My Half-Marathon Playlist and Pumpkin Mousse Mini Cheesecakes

It's ironic that I have a half marathon halfway through the school year, where I feel like I've almost completed the 2015 - 2016 half marathon. I feel like I've completely let go of the "eat" and "play" of my blog title, so here's a little play...this is my playlist, in case if you ever are in need of some upbeat music for a half-marathon or a workout. It goes over my time, but just in case I decide in the middle of the song that I downloaded that I want to switch it, I figured I'd add more at the end. I tried to make every fourth song, towards the beginning at least, a major motivation song for me. I couldn't snap a picture of the entire playlist, but here it is in two pictures.

Also, here is a recipe that was a hit at Thanksgiving...from my Pinterest, where you will also find a ton of high school math resources. It is No Bake Mini Pumpkin Cheesecakes, and they are out of this world. The only thing I would do differently is double the amount of graham cracker mixture because I had a lot of leftover mousse (not to worry--it was all eaten without the graham crackers.) I also used graham cracker crumbles which made it easier. And there are little plastic shot glasses at our local grocery store that makes it very easy to make a lot of little desserts.

photo from afamilyfeast.com

Back to math next time!

Teaching (and Learning) Grit by Having Students Solve the Rubik's Cube

It all started when my 17-year-old son came home from his summer teen tour and had some much needed down time. The normal teenager would probably just sleep or watch videos, but AJ decided he wanted to solve the Rubik's Cube. I remember playing with one as a child and could get one face complete pretty easily. But in "those days," the directions were all on a folded piece of paper (the horror!), and I did not have the GRIT needed back then...at least not with this puzzle. But he watched a video over and over again, and by the next day, he had it down. (As I am writing this, I hear the clicks from him solving his cube...it's a good "brain break" for him between homework assignments.)

Over same summer, I was planning for my new Problem Solving Seminar, and I thought I would make solving the Rubik's cube an assignment for the class around Thanksgiving. I thought it would be a good time for kids to practice...and perhaps get encouragement from their families over break. I decided I would have them watch the video my son learned from, and I would facilitate, but that I did not have to really solve it...after all, it was an assignment for them, and maybe I didn't really have to (gulp) solve it?! It felt really daunting to me, and yet, I knew my kids could do it. I just didn't necessarily want to--which I know does not make a whole lot of sense right now...but it somehow did to me then.

I asked the bookstore to stock Rubik's cubes...the only thing they needed to purchase for the course, and after avoiding lots of "when are we going to solve the Rubik's cube?" questions, we finally watched the above video together last week. I broke down the first few steps as such:

• The white cross on top with yellow in the middle
• The white cross flipped to the bottom with white in the middle and a partial matching T
• The entire white face with one full layer (top) complete
• The entire second layer complete

As we were watching the video and pausing A LOT, I noticed that many of the students were having trouble visualizing. Ironically, one of the top students in the class could not follow the directions at all at first. But most kids were still very interested...solving the Rubik's Cube is like a fun party trick to pull out-out of nowhere, so most were determined. Some asked me to share the video via Classroom Google, so they could watch at their own pace, which I did.

Oddly, I was able to see how to do the first three of the four steps, above, pretty easily. I say oddly because my spatial reasoning is my weak point as a math teacher. You could spin me around in my own driveway, and I will get lost. But I guess having played around with the cube a lot as a kid, I could do these steps fairly quickly. So once I realized my kids needed help, and I could help them, I started to want to solve it myself. But it was not until then that I felt the need to solve it. They needed my help in explaining it, and that I could do. But I didn't know how far I could get...that second layer blew my mind.

Then luck happened. I got an email from the Mathematical Association of America (MAA) highlighting an article about Dan Van der Vieren (known to students as Mr. VDV), a teacher who wrote his undergrad thesis on the Rubik's cube. I immediately followed him on twitter and asked if he was willing to skype with my class...and he said yes! And then the magic happened.

Via skype, and with pictures like the one to the left, he showed us how to get the entire second layer complete. This involved an algorithm. My students struggled through this (as did I), making mistakes and having to redo it all over again, but once they finally got it on their own the texts with pictures started pouring in...on a Saturday night?! And it coincided with me getting that layer complete as well. We felt so accomplished!

Mr. VDV, is skyping with us again on Wednesday (the day before Thanksgiving break) to get us to the next stage. This, more than anything else that I have ever taught, is teaching the kids tenacity and grit and stick-to-it-tiveness. I do have a student who wants to give up. I hope more than anything else, I can encourage him to stick with it and solve it. He will learn more from that, I think than anything he has learned in my class. If he learns how to do it, which will come not only from my helping him but also from his willingness to learn from his mistakes, I will feel like I have done my job.

Mr. VDV has tweeted with me regularly, sharing pictures like these to help me help my students--so incredible. I am so thankful to him...funny this is the case right around Thanksgiving.

 

Lastly, Mr. VDV has told me that his class has made mosaics with Rubik's Cubes, and now, of course, we HAVE to do this...next semester. I can't wait. He told me to register at http://www.youcandothecube.com/, which I did, and someone got back to me Sunday morning! They will ship all the cubes to you for the mosaic making; all we have to do is pay for shipping back. 

I am looking forward to my post when we actually create this. Another challenge, Mr. VDV told me, is to make our school logo as a mosaic. There is an app for that! The possibilities are endless.

I am not there yet...I haven't solved the puzzle fully. I'm 2/3 done, but I can do the entire 2/3 from memory...by Thanksgiving break, I hope to have it fully done, along with the rest of the students in my class. I finally am learning about the grit I have been talking about to my class. And it feels great.

Zaption: Easy Flipped Classroom--I Pinky Swear!

If you don't follow Richard Byrne, whose blog is Freetech4teachers, you must NOW. I have gotten a lot of great ideas from him, and today he did not disappoint. In this blog, he wrote about Zaption. Zaption is a site where you can take any video and add questions to it to make it interactive. Zaption calls these videos "learning tours". In about 5 minutes, I learned how to add multiple choice and free response questions to videos. Here's the video I watched to learn--so easy, I pinky swear.

I thought, nah, no math, I'm sure...but right when I checked it out, I saw a choice of a rational graph video, which I just taught, so it caught my attention. I had hoped to get to converting to vertex (standard) form of a parabola in my class today. Students had a test, and then they worked on this Desmos activity to introduce them to parabolas. But we did not get as far as completing the square.

Insert Zaption. I searched for a completing the square vertex video, and luckily, the first one I saw had an instructor who does it the same way I do. I was able to add a multiple choice question and two free response questions in a video that was less than 4 minutes. I added it to their homework assignment, and students will have to answer the question before they move on. Twice, I asked them to predict the answer, and then once I asked them to solve a problem on their own after watching the video. Afterward, I can look at the analytics and see their responses and how they did. I am assigning this for homework in addition to a light assignment on what we did get to cover.

Here is the video:
And here are the analytics, though none of my students have done it yet--though I can't wait to see it for myself.

The gallery is quite amazing. They have all different subjects and topics. Try it for yourself. If you do a flipped classroom or a modified flip, I think you will love it. 

If you are interested in learning how to use Explain Everything for your flipped classroom, click here.

Classtools.net: Some Fun and Quick Class Tools to Hook Students

This is a crosspost from the technology blog I write with ProfeSeiden, called Tech4Scots.

Classtools.net is probably one of the coolest things out there. It's really unique and students enjoy it. You can use it just for fun or as a learning tool. In a nutshell, you can create free games, fun activities, and diagrams in literally seconds. Here are some examples.

Breaking news generator:

I made this in about 30 seconds.

                                    

or use a pre-made picture from Anchorman:

Star Wars Movie Text:
Use this to scroll directions, for example, or to introduce something exciting (or otherwise not exciting, but you want to add some pizzazz...)

Fake Tweet:
To generate interest in a topic...haha I made this one up!

Fakebook:
Use "Fakebook" for character development, to give a series of historical events, to give debates and relationships between people...this would make a great assignment. Here is an example from Classtools.

BrainyBox:
This is really cool. You have to see it to believe it. There are six sides to a box, so there are six key events that students can write about...one side can be a video, one side can be a slide...click here to see it in action.

Fake Texts: 

This is just for fun...

                                                      

Random Name Picker:

This would be great for our department, as currently, we play "nose goes."

click here to watch it spin--when a name is picked, you will hear applause. You can also remove the student so that they are not picked next time.

Fruit Machine:
This is a slot machine...you can use as a random name generator, but I think it's great for a vocabulary word list. Put in words and spin, and when a word comes up, students need to define it                                              

Countdown Timer:
This is nice to display, and you can select a soundtrack as well:

Timeline:

Need a timeline tool for students? There are a number to choose from:

Arcade Generator:
Need one? No problem. There are some pre-made ones as well:

Fishbone or Burger Diagram:

Because, why not? Who wouldn't want this?

 There's more, too. Just go to http://classtools.net to check it out. There is a paid version as well for no ads.

Make something fun? Let us know in the reply section.

The Four-Color Theorem and The Pumpkin Time-Bomb

"CRAYONS!? We are COLORING? Wait, can I snapchat this????"

Yes, yes you may.

Here are the directions I gave to my Problem-Solving class the other day:

Take any map and color it so that no two adjacent states are the same color. Keep in mind that you want to use as few colors as possible so that coloring the map is not too expensive. It turns out that any map can be colored in at most 4 colors! And that this was the first proof proven using a computer. 

Here is the map I gave them, without telling them that they needed 4 colors...you may want to provide extras.

Here is the quick video I showed them after they colored, that talks about the four-color theorem.

After coloring the map, we drew the graph at the right, where each vertex represents a country and an edge connecting two vertices means those countries are adjacent. Then we colored the vertices and found the "chromatic number," that is, the least number of colors we can use. We needed at least three, as you can see by the red triangle drawn between Bolivia, Paraguay, and Argentina. The chromatic number for this map was 4. (And remember, for any map, this is the most it will ever be.)

Then we went on to scheduling committees, and I showed how you could make each vertex a club and each edge would represent any club that had a member in common, so a conflict in time. The chromatic number, in this case, would be the least number of club meetings required. We also answered some interesting problems that related to the Handshake Problem.

Here are my notes from class that day, that I took from my book. 

All in all, a fun class with a theorem that they have never heard before. And I am sure that they will never forget.

--------------------------------------------------------------------------------------------------------------------

Today, we did the awesome Pumpkin-time-bomb-activity from Mr. Orr. Very fun predictions, and we were only 4 off from what we guessed! I highly recommend that you read his post, check out the data, and also watch the video from Jimmy Fallon.

The explosion took us by surprise so we didn't get a picture, but one student ended up with pumpkin all in her hair! I was amazed at what the rubberband clump looked like at the end! We didn't do anything to it. That's what it looked like after the explosion!

The Radioactive Cube Investigation

This is a problem that was presented originally by my department chair 21 years ago. I have used it often ever since, but not since I began blogging. It is a great problem at any level in honors or Pre-Calculus. Though some can get it rather quickly, there are definitely some who need it to be broken down. Often, the answer I get without much thinking is "27 cubic units." It is much less. Hopefully, before you read on, you will try the problem. It is great in that it uses a lot of Geometry and nothing that students are likely to be working on at the moment.

I am lucky to have a new course with only seven students. However, four of these students got the answer to this problem rather quickly. The remaining three had the weekend to think about it, but got nowhere. Insert Unifix Cubes. I've had these for a million years.

Students who needed to taped them together like this:

And saw that there were 7 cubes in all that were radioactive...the first cube itself, and the other 6 that radiated from the 6 faces of said cube. So this was 7 cubic units so far.

Then, they cut paper and taped it around the cubes. Students saw that this created 3 4-quarter cylinders, so this added 3 cylinders with radius and height both equal to 1, so π cubic units. These quarter-cylinders came from the edges of the inside cube that radiated radioactivity as a radius of 1 between any two cube faces.

They then realized that they were missing the triangular pieces, shown above. This was from the corner of the middle cube, and it created eight 1/8 spheres, so 1 full sphere with radius 1. Or, 4/3π. 

So the total answer is 7+3π+4/3π, or approximately 20.6 cubic units of radiation.

Some visually talented students drew it like this:

The 7 cubes

The cylinders and spheres built in

Some final results

Students were very proud of themselves either way!

The Art (Benjamin) of Problem Solving

When I saw him in the crowd at Twitter Math Camp '15, I knew I recognized him from somewhere. Then it hit me...it was Art Benjamin, famous mathemagician and speaker whose DVDs I had shown in my classes some time ago. I was completely starstruck, and my colleague had to calm me down a bit...but then...then he was actually going to do a show for us? WHAT?? It was absolutely amazing. Art Benjamin is not only brilliant, he has an energy about him that catching to others. His love of math is pure and he engages his audiences by multiplying large numbers in his head (he converts some of these numbers to words to help him!)

Today in my Problem Solving Class, I showed this amazing and highly recommended Ted Talk video. Here, Mr. Benjamin squares 2 digit, 3 digit, 4 digit, and yes, even 5 digit numbers in his head, much to the surprise of his audience. He even can tell audience members the day they were born if they tell him their birthdays.

My students were in awe. They were perplexed. How did he do it? Well, we googled and found this video next, where he explains the secrets of how to square a two-digit number in your head.

And they could do it! Well, some could do it in their heads...it was hard! 

Here is his method.

Take any two digit number and square it:

For example, 23x23

First, find a number more or less than the number that is easier to square...in this case, we will use 20. Twenty is 3 less than 23, but you also have to go up 3 more than 23, like this:

26

|

(3 up)

|

23

|

(3 down)

|

20

Now, multiply the bottom and the top numbers: 20 x 26...easy to multiply 2x26 and add the 0, and get 520. Then, take the number you added or subtracted (3, in this case), and square it (9) and add it to the 520, and you get 529. 

Well, of course we had to try this out. We went to the Algebra 2 class next door and showed our newly learned talent during their brain break. They were impressed, and we taught them how to do it. Then a tour came in. I think the student on the tour was a bit scared when I excitedly asked her to pick a number any number, and we would square it for her. I just could not contain myself. 

So why does this work? Well, it's all about FOILing, if you don't mind that word. Essentially, what we did to square 23 was to say:

23x23 = (23 + 3)(23 - 3) + 3x3

Art Benjamin may explain it better, so watch the videos!

The other day I saw on twitter that he wrote a new book The Magic of Math: Searching for X and Figuring out whY, so I had to buy it. It's fantastic, and I can't wait to share more gems with my students.

But this is still not the best news. The best news is that I found his website, and I saw that he does shows. Lots of them. And he is doing one near my school. And I contacted him. And I contacted my head of upper school. And GUESS WHAT!! Art Benjamin is coming to do a show at my school in March! I am so excited. When I told my students that, they couldn't believe it. They can't wait, and neither can I. The president of my math club came into our class after we showed his videos, and we told him that he was coming to the school. His eyebrows went to the back of his head. He had watched a series of his videos before. He was so impressed that Art Benjamin will be at our school. So am I. I am so happy my school is hosting him, and I can't wait for his love of math to rub off on our students.