math, Number Sense & Numeration, Number Strings, Number Talks


I know it’s only Tuesday, but I’m in a “celebrate the little things” frame of mind.  It’s helping me cope, which is pretty important for teachers under stress.  And other humans of course.

This week, only 2 days old, I am teaching area and perimeter.  But I like to continue with Number Talks even when we’ve moved away from the computation portion of our work. Yesterday I started with one from Sherry Parish’s “Number Talks: Whole Number Computation” book. I chose one from the grade 2 section:  20-19, 20-14, 20-12.  We talked about how we could use all of our strategies from the math wall, but that counting up seems to work better than counting down.  We used the math racks for this activity, and I celebrated my own ability to say “subtract” every time instead of reading the problem as 20 TAKE AWAY 14.

Then today, we started with 20-19 (because one thing I have definitely learned from Cathy Fosnot and her Number String work is that starting with a helper problem is very important – this is not part of the Number Talks book work.)  Everyone remembered or quickly figured out that the answer is 1.  Then I wrote 30-19.  They weren’t so sure at first.  It took us a while to get to 11.  Some kids wanted to count all the way down (their go-to strategy).  Some wanted a math rack so I pointed out it doesn’t have 30 beads so what would they do, they didn’t have a plan. Some made random guesses AS ONE DOES!  We started to talk about our potential answers.  I purposely called on a student that I knew had the right answer AND that I knew could explain the thinking to share.  This child did a great job of noting that the helper problem was helpful.  If we think about how 30 is just 10 more than 20, but we still subtracted 19 then the answer should be 11, or 10 more than 1. I pulled out the math racks. I showed them 30-19 using a 20 rack and a 10 rack.  This way I could show how I added 10 more in but didn’t remove any more than I had the first time, leaving 10 more remaining after I “took away” or “removed” the 19 beads on the rack. After we did 40-19, someone noticed a pattern.  This is honestly the thing that makes me happiest sometimes.  Some groups of kids will notice patterns right away and then stop puzzling over the math because they have found the short cut.  But this class always takes a bit longer to see the pattern.  It’s fine with me, because we have a lot of good conversations along the way.  But I’m also glad when the pattern becomes part of our conversation too.  Even after this child thoroughly explained the pattern, some were skeptical.

Along the way I was drawing the number lines.  I decided to draw a new one each time because I wanted them to clearly see how each time the 19 didn’t change, but our starting and ending point did.  I also wanted to highlight the iterated units.

We talked about each of our strategies:  does it make sense to count up?  to count down?  to try and “take away” something?  to think of an addition problem that would help?

Two weeks ago I blogged about a moment when everyone was working independently.  It has rarely happened since. But it is happening, throughout our day.  Slowly but surely we are edging forward, and today’s math was a reminder to me that we are indeed doing good work. Not every day is easy.  In fact, today wasn’t that easy.  But this was my shining moment.

We’ll continue on with this tomorrow, but I will use some other number besides 19.  I am also going to write out today’s work on a chart paper because I think it will help us going forward and, therefore, deserves a spot on the math wall.


I need money for a taco truck

Sometimes I sit back at the end of a week and I can’t remember what even happened! That’s one of the reasons I’m enjoying my weekly reflections this year. It reminds me to sift through the feelings and find something positive. It’s easy to wallow in the discouragement of a busy week. I know I’m not the only educator who ends a week thinking, “That did not go as planned!” Or “I’m basically a failure and I’m wasting everyone’s time! Or “I wonder if it’s too late to trade this all in and buy a taco truck.” I mean, how many bad days can a taco truck operator actually have? I bet a taco truck driver never goes home feeling like a failure!

This week we talked about money. We finished the week being able to identify every Canadian coin and it’s value. We know why we need the cent sign and dollar sign. We even counted money quite successfully. We were not incredibly successful completing some math work sheets but everyone does understand that a horizontal math question and a stacked math question are asking us to figure out the same thing. That’s big learning for some kids. And we sang “Canada in My Pocket” a lot (though less than I would have liked.)

So yeah…clearly I was not a failure as a teacher. Nothing really exciting happened. Nothing made we want to rush home and blog. I don’t have any photos of our week. But we still had a successful week. Not a very exciting week, but, yeah, successful.

I’m thinking, however, that if I’m kind of bored with math (I didn’t even title my reflection last week!) then chances are other people are bored with it too.  This week we are moving on to some 2D and 3D geometry.  Or we might move on to area.  In the math long-range plan I am following shapes are up next, but I’m at a different place than I though I’d be at this point, so I might do area first.  Geometry fits nicely with the holidays because there are a lot of crafty projects we can do with our shapes.  Every day between December 1 and the last day before Winter Break gets harder and harder, and crafty math helps us get through. Plus we can talk about snowflakes a lot, and there is a lot of geometry in snow flakes.

Sounds like I’ve talked myself into area first.  Maybe we can figure out the area of the perfectly sized tortilla for my taco truck business.


Monday night and I just realized I never posted a reflection for last week! It was sort of normal, not very exciting week. I’m headed into a week of guided math in which I’ll be working with small groups to do sone learning about money (not very exciting) and everyone will be at other centres solidifying their math facts by playing math games.

It’ll be fine.

But last week I did notice how often our calendar is being accessed by kids. I saw a blog post this summer (I’ll try to find the link!) and decided I would display the whole calendar on our wall this year. I put up the 10 school months and then started the year, intending to find time to make it fancy.

One week in somebody added his birthday. Then we had to add everyone’s birthday. We added assemblies a field trips. During the first week of October somebody asked how many days until Halloween, so we added all of our major holidays, which lead to a lot of other holidays being added. There is a steady stream of people at the calendar counting how many days until this or that. The calendar has lead to many one-to-one conversations about time, counting forward and back, and important days for our classmates. (News flash: not everyone celebrates Christmas! This was news for many of my students.)

I’ve also been creating PicCollages of class photos to create a visual timeline. I need to get October printed! (Ugh!) it’s fun to look back at those memories too.

I haven’t done a class calendar in years. I thought it took too much time and space. But this very casual calendar, with no forced routine for its use, has been such a great addition to our class!

math, Math Workshop, Number Sense & Numeration, Number Strings


What does “-” mean in math? As in 5-2=

We had an excellent conversation about this during a Number String this week. I went off script after discovering that some of my friends didn’t know how (as in “no idea” how) to subtract 23 T-Shirts from their inventory in our math lesson.

This is what we decided:

The next day we talked more about “take away” using the math rack. Then we talked about how we can count back on a number line. Then we talked about how we can actually count up on a number line in order to find the space, or difference, between 2 numbers. One friend was very keen to keep explaining how adding and subtracting are opposites, and during one explanation solidified his own understanding of how he uses what he knows about adding to subtract.

I had my strings planned out for the week, but on Wednesday I realized we actually needed to do something different than planned. Literally everyone in grade 3 is doing well adding double digit numbers. They need more practice for sure, but the Strings were not moving us forward. At the same time a weaker skill (from way back in grade 1) popped up and I felt it was a good time to address it.

I’m thinking more and more and more about how math learning happens on a developmental continuum. Everyone travels along the continuum at a different pace. Hopefully nobody dawdles in one place for too long, and hopefully they remember what they’ve learned. I’m confident everyone has past experience with subtraction. However, for some reason, it didn’t stick. It’s for this very reason I had my grade 2’s dawdling in their own spot on the Landscape of Learning all week. They played games that had them practicing addition facts, and started creating their own flash cards to take home and practice. Next week they’ll be doing the same with subtraction facts.

Data Management, math, Number Sense & Numeration

Snow Day Math: Data Management

We had our first Inclement Weather Day on Friday, November 1.  In my school, and I think this is true in many schools around here, we double up classes on a snow day.  Few children come those days and it’s a great chance for kids to try things out in another room, see old friends, and get to know or reacquaint themselves with a new teacher.  For a teacher it’s a great chance to get caught up on things. I worked on some necessary paperwork that has been bugging me. The teacher I partnered up with did some Running Records.

For the last 80 minutes of our day, my teaching partner and I had the students together.  We decided to have them gather data this year on Snow Days.  We wondered how many children were in the school that day, and what kind of information we could get from the numbers.  We sent teams of students to each classroom to ask how many students were in each homeroom that day. We then gathered together and reported our data.  We organized it all on a chart.  We had a great discussion about the numbers:  Which class had the most students? Which class had the least?  Which classes had the same?  We wondered if the numbers will stay the same for every snow day.  Were the numbers smaller than usual because it was the first snow day and the day after Halloween? We noticed that some of the older classes didn’t have many children in them and the younger classes generally had more.

We even calculated the total number of students in the school. My grade 3 students were able to do this!!  We had a great conversation about a strategy for adding up 20 numbers.  I think they’ll be able to do this independently next time…or nearly independently anyway.  I suppose that depends on how long we wait until the next inclement weather day.  I’m thinking now that we should figure out what percentage of the student population came that day.  We were a group of grade 1, 2 and 3 students, so percentages are above our curriculum expectations. However, I bet I can procrastinate house keeping for a few more hours by figuring out how to make some circle graphs of this data.  They should certainly be able to read those.

Our plan is to do this every time we have a snow day, then compare the data over a long period of time.  I wonder what trends we will see!   I’m excited to share this data with the children who were not in school on Friday and see what they notice about the data.

math, Number Sense & Numeration, Number Strings, Number Talks

Number Strings/Number Talks

Math was fine this week. We started doing more place value work while working on “The T-Shirt Factory” Context for Learning unit by Cathy Fosnot. It’s always an interesting one, but I actually didn’t do it with my class last year.  We weren’t ready for it until much later than this and when we were ready for it…I forget what we did instead.

This week was Halloween. That means an interrupted day on Thursday because of the Halloween Parade.  I anticipated a day of difficulty on Friday as well, and while we’re at it, let’s just admit that Wednesday wasn’t going to be easy either.  See how hard it is to stay on schedule?  That’s why we didn’t exactly stay on schedule with the unit.  However, I didn’t skip math any of those days – even the snow day on Friday!

I did a fun mapping activity with a Halloween theme one day when I was pulled out for a meeting, and we did a lot of work with the base ten blocks.  But every single day I made sure that we were doing a Number Talk.

During a Fosnot unit, there will be a lot of Number Strings.  But when I am not teaching a specific skill and want to review things that I hope everyone already knows or that I know they need to practice, I go back to Number Talks.  This week we used some from the Grade 2 section of the book “Number Talks” by Sherry Parish.  We started with single digit numbers and I found out on day one that most everyone understands commutative property.  I repeated a talk that would reinforce this with double digit numbers on the second day.  On Wednesday, Thursday and Friday we talked about the “doubles plus 1/doubles minus 1” strategy.  These strategies are now displayed on our math wall so we can refer to them often.

This week, I am doing Number Strings to support the learning in the unit.  Because I can barely remember what day it is on most days I have to write my numbers on a Post-it note.  These will sit on my lap top all week or I will lose them.  I find it also has me thinking many times during the day about what we are doing in math, which is good for my brain.

Some of these are from the unit and some are from my head.  I know my learners well enough at this point that I’m sure we will need to do practice the skills that are in these strings multiple times.  They’ll be practicing them while doing the work in the unit as well.

I’m going to finish off my planning today by making my anecdotal record sheet for this unit.  (Just double checked and I already made one a few years ago! WOOHOO!