Does 8 = 14?

Welcome back!

In a flurry, summer flew by and here we are, sitting back in our desks in rows.

Wait a minute.

No, we're not. We're not, because that's not how today's students learn. At least, that's not what I think!

I've been assigned to a new school, a new set of kids, a new grade - basically, everything is new again. I've been wracking my brain trying to figure out what and how to teach this group. It's only been a few days (6 to be exact), but the picture is beginning to clear up a bit.

It's funny, when you are faced with a new group of strangers, how little you feel you know. I was so confident in my Gr. 5 math class last year, but now thrown into a group of Gr. 2 and 3 students, I feel a bit lost! I've taught the grade before - but it's new every time. I know the curriculum expectations, and I know my philosophies. What I don't know include: the kids, their needs, their skills, their interests, their behaviour blips, their attention spans, and their pasts.

But that's okay.  In fact, I prefer to not know much about them. It stops me from forming ideas about them that may not be true, in my room or in general.  A mom told me today at our open house that her son was excited to be at school because he liked me. Had I known about his past, I'd have assumed that he didn't enjoy school and then we may be in a whole other mess!  Fortunately, him and I are in a good mess - a mess called learning!

I always start off more or less the same, regardless of the grade, with the same questions.  Ones like:

"How many numbers are there, and how do you know?" and "How many ways can you build the number 14?"

The kids rotate through these centres, 10-15 minutes at a time depending on their age and "vibe" (if you're a teacher, you know what I mean ... we are always reading the kids ... when it is time to move on, we move on).

From this, I get a sense of:
- what sort of learners are they?
- are they comfortable with manipulatives?
- do they naturally go to manipulates?
- how do they organize (or do they organize) their work/thinking?
- are they comfortable talking about it?
- can they stay on task at this point in time?
- do they "get" this stuff or is it too abstract?

I found out by day 2 that this was all too abstract for most.

One girl asked me if 8 was 14.

Yes, you read that properly.  "Is 8 fourteen, Mr. Patrick?"

"Sorry?" I thought I had heard wrong.

"Does 8 equal 14?"

2 years ago I would have said "No. What does 8 equal?"  And that may have been okay ... at the time, for me.  I know better now.

I said: "Does 8 equal 14?"

She just stared at me.  So I said, "Let's get some counters and see."


The trick here is to explore fully WITH them.  EVEN THOUGH I know it's not right.  EVEN THOUGH it logically to me makes no sense at all.  EVEN THOUGH!!!!!! I need her to experience the answer.  She needs to be in control.

We got the counters (she picked them, because there are bread tags and blocks and animals and so on).

I said, "Let's get eight."  So she did. We counted eight together.  Good! She can count.  This is giving me information.

I said, "So is eight fourteen?"

She stared at me.  "Yes?"

I said, "Okay ... how many are here?"

"Fourteen?"

"Let's count them again."  So we did.

"How many are here?"

She said, "Eight."

I said, excitedly of course, "Yes! There are eight! High five man way to go!! WAHOOOOEY!!!!" (Okay maybe I didn't get that excited ... or maybe I did.  I don't remember.)  I circled the blocks on our chalk table (see, it comes in handy!) and wrote the number 8 over it. Then I said, "If there are eight here, I wonder how many more we need to get to fourteen?"

I knew at this point that she needed a push in the right direction.  We probably could have gone back and forth all day about eight being fourteen, yes, no, yes, no.

So we counted, with my direction, the original eight, and seamlessly continued counting new blocks until we reached 14.

These blocks went in a different pile.  We circled it.  I asked her how many were in it.

She counted them and found it was 6.

So I asked her, "So, now that we can see this, is 8 fourteen?"

She said, "No."

I asked her, "How many more do we need to go from eight, to fourteen?"

She double checked by counting the new blocks and told me it was six.  We wrote 6 over that pile, and I showed her the number sentence: 8 + 6 = 14.

She smiled, and I could tell she felt better.

The big idea here is that she didn't have the concept of numbers being their own values.  It may have been some sort of weird memory lapse, but the understanding wasn't there.  I needed to take the time, even if it seems silly to spend so much time of 8 not being 14.  I needed to give her an opportunity to EXPERIENCE the numbers.  It would have been unfair to just tell her the answer.  It would have been unfair to shut down her thinking right away by saying "No, go find out how many more you need." She was brave enough to ask me, a relative stranger (this was day 2).  How dare I shut her down!  So I didn't. We built up an understanding together.



Throughout this first week, I've found some number sense skills all over the place.

We've started working with ten frames and number lines, and are focusing on building a strong understanding of how numbers work together, so that we can start thinking about mental math and everything else.

If you don't know how numbers work, how can you do anything else?


The first weeks are messy.  They're muddy and unclear.  It is a scary place to be.  But, it's also important.  Every word I say or don't say - every extra minute I give or don't give - every nod I nod, every smile I smile, every example I choose to give or select not to ... they ALL  matter.  I'm forming their love or hate for math; I'm determining how they will approach, organize and eventually think.  I need to be sure that I'm doing it well.