Tag Archives: numberless problems

Numberless Math

BalletBoy has always gravitated toward just getting his math done. Ideally, he likes to have a page of all the same sort of problem, let me remind him how to do them, and then just do them all. However, as he’s gotten older, this has meant a struggle for him to some extent. As the math gets more complex, with more to remember, not having a strong foundation in the whys of math has led to more and more difficulties for him. If you’ve been reading this blog for awhile, you may note that he’s jumped around programs in the last year as a result. I’ve been trying to honor the fact that he’s pretty good at getting the algorithms memorized while still helping him understand the whys. Finding the right approach hasn’t been easy. Most things have been too easy or too hard.

Recently, the author of the excellent Let’s Play Math blog pointed me to the vintage book Problems Without Figures, which you can find as a pdf here. I immediately fell in love a little bit. Many of them have numbers, but there’s usually missing information so they can’t be “solved.” Instead, the question is focused on the process. If given this and this, can you find that? How would you do it? What other information might you need? Many of the problems can’t be solved unless you know more information. Others are easy, but they require a lot of steps. A ton of them require that you move between different measuring units. Many of them are filled with superfluous information.

There are also several trick problems. My favorite, by far, is the one that asks how you can find how old a coin dated 56 B.C. is. Obviously, a coin couldn’t be dated that (think about it…). The author of the book suggests that these should be sprung on students. I’ve already given the kids a few of these but warned them to look out for them. They were delighted to discover them and felt very clever doing so. I think it’s really good for kids to realize that the answer isn’t always straightforward, that it might be easier or harder than they anticipate, or that they might need different information than what you’re given or expect to need.

In general, I like the focus of having kids doing math that’s not about getting “the answer.” It changes the focus of math and makes it feel more approachable for BalletBoy. It helps kids with their writing as well. Mushroom has been using the Arbor School algebra series, which requires a lot of writing. I wish we had been doing these for a little while in preparation because they really focus a student on writing out a clear, step by step set of instructions for solving a problem. However, the small nature of the problems makes it feel like a doable task. Mushroom has struggled with the writing in the Arbor School series because it asks that he summarize everything he learned and give his own examples. This is such a small chunk and so specific that it builds good logical writing and thinking skills. Basically, it’s a great thing for kids to do for math, writing, logic, and thinking skills. Explaining how to solve a problem is just good across the board.

You may notice that many of the problems in the book are outdated. In order to easily use it with my boys, I updated the language for us. My next post is about that process and I’ll link to the updated version if you’d like to use it.