Freeform tangrams: an imagination game by J1

Who: J1, J2, and J3 (a late appearance)
When: just before bedtime
What did we use: two sets of tangram pieces

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J1 came up with a new game this evening. The rules:

• number of players: 1 or more
• playing pieces: 1 or more sets of tangram pieces
• designer: each round, one player takes the role of the designer, putting the tangram pieces into a configuration. This could be a random arrangement or intentional
• Taking a turn: in a clockwise order starting with the person to the left of the designer, players say what they think the tangram looks like from their perspective. After everyone has taken a turn, the players shift 90 degrees to their left and repeat the cycle, but this time they are looking at the tangram from a different orientation.
• Once everyone has had a go from all 4 orientations, the next player becomes the designer
• Advanced play: once someone has said what they think the tangram looks like from their perspective, the experienced players can add a comment to start building a story based on that object.
• Winner: everyone!

We played with J1, J2, and J0 taking turns as the designer. To give you a feel for it, here is one of our designs from 3 different orientations:

Here are some of the ideas for what we saw: person jumping out of a box, a wheelbarrow, an army officer, a flower, an 8th note in a mirror, a catapult, a road grader, a knife cutting an apple, the sword in the stone, I was surprised that no one said "poop," which just shows how engaging the two of them found this activity. I doubt it would have been as successful if I introduced these rules and asked them to play!

Our own puzzle book

Thai tangrams and pattern blocks (math games grades 1-3)

Grade 1

Homework 100 board
For homework, both students colored their 100 board to emphasize even numbers. They were excited to talk about the pattern the recognized: stripes on the page. This links back and we used to compare with one of the later patterns in our warm-up.

Warm-up patterns
Following our clapping patterns from last time, I thought it would be helpful and fun to add a visual component. I repeated the pattern cubes activity from last year.

For each pattern, I reveal one cube, then ask them to guess what color comes next and why. After we revealed the whole pattern, then we would clap the pattern, using hand claps for one color and lap claps for the other color of the pattern.

For the alternating pattern (in our case, red-pink-red-pink) we compared with their 100 board pictures of evens and odds.

Have blocks, will use them
After going through the patterns, the kids wanted to play with the cubes. They did several impromptu investigations, partly inspired by the fact that they both ended up with different collections of cubes. Here were some questions we discussed:

• how many block do they each have? Turned out to be 14 and 21.
• how many blocks are there all together?
• are there an even or odd number?
• which color is more?
• what are some different ways we could group and count?

Dotty six
The kids played dotty 6 with dice. This was something we discussed two weeks ago with the 2nd and 3rd grade classes.

Homework
Play dotty 6 (or dotty 10) with their parents and color the multiples of 3 on the 100 board.

Grades 2 and 3

Tangram investigations
After working on creating some animal and letter outlines, the kids were already pretty familiar with the 7 piece tangram set. This time, we added some more structure to the investigations:

1. sort the pieces by number of sides
2. Create new triangles from subsets of their 7 piece sets. These can be hard because the kids have the extra complication of needing to decide which pieces to include and which to exclude:
• Make a triangle from 2 pieces, 4 pieces, 5 pieces
• Make non-square rectangles of with different numbers of pieces
• Make a square from 2 pieces, from 4 pieces, from 5
3. Order the pieces from smallest to largest. This generated a lot of discussion for the shapes that were difficult to directly compare, particularly the square, the middle size triangle, and the parallelogram
• Which pieces are the same size?
• What are your reasons for the ordering? How do you know what is larger?
4. Area calculations: taking the smallest triangle as a unit, what is the area of all the other shapes? What is the area of all the shapes together?
5. Create squares using different numbers of pieces: 1 - 7. Are there any numbers which don't have a solution? What is the area of each square? Are there different ways to do it, for example, 3-piece squares that have different areas? 

Thai letters
Josh made 4 Thai letter outlines for ก จ อ ช:

The kids have several associated challenges:

1. find solutions for Josh's outlines
2. make their own, improved, versions of Josh's letters.
3. make their own Thai letter, vowel, tone mark, or number

Looking online, we couldn't find any tangram puzzles involving Thai letters, so this is our gift to the rest of the world!

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

Warm-up

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.

Homework

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

Second and Third Grade

Warm-up

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?

Homework

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