Data Management, math

Slice of (Math) Life

Way back in September, I had read about this neat activity from Marilyn Burns called “The Door Project“and had decided to use it to start my school year.  On day one I always like to take the students for a walk around the building.  If anyone is new, or even if they are just coming to my end of the school for the first time, I want to make sure they have a chance to orient themselves, find the washroom and drinking fountain – that sort of thing. On the first day of school, I combined that with some math.  It was our first provocation, if you will.

When we got back to class, I asked, “Did you notice how many different types of doors we have in our school?”  We took a look around the class, and started thinking of ways to sort the doors in our school. Some have windows, some don’t. Some are metal, and some are wood.  Some go to the outside, and some into closets.  I gave everyone paper, asked them to think of 2 or 3 categories to compare, and away we went.  (I’ve condensed it here – we actually spent a whole class period on this!)

It was a disaster. I just looked back to link you to my post, and found I didn’t write about it at all!  That’s how bad it was.  As I recall, we were having a lot of trouble managing our data.  The categories were all mixed up, the tallies were not organized, and nobody could do anything with the information we collected. I had intended to graph our data, but, alas, it was not meant to be.

Today we tried again.

I reminded everyone about this activity, and some sort of remembered it.  We quickly reviewed our door types.  I gave everyone a choice of paper – plain, lined, or graph.  They grabbed clipboards and pencils, and lined up like pros!

We made it all the way around the school, gathering all of our data, in very little time.  Nobody had to shut their door when we stopped to count!  When we got back to class, everyone was able to count their tally marks by 5’s and find their totals in record time!

I reminded them how far we had come.  I reminded them that in September this activity had been really hard, but now it was barely a challenge.  Everyone collected the information independently, found their totals, and is now ready (and able!) to graph it tomorrow.  Now I am sorry I didn’t keep our first disastrous attempt so they could see how far they’ve come! (Who am I kidding…I probably do have it and will find it on the last day of school when I am finishing my clean up!)

What a difference a year makes!

Just about every Tuesday I blog for the Slice of Life challenge over at Two Writing Teachers. You can read posts from others on that blog.
math, Number Talks

Number Talks: Week 1

I hadn’t decided yet if I wanted to start off by making this sound like I am a genius (which I totally am!) or if I was going to list all the sources of this idea and talk about how they converged into this seemingly-original idea.  But then I listened one morning this week to a podcast from Derek Rodenizer on voice.ed radio.  (You can listen to it here.  It’s only 5 minutes!)  He posted this graphic later on Twitter:

I think you can see the original Tweet by clicking on the picture.  Sorry, I can’t figure out how to post it!  

That podcast made me realize that this Number Talk idea was just that – an example of how sharpening my pedagogical sword gave me an idea that wasn’t/isn’t truly mine but is me knowing a bunch of stuff and then putting it all together and coming up with something different.

The “Introducing Multiplication” unit by Marilyn Burns starts with an activity where students are asked to work with partners to make posters about numbers.  Specifically, students are supposed to write down things that come in 2’s, or 4’s or 7’s, etc.  So this is partly that idea.  If you look on Pinterest under “math activities” you’re sure to see art projects students have made where they have written down all the ways to write a number, or what the number means to them. (If you don’t know what I am talking about, look at this.) This is partly that idea too.

On the first day of school, I told my new students I was going to write a number on the  board and they were going to tell me everything that number made them think or remember.  I then talked to them about how we put our thumb on our chest to show we have an idea, and that they could take as much time as they needed because math is not a race.  I wrote a 2 on the board.

I am not exaggerating when I say we talked about this for probably 15 minutes. Here is our result:


I have erased student names before posting here!  “(Blank) has 2 kittens.” used to be attributed to a specific student.  

It was so interesting and, I thought, successful that I couldn’t wait to do it for the rest of the week.  Here are our results:

I do not think it is a coincidence that we got more information for 2 and 5 than we did for 23.  This is a grade 2/3 class and most of the ideas on 23 came from the 3’s. Also, there aren’t a lot of every day things, like bike wheels and toes, that come in 12’s and 23’s.

There were some common themes:  each day they wanted to talk about someone who was the age that matched the number.  They know people who are 2, 5 and 12 – mostly siblings.  But 23 is too young to be one of their parents, and too old to be a friend or sibling (for most.)  When we talked about 23 as an age, it was clear they don’t really know what 23 years-old looks like. They guessed that I am 23, which I totally look like I am but I am not. They then guessed that our principal is 23, which is what she actually looks like (no this is not an evaluation year for me.) We settled on “Justin Bieber and college students” after some discussion.  Everyone finally agreed that a 23 year-old is a “young grown-up”.  But I think many of them are still not 100% clear on this idea.

My original goal was to start using Number Talk routines – mainly the one with the thumbs up instead of hands up.  I also wanted to start talking about them building on each other’s ideas, which they did.  I was busy building routines, not taking notes.  But I still feel like I got some important information from some of my new students.  This will help me going forward.  I had originally planned on doing dot-number talks for the week.  I have already prepared slides to use for this using Smart Notebook software, even though I do not have a SmartBoard in my class. I kind of chickened out because the tech-gremlins have been busy at my school over the summer and things were randomly not working.  I didn’t want to start off my school year muttering curses at them while repeatedly jabbing buttons.  I’ve saved that for the coming week just to give myself something to look forward to!

To read more about how a dot number talk can be used to start the year, check out this great blog post!


Multiplication Models

I wish I could remember how I was taught to multiply.  I have absolutely no memory of who first taught me about multiplying…which is kind of weird because I remember all of my elementary school teachers. I do remember doing “mad minutes” in Mr. Goodreau’s 6th grade class. I would bounce around doing all of the 1s, 2s, 5s, and a few other random problems that I actually had memorized. And I remember being in high school algebra class and writing down my skip counting for problems with 6s and 7s. Heaven forbid Mr. Creager should ask a question that involved 8s or 9s.

Excuse me while I go deal with some residual anxiety related to multiplying.

As a teacher, I’ve often wondered what would have been different for me had someone along the way pulled out some manipulatives, or showed me an array, or, you know, explained that there’s more than one way to answer a multiplication problem.

I introduce multiplication to my grade 3 students using a “groups of” model. Using lessons from Marilyn Burns “Lessons for Introducing Multiplication” book, I let them investigate (though I’m not now 100% sure I have been allowing them to investigate enough…topic for another night!) ways to figure out how many legs there are in their group, or how many pencils we’d have if I bought 4 boxes, or any number of other questions designed to push them to use skip counting or repeated addition and then connect that to multiplication.

I also teach my students about arrays. I get out the colour tiles and ask them how we can arrange them to show 4×3, for example, and we move on from there.

Why arrays?

Well, because Marilyn Burns told me to, at first.  Then I stuck with it because it made so much sense to me.  And years later I am still doing it because I see it as a model that makes sense to kids.  There are arrays everywhere, so it is easy to find ways for them to practice using them, as well as a way to connect them to why multiplication is meaningful.

Today I wanted my grade 3s to work on arrays.  Usually, I would show them an array and then we’d practice them together and we’d all walk away pretty happy.  However, today I decided to let them discover the array on their own.

I pulled out the colour tiles and put them in the middle of the group.  “We’ve been playing “Circles and Stars” and I am wondering if that always has to be played with chalk and a chalkboard, or if we could play it with these colour tiles.”  The colour tiles were our manipulative, and the array was the tool I wanted them to work toward understanding.  I am going to admit to being a bit nervous about this, and thought it might be a disaster.  But who am I to question Cathy Fosnot, right?  So I kept going.

A few of them suggested that they could use tiles to make circles and then fill the circles with other tiles.  That would be like circles and stars.  I asked them to show me, and they started arranging the tiles into circles.  They soon decided  that it is hard to make a circle out of squares.  Then one boy said, “You could think of the sides.  It has 4 so you could do 5 x 4.”  This is what he made.


“That’s a Minecraft circle!”  someone said.

I asked, “You think we could do it like that?  For every problem?”

A students said,”That would be hard.  That would be a lot of work!”

Another student had been watching the whole thing.  She finally said, “I have 2 plans now.  You could use the tiles to make dice….wait…you could have imaginary circles.  You don’t actually need the circles, just the groups of tiles.”  HOORAY!!

We took turns modelling that:

I asked them to count what they had, and some interesting counting things happened.  I know Melissa will be sorry if I don’t explain that, but it is kind of a tangent. 🙂  Let’s just say that even though they had groups of 4, they still counted by 2s and 1s.  (sigh)  But then another child said, “Well if we put them in lines, we can count by 2s.”  and he made this:


Someone counted by colours in groups and then they started, on their own, talking about other ways to arrange the 16 tiles we had randomly started with.  Like, seriously, they started making the division connection ALL ON THEIR OWN!

(By now I had switched out all the tiles so they were the same colour.  I wanted them to think about organizing the arrays without worrying about making designs with the colours.  This is a real problem with colour tiles and can often get in the way of the math learning.  I mean, patterns are important too, but making checkerboard patterns for everything doesn’t seem to help with the counting or understanding in anyway. It just slows kids down and causes them to hate one another because someone is always hoarding the good colour that everyone else wants.)

We talked about how each of the arrays we had made matched with the dice we use in “Circles and Stars”. Then I asked, “Now do you see how to play ‘Circles and Stars’ with colour tiles?”  And they did!

So I sent them off with a partner and a pair of dice.  We are now using a 10-sided die to show the number of groups and a regular 6-sided die to show how many in the group.

Here are some highlights:

  • On their own, one group found out about ones and zeros and what happens with them in multiplication.  🙂
  • On their own, each group figured out that organizing the groups into straight lines made them easier to count, and easier to count without having to go back to ones.
  • One girl started counting by ones.  I stopped her and encouraged her to try a bigger number. (Array pictured below) “I can’t count by 2s because I get confused!” I said, “Then try something besides 2s.”  I thought she’d do 5s, but she counted by 4s.  🙂
  • Slowly 2 of the 3 groups moved to this sort of group arranging:

I feel like my goal today was accomplished, and then some! The students discovered the array.  I felt like I was scaffolding, not rescuing them.  (A personal pursuit of mine.) And I think there was a healthy bit of discovering things that can lead to other things for us.  (Division, for example.)

I have an idea for my lesson tomorrow.  Two of my grade 3s were away today, and should be back tomorrow.  They will need to be in on this discovery.  And I want to really solidify what we did today.  BUT…instead of sharing my idea, I’d love to hear ideas from others.

And by the way, the grade 2s were all doing their Guided Math rotations while the 3s and I did this.  I blogged about my experiment with GM earlier in the week. I am still on the fence about it, but will finish out the week before I talk about it again.

Finally, because I know that many people visiting this post are new to blogging, I want to mention that it’s great to leave a “drive by” comment.  But the best conversations happen when people return to read comments left after their own, and then comment again!  After you write a comment, WordPress blogs allow you to click a box that will “subscribe” you to a post.  Every time someone comments on that post you’ll get a notification that will keep you in the conversation.  I recommend it!

You’ll have to log in to comment on my blog, leaving your name and e-mail address.  Rest assured that only I will be able to see your e-mail address.  It won’t be visible to anyone else.  I have this setting on because it helps to eliminate many spam comments.