Composition and decomposition (breaking a number into pieces or taking putting numbers together) is a key skill, whether the numbers are whole numbers or fractions, the bread and butter of addition and subtraction in grades K-5, and the prerequisites of 5-8 and beyond. It really helps students and teachers if the new skills and understandings we’re supposed to teach and learn are a lot like old ones, stuff we already know. (Math is often like that—or can be, when properly taught.) I’ve been playing race games with my students and with pre-service teachers for the last four decades or so, and I try to capture what it is we do that is so engaging and instructive for everybody.
Usually I introduce students (and their teachers, if I’m doing professional development) to race games in-person, by playing a game or two but I’ve realized that I need some kind of write-up that explains how to play a race game and what I thinking and saying to my students as the game progresses. Here’s a link to the latest version of that write-up in pdf format.