Jill, I have worked with such kids for about 15 years in a district where i visit for about an hour a week 20 times during the school year. of course, i get to do much more than you can do in an hour. thee most i would hope for in a single 45 minute session is to give them some sense of both the mysteries (in the sense of the things that we find so interesting about math) and the pleasures of the subject. i like to do several things with kids in a single time frame. so if i don't interest some kids in one topic maybe i'll grab them on another. here are a fe ideas. as i've got time to put down.
Games are sure winners. Two i like are "guess my rule" and my own version of "21", a nim-like game. Guess my rule goes like this: (i tell the students) "you give me a number and i'll give you back a number. who has a number for me?" 6. i'll give you back 10. [i'm playing the game as i would the first time i was seeing such kids. i've played this with first graders as well as high-schoolers-even college students when i want to introduce the notion of function. but the version i'm describing is for first-time bright fifth graders.] who else has a number for me? 18. i'll give you back 34. oh, don't give the rule away [i'll say if someone tries to explain to others what i'm doing]. if you think you know my rule, tell me and i'll give you a number. okay, i'll give you 11. no, 11 doesn't give back 15. you invented a different rule. it's not my rule. in my rule 11 gives back 20. when most students have figured out the rule i'd call on several students to explain the rule in their own words. don't let them say, "i was going to say the same as ..." when they say that, i respond, that's okay. tell me what you were going to say, even if it's the same thing. rarely do they use the exact same words. if they like the game, you can try different rules. one i like is n squared minus one because kids will guess the rule in two different formats [(n+1)(n-1) and ntimes n minus 1] and be surprised that there are two different ways of determining the result.
another activity. take any question from math olympiads for elementary students, announce that this is a "quickie" put it on an overhead, give them five minutes to work on it. then let them discuss their answers and solutions. they will enjoy that. Here's one: A book has 500 pages numbered 1, 2, 3, and so on. how many times does the digit 1 appear in the page numbers?
i also like to give one of my favorite problems. since this would take several visits, i suggest you give it and leave them with it as you depart. tell them you'll be happy to discuss it with them; then leave your school phone number. A rope thief who is an excellent climber and always carries a sharp knife enters a very large room where there are two ropes hanging about a foot apart, 100 feet from ceiling to floor. If the thief (no gender implied) wants to steal as much rope as possible, how much is that and how would the thief do it. the only problem is that if the thief cuts the rope at a point that would require a fall or jump of more than 33 feet the thief meets with an instantaneous (and gory) death. if you let them discuss it, they will concoct all kinds of wonderful gimmicks which i always listen to, then announce in a mocking tone of sadness that, alas, there are no trap doors, the ropes are not close enough to the windows, the thief is an excellent climber but not a very good thrower of knives, etc. etc. i have other ideas, too. but i've got to go to class. please let me know how it goes.