This is part of a new series about how to help yourself or your kids improve in mathematics. It’s based partly on my own experience of having to learn how to learn mathematics, partly on extensive tutoring experience, and partly on many conversations with homeschooling parents, as well as parents struggling to understand Common Core mathematics. Many future editions are already planned, but feel free to leave suggestions for future editions in the comments (open for paid subscribers) or by email to hollymathnerd at gmail dot com.
The first five posts are not behind the paywall; all future posts will be; this link will give you 10% off. If you’d like to get them but can’t afford a paid subscription, email me at hollymathnerd at gmail dot com and I’ll give you a free one.
Previous posts in the series:
Part 1: Addition and Subtraction
Part 2: Multiplication, Division, and Fractions
Part 3: The Major Key of Mathematical Fluency
Part 4: A Proof for this Approach to Numeracy
Part 5: “I’m Just Not A Math Person!”
Part 6: How the Sign Rules Work, and Why
Part 7: The Box Method of Multiplication
One way I manage wintertime depression—the kind of thing I experience when there’s so little daylight that the sun comes up an hour after I start working and has been down for an hour when I finish—is to do a lot of number theory problems. They’re fun, and challenging, and engrossing enough to get me out of my emotions.
I have long thought that number theory is something kids should be exposed to starting in middle school. My friend Gator wrote a brilliant introduction to modular arithmetic, something that typically only very advanced high schoolers in AP courses or math majors/minors ever learn, that’s accessible to middle schoolers: you can read it here.
For today’s post, I’m going to show you that number theory is both really fun and not at all beyond an average adult. Don’t worry, we’ll go slow and it’ll be fun!
Here is a problem from the book, 104 Number Theory Problems from the training of the US IMO Team. (IMO = International Mathematical Olympiad).
Sounds intimidating, doesn’t it? I promise, it’s not! You’ll understand it before I’m done.