double trouble

[topaz]

Morgan's homework today included this problem (reproduced here verbatim):

If you have one dice with the numbers 1, 2, 3, 4, 5, and 6. Expressed as a fraction, what is the probability of rolling a double (2 of the same number) in 25 rolls?

The probability that at least one number will come up twice is clearly 100%.  We're assuming that they're asking for the probability that at some point two consecutive rolls will turn up the same number.

This seems like a remarkably sophisticated problem to assign a sixth-grader.  It looks like it would have been a reasonable problem for my probability midterm in high school.  Does anyone here disagree?

Edit: The problem was not made up or handwritten by the math teacher -- it was submitted as part of a Math 4 Today handout that he gets assigned on a weekly basis.  For better or for worse, this was part of a standard curriculum math workbook.  (And they wonder is our children learning anything!)

Comments

[jwg.livejournal.com]

I'm impressed by the fact that such a question is asked of a 6th grader. (if course it should have been worded properly). And to me what is important is not the answer but how the student goes about trying to find the answer. In my year teaching 7th grade science (eons ago) I used to ask tough questions and ask the students to explain bow they'd find the answer trying to illustrate how the method used for problem solving is what will help solving other problems.

[dbang.livejournal.com]

I have a bit of a beef with asking young students to explain "how" they got an answer. My 4th graders complain about this incessantly. "Mom, the question is 'what's 18 divided by 9' and they want me to explain how I got the answer. can I write 'duh'?"

Of course I want kids to learn to think things through, but you have to ask questions complex enough that there IS a thought process required. For kids with a strong intuitive grasp of math, asking them to come up with some illustration for their problem solving just slows them down.

On the other hand, my youngest son, who is autistic, often writes down the thought process HE took to get to an answer and it's...well, it isn't a path any non-autistic person would grok. It amuses me to imagine his teachers scratching their head with "huh?"

[qwrrty.livejournal.com]

That makes sense, and the teacher tells us the same thing: she doesn't care so much whether he finishes a particular problem set or does every problem as long as he demonstrates that he understands the principles.

Unfortunately, I don't think that was the intended goal here. Maybe I should have posted a scan of the sheet. It's an 8.5x11 sheet with sixteen problems, printed in a 4x4 grid. There are four square inches of space for each problem, including the text of the question itself. There's no ROOM to explain your reasoning or show your work (a constant frustration when the problem set includes long division puzzles).

Of course he could write more on the back of the page about his reasoning, or use a separate sheet. It just seems like that's not the intent of the exercise here. This all points up some of our ongoing frustrations with the local school and its curriculum.