Puzzles, Puzzles, Puzzles.

It's a good Sunday. A former colleague texted me this puzzle today. 

Try it. It's a good one. You don't need to read Spanish to figure out what it's asking. I'm going to give this to my classes tomorrow. Will rich discussions take place? I am hoping so. And I don't think it will take up too much time. Try it, and THEN scroll down for a hint if you need it.

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What's cool about this problem is that all of the numbers are odd, and there is no way to add three odd numbers to get an even. An odd + an odd = even, and then an even + odd = odd. So there must be (as always) a trick. Should I give you the answer? Email me at lisa.winer@saintandrews.net if you want the answer. 

I am hoping that in class, we can talk about why this is the case: that even numbers can be represented as 2n, and odds as 2n+1, and so on. 

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Why else is it a good Sunday? A former student texted me this link today, which she said made her think of me: 11 Difficult Food Riddles That’ll Stump Pretty Much Everyone - Buzz Feed. She is a foodie and I am a puzzle freak, so this is truly the best of both worlds. I have blogged about giving a Plexer of the Day, and this would be fun to give when you have a few minutes left at the end of class. Here is the first one:

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It's also a good day because I love doing the Sunday NYT crossword puzzle. Here is a picture of Tiki and me working on it...

BUT YOU MUST LOOK BELOW FOR  SOME COOL PROBLEMS from the NYT!! This came out last month: Are You Ready For Math Whiz Camp?

The question below is my favorite question, but all 5 were great class openers. 

(Click here for a great article on BEAM, an experimental program in Manhattan for students with a high aptitude for math and who come from low-income populations).

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I really liked these Relay Race Puzzles from Chris Smith. I haven't tried them yet, but I hope to. You may need to join TES to view them, but so far, it has been free for me. TES has many resources to look through! Below is an example of two cards from one of the several relay races...many are holiday themed and directions are given as well. 

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I love this link from Mindhow.com that gives 12 challenging brainteasers. Here is one of my favorites.

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There are so many links with fun puzzles...I have them saved in a folder on Google Chrome so I can easily access them as well as save them when I find new ones. This is unrelated, but some of my students will soon be working on a project where they will teach a video lesson,  and a subset of that group will be using stop-motion animation. Here is a very cool professional video called "Fresh Guacamole" that I enjoyed watching that I will share with them.  So clever!

Me Retire? Ha!

It happened twice in the last week and never before. Two people, separately, asked me how long I've been teaching for.

Me: I'm in my 28th year of teaching.

Them: Wow! You must be getting ready to retire!

Huh?

My boss chuckled to himself at my reaction to the first woman, as we were at a conference together and chatting with others at our table.

Am I really ready to retire? No! And here's why.

• I'm 48 years old. Yes, I got my first teaching job right out of college, and got the offer the night I graduated college...and yes, it was weird that I called them back from the pay phone at the Econo-Lodge bar, where I was celebrating with my friends. Forty-eight is still young, right? RIGHT??? I was always the youngest in my group, and now I've got the most seniority in my department...I actually think I've had that seniority for like 10 years?? True, I've gotten to the age where I am generally older than my student's parents. But so what? They keep me young, so I've got to stay!

• It just keeps getting better and better. I feel sorry--actually very sorry--for new teachers. It's AWFUL. My student teaching experience was terrible. I was horrible and could not control the students. In fact, I was up for an award at graduation, and after the department chair observed me, I saw him shake his head at my mentor. I knew I was bad. The first year I taught, I had a horrible, horrible geometry class. There were two boys, in particular, that were rude and loved to disturb the class discussions (Jim and Bill. I still remember.) I literally did not know what to do with them. However, if I did not go through that, I never would have known how to handle classes later. And thankfully, with the bad classes, came the good ones, where kids would just smile and be happy and love your class. Sure on occasion, I still get a bad class - we all do - just a strange mix of kids. But you have good days and bad days, and my good days now FAR outnumber the bad ones. In the beginning, every day was a bad day. Every weekend, I had tears about this student or that student, and my grandmothers (in blessed memory) listened to my tortured soul. I never thought I'd last as a teacher in the beginning. NOW is the BEST, and why would I want to leave?

• The explosion of #MTBoS, or the Math Twitter Blog-o-sphere has changed my math department from 11 people to thousands. I update and change lessons constantly based on what my tweeps are suggesting. Sometimes they work, sometimes they don't. But in the beginning, all I had was me, that purple ditto machine (with toxic fluid), and overhead transparencies that left me with a perpetual blue/green tinge on the side of my hand, and maybe one other teacher who taught the same subject as me, who in my mind was so much better, there was nothing I could do to be that good. In time, came confidence, which you can't gain any other way, in my opinion, than from getting a clean slate each year and knowing what works and what doesn't.

• Apps such as Apple TV, Notability, YouTube videos, Google drive, and tons of others. Although not always perfect, these apps have changed my teaching tremendously. Technology has exploded and I can send students my notes in seconds, can work on documents on any computer with ease without emailing back and forth to myself or to colleagues, can find a great video to send my students if I want them to preview something (gosh do they love https://www.youtube.com/user/Mathbyfives), can create one wicked game of Kahoot!, and the list goes on. 

• Deep, reflective workshops. Don't get me wrong, back in the 90's, NCTM conferences were my jam. I went to them religiously. We were forced to join in college, and I went every year for YEARS, but I started getting annoyed when you had to leave one session 15 minutes earlier to ensure that you get into a session that you wanted. I attended Twitter Math Camp for the last two years, and it was AMAZING. But this year, there was a lottery, and I was bummed, because for me, I get A LOT out of talking about the workshops with a colleague that attends with me. In fact, I think I get more out of that than going alone, as we can discuss how to apply it on a deeper level in a setting that we both know. So I didn't apply, knowing not all of us would get to go. I hope they change that next year. Last week, I went to Jo Boaler's workshop on Teaching Mathematical Mindsets. It was great! She had us think deeply about how to get kids to problem-solve without worrying so much if they were right or wrong, but more about just getting them to think and talk mathematics without fear or stigma of getting it wrong. We did a really fun activity that I will add below...so good, in fact, that my boss and I dragged 14 boxes of sugar cubes back on the red-eye so we could do the activity that morning. This summer, I am going to take a course at Cambridge University on Thinking Mathematically. I just decided one day to look at the Oxbridge catalog, and boom there it was. I won't stop going to workshops because they make me think differently; they change me to make me a better teacher. I keep looking for new ones because I keep wanting to learn. Having an empty nest certainly makes that easier!

So no, woman 1 and 2, and all the others who will probably start asking in the future, I am not planning on retiring soon. I am having too much fun. NOW is the time to teach. To those of you who find teaching hard...know that confidence comes with years of experience, and it will get better, as long as you have the time to put into it. Find conferences that speak to you. Don't be afraid to apply for grants. See what's out there and just go for it. Network with the people you meet who may become friends for life. It's a big world out there, but mathematically speaking, there are many other people just like you looking for new, innovative ways to teach. 

What's my point? This old dog CAN and WILL learn new tricks. And I will do so for many years to come, G-d willing. Here's to another 28 years. 

Students then discovered formulas for an nxn cube - facinating relationships!!

A Great Conics Project Using #Desmos

I have assigned conic picture projects wayyyy before Desmos. My students did them by hand in the old days, and even on TI-83's (not easy) after that. This is the first time I ever did the project using Desmos, and it was a huge success. My students exceeded my expectations. Here is the project, some of which I got Mr. Sumerton.


Not only did students make great pictures, they did some pretty awesome math in the intersection part. And they told me that they really understood translating and conics so much better! Here are some pictures of their work.

What was even cooler is that some learned about trig curves and polar curves and how to rotate conics, even though they did not learn that in class.

And my other students, who saw the projects on display, were so impressed with their work! They wanted to know how the graphs were made, etc.

Above are parts of projects--I didn't take every picture because it would have been a lot.

Below is one full project, with the graphs made on Desmos colored in, the equations, and the points of intersection shown on Desmos and done algebraically. 

And here is a close-up of one student's intersection work. 

*Note: if you see any of these projects already online, please let me know, as we have a strict honor code on plagiarism. In addition, my students worked super hard on their projects and have gotten very upset when they see their projects copied online after I showcase their work on this blog. Let's keep sharing ideas and encouraging students to come up with their own  :)