math, Measurement

Detour to Measuring

This week we took a slight detour on to some measuring.  We spent the week talking about making sure the measuring tool goes from end to end when measuring length.  We talked about the difference between length and width.  We talked about why we need to use standardized measurement tools.  (Most of my class are in grade 3, and that is the year students move from non-standard to standard measurements.)

One of the activities we did comes from the Effective Guide to Instruction (Page 99 of this document).  Last week I wrote about how I wanted my students to make more intentional decisions about which tools they choose for their math.  The day before we measured the paper snakes, we had measured our shoes. As always, the two most popular tools were the connecting cubes and the “special stones”.  Before starting with the snakes, we had a talk about why they like these, and which one is actually better for measuring.  I was excited at the end when most of them were talking about using the connecting cubes because you can take them apart and put them back together in different shapes.  One student told us they can be used to go around the perimeter of things.  Several of them talked about how the special stones, the colour tiles and the pattern blocks slip and move around, but the connecting cubes stay put which makes them easier.

On to the activity:


Two children also tried to use rulers and measuring tape.  Discussing their experience was a great way to wrap up the lesson because even though these are specifically measuring tools they weren’t the best tools for this job.

We had a really good conversation about which method was actually going to give us the real length of the snakes.  Everyone agreed by the end that we have to measure every part of the snake’s length, and many of them wanted them put the cubes into connected towers.  I was sorry that none of them thought to do groups of 5 to help make the counting more efficient.  That’s something we clearly need to work more on. We recorded everything on a chart and that’s where we started on Friday.  We talked about why everyone had different answers, and why it was important to have the same answers which we get when we agree on the units.  I told them about the king’s foot and how this wasn’t even that standard, and that even though a lot of grown-ups still talk about inches for certain measurements, we are going to focus on the metric system and I think they’ll agree that it’s a lot more efficient.  I had them wander around finding things that were the same size as a 1cm cube.  Then we used the rulers and the measuring tapes to find things that are 10 cm.

“Jack” refers to the word Jack on our poem of the week which is called “Jack-O-Lantern”.  The hand washing sign is a rectangle, so we had a good conversation about length and width and how rectangles have a different length than width.  And I have no idea why there is a mandarin orange on the board marker tray.  #PrimaryLife

I think it’s so important for them to have these many points of reference.  It helps them to estimate measurements.  They all now know that their fingernail is about 1cm and they will always have that fingernail to help them measure.  We even talked about how for me it’s only my pinkie finger because I have grown over time.

Next week it’s on to addition and subtraction.  But we’ll be coming back to measuring on a regular basis. This is actually the second week we’ve spent measuring this year, so now I feel confident that everyone has a pretty good idea of how to do it, and we can focus on practicing.  We are also going to do a fair bit of our measuring during art and science, especially when we move on to capacity and weight.

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.