross country team -- and of the few who did, most of them ran Varsity.

Excluding the alternates, I was the only junior not on Varsity -- and for most of the season there was only one non-Varsity senior as well. This made running in JV races a lonely affair.

At the end of the season, our Varsity runners indeed ran in the postseason races. The section prelims and finals were both held at Mt. SAC -- and this underscores the importance of preparing for hilly courses and doing well at the Mt. SAC Invite. The state meet was held at Woodward Park in Fresno, where it's still held to this day. (Recall that Fresno is the one of the Central California cities that opposed Prop 7 and supports the biannual clock change.)

Meanwhile, my season ended at League Finals, which were held at a local university. At the end of the season, I received an award for the most improved JV runner -- but then again, there weren't that many JV runners in the first place.

Finish Line: Senior Year

For once, I was actually cleared in time for the opening time trial. If I recall correctly, my time was right around 19 minutes. At Woodbridge I set another personal best, but only by a few seconds as opposed to the huge PR's I'd set the previous two trips to this invite.

I knew from the start of the season that there was no way I'd make the Varsity team. Two seniors from the previous year had graduated, but two new freshmen had joined the team -- and they were already running under 16 minutes. (One was the younger brother of two other XC runners.) Of course, I wasn't named a senior captain either -- all four Varsity seniors became captains.

But this time, we had a full JV team. The incoming Class of 2000 juniors was a much larger class of runners, and only two of them ran Varsity. I actually end up finishing in first place at two of the JV dual meets held on our home course -- and my times continued to improve throughout the year. At the last dual meet, my time was just one second slower than my Woodbridge time.

League Finals were held at the same university as the previous year. I knew that it was my final XC race and so I wanted to run as fast as I could. Along the final stretch I couldn't help but stare at my stopwatch to make sure that I had a good time. My time for my final race was 17:43, which was good enough for fourth place. The winner was our alternate Varsity runner who finished exactly a minute ahead of me, and the only other JV senior (who had missed his junior year of XC) finished exactly a minute behind me.

It's now believed that the League Finals race was somewhat short of three miles. Using a conversion factor that we were given after the race, my time converts to 17:57 for three miles. Therefore I can still say that I'm a sub-18 runner. At the end of the season, I received an award for the most outstanding JV runner -- and this is less trivial since we had a full JV team.

I still consider breaking 18 minutes in XC to be one of my greatest personal accomplishments -- even when compared to my times on the track. I fell just short of breaking five minutes in the 1600. I suppose my goal for the 3200 was 11 minutes (in other words, 5:00/mile for one mile, 5:30/mile for two miles, and 6:00/mile for three miles), but I never came close. I think I only ran the 3200 once during my senior year -- and I believe that my fastest ever 3200 was actually the first two miles of the XC race held on our home course. Instead of the 3200, I often ran the 800 -- and I don't even recall much about my 800 times. (I believe my best time was about 2:20-ish.)

Cross Country is the One True Sport. Everything else is just a game.

Cross Country and Academics

Some sports -- especially football and basketball -- have a reputation for attracting students who aren't interested in academics. For players hoping to get into Division I colleges, it's often an uphill battle to remain academically eligible by earning good grades and high SAT scores.

But this isn't the case with Cross Country. It seems that most Cross Country runners have excellent academic records. Most of my teammates were part of our magnet program. I wasn't -- but only because most students apply for the magnet in eighth grade, while I was still attending another district at the time. (As I wrote earlier, I transferred in the middle of freshman year.) Two years later, I was finally admitted to the magnet program -- in fact, it happened on the very day of League Finals.

The magnet program is considered to be a year ahead of the regular program. Therefore as a junior, I attended English and history with the sophomores. Some of those students would become my JV teammates the following year.

I suspect the reason that XC runners, unlike football players, basketball players, or other athletes, do well in school is because XC runners are used to doing something difficult and boring (that is, running) for long periods of time. We're used to working hard, enduring, and being persistent as we strive towards a goal, a finish line, that might be far away. This isn't to say that other athletes don't work hard, but the difference is that they're used to getting quick, visible results. We XC runners are more likely to think in terms of the big picture.

That XC runners tend to excel academically is most noticeable when we take a look at the LA City Section Finals results. In both the boys and girls Division I races, the top school is Granada Hills -- a charter that's best known for winning national Academic Decathlon titles. Two of the other top teams are El Camino and Pacific Palisades -- other charters with strong academic programs. I doubt that any of the Granada Hills Varsity runners are also on the Academic Decathlon team. Instead, the rigorous academic environment invites both Academic Decathletes and distance runners (who again are used to working hard for long periods of time).

In my last post, I wrote about Floyd Thursby, who decries teachers who don't want to work the Tuesday before Thanksgiving. He once also wrote about the last week of school -- and how many schools have teachers turn in grades early, so the last week is wasted. Many students believe that they're entitled to a week of no academics at the end of the year anyway.

But that's not the XC way of thinking. Taking the last week off of school is like pulling up in a race before crossing the finish line. We need to run hard through the finish line -- and so likewise students need to work hard through the last day of school.

Senioritis wasn't in my mind when I was in the twelfth grade. I worked hard on the XC course throughout my senior year, and I believe that I'm one of the few seniors to PR in my final race. The other senior who won the JV race that day was a Varsity alternate, and so League Finals would not be his final race. (As an alternate, he did run at Section Prelims.) I was the rare non-Varsity senior who actually worked hard to improve my times my final year.

And in fact, I worked hard academically during my second semester of senior year. I'd never earned straight A's in a semester before, always ending up with at least one B (often in English). But I failed to reach my goal -- instead I ended up with all A's except for two B's, both in English. (The extra English class was required by the magnet since I was a year behind, as stated earlier.)

I want to encourage my students to think more like distance runners -- even if they never run more than a mile at a time. Just before I started working at the old charter two years ago, I wrote about distance running, and how I'd mention it in class to encourage students to work harder. It failed -- because bringing up past events or comparing the students unfavorably to myself aren't effective ways of getting them to make better choices. If I wish to convince my students in the future to think like distance runners, I should do so more subtly.

McFarland USA

Christmas specials started airing on CBS last night with the classic Frosty the Snowman. I wrote before that no school would actually hold classes on Christmas Eve (as shown in the episode) -- that would be even worse than Floyd Thursby Day. In New York, school regularly lasts until December 23rd, unless this is the weekend (as it is on Sunday this year). Thus this year, no school will be open later than Friday, December 21st.

One of my favorite Christmas specials airs on CBS tonight -- Robbie the Reindeer. As it turns out, Robbie is Rudolph's son, but unlike his father, Robbie gets to participate in the Reindeer Games. This is a competition similar to, say, a Cross Country race. (Indeed the steeplechase, in which Robbie competes, is actually a distance event in track -- the 3000 steeple.) Yes, that's why I like it -- because it reminds me of my own days of distance running. I'm glad that the Robbie special is airing today -- on State Meet Saturday.

The one beef I have with it is an inconsistency with the original Rudolph (which will air this upcoming Tuesday). In the original, Donner is Rudolph's father, but in tonight's special, Donner is Rudolph's daughter-in-law. Thus not only has Donner switched generations but genders as well.

Three years ago, there was actually a Cross Country movie -- McFarland USA. When the movie first came out, I briefly mentioned it on the blog. But every year on State Meet Saturday, I watch this movie again. So I turn it on right after the Robbie special.

Here is a description of the movie as written on the back of the DVD case:

In the tradition of Disney sports movies comes McFarland, USA, based on the inspiring true story of underdogs triumphing over tremendous obstacles. This heartwarming drama follows novice runners who strive to build a cross-country team under Coach Jim White (Kevin Costner) in their predominantly Latino high school. Everyone has a lot to learn about each other, but when Coach realizes the boys' exceptional running ability, things change. Beyond their talent, it's the power of family, commitment to each other and work ethic than transforms them into champions -- helping them achieve their own American dream.

Indeed, McFarland USA takes place on the first State Meet Saturday, back in 1987. (And no, it wasn't called Small Business Saturday back then.)

One thing I notice about the movie is that at no point is the distance of the race ever mentioned. It's possible to deduce the distance from a few clues in the movie -- first Coach White drives alongside his athletes and notices that they're running at 12mph, or 5:00/mile -- and then later on, they cross the finish line at around 15 or 16 minutes. But the words "three miles" or "5K" are never explicitly mentioned in the film.

What makes this amazing is that a detailed description of the scoring system is given. Just as Coach White explains in the movie, first place counts as 1 point, second place as 2 points, third place as 3 points, and so on. The point totals for the top five runners are added up to give a team score -- and of course, the lowest score wins.

Indeed, this is what makes the final scene so dramatic. For most of the season, Danny Diaz is McFarland's slowest runner -- he's only on the team to join his two older brothers. Yet due to an injury, the school's fifth runner finishes well off his usual pace. But much to the coach's surprise, Diaz comes in as the fifth and final scorer -- and his points are low enough for McFarland to win. Thus the movie successfully explains why his finishing as McFarland's fifth runner is so significant -- yet the film never specifies the exact distance of the race!

(Hmm, I wonder whether leaving out the distance is intentional. Perhaps the filmmakers wanted to inspire young high school students to try out for XC, but mentioning the distance might scare the potential runners away. Instead, focus on the fun and camaraderie displayed by the McFarland team.)

In the movie, the State Meet takes place in December -- and it appears to be in LA (since I thought I recognized Griffith Park in the background). In reality, the State Meet has never been held on any date other than the last Saturday in November, and it has never been held at any location other than Woodward Park in Fresno. What really makes the timing off is that the date the section finals, or "state qualifier," is given as November 26th. In 1987, this was a Thursday -- in other words, this was Thanksgiving Day. It's unlikely that a XC race would ever be held on the holiday itself. (That the coach rewards his runners by taking them to the beach on Thanksgiving is not an error -- this is California, after all.)

Here is a link to the actual results of the 1987 State Meet as depicted in the movie:

https://www.athletic.net/CrossCountry/meet/90000/results/355173

As you can see, the details of the race are correct in the movie. Danny Diaz really was McFarland's fifth finisher, with a time of 18:04. The distance of the race is 5K (5000 meters), which is a little more than three miles -- therefore my best time wouldn't have beaten Danny's. If I'd been in this race, my best time would have been closer to McFarland's sixth finisher (18:31).

A major theme in this movie is race -- as in ethnicity. (Yes, this is near the bottom of a vacation post, which is when I often write about race.) "White" is the name of the coach, but it's also his race. The runners, meanwhile, are all Hispanic. Thus when the runners call their coach "White" (or Blanco), the name has a double significance.

The first race that appears in the movie is an invitational. McFarland finishes in last place because they weren't used to running hills. (What did I say about hilly XC courses earlier?) So instead, White has them practice running on some mysterious white mounds in their hometown. The mounds turn out to be freshly picked almonds -- which offends the runners, many of whom spend hours every day doing the back-breaking work of picking them! (This explains why a recent DST/time zone proposal referred to the Central Valley as the "Almond Time Zone.") My own coach freshman year had to come up with some creative "hills" (either the bleachers at our school or the side of the flood control channels/riverbeds that I described earlier). My new school was closer to some real hills. (On that hill there was a hose that we sometimes drank water from, just like the runners in the movie.)

The next day, Coach White forgets his daughter's fifteenth birthday. Later on, he makes up for it with a traditional Mexican quinceanera. The family begins to embrace their new community.

Eventually, McFarland wins its first race -- a dual meet against Clovis, 27-28. Notice that the sum of the first ten natural numbers is 55, and so a score of 27 (or less) guarantees a victory. My own coach freshman year gave us the rule of thumb 1-2-5-9-10. These add up to 27, so if our school had the first, second, fifth, ninth, and tenth place finishers, we'd win the meet.

Oh, and Coach White has his runners prepare for the SAT. Yes, what was I saying about XC and academics earlier? At the end of the movie, it's revealed that all seven runners attend college. In fact, no one else in their respective families had yet to finish high school, much less college.

McFarland's XC Team -- and My Team -- Now

At the end of the movie, it's revealed that McFarland won nine state titles from 1987-2001. But it hasn't won any since. What happened?

Well, in 1987, McFarland won the Division III race. All the schools in the state were divided into three (now five) divisions based on enrollment. Since McFarland was a small school, it was always placed into one of the smaller divisions (from III to V).

But nowadays, divisions aren't based on enrollment but on performance. Due to its recent success, McFarland has been pushed up to Division I, where it must compete against Southern Section schools that are several times its size. Last year, the only the girls team advanced to state (where they were buried) -- the boys didn't make it at all. This year, McFarland had only a lone individual girl at state -- her teammates didn't advance. The winning Division I teams in boys and girls are both from Great Oak in Temecula. (Great Oak has over 3000 students, while McFarland has a mere 700.)

As for my own team, I still keep up from time to time on its website. As I wrote earlier, we now have league races on Wednesdays, not Thursdays. The dual meet has fallen out of favor -- instead, our league now has two cluster meets (where all teams in the league compete) and League Finals.

The highlight of our season is still Woodbridge, where many of our runners still set PR's. But the event is no longer held at that high school -- instead it's at a nearby park. And while my Woodbridge races were always in the morning, now the races there are in the late afternoon or early evening (when it's supposed to be cooler). From time to time, my school advances to the State Meet.

One of the senior captains (from my sophomore year) eventually became a math teacher at our school, and he coached the girls XC team as well. Recently he stepped down from coaching, but still teaches math. I wonder whether he ever mentions the endurance of XC runners to inspire his students to work hard at math -- which is what I once desired, and still desire, to say as a math teacher myself.

Conclusion

Ah yes -- Thanksgiving break is almost over, and it's time to start thinking about math (and other classes) again. Maybe someday I really will inspire my math students to think like distance runners -- but that's neither here nor there.

Both of my districts will reopen on Monday, and so that's when my next post will be. I hope you enjoyed your Thanksgiving.

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