Table Groups!

While seating students in table groups is far from a new idea, it's new in my classroom.  I have been struggling with the best way to seat students given that my classroom furniture consists of only right-handed desk/chair combos.  It's not practical to seat students side-by-side with these desks.  Putting them in groups of 3 is possible in a T shape but this set up ends up taking up more floor space than I am willing to give, even in my large classroom because I need 9 groups to accommodate all of my kids.  

Unfortunately, this style of desk isn't as flexible as single desks with separate chairs and doesn't lend itself to seating students in groups. 

I'm taking a graduate class on Kagan's Cooperative Learning Strategies.  I was already very familiar with the structures but some of the rationale on team building is new to me.  I've been enjoying the class and I came home from it last weekend inspired to change my classroom set up.  I ran through a mental inventory of what is in my classroom and I realized that I had 5 trapezoid tables that could each seat two students.  I decided to use one trapezoid table plus two of the old desks per group.  I managed to get one more table from a coworker who had extras so I had enough to make 6 groups.  Students can get in and out easily and can work together.  The best part is that my classroom now feels huge!  There is a lot of space to move around. 

Here's a table group in my redesigned classroom!

Changing my classroom set-up felt like an impossible dream until I got creative and decided to let go of some things I thought I needed (separate tables for pull out groups).  The first day of the new set up (Tuesday) was rough as my students are just not used to sitting around a table and not talking constantly.  We're working on understanding when we talk to each other and when we work alone.  Wednesday and today were nearly perfect with my lower group of students.  My advanced groups are having a harder time containing themselves but I have confidence we'll model correct behavior and have everyone in line before Christmas break.  A few students have surprised me already at how well they're working together; I listened to some awesome coaching by a few pairs when we worked on volume problems using Rally Coach.  For those of you familiar with structures, we've done Rally Coach, Showdown, Quiz Quiz Trade, Takeoff/Touchdown, Timed Pair Share, Rally Table, and more just this week. 

Have you come up with a creative solution to a near-impossible problem?  Let me know about it.  I'd love to be inspired by your great idea!

Mathematically yours,
Miss B

Christmas Wish List

I’ve seen many suggestions of Christmas gifts for teachers floating around the internet.  Pinterest is full of adorable crafts and sweet treats to thank teachers this time of year.  As a middle school teacher in a relatively poor community, I don’t receive many gifts and that’s OK.  I decided that I would, however, put together a teacher's wish list from my perspective.  These are my top 5 most desired Christmas gifts in order of preference.

1.     A note of thanks.  Have your child write me a note about what they enjoy about class and what they’ve learned.  I keep notes like these in a box and I read them on days that have been particularly rough.  Everybody loves warm fuzzies! 

2.     A commitment from you to follow up with your child nightly regarding homework assignments.  One of the biggest frustrations I have is the lack of homework completion from my students.  Check in each night, ask to see homework, have your child explain the assignments to you, and follow up with the school’s homework hotline, online gradebook, or teacher if you think your child is not being responsible. 

3.     Your time at school.  Come to a concert, to a PTA meeting, or to chaperone a field trip.  Your children and their friends will appreciate your presence and support.  I will appreciate the opportunity to get to know you as more than Mrs. Smith at 123-456-7890. 

4.     School supplies for your child.  Spend $10-20 at Christmas per child to replenish school supplies for the second half of the year.  Check the condition of binders as the rings may have warped.  Then buy a few packs each of pencils and looseleaf.  I’m so happy when kids come to my room with these simple supplies; last school year I gave out approximately 700 pencils over the course of the year.  Think, too, about semester long classes which change in January and what supplies will be needed for second semester. 

5.     Classroom consumables. If you insist on giving me “things” for Christmas, please make a donation to my classroom.  Some of the items I purchase myself that we use are listed below in order of greatest need/use:

a.     Tissues

b.     Yellow #2 pencils

c.      Loose leaf paper

d.     Dry erase markers

e.     Post-its of any color of size

f.      Unscented hand sanitizer

g.     Sanitizing wipes

h.     Ziploc bags (sandwich, quart, or gallon)

i.       Paper towels

j.       Napkins, small cups, and small plates

k.     Small individually wrapped candies for rewards (no gum or lollipops per school rules)
l.    Glue sticks

I really would appreciate these items.  Just the fact that you would be saving me a trip to the store would be a great joy!  

Fellow teachers, what’s on your Christmas list?  If there are teachers on your list, what are you giving them this December? 

Problem Master and Mountain Climber

My Facebook status this evening sums it up: "That was the kind of awesome day of teaching that will get me through until Christmas."

Have you ever had a day like mine when the lesson goes seamlessly (or nearly so), the kids enjoy what they're doing, you enjoy what you're doing, behavior problems are non-existent, and the learning conversations are rich.  

The best compliment I got from a kid today, "You know, Miss B, this is the highest class but we do the most fun stuff." ("highest class" = most advanced class offered to 8th grade)

So, what caused this awesome day?  Two new activities.  

The first activity was for my Algebra I class.  We have been studying probability for several weeks and it's been slow going.  Many of my students are struggling readers, so the questions are difficult for them to answer independently.  I decided to use an activity that I adapted from a math blog (I think it was ispeakmath but I cannot find the post now for anything and would love to give credit if anyone knows).  We'll call it Problem Master.

Problem Master Directions

1. Create one problem per student on the topic you're studying. (I used a mix of all the kinds of probability questions we're responsible for in 8th grade: simple, independent, dependent, sample space, permutations, and predictions from experimental probability.)
2. Assign each child a different problem.  Have them work out this problem (I used scrap paper for this step) and check the answer with you.  They need to understand and be able to explain how they arrived at that answer.  
3. Create a packet (or use notebook paper) with a numbered space for each problem.  I have 21 students in Algebra I, so I had 21 problems and a packet with that many spaces.  
4. The "Master" of the problem gets a copy of the question in green.  They glue it into the packet and show the work needed to solve the problem.  They also get a yellow sheet with 20 copies of their problem to give to classmates when they pair up.  You'll need to print one page with all of the questions once on green paper and then make a yellow sheet for each child with their problem duplicated enough times for everyone else in the class.
5. Each child then pairs up with another member of the class, they trade problems to solve, work independently to solve the problem, check their partner's answers, and they coach as needed.  
6. I had students grade each other with smiley faces for how much help they required.  
7. When a pair is finished, they return to a designated area to meet a new partner.  (Rarely was anyone waiting for more than 1 minute.  You could choose to have a secondary assignment for anyone waiting or call out switching times, but my kids were able to handle this bit of freedom because they could work at their own pace.) 
8. I had students carry their glue stick and scissors around with them.  We only cut out one problem each time we paired up instead of cutting them all apart at the beginning because I wanted to avoid them losing a pile of little yellow papers!  Envelopes or baggies would also work, but giving them an entire sheet limited my prep significantly and made it easy when we realized we would like to finish the activity in the next class period.  

We worked on this activity for almost an hour of our 90-minute block.  The kids were engaged the whole time and were taking their responsibility seriously.  They weren't happy that we didn't have enough time to finish and begged to get more time next class.  I'll happily oblige because they were doing an awesome job!  
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With my morning class going so well, I worried some about the potential of my afternoon class.  After all, could I manage two new group activities in one day without pulling out my graying hairs?

This activity probably exists out there in one form or another, but I invented it last night without any direct inspiration.  It's called Mountain Climber. 

My students were very complimentary of my artwork.  Bless them for loving my scribbles!  Coming soon, there will be a picture of the poster we used to track our progress in the "game."  For now, just picture a crude half-mountain drawn on poster paper.  Starting at the bottom and going up the side, there are labels reading "level 1,"  "level 2," all the way to "level 10" and the groups all have a little mountain climber clip art icon colored a different color that they move up the poster.  

Mountain Climber Directions

1. Each group is assigned a different colored marker.  My grouping scheme is discussed here.  I used groups of 3. 
2. Create a variety of problems/tasks related to the topic you're working on and level them from easiest to hardest.  Put each problem on a separate page (half page, etc) and make enough copies for the number of groups you'll have.  I chose to make 10 problems, but this can be adapted to the difficulty level of the topic and the amount of time you have. 
3. Students provide notebook paper.  Pass out one record sheet per group and one copy of the level 1 problem to each team. 
4. Students work in their groups to solve the problem.   Group roles are recorder (writes on record sheet discussed below), messenger (delivers paper for corrections), and scorekeeper (keeps track of group progress).  
5. As the students work on a problem and reach a consensus, the recorder fills in the record sheet, the messenger brings it to the teacher for checking, and the scorekeeper moves the mountain climber up a level when they get a problem correct. Give them the next level of problem when they get a correct answer.
6. I emphasize accuracy over speed in this exercise.  You can see there are three columns on the right of the record sheet.  The first time the group gives me their paper, they get 3 points for a correct answer.  Each subsequent time, they earn less points.  This is a good motivator to help them reach a consensus before bringing me the paper!   The team with the highest point total at the end is declared the winner.  I do not care who finishes the 10 problems first.  

The kids were very excited to play Mountain Climber.  I teach a competitive group in Intermediate Algebra, so they all wanted to be fastest.  Some groups started to realize that they needed to slow down and read the questions carefully so they could get their points.  I had one instance of a team that tried to "divide and conquer" on a problem.  I marked an X in their first box for that problem, and they went back to helping and coaching each other as I'd asked.  Despite that one very minor incident, the activity went well and the kids again begged me to let them finish next class. 

My students want to do math problems.  That's my definition of winning! 

Mathematically yours, 
Miss B

Notebook Check Strategy

I refuse to spend time grading notebook organization.  I know teachers who do this and I remember taking many classes in school in which there were binder checks.  Personally, I think trading notebooks to check them in class is a waste of instructional time.  Collecting them to check myself is just plain daunting.  And for what?  It's not like grading a student's organization indicates their mastery of the content the subject requires them to learn.  I'm terribly disorganized when it comes to paperwork, but I know my math! 

The only benefit of checking notebooks in the traditional way is that it encourages students to have the life skill of being organized.  I've started a notebook check this year that goes a step further to ensure a student is familiar with the location of papers in his binder.  After all, I want students to be able to reference their notes as needed to help them attack problems.  When we have a few minutes at the end of class to spare, I pull out a stack of "cat cash," the money in our grade level economy.  I name a paper and award $5 to the first child who can find it and $1 to any other student who can find it before I call out the next paper.  The catch- it must be in the binder rings in the right section to count.  I run through three or four papers and that's it.  In about 3 minutes, we've checked every binder in the room.  I've done this twice so far this year and the students have responded well.  I've reminded them of this system when I pass back papers and it appears that this year more students are actually using the binder rings instead of a folder or the pocket inside the binder's cover (or the trash can). 

What do you do to encourage your students to be organized? 

Classifying Systems of Linear Equations.

 I set my students to work today on a sorting activity for systems of linear equations.  Systems is a review topic from Algebra I, but a topic that still gives many of them trouble.  I gave the students this paper to cut apart:

After a few minutes of cutting, I gave them this chart onto which they pasted the vocabulary and examples after solving the systems on the reverse of the paper.  

 They ended up with a chart like this one. 

What worked well: The students were able to self-check because they knew there would be two of each type of system.  Since there were 6 graphs, the students had a couple of opportunities to practice the solutions to each kind of system. 

What needs improvement: I should have labeled the systems and graphs with A-F prior to copying the sheets; I had the kids do the labels instead.  The kids complained that the graph paper was too small, though most of them managed just fine. 

UPDATE 1/6/13: The files shown below are available for download as a pdf.  I've marked the graphs and systems A-F as indicated above.  Thanks for visiting!   

Implementing Rich Mathematical Tasks

My school system is partially through the transition to Common Core Mathematics.  Our lower elementary grades have fully transitioned, HS Geometry has transitioned, and 8th grade has transitioned to the point where we're teaching both the old and new together this year!  As part of the transition, 8th grade students who previously passed Algebra I in 7th grade are enrolled in a course we've titled "Intermediate Algebra."  The course resembles traditional Algebra II in a lot of ways and is designed to fill the gap that would be made by students moving directly from our state's Algebra I/Data Analysis curriculum into CC Algebra II.

One of the expectations for the course this year is that I provide my students with rich mathematical tasks with an open-ended quality.  I was a bit hesitant to get started with these as the students I teach haven't had many experiences with open-ended problem solving.  I feared they would be frustrated by the lack of rigid structure and be very needy.

Here's how I organized the task process in my room.

1. I presented the concept of a mathematical task as different from a BCR (the style of constructed response used on MD state testing which is quite formulaic) and explained to them that there are so many correct ways to answer a task that they should answer a task in the way that makes the most sense to them mathematically.  I stressed that I was not going to be answering lots of questions during this task, so they were to rely on their group and "figure it out."  (I still coached a minimal amount when groups were quite astray, but I wanted them to feel independent.)
2. I assigned groups of four, making sure each group had at least one or two strong math students and a mix of boys and girls.  (Side note: I use pocket charts for grouping and it has been a breath of fresh air this year.  Something about this system, perhaps the groups being on the wall when kids enter the room, has kept the whining/eye rolling/ugliness entirely at bay this year.  I so much as mention the word "group" and their little heads spin to the back wall to check out who they'll be with, but they don't complain!)    
3. I presented the task they were responsible for, indicated the variety of materials available, and set them to work.  
4. After 30 minutes the first day, none of the groups were even close to fully answering the question.  Most had talked for 90% of their time and written very little.  All the groups stayed on topic and remained focused during that time frame.  
5. The next day, I made some general comments about the task and gave a small insight or two into the problem to give a few hints related to common misconceptions.  The groups reconvened and were charged with finishing their answer. 
6. We did a jigsaw grouping to share out.  Two students stayed put and presented their group's work to two students who came from a different group.  We rotated again so all students had a chance to present and a chance to review another group's work.  
7. The original groups had some time to debrief about what they would change after getting input from other classmates.
8. Homework was to write a reflection on the process. 

The tasks I'm using this year are from the Dana Center.  This is a great PDF resource to download if you teach Algebra I or II, or possibly even pre-Algebra with motivated students.  You can scaffold more or less depending on your group of students and the relative difficulty of the task.  This week, students worked in groups of four on the "Extracurricular Activities" task, part B.  The task gave students a scenario and asked them to write a function to model the scenario and find its domain and range.  From my description, I'm sure you're wondering why I needed to devote even 15 minutes to this problem.  We actually spent nearly 90 minutes in class spread over two days plus one night's homework on this task.  Here's why: 

• The problem is embedded into the task in a way that students must make meaning of the situation.  Since the meaning wasn't immediately clear to the students, most every group restarted or made significant revisions to their work during the process.  (Make sense of problems and persevere in solving them.)
• Students have various ideas about the meaning of the problem and how to go about solving it, so they have rich discussions. My students were holding each other accountable for their ideas, asking pertinent questions to better understand their classmates' points of view.  (Construct viable arguments and critique the reasoning of others.)
• Students were able to use any of the materials in the room, so some groups gravitated toward calculators, while others preferred to sketch a graph by hand or write out a table.   (Use appropriate tools strategically.)
• The real world context leveled the playing field in an unexpected way in at least one group.  I overheard one student who is a weak math student leading his group through this task at the beginning because he was the only one with the real-world background knowledge to understand the problem.  His more "book smart" teammates were lost without his guidance.   He was more engaged in this task than I've seen him since school started. 

I was very proud of my students this week.  I wasn't really looking for their work as the final product.  I was hoping to see them demonstrate the eight Standards for Mathematical Practice.   I highlighted a few above, but I can honestly say that I saw all 8 standards in play during this process. 

Some students were already asking to do more tasks on Tuesday before we finished our first task.  They loved the interaction and I loved how involved they felt in solving the problem.  

Why my job is awesome

a.k.a. I'm going to show off a little and tell you about one of my wonderful students. 

Last year, I taught a very nice, smart, and motivated class of students.  I once joked that I could assign them the entire textbook, leave the room, come back hours later, and find them in the same place I left them, apologizing to me because they weren't able to complete the entire assignment in that amount of time.  They were literally that amazing of a group of kids! 

One of the standout personalities in that class was a student whose math confidence wasn't very high.  While very smart, this student never felt comfortable with math as quickly as most students in the group.  This student worked very hard to understand the material throughout the year. 

Today, I checked my mailbox in the afternoon and found a very fat envelope.  Inside was a letter, a piece of chocolate, and a bottle of wite-out. 

The letter was touching.  I won't repost the whole thing, but I will quote a few of my favorite sentences. 

I truly enjoyed being in your class.  Math, for me, is my least favorite subject.  It is so confusing, disorienting, scary, easy to get wrong, and a HUGE stressor/frustrator.  (Oh yeah, it's bad.  The night before 6th grade I had a minor freak out...over math class!)  Yet in your class, when I did figure it out, I felt on top of the world.  [...] And everything was so fun!  I looked forward to class.

This student include a "personal and used" bottle of wite-out signed on the bottom as a gag gift/inside joke.  I am a wite-out queen.  My kids are always poking fun at me for my obsessive use of wite-out.  I write in pen on any papers I project under the document camera because it shows up easier than pencil.  Unfortunately, if I don't write so neatly or I make a mistake, I can't erase it.  Therefore, I always have a supply of the wite-out runners and use them generously.  I got one from a girl in that same class for a Halloween present last year.  :)

I'm adding the letter and wite-out to my teaching keepsake box.  Letters like this one, while few and far between, are what keeps me going as a teacher.  What keeps you motivated?