## Wednesday, June 17, 2015

### Mystery Numbers and a Tricky Pattern (math games grades 1-3)

who: Baan PathomTham grades 1, 2, 3
when: Tuesday morning
where: in school
what did we use: a pack of playing cards, some cube dice

While our second time with the older kids, this was actually our first time with the new 1st grade students since both were out sick last week.

Warm-up
This time, we wanted to play a tricky pattern game involving various ways to write numbers. To start, we all practiced writing the numerals 0-9 using Thai and arabic numbers. To help show the commonality of value, I also included little dot pictures for each. After that, we played a game where I started a sequence, then each child tried to guess and draw a number that would continue our sequence. Here is an example. The guesses that are crossed out are values that don't fit my rule:
 This is a re-creation of the actual play. Obviously, the kids have better handwriting than I do

This is a strange game where wrong answers give you more information than correct answers. See if you can figure out what is allowed to come next.

Our friend: The 100 board
We had used 100 boards last week, but I realized that the kids would need a chance to really examine them, notice, and ask questions about what is there. Here are the types of things we discussed:
• what is the largest number?
• what is the smallest number?
• how many spaces are there across the top? what about down the side? what about the long diagonal?
• when we go down, do the numbers get smaller or larger?
• when we go to the left, do the numbers get smaller or larger?
Another dice challenge: Race to 20
Armed with our 100 board, we were ready for a new dice game. I think this was my own invention, but I spend so much time reading about games and mathematical activities, that it might come from someone else. If you know who I should credit, please tell me in the comments.
# of players: 2
tools: 2 dice, a 100 board, a small object to mark our position
Game play: first player rolls both dice, chooses one value and adds that to the accumulated sum, moving the marker up to our new position. The next player takes a turn in the same way.
Winning: the first player at or over 20 wins .
Obviously, this gives some adding practice, along with reinforcing the 100 board as a tool for visualizing. After playing a couple of rounds, though, some strategy emerged when we got over 10 as we started to notice that adding smaller values was better than adding larger values. This was a slightly tricky observation since strategic errors don't necessarily lead to a loss, they just increase the probability that the opponent will win.

Most components can be varied: increase the number of dice, use non-cube dice, change the target from 20, increase the number of players. The last one, however, is a bit dangerous as it makes the game even less strategic, though I think that could also be fixed by creating partnerships for a 4 player game.

Homework
Homework this week is to play the Race to 20 (or a higher target) 5 times with a parent or friend and to test their parents with the original pattern rule.

Warm-up
We started with a couple of mystery number puzzles:

• Mystery couple 1: two numbers that add to 10 and have a difference of 2.
• Mystery couple 2: two numbers that add to 12 and have a difference of 4
Several students created their own puzzles to challenge me:

• Student mystery a: add to 16 and difference of 7. I told them to figure out the product of their two numbers, I would write down the product as well, and they could come back and check me.
• Student mystery b: add to 20 and difference of 5. Good to see some fractions come into play!
We didn't prescribe any particular way to attack this warm-up challenge. For students who were guessing-and-checking and got a bit stuck, we did help them organize their information into tables to make things clearer.

Challenge Josh: make 31 strategies
From last week's homework, kids came prepared with their variations of the make 31 game. For simplified games with either 1s and 2s or 1s, 2s, and 3s, they got to choose the target value and whether to go first or second. To my delight, there were conflicting views in each class, where kids had the same target value, but disagreed about whether to go first or second. I paired up those groups and we got to test it out. In a couple of cases for each class, I accepted the challenge and played against the kids. The results were mixed, I scored my share of victories, but was defeated twice.

More dotty dice
Remember, this family of games is itself a variation of tic-tac-toe, so we have a 3x3 grid, roll a cube dice, and add that number of spots to a square in our grid.  The first version we played was for each square to be filled when it got 6 dots, then the winner was the first to get 3 filled squares in a row. As an alternative, we tried playing so that the objective was to get a straight line that added up to 20.

This version proved unpopular for two reasons. First, squares would get filled with so many dots that it was hard to tell how many were there. Unsurprisingly, that was exacerbated because not every player was very neat about their dots. Second, it was possible to overfill a row so that it already had more than 20.  This week, we introduced a couple of fixes.

First, instead of using dots, we raised the idea of using tally marks. As far as I can tell, this is the whole point of tally marks, so not a surprise that it comes in handy for this problem.

Second, we changed the objective so that the target was any multiple of five, with the restriction that all squares in the line had to be greater than 0 (none could be empty). This variation proved quite popular, so it became the standard for the rest of the class. When played to win, this provides a lot of practice adding since there are so many lines that need to be checked.

 Challenge: what square was last played in the RHS version?

Homework
Play 5 rounds of dotty dice, either with the target being a multiple of 5 or, for a more challenging game, multiple of 6, 7, 8, or 9.