Unit Circle Art IV

It's that time of year again for my unit circle projects!

My requirements are that it can't be made out of paper and has to contain radians, degrees, and ordered pairs.

See my previous posts here:  Unit Circle Art I, II, and III.

This is the rubric I used to grade them and they later taped into their INB.

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:

Solving Equations

Both of my 9th grade Algebra I classes had 8th grade algebra so the majority of my course is review.

I started the year with solving equations by using Katrina Newell's equation flip book. (I loved that this included infinite and no solutions as well as fractions and multi-step equations with variables on both sides!)

I used my new document camera to show them how to put it together and we used my mini staplers for the first time ever- it went pretty smoothly.

Next we followed up with an equation card sort.



This is the first time they've ever done a card sort (to my knowledge) so here's how I introduced it.

"Get out all of the pieces that have numbers on them."

"Can you tell which piece is the original problem? Since you all have different problems, what is a hint you could give to pick the original problem?" (It's the longest one.)

"Now can you put the piece with numbers on them in the order they are being solved?

"Now look at the pieces with words. The word Given should go next to the original problem. Now can you put the words in order of what's happening in the problem?"

Then I went around giving feedback and checking answers. Each group also had one extra step that didn't belong.

One bag had two subtraction property pieces and it did not sit well with them that you could do that twice in a row until I pointed to each step of the problem and ask how they get there from the line above.

Each group rotated until they had done all sorts.

Then we used dice to play this partner dice rolling activity from All Things Algebra.

Digital and Video Answer Keys

Last year I finally got the genius idea to make digital answer keys for each INB page. While that takes a while obviously, I was writing them out every year to have an answer key for absent students.

This year, I only have to do the first couple in each unit. I also thought I would upload them somewhere in Google Classroom for students to access.

I also never thought of saving them as a pdf so the formatting won't get messed up. So this year I will save them as a pdf and upload to my google drive. I'm thinking I will create a google doc or spreadsheet with the pdf links and post it in Classroom. Then there is only one post for students to look for and I can update after each lesson with the INB answer key pdf.

The big project I wanted to do over summer but procrastinated never got to was to make a video of myself explaining and writing out the notes for each skill. But multiply that times 4 preps and we're talking at least 120+ videos.

Ov. Er. Whelm. Ing.

What I did do was update all my powerpoints and then saved each slide as a JPEG. My idea is that I can use the Show Me app on my ipad, insert the pictures, then record my voice talking while I fill in the notes with a stylus.

I've never actually used the ShowMe app but I think I can get a link to the video and add it to the previously mentioned doc/spreadsheet. So there would be a video and pdf answer key for each skill.

It sounds simple in my head but so time consuming. I thought maybe I could do it after I teach the lesson so it will be fresh and also spaced out over the year instead of trying to do them all at once in the summer.

But I don't wanna. Lol

Advice?

Tips?

Feedback?

Points, Lines, and Planes...Help!

This is Skill #1 in geometry for me and we can all agree that it's super important and full of so many little details. Over the years I have come up with so many ideas to tackle this skill with and I still don't really feel successful.

One of my favorite activities is what I originally called my hands-on naming review. I made segments and arrows out of pieces of pipe cleaner and little fuzzy balls and cut letters written on construction paper.

This year I tried the same activity with play dough and letters I cut out from my Silhouette Cameo. The students really enjoyed it but it took much longer for them to roll up the play dough and make all the pieces. I felt like they weren't really paying attention to the symbols or notation and it was like pulling teeth to get them to refer back to their notes.

So I thought I would share what I did and see if you have any feedback. I need a better flow and to shorten up how much time I spend but hopefully in a more efficient way.

First I did blind sketch; students describe a drawing to the other person and they draw it without seeing it.

We made a list of all the vocabulary words they used while describing the pictures.

Then I had them sort this cut up answer key from a graphic organizer.

The next day I passed out this page for their INBs. The left side is the 'answer key' to the card sort so they could compare their work. The right side we filled in together.

Here is the hands on naming review:

And some play dough pictures:

Next I plan to do this worksheet activity with the tissue box model below.

I thought I would follow up with a Kahoot and another worksheet that I don't have a copy of.

I've also used this in the past:





What am I missing?

What am I not doing enough of?

What is the magic key to unlocking the unicorn dust of points, lines, and planes?

Concept Attainment Fail

It's always hard for me to transition from beginning of the year fun stuff and procedures and routines into the first skill in unit 1. Even though I already have stuff I can use, I always feel like I need to change something up or start off with a bang.

One of my goals for the beginning of the year was to use concept attainment as much as possible. I decided to make a year long powerpoint for each course so I could share them at the end of the year.

And then I forgot that that was one of my goals.

I thought of it last minute and hastily threw together two slides to introduce function operations in Algebra II.

Basically I displayed this slide and said I have these two functions on the left and the end result is the function on the right. What happened?

I just made these up and didn't even realize that I got the same answer for the last two examples.

I think I should have made them all positive to make the patterns easier to see. When I first showed this to the class, the bottom answer said 2x - 2 which definitely threw them off.

Should I have done 4 different examples on one slide for each operation? Or four different slides for each operation? I felt like doing addition and subtraction was enough to lead into the fact that we can combine functions in different ways.

They thought both slides were just combining like terms or that they were being set equal to each other and then doing opposite operations.

We got through it but it was definitely not a smashing success. Then I basically went straight into lecturing and then they just worked a bunch of examples.

Not exactly what I was going for.

I learned concept attainment as a column of examples and a column of nonexamples and they look for patterns. I couldn't think of a good way to do that for function operations so that's why I explained it and have no titles at the top.

What could I have done to make this better?

How do you introduce function operations?

Student Growth and Smart Goals

I don't know how your school works but at ours new teachers are evaluated once a year until they get tenure and then every other year after that. We also use the Charlotte Danielson rubrics. This is my year to be evaluated and I have two ideas that I need to flesh out for the student growth section.

The only tracking we've done this year is to separate the freshman class into higher and lower students. Which when there are only 7 lower, I think it would have been just as well to mix them with the others. But...not my decision.

Anyway, I basically want to compare their growth over the year and hopefully show more growth in the lower class than the larger. That one's pretty straightforward I guess. Although I hate that it's based only on EOCs but again...not something I can control.

The other one is lofty and maybe not possible. I'm trying out whiteboarding this year in Geometry only and I'd like to somehow measure something and look for growth. My principal doesn't want me to compare the results to last year because the students are different and it's comparing apples and oranges. I don't want to use a control group because when I want to try something new, I want to do it for everyone and also with four preps, I don't want to add extra prep.

I posed the question on Twitter and got these two responses:

hmm, could you collect some sort of student survey data? perhaps something about rating themselves as mathematical communicators before and after deployment of whiteboards?

— Geoff Krall (@geoffkrall) August 23, 2018

Perhaps how "fluid" their thinking was while using the whiteboards (the word "fluid" may require some unpacking )

— Geoff Krall (@geoffkrall) August 23, 2018

What about their confidence and willingness to make mistakes while trying something new?

— Jae Ess (@jaegetsreal) August 23, 2018

Now I love a good survey and a good Google Form so this sounds so great. What else can I measure? Should I have students rate themselves 1-5 for each so I have actual numbers for comparison?

Better make a list:

• Mathematical communicator
• Fluid thinking
• Confidence
• Willingness to make mistakes while trying something new
• Ability to follow directions
• Willingness to work with someone new
• Willingness to take instruction from someone
• Ability to disagree with ideas without disagreeing with a person
• Math ability
• Interest in math

What other things would you expect whiteboarding and discovery learning to affect?

How to...Planning Docs

In my own personal effort to #ExpandMTBoS, I'm continuing a category of blog posts called 'How To' so I can share the strategies behind the resource. I hope new and veteran teachers alike can find something useful. Click on the tag to the right for more posts!

Last year I started using Google Docs for the first time for lesson planning. My lesson plans are fairly simply but I have four preps. So basically I make a table and type brief descriptions. 

I like that on Google Docs I can share it with my principal and also create a table of contents so he can click ahead to the correct week. Link here.

This year I also decided to create a spreadsheet that I'm calling a 'daily log'. I plan to specifically list what I did in class each day. I'm curious to see how it actually lines up with my lesson 'plans'. Link here.

Now tonight I just realized that I should start uploading resources to Google Drive and linking them. Then I will have built in plans for next year! Which reminds me of another idea where someone mentioned saving their INB pages as pdfs so the formatting doesn't get messed up. I haven't noticed that happening but it has happened with some of my INB answer keys.

What documents do you use to help you plan?