The Locker Problem and Why the why is important

Today I had one of my classes solve the locker problem.  The basic premise of this problem is that a group of students is running up and down a hall in the school opening and shutting one hundred locker doors.  The first student opens all the lockers, the second closes every other one, the third opens or closes every third one and so on.  The question that then comes up is which lockers will be open after all one hundred kids get done.

A couple years ago, I was struck by the idea of making the problem more three dimensional instead of just a story on paper.  (Thanks to reading Dan Meyer of course.)  I also thought this might lead to the students generating the question instead of me putting it out there.  So I created this video and Google site.  I showed the video today as the kickoff to the problem and for the first time ever I had a student basically solve the problem out loud at the end of the video.  He looked at my video ending showing lockers 1, 4, and 9 open and said well all the square numbers are going to be open!  Now this is one of the better students I have ever had and fortunately most of the other kids were more interested in seeing what exactly was going on instead of listening to him.  More importantly, I was able to catch him from blurting out the more important "why"were only square numbered lockers open.  While the other students got to work on figuring out what lockers would be open, I pulled him aside and asked him why he thought it was square numbers, which he quickly explained to me (again not surprising, he's a good thinker) and so I set him off to another task and told him not to help anyone else. 

The rest of the kids were working in groups and many came up and told me square numbers would be the lockers that were open.  At this point, I was wondering if I would have to come up with something else to do with the remaining class time.  In year's past, kids took at least the whole period to get even to this point.

So as I often do when we are problem solving, I replied that their answer was great but why? And here is where the rest of the kids got stumped.  For the most part, they spent the remaining class period trying to figure out the "why" of the problem.  They watched the video time and again, they went back to their notebook items and made great connections (such as the people opening and shutting lockers were representing factors, the lockers were representing multiples.)  Still they had a lot of trouble with that question "why."  I even had one student tell me that I wasn't allowed to ask "why" for the rest of the week.  (I was most proud of that, apparently I've been doing my job and actually making her think!)

In the end, I had to give some hints and talk some parts through as they watched the video, but most of them were able to explain the "why" by the end of the period.  Tomorrow we will see how they did on their "Locker Problem Home Enjoyment."  I wanted to know some more "whys!"

Think Dots

This week's #MSSunFun post is about favorite ways to practice.

 I use a variety of ways to practice as I don't want kids to get bored doing math.  Just giving them practice problems or worksheets might work for some but will definitely turn others off.  I use a variety of games most often to practice, at other times I'll have students do some writing and reflecting and yes at times I do have them do some problems or even a short worksheet.  However, my most favorite way to have students practice applying their math skills is Think Dots.

I'm not sure exactly who I got the idea of Think Dots from.  It could have been in a Rick Wormelli book.  It could have been when we had Nancy Smith present on using differentiated instruction in math and science.  Anyhow whoever I got the idea from, thank you!

The basis idea behind Think Dots is that a student will work with another student to solve and discuss a minimum of six problems.  These problems could be all about one topic or about a number of topics.  I tend to use more word based problems that make students apply whatever we are learning (say prime factorization) but you could do Think Dots with mental math problems or even rote skills.

I print out the six problems onto a piece of card stock which I then chop into six pieces.

  On the back of each piece I use colored dots that our fantastic librarian (Thanks Kim!) gave me.

 Originally they were designed to be level books but we stopped doing that soon after she got the dots in and thus had no use for them (lucky me!)  I put one dot on the back of one card, two on another, three on a third, and so on.  I try my best to make them look just like dice.  Then I hole punch the upper left hand corner of the cards and use a ring to hold all six cards together.  Now the Think Dots are ready to go.

I pair students up (depending on the skill being done, I will often "make" the groups because I may have differentiated the questions for readiness) and give each pair a set of Think Dots.  I also give each pair a small stack of sticky notes and a dice.  The first student rolls the dice and has to answer the question that matches up with their roll.  They are asked to not only talk the answer out with their partner but also write a synopsis of their answer on the sticky note which they then attach to the Think Dot cards.

After the first partner has answered his or her question, they move on to the next partner who rolls the dice and answers the next question.  The activity continues in this way until all the questions are answered.  Once all the questions are answered, students turn in their cards to me (sticky notes attached).  This allows me to look at their understanding later and possibly be able to clear up some misconceptions the next day.

I love this activity for a lot of reasons.  It gets kids talking and writing about math.  Kids are up and working with a partner.  I'm able to get around and sit with groups and listen to answers and provide a thought as well.  Because of the nature of the problems, I'm able to differentiate them to meet students readiness levels.  It gives me good feedback on where kids are, both from what I hear and what I get back on the sticky notes.  Lastly, the kids enjoy it.  Oddly enough, they love to roll dice, they like talking with one another, and they like the fact they aren't just doing a packet of problems.

I highly recommend giving some version of Think Dots a try.  Here is a sample of my prime factorization Think Dots.  Please feel free to try them.

Alphabetical Numbers

So I missed last week's #MSsunfun post on games (darn it all!) because school just caught up to me and I became super busy.  I decided that I needed to make sure I posted this week, even though it was just going to be a short post on organization.

This year, I'm trying something different in terms of getting back papers (quizzes, home enjoyment, exit cards, etc.)  My wife teaches fifth grade and has been using a form of this idea for some time now and I figured I would go ahead and try it.  I've given each student in a particular math class (say math 1 my first math class) a specific number that corresponds with their last name alphabetically.  For instance, if Michael Adams is the first name alphabetically in my class, he gets number 1, Janie Betts is the second name alphabetically, she gets number 2 and so on.  In addition to writing their name on each paper, students are expected to write the number as well.  Then when I pick up all the work, I am able to simply put the work in order by the number and see who is missing and then I can go right over and approach them.  Right now I'm still getting used to doing this as are the students so I need to remind them and need to go back and look at what number goes with whom when I'm missing a number but I think both of these problems will soon go away as we get used to the system.  The other potential problem is that I teach on a three person team and we mix the kids up for different classes, so if my teammates try to do this, kids will have different numbers.  At this point, neither of them is using this method so it isn't currently a problem.

Overall, I'm happy with how it affords me a little more time which over the year will add up to a lot more time!

My Home "Enjoyment" policy

This week's #MSSunFun post has to do with homework, specifically homework policies.  My homework policy is really just a combination of things that I have borrowed and stolen from others over the year.  For instance, this year for the first time I'm not calling it homework but rather refer to it as home "enjoyment" thanks to an idea from Sam Shah (@Samjshah).  The thought is that it shouldn't be viewed as work and so we shouldn't call it work.

My journey to where I am now in terms of homework started when I first began teaching over ten years ago.  I originally assigned homework just about every night and graded it, in fact I counted it for as much as 50% of students' grades!  Over time, I realized that homework really is practice and counting practice toward the grade isn't really fair.  We don't count practice toward the final score in a soccer game for instance.  However, I do feel that students need to practice in order to do well so I go do insist that students complete the homework I assign them.  Along this line of thought, I'm instituting a type of responsibility binder much like Julie Reulbach (@jreulbach).  This will be a great way for me to get some data on which kids are completing assignments and which aren't.  I also go by an idea I heard from Rick Wormelli which is "the penalty for not doing your work is, DOING YOUR WORK."  Therefore, students who do not complete their homework are responsible for staying after school to complete it.  (this isn't really a problem in our district as the K-5 school gets out about 45 minutes later than we do and kids can take that bus.)  We are trying something new this year by having band and orchestra after school (it used to be during a time in school we called "enrichment.")  so I'm not really sure how that will play out if a kid doesn't do his homework and needs to go to band or orchestra.

So to sum it up my homework policy is basically this:

• Homework is practice and as such is not graded
• I still expect everyone will complete their homework
• If you do not complete your homework, you will have to complete your homework (after school)

Looking forward to reading some others thoughts on homework and how they manage it and probably stealing a couple other ideas!

How I set up my classroom

This week's #MSsunfun post is about classroom set up.  This seems like it is going to be a great set of blogs to follow as it is super interesting to see how other teachers set up their classrooms.  I posted about my classroom set up a couple years back.  Of course since then, I have moved classrooms twice (and a total of 5 times the past 7 years!)  Last year, I was in a classroom and a half as I was also teaching science and needed the extra room.  This year I'm back to a regular sized classroom although its shape is a little different than I'm used to because it is at the end of the building not in the middle.

Anyhow, onto how I set up my classroom.  Every summer, the custodians take all our furniture out of our classrooms which basically gives us a blank canvas on how to set it back up.  (They will put the furniture back as it was, in differently if you ask, etc- the custodians are great!)  Last year, when I moved rooms I went from plain old tables to science desks (you know the black ones made heavy wood that fit two kids on a side).  If you read this blog, you will know that I learned about Dry Erase paint and decided to make over the science tables.  I painted the table tops with this paint which enables kids to write notes, do math problems, draw, etc and also allows me to stop by and while discussing a problem with a student to actually write stuff out.  Both the kids and I loved it last year.  So, I took the tables with me.

  Its looking like I will need all 12 tables as I have class sizes of 24 students again this year (possibly even higher if more people move into the district.)  Because my classroom is long and narrowish I decided on doing four groups of three desks.  I like to group the desks because most of the work I do has the kids working in groups either of my choosing (or random choosing) or their own choosing.  The groupings of three actually should help with discussion and group work.  Later in the year, I use a different way of assigning seats (I'll post about it later) but to start the year off I allow students to sit where they choose.

When I set up the desks, I allowed for extra room in front of the Smart board so that I can put a carpet there and work with small groups on certain skills at times during math classes.  I also made sure to leave plenty of other spots around the room for groups to go to as I've noticed my 6th graders just LOVE sitting on the floor (well unless we tell them they have to at an assembly.)

I myself don't really use a desk but instead have a long table on which my desk top computer (the one that runs the Smart board) sits along with my ELMO.  I figure I spend most of class walking around or sitting with different groups that there isn't much of a reason for me to have a desk.  When I'm on my prep break and need to correct, the table works just fine.

I've always tried to put all materials that kids will need together in one spot and this year is no different with me having this nice white cubby set up where I can put dice, playing cards, crayons, staplers, and the like.  I make sure to go over this early in the year, telling kids they can use whatever they want but reminding them that they are responsible for picking up after themselves or the stuff won't be there anymore (the whole with rights comes responsibility thing that is so important in middle school.)

The other thing I do is use mailboxes to pass out things like homework, classwork, notes, etc.  I find this much easier than passing it out at the beginning of class or having a student in charge of passing stuff out.  I make sure early in the year to practice with students what they will do when they enter my room (go to their mailbox, grab EVERYTHING in there) and so it works pretty well.  I have three classes and so have three sets of mailboxes.  I suppose I could use one and share but I don't really want to rush between classes to put papers into mailboxes (especially if I tier assignments and need to pass out different stuff!)

New to me this year is having raised shelves to put student notebooks.  I love this because it gives me more room (as these shelves are right above the mailboxes.  Again, I practice with kids getting their notebooks as they enter and we will have to see how these new shelves work.

You probably noticed that my walls are pretty bare.  I do have a few math and inspirational posters that I put up but I like to keep most of the wall (and blackboard) available to post student work as the year goes along.  I'll include some updated photos throughout the year.

Well, there you have it.  That is how my classroom is set up for this year (starting for us in about a week and a half now!)

Math Notebooks

So this week's #MSSunFun post is about how we set up math notebooks with our students.  This is an exciting post just like the first day one because once again I'm going to get to "borrow" a bunch of other great ideas!

Anyhow without further ado, here is how I do my notebooks:

I use these large black binders for each students' notebook.

These binders are available because my school has done student led portfolio conferences for the past ten years and as we have moved toward more and more technology, including going 1 to 1 in both 6th and 7th grade, these binder have become obsolete for portfolios.  Therefore ,binders make great notebooks because they are free!

I have students set up their binders by following the order of our units of study.  We begin the year with whole number sense and follow that with fractions, decimals, geometry, measurement, data, probability, and algebra.  Each of these unit topics is a different divider in their binder.

Inside each divider I start the year off with a number of papers that I have already copied for the students.  The first paper is the KUD (what I want kids to know, understand, and be able to do) for that particular unit.     Here is one for whole number sense.  I also include a sheet to record notebook items (which I'll talk about later), a sheet to record exit cards, and a sheet to record how students did on their understanding of standards on quizzes.   I will admit that I need to do a better job of really showing the kids how to fill out these forms, reminding them early in the year to fill them out, and giving them more time to fill them out.

Once I have all these forms and papers in the binders, I store them here.

Students then grab them every day when they come into math class and go to their mailboxes and take out the papers that need to go into the binders such as this notebook item, returned quizzes and exit cards, and activities or homework.  I have students keep notebook items, quizzes, and exit cards for the whole year. (and in fact, I recommend to the kids that they keep the notebook items throughout middle school as they will only help as the kids do more advanced math.  I'm sure you can imagine how many kids listen to me about this though:)!   Activities and homework are cleaned out at the end of each unit.  Some of you might be wondering why I do notebook items instead of having kids take notes.  I have found over the years that middle school students don't have much of an idea on how to take notes.  By giving them basically a graphic organizer I help them get the idea of taking notes while making sure they get the information I want them to get.

So there you go, that is how I set up notebooks for my kids to use during their year of math with me.  I'm looking forward to seeing some other ideas and adapting them to fit my class!

The First Day

This is my first post in the Middle School Sunday Funday blog (#MSsunfun) that I had previously blogged about.  As I mentioned, each Sunday, a group of us Middle School teachers will be tackling a specific topic.  This week's topic is "What does the first day of school look like in your classroom?" 

I'm going to talk about the first day of "actual" class in my classroom.  The first day of school we have limited time in normal academics as we do a "student inservice" where the kids learn about the school, discuss our core values, and such.

I start the first class by getting the kids up and moving around by playing "vacation human bingo."  We spend a lot of time playing games and doing activities that involve getting up and moving around in my math class so this is a good introduction to that.  This is a "get to know you" activity where students go around and ask each other to sign their bingo board under a category that they did over the summer (such as visited three other states, etc.)  Each student can only sign another student's bingo board once so interaction with many different people is encouraged.  After a short period of playing time, we sit down and go over our boards.  This provides even more of a chance for the kids to get to know one another.  Next I go over class expectations, unit of study, my grading policy, etc.  Since we are a 1 to 1 school, I share this document containing much of that information with the kids (and their parents) before school and ask them on this first day if any of them have questions about what math will look like.  Then to wrap up I've begun using an activity I borrowed from Lisa Henry (@LMHenry9) where I give the students a bunch of numbers (32 to be exact) and sixteen things about me (such as number of siblings, number of my house, year I graduated high school, etc) and have them guess which ones go where.  As I walk around, I get a little feeling about the kids' ability to estimate and reason when they guess at what year I was born in (no, 1905 isn't correct!)  Finally I end the first day by assigning the first homework assignment.  I ask students to write about themselves in a million words or less (I borrowed this from Paul Bogush, @paulbogush).  We being school on a Wednesday so I make this assignment due the following Tuesday (thereby giving the students some time to think and actually write about themselves not just rush through.)

Overall, I like how the first day runs.  It gives the students a good idea of what math class will be like plus they get to play with numbers a bit too.  I'm looking forward to seeing some other ideas that I can "borrow" as well.

MS Sunday Funday Blog postings

Earlier this week, Julie Reulbach (@jreulbach) posted a survey looking for middle school educators who wanted to connect.  (Here is the link to her blog with the survey).  She had an amazing response to her survey with over 80 middle school math teachers responding. (link to her blog showing the results of the survey.)  Out of that came some good discussion on twitter with Julie, @4mulafun, @Borschtwithanna, myself and others.  We decided on the heels of the increasing popular #made4math Monday blogs, that we would add a new middle school math blog day.   After much discussion, we decided on Sunday to be the day to post blogs (largely because we wanted to use the name MS Sunday Funday for the blogs!)  The goal is to get as many middle school math teachers blogging and sharing ideas as possible with a common blog theme each week.  We decided to come up with a couple topics to start off with (first day activities, how you set up your math notebooks) and then we are going to go with a survey to get weekly ideas. Here is a link to the survey for new topics. The first blog post will this Sunday with the topic being "What do you do on your first day of school?" (of course, you don't have to wait until Sunday to publish your posts) Once you are done, tweet the link to Julie, @jreulbach so she can make a running list.  Please consider joining us even if you are not a math teacher.  Here is a link to the list of future topics that will be published in advance.  Julie has also provided a link to a spot on the MS Math wiki for those people who do not have a blog but would like to add a post. Looking forward to some great sharing!

A look at some summarizing techniques I've used

About a month or so ago on twitter, we were discussing summarizing techniques and I mentioned a few different ones that I have used and that students have enjoyed doing.  @Druinok said she would love to hear more about them and suggested I write a blog post about them.  So after much procrastinating and some summer vacation time, I'm finally getting around to it!

I've used a variety of summarizing techniques in the past, both written and verbal which have allowed my classes to interact with one another as well as share something that they learned or a question that they still have.  A number of these I've borrowed and adapted from Rick Wormelli who has a ton of great ideas, including many summarizing techniques.

The first summarizing technique I've used isn't really creative or anything but with my grade having gone 1 to 1 last year is something that has worked well (and something I've blogged about in the past).  I've found that kids like using Wallwisher to post a quick comment or question about a particular lesson.  I had tried this in years past but it didn't seem to be worth the time it took to log into computers, etc.  With students each having their own computers and not needing to log in, etc it has become much easier and works well.

Another technique I've used is called "Share One, Get One."  In this activity, students fold a blank sheet of paper into thirds one way and then thirds the other way (thus making a 3 x 3 grid or 9 boxes.)  Then after doing a class reading, after a class discussion, video, or activity, each student fills out the top three boxes with something that they have learned, questions they still have, or something they wonder about.  Once everyone has done that, students get up and moving around the room talking with one another.  They share one idea from their sheet with another student and have that student share one with them in one of the remaining six empty spots. (Hence the name share one, get one)  I've found that kids love this for a number of reasons.  First, they are up and about moving around.  Second, they get a chance to interact with a variety of their classmates.  I like it because kids get a chance to experience a variety of opinions and ideas from the lesson.

Another technique I use is called "Summary Ball."  In this activity, students all stand up and think about something they learned or a question they have from the day's lesson.  I get out a soft, even Nerf like ball and give it to one student to start.  That student needs to make a statement about something they learned or about something they still are wondering about and then throws the ball to another student and sits down.  The student who receives the ball needs to make a statement or asks a question and then passes the ball along.  This continues until everyone has had a chance to say something.  If someone can't think of something, they can pass and then someone will come back to them later.  Kids like this because they are active and get a chance to throw the ball around.  I like it because all the kids are in involved and it gives everyone a chance to say something.

                                           photo courtesy mag3737

A last technique I use is called "Snowball Fight."  In this activity, students write something they learned or a question they still have on a piece of scrap paper.  They then crumble the paper up and once everyone is ready start tossing the paper at each other.  We do this for a minute or two and then students need to pick up one of the pieces of papers and we go around and read them.  It should be pretty obvious why kids love this and I like it because it involves everyone (plus I get involved and get to throw paper at the kids!)

                                             photo courtesy photosteve101

These are just a few of the many techniques that I use over the course of the year.  I've found that kids enjoy these quite a bit, even asking to do these at the end of classes.

In the last two years, I have moved from a more traditional grading system of tests and homework to a standards based grading system where I grade students on various "skills" such as operations on fractions. I tend to gather their grades through quizzes (which are directly related to two or three specific skills) and projects. I'm loving how this works as it gives me a lot of information about what students are good at and what they are challenged with. At the same time, I've used almost daily exit cards in my math classroom for the past 8 years. I love these formative assessments because they allow me to get a quick "dipstick" into where my students are as a lesson progresses.

My problem (I guess not really a problem, more of a question) is how do I combine the two (standards based quizzes and exit cards)? I don't really want to start "grading" the exit cards but should I somehow include them as they do show student understanding of a particular skill. Does anyone have a thought on how I could combine the two (or if I even should combine them- maybe I should just keep using them as I do)? does anyone combine both SBAR and exit cards in their classrooms (math or otherwise?)

Any feedback would be great!

The Day in.....

Last year, I began to use a Google Presentation to send my students a quick blurb about what we would be doing each day in math and science. I did this for a number of reasons. First, I felt it was important for the students to see what we were doing and to see connections to what we had done. Second, it stopped the "What are we doing in class today?" questions that kids always ask. I love how if a kid does ask me that someone else in the class tells them to look at the "Day in..." This has also been a great way to keep parents informed on what is going on in class. I have a number of them who subscribe to the presentation. Several have told me it makes it that much easier for them to have discussions with their middle school students who normally don't say more than a few grunts. Lastly, its great for me to be able to go back and see the progression of the year through the different lessons I have done. Obviously it isn't a full on lesson plan but it gives me a good synopsis and I can go back to it to see which parts I need to tweak in the future.

As I said, I started doing this last year and it was moderately successful in all of those aspects but I didn't really follow through because the kids weren't using it as much as I'd like. This was due to the fact that middle school kids are often not a group that looks to the future even the very near future and so they wanted to check the "Day in..." right before class. Without access to computers this was difficult. This year, we are a 1 to 1 environment and the "Day in.." is working great!

There are a few tweaks I want to do. I need to include a more "student friendly" version of the standards that we are going to be touching on each day. I think there is still some disconnect from the kids understanding of why we are doing a certain thing each day. From a stylistic point, I have just added a new slide at the end of the presentation. At first this seemed easy enough to me, but now I'm realizing that we are some 120 slides in and it might be hard for kids to get to the current slide. Next year, I'm going to add the slide at the beginning so the show will go in reverse order.

Overall, I'm very happy with how it has turned out, especially with our 1 to 1 environment. The kids love using it to know what is going on and are actually upset if I miss a day for some reason! In fact, I've had a number of kids tell me that they wish they had one for their Language Arts class too (hint, hint Katie!)