## Monday, December 1, 2014

### Math Games Class 5

Who: Baan Pathomtham 1st and 2nd grade classes
Where: Bangkok, Thailand
When: after science and before lunch

Special note for class parents:
Thanks to all the parents who have been playing the math games with the kids. They were really excited to talk about it and it shows how much they appreciated working on the challenge with you.

The homework this week is to investigate some patterns. We haven't found a great translation of this word into Thai as there seem to be different words for each of the slightly different meanings. As you help the kids with their work, you can encourage them with the following questions:

• What do we notice?
• Why is this happening?
• What do we think is happening next?
• What can we do to test our prediction?

It will be great if you can spend some time talking about these issues, even if you don't feel that they got to a particular "answer."

Today, we had a slightly different lesson plan:
• Skip counting
• Talking about the snugglenumbers game from last time
• Exploring some patterns

Skip counting
For each class, we gave them a number to skip count and P said an initial number.  For example,
skip count by 2, starting with 0. We would go around the class at least twice. Today, we skip counted by 2, 3, 4, and 1/2.

This was intended as a fast warm-up, so we didn't choose anything that was particularly challenging. Even so, it proved to be good practice for nearly every student.  Also, there was a moment of deeper interest in the 1st grade class when we were skip counting by 4 starting with 1 and someone asked: "will we get exactly 100?"  That led to a good discussion of the pattern and then the class was really interested to keep going to see if they were correct.

Snugglenumbers game
The kids were all enthusiastic about this game which, frankly, has surprised us a bit since the game play is very limited.  They wanted to talk about whether they won or their parents.  For grade 2, we posed the following questions:
• Are there any numbers that are very helpful? if so, can you say which are the most helpful and why?
• What is the maximum possible score? Does it matter whether you are playing with one deck or two?
We didn't have an exhaustive discussion for either set of questions. For parents at home, I would encourage you to discuss these questions with your children.  Full disclosure: J1 and I had already discussed the question of the maximum possible score last night, so I had sworn him to secrecy for the class today.  As it turned out, we didn't really discuss this in grade 1.

Patterns
This activity was shown to us by David Ott, the K-12 math coordinator at ASL, one of whose recent exploits can be seen here: Family Math Night.

Set up: using construction blocks, I set up 5 patterns, the hide them in rolled-up paper, then hide those in a small bag.

The big reveal:
One pattern at a time, one cube at a time, I reveal the colors. At most steps, I will ask the kids for a show of hands to vote which color they think comes next.  Rotating around the room, we then ask for some explanation of the choice. I will usually also tease them a bit to encourage them to think more broadly. When they have all settled on a particular pattern and agree (which I don't force or encourage) then I whose the whole stick and ask them for a continuation, for example, what color is the 20th or 40th or 100th cube in the sequence.

The reaction
The kids absolutely loved this activity.  They were really excited to predict what would come next, eager to argue their view in the voting and then really emotional when the next cube came out and either matched their expectation or disproved their prediction.

Here were the patterns we used today:
 Simple tools to cause mathematical delight

What is the color of the next cube for the pattern on the far left?  If the glare makes it hard to see, it is pink-red-pink-pink-red showing. What is your reasoning?  How many other possibilities can you think of for that color and what is your justification?

If the pattern in the middle stick is repeated, what is the color of the 100th cube? What if I tell you that the pattern I want to extend is increasing whole number red series with a single green separating the runs of red?

P introduced this game two weeks ago and blogged about it here: http://3jlearneng.blogspot.com/2014/11/math-games-class-3.html. As she wrote at the time, this is a really good game.  We played two rounds at the end of each class and I was really struck by how much respect the kids showed to themselves and each other.  They took their time calculating, didn't get frustrated, and those who discovered their number faster were encouraging for the other students. To recap: everyone is dealt a card that they hold on their forehead and the teacher reveals the sum of all the cards.  Students then try to figure out which card they have.

In second grade, we played with a full deck, making J= 11, Q= 12 and K= 13 (A=1 in both classes). In first grade, we took out the face cards so we had A through 10.

One other modification is once there are 3 or fewer students left and they seem to be stuck, we tell them the sum of the cards from the remaining players.

I would encourage families with several kids to try this at home.  An alternative version is to have everyone take a hidden card, then reveal sums of 3 cards.  Feel free to experiment and see if you can find another version you enjoy.

Homework
We asked students to work on the two more complicated patterns, the increasing reds with green punctuation and the increasing pink and red stick.  The questions they were asked were:

1. What is the color of the 100th cube? How do they know?
2. If the red/green pattern has a red cube in the 100th place (a strong consensus among the classes) then what is the place of the closest green cube to 100?
Note: these questions can be answered by brute force, building the sequence or writing it down. What we would like to encourage is, of course, looking for patterns. For example, for the red-green pattern, do they notice anything about where the green blocks appear?  Can they make predictions about when another green will occur?  In the pink-red pattern, can they say when a block of reds has ended, do they notice anything about those places?