In Algebra 2 . . . I used these cards:
Hi Students! Here's a deck of cards. Each one has a polynomial function and its graph.
The degree of each polynomial is determined by its highest exponent. Talk with your group and agree on the degree of each one.
The leading coefficient is the number in front of that term with the highest exponent. Talk with your group and agree on the leading coefficient for each card.
Now we are going to focus on the ends of the graphs. Look at the left side. Does it point up or down? What about the right side? What you are looking at is called the "end behavior". Group the cards according to end behavior. Show me when you're done.
Next I want you to look for similarities in each group. What do the degrees have in common? What about the leading coefficients?
In 5 minutes or so, all of the groups had identified what the groups had in common according to even/odd degree and positive/negative leading coefficient.
We did some practice once they had this figured out.
Oh, and then I played some music and showed them some polynomials one at a time and they showed end behavior with their arms. And there was dancing.
This used to take me 4 minutes. I would write four rules on the board and they would copy them down.
Today it took 24.
But it was fun. And later I saw somebody end-behavior dancing in the hallway.
This approach is better than just telling them, right?
Thursday, January 10, 2013
Wednesday, January 2, 2013
Most Read in 2012
My blogging slowed down a lot this year. I had half as many posts in 2012. This fall has been especially rough. I added some new responsibilities at school and in general have been all "How can I survive today?" instead of "Let's reflect on teaching practice and write about it" or "I tried this cool new thing I'd love to share".
I guess that is okay. I mean, I never wanted blogging to be this thing that stresses me out. I just thought it would be a way for me to stretch myself as a teacher, and it has. Just taking the time to think about what I am doing that is worth posting forces me to reflect and improve. If someone else can benefit from what I share, then that is a bonus!
I don't want to stay in survival mode, though. Here's hoping I can find the time to be more creative and adventurous in 2013!
Anyhoo . . . Last year I started the tradition of compiling my most-read posts at the end of the year, so here's this year's list (a bit shorter than the last one):
Green Pen is the New High Five: I still use this on a regular basis in my classroom. A correct answer earns a green star and a green pen and the responsibility of coaching someone else near you.
Visualizing Volumes: I used party decorations to show volumes of rotation in calculus.
Pieces Final Project: Using function families and restricted domains to create a picture. Posting this resulted in a lot of great feedback which will improve the project for next time. This totally solidified my love for blogging!
2 PIzza Boxes and a Hot Glue Gun: I glued together two pizza boxes to create privacy for test taking without moving desks. The truth: I discovered two incidences of cheating while using these. While they will prevent accidental glancing around, they can't prevent deliberate cheating.
Factoring Before You Know How: An activity to introduce (or practice) factoring trinomials.
Dry Erase Practice Folders: Use recycled file folders and dry-erase contact paper (or laminating?) to create re-useable skills practice.
And one more post that wasn't read a lot, but I am just proud of it:
Teaching Students to Coach: A nice little video that paints a perfect picture of how I want my students to work together.
Here's 2011's Top 10 List.
I also want to take a minute to thank all the very kind people out there in the math blogosphere. I started this blog thinking that I have received so much from all of you that I would try and give something back. The truth is that I could never compete with the generosity and kindness of the math teachers whose blogs I read, who also take the time to comment here and help me improve. I don't want to mention names because I know I will forget someone, but I am really grateful to be a little part of this community. Thanks to all, and happy 2013!
I guess that is okay. I mean, I never wanted blogging to be this thing that stresses me out. I just thought it would be a way for me to stretch myself as a teacher, and it has. Just taking the time to think about what I am doing that is worth posting forces me to reflect and improve. If someone else can benefit from what I share, then that is a bonus!
I don't want to stay in survival mode, though. Here's hoping I can find the time to be more creative and adventurous in 2013!
Anyhoo . . . Last year I started the tradition of compiling my most-read posts at the end of the year, so here's this year's list (a bit shorter than the last one):
Green Pen is the New High Five: I still use this on a regular basis in my classroom. A correct answer earns a green star and a green pen and the responsibility of coaching someone else near you.
Visualizing Volumes: I used party decorations to show volumes of rotation in calculus.
Pieces Final Project: Using function families and restricted domains to create a picture. Posting this resulted in a lot of great feedback which will improve the project for next time. This totally solidified my love for blogging!
2 PIzza Boxes and a Hot Glue Gun: I glued together two pizza boxes to create privacy for test taking without moving desks. The truth: I discovered two incidences of cheating while using these. While they will prevent accidental glancing around, they can't prevent deliberate cheating.
Factoring Before You Know How: An activity to introduce (or practice) factoring trinomials.
Dry Erase Practice Folders: Use recycled file folders and dry-erase contact paper (or laminating?) to create re-useable skills practice.
And one more post that wasn't read a lot, but I am just proud of it:
Teaching Students to Coach: A nice little video that paints a perfect picture of how I want my students to work together.
Here's 2011's Top 10 List.
I also want to take a minute to thank all the very kind people out there in the math blogosphere. I started this blog thinking that I have received so much from all of you that I would try and give something back. The truth is that I could never compete with the generosity and kindness of the math teachers whose blogs I read, who also take the time to comment here and help me improve. I don't want to mention names because I know I will forget someone, but I am really grateful to be a little part of this community. Thanks to all, and happy 2013!
Sunday, November 18, 2012
Dry Erase Practice Folders: Made 4 Math
A while ago, my calculus students were working on derivative shortcuts. I was trying to think of a good way for them to practice and self-check independently. Assigning problems out of the textbook to be checked in the back doesn't work because those answers are simplified. I really want students to just practice the rules without getting distracted by algebra.
I ended up using recycled file folders and dry-erase contact paper to make these re-useable dry erase folders. They were a huge hit.
To make the folders, I cut off about 2/3 of the front flap of a file folder. The inside of the back of the folder is now exposed. I covered it with a small sheet of dry-erase contact paper. I found a big roll online for about $20. There is enough in the roll for 60 folders, so it will last a long time.
I cut the remaining portion of the front flap into tabs, one for each problem. I lifted up each tab and wrote the solution underneath. This took a long time. Next time, I will try to use a set of problems that I already have typed up. On the up side, it is a one-time thing. These can be re-used again and again and again.
When they are done, they can flip up the tab and check the answer.
Then erase and move on to the next problem.
I ended up using recycled file folders and dry-erase contact paper to make these re-useable dry erase folders. They were a huge hit.
To make the folders, I cut off about 2/3 of the front flap of a file folder. The inside of the back of the folder is now exposed. I covered it with a small sheet of dry-erase contact paper. I found a big roll online for about $20. There is enough in the roll for 60 folders, so it will last a long time.
I cut the remaining portion of the front flap into tabs, one for each problem. I lifted up each tab and wrote the solution underneath. This took a long time. Next time, I will try to use a set of problems that I already have typed up. On the up side, it is a one-time thing. These can be re-used again and again and again.
Now students can work out a problem in the dry-erase area.
When they are done, they can flip up the tab and check the answer.
Then erase and move on to the next problem.
My students really loved these. Since I had made multiple versions, they asked if they could take home an extra one for practice.
In the future, I can envision a file crate full of these . . . labeled by skill . . . so that students can just grab and work on whatever as needed. It hate to think about making all of those, but I it just might be worth it.
Saturday, November 17, 2012
A Story
Today is national adoption day. I would like to share a personal story. If you are not into that kind of thing, feel free to move on. I will be back to my mediocre math-ed musings in no time.
This is a story of a math teacher (that's me) and her husband, a principal of a small K-12 school. These two were struggling with infertility. There were four years of wanting to be parents, and no babies appeared.
This is the story of a courageous 16-year-old. She had an unplanned pregnancy, and she didn't know what to do. Others told her to end the pregnancy. She didn't want to. Instead, she carried that baby for nine months. She endured the judgmental stares of strangers as her stomach grew and her discomfort increased. She said no to the usual high school fun while she stayed home, ate healthy foods, and made regular doctor appointments.
She chose the principal of her little K-12 school and his math teacher wife to be adoptive parents. She went through hours (and hours) of labor. And then, she put her baby in that math teacher's arms.
Today, I am just so thankful for the gift that she gave us.
I am thinking about the sacrifices she made for the baby she wouldn't take home.
That baby is now three years old.
She's beautiful. She's smart. She's vivacious. She's hilarious.
We are pretty much head over heels.
And we were given the honor and privilege of guiding her through life.
This is a story of a math teacher (that's me) and her husband, a principal of a small K-12 school. These two were struggling with infertility. There were four years of wanting to be parents, and no babies appeared.
This is the story of a courageous 16-year-old. She had an unplanned pregnancy, and she didn't know what to do. Others told her to end the pregnancy. She didn't want to. Instead, she carried that baby for nine months. She endured the judgmental stares of strangers as her stomach grew and her discomfort increased. She said no to the usual high school fun while she stayed home, ate healthy foods, and made regular doctor appointments.
She chose the principal of her little K-12 school and his math teacher wife to be adoptive parents. She went through hours (and hours) of labor. And then, she put her baby in that math teacher's arms.
Today, I am just so thankful for the gift that she gave us.
I am thinking about the sacrifices she made for the baby she wouldn't take home.
That baby is now three years old.
She's beautiful. She's smart. She's vivacious. She's hilarious.
We are pretty much head over heels.
And we were given the honor and privilege of guiding her through life.
I am feeling pretty grateful today.
Tuesday, November 13, 2012
A Typical Tuesday
I had grandiose ideas of capturing my day in photos. The truth, as you will see, is that the dream was lost somewhere between first bell and the end of the day. But here's what I managed to capture:
5:25. I meet my "running partner" via FaceTime. I'm in my basement on the treadmill, she's at her house down the street on the elliptical.
7:15. Time to get out the door. I grab the chocolate chip cookies I made last night. They'll be doing what chocolate chip cookies do best . . . bribery. All week student council (I'm the sponsor) will be asking our students to donate so that we can buy gifts and Christmas dinner for families in need. I'll be exchanging cookies for donations.
7:25. My commute. Note to self: Clean windshield.
7:40. Deliver cute little girl to daycare.
7:48. Arrive at school. Students are waiting for me at the door. One needs to work on test corrections, another needs help catching up, a third has questions on his calculus assignment. I open my email, but there is no time to read it. A girl comes in with posters she made advertising our student council fundraiser. The student council president has a question for me, and another girl needs to take a makeup test.
8:10. My principal walks in. Would I mind attending a panel discussion this morning? Our school is having some type of efficiency/improvement review and they need teachers to talk with the visitors. I am willing, but surprised and unprepared. Thankfully, this isn't typical at all. I quickly write out some notes for my colleague who will be taking my class.
8:18. My first hour class begins. I give them quick instructions and record their assignments that were due. Thankfully the lesson involved a self-guided sheet. Students were reviewing horizontal and vertical translations of parent functions and discovering the "flip" transformation.
8:30. Off to the meeting. I grab a few items to copy in case I have time while I am in the office.
10:00. Meeting over. It lasted longer than expected and my planning period is now over. I make a few quick copies, quickly finish a student council fundraiser display in the teacher's lounge, and head to my third hour class.
10:07. Bless their hearts, they started without me! I am thrilled to find that students are already working on the bell work when I arrive. I walk around recording assignments, checking bell work, and signing off on check points on the new lesson.
10:53. Sit down at my desk. Prepare envelopes for donation collections, take my first glance at my agenda for the day, notice the email from my principal asking if I'd go to that meeting this morning . . .
10:58. Advisory class. They have AR time. I catch a breather, record some test grades, collect my thoughts, and check a couple of items off the to-do list.
11:28. Calculus class. Implicit differentiation review.
12:16. Lunch. Chef salad.
12:51. Physics class. Discuss work and kinetic energy.
1:45 - 3:25. Two more Algebra 2 classes.
3:25. School is over. Several students come in for makeup work and extra help. A few of these are regulars. I am really proud of how hard they've been working.
3:45. I count the donations collected that day and email the total for tomorrow's announcements.
4:06. I have so very much to do, but I have to pick up my daughter so it is time to call it a day.
5:25. I meet my "running partner" via FaceTime. I'm in my basement on the treadmill, she's at her house down the street on the elliptical.
7:15. Time to get out the door. I grab the chocolate chip cookies I made last night. They'll be doing what chocolate chip cookies do best . . . bribery. All week student council (I'm the sponsor) will be asking our students to donate so that we can buy gifts and Christmas dinner for families in need. I'll be exchanging cookies for donations.
7:25. My commute. Note to self: Clean windshield.
7:40. Deliver cute little girl to daycare.
7:48. Arrive at school. Students are waiting for me at the door. One needs to work on test corrections, another needs help catching up, a third has questions on his calculus assignment. I open my email, but there is no time to read it. A girl comes in with posters she made advertising our student council fundraiser. The student council president has a question for me, and another girl needs to take a makeup test.
8:10. My principal walks in. Would I mind attending a panel discussion this morning? Our school is having some type of efficiency/improvement review and they need teachers to talk with the visitors. I am willing, but surprised and unprepared. Thankfully, this isn't typical at all. I quickly write out some notes for my colleague who will be taking my class.
8:18. My first hour class begins. I give them quick instructions and record their assignments that were due. Thankfully the lesson involved a self-guided sheet. Students were reviewing horizontal and vertical translations of parent functions and discovering the "flip" transformation.
8:30. Off to the meeting. I grab a few items to copy in case I have time while I am in the office.
10:00. Meeting over. It lasted longer than expected and my planning period is now over. I make a few quick copies, quickly finish a student council fundraiser display in the teacher's lounge, and head to my third hour class.
10:07. Bless their hearts, they started without me! I am thrilled to find that students are already working on the bell work when I arrive. I walk around recording assignments, checking bell work, and signing off on check points on the new lesson.
10:53. Sit down at my desk. Prepare envelopes for donation collections, take my first glance at my agenda for the day, notice the email from my principal asking if I'd go to that meeting this morning . . .
10:58. Advisory class. They have AR time. I catch a breather, record some test grades, collect my thoughts, and check a couple of items off the to-do list.
11:28. Calculus class. Implicit differentiation review.
12:16. Lunch. Chef salad.
12:51. Physics class. Discuss work and kinetic energy.
1:45 - 3:25. Two more Algebra 2 classes.
3:25. School is over. Several students come in for makeup work and extra help. A few of these are regulars. I am really proud of how hard they've been working.
3:45. I count the donations collected that day and email the total for tomorrow's announcements.
4:06. I have so very much to do, but I have to pick up my daughter so it is time to call it a day.
Saturday, October 27, 2012
Friday Favorite: Sound Buttons!
There are moments in the classroom that call for spontaneous applause, or canned laughter, or a drum roll.
For years I have had this urge to play sound effects in class. I never figured out how to pull it off, until recently.
I was playing with my new phone the other day when it occurred to me that there is probably an app for that. Sure enough, there is! If you search for "sound buttons" or "sound effects", you will find that there are tons of options to choose from. I have tried a few. I don't know if the one I am trying out is going to be my favorite, so I am not recommending a specific app at this point. They all look something like this:
Anyhooo . . . . imagine this:
*Gong* Bell work is over.
*Bugle call* Time to learn new math!
And there's a fraction . . . *Evil laugh* or *man screaming*
That's the right answer, Johnny! *Applause/WooHoo/Bingo!/Yes!*
I'm sorry, that's incorrect . . .*Buzz*
I am having wayyyy to much fun with this thing!
In related news, my students were smiling as they worked away on completing the square . . . with fractions . . . on a Friday . . . after losing a big football game the night before.
For years I have had this urge to play sound effects in class. I never figured out how to pull it off, until recently.
I was playing with my new phone the other day when it occurred to me that there is probably an app for that. Sure enough, there is! If you search for "sound buttons" or "sound effects", you will find that there are tons of options to choose from. I have tried a few. I don't know if the one I am trying out is going to be my favorite, so I am not recommending a specific app at this point. They all look something like this:
Anyhooo . . . . imagine this:
*Gong* Bell work is over.
*Bugle call* Time to learn new math!
And there's a fraction . . . *Evil laugh* or *man screaming*
That's the right answer, Johnny! *Applause/WooHoo/Bingo!/Yes!*
I'm sorry, that's incorrect . . .*Buzz*
I am having wayyyy to much fun with this thing!
In related news, my students were smiling as they worked away on completing the square . . . with fractions . . . on a Friday . . . after losing a big football game the night before.
Factoring ax^2, Teensy Tweak
Sometimes, it is the littlest change that makes a big difference. I feel like I am splitting hairs here, but this adjustment to the airplane method helped my students tremendously this year. I've written about it before, but here it is with an ity-bity change that seemed to help:
Say you are trying to factor this . . .
In this situation, the 6 has to be split into 3 and 2 before reducing.
Students didn't have any trouble with that.
Say you are trying to factor this . . .
You start by putting 2x in the front of each binomial. This feels wrong. It should.
So, to cancel out the extra 2, you divide by 2 right at the beginning. This was my teensy tweak. I used to have students do this at the end. It makes more sense here, and students are less likely to forget.
Then continue normally, multiply a and c. Find two numbers that multiply to get ac and add to get b. Put these at the back of each binomial.
Then, with the two already hanging out there, you just look for which binomial can be reduced by 2.
Ta daaa.
In this situation, the 6 has to be split into 3 and 2 before reducing.
Students didn't have any trouble with that.
Disclaimer: This is not my method. I saw it first while observing another teacher. I have seen others write about it as well, so I am not sure where to give credit.
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