Mission #2 from Exploring the Math Twitter Blogosphere was to 1) jump into the pond and start tweeting (introduce yourself, tweet @ someone you have been following, etc), and 2) write a blog post about tweeting.

I started tweeting because the head of IT at my school suggested I start a Twitter account that I could use with my students. I looked at her skeptically, but in a moment of weakness went ahead and created an account. For eons I didn't even tell anyone I had taken the plunge! But then I had to ask Son #3 some questions about Twitter, so he ended up being my first follower. Shortly after that, the sweetheart girlfriend of Son #1 requested to follow me. Wow! I had a following!

But it was not too long after, that Son #2 sent me the link to Dan Meyer's Ted Talk....and well the rest is history: I went to his blog, which led to his 3 Act Activities. His site also led me to follow him on Twitter. And BOOM! All of a sudden I met all these amazing people! I poked around their sites, "borrowed" ideas, downloaded worksheets, looked at games, and found interactive notebook ideas. Who WERE these people??

They were the ones who make me want to go to Twitter Math Camp!

Yes, I almost cried when I found out the Twitter Math Camp was in Philly the same time they were, but didn't know it until it was over. (Yes, I would have crashed it just so I can get Fawn Nguyen's autograph! :) Please tell me there will be a 2014 Camp. Please tell me it will be somewhere that I can get to without spending tooooooo much $!!

My biggest difficulty is not being able to spend as much time as I would like reading everyone's tweets. I follow almost exclusively math teachers. There are so many good ideas out there it makes my head spin, but already I have made subtle changes to the way I do things in class. The Silent Partners Quiz (previous blog post) came from something I saw that someone else did. (Man, if someone has a way they keep all these good ideas organized, please post!!) The Interactive Notebook also came from having read tweets and then visiting blogs.

Bless you all. And thank you for your kindness to those of us just starting out!

## Saturday, October 19, 2013

### Silent Partners Quiz

I had to give a right triangle trig assessment to my seniors. I always hate wasting time assessing them on stuff they were supposed to have dealt with sophomore year, but I knew I had to, so the question was how to do it so it was the least painful for all of us (especially me). Also, one of my students is dealing with a concussion and I have to have all sorts of accommodations in place for her.

Below is the question I put up when we first started the Trig section. It was the teaser. I put them into groups of 4 and had them come up with questions, statements, whatever.

Below is the question I put up when we first started the Trig section. It was the teaser. I put them into groups of 4 and had them come up with questions, statements, whatever.

I think I originally saw a picture like this on Yummy Math or some variation thereof. In the spirit of making the problem more rich (and because Hubby and I heat with wood that we take from our property...often in situations just like the picture!), I chose to ask how many logs I could get from the tree.

Most saw the right triangle right away, and many wanted to use Pythagoras (aka The Greek Geek) to find out how long the main part of the tree was. They were told that it was too dangerous to get up on the trunk and actually measure it, the tree it is hung up in is too skinny too climb. They had some more thoughts and then asked

**the**question: "If we don't have 2 sides, how can we do this??" Huzzah! And off we went into discovering (all over again) about trig ratios.
SO, when I was trying to figure out what to do for an assessment, I realized: OH! We never answered the teaser question! I paired them up (thus taking care of the one with the concussion), put this pic back up on the board, and pointed out that the angle of elevation was 40 degrees and that Hubby and I measured out 100 ft on the ground. Then I gave them one more question that related to our Precision Machine Shop and gave them these instructions:

- You and your partner must answer these 2 questions together. Be sure I can see your work.
- You may ask each other questions, make observations, etc, but not a single word can be spoken aloud. Everything you want to ask or point out has to be on paper. (Yeah, this is not original either. Love all of you bloggers: I saw someone had done this on the larger whiteboards, but I only have 5 of the larger whiteboards, so I had to resort to pink paper ....Breast Cancer Awareness Day at school).

I was blown away. For all the times I have let my students do partner quizzes, I would wander and listen, but never had a record of their thought processes. I was AMAZED at how many of my 23 students would have bombed this quiz because of their inattentiveness to units of measure. Only one grouping (the only trio!) made an error. Not one of the three thought there was anything wrong with an answer of: "Seven 18 inch logs can be gotten from this tree." This in spite of the fact that the picture they had in front of them to work from had 100 ft clearly labeled on the ground. Yowch!

Needless to say, I have to figure out a way to incorporate more dimensional analysis!

## Monday, October 14, 2013

### Interactive Notebooks

As a major "lurker" in the MTBoS, I have come across some fabulous people who share freely of amazing resources. I forget where I first saw this idea of the Interactive Notebook, but Crazy Math Teacher Lady has been doing some phenomenal stuff with it!

Check out Oct 7 of her 180 days of Geometry blog:

I had been doing some things like this, but never had the students keep a special notebook for it. Sometimes these pages would make it into their binders or spiralbound notebooks and sometimes they just went into the deep dark black-hole called BackPack.

This year I have two Geometry classes that have lots of students with special needs. Notetaking was going to be a challenge for them. I felt that I might better assist ALL the students (and maybe even have them refer to their notes) if we had this kind of notebook: page numbered, dated, and filled in.

In my quest for how to be more organized about it, I have come across this site, which has some useful ways for the students to make a table of contents, and has an assortment of rubrics if you decide to grade your students' notebooks. It also has some great activities.

But if you are just starting out with this, then you want to visit Sarah at Everybody is a Genius. WOW. If you have any questions on how to get started, what resources are out there, etc., she has got it all. I have learned so much from her blog!

We had been doing special angle pairs, particularly with parallel lines. I decided to jump right in to special parallelograms (using Sketchpad) so they could see places where some of these special angle pairs show up. They were given an Always Sometimes Never sheet and asked to construct the special parallelograms then make conjectures. I could see at the end of the period we were going to need a way to keep all that amazing information to hand. So this is what I made for their notebooks:

and after we get this into our notebooks, I will have them work with their partners to fill in under the "pie" pieces ( I also put notes on the underside of my pie pieces to remind me what supplementary meant, as well as that funny upside down T symbol!)

Check out Oct 7 of her 180 days of Geometry blog:

I had been doing some things like this, but never had the students keep a special notebook for it. Sometimes these pages would make it into their binders or spiralbound notebooks and sometimes they just went into the deep dark black-hole called BackPack.

This year I have two Geometry classes that have lots of students with special needs. Notetaking was going to be a challenge for them. I felt that I might better assist ALL the students (and maybe even have them refer to their notes) if we had this kind of notebook: page numbered, dated, and filled in.

In my quest for how to be more organized about it, I have come across this site, which has some useful ways for the students to make a table of contents, and has an assortment of rubrics if you decide to grade your students' notebooks. It also has some great activities.

But if you are just starting out with this, then you want to visit Sarah at Everybody is a Genius. WOW. If you have any questions on how to get started, what resources are out there, etc., she has got it all. I have learned so much from her blog!

We had been doing special angle pairs, particularly with parallel lines. I decided to jump right in to special parallelograms (using Sketchpad) so they could see places where some of these special angle pairs show up. They were given an Always Sometimes Never sheet and asked to construct the special parallelograms then make conjectures. I could see at the end of the period we were going to need a way to keep all that amazing information to hand. So this is what I made for their notebooks:

and after we get this into our notebooks, I will have them work with their partners to fill in under the "pie" pieces ( I also put notes on the underside of my pie pieces to remind me what supplementary meant, as well as that funny upside down T symbol!)

On the left side I will give them some problems involving angles and lengths of various parts of diagonals. I think I will give them at least one problem where they will need to use the Pythagorean Theorem to find a side length of the rhombus, since we reviewed the Theorem while doing distance formula.

I don't anticipate being great at this right away. And I am starting it already a month into the course. But, I will learn, they will have a resource, and we will all get better at this as we go.

## Saturday, October 12, 2013

### Four = Eight (almost)

I am taking part in the Exploring the MTBoS challenge. This week's challenge had two different prompts: share my favorite rich problem or share what makes my classroom unique. Since most of the really cool, rich problems I am currently doing have been shamelessly "borrowed" from other people, I thought I would share what makes my classroom uniquely mine.

If you have read the book

*The Four Agreements*by Don Miguel Ruiz, you may recognize these signs that hang above the window in my room:
For years these have been the four rules of my classroom. During the first day or two, we go through them and decide what they might mean in the context of being together in this classroom and in our friendships and relationships outside of the classroom. These have had the added benefit of tying in nicely with the math classroom. Ask any student in my room, especially the Geometry students, how many times I have just POINTED to rule number three as they worked. "Oh, right...."

In the last 2 years I have been trying to really incorporate the Eight Standards For Mathematical Practice in all aspects of my classes:

What I have noticed is how well these eight standards match up with the Four Agreements.

**:**

__Be impeccable with your word__
MP 3: Constructing viable arguments and critiquing others' reasoning requires a great deal of thought. Students must learn to put together words and thoughts in a logical manner: both to present their arguments, as well as to refute the arguments of others. All the while, they must be careful to attack the thought process, not the thinker.

MP 6: We are asked to attend to precision. That means we need to use the best possible language to describe what is going on. No longer will I fill in the words for the students. They use the word boards, the magnetic theorems and postulates hanging up, and or their notes and or their phones, but the responsibility lies with them. For me, I may need to look long and hard at all the little "cute" ways I refer to parabolas (happy vs sad) and instead help them identify what transformation has occurred - a reflection (not a "flip"!) across the x axis? I know this will be a challenge for me!

MP 7, 8: Both of these require excellent communication skills along with precise language.

**:**

__Don't take anything personally__
MP 3: When someone has inadvertently NOT been impeccable with their word, know that they are not attacking you as a person. They are attempting to say something about the logic chain you put into play. We remind each other how to use more precise wording, and use "I" instead "you".

**:**

__Don't make assumptions__
MP 2: It is too easy when we first begin to reason abstractly to assume something is happening, say, in a pattern, without really probing. Students frequently want to make the quick jump, but often they need the manipulative first, which allows them to SEE. From there they can talk about the assumptions they made and how that led them down the wrong path.

MP 6: Lack of precision in a drawing (neglecting tic marks, right angle markers) can cause another to go astray. Assuming that those lines are parallel because they LOOK parallel can lead to disaster.

__Always do your best__:
MP 1: Make sense of a problem and persevere! No giving up! Keep plugging away! I teach at a vocational school and I often tell the students that as tradesmen, frequently they will be stumped by a broken down car, a furnace that isn't working, or a patient that is not responding to physical therapy. It is their responsibility to pose questions that will lead to answers. Just saying: "Sorry, I don't know why your burner won't turn on!", is not an option and will not lead to a paycheck!

MP 7: Some days students will not want to find the pattern, will not want to "guess the rule", will not see that 16x^4-9y^4 is just a difference of squares! They will not

__want__to stretch their brains, and we will find it easier just to tell them, or at least give them so many hints we might as well have told them! But if we do that then we have not allowed them to do their best. Since this applies to me, as well, if I give in, then I have not done MY best either.
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