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.

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Do you think they were having difficulty with the vocabulary or with the concepts? Students certainly aren’t accustomed to having decimals as part of fractions, so I can appreciate them having difficulty understanding exactly what that means. Not so sure about why dividing by one can be so conceptually difficult for some students.

I don’t think it was with the vocabulary. I had set up the problem as a long division problem and during my explanation I asked showed them a whole number over one as a fraction. I’m not certain if they are still having difficulties with division and fractions as a whole, or if it has some relation to not having a solid understanding of their multiplication facts and how that relates to division. I feel like, if I had more time, it would be a topic that I would have like to explore more with them to find a way to help make the concepts more natural for them.

I’ve found that too! Even my high school students will plug 6 divided by 1 into their calculator to get an answer.

But a problem might by the types of words you are using. Yes they should be learning these math terms, but breaking it up into language they will understand might not get you as many confused shrugs. Because I even had to re-read the statement to understand what the warm-up was asking. Also, the decimal probably didn’t help your cause.

But even when I broke it down in to pieces and asked something like “what number can I multiply by 1 to get 3?” there was still some kind of variability in the answers. Even in fractions, they had a hard time recognizing that 24 over 1 is the same thing as 24 divided by 1 and that is just 24. I can’t figure out if it’s a sticking point in the multiplication facts or if it’s the concepts that are distracting them from the basic arithmetic.