We have entered the world of rational numbers in 6th grade. We are working on building our fluency with different representations of fractions: moving between fractions, decimals, and percents. A perennial question that emerges, "Is 0.99999 (repeating) the same as 1?"
This year, I asked the class to tell me what they thought before any explanation was given. There was a clear majority who felt like 0.9999... was not equal to one. There was heated debate and we had to work on how to speak to each other so we could understand the other's point of view. We recognized that repeating the same response is not going to help someone see another point of view. The challenge is finding another way to explain it help someone see from a different perspective.
We capped off the discussion by watching the ViHart video (above). There is a lot of information to take in and unpack, but there are some very convincing arguments. For homework, the class was asked to reflect on where they stand on the questions now. Many students found reasons to change their thinking and a few are steadfast in their belief that 0.9999.... is not equal to one.