When I introduce an idea and have students practice a few problems in class to see if they are getting it, I walk around and individually help students. Neighboring students other also help each other out.
What do you do, however, when a few students who “get” things right away finish before the others? The rest of the class seems to get it, but it just is taking them a while to work out the problems. What do you do with these kids? Do you just have them sit quietly?
Sometimes I’ve had them: (1) make up their own problems for me to possibly use on a future assessment, or (2) walk around and ask if anyone else needs help. Most of the time I let them sit. I feel like I should have a good way to deal with this. But I can’t always ask them to make up their own problems or walk around. It’s a temporary solution.
Ideas? Strategies? Do we all struggle with this?
Currently, I’m thinking that each time I put problems up, I should put a couple up, and then put one “challenge problem” too — and then have the expectation that students finish the standard problems, and say that if you don’t have time to get to the challenge problem, that’s totally okay.
Continuous Everywhere but Differentiable Nowhere 
I like the challenge problem idea. Many students who finish early actually enjoy feeling the accomplishment of getting it right.
You could also ask them to prepare to put one of the problems on the board to teach the class in a few minutes. You could have them teach it out loud or just write the work up there.
If it is an extra long time, you can keep some Sudoku or other math/logic puzzles in the room for them to work on. I have this game called “24” (not sure how famous that is) where students get 4 numbers and using +, -, x, / they have to make the number 24 out of them. The smarter students enjoy pulling that out and challenging their math skills.
I’ve heard two solutions:
1. Put up more problems than any of them are likely to finish. The quicker ones will get farther. I like your challenge problem idea better, though.
2. If you notice Billy is done announce to the class, “Billy is an expert on this problem and open for business. You don’t have to wait for me, you can ask Billy to help you.”
I do #1 more than #2. Mostly because kids are resisitant to moving around.
First, let me say, I’m not good at this either. Help other students. Work on other homework. Would you like a puzzle? Enjoy your nap….
I used 24 with one of my Algebra 1 students last week. We didn’t have quite enough time to complete a card, but I’ll pull it for her again in the future. It is aimed more at her level than your students, but I’m borrowing the deck from my sister who was the type of student who got things done first.
omg is it snowing on your blog? I thought there was something wrong with my eyes.
@Dave, Kate, Sarah: Thanks so much for your replies.
And yes, it is snowing on the blog! WordPress lets you add that feature until January 4th, when it’ll turn off. Cool, no?
Do you have computers with Internet access in your room? If so, couldn’t they get on selected sites and further their knowledge or be challenged by other things? If I ever put up challenge problems, I’ll get a few that want to tackle it but I’ll also end up with sandbagging. Some students don’t want to do more work, there are games that make the work more engaging.
Simply have them study next topic