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.