## Wednesday, May 28, 2014

### Van Gogh in Post-Its

It seems that every year I try to do something ridiculous in the name of mathematics. Last year, my students and I created a humongous triangle out of toothpicks. This year, I wanted to do something a little prettier, and so, I decided to create a Post-It mural of Vincent Van Gogh's Starry Night on my classroom windows.

Students were tasked with calculating how many Post-Its would be required to cover the windows and approximately how long it would take me to finish. They were supplied with the following information:
• Each Post-It is 3 inches by 3 inches.
• There are seven windows. Each window is 40.5 inches wide and 80.5 inches tall.
• I can place 17 Post-Its on the window in 2 minutes.
After school that day, I got started on the windows. I started at 3:45 and finished at 9:15 that night. I placed 2,730 Post-Its on the windows. When I got home, I created the time lapse video below to show the students the very next day. (This was created using an App called "Lapse It". It's very easy to use and costs only \$1.99.)

Van Gogh's Starry Night in Post Its from Nathan Kraft on Vimeo.

Many people have asked how I created this. I took the original painting and fit it to a grid I made on Excel. I then looked at each individual grid space and decided what color each should be. This was a little tricky as it is not easy to show good definition in Post-Its. You can see the side by side of what I created in Excel below.

The other challenge was trying to pick the right color for each space, as Post-Its are only available in so many colors. There are nine colors shown here: black, white, gold, yellow, dark blue, light blue, lavender, orange, and hot pink.

The best part of this project was that the Post-Its gave the windows a stained-glass effect. The two pictures below are taken inside with the lights off and outside with the lights on at night. And after a month, the mural is still intact. Not one Post-It has fallen down.

Finally, I'd like to thank Andrew Stadel who was partly responsible for inspiring me to do this through his File Cabinet lesson. And a special thanks to Blair Miller who tweeted that mine is better.

## Saturday, March 1, 2014

### Guessing Percents

This is my first year teaching sixth grade math, and one topic that students have to understand is how to construct circle graphs. This is a part of the old Pennsylvania math standards which are currently being phased out because of the Common Core. (Note: Circle graphs are not mentioned in the Common Core standards (prove me wrong), though finding angles and percents are.)

These sixth grade students have some familiarity with common percents and how they relate to fractions (50% = 1/2, 25% = 1/4). They have experience measuring angles and can identify straight and right angles. They can convert fractions to decimals. But how all of this relates to circle graphs is a mystery to them.

I'm preparing them to create these circle graphs, and before I explain to them how to do it, I present them with a few simple ones to see if they can guess the percents. Here is the first one:

Me: Ok, can someone pick a sector and tell me what percent it represents?

Ray: The green one is 50%.

Me: How do you know?

Ray: Because it looks like half of the circle, and half is the same as 50%.

Me: Ok, how many agree with that?

(The majority of the class raises their hands.)

Me: Great! I'll write 50% in here. Now, what else do you know?

Dana: The purple one is 25% because it is one fourth.

Me: Ok, how many agree with that?

(Again, just about everybody raises their hands.)

Me: Alright, we'll put 25% here. Hmm. I'm guessing these last two are going to be tougher. Can someone tell me something about these last two sectors without telling me the value of either sector?

Winston: They add up to 25%.

Me: How do you know that?

Winston: Because the circle represents a whole or 100%, and all of the sectors' percents need to add up to 100%. So if we know the other sectors add up to 75%, we can subtract that from 100% to find the remaining percent.

Me: Great! Does everyone see that? In fact, when you look at red and orange sectors together, they look like they're the same size as the purple sector. So a total of 25% makes perfect sense to me. Can anyone tell me anything else about these two?

Janine: The orange one is bigger than the red one.

Me: So?

Janine: So the percent for the orange one should be bigger than the percent for the red one.

Me: Ok, do you have a guess as to what those two percents could be?

Janine: Well, I'm guessing that the orange one is 15 and the red one is 10.

Me: How many people agree with Janine?

(Again, a bunch of hands go up, but not as many. Some students are squinting at the board, trying to come up with a better guess.)

Me: It doesn't seem like we're too sure this time. (Peter is eagerly waving his hand in the air.) Yes, Peter?

Peter: I'm pretty sure that Janine is right, because it looks like you could fit two red pieces inside the orange piece.

Me: Can you come up to the board and show us what you mean?

Peter: If I use my hand to measure the orange piece, I can fit two hands along the edge of the red piece.

Me: How many agree with Peter and Janine then?

(More hands go up.)

Me: Ok, then I'm going to write Janine's original answers in. Now, does anyone know a good way to make sure that our numbers make sense?

Egon: We could see if they add up to 100.

Me: Do they?

Egon: Yeah.

Me: Great! Ok, I guess we have to check to see if we're actually right.

(One at a time, I remove each white box that is covering each answer, and everyone is relieved to see that our guesses were correct. Ray looks skeptical.)

Me: What's wrong, Ray?

Ray: I don't think that's right. To me, the orange one looks bigger...maybe 16 or 17%.

Me: Well, to be honest, I got this picture off of the internet. And we all know how reliable the internet is. Maybe I shouldn't be so quick to assume that all of the numbers are right. Do you have any ideas about how to check to make sure that it's right?

Ray: We could measure the angle.

Me: Actually, we're in luck. I think there's a protractor tool in Smart Notebook that lets us do that. (I pull up the protractor and quickly measure the angle.) It looks like it's about 55 degrees. It's a little hard to see on here. So, what does that mean?

Dana: That's in degrees. We want percent.

Me: Yeah, so how do we change the number of degrees into a percent?

Ray: We could turn it into a fraction.

Me: Yeah, but...we know the part is 55 degrees. What's the whole? How many degrees are in the whole circle?

Ray: 180. No, 360!

Me: Is that right, class?

(I get some nods.)

Me: Alright, you guys tell me. 55 out of 360. What is that as a percent?

(Some kids punch some numbers into their calculators.)

Louis: I got it.

Me: What is it?

Louis: 0.152777...

Me: Ahhhh! Stop! Round it off to the nearest hundredths.

Louis: Umm, 15 hundredths.

Me: And what is that as a percent?

Louis: 15%.

Ray: Well, I was kinda right. I did say it was bigger than 15, and it wasn't exactly 15.

Me: Yeah, maybe. Or maybe I made a mistake when I measured the angle. To be honest, I think guessing these percents and only being off by a degree or two is really good. Let's try some more...

We then go on to try another one on the board (see picture below) and we have some more great discussions/arguments.

Once the students started to get the hang of it, I gave them two graphs to try (one easy and one hard). They were on paper and I encouraged them to use whatever tools they thought might help them get the answers (rulers, protractors, calculators).

They worked with partners and I walked around to check that each group had the right answers for the easy circle graph. With only a few exceptions, everybody seemed to have a pretty good feel for how the different sectors related to each other and what the percents should be.

The tough circle graph certainly proved to be more of a challenge, and it was great to be able to talk to the students about their reasoning and question them when something didn't make sense. The student below thought that sector C was 10 and sector D was 5, probably in order to make everything add up to 100. I pointed out that this wouldn't work because it means you could fit two D's into one C, or in other words, C is twice as big as D.

This student used his ruler to cut the graph into quarters and make better guesses about each percent.

This student assumed that sector B was about 30 degrees, then chopped the entire graph up into 5 degree segments.

Though it's not obvious, this student used the protractor to measure the angles and converted them to percents. He had the closest, though not the exact answer.

After the students were finished these graphs, I had a spreadsheet ready to go that would calculate the total error in degrees for each graph. Students volunteered their answers and, after all five percents were entered, the spreadsheet showed their error score. It was fun to see the students get excited. After seeing their error and some of the other students' thinking, I allowed them to revise their answers and try again.

I loved seeing all of the different approaches used and listening to students argue with each other. As a bonus, there were definitely some bragging rights for the kids who got the closest. While many students heavily relied on using other strategies, they now saw the benefit of using a protractor and were eager to know how to convert those fractions into percents.

## Sunday, October 6, 2013

### Death of a Marker

One thing that I find very irritating is when one of my students leaves the cap off of a dry erase marker. This happened a couple of weeks ago, and to illustrate how deeply it bothers me, I had a funeral service at the beginning of each of my classes. Standing next to a grave of dead markers (which is basically a box with a foam tombstone attached), I said the following:

"I regret to inform you that this morning, at approximately 7:40 A.M, I entered the classroom and noticed that the cap on Black Dry-Erase Low Odor Chiseled Tip Expo Marker was not firmly attached. I feared the worst, rushed over to Black Dry-Erase Low Odor Chiseled Tip Expo Marker, picked it up, and attempted to draw a squiggle on the board. Alas, nothing came out. Black Dry-Erase Low Odor Chiseled Tip Expo Marker's life force was depleted.

Today, we honor the life of  Black Dry-Erase Low Odor Chiseled Tip Expo Marker. No, you weren't perfect. Mistakes were made. But, you were a bold marker. You helped us solve the most difficult of math problems. It seems like just yesterday we were writing the one-hour delay bell schedule on the board.

You were taken from this world too soon. Your last act was to write "Hi Mr Kraft" on the board with a smiley face underneath. Little did I know, that you were really saying good-bye. I will miss you Black Dry-Erase Low Odor Chiseled Tip Expo Marker. Say "hi" to Red for us."

---------------------------------
Here is a picture of Vigo the Carpathian from Ghostbusters II. Some of my students find this poster disturbing. I don't know why.

"Death is but a door. Time is but a window. I'll be back." -Vigo, the Carpathian

## Monday, September 23, 2013

### My Son's Bedroom

Disclaimer: No math here. Sorry.

Due to some recent events, I had to sell my house. This isn't a huge deal for me. A house doesn't mean very much. The things inside it don't mean very much. But to my son, this house and the things inside it mean a great deal. He likes the neighborhood. He likes his yard. He likes his friends. He never wants to leave.

For the past couple of weeks I've been packing every room in the house and the thought of leaving really hasn't bothered me that much. It has felt more like a hassle than anything else. But tonight, I finished packing my son's bedroom, and when I finished, I saw an empty room which was once filled with toys, and paintings, and planets. I am dreading the moment when he sees it too, and he realizes that we really are leaving.

I thought that I didn't care about this house, but because my son loves it so much, I do too. I am so sorry for what he has been through and continues to go through every day.

People say that kids can overcome obstacles...that they are "resilient". That's a load of crap. My kid shouldn't have to be resilient.

## Sunday, August 25, 2013

### Trying to Be Less Awesome

I see that a lot of people are blogging about changes they're making in their classrooms to become more awesome. As the antithesis, I'd like to talk about how I'm going to be less awesome. Yeah, that's right. Less awesome.

It all started about ten years ago...

I hated being an engineer. There, I said it. I hated it. I hated sitting in a cubicle. I hated waiting for the end of the day to come. I liked the people that I worked with, but what I was doing was terribly BORING. Don't get me wrong, some people love engineering. And there were certainly aspects of my job that I did love. But most of it was a bore and I had no motivation to become better at it.

The thing you should know about hating your job...you also learn to hate time. For me, there was too much of it. I had to sit at my desk for too long, and I couldn't wait for the end of the day to come. I would constantly watch the clock. I would unsuccessfully try to will the minute hand to move faster. Time sucked. It sucked the life out of me. And that was a terrible feeling to have, because I wanted to live every second of my life like it was amazing. And this most certainly wasn't.

And so, I ventured to do something else...teaching. Why teaching? I think it was because I liked performing for others because I did a lot of that as a mascot, and some woefully ignorant part of my brain thought that that was what teaching was all about. If somebody now asked me why I teach, I'd probably say: I want my students to do amazing things with their lives. I want them to have good role models. I want them to see how much life has to offer. I want them to see the beauty in math and figure things out and feel successful about it. But in all likelihood, if somebody asked me this, I'd leave out one of the biggest reasons I do it...that Nathan Kraft, who sucked at being an engineer and hated it, could still be awesome at something...anything.

I was going somewhere with this...

Oh yeah! I used to hate time. I cursed it. I wanted it to go by faster. And now that I'm trying to be this awesome teacher, it seems like I never have enough. I can't make every lesson as fun as I'd like it to be. I don't assess things as much as I should. I don't tutor all of the kids that need it. I don't read every blog post or attend every webinar or go to every conference, because when it comes down to it, it's freaking impossible to do. And if you try to do all that stuff, it robs you of your soul.

Am I being too dramatic? No! Trying to be awesome eats up so much of your own personal life, that it can screw things up for you. You don't eat right. You don't exercise. You stop prioritizing your family and friends. You sit down to write a blog post when you should be playing with your son. (Ooh, irony.)

So, I don't need to be as incredibly awesome as I thought I had to be. I don't need to prove to anyone that I am awesome. Because life should be balanced and we shouldn't be sitting at a computer screen all day. We shouldn't feel the need to prove anything to anyone. Sure you need to be a great teacher. But you also need to be a great friend, and son, and father. Don't try to be an awesome teacher. Try to be an awesome person.

Now if you'll excuse me, I need to go time travelling with my son to fight skeletons who want to eat our brains. You can thank me later, when you realize that your undigested brains are still very much intact.

## Sunday, August 11, 2013

### 51 Days til Halloween?

I really like the following activity and I've blogged about it here.

Which is why I got really excited when I saw this Halloween decoration the other day at Michael's:

You can display this decoration 51 days before Halloween! Or can you?

What if this decoration can't display each number between 1 and 51? Would that constitute as some sort of false advertising?

## Sunday, August 4, 2013

### TMC13 Recap - (Where I basically just talk about people behind their backs.)

This was supposed to be a recap of cool things I learned at Twitter Math Camp 2013 (TMC13). But then I thought, the hell with you people. You should have been there. It's your fault that you don't know what happened. Why should I fill you in on every little thing? Let this be a lesson to you. Next time, you can get yourself off of that damn couch and attend a conference.

Alright. Maybe your lameness can be blamed on having a horrible childhood. Or maybe you're too poor to make the trip. I guess I can cut you some slack.

I'm not going to give a detailed description of presentations I attended. There are already a lot of people already doing that. To me, the coolest thing about this conference is meeting all of the people I've been following in blogs and on twitter. These people have had an amazing impact on who I am as a teacher. I couldn't pass up the opportunity to meet them, exchange more ideas, and have some fun in the process. So this is basically an homage to those I've met and how awesome they are.

Every year I try to achieve some sort of ideal in my practices. Fawn Nguyen epitomizes what that ideal should be. I don't know anyone who blogs as honestly or as intelligently as she does. She is obviously an amazing teacher and I strive to be just like her...just taller and less Vietnamese. She did a presentation on Conway's Rational Tangles.

John Berray is another great teacher, which I didn't really realize until I attended his session this year at TMC. He is obviously a great performer in the classroom and I have to believe that his students adore him. He does this great activity called Shot at the Glory. Check it out.

John also taught us the best way to open bananas. (This isn't him in the video.) I tried it out this morning and it works like a charm.

I met Max Ray during the EnCoMPASS fellowship and was impressed by his notice/wonder talk. He has such a natural sense of humor and I could just listen to him talk about anything. He's also written a book which will be out very soon. I'm so excited to read it! (He also gave me free passes for me and my son to use at the Elmwood Park Zoo. Nice guy.)

Michael Pershan is probably one of the most reflective teachers I've met. I envy his curiosity and enjoy reading and listening to his thoughts. And the highlight of my trip has to be his performance of "99 Problems" at karaoke. I don't think anyone was expecting that.

Ashli Black impresses me how she is able to immerse herself in this strange mathy world of ours, traveling to anything and everything including PCMI. I attended her presentation on building algebraic thinking. It was a great hands-on activity that can spark a lot of great conversation in the classroom. I also have to give her a shout out for suggesting I read Embedded Formative Assessment. The research on feedback is very surprising.

Lisa Henry did an amazing job on organizing all of this and I can't thank her (and her husband) enough for doing it. I'd also like to thank her husband for not punching me in the face after I sang "Paradise by the Dashboard Light" with his wife.

It was cool meeting Nik Doran, because he's British and I've been watching a lot of British TV lately: Doctor Who and Sherlock. He's no Benedict Cumberbatch, so I closed my eyes and pretended he was. (What? No. I'm not in love with Benedict Cumberbatch. I mean, yeah, he's incredibly handsome and quirky. But love? No. I mean, I like him. Let's change the subject. This is making me uncomfortable.) I'm also impressed with how he's trying to bring this weird twitterblogosphere thing to the UK.

Sadie Estrella is full of piss and vinegar, which is a testament to how passionate she is about life and teaching. I also think she could beat me up.

Chris Robinson is a great resource who also lives in Pennsylvania. I'm always impressed with the amount of time he gives to this math community. It was nice to share our aggravations over how stupid Pennsylvania is being over their implementation (or non-implementation) of the Common Core Standards.

Eli Luberoff is the founder of desmos.com and gave a great presentation of his software. I've never seen math teachers get so excited over software features. He's also a really nice guy who is genuinely interested in how people are using desmos and how he can improve it for them.

Jen Silverman threw a cardboard dodecahedron at my face as I was trying to drink my coffee.

Christopher Danielson is a very insightful guy and I love his lessons on food (Oreos and Tootsies) and his conversations with his children. He gave a great presentation on the two of the Five Practices for Orchestrating Productive Mathematics Discussions: anticipation and connecting. We were asked to see how many ways we could cut a tootsie roll into four equal pieces. I came up with the following solution, which I wasn't sure about at first, but it works. It's just weird because the four pieces don't have the same shape.

Mark Sanford is starting his first year of teaching. I think it's incredibly awesome that he has tapped into this community before his teaching career has even started. He is so lucky to have so much great direction from the get-go.

The Mathalcious team is basically the Justice League of math education. Karim knows how to find talent (Chris Lusto, Ginny Stuckey, Matt LaneKate Nowak), and I am continually impressed by what he and his team have produced. I am also grateful to now have an understanding of the "romance cone" which is a graphical way of representing the dating rule of "half your age plus 7".

Sean Sweeney, Rachel KernodleJulie ReulbachKate Nowak, Chris Lusto and Greg (something or other) did a great job ending the conference with a parody of Tik-Tok by Kesha. At the last minute, they asked me to go up on stage with them and dance, but I'm glad I didn't. It was too much fun to watch.

Greg (in the video above) gave a quick talk on how he uses his ukelele to teach students. Apparently, when students are working and he is playing his ukelele, the students think that he is too busy to be bothered, so they look to each other for help. He still walks around the room and monitors their progress, but he is no longer a crutch for the students. Genius.

Julie Reulbach (also in the video above) always has an infectious smile on her face and is perpetually happy. I'm so glad that I got to know her a little better.

Kate Nowak (also in the video above) had a great t-shirt with the following image. Kate also asked me to sing Van Halen's Hot for Teacher at karaoke. How could I refuse?

Shauna Hedgepeth gave a great presentation on some of the activities she does with her statistics classes. The coolest part was that I'm able to take any of those ideas and use them in a middle school classroom. She also had us running up stairs to find our horsepower.

Steve Leinwand has a loud booming voice, which fits him because he seems like the authority on mathematics education. I'm still impressed that he came to the conference which shows just how cool and involved he is.

Sam Shah is a lovable guy and fun to hang out with. I was a little worried that I offended him because I told him that I did not enjoy watching Real Housewives of...Wherever, but I think he's forgiven me. I'm so glad that I got to spend some time with him my last night there. He taught us how to play a really cool word game called Contact.

And what did I provide in return for all of their awesomeness? My amazing dance moves!