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

Subtract

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.

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

Subtraction

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!

math, Mathematical Processes, Number Sense & Numeration

This week we did…something

It was a weird week for math. I spent some counting routine time counting backwards. They’re pretty good at it. I thought they could be independent as a small group while I worked with some people on something else. I was mistaken. We’ve still got some social collaboration and problem solving things to sort out. That’s the thing I’m reflecting on most as I move forward into next week. I know where I’m going lesson wise, but am still sorting through some of the mathematical process teaching I need to do.

Because of the work I’m doing to spiral in math this year I am feeling like I don’t have a lot of things to use for comments on progress reports. I’ve decided to focus my commenting on some of the mathematical process skills.

This week I’m realizing that so far I’m doing a lot of the selecting when it comes to the tools we use. I put a lot of work into making sure everyone knows how to use the tools properly. Now it’s time for me to talk about how the tools have specific purposes for which they are best suited. We can’t always choose the colour tiles because we like how they stack! It’s time to move along and choose based on what each tool helps us understand. I’m doing some guided math rotations this week, and want to come up with some opportunities for kids to articulate why they chose a certain tool.

That is going to lead us to some communication work. We’re doing okay with this when I am poking and prodding. Now it’s time for the students to think about being really clear with their communication. I’m going to jump in and set up a FlipGrid they can use to explain something they’ve done. They’ll have to think about how to make me understand their thinking when I watch the video at home (cause you know I’ll never find time or a quiet spot where I can view these at school!)

Finally…actually, I’m going to stop there. Don’t need to set too many goals at once, right? I’m also diving into “The T-shirt Factory” Context for Learning unit with my grade 3s and we’ll need to be focused on that math at the same time. Not totally sure what my grade 2s will do next week, but I’m sure I’ll get it sorted out.

It’s important to have a focus on teaching and doing math. But the seven processes are an important part of that we can’t neglect. In a problem solving based classroom students need to be able to do more than accurately find answers.

math, Number Sense & Numeration

Making 10

You know when something goes so well on Tuesday that you assume Wednesday is going to be a piece of cake and then on Wednesday everything goes so wrong that you have to stand back and ask, “What was THAT?”  Well, that was my Wednesday.

On Monday we made groups of 10 to count totals of stuff.  I took pictures.  We congressed and talked about how efficient it is to count groups of ten.

On Tuesday we made groups of 10 and then created a chart where we recorded how many groups of 10 we had, how many loose (ones…the singles that didn’t make a group of 10) and noticed how those related to the number I wrote down for the total.  I was blinded by all the lightbulbs going off over the heads!  We ended the day with a fun writing activity. I had a number which I flashed to everyone.  They had a white board and they had to recreate our chart.  If I showed 47, they had to write “4 tens, 7 loose = 47”  but in a chart that I don’t  have a picture of.

On Wednesday we counted stuff and I asked them how many they would need so that there would only be groups of ten – no loose, or single, items. It was a disaster.  Kids were doing all sorts of things but making groups of 10 was not one of them. Figuring out how many more they would need was also not one of them.

On Thursday I took a step back. Or maybe sideways. I had some great counting items from the resource centre.  I had bowls to put them in, which meant that everyone had somewhere around 50 items, which was a manageable number for everyone.  I started by showing them a math rack with 5 red beads slid to one side. “How many would I need to slide over so that I would have 10 beads on this side?”  They got it easily.  Then I pushed 10 over and asked how many I would need to have 20.  Then I did 15, and asked about 20.  Then I did 7 and asked how many would I need to push over to have 10.  I repeated with a few more numbers – if I had 8 how many would I need?  What if I had 12?  or 18? Then I handed out the bowls and everyone made piles of 10 and I asked them how many they’d need to have only piles of 10.  And they could tell me. I took pictures so we could discuss as a group. I am happy to report that THEY GET IT!  Then we played “Tens Go Fish” and all was right in the world.

My family will be driving for the holiday weekend, so I may not end up posting about Friday.  But my plan is to do a bunch of backward counting.  We have a holiday on Monday and I am away on Tuesday so I don’t want to move forward with the next lesson in the “Collecting and Organizing” Context for Learning unit.  We haven’t done any backward counting, so this seems like a good way to spend our math time tomorrow.

I’m wondering at this point of working with a new tool was actually part of the key to this success.  We have done a lot of work with my counting jars, and I think they already know the answers for many of these jars.  They remember that there are 8 bottle caps in one jar, and 47 beads in another.  Are they really thinking about these numbers still?  Or are they just sort of multi-tasking – half paying attention the materials and the piles of ten while also thinking about Minecraft? I feel like having a new item to count got them thinking about the counting again.

Another interesting thing happened on Thursday.  A child who keeps telling me that grade 3 is too hard listened to me give the instructions for “Tens Go Fish”. As I neared the end he got excited. “Madame!  I played this game last year with Madame G!”  It was the most enthusiastic I have seen him in math.  Making that connection to the familiar was so important for him! Was the game maybe too simple for most grade 3 students?  Yes.  Was it still useful? I think so.  They could think about this in a different way as grade 3s than they had as grade 2s. They are now pretty proficient with making tens, for the most part anyway, so this really was a practice.  But they are now thinking about how making tens is useful for problems like 32+18, or 17+13.  Next, the grade 3s are moving on to triple digit numbers, and I feel excited about what this will mean for their understanding.

 

 

math, Number Sense & Numeration, Number Talks

Estimating and Number Lines

This week we were focused on two things:  estimating stuff and counting to see if our estimate was close.  I’m feeling really good about it!

There were some fun activities we did that I think really helped.

First, I had some small jars full of stuff.  We started the week by reading a book about estimation.  Then I held up one jar at a time and asked everyone to estimate how many were in the jar.  After the second one, I sent them to their tables to practice.  They had a great time estimating how many paper clips, beads, erasers or rocks were in each jar.  We did this on Tuesday and on Wednesday.  (We didn’t have school on Monday.)

We also played a game that I first learned this summer during a free week of online PD offered by Christine Tondevold.  There were new webinars every day, and one of them featured Graham Fletcher.  He dropped counters into a container but students couldn’t see what he was doing.  They had to rely on their hearing to count along and then identify how many were in the container.  We did this each day last week as a counting routine at the end of the lesson.  On Thursday, I started with this activity.  We had estimated enough times this week that I was ready to take it to the next level.  I pulled out one handful of counters. I asked the class to estimate how many I had.  They turned to a partner and discussed, then I constructed a number line as we went along to show where everyone’s estimate fit on the number line.  They were all convinced that I had no more than 12, so that was the last number on my line.  Then, I dropped them while they counted.  I had 17, so we had to stretch out the number line.  Next, I took 2 handfuls and asked them to estimate.  They did a quick turn and talk.  The first child I called on said, “Well how much is 17 and 17?  Cause if you can fit 17 in one hand then you probably have double that amount.” I was excited about this response!  The child is in grade 3, and I thought this was prefect reasoning. I annotated his explanation as he explained how he added 17+17 (sorry…had to erase that before I got a picture.)  We all agreed that it was pretty likely that I had 34 in my hand.  We started to count.  I had 37, which we all agreed is pretty close to 34, so 34 was a good estimate.

After we had counted them, one of my friends suggested that maybe I had 47.  Win some, lose some, right?  But I put that on the number line and we discussed our answer of 37 again and I think that friend understood that I had 37 and how far away from our estimate 47 is.

An interesting thing happened while we were counting.  Thirty-seven is a high number for some kids to hold in their head so they were using fingers and counting out loud to aide their working memory. I wanted to talk about this strategy so that those who hadn’t done it would know it’s a strategy they could use.  One friend said that he had actually only been able to count to 10 on his fingers at first so each time I got to ” a group of 10″ (“Like 10, 20, 30…like that!”) counters he held up 1 finger. He knew he had 3 fingers and that is 30 counters, then he just had the 7 to go with the 30.  I tried to draw that thinking too.  This strategy actually lead really nicely into our lesson.  We are working on the “Collecting and Organizing” Context for Learning unit next, and counting stuff is the beginning of that unit.  He introduced to us the idea that things can be put into groups of 10 to help with organizing and counting.

We did a bit more counting on Friday.  Everyone tried to make groups of ten, but many aren’t yet convinced that this will help.  We’ll dive deep into this unit whenever we go back to school (hopefully Monday!) and I feel confident they will have it by the end.

We finished on Friday with the “Flying Cars” Esti-Mystery from Steve Wyborney’s new Esti-Mystery set.  It was a huge success and the students were so excited that their estimate was so close to the real answer.  I was so excited that their ability to both reason and explain their reasoning had come so far in just one week.

Up next on the spiralling document I have been following is more counting (forward to 100 for grade 2 and 200 for grade 3).  This week we did some hundred chart puzzles.  I had some made with 101-200 charts for the grade 3s to work on.  They all did pretty well.  They can now become a centre when I need everyone to do independent activities while I run Guided Math groups.  This will become really important in about 2 weeks (depending on if/how long schools are closed for the strike) when I want my grade 3s and grade 2s working on some different units. We also need to be able to count backward (from 50 for grade 2 & 3, and from 500 by 100s for grade 3s) so that will be the focus of our counting routines next week.

And look….nobody went to the washroom during our Number Talk that day!  Interpret that as you will.