This whole circle is built from activities described in the book Games for Math by Peggy Kaye.
- Topic: Reducing Fractions. Book: Fractions in Disguise by Einhorn. A millionaire collects fractions for fun, but then a villain steals a rare fraction and tries to disguise it. Only reducing the fractions to their true values can find the lost fraction.
- Topic: Addition, Subtraction, Number Properties. I performed a math magic trick. Each kid picked a three digit number where no two digits could match, e.g. 581. Then I turned all their numbers into 1089 by:
- Reverse the kid’s number.
- Subtract the smaller number from the larger. (e.g. 581 – 185 = 396).
- Reverse the result and add it to the result (e.g. 396 + 693 = 1089).
- Topic: Logic, Strategy. I taught the kids “Tapatan” a tic-tac-toe like game. Each person takes turns placing one of their three stones on the board. After all six stones are placed, you take turns sliding the pieces from point to point along the board lines. You cannot jump over another piece or land on top it. The first person to get their three stones in a line (vertical, horizontal, or diagonal) wins.
- Topic: Logic, Addition. I gave the kids a series of ‘number bubble’ puzzles. Place the given digits in the bubbles to make each row add up to the required sum.
How did it go?
There were only two kids this week, so it was a good, focused circle. My daughter had a few angry moments, but settled down after some warnings.
Fractions in Disguise
Both girls really enjoyed this book. The mystery of the stolen fraction was quite compelling, but they were each a bit reluctant to spend energy trying to reduce the fractions in the book.
The kids were quite impressed by this trick. Right away they started trying to figure out how it worked. One girl noticed that the middle digit is always 9 after the initial subtraction. Both kids wanted to try again several times.
I told them there is one class of numbers that the trick does not work for. Eventually, my daughter stumbled upon it. If the first and last digits are consecutive, then the final answer will be 198 instead of 1089. For example: 231 – 132 = 99, 99 + 99 = 198. We noticed how the subtraction always results in 99 in this case.
This game proved to be pretty fun. The girls quickly started thinking a move or two ahead to make sure they didn’t let their opponent win. My daughter was quite a poor sport whenever she lost, crumpling up the board, or throwing the pieces. The other girl was very calm during these tantrums. There is a lot more to this game than to tic tac toe. We added one extra rule: you cannot undo a move on your next turn, i.e. you can’t move a stone back to the same place it had been the previous turn. This helps prevent stalemates.
Both girls quickly got the idea of these problems, and had some good insights. On the first class of problems, with the 4 bubbles in a cross shape, my daughter quickly noticed that you should always put the middle two numbers together, and the largest and smallest together.
Later, when we switched from the L-shaped 5-bubble puzzle to the cross-shaped 5-bubble puzzle, both girls independently realized that they could reuse their answer from the L-shape. This was a great insight.
We stayed late at circle a few minutes, because both girls wanted to finish all the bubble puzzles.