math, Number Sense & Numeration

For real?

Day 3:

A student said, “But I thought you said we were going to do multiplication.”

I replied, “You are doing multiplication.  This…the stuff we’ve been doing today…that’s multiplication. Here, let me show you.”  I drew an array, then wrote “2 groups of 4” and then 2×4 on the board.  “See how all three of these are different ways of showing 8?”

They were not impressed. “That’s it?  That’s multiplication?”

Me, looking around, “Um…yeah. Sorry.”

Imagine feeling disappointed because multiplication makes sense the first time you try it.

We’ll see how they feel about it next week when we move on to proportional reasoning.

math, Math Workshop

Mea Culpa

I never give out traditional worksheets for math.  Like, seriously…never.  Maybe once time this whole year, and that was for a child who was absent. But I am starting a new Context for Learning unit with my grade 3’s and they need all of my attention to get them going.  So I need the grade 2’s to work quietly.  I came up with some good independent workshop centres for them to do, with plans to bop in and out as my grade 3’s got busier.  But they really needed me, so my time with the 2’s was limited.  The activities were really good too, did I mention that?

On Friday (I know…who does this kind of stuff on a Friday?)  I gave them their games and put them work.  Over the weekend I rethought some of the noisier activities and added two that would require basically no talking between the participants.  Then on Monday I spent the whole time redirecting grade 2’s and asking them to work quietly. It seems they were having too much fun, so even though they were doing the math I had given them, they were also loud.

I decided they could do some worksheets today. They could quietly work on some addition and subtraction practice without me having to intervene at all. I dug out my dusty grade 2 commutation worksheet black line masters and copied a few. I passed them out, sent my grade 2’s to tables, and got to work with the grade 3’s.  Things were going OK!  I knew it wasn’t the most engaging work, but hey…Mercury is in retrograde and there’s a full moon on the way. Sometimes you gotta do what you gotta do.

As I started marking the worksheets later in the day, I saw lots of problems that looked like this:


For those who have not taught Primary students, let me interpret.  Both of the answers are correct.  The little 10 floating in space between the 8, 2 and + is the correct answer to 8+2, and the weird 114 under the 7 is there because 7+4 is 11.

I have always had a child or two do this, but never the whole class.  I’m gonna take full responsibility here.  I mean how did I not see this coming, right?  I think this is why teachers in older grades think we aren’t teaching math to the little people. They arrive in a class where the teacher expects students to complete worksheets or do work from a textbook and the kids look like they can’t do math when really what they can’t do is a worksheet. That’s a whole set of skills that they just aren’t going to be taught in my class. I don’t think I’m alone in this.  Every child answered all or most of the questions correctly, it’s just that they didn’t know how to communicate this…there were weird circles all over the place, floating numbers, and even a few pictures that seemed to come from nowhere. A bunch of them did the worksheet in marker, even though there were sharp pencils aplenty in the can. It looked, at first, pretty terrible.  But because I know my mathematicians, I could find the answers and interpret the hieroglyphics.

Next week my grade 3’s will be in a more independent place and I can get started on a unit for the 2’s so everyone will be engaged in work that is moving them forward instead of practice.  We’ll be able to do our regular Math Workshop work then, and I can spend more time conferring with groups instead of trying to get one group off the ground and the other group off the ceiling.

math, Number Sense & Numeration

Finding Connections

A few weeks ago, I sort of made my husband famous when I wrote about how he and I had each solved a problem about a good deal.  I had used an elegant solution, to quote Cathy Fosnot, and he had used the long division algorithm, which was just fine, also to quote Cathy Fosnot.  (You can hear the whole thing here.)

I had occasion to ask my husband to solve some math problems again this week, and I thought I should make sure that everyone knows he is my go-to double-checker. His methods may be old-fashioned, but he gets the job done.

I have applied for a Teacher Learning Leadership Project grant (TLLP) and am pretty close to getting it approved (I HOPE!!)  At the beginning of the month, I received a request for some clarifications about the project, which is apparently what they do.  Makes sense.  I am asking for just shy of the maximum allowed amount of money, so I’m actually glad to know they are making sure people are being fiscally responsible with this money.

One thing  I was asked to do was to make sure my budget aligns with the project goals.  I went over the entire thing with a fine-toothed comb, making sure I had the right number of days, and had figured it all out properly.  I have to account for the number of days each member of the project will be out of the classroom, and how much it will cost to provide coverage for the class.  My principal is joining, so I have also had to account for the extra money paid to a “teacher in charge”.  One member of our group doesn’t actually teach at my school, so I have factored in some mileage for her.  Even though I’ve been over it a few times, I needed someone to double-check it all for me.

I suppose you could say we worked as a team here.  I gathered the information we needed, and organized it into problems.  My husband, new to using an iPhone took one look at the work I needed him to do, pointed at his phone and asked, “Does this thing have a calculator on it?”  I showed him, and he proceeded to answer each question  on it’s own.

Again, the interesting thing here is that he didn’t see that he could solve one and use it to solve the others.  The 4 day option is double the 2 day option, but he didn’t use this. I think I am paying extra close attention to this right now because in my class we have been talking about splitting.  If we know that 40 + 50 = 90, then we don’t have to start over to solve 44+50.  We know it is 4 more than 90!  For some people, this might not be a huge revelation.  But for me, when I first learned to do math without using algorithms, these important connections between problems were completely missing. The only time I used anything like this was when I figured out 3 x 7 = 21 (for example) and then found all the 3 x 7 or 7 x 3 on a Mad Minute and wrote 21.  But I wouldn’t, for example, notice that if I knew 3 x 7 = 21 I could use that to help me with 3 x 8.

Connecting is one of the 7 mathematical practices in the Ontario Mathematics Curriculum: Grades 1-8 (2005).   On page 16, it says:

Experiences that allow students to make connections – to see, for example, how concepts and skills from one strand of mathematics are related to those from another – will help them to grasp general mathematical principles. As they continue to make such connections, students begin to see that mathematics is more than a series of isolated skills and concepts and that they can use their learning in one area of mathematics to understand another. Seeing the relationships among procedures and concepts also helps develop mathematical understanding. The more connections students make, the deeper their understanding. In addition, making connections between the mathematics they learn at school and its applications in their everyday lives not only helps students understand mathematics but also allows them to see how useful and relevant it is in the world beyond the classroom.

Since I have started to focus on teaching students to see the connections in math, I have noticed an increase in their over all number sense.  For many, as soon as they see a connection, it’s like a switch was flipped and they “get it”.


math, Number Sense & Numeration

Money, Money, Money

According to the TIPS4Math scope and sequence maps found at edugains, it was only going to take me 5 days to teach money.  I had 5 days before March Break, so it seemed a perfect match.  I mean, I thought it would take more than 5 days, but I had 5 days and wanted to believe that if I had enough faith I could finish all of the math stuff in those 5 days.

Then on Monday I found out we didn’t have to be at school on Friday.  (I pay really close attention to calendars, obviously.)  But that didn’t matter, because I had technically started doing some things with money the week before, so I was going to be OK.

Let me stop right here and say that if all I wanted to do was check the curriculum expectations off my list, then I would have been “finished” with all of the money stuff after 5 days.  I seriously would have.  But, I don’t know.  Money just seems like one of those things kids should not just do.  They need to understand money, even when they are 8 or 9, right?

Here’s what we did:

  • We dumped money out and identified coins/bills.
  • We made combinations of coins that were equal to a dollar, or $20 for grade 3 students.
  • We counted piles of coins & bills to find their total.
  • See…I’m practically done a day early!

If you haven’t ever seen The Pancake Menu, take a look here. Such a fun book and activity! We read that and talked about it, but I didn’t want to make pancakes again, so I told my grade 3’s to come up with their own cafe idea.  Then we ran out of time, so on Wednesday night after school I bought a bunch of stuff for ice cream sundae’s, plus root beer and dragged it all to school on Thursday.  I gave the grade 3s a blank menu and they figured out prices.  I told them each grade 2 would have $1, so they had to keep the prices low.  They did pretty well with this, double checking the addition with different combinations of toppings for the ice cream.

They gave each child a plastic Loonie, which I had to explain was a problem if they didn’t want to make all sorts of change.  So they counted out a dollar in different coin combinations for each of their grade 2 classmates.  Except some of the kids got more than $1 and some got less than $1.  Then the grade 2s came to the table to give their orders and everyone gave up on counting money because there was ICE CREAM within their line of sight and the grade 3s were in a panic that we’d run out before it got to them.  They were just taking all the money and the grade 2s were trying not to climb over tables to get their sundaes and thus did not care about receiving change. I was busy scooping out ice cream and training kids to use the whipped cream in a can (#VitalLifeSkill).  Then when everyone asked for seconds, I said, “Depends on how much money you have left.” and that’s when they realized they’d been ripped off by the ice cream sellers.  The entire class stared silently at me and my half-full bucket of ice cream, unsure if I was actually going to keep the rest for myself.  (I’m not going to lie – it crossed my mind. I had homemade hot fudge!)

Morals of the story:

  • You can cover all the money expectations in 5 days.
  • You will not have actually taught very many kids to use money.
  • You can’t assume children will have all had root beer floats. (#LifeChangingEvent)
  • You can assume someone will complain about not getting a third sundae, even though they have all received a second sundae for free.

When we get back from March Break, I am going to have everyone write out their orders for the grade 3 students, and they will figure out the actual totals, and then I will have them count out the right amount of money they would need to pay a cashier.  I will not be giving them more ice cream until at least June.

One day, not that long ago, my daughter, who is in grade 1, was convinced she had $21.  Can you see why?

She wanted to buy something that cost $21 and I told her she’d have to use her own allowance because it was something junky.   She names every coin, but she’s not unitizing the money yet, and doesn’t really get that each coin has a different value.  She can count by 5s and 10s, so she can count dimes and nickels if I am next to her walking her through it.  She’ll get there though!

math, Number Sense & Numeration

Math Is Everywhere!

The other day we arrived at school about 5 minutes later than usual.  It isn’t much, but it means we have arrived after the first bus has dropped off some children.  My 5 year old walked up to the boot line and started counting.  “1, 2, 3, 4, 5, 6, 7 and I am 8!  I am the 8th one here today Mommy!”  He was unitizing the pairs of boots and knew that 2 boots is equal to 1 child.  I was also impressed that he knew about “8th”.  He, for a long time, only seemed to understand 1st and last.  I suppose some of that comes from being the second of two children, one of whom is keen to point out when she has beat her brother at everything. He understands first because he’s been last a lot.  But eighth?  That was interesting.

This week I started participating in an online writing challenge I’ve been participating in for 11 years!  The participants are mostly writing teachers, definitely people focused on literacy.  I’ve been surprised how many, in just the first 2 days, have posted about their gratitude for not having to teach math because they 1) don’t feel competent at math, and/or 2) don’t like math.   I honestly don’t know how anyone could possibly spend any time in an elementary school environment and avoid doing math!  The boots are just one example of the math that I see all around us daily.

My school’s electives have just wrapped up, and every single week I found myself integrating quick math lessons into our cooking.  I know you’re thinking about measurement, but there were a million opportunities to count things. Did we have enough cookies for everyone to make an ice cream sandwich?  Were there any cookies to take home?  How many brownies would each person get?  Did we have enough bowls for everyone to have a serving of apple crisp, including the office staff?  If we counted up the number of children in the group, took into account the number of kids who said they hated pineapple-upside-down cake, and divided all the pineapple up, would there be enough pineapple to eat plain?  These were important questions that had to be answered.


Of course we do a lot of intentional math, but incidentally there is math around every corner, in every classroom, and definitely in every line of items or children!  Maybe the trick is to get the grown-ups to stop treating it like a room to be avoided.