when: just before bedtime
the value of being aliveJ1: Daddy, now I've got a question for you
J1: if I get a new book every time I write 20 pages in my journal, how valuable is each page?
J1: The books are about 150 baht
J0: How much?
J1: let me check, I think the price is on the back cover . . . 169 baht
J0: if you could tell me what I need to calculate, I'll calculate for you
J1: hmm, so 20 pages is 169 baht, I want to know how much one page is, so I need to divide by 20.
J0: do you think it will be more or less than 10?
J1: less than 10
J0; Are you sure? How do you know?
J1: Well, 10 * 20 is 200 which is more than 169
J0: what about 5 baht per page? Is it more or less than that?
J1: More, 5* 20 is half of 10*20, so 100, which is less than 169.
<we figure out that the amount per page is 8.45 baht/page>
J1: That's not very much!
J0: How much did you get for your birthday?
J1: [x] from grandma, [x] from grandpa
J0: well, how much is that per day. Is it more or less than 10?
J1: More than 10
J0: how <interrupted>
J1: how do I know? well . . .10 * 365 is ...
<some discussion of whether he was right, various other estimates of the amount of money per day>
J0: How does that compare with each page of your journal?
J1: More...but what if I include the [present a] and [present b]?
<he estimates how much different presents cost, figures the total, estimates how much that is per day, etc>
J3 (who has been listening all this time): wow, J1, that's a lot of money!
J3 explores bricksEarlier in the evening, J3 has been building sticks with 1x1x1 TRIO cubes. She made four, all the same length, then handed two to me as drumsticks. I counted the cubes in one (I got 11) and then she counted one of hers (she got 12). I put them side-by-side and we saw they were the same length.
J3: but...daddy, I really counted 12, you are wrong
J0: are you sure they should have the same number.
J3: yes, let's count them again, together
<I point at the cubes and she counts them, 11>
J3: Ok, now I'm going to build a shape and you see if you can make a copy. It will be tricky!
A birthday puzzleWith their current ages expressed as whole years (you know, the way everyone talks about ages, except for mothers of very small children):
- What is a number sentence that relates the ages of J1, J2 and J3? Hint, oldest is 8, middle 5, and youngest 3
- Will this ever be true again?
- Was it ever true in the past?
- When/why not?
- What about multiplying? Will it ever be the case that AgeY(J1) = AgeY(J2) * AgeY(J3)?
- Was this ever true in the past?
- When/why not?
J2 wanted to investigate more precisely, so he asked to work things out in months. That meant we had to calculate how many months are between them.