Sunday, April 9, 2017

Having a Unit Circle Tournament Using Purpose Games

If you want students to know their radians, sines, and cosines quickly, then this is the game for you and your students--especially if they are a competitive group like mine.

Students will be given a radian, point, quadrant signs, or an axis label and they have to click on the blue button quickly that matches it. And it's timed! I ask students to shoot for their best time with 100%. One of my students made top 5 of all players in the world with 37 seconds. We have no idea how she could do that!!

Click here for the link at Purpose Games. In the past, my students have logged in and played the game to try to get their names on the leaderboard. I assign it for homework the night after teaching the unit circle and give a bonus point to the top 3 students. But this year, I found the tournament section!

I discovered that there are lots of things to do on this site, but all I have tried so far is to click on CREATE at the top and create a group.

I entered in all of the info and I actually did make it public because when I initially tried invite only, I couldn't get it to work right. No one else joined other than my classes, so I think it's fine to do it that way.

You can name the group whatever you want and even can add a picture. Then click on create a tournament, in the yellow box. On the original, I did write some clever things, but for show here, I didn't. 

Enter the name, description, and when you want the tournament to start and end. Save the tournament.

Search for "unit circle" in the search box below and click enter.

Lots of choices pop up. I choose the one by felliax08. Click on "add game." Then click "publish" at the bottom. You will get a link, and you can share it with students and the tournament is on!
A few things to note: π/2 is not on there. Also, "x-cosine" means click on the button that is the x-axis, and "y-sine" means click on the button that is the y-axis. There is a glitch for quadrant signs. x,x means +,+, etc, so the plus signs come out as x's. Otherwise, it's all good, and my kids really enjoyed playing it. There was a lot of chatter about it the next day in class. AND they know their unit circle!

Tuesday, April 4, 2017

Ted-Ed Virus Riddle

My third Ted-Ed riddle was published yesterday. Here is the link to the actual lesson:

This was a fun one to do because it required me to research some Discrete Math topics that I learned back in grad school, like Hamiltonian Paths and circuits. The playful ending of the "Traveling salesperson" is a famous graph theory problem that students likely don't know about yet.

It's not a particularly difficult one, but certainly can stump a class for a good five minutes. Show it in class and be sure to show the second part even if kids get it right so they learn a little bit about graph theory and Sir William Rowan, not THAT Hamilton!

Here are links to my other Ted-Ed riddles:
This one is more "mathy" and great for higher levels, though MS kids do enjoy it, too. 

This one is an easier one that takes some time for kids to figure out. This could be done with all levels and I love having students "act" out the part. 

And here's an all-time favorite that I did not write, but I love to do with kids. Again, having them act it out is very fun!

Monday, April 3, 2017

Algebra 2 Honors Unit Circle Projects 2017

Each year, I give my students a Unit Circle Project to help them to remember the Unit Circle and to show off their creativity. Entries from two years ago were also great and can be found here. This year, students also rocked their projects. I think this is the hardest working class I've had in a very long time, and I am so proud of them. Students are told that they are not allowed to use project ideas already posted on the Internet, as that would be plagiarism, just as copying a paper is against our Honor Code. I showed them some projects I found online and told them theirs should all be original. I use guidelines and the rubric from, and also tell students that they must make their own circles and not use pre-made materials for them. Here are some of their projects:

I've seen these crayon melting effects on Pinterest!
"Arc" Reactor! Such a clever name (Ironman)

Look at the pepperoni, pineapple, and pepper cut-outs. The crust is very creatively done,
and there is real oregano sprinkled throughout!

A play on Dr. Suess

This student drew this by hand and dedicated it to her father. 

Beautiful hand drawn peacock!

This student "made" her own lampshade from scratch!

Though I did get a few dartboards, this one actually works with magnetic darts!
The student put a magnetic sheet under his hand drawn board.
I liked the "Stonehenge" look of this, particularly as I am traveling there this summer!
Stay tuned for my blog on the Unit Circle Tournament, which I will try to blog about later this week!

Sunday, March 26, 2017

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.
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 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. 

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:


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).

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. 


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


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!

Tuesday, March 14, 2017

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!


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, 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 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!!

Thursday, March 2, 2017

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  :)

Saturday, February 18, 2017

A Negative x A Negative = A Positive

What do you do when your flight is delayed 2 hours because your President happens to live in the town right next to yours? Blog. It's been a while.

It's been a crazy few months. A few weeks ago, I went to my uncle's funeral - the second funeral in the same family within a few months. Due to the funeral, I missed a culminating event/fundraiser that I worked really hard on and did not get to see it through. Of course, I was happy to be with my family in our time of need. But the timing was rough. Well, there never is a good time.

Today, I was flying to NJ for a fundraiser for my best friend Debbie who has been diagnosed with ALS. Not only is she going through some of the hardest moments of her life, but other friends of mine seem to be going through very difficult times as well. And for whatever reason, I truly, deeply feel their pain. And my aunt's pain, who lost her mother and husband within a few months. It feels like everything is hitting at once.

And it's February. Which in the teaching world, means it's the Longest, Shortest month. Kind of like a full moon.

Little, stupid things, too are making me crazy. My font now must be humongous because I can't see small print anymore. And in the bathroom at the airport, I noticed a huge smattering of gray hair--where did that come from??? The voice in my head asks, "Are my pants too tight from the excessive tortilla chips I ate last night?" And like Nora Ephron, I feel bad about my neck. 

OK. I must stop. I HAVE to write about some feel goods...some things that are going well so I can focus on the positives. Here we go. First, the math.

1. I love my problem-solving class. It is flexible enough that I can decide last minute to add the algebra of set theory and truth tables and take out probability because it will better serve the students in the class (who have had exposure to probability before or will soon.) So far this semester, we have studied sequences such as triangular and oblong numbers as well as the method of finite differences, the Fibonacci sequence and the Golden Ratio, the tower of Hanoi and its relationship to fractals and binary numbers, set theory, several puzzles and problem sets. Below are the interlocked Mobius Strip hearts we made for Valentine's Day. These kids jump into whatever I give them. They are a small class, but they are a mighty class, and they are smiling often. Takeaway: Teaching students math that they would not have been exposed to in the normal math curriculum is EXTREMELY rewarding! Solving problems in life is a hard thing to learn, but it's doable.
2. My Algebra 2 Honors class is so strong. They are cute and active, and boy they want to do well. We have been working on conics, and this year, I gave them this Desmos Conics Project I am excited to see their masterpieces! I think it took me 3 hours to make up a test that was challenging enough and not just regurgitation, and yet not too challenging. Here is their conics test, and here is their review sheetTakeaway: Challenging students is important, and making them think rather than just practice exercises can foster deeper learning. Tackling challenges in life is no easy task. But if you break it down one step at a time, it becomes more manageable. 
3. My Pre-Calculus students did exceptionally well on their trig unit. This year, I had them cooperatively unwrap the unit circle and create the sine and cosine graphs using spaghetti. A student said it really made sense of graphing for him (Goal!) I will definitely use this every year. We also created a human Unit Circle, and I played music as students walked around the spots on the floor marked by tape. When the music stopped, students froze and as I gave them directives (Give your x-value! Give your radian!), they tried very hard to each name them correctly. It was also a nice way for them to see which student was their "reflection point." These visuals, I believe, helped them to make concrete of the abstract. Finally, they also created unit circle projects, which I have been doing for many years now. Takeaway: Making math come alive for students definitely works. Life has its ups and downs, like a sine curve, and you have to know that where there are downs, there also are ups, and you have to create a healthy balance.  

4. It's our season for math club (Mu Alpha Theta), and we have been practicing every Friday after school since September. I probably get about 16 students who regularly dedicate their time to Algebra 2 practice, and 4 other math coaches simultaneously work with their teams. As I mentioned, this is a very strong Algebra 2 group, and at our last competition, they placed, and we had a student place as well. We are in our 6th year in the club with about 85 members, though honestly, I would say that 70 have truly been active...still, that's over 10% of the school who enjoy math enough to be working on it on a Friday afternoon! We came up with our shirt theme this year, POKEMAO, a play on Pokemon, of course, where MAO stands for "mu alpha theta" our math honor society. Takeaway: This club started with probably 15 people its first year and has grown so big. Take risks and try big things. Surround yourself with likeminded people and you will always feel good about yourself. 
5. I just got back from a school immersion trip to Greece. We traveled all around Athens and Delphi and more and studied math, history, and architecture. We took 13 students. It was amazing. Kalemera!! #sograteful Here is the Athens Math Treasure Hunt from and the Answer KeyTakeaway: You learn more traveling that you do anywhere else. Sometimes when you feel like your life is in ruins, take the road less traveled. 

And not math...

6. I didn't take a picture, but my friend and I took up Pam's idea and did our 30-day happy teacher challenge in our faculty workroom, where we printed out positive challenges to do and hung up stickers for teachers to use as they accomplished them. It did not take off as much as I had hoped, but those who liked it really liked it and used it. Takeaway: you don't have to make everyone happy. Making a few people happier is still an awesome goal. It's easy to say the glass is half-empty and spread negativity. But it's more of a challenge to say it's half-full, and more rewarding, too. 
7. I have not had enough time to work on my Ted-Ed project, #StudentsTeachingStudents, but I been thinking about it. I've had students in my math club make short videos to teach other students. Over spring break, I will be creating a guide for students so they know how to make the videos. I also found an interesting app called Groupboard that I want students to use if they remotely peer tutor. Takeaway: Kids love to teach other kids! And I learn more from them every day than they do, me, I am convinced. 

8. I am SO excited to see and celebrate my friend Debbie tomorrow! Over 200 people are going to her fundraiser, and some are friends I have not seen in years and years. Our friends from California and France are coming as well as several from NJ. My sister is coming. My aunt (the one who just lost her mother and husband) will be there. Friends of mine that I worked with when I was a public school teacher will be there (I've been teaching in private school for the last 23 years). And tons and tons of Debbie's friends from work and community will be there to support her. Takeaway: Through the most awful things in the world, you can find good and hope. Friendship is a gift and should not be taken for granted.
A picture from 6 years ago
9. Next week, I am going to a Spark Women's Retreat, which is a branch of JWRP, which I've blogged about here. I've done more with these strong women in a year than I've done with any other group. When I am with them, I feel lighter, stronger, smarter. This event is at a spa so I will be learning, soul searching, and relaxing at the same time. Takeaway: As my son has posted on his wall at school, "Happiness is something that must be shared." Rest is necessary to strengthen one's soul. 

10. I have friends and family that I can rely on. I have a mother-in-law, a brother-in-law and a sister-in-law and brother-in-law that are all within a mile of me if I need anything (less actually.) My work friends are my lifeline. I speak to my sister every Saturday. Although I have lost some cherished loved ones in the last few years, I still have a large extended family that constantly support me. Takeaway: Although I lost my parents early in life, I have a large network of family and friends. Be thankful for your people and for those who nourish your soul.

11. My son is halfway through his freshman year in college, and I took a bus and saw him last week. We spent the whole weekend together, and it was wonderful for me to see what a hardworking, dedicated, and mature man he is. His smile fills my soul with joy. On the other hand, anything he gets even remotely upset about, I end up getting upset about. Ah to be a parent. But I wouldn't have it any other way. I am so grateful for our talks and texts. Takeaway: A mother's love is like no other. Take in every moment with your children. They grow up way too fast. 

12. And least but certainly not last, my husband is always there for me and puts me first. After 23 years of living in the same place, we have upgraded our vanity area in our master bathroom. Not that exciting, but you know how it is. My husband has dedicated so much time completing this for me even though it was really not a priority for him (truth be known, he really did not want to do it.) He knew it would make me happy, and we haven't done much around the house in a while. It's amazing to me that he is so reliable and completely dedicated to both me and our son. If I need anything, he jumps. Well, he would, except that he has a bad back. He cooks dinner for me every night. He takes care of me. I can do and be so much because he will do all the little things I ask of him. Except for getting me a puppy. Haha I know he's reading this, because he does that, too--supports me in my endeavors. He's underappreciated, and I need him to know how much I do appreciate him and love him. Takeaway: I am thankful and grateful to have such a support system. When there bumpiness in life, don't lose sight of the things that are in front of your face. 
24 (?) years ago

No backsplash yet!
So, I was 2 hours late landing. The rental car lost our reservation. I had plans to have dinner with my friend who flew in from California for Debbie's event tonight, and we won't get there till super late. What do they say, G-d watches you make plans and then laughs. It's OK. I was inconvenienced. But what I now realize, after writing this, is that there is so much good. So maybe it's a good thing Trump came in today. Because I might not have realized how good I have it.