I’ve found it interesting how much difficulty some of my students have with multiplying and dividing by 1. I think they do know, at some level, that one times any number is just that number. But it seems like when it is applied in someway, they have a hard time seeing it.
For example, there was one problem that we did on the daily warm up. We were creating an estimate and had rounded our divisor to 1, and the dividend to 0.25. When I asked what my quotient would be I got a lot of confused looks and shrugs. With enough prompting, they could see that the quotient was 0.25, but I’m not 100% certain that all of them really saw it.
I’m not sure if this is because they feel overwhelmed by the fact there was a decimal in the answer, or if they really don’t have a solid grasp of that particular math fact.