If you had an hour a week to spend with a low-achieving 3rd grader, over say, six weeks, what would you focus on with them?

It's a good question. I've gone through it many times.

You can't do much with an hour in a week for six weeks, even with a 3rd grader. That's the bad news. The good news is that if you get him or her to work with you, and give them a second hour, you might be able to do something. What I would focus on depends on what I find out about what they can do. It also depends on how they take in information. Most people (almost all) learn either by hearing or seeing. Most younger children learn better by doing than by being told.

Always try and make some of what you do physical. You didn't mention the subject area, but I'm assuming mathematics because that's where you listed it.

Find out what your jurisdiction expects a third grader to do. Talk to the teacher if you are the parent of such a child. The process of learning is an extremely complex task. Don't take it on if you are flying blind and are unable to talk to the teacher. You need to be the parent or you need to take the parent along. In almost every place, no teacher will talk to someone who is unrelated to the child.

When you know more about the child, post again. I don't know exactly how you can contact me again (perhaps making me a friend), but when you know more, you are perfectly welcome to contact me again.

I'm not sure if this is exactly an opinionated question but I'm going to answer in my own personal opinion. In third grade I really struggled with memorizing Division and multiplication so honestly I would work on that and memorizing the multiplication table and just I guess how to do division and I would also teach that third-grader all of the life hacks for remembering answers to multiplication questions. For example I would teach them the products of 9 lifehack.