Wednesday, June 24, 2015

Deep Tic-Tac-Toe and tangram initials (1-3rd grade math games)

Note: we did 1st and 2nd grades in parallel this week.

First Grade


Our simple warm-up this week was a little before/after game with the days of the week and the months of the year. Starting out, we had a little discussion (debate) about what day it was (Tuesday, at the time). Then, what came immediately before and what came immediately after?

For months, no one was quite sure of the current month, so we talked about that for a moment, then talked about which months would be coming up. We should keep repeating and integrating into some other games so the students can get more comfortable with the sequence of months.

Clap and pat patterns

Moving on from the warm-up, I asked if they could guess some clapping patterns, where I would either clap my hands or pat my lap. Too easy, they both exclaimed. Okay . . .
Pattern 1: I clap 5 times and then ask them what comes next.  More claps! (admittedly, this was easy)
Pattern 2: Alternate clapping and patting (C-P-C-P-C-P) and then what comes next. Again, pretty easy for them to continue C-P-C-P. It was actually a step trickier for them to continue if I ended my sequence on a clap (so their continuation goes P-C-P-C etc)
Pattern 3: Same deal, but pattern is C-P-P- C- P-P etc. At this point, they were clapping and patting along with me to make sense of the patterns.
Pattern 4: C CP CPP CPPP CPPPP CPPPPP etc. Now, here's where it got complicated! We did this one several times.

Next time, we will do these patterns visually as well as aurally.

Tic-tac-toe Game

We played a couple rounds of classic tic-tac-toe (also called X-O here in Thailand). As we played, I asked them questions about what they noticed:

  • how many spaces are there on the game board?
  • how many lines do we draw to get those spaces?
  • What shapes are the spaces?
  • When we draw the board in the usual/lazy way (2 horizontal lines, 2 vertical) do all the spaces have the same number of border edges?
  • If we made more lines, how many spaces would we get?
  • At the end of the game, how many Xs and Os are there? Is it the same number for both?
  • Do they prefer to go first or second?
We had several reasons for playing. The first is to encourage their habits of noticing and wondering. Even in such a simple game, there are a lot of mathematical things they can see and talk about. Our second reason is to prepare for the huge number of tic-tac-toe variations that we can play with number recognition, arithmetic operations, and more involved strategy.

A colorful pattern

We continued our exploration of the 100 board and the bead abacus with a coloring activity. This time, we wanted to color the even numbers (multiples of 2) and not color the odd numbers. For both of the kids, though, they preferred to use different colors for the two types of numbers rather than leave anything entirely plain. As they worked on each new number, they used a 100 bead abacus to figure out whether the number was an even or an odd.

Before beginning the activity, I asked if they had a guess about what pattern would result at the end. There seemed to be a consensus that we would get a checkerboard pattern. After working for a while on the first row, though, one student suddenly had the idea that the evens and odds would be in alternating columns. An interesting conjecture!

I promise pictures of the results next week.


Play X-O 3 times with a parent or older sibling and finish coloring their 100 boards.

Second and Third Grade


We used a warm-up game similar to last week. When someone has two secret numbers, can we figure out their values if we know the sum and the difference?

Tangram intro

In class, we worked on classic tangram rabbit and fox outlines. This was a really good exercise in paying attention to detail. For most of the class, students would claim to have a solution and we would point out something in their outline that didn't match the target (for example, a horizontal line where it should be on a diagonal or vice versa).

As with tic-tac-toe for the 1st graders, there is a lot to notice and wonder about in the simple tangram puzzles. For example:
  • How many pieces are there? What are the shapes, what are the sizes?
  • If we are using only some of the pieces, can we make the same shape in different ways? Trying to make different types of right isosceles triangles is one version of this.
  • Which edges match exactly?
  • What angles can we match up?


Make their initials with the 7 piece tangram. As many versions as possible and, if they want, try out other letters/other shapes.

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