math, Number Sense & Numeration

Update: Assessment

I’m interviewing everyone in my class to make sure my report cards are up to date and accurate. It’s been very telling!

I often get one-on-one time with students, but they are usually at different places in their work. During the interview, I’m asking the same 6-8 questions, and talking about the strategies the kids use from beginning to answer. One question in particular is standing out because so far my friends fall into 3 categories.

The question is: I have 7 crackers, you have 9 crackers. How many do we have altogether?

One child said, without pause, “16.” This child was confident, and didn’t falter at all when I asked how he’d gotten the answer so quickly. “I just know things like that.” When I asked other questions he was equally confident and had very efficient strategies.

Another child, same question: “…mumble…mumble…it’s…16?!” I asked for an explanation. “Well, I know 9 is almost 10, so make it 10, then 10+6…yeah…16.” Earlier in the year this child told me he solved problems by reading my mind until he found the answer. I’d say he’s made excellent progress in his meta cognitive and communication skills!

Another child, same question: “….2?” I repeat the question. “7!!!!” I repeat the question. “9!” I take a handful of counters out of the nearby basket & make a pile of 7, and a pile of 9. Then I say, “These are mine. I have 7. These are yours. You have 9. How many altogether?” Response: “If I take away 2, then we’re even!” And “Is it almost time to eat?”

So I put the counters away and write on a piece of paper “7+9” and the child says 16. Rote memorization for the win!

There are three things going on here, and if I made each of these three the team captain I’d have no trouble finding people in the class with similar thinking to fill their teams. Each of the other questions I’m asking further shows the thinking behind the answers I’m getting from the class, including showing me the preferred strategies each child has. It’s so much more interesting than just getting a worksheet filled with answers.

Data Management

Which is your favourite?

Halloween is a great time to gather some data and manage it. There’s so much candy to sort!

In my ongoing effort to do things like surveys and graphs in a regular basis instead of as a separate unit, I planned to ask everyone about candy today. I already knew that everyone could come up with a “What is your favourite _____?” Or “Which _____ do you like best?” question. I decided to change the question. Instead, I told the class that I think all candy falls into 5 categories: chocolate, gummies, hard candy (lollipops and Jolly Ranchers), gum and liquorice. Nobody fought me on this. I’m just realizing now we could have had quite the debate about this. Where, for example, would Laffy Taffy and Starburst fit? And what about Reese’s Pieces? But nobody thought of those until just now!

Because I was asking which candy they liked, they could answer more than once. Only voting once is always tricky for kids with a question like this because they like so many things. And, I explained, I actually don’t like liquorice but am willing to accept that some people might.

Here are our results, tallied and then graphed:

We counted the chocolate tallies. As I tallied the gummy votes, someone pointed out that gummy and chocolate were the same. We talked about how we could tell without counting, which was actually a revelation to several students. However, they noticed it on their own for hard candy and gum. I’m glad we could talk about this one-to-one correspondence because it will come up again when we start talking about multiplication.

Since we have 22 students, and only one was away, we had to figure out who didn’t like some of the candies. We talked about how many people were not voting for each candy categories. Finally, we talked about how just because I don’t like liquorice doesn’t mean I shouldn’t buy it for them. (Nice of me, right?)

I’m going to add this to our math walk tomorrow. I want it up to remind everyone about organized data, and how it’s so much easier to follow along with than the other kind (haphazard tallied scattered abroad.). By the end of the month I want everyone to be able to come up with a good question and gather data. We’ll mostly be doing this during social studies as we begin our study of world communities.

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! 🙂 )

Here is another of our questions:

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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!