Monday, January 12, 2015

Calendar Tricks and Break the Bank (math games class 8)

Who: Baan Pathomtham 1st and 2nd grade classes
Where: In school
When: after science and before lunch

As our warm-up today, we played calendar games (one for the 1st grade and 2 for the second grade).

Choose one month on the calendar. In my examples, I'll use January this year:

 Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Without telling me their choice, the children select a 2x2 square with 4 numbers and add them all together. They tell me their sum and then I 'magically' know which square they chose and write it down.

For example, they might say 44 and then I write down:
 7 8 14 15

Homework: to think about how I know which numbers they chose.
They should play with some examples and look for patterns. In particular, what is the smallest sum they can make? What is the largest sum? Do either of them depend on the month? In a given month, if they form as many sums as possible, do they notice something about all of the sums?
One point we did discuss was whether the 4 numbers are related. Because weeks are organized in rows, we know that any square has the following pattern:

 N N+1 N+7 N+8

Parents: using concrete examples, ask your children to explain this pattern. Why are the numbers on the lower row 7 greater than the upper row?

Determined Determinant

We only showed this next trick in 2nd grade. I'm not going to go through all the details since the kids wanted an opportunity to try to amaze their parents. Here's what you'll be asked to do:
1. As before, choose a month on the calendar
2. Without telling your child what you've selected, choose a 2x2 square with 4 adjacent numbers
3. Now, multiply the bottom left by the top right
4. Multiply the top left by the bottom right
5. Subtract your second product from the first
7. They will tell you the answer you got
Just to make this a bit more clear, using our example from above:

 7 8 14 15

You now calculate $14 \times 8 - 7\times 15$, but don't tell your child what you are doing. They will tell you the answer.
Homework: Again, try to figure out why this works. Play with patterns, look at parts of the calculation. Have fun practicing multiplication and think about different ways to do the calculations.

New Game: Break the Bank

For the first time, we are playing with dice. This game comes from math 4 love.
2. Repeat 6 times for the 2-digit game, 9 times for the 3 digit game
4. If your sum is 100 or greater (for the 2 digit game), you get 100 points. If it is 1000 or greater for the 3 digit game, you get 1000 points
5. If your sum is lower than the threshold, you calculate your points as Threshold - sum
6. Player with the least points wins
Homework: Play this game as often as you can. Think about these other questions: what is the largest sum you could get? What is the smallest sum you could get? If you knew all of the numbers before entering them into the grid, what is the best sum you could achieve? Can you always form numbers that stay under the limit?

Observations

The children really enjoyed these tricks and games. As we were playing with them, there were many opportunities for interesting little discussions and ideas from the children. As a result, these activities were much more engaging and stimulating than we might have guessed from the written explanation on the page.

Example: Nikki's idea for 7x15
During the Determined Determinants trick, Nikki needed to calculate 7x15. She got several pencils out of her pencil case and said:

• here are 7 pencils
• this pencil is 15
• two of them are 30
• Grouping them in pairs, I can skip count by 3, so 30, 60, 90
• I have one pencil left over, so I need to add another 15
• Together, I get 105
P asked whether someone taught her this technique. She said that she discovered it on her own.

Example: I know I've busted!
Playing Break the Bank, Tanya exclaimed: "Oh no, I know I've already busted!" Looking at her grid, she had five numbers filled:

 6 4 2 5 6

Jin and Ji Ping were next to her, so I asked the there of them: "Are you sure Tanya has busted already? How do you know?" Part way through the discussion, one of them said: "no, this just adds up to 95, so it isn't busted." They thought for a bit more and then realized that the next digit would add at least 10, so, busted indeed.