How long does it take to make a thousand?

Because I won’t be teaching fifth grade math next year, I am trying to get up some old draft posts that I never finished. Here is one about a place value activity I did in the Fall.

Whenever an activity turns out to be more difficult than I expect, I figure that it was that much more of a learning experience. But I am still trying to understand what happened when I asked students to make one thousand using blank hundred grids. Even with groups of four racing to see who would finish first, it took an hour.

The point of the activity is for students to discover that they will need ten hundreds to make a thousand. At the same time they see the counting patterns on a ten by ten grid (which is something we might falsely assume they’ve noticed before).

The activity doesn’t require a lot of upfront instruction. You give the students blank hundreds grids and tape. You present the task and walk around.

One of the biggest challenges is getting the students to talk to eachother. When we did it, students began writing numbers without agreeing who would write what section. Some students didn’t accurately figure out where one person’s numbers would end so that they could start with next number. I had to hustle around the room to point out what people were doing among each group.

Some students also weren’t efficient writers. Many didn’t rely on number patterns such as the repeating digit in the hundreds or tens place to help them write faster. I didn’t want to tell them the patterns, but I sometimes stopped them to ask how some students were moving faster than others.

When they finally taped their hundreds together, it was very exciting. I can’t pinpoint exactly all the learning that happened, but the fact that it presented so many stumbling blocks leads me to believe it was a worthwhile experience. It also allowed us to make ten thousand, which was really exciting to hang in our classroom.


May 24, 2012 at 6:12 pm 1 comment

Oh, the Places You’ll Go!

As usual, I disappeared after the start of this school year because work just got too crazy for me to keep up with a blog.

Among the many things at school that kept me busy, there was this:

And on top of all that there were field trips and small remediation groups and benchmarks and PD sessions….

Now that I’m back, I have another piece of news, which is that I am changing from fifth to eighth grade.

I know lots of teachers change grades quite often, but this is a really big deal for me because I have been teaching fifth grade for seven of the nine years I’ve been teaching. When you’re my age, seven years is almost a quarter of your life. It is also the grade where I really found myself as a teacher. It is where I first got results I could be proud of. It is where I proved those results were sustainable. It is where I first taught centers. It is where I rocked my sweet Fraction Girl costume. It is where for the first and only time I cried in front of a class. It is where I met the mayor. It is where I once had blood, puke, pee and snot coming out of different children’s bodies all at the same time.

Switching grades also feels like a big deal because I have been the only fifth grade math teacher since my school was opened. This has been great in terms of continuity from one year to the next. But sometimes I worry that I’ve sent the wrong message by staying put. I want teachers to see that it is possible to make changes in your career without leaving the classroom. Change is healthy.

But I’m not writing to explain why I made my decision. I’m writing because it’s important to say that sometimes even when a decision is good, it is painful. On top of being completely terrified that I will fail, I will also miss my beautiful, earnest, well-meaning, troublesome fifth graders. There are times when they are so incredibly lovely that it actually hurts. Fifth graders give Valentine’s Day cards that say, “Hugs and kisses.” Fifth graders call their teachers to wish them a Happy Mother’s Day. Fifth graders think I’m hilarious.

Every year, I read my students Dr. Suess’s Oh the Places You’ll Go. I’ve always felt like I’m reading it as much for myself as I am for them. This year is no exception.

May 24, 2012 at 6:05 pm 1 comment

How much of a class should be conceptual and how much should be procedural?

This question came up at a professional development session I led last Saturday. I tried to answer it by sharing my daily class routine and giving some examples of how I’ve taught for conceptual understanding. But as I left the session, I found myself wanting to consider the question in greater detail.

Ratio is a hot topic in pedagogy these days. Teachers think about the ratio of student talk to teacher talk. They think about the ratio of lower-order thinking questions to higher-order thinking questions. Ratio is important because it ensures differentiated instruction.

But as I tried to figure out an appropriate ratio of teaching for conceptual to teaching for procedural understanding, I realized that it couldn’t be done. Teaching for conceptual understanding is like being a vegetarian: Vegetarians don’t eat a high veggie to meat ratio; they stop eating meat. Not only that, most vegetarians stop eating meat for a reason, and that reason impacts many of their choices, not just what they choose to eat.

The same commitment applies to teaching for conceptual understanding. If you believe that math is something that can and should be understood by all students then you give up teaching rote procedure. Conceptual understanding becomes the foundation of everything you do and all the choices you make. Sure, just like vegetarians might have a little fish or egg now and then, the conceptual teacher might have to do a little “drill and kill.” But the basic belief about math making sense is always present.

This doesn’t mean that a teacher who is new to teaching for conceptual understanding can’t shift approach gradually. It means that teaching for conceptual understanding requires more than a five minute addition to the class routine. It requires a shift in mindset. To get yourself in that mindset, let me share a few things that I often see teachers who are committed to conceptual understanding do:

1. Introduce every topic in a way that relies on student sense-making.

“See how this looks like an array? That means it’s multiplication!”

2. Correct every misconception by reminding the students “why.”           

“You forgot the zero. Remember how this 3 is really 3 tens? When you multiply it, it’s still going to be tens.”

3. Encourage students to ask questions and make connections.

It’s almost the New Year. Lots of people make resolutions about their diet. Maybe this year it’s time to go on a different kind of diet.

December 20, 2011 at 11:24 pm 3 comments

Replicable Practice

Another old post that never got its wings…. until now.

My school started a new approach to professional development last year which was to identify a “replicable practice.” A “replicable practice” is an instructional strategy that produces measureable results in student achievement and that can be shared with other teachers. Instead of asking teachers to name an instructional weakness that they’d like to work on, my administration asked teachers to name a potential area of strength that they would like to develop further.

I think this is a really empowering way to put a positive spin on professional development, and I am embracing it wholeheartedly. In fact, I have been planning to use my blog as a part of sharing my replicable practice with others. So, I am not only happy but compelled to tell you about…

Wait for it…


Okay, let’s all take a deep breath here.

I mean, 32 students moving around the room at the same time to places where they will be unsupervised to work independently? It is a lot.

But before I say anything I must say that I am incredibly grateful to have had another teacher in the room for half an hour with each class every day. My partner teachers will remain nameless because this is supposed to be an anonymous blog, but WOW. Working with inclusion partners made my particular version of Centers possible this year. I definitely feel like I got twice as much out of Centers as usual.

In previous years, I did Centers by myself, and there was still a huge benefit to having a regularly scheduled time to work with students in small groups. There are many different ways to arrange Centers, depending on the number of students, the number of teachers, the space and the resources. Over the  years, I have tried:

Three stations with one teacher

  1. Independent Work Station
  2. Game Station
  3. Teacher Station

Four stations with one teacher

  1. Independent Work Station
  2. Homework Check Station
  3. Partner Station
  4. Teacher Station

This is the simplest way to do Centers. Each group of 8 goes to each station for 12 minutes each day. You put a basket at each center with the materials students will need for that day.

Four stations with two teachers

  1. Independent Work Station
  2. Game Station
  3. Teacher 1 Station
  4. Teacher 2 Station

Five stations with two teachers

  1. Independent Work Station
  2. Computer Station
  3. Art Station
  4. Teacher 1 Station
  5. Teacher 2 Station

The set-up you choose depends on what you want the students to do and how many resources you have. For example, I wanted the students to work on computers, but I only had four. So, I set up a system where four students got to use the computers each day. When they weren’t on computers, they were at the art station.

For the purposes of my “replicable practice,” I’ll begin by sharing how I did centers last year, which is the last setup I mentioned above. Since it does require such complicated planning, I’ll just start with…


Basically, there are four centers over two days. We do this because I only have a partner teacher for half an hour with each class.


My partner teacher takes her group to a free classroom while I manage the other three groups in my classroom. There are two tables in the back for one group to share. Then one group is with me, and another works independently.

This is just one idea of many. I’ve done lots of variations, and they’ve all been great.

November 10, 2011 at 5:00 pm Leave a comment

Making Best Practices Automatic

School is on Monday. I have been going to professional development workshops, planning with my grade level team, discussing details with my principal, and producing: posters, seating charts, homework, activities… The list goes on forever.

Then last night I woke up in the middle of a deep sleep, suddenly realizing, “Oh my gosh, the students will be there.”

This might sound like a silly realization, but it takes a real mind-shift to start thinking about “the first day of school” as “the students’ first day of school.” If you do start thinking about it this way then you start to think about how intimidating it can be. And how exhausting. And how boring. Really, if we’re honest, about 99% of what we do on the first day is going to be blocked out by all the overwhelming emotion that comes with just showing up after a long summer break.

It is these concerns that make me so grateful for my lesson planning template (download sample here). I imagine that at first glance it would appear pretty complicated. It started out a simple place to list the objective, the agenda and the materials. But  as I have added new “best practices” to my repetoire, I have added to the template. For me, it is a constantly evolving document that reminds my present self what my past self found was important. When I make changes, it becomes a gift to my future self.

You will see that I have broken things down into 5 minute chunks. That’s because I used to be really bad at budgeting time and keeping the lesson flowing. You will see that I put a place to record “sparkle,” the place in the lesson where something magical will happen. Every lesson should have some sparkle. You will see that I broke my 5 minute chunks into what the teacher does and what the student does. I did that to remember to plan exactly how the students would move between activities.

The part that stood out to me today was the reminder to highlight my movement breaks. The students are going to need that.

Thank you, past self. All last week, I kept thinking about my first day back. Now it’s time to put myself in my students’ shoes. It is their first day back.

July 7, 2011 at 10:01 pm Leave a comment

Coming Back For More

I am getting ready to teach place value for the seventh year in a row. But I am totally not bored. In fact, I am pumped that I’ve been able to collect better and better ideas for teaching the topic as time has gone on. It makes me proud. It makes me feel like a professional. And it makes me want to keep teaching.

For example, I used to give my students digit cards to do place value games. They were just cards with single digits. They worked. My students learned.


…it is just as easy and MUCH more meaningful to use value cards.  They are cards with multiples of ones, tens and hundreds that can be stacked to make multi-digit numbers. With value cards, students have to think about a digit’s value as they are building numbers like 395 or 1,026. They are learning the purpose of place value while developing the understanding needed to write numbers in expanded form. 

I don’t remember who shared the idea of digit cards with me, but I am grateful. The idea didn’t just help my students. It got me excited to keep learning and growing as a teacher.

And now I’m attaching my digit card templates for someone else out there. Simply print them out so that the different place values are different colors, and go. I hope they get you excited to teach place value one more time.

July 5, 2011 at 10:50 pm Leave a comment

Math on the Mall

It’s been a really long time since my last post. Did I really not take a single photograph of my students since Halloween? There is a dark period in teaching that lasts from November to April of every year. I still teach my heart out, but I can’t take pictures of it.

The bright period starts as the school year is wrapping up. Suddenly the exhausting days don’t seem so bad because a break is coming. I start to get excited about making changes for the next group of students. I try to work on things that I will need when I am tired. It’s like stocking up for the winter.  I HIGHLY RECOMMEND IT. Last year, I wrote my February decimal unit over the summer. I am convinced my students would not have learned decimals if I hadn’t.

I also start to take more pictures. Like these from our field trip to the National Mall…

If you’re like me then every time you hear about something like math on the mall you think vaguely about how learning is so much better in an authentic context. But it goes at the bottom of the To DoList because it is non-essential. I wish it didn’t.

Math on the mall gets students to talk about mathematics as if they actually care about it personally. I was amazed to hear my students eagerly discuss the angle of fountain jets.

Math on the mall is memorable, and it engages students with many different interests. There is plenty to see inside at the museums and outside at the National Sculpture garden. We explored lines of symmetry and tried to estimate the volume of the sculpture shown below.

One of my colleagues has three different versions of a sheet she’s written for various visits to the mall. They have a rich variety of problems for different locations (1, 2 and 3). There is also this math on the mall sheet for highschool students.  I adapted part of the MAA field guide because it was a bit difficult for my kids. I also incorporated ideas from an NCTM article about why things are shaped the way they are. This is the student sheet I compiled:

We did the sheet on our walk from the American History museum to the US Capitol. We did not get through it all, but we had a lot of fun on what we did. It is probably easier if the teacher shows the students a wrench and a piece of paper with different shapes cut out of it. I had to print paper wrenches and paper lug nuts

Washington, DC provides so many free opportunities for learning in many different subjects. It just takes that end of year burst of energy to take advantage of it.

June 1, 2011 at 1:30 am Leave a comment

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