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.
One thing I’ve found interesting in student thinking is how students decide what operation a story problem calls for. When I was asking one student why he had decided one problem was a multiplication problem, it was because one of the items in the problem had units of something per something. Despite having worked to not connect specific words to specific operations, and stressing that you need to think about what the problem is asking, he still saw the word “per” and automatically assumed the problem was asking for multiplication (it was really a division problem). This was even with a specific set of notes, with a very similar problem, where we went step by step and solved it as a division problem.
It makes me wonder if there is a way to teach students how to look at story problems that allows them to move away from latching onto specific words and helps them to be more successful solving the problems. We’ve attempted having them write their own stories, in the hope that if they are writing a story using that operation, it would make it easier to identify that operation in a problem they are given. It seems to help some students, but other students still have difficulty in identifying the correct operation. I know it was something that even I had problems with up until college, when engineering courses present you with only story problems. I feel like there has to be a more efficient way, rather than hoping that constant exposure will make all the pieces click into place.