November 22, 2014

Age vs. Birth Year (#tmwyk)

Last night I was talking to my 13 year old foster daughter (she's been here for over 3 months! hard to believe!) and the conversation wound around to my college 80's themed dodgeball competition, which somehow transitioned to J asking what year her friend Katie was born if Katie is 30 now.

You can figure that out.
J: I don't know
Well, how old was she in 2004?
J looks at me like this is an equally difficult question and she has no idea why I asked it.
It's 2014 now, how old was she in 2004?
J: Oh. She was... 20.
Okay, so how old was she in 1994?
J: She was 10... So she was born in 1984!

Conversations about the 80's continue. Then J asks what year I was born (I'm 29), then answers her own question - 1983! I shake my head, "I'm one year younger than Katie." J realizes that I was born in 1985, and proceeds to share her thought process (which I don't remember word for word but I love that she already knows we're going to have this conversation and wants to share). We discuss how it seems like one year younger should mean subtract one from the birth year, but it actually means I was born one year more recently.

Then J turns the conversation to how old she will be in the future.

J: How old will I be in 2025?
You can figure that out.
J (pulls out a chair and sits): Let me think about this... In 2015 I'll be 14.
(Mentally I'm super excited that she's about to use the count by decades strategy I walked her through earlier)
J: In 2016 I'll be 15.
(Mentally I'm sad she didn't use the strategy but interested to see if she'll count all the way there. And keeping my mouth shut with a neutral/interested expression on my face.)
J: In 2017 I'll be 16.
(Her face lights up and I realize the alternate strategy at the same time she does.)
J: So in 2025 I'll be 24!
What did you just realize?
J: Since I was born in 2001 I can find my age by subtracting one from the year! So if I forget how old I am I can always ask someone what year it is.
People might think you have a concussion if you don't know what year it is.
J: Well if I forget what year it is I can always ask myself, "How old are you, J?" (we laugh because she asks this very expressively, sometimes 13 is a really fun age) ... In class today they were asking us about what life would be like in 2050. So I was wondering how old I would be and I figured out that subtract one thing.

So then she wanted to know what year it would be when she turned 99. My first thought was year 3000, but as I was thinking that she was saying 99+1=100 so I realized that it would be 2100, not 3000. While I was realizing how much more sense that made, J was saying how it wouldn't really be 100, it would be 3000. I should have asked her how she got that, but I was doing too much thinking of my own so instead I went with, "You were born in 2001, how long from then is 3000?" She realized her mistake and then I shared that I'd done the same thing!

Conversation turns to getting old and how long she wants to live and me telling her that 70 is not old enough to plan on being done living. I told her that the average lifespan is in the 70's and that average means middle - so lots of people live longer than that. That factoid didn't lead to her doing any more math, which was just fine with me.

Things that make me happy about this entire interaction:
J asked all the questions.
When I took her down a path where I modeled a strategy, she figured it out and continued the strategy on her own.
She was thinking about math and patterns outside of her math class (during the morning, plus this conversation).
She wanted time to think, and told me as much.
She didn't just tell me the pattern (year - 1=age) she also told me why (I was born in 2001).

November 21, 2014

Distance Graph

We are working on slope in my Fundamentals of Algebra classes. In my Laying the Foundation/NMSI training last year the leader recommended using piecewise graphs as a natural way to compute slope repeatedly and to provide opportunities to compare slope. Today I did just that!

I gave my algebra students the graph below, without a story or any questions to answer, and asked them what they noticed and wondered.

Here is a record of their noticings and wonderings pretty much verbatim

My SMART board has been so spastic. It is now connecting
words even if I pick up the pen between them.
A student added the 7 hours observation during our discussion later.

Once I had everything recorded, I asked them to be more specific. "Someone said 'It is increasing' what is 'it'?" I pushed them until they read the entire label on the y-axis. Then I asked, "What does that mean?" Someone would realized that the person is walking away from home. To drive the point home I pointed to the graph - "This isn't a mountain. They aren't necessarily walking uphill. The graph is telling you distance from home, not height." I continued to pull together their various noticings and wonderings until they had a complete picture. I was so impressed that when I asked one class about their "goes positive, then goes negative" observation they identified that as positive slope and negative slope! These Transitions to Algebra workbooks from EDC just might be working!

I shared that this type of graph is called piecewise in response to their wonderings (What are the letters? Why would it be non-linear? Can there be more than one slope?), and told them that their task would be to find the slope of each piece. Then I apologized for my failure to photocopy the blue grid lines and we filled in the distance table as a class. Except I skipped 6 hours so they would have to figure that out independently. Then I sent them on their way to complete the rest of the task.

I was so happy that they managed to figure out the story with little prompting and answer several of the questions on the handout before they even got the handout with the story and questions! They were eager to get to work on the handout when they did get it because they already understood the context. It was awesome.

November 17, 2014

Unit Plans and Requests

I miss writing here. I really want to process how Algebra 1 is going because I'm putting so much work into that class (90 minutes every day and I'm not following a particular book). So far all I've managed are my short notes in my unit plans, but that's better than nothing. This month has been dedicated to writing the second edition of Nix the Tricks, but it wouldn't hurt to take a break to write about something here. So, here's the deal. Below I'm going to embed my unit 2 plan for both Algebra 1 and PreCalc. Then I'm going to ask you what you want to know about. I took most of the Algebra 1 lessons from the MTBoS and PreCalc isn't much different from last year so nothing in particular jumps out at me as urgent to share - that means you get to pick!

Browse away:

Now ask some questions! They don't have to be about a specific lesson in these plans, I'm happy to write about class structure (and how frustrating it is when that structure is ruined for my PreCalc class a million times in a row due to short days and field trips) or anything else you're wondering about. So comment! Please!

November 6, 2014

How to Not Quit

My district is under a lot of pressure. Test scores dropped at the high school. One elementary school was already labeled as level 4 (level 5 means state takeover). Half that elementary school was handed to a private charter (stories I hear are crazy - having half a school privatized sounds like a nightmare). On the other hand, the high school met the 3 year progress goals set by the state and the elementary school in question had a big improvement in test scores (pre-privatization). It's really easy to get caught up in the negative and the demands to work harder/smarter/magically better with kids who seem to have more issues every year. Grades were due for quarter one today so pressure has built to a maximum and many people were venting their frustrations. So we took the time during our team meeting to step back and made this list (among others):

What practices can we employ to feel good about our job:
a. Avoid negative talk/people. Replace with positive affirmations.*
b. Leave work at work
c. Attend school events (reminds us of the big picture)
d. Have a passionate hobby (have something other than teaching)
e. Don’t sacrifice your philosophy for other peoples' goals
f. Sing and laugh ’til you cry because you wet your pants.**
g. Eat lunch with people who laugh, sing and improve your outlook.
h. Exercise, both your body and your mind.
i. Sleep, many hours, every night.

*I shared the One Good Thing blog, and vowed to go back to daily posting.

**We rephrased this bullet point many times, and laughed about all possible phrasings.

What would you add to this list?

November 4, 2014

November Goal

First, an announcement:

Nix the Tricks is now available in French!

The translation is titled Terminé les Trucs (you have no idea how much work it took to find a title that I was happy with, thanks for everyone who helped brainstorm). Caroline Arcand has been hard at work translating the finalized document. I learned a few new things - did you know the acronym for multiplying binomials is PIED in French instead of FOIL? Whether it's a foot or a fencing tool it's still a trick, so now those who speak French in math class can learn alternatives. The translation is available at the same download page as the English version; share it with all your French friends!

Second, my goal:

I'm setting a new NaNoWriMo goal - 30 new tricks in 30 days. Luckily (or unluckily?) we already have that many tricks described in the For Review google doc. So my goal for the month is less about writing and more about formatting. Because of this I have a stretch goal - the Vocabulary google doc is filled with great definitions - what if this was a glossary at the end of the book? My bet is that if someone filled in that document with terms in the book, as a community we could build some great definitions. If you are willing to be that someone, please leave a comment.

So, please hold me accountable! Tweet me (@crstn85) occasionally this month to ask me whether I'm working on edit, typesetting or images that day, because I should be working on one of those every day to reach this goal!