I was hoping that you would reply..Your estimates surprise me in two ways. I am skeptical that the numbers are that large. But also, problem 1 is first because I thought it would be the easiest. You can visualize a clock and see that in half an hour it will be 10:05 and then add an hour.

For the second one would it matter if I said 100 days instead of 37? I had in mind that they would realize the relevance of 37 being 2 more than a multiple of 7.

For the third, yes, I could tell them how many days. Here I can well imagine using pencil and paper. It could be tough to get it all organized in the head.

I see these questions as being different from finding alternative ways of multiplying 18 X 12. Asking them to do this multiplication is telling them what calculation to perform, even if the detailed method is not stipulated. It has no specific real world connection.

Another story. I have told this before also, but I swear it is true and it will explain why I am skeptical of the 90%

I was in a generic McD type of place. One line over the amount due, let's say $16.27, was announced. The customer gave the cashier some money and received change.

Customer, No, I gave you a $100 bill, not a $20.

Cashier, checking the drawer. Oh! I am sorry. Yes you did.

Total crisis. The cashier had rung it up as 20, the register said the customer was to get $3.73 in change. Nobody knew how to reset the cash register so that 100 could be entered. The cashier talked to an older cashier. No idea. They went over to talk to the guy doing the french fires. Nope.

I intervened. Everyone agreed that 100 was 80 more than 20. I explained that since the customer had given the cashier 80 more than the 20 she rang up, the cashier should give the customer 80 more in change than what the cash register said. Everyone agreed that this sounded fair, it was done, and they could go on to the next customer.

There were either three or four people behind the counter, and one customer, all trying to think of how to figure out how much change was right.

This seems pretty basic. I would love to believe 90%, or even 75%, with my questions but I am not so sure.

I thank you for your estimate, and I would like to hear from other teachers. Or from other parents, except that I have found that everyone's child is at the top of his/her class and very advanced.

I may do some experimenting with some random 12 year olds.

Added: I assume that if, with the clock problem, I asked what time it would be after five and a half hours the number of correct answers would go down?