Subtraction Games (math class 2)

Who: Baan Pathomtham First and Second grade classes
Where: at school
When: mid-morning

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Today was our second session playing mathematical games with the younger kids at J1's school. Another fun session with a new game the kids can teach to their parents.

As usual, we were too occupied to take any pictures.

Agenda
We are settling into a standard agenda:

1. Warm-up questions: quick questions that are intended to require 10-20 seconds of thought, but are not very challenging for the kids.
2. Mathematical observations: based on a picture, the kids practice making observations about number, measure, shape, sequence, etc.
3. Something from an old game
4. A new game
5. Homework

Old Game: Euclid
As a reminder, the rules for this game are here: Euclid's Game.
Last time, we played on a 100 grid with the second graders and a 60 grid with the first graders. This time, we had them all on a 100 grid.

To start out, we had a refresh by playing the game once: the kids on one team and I was on the other team. As we played, I did the following things to spark thoughts about the game:
(1) always explained full equations to justify my moves. Example: 40 (pointing to the 40 that has already been crossed) minus 5 (pointing to the 5 that has already been crossed) is 35 (crossing out the 35)
(2) I got them to say full equations and had one student per turn cross out the number for their move.
(3) I asked them to confirm my calculation.  Sometimes I said the wrong answer, so this wasn't an empty activity.
(4) I asked them what was the largest number we could cross out in our game (once the first two numbers had been chosen)
(5) I asked them to look for emerging patterns in the numbers we were crossing out.
(6) I asked them to look ahead in the game to see who was going to win.
(7) I asked what would happen if we somehow manage to cross out 1 in our game.

After playing the game to make sure we all got the rules, I posed the following:
- last week, I saw two students play a game where the starting choices were 60 and then 36.
- What pattern of crossed out squares do you think emerged by the end of the game?
- Do you think you can start with 60 and 36 but get a different pattern?
- Who do you think won?

Look: another 100 grid for you to cherish!

Note: even though this game seems to only involve subtraction, analyzing the game and finding a winning strategy is more related to multiplication, division, and factoring.

New Game: Card subtraction
Source: Motion Math

Another subtraction game with a nice feature that many people can play at one time.
Prep: take a standard deck of playing cards and remove all 10s and face cards.

Each round:
- Deal 4 cards to every player
- Deal 2 cards in the center, the first of these becomes the 10's digit and the second the ones digit in a 2-digit number that is the Target
- players make two 2-digit numbers with their 4 cards and find the difference.
- Players then find how far their difference is from the Target and this gives their number of points.
- Lowest points win

For example, say we deal 5 and 3 as the central cards, making the target 53. Now, let's say one player gets an 8, 7, 2, 3.  One way they could play is making 38 and 27 for a difference of 11.  That is 42 away from the target for the round (remember 53), so they could claim a score of 42 points. Think about it and you will see that there are other combinations that get much closer to the target and score far fewer points.

Observation: the two digit subtraction problems that come up in this game were challenging for the kids.  When playing this game with your children, encourage them to use the following tools to help with their calculations:
(1) write down the calculations on a piece of paper
(2) use concrete objects to work on the subtraction questions
(3) use the 100 grid from the Euclid game.  Ask them to show you how they can use this grid to help them analyze a subtraction problem.
(4) use a number line.

Let us know what other strategies you use.

Finally, encourage them to look for patterns and relationships.  What pair of 2 digit numbers could they form that has the smallest difference? What about the largest difference? Which grouping gets closest to the target? which gets farthest? Are there several combinations that are the same difference from the target?

Homework
Euclid:
- play a game with your parents and show the grid to us at the next class
- try the game starting with 60 and 36.  See if you get the same pattern we got in class?

Card subtraction:
- play this game with your parents or siblings for 5 rounds (or more!) and bring us the scoresheet.