## I Almost Ran Over A Student To Show An Example of Inequalities

9/5/2013

The TI-Nspire CX & CBR 2
Solving linear inequalities in class had easily become a mundane topic to me. Students' prior knowledge was good, although they struggled a bit when the discussion changed to include absolute value inequalities.

"Why is it so important we're able to phrase the distance from an object like that?" I had heard on several occasions. I DID have access to a Texas Instruments TI-Nspire CX as well as their CBR 2 (Calculator-Based Ranger), which had been useful in the past with a ball bounce lab and I fully intend this school year to do the Bungee-Jumping Barbie lesson.  With CBR 2 and TI-Nspire CX in hand, I began to collect data in the hallway outside my classroom during a passing period with students walking by at a variety of distances away from the sensor. This was insightful, but did little to give relevance to the idea of absolute value inequalities as I had set out to do.

So after thoroughly banging my head against the drawing board, so to speak, I decided to relate the back-up sensor (and camera) on an automobile to the compound inequalities and absolute value equations we had been investigating earlier in the week.

She seems to have a lot of faith in my backing skills, huh?
After searching far and wide to find a teacher's vehicle new enough to include a back-up sensor system, I then found two "willing" students to help me stage and record an example of the alarm system at work, with visible warning lights above the rear window in the photo shown).

We -- er, actually, -- backed the vehicle towards our volunteer (pictured here, seen through the vehicle's back window, exercising every ounce of trust she can muster up) and measured her distance to the sensor when it changed intensity and/or volume. The video was simple enough to capture, so I uploaded it to YouTube HERE, if you feel the need to use it in 3-Act-Math format (and because I always enjoy working a Dan Meyer shout-out into a blog post).  My intent was to use the video clip as an Act 1, then the photo below for Act 2 to include some accompanying details and measurements. I have not managed, at this time, to accumulate the necessary camera shots for an Act 3, but hope I can do so in the not-too-distant future.

Image reflects data collected from observed alarm-distance relationship.
I found a screenshot of the new backup sensor/camera system available for the new Chevy Silverado and labeled its colored guidance lines to correspond with the observed distances when the audible and visible alarm system was set off during our trials.

The prompt I gave students was that they needed to be able to provide enough information about the inequalities associated with each tone, so that we could construct a "poor-man's vehicle backing system." To be fair, earlier in the week, we had created several of our own programs to use with the TI-84 Plus (now available in the TI-84 Plus C with color screen and rechargeable battery, which I've grown to appreciate quickly) calculators, including Quadratic Formula, Distance Formula, Slope Formula, and Midpoint Formula programs. I aim to include links to these files as soon as my school webpage editor is properly troubleshot. For now, you may browse my classroom webpage using THIS link.

While this particular prompt may not fit the ideals for the Common Core State Standards for Mathematics, I feel it does give some worthwhile insight into how computer programming logic has a place in a vital component of vehicle safety systems. Sometimes, this sort of insight is enough to squelch the "But when am I ever going to USE THIS STUFF in real life?" questioning that can occur frequently with math topics.

If using the 3-Act Math format, this could serve as Act 3 for the time being. Sorry.
The relationship I had hoped students would construct, or at least mimic, in their analysis of the video clip I created and the accompanying photo shown above.

Most importantly, I wanted to see that students had the wherewithal (yes, I used "wherewithal" in context on a math blog entry) to only include, for example, "6 feet" as part of a single interval instead of assigning it to more than one interval. My hopes in this was to have some sort of reinforcing example to refer to when we begin our look at functions and how each input value can only have one output value.

With this sort of application to the simple, compound, and absolute value linear inequalities we have used this unit, I hope that my students have some sort of foundation or respect for how this topic is relevant and useful in real life.

The female student in the video seems pretty bold to stand firm, knowing that I'm backing up straight towards her and, truth be told, there was a Counselor's meeting going on while we were filming in the conference room directly behind her. So, I had some explaining to do when I ran across a couple of those counselors towards the end of the school day, but did get some head nodding and encouragement that the lesson potential for what I was doing sounded pretty interesting to them.

In conclusion, this lesson has been the most fun I've had ALMOST intentionally backing over a student in my teaching career. Just wanted to put that out there. Please let me know your thoughts on this lesson and check my Twitter feed to see when I've been able to post those TI-84 programs, if you are interested in when I have those posted. Thanks!

--Keltner--

## Remind101: a great resource for sending reminders to students

8/18/2013

I have used Remind101 numerous times within the past year, with exceptional results and feedback from recipients. I have introduced it to colleagues, students, preservice teachers, and even community organization leaders. I've even printed off small flyers to distribute at our school's Parent Night coming up (keep reading, I've included details and file links below)!

Allow me a little bit to provide some background on Remind101. The online resource at Remind101.com, and its associated app available for iOS and Android, allow teachers to send text message reminders to their students in a safe manner such that they do not need to see the students' personal cell phone number nor do the students need to see the teacher's personal cell phone number. If the recipient prefers, they can sign up for email reminders instead.

Teachers can individualize unique groups depending on grade level, class period, or even an organization they sponsor or coach. Students, parents, or colleagues are asked to send a simple text message to a predetermined phone number (which I learned from Remind101 customer support staff are now designed to select the area code closest to the user's location, somehow) and the message they send is a simple "@______" code. A message is returned to them, asking their full name, so that it can show up on the teacher's Subscribers list.

From there on out, the teacher can send messages instantly or schedule them to be sent at a preferred time, with a 140-character limit. One thing I learned by experience is that if a URL link is included in the message, a URL-shortening feature is applied (it's been a while since I've used it, but I vaguely recall a "http://remi.nd/_____" format to it).

Anyhow, I created some index card-sized registration instructions for the first day of school, as well as for our school's Open House night this coming Tuesday. It took some effort and I gave the paper cutter a heck of a workout to chop down the notes to 3-inch by 5-inch size, but they are ready to go and are featured on THIS tweet, the photo of which is included below.

I received a handful of responses about the notes I'd created as well as the images I'd included on the back of the notes to make them a bit more eye-catching than a plain piece of paper on the first day of class. (NOTE: The figure made out of 30 playing cards is based on a George Hart design I saw and plans for it can be found HERE, towards the bottom of the page, if you want to try to create one yourself)

I created my notes using Microsoft Word and have included the files below. Please comment on this post if you find issues with either file.
• HERE is the file in ".doc" format for Word 97-2003
• HERE is the file in ".docx" format for Word 2007 and newer

For entertainment sake, I've included a gallery below of the gimmicky images I used for these notecards to give a better preview of what I've created and shared. If you would like to make your own or modify the designs I've used, I had good luck in performing a Google search for "dynamic images," which allowed me to edit the text that appeared within each image.

In closing, I wanted to share my POSITIVE experience I have had since beginning to use Remind101 regularly.
• I was selected as one of eight teachers on the Kansas Teacher of the Year team this past year. We were asked to appear at numerous colleges around the state during the past semester, as well as at one another's school districts and other education-related functions. To try my hand at using Remind101, I asked the other members of the team to subscribe to my feed and would send reminders of the address where we would be appearing in the near future, sometimes including a URL for an uploaded campus map of where we were scheduled to appear. Their feedback was great and I hope that I was able to encourage them to use Remind101 in their own classes and activities in the coming year, especially since I forced a couple of them to download the app while they were looking over my shoulder at how it worked.
• As the adviser of the National Honor Society chapter at my school, I often times try to recruit students for community service opportunities and handing out a personal note and tracking down numerous students during the school day has proven a losing battle on many occasions. Prior to the end of last school year, I gave instructions at a group meeting on how they could subscribe to text reminders for NHS. One recent tradition we have enjoyed has been to work the registration tent at the Ironman Kansas 70.3 triathlon in early June, at Clinton Lake which is just outside of Lawrence, Kansas. In the past, we have been charged with one shift, the evening before the actual event. This year, we were given TWO shifts on separate days, so I needed to round up TWICE the volunteers! Remind101 helped me easily spread the word to students and some of their parents and, as my wife noted later, it did not make near as big an impact on our cell phone plan as the year prior where I had to look up students in the phone book and try to reach them at home, if they still had a landline. The amount of simplicity and stress reduction I was afforded by using Remind101 is immeasurable. I greatly anticipate seeking volunteers for our next volunteer opportunity at The Color Run in Lawrence, Kansas, on September 14th.
• This school year, already, I have bragged about Remind101 to numerous colleagues, administrators, neighbors, and school board members. The alternative our district's central office staff and building secretaries are able to use is Blackboard Connect, but it is not available to teachers, coaches, or sponsors at this time.

I have easily come to appreciate the ease and simplicity of implementing Remind101 in my classes from day one in each of the courses I am teaching this school year and look forward to sharing this resource with more teachers in the future, but first I have to recount and be certain I have enough cards for our Open House on Tuesday, so I can show some #R101LOVE to the parents who attend and ask how exactly I am texting their students and whether they can receive the same reminders (NOTE: this weekend alone, I am aware of EIGHT parents who have subscribed to the class their child belongs to.).

--Keltner--

## The IPEVO WS-01 Wireless Station for iPad: Product Review

4/2/2013

My IPEVO setup for a Pi Day activity.
A little more than a year ago, I received an IPEVO Point 2 View USB Document Camera for serving on my school district's Technology Committee. If you haven't heard of IPEVO before, they are definitely worth a look (especially with a price tag of \$69, making it feasible to purchase your own personal doc cam if you choose to do so) and make a collection of other products intended for educators and businesses.

I signed up for the company's program, called Wishpool, that gives away products to educators who show that they could effectively utilize the product in their classrooms. They ask for some contact information to confirm you are an educator and a brief response as to why they should make your wish come true and should receive their product of the month.

My wish was granted in early March and I received an IPEVO WS-01 Wireless Station for iPad and USB Document Cameras, which allows me to use the free IPEVO Whiteboard app from the App Store to quickly and easily display the live view from the document camera to show a demonstration, example, or other image to be shared with the class. On their iPad, users access the wireless signal broadcast by the WS-01, so they can tap into the live view or even take a still shot of what is seen. I was impressed to find that zooming in/out and panning around the camera shot is the same intuitive interface that makes the iPad so user-friendly by reputation. Nice job, IPEVO, in this aspect of your app's design.

One of the most obvious benefits of this product is that it is not confined to a single location in the classroom, which opens up all sorts of possibilities for math, science, social studies, and reading classrooms. Students can easily display their work to the entire class without having to awkwardly contort a dry erase board so everyone else can see their results, or crowd around a single lab setup where the students at the back of the crowd miss out, or point vaguely at a map and miss out on detail, or highlight a reading passage to one another when only one document is available. These all become available with this setup in the classroom in a quick, easy, and affordable manner.

A screenshot from an example I did with the IPEVO Whiteboard app.
Another inventive feature for use with the iPad is the fact that the WS-01 has a dedicated SD card slot on board. This makes memory card access from the iPad simple and practical in a number of situations, allowing the use and sharing of files on an SD card without otherwise tying up the dock connector on the iPad (which allows you to continue projecting, whereas the Apple Camera Connection Kit would require use of the 30-pin dock connector on the iPad). For the sake of continuity in the classroom, this convenience is a great piece of forward thinking.

The IPEVO WS-01 also works easily with PC & Mac computers to project a live view from the camera. Showing examples in the classroom is no longer limited to the reach of the document camera's cord. I would appreciate this convenience but have only dabbled in it enough to raise my eyebrows appreciatively and wait for the next time I'll need to utilize the feature (NOTE: I received this product in the midst of a struggle of projecting from my old school-issued MacBook, so having access to an iPad app that allowed me to work with a document camera was a saving grace). Being able to use the IPEVO Point 2 View camera in a wireless setting but still use my computer could prove rather convenient when considering screencasting potential in the near future.

As far as negatives go on this product, I have a hard time coming up with any downs. One thing I expected to see within the IPEVO Whiteboard app was the possibility to capture a live video clip, but that is the wishful screencaster in me speaking (and I also realize this is different if using the IPEVO Ziggi-HD camera instead of the IPEVO Point 2 View camera). Perhaps in a future update of the app, this could be included, but I am exploring other options to allow me to record through another app that does not have all the functionality that the IPEVO Whiteboard app DOES have. The other critique I came up with was the amount of battery life the WS-01 has, but after considering my thoughts more carefully, I am encouraged to find that I have already used it so much that I have to remember to plug the unit in when I leave school so that I may use it the next day. Also, the fact it is beaming a wireless signal continuously while providing power to a USB camera makes me relax a bit more. All things considered, it does a pretty good job at almost getting me through an entire school day without powering the unit down from one class period to the next. The unit has a built-in USB dongle that can allow for charging via USB on your computer, as well as a lengthy cord to its AC adapter (roughly 5 feet long) which is noted to be the only power adapter used for wall-outlet power for the unit.

My daughters have had fun "playing school" with this device as well. I've included a couple of screenshots from our lesson last night on measuring objects around the house (to the nearest half inch). We were able to use the WS-01 on a countertop in the kitchen, out of reach of their 2-year old sister and pinch-to-zoom as well as pan around the image to add a little clarity to specific measurements of the crayon and colored pencil we used.

All in all, I'm incredibly grateful for having the opportunity to implement this document camera setup in my classroom at such a small price. The IPEVO Wishpool program made it possible, so I want to include a note of thanks to them for not only a fine product line, but also for their continued support of educators. If you have the time, I highly recommend taking a look at the latest offering on the IPEVO Wishpool website, but moreso taking a browse around IPEVO's website at some of the unique classroom-friendly, budget-conscious products they offer.

Now, if you'll excuse me, I need to go make sure I've plugged in my equipment so it is charged up for class tomorrow.

--Keltner--

## One of these things is not like the other--Pizza Packaging

2/3/2013

A collection of boxes from local shops led to some curiosity.
I was trying to use an example with pizza box design in our polynomials unit, but needed to cater to (yes, pun intended) the visual learners in the room. So, off I went to play the teacher card and ask for an unused medium box from several places to see if one store held an advantage over another size-wise.

Of course, the shops obliged, so I should give a shout-out here to Pizza Hut, Gambino's Pizza, and Wheat State Pizza. I hope to time this to influence a bit of Super Bowl ordering hysteria, but a math teacher's endorsement is probably not big on their respective radars, let's face it.

Focus your attention, though, on the center box in my photo. It seems to have a chunk missing out of that front edge, no? That box belongs to Pizza Hut, called their new Eco Box, and had previously included some text on the box boasting it would "keep tons of cardboard out of landfills annually." Of course, the math teacher in me wanted to quantify just how many tons of cardboard they were talking about.

Old Pizza Hut box. Click image for source link.
I also must disclose, a significant amount of my information and some graphics came from a blog post on Chainalytics' website written by Rich Lindgren as well as a post of the same article on Packaging Matters' blog.

They begin by taking note of Pizza Hut's previous box design. Nothing out-of-the-ordinary. Just a standard, rigid, corrugated cardboard pizza box. As a math teacher, if you have not unfolded one of these boxes to show how the volume of the box can be shown from its flat template, I highly recommend it for the sake of the visual learners in your class.

Label the height of the box as "x )" and the subsequent size of the width could be described as (16 - 2x) with respect to the overall width of 16 inches for the template less x inches for the left and right edges, and the length as (32 - 3x) / 2 to account for the front edge folding over itself and the back edge of the box. Showing students that the volume of the box, V = x (16 - 2x) ((32 - 3x)/2) , has many values has led to interesting conversation for me but mainly drives at the inquiry as to why the maximum volume is NOT utilized, which lends to the idea of perhaps rephrasing the function so that we can more easily state that the base must remain a square. If you have suggestions on this, please include them in the comments below.

The Pizza Hut Eco Box. Click for image source link.
Anyhow, enter the Pizza Hut Eco Box. Again, nothing out-of-the-ordinary at first glance. But that front edge is different than your average pizza box, actually it is half the height of the front edge but does not hamper the box's performance at all.

Earlier versions of this box claimed they would "keep tons of cardboard out of landfills annually." My skepticism got the better of me, so here I am writing a blog post about it.

Box flat comparison. Click image for source link.
Turns out, that little missing strip of cardboard really has a big impact when extended upon Pizza Hut's annual sales projections. Packaging Matters' blog post saved me some time in calculating, and visualizing, those figures.

Okay, I'm buying into the "tons of cardboard" savings claim now, because I realize Pizza Hut is a pretty big player in the world of pizza.

Plus, this visualization also gives me yet another example in calculating percent change, which are fun to accumulate.

Visual of annual cardboard conserved. Click for image source.
Quoted straight from the Packaging Matters blog post:

Now 4% does not seem like a huge number, but at Pizza Hut USA volumes (estimated 675,000 boxes per day), that is an annual reduction of over 46 million square feet of corrugated board.  To put that in perspective, that would be an NFL Football Field w/o end zones over 128 feet high.

With an estimated half-cent savings per box, it is not likely to come with a price drop on their menu, but the cost savings the company will incur is likely to be in the millions of dollars.

And while only shaving off about two inches of space these flat boxes will occupy on a stockroom shelf is not a substantial victory in clearing kitchen space, it is indeed a case of "less is more."

Again, I want to thank local pizza shops Pizza HutGambino's Pizza, and Wheat State Pizza, for allowing me to play the teacher card and get a "free" box from them. I'm sure they are going to get some business out of me in the future. And while I'm at it, I'd be remiss if I didn't tell you that their stuff is worth a try, if you are in the are.

Also, I tried to time this post on Super Bowl Sunday, the capstone of the week with the most pizza purchasing power annually (an anticipated 4 million pizzas purchased in 2012, not including homemade pies or frozen pies). I'm not trying to soak up any spotlight, but figured it was appropriate timing for this topic.

And just like the rest of you, I'm rooting for Coach Harbaugh's team.

--Keltner--

## My remarks to the Kansas Senate and House Education Committees

1/27/2013

Recognition with Senate Resolution No. 1705
This past week, the 2013 Kansas Teacher of the Year Team was invited to Topeka for Legislative Recognition Day.

We were invited to visit the Senate Chambers and were recognized with Senate Resolution No. 1705 and met with some personalized commendations from the Senator from our respective district in the state of Kansas.

Prior to that, we were invited to give some brief remarks at the joint committee meeting of the Senate's and House's Education Committee. My remarks are included below in italics.

Chase Austin (pink tie) with his dad and A.J. Foyt
Hello, my name is Scott Keltner and I am a high school math teacher in Eudora. I appreciate the time you have dedicated to allow us to meet with you today. I am Kansan, through and through, by way of Emporia State University and Cowley County Community College, back to my upbringing in Medicine Lodge.

All through my childhood, though, NASCAR had little to do with my life.

But that first week of student-teaching, it became obvious that I would not survive class on Monday morning without knowing who won the race on Sunday afternoon.

That’s also when I discovered it would be necessary to make math relate to my students, that relying heavily on dry lessons from a textbook would not suit my constituents, especially in the class I taught with a female student who insisted on being called Bubba.

I designed lessons to incorporate racing terminology, strategies, techniques and puns to please the audience.  The students loved it and didn’t even realize they were doing math, thinking they were only talkin’ ‘bout racin’, roughly a decade before the Common Core came about.

My second year of teaching in Eudora, I had a student who was gone numerous times because of his racing talents. This year, he will actually be driving in the Indianapolis 500 for A.J. Foyt Racing in the number 41 car. His name is Chase Austin and I hope you take note of his efforts. The bond that he and I formed still persists, as he comes to visit my classroom whenever he is back in town.

I tell Chase how I am teaching a particular topic and he refers back to the way I taught when he was a student, asking why I changed the way I teach it. As Chase can attest, not every race can be driven the same way. The same thing goes in education, as a teacher strives to tailor-make a lesson to the students from one year to the next. A lot has changed in education since No Child Left Behind was instituted when Chase was a middle school student.

He also points out the new technology I have in the classroom since the days he was there. The graphing calculators he used in my classroom
(at which time, I pull out an old TI-86 from my pocket) were traded away for an upgrade (at which time, I pull out a TI-84 Plus from my pocket)  but at no out-of-pocket cost to our school district. Now those have been upgraded to yet another version (at which time, I pull out a TI-Nspire CX CAS from my pocket, greeted with chuckles from the legislators)  still at no direct cost to our district. The SMART Board on the wall of my classroom has a similar story (I'll elaborate on that story another time), making my classroom look like a collection of tech-y garage sale finds. There are numerous opportunities available through the use of technology in the classroom, and we must secure access to these tools to see that our students are Career and College Ready and able to utilize their specific skill set towards a successful future.

Flat Ridge Wind Farm, near my hometown in Kansas.
With the passage of items like Senate Bill 155the Career and Technical Education Law, Kansas teachers and students are able to prepare a workforce ready and able to tackle the next big opportunity that arises, helping elevate Kansas to heights greater than the mammoth wind turbines that dot the Kansas skyline now and into the future.

So, with continued support for bills like the Career and Technical Education Law and helping schools utilize technology tools to create a Twenty-First Century Classroom, we can ensure that Kansas students will remain in the race instead of stuck at a pit stop, watching others pass them by. Kansas kids and Kansas teachers deserve that opportunity to provide for the future successes of our state.

A successful race isn’t won solely by the driver. There are a lot of people that helped get to a winning position. The fact of the matter is, we’re all in this race together.

Yup, the only one of the group to get stopped by security.
I was able to meet up with several legislators after our time during their committee meeting. I have to say, it's pretty nice to have that many people in an authoritative position seeking out what you are doing in a classroom, commending the work you do, or just asking your opinion on how the Common Core State Standards will affect your classroom instruction. I think both them and I were glad that most of the people in the Capitol Building were wearing name tags, though.

If I'm going to do any name-dropping, though, I feel obligated to acknowledge the warm welcome I received from Senator Tom Holland from my home district.

I'm not sure that even he could have helped me out in getting through Capitol Security entering the building, though. I set off the metal detector twice, then "got the wand." One of my fellow Teacher of the Year Team members snapped the photo at left. In the end, I made it in the building and our Team was even invited into Governor Sam Brownback's office for a conversation with him on what it is like to be governor, how often he speaks with President Obama, and he reciprocated by seeking out our opinions on a number of issues he is currently faced with at the state level.

I am looking forward to the other opportunities that are up and coming for the Kansas Teacher of the Year Team (check out our schedule of appearances HERE), but realizing all too quickly just how big our state is. I'm looking to check out some sort of "Learn Spanish" on CD--or "Sooo, You Wanna Learn To Speak Canadian, Eh?"--so I have something to listen to along all the miles we log through this entire experience. Any help out there--I mean, OOOT there?

--Keltner--

One last note: I referenced auto racing several times throughout this post and how it relates to my students, namely Chase Austin because I taught him. Did you also realize that NASCAR driver Clint Bowyer is from Emporia, Kansas? It was to hear several funny stories about Clint from his former teachers when we toured the Emporia School District this past Wednesday, Jan. 23rd.

1/26/2013

A view overlooking Kansas Highway 10 through my town.
Give them something they can relate to in real life, right? Well, quadratic functions have numerous applications (most noteably Dan Meyer's basketball shot example using the 3-Act structure) but some are a stretch of the imagination for most algebra students. I don't think I knocked one out of the park on this activity, by any means, but it definitely had students engaged and talking.

To elaborate on the picture at the left, our town is working on a grant application through the Kansas Department of Transportation to install a pedestrian bridge over Kansas Highway 10 and seeking community support for the project. You'll understand why this pedestrian bridge relates to the lesson shortly, I swear.

My 2-year old daughter & TI-Nspire CX.
I used the TI-Nspire CX handhelds available to my classroom and was able to import pictures of objects that stressed the properties of quadratic functions in standard, vertex, and intercept forms each with a different context that I felt emphasized the form students were focusing on. (The .tns file for the activity can be downloaded HERE)

Standard form
The y = a*x^2 + b*x + c form (yes, this post is letting me see how little formatting I can do with text on my blog), is where our focus began in our quadratics unit. I related this form to the path seen in Angry Birds (shown in the screenshot album below) since the path of the previous shot was visible on screen. I set up sliders to allow students to modify values of a, b, and c and watched them try to map the previous shot they saw. Some comments I heard:
• "Dude, you gotta change c so it's your y-intercept to put the bird in the slingshot!"
• "Yeah, a has to be negative so it's concave down, but make it barely negative so the graph gets wider! Duh!"
• "Whoa, changing the value of b only swivels the graph from side-to-side!" (this was important as we worked later in the unit to factor quadratics)

Most importantly, students were able to connect each constant (a, b, and c) to its unique impact on the shape of the graph, on their own terms--I just used Angry Birds to facilitate the process. The students carried their momentum into Vertex form next.

Vertex form
The y = a*(x - h)^2 + k form, where the vertex is located at (h, k) was a fitting place for me to use Dan Meyer's basketball shot example , because students thus far were struggling with the idea of why symmetry was important in quadratics. They had already aced the idea of wider/narrower graphs and how that was critical to the graph's shape, but I used this to emphasize how each point on one side of the vertex also "secretly" corresponded to another point on the opposite side of the vertex.

Intercept form
The y = a * (x - p) * (x - q) form that is shown many different ways in many different textbooks. This was going to be the grand finale, bringing in the pedestrian bridge project I'd mentioned earlier (the public information presentation can be found HERE, if you want to know more). I included an example photo of a pedestrian bridge in our state (over Kansas Highway 61 in Hutchinson) and students fit the graph by noting the x-intercepts on the scale that was overlaid on the photo. (Side note: they could also manually enter a value for the constants, they did not need to manually adjust values as small as shown).

Several students also asked about why the towers at each side of the pedestrian bridge had to be so tall, which led us into a side discussion about height clearance and its importance to road traffic that would travel beneath (a decent review of inequalities).

So, as I was arriving at school the day after doing this lesson, the school secretary told me how cool it was to hear about my lesson at the Site Council meeting the night before. Apparently, my principal talked up the lesson during the public informational meeting THAT night in front of city administrator and some other city staff involved in the project, as well as numerous citizens in attendance. So, I received a couple emails that next day from several people expressing their thanks for having beefed up support for the project while also teaching the concept of the bridge in class.

It's fun to have those "I wish my math teacher did things the way you do" moments, with the idea that parents who were at that meeting probably gave their students a pop quiz when they got home without my prompting. Sorry about that, kids.

I'd mentioned a link for the TI-Nspire activity earlier, but HERE it is again if you want to use it or modify it for your own use. Even if you don't have a TI-Nspire handheld, you can give it a test-drive using the TI-Nspire Document Player HERE (open the Doc Player first, then download the activity and open it through the Doc Player interface).

--Keltner--

## Calculating Interest: How My Late Grandmother Got My Gears Turning

1/19/2013

Grandma made PLENTY of popcorn when we visited.
Consider this example, that might very well appear in a math textbook:

How long would you leave a \$50 investment in a bank, with 2% interest, compounded annually, to yield a balance of \$500?

Applicable, yes, but how enticing is it, really?

My grandmother passed away several years ago, and I miss her plenty. I'm certain my daughters would have enjoyed meeting her and hearing some of her stories, too. Or the way she could teach a new card game almost every time I went to visit her.

One of my favorite memories of visiting Grandma's house was how she would make enough popcorn to fill half a paper grocery bag, then keep it warm in her stove. And she was always generous in using salt on her popcorn, which I consider an extra perk.

Grandma
What really got me thinking, though, was when my parents told me they had found some savings bonds at Grandma's house and bank that were in my name, dating back to just after my birth. Grandma never brought it up to me, nor did she bring it up to my parents. This generous act on her part gives rise to the name of my blog: Good for Nothing (see blog post HERE about the relevance of the name). Grandma made a grand gesture with no expectation of recognition or grand reward in return. She truly did something good, for nothing in return.

The math teacher in me can't leave this alone though. Knowing the end balance of these savings bonds' values, I'm curious about what the interest rate was, but realize that Grandma kept adding to the collection of bonds, which would make this more of a recursive function.

Nevertheless, I greatly appreciate her generosity, even long after she left this world. It definitely makes for a great Act 1 in the 3-Act lesson format, and I'd love to figure out how to get through Act 2 to find the result in Act 3, but am uncertain as to where to go next.

This might be a better example to leave to rest though. Take a moment with your Grandma next time you are with her. She just might bless you with this sort of curiosity someday like mine did.

--Keltner--

## An Application of Systems of Inequalities in 3-D: the Kansas Airspace Analysis Tool

12/28/2012

An EHS student and KDOT official interact demonstrate the Airspace Awareness Tool.
Here's a conundrum being faced in the state of Kansas: harnessing the state's great potential for wind energy while also safely advocating for aircraft traffic servicing the state's 138 airports and abiding by the siting guidelines for industrial wind turbines.

The state of Kansas approved a landmark piece of legislation in 2009, the Kansas Net-Metering and Easy Connection Act, which not only allowed for citizens to connect their energy generators to the grid but also standardized a 1-to-1 buyback policy (they would earn credits from their utility provider at the same rate that they would purchase energy from the same provider).

Here's where the math comes into play: industrial wind turbine installations are subjected to a battery of governances before the FAA (Federal Aviation Administration) gets their chance to have a say. Wind farm developers would then submit their site proposal through the FAA's Obstruction Evaluation process. Affected projects would include:
• Any construction or alteration exceeding 200 feet above ground level (which requires a lighted beacon to make it visible to aircraft, common on water towers in my area)
• When requested by the FAA (and sometimes as an anticipated last step in the developer's proposal process, which can negate a substantial amount of work, just to have to start from square one because the project might interfere with safe air travel)
• Any construction or alteration located on a public use airport or heliport regardless of height or location
• those located within 20,000; 10,000; or 5,000 feet or public use or military airports at varying height levels depending upon proximity to those airports (THIS is where the lesson focuses, on how to visualize these criteria before the FAA comes a-callin')
These criteria hardly lay out like a list of constraints for linear programming or a system of inequalities, but the logic involved definitely could be used in the same breath as one another.

Try some of the requirements in the applicable city ordinance in trying to obtain a wind turbine on our high school campus, as part of the Kansas Wind for Schools program:
• Blade-tip clearance, at its lowest point, shall have a ground clearance of not less than 25 feet tall
• Overall height of 60 feet or less to fit Micro-WECS (Wind Energy Conversion Systems) class of devices
• Minimum setback (measured from the closest adjacent lot line or parcel line or above ground public utility) of 110% of the device's overall height [Example: a 50-foot tall turbine would need to have a 55-foot radius clear of it to the nearest property line or easement]
• No buildings within 110% of the device's height where the turbine's collapse could potentially damage another building of the property owner's
• Ensuring that the noise emitted from the wind turbine shall not exceed 50 dbA within 100 feet of the nearest property line, except during short-term events such as utility outages and severe windstorms. [NOTE: The math involved with decibels is a great application to logarithms and how exponential behavior applies to the height-noise relationship in this case]

Do the phrases "not less than", "within", "n feet or less" start looking like the real-world examples we would hope to incorporate when teaching systems of inequalities? This gives students not simply an opportunity to see that our turbine site is a solution to the system of inequalities, but can drive some curiosity as to where else a turbine might be positioned and still satisfy all these criteria.

Check the brief video tutorial below on how to use the Airspace Analysis Tool (link to actual site included HERE), a product of the Kansas Department of Transportation Division of Aviation in conjunction with Burns & McDonnell Engineering (Please note links on the User Agreement page that help out with loading the Google Earth Plug-In necessary to use the site. From past experience, this has not been as successful using Safari as it has on Chrome, Fireforx, and Internet Explorer).

A screenshot from the Airspace Analysis Tool, near Lawrence, Kansas.
Now, the fun, behind-the-scenes news about all this: KDOT actually unveiled their Airspace Analysis Tool IN MY CLASSROOM at a press conference hosted on a teacher inservice day (i.e. supposedly no classes in session). Here's the news story from the Lawrence-Journal-World.

Their personnel said it would be nice if we could have some students available to play around with the project and give their candid feedback. To their chagrin, I almost needed to bring in more chairs! Thank goodness some of the media on hand chose to stand and work behind their tripods and cameras, to catch the multiple perspectives of KDOT staff and students interacting.

Students were anxious to see their project because it touched on a topic they had some curiosity about, and liked the potential to see some engineers in action. To show up at 8 a.m. ON THEIR DAY OFF was a remarkable thing for them to do and made another tally mark in the column for times I've loved my job.

Situation hopefully made safer by the KAAT. Click image for image source link.
While students had an opportunity to try out and manipulate the tool during our press conference, they investigated the maps with relative ease because of their awareness of the familiar interface, Google Earth (even mentioned on the Google Earth blog after its release for an innovative use of their software). When the folks with Burns & McDonnell and KDOT asked for feedback on the beta version they released, our students swung for the fences and suggested another visual aspect: avatars. So now, the KAAT includes superimposed images of the device proposed at a location, as well as for existing structures on file. For those in the aviation industry, as well as in the land development and construction industries, this has been a welcome addition. As mobile devices become ever-present around us, this interface very well could find its way being incorporated into the cockpits of aircraft to help with flight instruction feedback in real time.

Since its release, the Kansas Airspace Analysis Tool (KAAT) has garnered national attention for its innovative ideas and interface, not simply for helping wind energy developers but also companies and communities who are looking to install water towers or cell/communications towers.

Here is part of one announcement I was able to retrieve (and HERE is a copy of their online newsletter announcing the recognitions), touting the acclaim that the KAAT has received:

Some of the awards received presented to the KAAT project.
• For the first time in the history of the National Association of State Aviation Officials’ Awards, a single state received both the State Most Innovative Program Award and the NASAO Center Outreach and Education Award for two separate programs.  The State Most Innovative Program Award was presented to the State of Kansas for the Kansas Airspace Awareness Program - Aeris Vigilis (Airspace Guardian).  The NASAO Center Outreach and Education Award was presented to the State of Kansas for its “Ops for Cops” program.  The program partnered KDOT, the Transportation Security Administration, Drug Enforcement Administration and airport managers to provide tactical and legal information for law enforcement officials called to airports.  Kansas also received a national best practice recognition for its continuing legal education program in partnership with the Kansas Commission on Aerospace Education.
• The KDOT Aviation team received word that the Kansas Airspace Awareness Tool, a major component of the Airspace Awareness Program, will receive the American Association of State Highway and Transportation Officials (AASHTO) President’s Award for Aviation in November.  The Tool was recognized in April by the American Council of Engineering Companies with an Engineering Honors Award.

Since the unveiling of the Kansas Airspace Analysis Tool at our school, student have made contact with some of the personnel on hand for this event and gained insight into numerous STEM-related paths that could potentially open other doors for them later.

My favorite experience from all of this comes from a comment a student shared with me a few weeks later:
"Mr. Keltner, you know those algebra problems with the 'a plane flies with the wind between towns in 2 hours but the return flight takes 3 hours because it's going into the wind?' Well, Mr. Young from KDOT took me up in a plane and let me try the controls for a bit and I looked at my clock and could SEE that problem playing out along our trip as it was happening!"

So, I hope you enjoy this potential class project you can utilize. Granted, it is for the state of Kansas, but I think the technology and the ease of integration into class speaks well for student engagement and enjoyment. I know my students have enjoyed it and have bragged to me about being able to put a 2,000-foot tower in their back yard. I guess that goes to show you, the sky is the limit. Only in this case, they can actually SEE it.

--Keltner--

One last shout out to the folks at Burns & McDonnell and the Kansas Department of Transportation Division of Aviation, namely Director of Aviation Edward Young who gave our students a wonderful opportunity when he selected our school for the unveiling of his project. Thank you for allowing us to be a part of this project.

## Coupon Composition: Just In Time For The Holidays

12/3/2012

In the spirit of Black Friday, let's see if we can save some green.
Whether you are guilty of joining the Black Friday "festivities" or not, this lesson contains something for you to be aware of in your shopping with coupons.

If you have multiple coupons, of different discount types (amount discount vs. percent discount, that is), then there is a particular way to apply these savings that will earn more savings than the other.

Long story short:
Apply the percent discount before applying the amount discount for more savings.

The concept relies on the concept of composition of functions, commonly written in the form f(g(x)). These are functions that evaluate in one functions and then another, in a particular order. The topic puts emphasis on evaluating with the order of operations as well as other properties like the commutative property and associative property, both of which are staples in algebraic concepts.

Remember, always use the percent discount FIRST when given the opportunity.
Teaching this lesson in class works well, mainly due to the fact students get so wrapped up in seeing whether they know how to reap the biggest reduction on their purchases in the future.

To help solidify their learning, or ward off skeptics on the topic, we try a couple examples: a \$50 purchase and a \$100 purchase, for ease of computation.  Follow along:

For a \$50 purchase:
• \$10 discount applied first: \$50 - \$10 discount = \$40, then \$40 - (0.2)*\$40 = \$32 final price
• 20% discount applied first: \$50 - (0.2)*\$50 = \$40, then \$40 - \$10 = \$30 final price
For a \$100 purchase:
• \$10 discount applied first: \$100 - \$10 discount = \$90, then \$90 - (0.2)*\$90 = \$72 final price
• 20% discount applied first: \$100 - (0.2)*\$100 = \$80, then \$80 - \$70 = \$70 final price

It is no strong coincidence that there is a two-dollar difference between these scenarios. This is the critical piece of what I'm trying to convey with this post (oh, and it's a fun math lesson to teach).

In using the dollar-discount first, the consumer or retailer is causing the percent-discount to be applied to a smaller value, therefore not letting it stretch as far as it could otherwise. It is, in essence, as if you are also taking the percent OFF of the dollar discount you wish to use (note the examples above, where there is a \$2 difference and \$2 is 20% of \$10).

In applying the percent discount first, your percent covers the larger original purchase price and stretches further. This is the gist of why the percent coupon should be applied first, when you have the opportunity.  NOTE: Some retailers have a point-of-sale system which is programmed to use the dollar discount first, no matter when you had a coupon to the cashier, so you might be forced to play their game and sacrifice part of your savings. I will not name names, but have had a couple of disappointed students bring in receipts and show me how much MORE they could have saved if the register didn't force the order of discounts applied.

I'm making a bunch of links in this sentence if you would like either the TI-Nspire file I have shown up above in the slideshow, or the original presentation and handout I did for this topic to earn T^3 Instructor status a few summers ago. (Don't have a TI-Nspire? Try running the TI-Nspire file through the TI-Nspire Document Player without a need for download of software.)

A 101qs.com entry I posted in May, 2012. This was a head-scratcher but good example.
I managed to take a trip to an outlet mall, where I saw a curious sale display, pictured at left. To use the word "PLUS" in this instance seemed additionally confusing (yes, pun intended there), and caught the ire of Dan Meyer on his blog shortly after I'd posted the photo to 101qs.com.

This, and other sale opportunities like it have been a common cause of commotion in class among my students who have heard me teach this lesson. They are able to bring up new shopping adventures they have had, where they might have corrected the way a cashier had rang something up, or a discount was applied more favorably than they expected, or the discount merely balanced out the sales tax they would have paid anyway.  Regardless, the lesson sticks.

Applying similar, consecutive discounts have proven to be a decent introduction to exponential growth, since students are aware that "50% off, then another 50% off does not make the item FREE."  For those students who are very shopping-savvy, these applications hit home for them much more quickly than any compound interest problem ever could.

Speaking of interest, I hope this sparked some of yours. Have a good day and enjoy the holiday season, saving all the while!

--Keltner--

## Kansas Teacher of the Year State Awards Banquet reflection

11/16/2012

KToY banquet trophy & program.
Tonight was the state awards banquet for Kansas Teacher of the Year in Wichita, Kansas. I was one of eight finalists statewide recognize for that achievement, the only one of whom was male, which has become a point of humor more than once already.

As a finalist for Kansas Teacher of the Year, I will now have the opportunity to join with the other finalists at numerous appearances to advocate for the teaching profession, as well as working with current and preservice educators, across the state of Kansas. I look forward to the opportunities to speak with legislators, administrators, and community members across the state as part of this program.

Having met and spoke with teachers who have already been part of this program in the past, I have had the chance to see what a substantial impact being a finalist for Teacher of the Year can have on one's teaching styles.

As part of the banquet tonight, time was given to introduce each of the finalist teachers and describe some of the characteristics that made them suitable for finalist for Kansas Teacher of the Year. After their introduction, time was given for each teacher to make some remarks about their role in education, their experiences in teaching, or what a typical day in their classroom might look like. Below, please find the comments I made in my time to expound upon my teaching experiences and what led me to choose a career in the teaching profession.

Gypsum Hills, south-central Kansas
After having the opportunity to work as a teacher's aide as a junior in high school, I'd found a career path. Tiger Woods would have to hold things down on the PGA Tour himself. I was abandoning that pursuit to become a math teacher.

I had the opportunity with a summer job to work alongside Mr. Ferguson and Vern, a pair of my teachers I learned under just a few years before.  We were setting roof joists on a shelter house in the Gypsum Hills of southern Kansas. As we worked, I had an opportunity to talk about my career path with Vern (Mr. Buell was far too formal a term for him to accept), my legendary and influential math teacher during my sophomore year. He didn't exactly share the secret of  life, but made a funny comment about Mr. Ferguson, the social studies teacher who was working on the roof with us. He said "Now, Max is a social studies teacher, so we have to talk a little slower with all our measurin' so he can keep up."

With a few years teaching experience now under my belt, I'd like to try and paraphrase that comment: Teachers are all in this together. We can't just focus solely on how well a student can write a summary paper, or map out a chemical reaction, or solve an equation involving some really intimidating-looking fractions.

My alter-ego, Slope-R Mario.
So now, in my classroom, we work to incorporate real-life experiences with students to make topics much more engaging and long-lasting than a bunch of numbers on a textbook page. It might involve creating a giant Jenga game made from 2 x 6's, or creating a Sierpinski triangle out of pennies in the school parking lot, or how we determined if students' backpacks were a tolerable weight by doctors' recommendations, or even result in my wearing overalls and a fake moustache to take on the persona of Super Mario so students get the topic of slope.

Regardless of their topic, time, or trade, I strive to make learning relevant to my students, whatever their background or career path. Learning experiences among my students can read almost like a collection of inside jokes, where "you had to be there." With the mentality that "we have fun, but we get stuff done," students take with them a collection of experiences we shared together.

I do have to admit, about a year ago when I had the chance to work on the Extreme Makeover: Home Edition house outside of Ottawa, Kansas, I was taken back to that day on the roof with Mr. Ferguson and Vern. I found myself working again on roofing joists, just down the wall from a pair of men who were working on the same task. When I heard them bickering about fractions and how to properly space some beams, I was ready to help them out. But like Vern said, I had to make sure to talk a little slower with all the measurin' so they could keep up."

Thank you.
____________________________

I hope you look forward to hearing about  my adventures as a part of the Kansas Teacher of the Year Team as much as I look forward to sharing them. Stay tuned.

--Keltner--

## Scott Keltner

Math teacher and loving it. Tech-savvy because it's necessary. Husband and dad (only male in the house besides the dog).
Kansas, USA