What do you know about infinity? While teaching about fractions and decimals I often talk about the density property of numbers, or the idea that there always exists another real number between any two given real numbers. For example, can you name a number between 1 and 2? How about 1.5? Can you now name a number between 1 and 1.5? Sure you can! Let's pick 1.4. Can you name a number between 1.4 and 1.5? No matter what numbers you pick, you can always name a number between them, and you can do this forever.
Can numbers be infinitely big and/or infinitely small? Are there different sets of infinite numbers? These are great questions, and the just the very sort I want kids to ponder as they think about numbers and our system of numeration.
Here are two videos I like that nicely capture these questions and ideas.