This bulletin board is posted outside my classroom to recognize Breast Cancer Awareness Month in October.
Breast cancer affects more people than we easily realize. I learned that this week. As I started to piece this bulletin board display together, a number of passersby made casual comments to the effect of "That's really cool, Mr. Keltner. My ______ (friend, aunt, grandma, father, brother's roommate, and many other examples) is a cancer survivor." If comments like that don't make you glow inside and out, I don't know what to tell you.

After a colleague shared that his mother is a cancer survivor, I'd heard enough. I couldn't just keep all these blessings to myself. I had to share this list of loved ones with others. So, as you can see above, I've begun to accumulate the names of cancer survivors on the four-foot tall pink ribbon adorning the bulletin board.
Nancy and the late Larry Holmes, 2006.
I'd like to share a bit about the woman whose name I made sure to include FIRST and foremost on that big ribbon. 

Her name is Nancy Holmes and I came to know her through a summer job I held with a Full Bright Sign & Lighting, a job that has given me numerous opportunities for real-life math examples in class. It didn't take long to learn that this woman was a fighter, not just advocating to get things done properly and efficiently in the workplace, but that she was a breast cancer survivor. Both breasts. Treated and diagnosed at separate times.

Also through this summer job, I came to know Larry. To say he was a gentleman is an understatement. He, too, was a cancer survivor and married Nancy in 2006 after having met during their treatment while each battling cancer. So, when I hear celebrities talk about a "power couple," I know they could not even hold a candle to Nancy and Larry.

Homecoming King Owen Phariss and his TWO Queens, Audrey Hughes (left) and Rachel Heeb (right).
What's more, Nancy's son Owen is her pride and joy. A success story for what someone can do with Down's syndrome (and his mother's strength and determination), Owen was named Homecoming King at his high school during his senior year, a noteworthy occasion not just for him but also for his QUEENS. That's right, the queen voting resulted in an exact tie, so two girls were crowned.

So, all the amount of time spent on this bulletin board pale in comparison to the energy Nancy has spent through her fights with cancer. Yes, fights.

And while I feel like this bulletin board definitely is something that is Pinterest-worthy, I hope that students, staff, and other passersby are able to soak in the awareness that it is intended for. I hope they are willing to honor a loved one and post their name to acknowledge the fight they have endured.

In the meantime, if you have someone whose name you would like me to post on this display among other cancer survivors, send me a comment, a tweet, or an email. Until next time, THINK PINK.


Slope-R Mario on the scene!
When I tried last year to demonstrate slope using GPS receivers, I ran into issues: poor signal, dead batteries, not enough receivers for a BIG class of students, among others.

This year, I tried to do something over the top. The formula that students are familiar with for slope uses m to represent the value of the slope, or rate of change, for the function or relation.

When I looked at the four types of slopes I would be teaching (positive, negative, zero, and undefined slopes), I mashed together examples of their graphs to create a peculiar image, which I later twisted into a logo for a character who visited class.

I managed to make a logo VERY similar to the one on Super Mario's hat in the Nintendo game series!

Slope-R Mario's logo
AND it demonstrated the types of slope I was going to demonstrate in class (with labels placed adjacent to the appropriate line) to help illustrate it to students!

I'm not able to hold a candle to Matt Vaudrey's Mullet Lesson, but hoping to have fun trying. He made a much more compelling case for ratios than I think I was able to do.

Now, all I needed was a costume to seal the deal. Being so near to Halloween time, I was able to score a Super Mario hat from a neighboring teacher's son, some overalls from the husband of our daycare provider (also a tribute to my high school math teacher, Vern, the focus of this earlier blog post), a mean mustache from the video-editing teacher in my building, and print off a couple of logo medallions to complete my transformation into Slope-R Mario status!

The evolution of my Slope-R Mario idea, coming to life!
I'm attaching screenshots of the notes I used with this lesson. My trademark stick-figure diagrams for types of slope are a favorite from year to year among my students. Simple but effective. 

I was also able to insert a collection of images with Super Mario that showed him travelling along paths that incorporated the different examples of slope we were discussing.

Check them out below.
So, a good time was had by all. Students got to make fun of me for dressing up so goofily (if that's not a word, it should be and I should trademark it like Anthony Davis trademarked "Fear the Brow" prior to being drafted in the NBA).

One side-effect of this lesson I didn't anticipate was seeing students correct their peers when someone interjected a "Mr. Keltner, you're tall and skinny, so you should have dressed up like Luigi!"

A bystander was quick to point out "He dressed like Mario because of the 'M' on the logo, since we're doing slope today. It was cool how he made the logo to show the different slopes, right?"

The first student agreed, but then quickly retorted "So does this mean when we do parallel and perpendicular lines, THEN you'll dress like Luigi?"

Stay tuned and find out. Slope-R Mario, course clear (that's a Nintendo reference).

How my high school friends picture a math teacher.
So, this past Sunday, September 9th, I was named the Region 3 Secondary Level Kansas Teacher of the Year and proceed as one of eight finalists to be considered for Kansas Teacher of the Year.

Leading up to this past Sunday's banquet, nominees from the region's school districts were asked to have a 2-3 minute acceptance speech prepared in the event they were named the Finalist for our region. Not expecting to be THAT teacher, I prepared a brief collection of "thank you"s and a short reflection on what brought me to be a math teacher. I promise, the graphic at left will make more sense in a little bit.

Anyhow, my acceptance speech went like this:
First off, I need to thank my wife who is sitting over here...about 24 miles west of here with our daughters, earning more points for her Mother of the Year title. Without her support, I would not be able to do this job I enjoy so much. I am truly a lucky man to have her in my life.

I would like to thank Security Benefit for their sponsorship for this recognition program for educators in the state of Kansas and the State Department of Education for their willingness and ability to put on one heck of a party tonight.

Well, here goes...

Teachers need students, but moreso students need teachers. As the son of two teachers, I have all my life been part of a community of learning. From the Home Economics teacher who plumped me up with a hefty diet of French fries as a toddler--OBVIOUSLY (author's note: I've put on about ten pounds since age 2 and just grown straight up to my tall, lanky stature I currently possess)--to the math teacher who balanced me, and every other teacher's newborn baby, standing upright on his hand like some ill-conceived circus sideshow, I have always been a part of a community of learning.

And that math teacher, Mr. Vernon Buell--the one who wore overalls to class on a regular basis and such that I have worn more neckties TONIGHT than he did in his career--served as my vessel by which I was to become a high school math teacher myself.

You see, when I graduated high school, my church invited seniors up to the altar to be recognized by the congregation and say a few words about their name, where they planned to attend college, their intended major, and career goals. When it came my turn at the microphone, I stated "Hello, I'm Scott Keltner, I plan to major in mathematics education at Cowley County Community College, and intend to become a math teacher to become the next Vernon Buell."

I felt encouraged when a laugh came over the audience, but Vern was serving as an usher that Sunday and stuck his head through the back doors of the sanctuary and boomed loudly 
"You can try like [heck], boy, but they ain't never made another one like me."

How true.

And so now, I've found myself as a teacher loving what I do. That love must have rubbed off on my students, as the past two weeks has brought three current and former students to tell me of their plans to become a math teacher themselves, saying they were partly influenced by me.

And although I know it would be a stretch of the truth, I'd love to tell THEM "You can try like [heck[, kid, but they ain't never made another one like me."

I think all teachers are somehow influenced by a former teacher we had in class, or encountered somewhere along the way. Vern (my high school math teacher in Medicine Lodge, Kansas) obviously has had some substantial influence on my career path, as well as the stubbornness I think I've acquired over the years. My "Methods of Teaching Mathematics" professor was Dr. Connie Schrock and she made a great impact on some of the habits I have in the classroom, but also managed to coerce me into taking a date to a PTO BINGO Night because she needed volunteers to work the event, saying since I was on the college's tennis team at the time, it would be like having "celebrity BINGO callers." Not being able to find a good enough excuse to get out of it (and having survived the guilt trip when Dr. Schrock accused me of lying that I had a date, which was in itself demeaning enough because it had been a pretty slow semester or two for my love life), I took the date to BINGO Night. Needless to say, that date is not now my wife, although Dr. Schrock did do a good job of talking to her and building me up, saying what a great guy I was among many other great compliments. Or, at least that's what she told me she was saying to her.

Nevertheless, if you get a chance to thank a teacher, although today is far away from Teacher Appreciation Day (Tuesday, May 7, 2013 is this year's observance), take the opportunity to tell them how much of an impact they make and how the world can "try like [heck], but they ain't never gonna make another one like them."


I feel obligated to include some sort of reference to "The Wizard of Oz," being that I have lived in Kansas my entire life. I try to take advantage of my students' familiarity with the film in several instances though. 

One of my favorite such examples is when the Scarecrow inaccurately recites the Pythagorean Theorem once a brain is decreed upon him (note also how Scarecrow magically moves from the middle of the characters to the far right of the frame after confronting the Wizard). His mishap is recreated by a glasses-wearing Homer Simpson who makes the same mistake, but is corrected by a gentleman in the bathroom stall behind him.
Another mention of "The Wizard of Oz" in class comes up when I emphasize to my students how absolute value measures the distance a number is from zero on a number line. We cannot have a negative distance, so an absolute value will always be non-negative (when a student usually tries to correct me and say "You mean greater than or equal to zero" and suddenly finds that the statements are equivalent).

I paraphrase what the Scarecrow said when first meeting Dorothy (pictured at left): "We can go both ways." The same can be said of absolute values, in that they measure the same distance from a central reference point; in the general case, a number's distance from zero.

In introducing the concept of absolute value this year in Algebra 2, I emphasized greatly the importance of that feature, that absolute value equations would measure the same distance from a central reference point. Refer to the example here:

Solve the equation | x - 2 | = 3. Check your solutions in the original equation.

Diagramming "a number whose distance from 2 is 3 units."
I interpreted the equation, telling them that it is asking, in Algebra terms, "What number's distance from 2 is 3 units?"

They started talking, but only focusing on using that distance in the positive direction, citing 5 as the only solution. This diagram helped them clarify that -1 is also 3 units away from 2. We substituted each value back into the original equation to check our work and conclude that each apparent solution was indeed a valid solution (a great time to introduce the idea of extraneous solutions and emphasize how our conclusion would have differed if we were discussing money, volume, unit sales, and other applications.

I then decided to give an open-ended task to end class that day. I asked students to find something in real life around them that involved the same distance away from a central point. The example I gave was that I parked my car that morning so it was the same distance away from the striped lines on each side of my parking spot, making sure to point out how disappointed I would be if all students returned the next day having simply taken a photo of their car in the parking lot. They came through with some great examples, as shown in the slide show below.

Students brought their cell phones to class and were able to display a screen shot using the IPEVO Point2View document camera I have on my desk (they are excellent for what I use it for and allow quick, easy interface via USB interface including quick screen shots when desired). They were able to sketch on top of their photos using the SMART Board in my room as well, even being able to accept suggestions from classmates on examples of absolute value within their own photo that they had not acknowledge.

I aim to do more of these sort of open-ended, scavenger hunt-like examples where students find examples of math around them. I'll call it "Have My Stu's Do A 101Q" to give proper credit to Dan Meyer's 101qs.com website for posting examples of photos meant to drive student curiosity. I might even be able to coerce some of them into posting to Twitter with a class-named hashtag.  Only time will tell. Like the Scarecrow said, it "could go both ways."

Before I go much further, I must declare this post topic was prompted by a student who asked in class this week:

"Mr. Keltner, what's your favorite test question ever?"

My face must have expressed something as sinister as The Grinch, because he quickly said "Oh, look at him. He's plotting a new favorite one right now."

Actually, one of my most enjoyable testing experiences was the culmination of a three-week long practical joke I played on a student, in my first year of teaching. My students knew by then that I had played two years of college tennis and, since our school does not currently have a tennis team, they asked if we could start sort of a Tennis Club to get together and just go play from time to time. No big deal.

The first time we actually went to play, though, I brought my accumulation of 5 rackets and a couple extras I'd borrowed from the P.E. teacher to make certain all those tagging along would have one to play with. When we arrived at the tennis courts, I dropped my bag near the gate and an enthusiastic, athletic, left-handed (you'll see why this is important soon) student crowded in front of his buddies to get 'dibs' and asked me "So, does it matter which one we use or not?"

My collection of racquets, as well as the "lefty racquet."
Without missing a beat, I shot back a question of my own: "Wait, you're a lefty, aren't you? Then you'll need the one with the extra crossbar on the throat of the racket." Indeed, I had one such racket, supposedly built to offset some of the twisting that can come from off-center contact with the head of the racket. 

A lefty righting--er, writing.
He shot back a puzzled look and said "Wha--why?" I did my best, grossly exaggerated impersonation of a left-handed person writing as if they were trying to write while holding an overstuffed teddy bear in front of them. "You know how lefties tend to write like there's someone directly in front of them? Well, that crossbar is supposed to offset that tendency so you don't constantly hook your shots into the fence."
"Oh, well why do you have one?" a student from the back piped up, not helping my case at all.
"I won it from a guy who couldn't pay his wager in cash." I responded, again without missing a beat.

And so, Tennis Club went on, a good time being had by all, right- and left-handed players alike.

Now, how does this relate to a test question? Fast-forward a few weeks in the Statistics class I was teaching with all the Tennis Club enrolled in it.  We had an exam coming up, one component of which was categorizing variables as qualitative or quantitative, as well as discrete or continuous.  I incorporated the question below into the exam, letting our left-handed student finally discover he had been the butt of a joke for quite some time (in the mean time, we had gone to play 3 more times, each time with him racing to get the "lefty" racquet). Here it is:

Categorize each of the variables below as discrete or continuous:





The Olympic gold medal-winning 100-meter dash time.

A city's ZIP code.

Amount of annual rainfall in Keltner, Kentucky (yes, it's a real town).

Number of weeks we can trick [lefty student's name here] into believing there is such thing as a left-handed tennis racquet.

Average wait time at a stop light in the Kansas City metro area, in seconds.

So, as more and more students progressed through the exam and saw that question, I heard snickers break out in little spurts from those who were "in" on the joke.  Eventually, the student at whose expense the joke was made arrived at that part of the exam and, breaking the traditional silence during exams, blurted out "Keltner, you're a jerk." The rest of class erupted in laughter and went on completing the exam.  Again, a good time was had by all.

Recently, I found out that the lefty student was going to get married and I insisted on having the right to include this story as part of a speech at his ceremony. He declined the offer.

So, until I am able to include an open-response item on an exam to the tune of "Spell 'asymptotic behavior'," which I am certain students would treat as a trick question ("Did he misspell it on purpose so we'd get it wrong or is it really as easy as copying what he wrote?"), I have to sit back and take solace in the outcome of the elaborate practical joke that wove its way into a Statistics exam.

I want to leave you with the words of George Fritz, a quick-witted rancher from my hometown who, if you had never met him before, it didn't take long to make his acquaintance. An oft-used joke he would play on a new face went like this:
   "I bet you a dollar I can tell which shoe you put on last each morning."
   He would then proceed to scan the person up and down, looking curiously at their shoes briefly, then look them in the eye again.
   "Your left. You put on your left shoe last each morning."
   The newcomer would often look befuddled, second-guessing as to whether his prediction was accurate or not, as George would interject: "Well, don't you always put on one shoe, then whatever one's left, you put that on last? So, you put on your left shoe last?"
   Of course, as the person reached for their wallet to pay up on the wager, George would insist you donate the dollar to your favorite charity: yourself.  I never grew tired of seeing him get the better of someone with that joke.

Time? More like my old locker combination...
I become curious at the layout of clocks used in classrooms from time to time. Some clocks digital, some analog. Those with 24-hour time format "cheat sheets" like the one at left bring up a curious topic in math I do not often get to incorporate directly into regular course curriculum, but I think it bears mentioning. 

Allow me to dwell on the 24-hour time format a bit longer, with a military focus. Here are some phrases commonly heard (or slightly paraphrased) in movies associated with the military:

"Reveille is at 0500." Fine. I understand that. They blow the bugle at 5 a.m.

"Lunch at 1200." Gotcha, I know that means at noon. Just tell me where.

Pictures used from Pyxurz online database. Click image to be taken to source site.
"Maverick, there's a bogey on your SIX." No need for an explanation. Hit the brakes and watch him fly by. If only I had a nickel each time I made a "Top Gun" reference with my students and colleagues...

But "Debriefing at 1630"!?!? I have to pause and ponder for a little bit. 

My mind thinks "How many hours past 1200 is that?" Therein lies an example of the importance of remainders.
Going from 24-hr. to 12-hr. time
Military time, or 24-hour time, is a very useful and visible example of why remainders play an important role in everyday life. This is one topic I find interesting to emphasize among my students when the opportunity presents itself. 

Whether students/soldiers/civilians/passersby realize or not, they have lunged headlong into a key concept in number theory: modular arithmetic.

I created (what I felt at the time was) a good introductory worksheet on modular arithmetic, using students' complaints about "always having the same thing for lunch" and made up a rotating set of dishes served in a neighboring school's cafeteria. A scan of the original, older version of it and the answer key is available HERE, if interested.

Symbolically, this tells us that 16 == 4(mod 12), or that when divided by 12, the numbers 16 and 4 have the same remainder.  By similar measure, I could quickly determine that a football coach saying "kickoff is at 1900" is not just due to the fact he is a social studies teacher and currently talking about the 1900's in U.S. History class.  Since 19 == 7(mod 12), he is referring to 7:00 p.m. for kickoff time.

But remainders go beyond just telling time. Suppose today is the 5th and I need to know what day of the week the 19th falls on? You may not use the word "remainder" but somewhere in your logic, the concept does rear its head at you. Admit it.

Examples of a UPC, ISBN, and IMB.
Remainders become prevalent in other, more visible ways, around us in everyday life.  Try these scenarios:
  • You are in line at the store and an item's bar code does not scan, so the clerk enters the UPC manually, only to receive an "Invalid UPC" prompt on their register.
  • You need to order a textbook for a graduate course, but find the book title, subtitle, edition, author(s), publisher, and publish date to be an exhaustive list of information to compile to verify you order the appropriate book.
  • You are baffled by the small series of tick marks that appear on junk mail you receive, but have a hunch it helps automatic sorters at the Post Office begrudgingly deliver those items in a quick, efficient manner without having to read your misspelled name and incorrect address or, my favorite, "Or Current Resident" on the name line.

These are all valid applications of UPCsISBNs, and IMBs; and no, that's not a competition for more acronyms than you'll hear in a staff meeting about NCLBCCSS, or SBG

I tend to focus here on UPCs and ISBNs, because they are the most readily available examples I use in class when a student brings up this topic.  Not once have I been interrupted with a "Do we need to know this for the test?" I like to think it is because students are engaged in the topic, since it is applicable to a plethora of things around them.