## Monday, June 30, 2014

What did we do?

Yesterday, we followed the plan very briefly sketched in our previous post.

Playing with the Balance
I started with the boys together playing with balance for a bit. They did a couple of rounds of some of the basics: finding a sum (add one weight to an empty side to balance the other side), a difference (add one weight to the lighter side), and then adding 2 weights (e.g., add weights to balance when you start with 9+6 on one side against 10+4 on the other).

This was a version Jate got after some playing around adding and removing weights on the left side of the balance:

Jin started asking about multiplication ("how much is 8 groups of 5?") and I challenged them to figure out a way to do these calculations on the balance.  I'm not sure how much progress they made in finding a technique because this devolved into causing the balance to crash. Their technique for a fun chain reaction:
(1) have a moderately heavy right side (maybe around 20 units)
(2) add a lot of weights to the 10 peg on the left side (getting to 40+ units)
(3) let go,
The result is that the left side crashes down, those weights fall off, then the right side crashes down and, if you are lucky, those weights also fall off.  If there are any weights still on the balance, it will crash one last time.

I didn't particularly encourage crashing the balance, so they found something else to do.

Percents and fractions

Jin moved off the balance first and went into the box of toys.  He found a collection of fraction and percent cards and set up a game of war (draw random cards and whichever card is larger wins). At first, they played together with just percents, so it was essentially the same as comparing whole numbers.  Mommy got involved and challenged Jin on fractions, accompanied by the fraction chart for reference.  This seems like a promising game for future warm-ups.

Abacus warm-up
Mommy next moved on to the Abacus math exercises.  Jin counted by two from 0 to get a sequence of evens, then again starting at 1 to get a sequence of odds.

Addition table
Warm-up done, Jin then investigated some patterns in add table, starting with highlighting the number bonds for 10 and 5. Jin noticed the SE diagonal was evens, so filled that.  Jate got his own copy and started filling the parts that seemed interesting to him (10 number bonds and the NW corner).

Some Venn
I didn't see how Mommy transitioned to venn diagrams or all of that discussion.  I came in after the whiteboard had most of this on it:

I started asking about friends who I knew to be only children (no brothers or sisters). That led to a bit of discussion about where they should go in the diagram, with Jin eventually writing them outside the two strings. I'm not sure he was satisfied with that approach, though, as he scribbled out the names.  I think we should come back again another time to the idea of elements that aren't part of any of the named sets.

In the meantime, Jate had been playing with the hundred board tiles and came up with this picture.

Actually, 90 and 99 hadn't been completed, so we asked Jin if he could guess the pattern and finish the picture. He did and we were off to dinner.

Bedtime
The requested book was A Place for Zero. They had read it before and both were interested in telling me how the machine worked to create new numbers from old ones. Both were really excited to discuss what would happen if Count Infinity got sucked into the machine as an addend (they thought another infinity would come out, no matter which other addends got sucked in.)

Finally, they asked about "that turtle program," so we wrote some pencil code. Jin said what he wanted the turtle to do and Jate helped with the commands that he remembered from 2 weeks ago. I was really surprised how much Jate remembered.  Here is the simple code they wrote: gun

Tomorrow
Not sure how much time we will have, but here are some ideas:
- Jate play w balance by himself
- more simple pencil code after dinner
- baking with Jate (probably do this on Wednesday)