Special Right Triangles: Tic-Tac-Toe Method

I've always taught special right triangle by comparing similar triangles, writing proportions, and cross-multiplying. Last year I tried this investigation for the first time that also doubled as a project with mixed results. I tried it again this year but without the project piece. And I'll be honest, this year I walked around giving some hints and last year I didn't help at all. Why? Because I felt like my class was so needy and had to start learning to be more independent. This year I didn't let them talk until they had finished the whole page front and back. Then I asked them to compare with at least two other people. That part went really well.

Then we went on to basic INB notes. Some students really took the lead in shouting out what to do. While it wasn't cross-multiplying, they were using patterns and it seemed to work.

And then...

Is it weird that y doesn’t equal something with a square root of 3? Since it’s a 30,60,90? Also why does putting it over square root of 3 work? Or is this wrong pic.twitter.com/o1yXYwmXUK

— Elissa Miller 🦄 (@misscalcul8) September 3, 2018

A student asked this question on Friday and I told him I would find out and explain Tuesday.

Which led me to this:

I used these from @MrsNewellsMath last year and my kids grasped it! https://t.co/thop7WWrmR

— Breanna Davis (@MissDavisSCSD) September 3, 2018

I really loved her materials but I had already 'investigated' the patterns and already had INB notes. What to do....

Strips to the rescue!

We made a Math Tools pocket at the beginning of the year and added calculator strips. I turned her charts into strips and we used them to practice with dry erase markers and then write in the answers.


I color coded the 'levels' that Katrina mentioned in her post.

Using the tic-tac-toe method, we decided first which column the given information goes in and then how to solve for x. This really helped them see when we need to multiply and when to divide. Once we had x then we could fill in the other two columns.

Two students figured out shortcuts to the patterns without doing the work. I explained to them that that was my goal but when I led with that in the past, everyone would get confused and so I need to teach a structure that EVERYONE can fall back on.

I felt like this really cleared things up from where we left it on Friday. Next time I teach it I will do the strips right after the investigation and then they can use the strips as a reference for the INB notes.

Thanks Katrina!

My Flavor Is Confidence

Virtual Conference on Mathematical Flavors

Your teaching practice has an impact on how your kids think about mathematics. Our classrooms are little bubbles and while kids are sitting in them, they are picking up all kinds of signals about mathematics. You might have students leaving a year with you thinking mathematics is collaborative, or that it requires taking risks, or that it is hard but hard is okay. We all have our own unique flavor of mathematics that we are imparting to students through how we orchestrate our classes day in and day out. So here’s the formal prompt:
How does your class move the needle on what your kids think about the doing of math, or what counts as math, or what math feels like, or who can do math?

It took me a while to wrap my head around this concept and a lot of different 'flavors' ran through my head. But then I thought about what 'leaks out' of who I am, what students remind me of after they graduate, and what they write to me in their semester reflection papers.

I think my flavor is confidence.

• Confidence in your own personality and being 100% on brand. It took me decades years to cultivate my own confidence and now sometimes I think I might be a little on the arrogant side. lol I model this especially through my two nice things procedure- they hate when I make them say two nice things about themselves and I always give a little speech about how you know yourself better than anybody else and you should know more nice things about you than you know about anybody else. I feel like I show this through my work ethic because students come to me with new ideas. I think that shows they know that I go above and beyond in all aspects of my job. Students will tell me when they see chevron stuff they think I should buy, they send me pinterest ideas, they tag me in memes...I think that by being 100% myself, I give them permission to be 100% themselves.
• Confidence through consistency. When you have students years in a row, I think this comes kind of naturally but I think students enjoy math with me because they know my rules, procedures and routines. They know I'm going to show up every day and they need to also. I have so many kids who come back after doctor appointments and such 'just for my math class'. They also know they are working every day, all hour, and no free days. Even though they'll never admit it, I think they enjoy knowing they are going to work and learn on a daily basis. Or at the very least appreciate it.
• Confidence through finding mistakes. I make an emphasis on finding your own mistakes and fixing them and I think that builds a sense of independence. I make a big deal of not erasing all your work and fixing small mistakes. I post answer keys often so they can check their work and work at their own pace. This helps them realize how they learn and that they don't need me for every little thing. I also hope those skills transfer over to personal life too.
• Confidence through freedom. The culture of my classroom is very laid back; we make a lot of jokes, students don't have to ask permission for little things, I have a lot of supplies available that they are free to take, we have a lot of random conversations, etc. Students who finish early casually wander over to students who aren't done yet or struggling and help. I love this because they are hearing different perspectives and the freedom to decide which way works for them. And freedom to learn from someone besides the teacher.
• Confidence through creativity. While I am very consistent and routine, students also know I'm going to take a creative approach to things. They might not know exactly what to expect but they know I'm not just going to take the normal route. When they start to expect that, I think they raise their own standards as well. Sometimes their expectations are higher than mine are and we both take turns rising to the occasion. There is always a way to express yourself.
• Confidence through risk taking. While I love trying new things and I think my ideas are awesome, I am also really good at admitting failure. I don't think that's something students are necessarily used to seeing from teachers. Right now I'm having really good luck with students being willing to shout out answers, even wrong ones and I hope that in some small way, it's because I've been willing to be wrong.
• Confidence through problem solving. While I wish I could say that I mean this in a purely mathematical way, I don't. I mean this in a more practical way. I ask students for feedback often and when I see problems I brainstorm with them on solutions. They constantly see me trying to improve and make things more efficient. After I admit failure, I want to fix it. 
• Confidence through persistence. I don't give up on keeping them from giving up. I don't give up on ideas that fail. I don't give up on trying to change their attitude and feelings about math. I don't give up on making them say nice things. I don't give up on positive vibes.
• Confidence through showing up. I show up to work every day. I show up for them when I can tell they are upset, mad, or panicking. I show up when their grades start going downhill. I show up when they've just had their hearts broken. I show up to their games. I show up for them and I show up for me.

Confidently.

All The (Good) Things!

I don't know why it is so hard for me to be consistent in blogging my one good thing when I can tweet it. But I thought I would do a mash up of all the good things from the past three weeks that I can remember and then start fresh next week!

• A senior that's not in my math class this year has been calling me on his teacher's classroom phone between 7th and 8th hour and just chatting for the 3 minute passing period. I don't know why and he gave me a lot of grief last year but...I guess he misses me? lol
• Today a senior I don’t have in math class came to me for help with his online college math class. As he walked out of the room he turned back and said “You’ll be happy to know I even used Desmos.”
• Doing function composition in Algebra II a girl said "I'm really enjoying this. I just wanted you to know that."
• The students like function composition with numbers to plug in better than just simplifying functions so on their practice the last first 6 were simplifying and the last 3 were with numbers. One boy said that was like the 'dessert'. Another student told me had done the last 3 first and the boy says "You ate dessert before dinner?!" As I was walking around helping students, a student asked for help and then said "Ok, you can go back to having dinner with T*****." Lol
• Former student who sat through trig senior year doing nothing and failed-getting zeros (it wasn’t required), messaged me today to ask if she should do an 8 month program or 2 year associates degree for medical assisting.
• Reviewed metric conversions, fractions, and percents with Algebra I freshman....overheard “Ms. Miller makes it seems so easy”
• I got a new document camera and it's SUPER awesome and I will be getting a new ipad soon!
• I use google photos all the time but it just occurred to me to take pictures of student work as I walk around, sync it, and then display it on the SMART board
• I've heard some kids talking about working on Delta Math and saying it's fun or they did it at home or they're ready for week 4 or they like it so BIG WIN
• A student who has anger problems is behind on some assignments, apparently got in an argument with his mom about Delta Math, and had a bunch of excuses for another teacher about the work; when he came to class today he asked for help a few time and thanked me each time. His mom e-mailed me tonight to tell me he was half done with Delta Math.
• My freshman are ON. IT. I love them already.
• My 'lower' Algebra I class has only 6 students in but we are already vibing; they shout out answers and if they're wrong they just shout out some more. They are doing so good and I hope it lasts forever.
• The students asked me if I was going to our county fair to the demolition derby; I haven't been since I was probably a teenager myself. My sister wanted to go and one of my students was driving in it so I went. I saw a few students as we walked in but when we got to the grandstand a whole giant group of students from my school were sitting together and they literally cheered for me as I walked by. I mean.....I can't even!!!
• So far we haven't had any technology problems!
• Each day flies by so fast; I have no classes I dread, I have no troublemakers, and I just enjoy it!
• I've gotten a lot of positive feedback on Twitter and Facebook on my #teach180 posts 
• Just kids who tell me they love me and give me fist bumps and high fives every day

This is my purpose and my passion- these are my people.

Odds and Ends

I've used this activity for the past few years, using foam circles from Dollar Tree that I labeled with sharpies and stuck up all over the room.



My ceilings are too high to reach and I felt like that always threw them off. This year I got the bright idea to cut up tissue boxes and use blank yard sale stickers.

I gave them the worksheet with a picture on it too and asked them to make sure the stickers were in the right place. Sadly they were nowhere near sticky enough and repeatedly fell off. Now I feel like I need some laminated circles and hot glue them to the box. Any better suggestions?

This was the last activity before their quiz. After like 6 DAYS of point, lines, and planes, the grades were still bad. I think the highest was an 86% and the majority of the class was between 50%-75%. Why is this so hard? It's like the more time I spend, the worse it gets. I hate that it's the first lesson of the year because it drags on forever, they get a bad grade, and then they decide that geometry is too hard and they're going to fail.

Moving right along....

I used this 'number line' to introduce absolute value equations.

Questions I asked:

1. What is something weird or unusual about this diagram?
2. What is something familiar about it?
3. What kind of math thing could it represent?
4. If the pink magnet was a number, what would it be?
5. What is three magnets away from the pink magnet?
6. Why are there two possible answers?
7. What is two magnets away from the star?
8. What could the magnets represent?
9. Can you have a negative distance?
10. What is the definition of absolute value?

This was done in about 2 minutes and then we jumped right into INB notes.

And here's a fun video of us playing Grudge Ball but I call it The X Game because there are no balls and there are X's.

Any time they run to the board, it's a win. =)

Function Composition: An Intro

I'm pretty sure I got this original task from @pamjwilson but I can't find the original file or link. I found this one which is where I got the questions from.

I tried this before with my own family tree but it just brought on way too many irrelevant questions so my friend @howie_hua suggested I used the Kardashian family. I knew there was a big famous family that was obvious so thanks for helping me out.

I posted this photo in Google Classroom and had the students leave it open on their chrome books:

Numbers 6-10 is where the real meat is; here we have to discuss what comes first and where to start.

The above questioned helped them establish that order matters.

As students were writing their answers on their desk, I went around taking pictures, synced it with Google Photos, and then was able to immediately show them their classmates responses. #winning

Next we labeled index cards and baby post-its.

They are color coded on purpose- these are the three colors of baby post-its I had. Lol.

When I did it in class, we wrote the f(x) on the lined side of the index cards but then we had to keep flipping them over so I edited the slides to put the label in the top left corner.

Then I showed them a problem like this (the answer doesn't show at first):

And we talked about what color post-it to use and which index card to stick it on.

Then they would simplify it on their desk and I would click the slide to show the final answer.

Tomorrow I will follow up with this function composition match without the index cards which also throws in some square roots and putting a function inside itself and finally INB notes.

Here's the powerpoint: