math, Number Sense & Numeration, Number Strings

Back in the groove

On Wednesday of this past week I realized I had gotten back into the groove of teaching math. I had been in it but fell out at some point. I knew I was not enjoying math and that I was feeling every day like I had missed the mark – the lesson was too easy, or it was too hard, or there were some interruptions that derailed us too easily. At some point I realized that there were so many different math strategies being used in the class that it was hard to have a conversation about our math. I decided that this week we would talk about all the strategies but we’d focus on making sure everyone could use a number line. We finished the Fosnot “Measuring for the Art Show” unit in about 3 days (should take more than that, and has typically taken me 10 days.) I decided to spend some time doing number strings and reinforcing the use of the number line to do it.

Here you can see we are using a lot of different strategies. Someone even suggested the traditional algorithm and several students knew how to use it. I’m crediting “at home learning” for that because this hasn’t happened in many years for me!

After two days of this, I asked everyone to complete three problems that I put on the board. They each have a whiteboard they were using to do this. “Do these three problems, and then you I want to take a photo of you and your work. Then you can clean up for lunch.” I thought that was good! But several of them were annoyed at ONLY being given 3 problems. I had to add more to the board. So, to recap, they wanted to do more math instead of get lunch.

I finally said, “Look, if you want to do this all day you could make up problems for each both er.” Then they spent the rest of the day making up problems for each other. A few of my friends weren’t sure what to do. I cancelled reading groups for two days to do math groups instead. By the end of that they knew how to add double digit numbers with the Base-10 Blocks and with the number line. We’ll get to the mental math eventually, but I needed to give them a few strategies to hang on to until then.

This week we’ll move on to another Fosnot unit called “Ages and Timelines” which has us focused more on subtraction, or rather “finding the difference” between two numbers. I feel like it will be a good fit for us.

I’m not sure if completing all of my math interviews would have helped. I still have a few to go (lots to go!) but what I already know about the class is that we are coming to the math from a variety of places. One of my small groups clearly knew what they were doing even though they had struggled with the first lesson and had given themselves a ūüė¶ when I asked everyone to self assess. I asked them to explain.

Them: Well, I didn’t know this is what you meant.

Me: You don’t know I wanted you to add the numbers?

Them: No.

So, to recap, after two days of me saying “Add these numbers up.” They didn’t know what I meant. Like I said, we’re coming at this from a lit of different places. But I think we’ll mostly be in the same place, together, by the end of next week.

math, Number Sense & Numeration

We can make our own number lines!

I’m not going to lie: ¬†making the jump to drawing number lines independently has taken a while! ¬†All the grade 2s can explain what I am doing on a number line, and all of them (ok, most of them) can describe a strategy and when I draw it on a number line they confirm I have drawn what they were doing in their heads. ¬†But to make their own? ¬†That’s been hard.

We had completed all of the activities in “Ages and Timelines”, one of the Context for Learning Units, and people were still referring to tools (hundred chart mostly, they they tried to use math racks unsuccessfully) so I wanted to spend an extra week just talking about how to use that number line AND draw it independently.

One day last week, I created some Smart Notebook slides and we all sat down the chalkboards. ¬†Here’s the first one,along with some notation to show that people were flexible with strategies…they used both addition and subtraction to find the answer. I will say that those who added were surprised some had used subtraction, and those who subtracted were surprised that addition could be used, so we had a great conversation about this slide! (Oh, and we are collecting paper towel tubes for science! ūüôā )

Here is another of our questions:


I wandered around and captured some number lines. ¬†Now, this might not be beautiful to you, but darn it! ¬†It is gorgeous to me! ¬†Look at the line, the iterated jumps, the acknowledgment that 4 jumps of 1 is the same as 1 jump of 4…*sigh* ¬†I’m smiling again just thinking about it!


I caught one person who was struggling, and handed that child a hundred chart, with a 25 chart on the back.  For this problem, this child was able to use the 25 chart, but for later problems, had to use the 100 chart, and did! img_0677.jpg

Another beautiful number line… Another great demonstration of the iterated units drawn evenly and there even arrows on the end!


One of the most amazing things that happened is shown here. ¬†One child had a 100 chart and was using it well. ¬†Another had no strategy and was looking around the room to see if she was alone in this dilemma. ¬†As soon as she spotted the 100 chart, she scooted over to it. ¬†However, upon arrival, she realized she wasn’t sure what to do. ¬†The other child showed her!!! ¬†(There is a sock on one child’s hand because we use them to erase the chalkboards!)

So, it took us an extra week, and I am quite sure the number of grey hairs on my head has doubled since March Break. Next week, mixed in with some probability to math workshop centres, I am going to be sitting at a table interviewing these lovely grade 2’s to see what they can really do all on their own. ¬†Can’t wait!


#notabookstudy: What Next?

We are still working on the “Ages and Timelines” investigation. ¬†We worked out the difference between the ages of Carlos and his family, etc. ¬†Next, it was time for everyone to calculate the difference between themselves and their family.

I expected, anticipated, that some would have a tricker time than others.  Given the ages of their siblings, which are not always nice landmark numbers  like 10 or 15, I knew some would struggle a bit.  I also anticipated that because this part of the investigation is more for individuals some would struggle without a partner to talk through the work.

I was right.

But what I didn’t expect was the number of children who came with the answer. ¬†I said, “How old is your mom?” and they said, “She is 33, and she was 25 when I was born.” ¬†I didn’t expect so many children to then have trouble putting this together as a number line. ¬†I mean, if you know where to start (8) and where to end (33) and you know the number of jumps in-between (25) then making the number line should be easy, right?

It wasn’t.

So my next step feels like a backward step, but I have decided it is a sideways step.  We need to go around this obstacle, learn a little bit more about number lines, and then move forward.

ALSO: ¬†I didn’t anticipate the halves. ¬†As in, “I am 9 and 1/2.” or “My brother is 14 and 1/2.”

I feel like this week, so far, 2 days in, has been all about being responsive to student understandings. ¬†In the example above, I felt I had two choices. ¬†One would have been to teach that child how to deal with the halves. ¬†We could have talked about using a decimal, or about using the fraction to figure out a more accurate answer. ¬†My other option, the one I chose for this child at this time, was to say, “We are going to forget about the halves for now.” He has a tentative grasp of this whole “finding the difference” concept. ¬†Letting him stick with the whole numbers will help him solidify. ¬†Talking to him about the decimals or fractions would muddy the water. ¬†He’s in grade 3, the curriculum doesn’t require us to talk about the decimals or adding/subtracting fractions.

For the next two days I am going to do a part of this unit that my colleague skipped with her class: creating a timeline.  She felt it was confusing her class, but I feel like it will be useful to mine.

And at the end of the day, isn’t this responsive teaching what ditching the textbook is supposed to be about?