Math Assessment

We give the students an internal math assessment three times a year. While looking at the assessments, I noticed that one of the first grade girls made an interesting mistake.

The problem was something like this:

33, 43, 53, ___, ___, ___

She filled in:

33, 43, 53, 36, 37, 38

I looked at that for a while and wondered what she was thinking when she answered that way. She can count after all.

Then I noticed that if you turn 43 around you get 34.

And then if you turn 53 around you get 35.

If that is what she did, she got the problem right. Too bad you cannot write numbers however you want.

Thinking Time

I started playing tennis about a year ago. I suppose I should say that I started taking tennis lessons about a year ago.

Yesterday during the lesson I had a lot on my mind. I was thinking about how I would continue to use my class's interest in the book Mr. Topsy-Turvy. The book is silly, and the students really enjoyed it, so I took it as an opportunity to talk about topsy turvy things. In the process it was great to see the kids really working their brains to turn sentences around the wrong way. (If they know the wrong way, then they won't say it that way my theory goes, but I have mixed feelings about it.)

I was thinking about the weekend and I was thinking about my tennis game and concentrating on the instruction I was being given. I was thinking about lunch because I was hungry. I had a lot going on in my head.

Except for when the coach says in his best English, "Drinking time!", the tennis lessons are all in Japanese, so I have to concentrate more than my fellow students. On top of that, they play futsol right next to us.

Then when we were practicing our serves -- more intense concentration -- the coach told me that he would be leaving at the end of the month, which was rather shocking. In addition, the assistant coach is also leaving, although not together per se. (They wait until the last minute to make announcements in Japan.)

So after the coach gave his announcement I needed some time to think about them leaving and I had questions like: What would they do from now? Where would they work? But of course I couldn't ask them because they are personal. I was also thinking about the proper response in Japanese. What should I say?

This all got me thinking more. I started thinking about my own class and how they are all ESL/ELL/EAL learners. All of them.

This year I have been more conscious of  giving the first and second graders time to think. I hope I am giving them enough. Just because they don't react right away doesn't mean they are not thinking about what we are talking about.

And now I am wondering what else I can do besides oral answers in English.  Maybe having them draw or write in their own languages might also help [those that need it].

Can You Make a Sphere From 2-D Shapes?

This is a question I posed to my class this week.

Our current unit's central idea is: We are from all over the world. Now we live together in Sendai. I wanted to do more art projects this year with my class (with art being the traditional definition) and I thought that linking Sendai's famous Tanabata Festival to math would be a thought-provoking project for the class.

Since tanabata decorations are streamers with a ball on top (I thought they were shooting stars, but apparently they are flowers) my idea was to have the students make it all.

One group started by making circles, having mistaken a circle for a ball, or sphere. But it was a really cool pattern. So I reminded them what the project was again and sent them on their way.

I went over to the other group (who were protecting their sphere like it was something out of Skunk Works)  where I found them working on good ideas, but they were all working separately. I understand that some  people work better alone, but I want these kids to build their collaboration skills, so I encouraged them to work together.

I went back to the other group to find that they started using hexagons. Wow, I thought. It is like a soccer ball. Thinking that they were thinking the same thing, I asked why they were using hexagons. Their answer was that they resembled circles. I really liked how they are putting trapezoids together to make hexagons as well as the rhombi. 

They attempted to roll the hexagon sheet into a ball, but it collapsed on itself.

I think we will have to use some different materials.


Just seen on T.V. -
Doubling the size of a wheel makes it twice as heavy.
Really? I have to test that property.

Does 2+4 = 4+2?

Today we were talking about the many different addends for a certain sum. On the whiteboard I put up ____ + ____ = 6 and I had the students come up with different possibilities.

I think their answers were along the lines of
3,3
4,2
5,1
6,0
2,4

I looked at the last one and I thought to myself, are 4 and 2, the same as 2 and 4?

So I posed this problem to the class: Suppose we are looking at our own class were our equation is ___ + ___ = 8. What are the two addends for our own class?

Again I got answers like:
4,4
5,3
3,5
7,1
8,0

My thought was 3 and 5 since we have three second graders and five second graders. But when I started asking the students about why they thought of those number combinations, I was impressed.

The boy who said 4,4 was thinking of 4 boys and 4 girls. Someone else said the combination was 8,0 because we were all Grade 1-2 students.

I was hoping someone would talk about our nationalities, but maybe it is better that did not happen. Nationality can be a sensitive topic.

After asking some more questions, we found out that we have four 7-year-olds and four 6-year-olds.

I wish we had more time today. We should look more into these sums.

The Four Color Problem

While reading The Elephant in the Classroom, I came across an interesting problem called "The Four Color Problem".

In the 1850's an Englishman named Francis Guthrie was put in charge of making a map of England and all its counties. He came up with a solution that you only need 4 colors to color a map so that there are no adjacent areas with the same color.

I gave this problem to my third and fourth graders last year, and they solved in in 10 minutes. I should have made more parts to it.

This year I tried the same activity (I am going to make some more) to see if they could do it.

It was fun to watch them puzzle over it at first, and then run with it when they figured it out.

iMovie Role Play

Our school just got iMove on 5 of our 20 iPads. The Grade 5-6 class made some really cool trailers on them and I was green with envy.

After kicking the idea around for a little while, I decided to try it out with my class.

The video evolved several times from when I first thought of it. At first I was going to use puppets to make a video of the kids themselves. But I decided against that when I saw how much time it would take them and how much time I would have to leave the rest of the class alone.

Then I decided to do a general movie trailer for our class. A kind of introduction for the world. I also wanted to see if iMovie was something that we will be able to use this year.

I am happy to say that it was better than I had expected.

I am not that happy with the final product, but I am happy with what the students showed they could do, and with a few things I figured out.

The project started out by brainstorming words that describe us. As with the class needs/rules, there was a lot more steering. That will happen a lot this year with this group of grade 1-2's.

The kids did come up with some impressive words though. We had teamwork, thinking, helping, our ESLRs, and some others I can't remember. (This is becoming a problem as I have used an iPad for photo "note-taking" and then I don't remember which iPad I used. One more reason for me to get one for myself.)

I also saw how having the kids act out vocabulary words is a great way for them to show the meaning. It was amazing that the students used the ESLRs in the brainstorming session, but could not give very good examples of what they were. Role playing allowed me [or will allow me] to grab their attention because they were so into the movie.

I can't wait to have them make their own movies. I would love them to create trailers for books.

I hope iMove will be OK on Monday and let me upload the movie to Youtube.

Just Do It

I don't normally inflate myself or try to point out what I did, but I am going to this time because I want this lesson to stick with me.

That was my idea.

This morning I was talking with the Grade 5-6 guy, and I looked out and noticed the corn was all smashed. We talked about it a little bit, and I mentioned, in my mind at least I don't remember if I had said it out loud or not, that he should take his kids out and look at it.

He did. I didn't.

From what I saw it was awesome. His kids were engaged. They had fun. They learned. We did a math assessment - that we didn't even finish.

Now, my class of Grade 1-2s would have had a completely different learning experience. After all, I brought out one of my students and asked him what happened to the corn and he said ants ate it. But I think that we could have learned a lot just asking questions and asking, why?

Here is the exchange I had with him:

Me: Why do you think ants ate it?

Him: Because there are ants there.

Me: Could ants push the corn down?

Him: Yes

At that point I am sure other kids would have challenged him.

I missed one of the greatest teaching chances I have seen in a while, and the lesson I learned today is to never pass up an opportunity like that again.