I sat down with one of our tech gurus at school the other day so she could ask me about how I use twitter. Here's the result:

## Thursday, September 27, 2012

## Wednesday, September 26, 2012

### Odds and Ends

Just a few things that have been percolating in this teeny tiny brain of mine lately....

1. One of my precalc kids asked yesterday why synthetic division works. Although I love doing the process (hate long division!) I'd never really considered why we could do it. To compare the two division strategies, I wrote a problem and worked them out side by side. And you know what? They're really the same. Magical. One of our Algebra 2 teachers here doesn't like synthetic division (because it only works in minimal situations, he says, even though I gave him a document to show him otherwise) and therefore doesn't teach it. Drives me nutso.

1. One of my precalc kids asked yesterday why synthetic division works. Although I love doing the process (hate long division!) I'd never really considered why we could do it. To compare the two division strategies, I wrote a problem and worked them out side by side. And you know what? They're really the same. Magical. One of our Algebra 2 teachers here doesn't like synthetic division (because it only works in minimal situations, he says, even though I gave him a document to show him otherwise) and therefore doesn't teach it. Drives me nutso.

## Monday, September 24, 2012

### Organization (#Made4Math)

I found a new website on Friday that I'm going to use for my #Made4Math submission (and this is just a total coincidence because it's a Monday and I was typing this today!).

I've been keeping track of students who don't turn in assignments using Hedge's SWHHW form. But after having the students fill out the quarter-sheet piece of paper, I wasn't sure what to do with them. I'd been throwing them in a little crate with the idea of one day sorting them to go so I could talk with parents at conferences about why their son/daughter wasn't doing their homework. But you all know they were never going to get organized!

Until I saw an app called Three Ring. It's billed as an app to "Quickly and easily digitize student work and build the resource for authentic assessment in your classroom." I guess you could use it to take pictures or videos of student work/performances so you have evidence? Anyway, I'm using it to take pictures of each of the forms the kids fill out (using my iPad, but I think you could do it on your phone, too), and then I can assign it to an individual student (or class, if necessary). It's searchable by student or class.

Here's the link to Three Ring in the app store.

## Friday, September 21, 2012

### Changes

I keep a spiral notebook of all of my precalc notes. I started it in 2004 when we got our new books and have edited through the years by stapling on the new versions. Some pages have 3 - 4 edits and some I totally skip altogether.

Now:

It hit me today how different my notes (and my class overall) are then they used to be.

Then:

Now:

Same section, same material.

Amazing.

## Tuesday, September 18, 2012

### Setting Expectations

I'm not that good at promoting consistency in my classroom. Sure, I talk a good game, but if I try something and it doesn't work I usually move on and forget about it.

I've never used warm-ups on a regular basis in class. I've never done exit slips before. I heard/saw a lot of people talking about both and was envious but had a hard time envisioning how to use them on a daily basis. Why would the kids work on problems that weren't graded? How could I expect them to work on something that I didn't grade?

Despite these questions I decided this summer (amidst #TMC12 and the decision to adopt interactive notebooks) to give them both a shot. And so far I'm proud of how I've used both warm ups and exit slips in class. I'm not as good in precalc at putting up a warm-up question (I need to do something on a daily basis) but I definitely do it a lot more than I used to. And we've had some interesting conversations/explorations when I do give them a warm up. I haven't done any exit slips but I'd like to incorporate them when we start to cover new material (which honestly hasn't happened yet).

In my two Algebra 1 classes (honors and integrated/general) I've done some sort of warm up every day. A couple of days I've given them a quote and asked their thoughts on it. Yesterday's was a quote from Walt Disney about pursuing dreams; it really sparked some interesting conversations about what dreams they have! (Found out that a student I helped out last year is a competitive ping pong player and has even traveled to China to play!) I'd like to do something like that weekly; I found a website yesterday that had a lot of good ones on it.

In my integrated class the warm-up has taken on a life of its own; sometimes I feel like we spend more time on it than going over homework problems (which I'm definitely ok with!). Today I asked them to write down examples of three problems: one in which you would divide before multiply, one in which you would subtract before add, and one in which you would add before doing an exponent (can you tell that we talked about Order of Operations yesterday?). Then I let several students write their answers on my tablet pc so I could project them and we could discuss what all of the answers had in common. I know some of the kids tune out, but questions like that really get the kids thinking and remembering exactly what it was that we were talking about. I also use an exit slip with these guys; it's a great way to see what they've "gotten" from the daily lesson and if I need to spend more time on it (or with individuals). After yesterday's Order of Ops exit slip I noticed that one boy just wrote down nonsense answers (and put it in the red bin, which means he knew he was having trouble). I was able to check more often with him today in class to make sure he understood how to do problems and how I wanted him to show his work (even though I told him he could use his calculator for the actual calculations).

Although I sometimes give the students points for the exit slip (2), I often don't. Yet the students still do them without prompting and often ask where the exit slip is if I haven't passed it out yet.

I'm really happy with how things are going so far this year! Hopefully it'll stay this way... and I know that setting consistent expectations is truly the key.

I've never used warm-ups on a regular basis in class. I've never done exit slips before. I heard/saw a lot of people talking about both and was envious but had a hard time envisioning how to use them on a daily basis. Why would the kids work on problems that weren't graded? How could I expect them to work on something that I didn't grade?

Despite these questions I decided this summer (amidst #TMC12 and the decision to adopt interactive notebooks) to give them both a shot. And so far I'm proud of how I've used both warm ups and exit slips in class. I'm not as good in precalc at putting up a warm-up question (I need to do something on a daily basis) but I definitely do it a lot more than I used to. And we've had some interesting conversations/explorations when I do give them a warm up. I haven't done any exit slips but I'd like to incorporate them when we start to cover new material (which honestly hasn't happened yet).

In my two Algebra 1 classes (honors and integrated/general) I've done some sort of warm up every day. A couple of days I've given them a quote and asked their thoughts on it. Yesterday's was a quote from Walt Disney about pursuing dreams; it really sparked some interesting conversations about what dreams they have! (Found out that a student I helped out last year is a competitive ping pong player and has even traveled to China to play!) I'd like to do something like that weekly; I found a website yesterday that had a lot of good ones on it.

In my integrated class the warm-up has taken on a life of its own; sometimes I feel like we spend more time on it than going over homework problems (which I'm definitely ok with!). Today I asked them to write down examples of three problems: one in which you would divide before multiply, one in which you would subtract before add, and one in which you would add before doing an exponent (can you tell that we talked about Order of Operations yesterday?). Then I let several students write their answers on my tablet pc so I could project them and we could discuss what all of the answers had in common. I know some of the kids tune out, but questions like that really get the kids thinking and remembering exactly what it was that we were talking about. I also use an exit slip with these guys; it's a great way to see what they've "gotten" from the daily lesson and if I need to spend more time on it (or with individuals). After yesterday's Order of Ops exit slip I noticed that one boy just wrote down nonsense answers (and put it in the red bin, which means he knew he was having trouble). I was able to check more often with him today in class to make sure he understood how to do problems and how I wanted him to show his work (even though I told him he could use his calculator for the actual calculations).

Although I sometimes give the students points for the exit slip (2), I often don't. Yet the students still do them without prompting and often ask where the exit slip is if I haven't passed it out yet.

I'm really happy with how things are going so far this year! Hopefully it'll stay this way... and I know that setting consistent expectations is truly the key.

## Thursday, September 13, 2012

### It's hard for me to imagine.

I had to give all of my freshmen timed tests this week intended to measure their math computation and problem solving skills. I could tell some of my honors kids struggled with some of the questions but overall were fine (not surprisingly). But my general kids? Ouch. This one's typical for my class of 14. I definitely have my work cut out for me this year!

## Tuesday, September 11, 2012

### How fast is Usain Bolt?

Pretty fast.

I gave my precalc kids a list of the men's 100 m world records and asked them to compare Bolt's times with them. Is he on track? Is he ahead of the pack? Is he lagging?

They're plotting the points, coming up with a line of best fit, then making some predictions (like what will the record time be in 2015 and when will it be 9 seconds?). Then I'm asking them to do the same process on their calculator and do the linear regression.

It always makes for an interesting conversation!

The question also came up in class as to how long it would take him to run a marathon. After some fun conversions, here's what we came up with:

I gave my precalc kids a list of the men's 100 m world records and asked them to compare Bolt's times with them. Is he on track? Is he ahead of the pack? Is he lagging?

They're plotting the points, coming up with a line of best fit, then making some predictions (like what will the record time be in 2015 and when will it be 9 seconds?). Then I'm asking them to do the same process on their calculator and do the linear regression.

It always makes for an interesting conversation!

The question also came up in class as to how long it would take him to run a marathon. After some fun conversions, here's what we came up with:

67.3 minutes. We know it's not possible, but wow. (The world record is 2:03.38)

Here's the document I gave the kids:

## Monday, September 10, 2012

### Lesson learned: Don't become an accountant

For the first couple of weeks in precalc we review a lot of the topics they learned last year in Algebra 2. Domain, range, even, odd, increasing, decreasing, constant, compositions, parent functions, piecewise functions, linear regression. Just typing all of those words bore me. :)

My goal is to review those in ways so that the kids are reviewing them as they apply them.

One of my newly-favorite activities (that I got out of this book) is called "A Taxing Problem". It leads them through writing and graphing several different piecewise functions with different conditions. First is a strict percentage on what you make (depending on your income). Then comes a little bit of an ease so that you pay smaller percentages on the smaller amounts of money but then as you make more you pay more. (For example, you'd pay 15% on your money up to $22,100, 28% on your earnings from $22,100 to $53,500, 31% on anything $53,500 to $115,000, etc.) That's a fun function to write!

The next step is adding in a standard $6950 deduction. The kids want to start off by subtracting that from their variable in the previous function, but what if that moves them down a tax bracket? Everything's messed up. So they have to figure out how to apply the deduction and still end up in the correct tax bracket.

We've spent two days in class on the problems (one more day than I'd planned) but I've heard so much good conversation and collaboration that I didn't want to stop them. Several girls told me today that I was making their brains hurt, and one of my "smart" kids said he'd been struggling and asked if we were going to go over the functions tomorrow. I'm guessing that these kids haven't really had to *think* in a class for a while (no offense to their previous teachers, of course).

Tomorrow we're moving on. I'm going to have them figure out if Usain Bolt's 100m world record is really as good as people say it is.

My goal is to review those in ways so that the kids are reviewing them as they apply them.

One of my newly-favorite activities (that I got out of this book) is called "A Taxing Problem". It leads them through writing and graphing several different piecewise functions with different conditions. First is a strict percentage on what you make (depending on your income). Then comes a little bit of an ease so that you pay smaller percentages on the smaller amounts of money but then as you make more you pay more. (For example, you'd pay 15% on your money up to $22,100, 28% on your earnings from $22,100 to $53,500, 31% on anything $53,500 to $115,000, etc.) That's a fun function to write!

The next step is adding in a standard $6950 deduction. The kids want to start off by subtracting that from their variable in the previous function, but what if that moves them down a tax bracket? Everything's messed up. So they have to figure out how to apply the deduction and still end up in the correct tax bracket.

We've spent two days in class on the problems (one more day than I'd planned) but I've heard so much good conversation and collaboration that I didn't want to stop them. Several girls told me today that I was making their brains hurt, and one of my "smart" kids said he'd been struggling and asked if we were going to go over the functions tomorrow. I'm guessing that these kids haven't really had to *think* in a class for a while (no offense to their previous teachers, of course).

Tomorrow we're moving on. I'm going to have them figure out if Usain Bolt's 100m world record is really as good as people say it is.

## Tuesday, September 4, 2012

### How to get a class mad at you. . .

(Alternate title: I gave them a problem to work on and they hated it. And me.)

So my precalc class isn't enjoying the problem I gave them to do today... but I've heard some awesome conversations!

Here's what they were given:

"Given f(x) = 1 - x and g(x) = 1/x, how many different compositions can you make out of these functions?"

(I found this problem several years ago and have always given it as a mini-project to be done individually. Thought that it might be more interesting worked with someone.)

The class started in silence. They weren't quite sure where to start, but after considering it for a few moments they started talking and writing.

I wandered around offering some suggestions - simplify that... what happens when you do this?... have you seen this before?

Had a very interesting conversation with one girl who was getting frustrated. She pulled the, "I'm never going to have to do this in the future!" line, so we talked about what skills she was actually working on.

Working with a group

Communication

Problem solving (start small, work bigger)

Algebraic skills

I think I won her over (though she told me she was going to become a hobo so she wouldn't have to do math).

Everyone seemed ok by the time they left class. Not giving them a homework assignment helped.

:)

So my precalc class isn't enjoying the problem I gave them to do today... but I've heard some awesome conversations!

Here's what they were given:

"Given f(x) = 1 - x and g(x) = 1/x, how many different compositions can you make out of these functions?"

(I found this problem several years ago and have always given it as a mini-project to be done individually. Thought that it might be more interesting worked with someone.)

The class started in silence. They weren't quite sure where to start, but after considering it for a few moments they started talking and writing.

I wandered around offering some suggestions - simplify that... what happens when you do this?... have you seen this before?

Had a very interesting conversation with one girl who was getting frustrated. She pulled the, "I'm never going to have to do this in the future!" line, so we talked about what skills she was actually working on.

Working with a group

Communication

Problem solving (start small, work bigger)

Algebraic skills

I think I won her over (though she told me she was going to become a hobo so she wouldn't have to do math).

Everyone seemed ok by the time they left class. Not giving them a homework assignment helped.

:)

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