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Place value can be so challenging to students. I also have had many questions recently.
I would tend to ask an additional question before I evaluated if they understood the difference between hundreds or tenths. What might it look like to ask about an application of .3 Vs .30... Where in the world might each of those make more sense or be applied?
I also just had a similar issue and was encouraged to do a number talk called more or less than 10. We gave problems such as this :
8.75 + 1.9
We asked students to reason if it was more or less then 10 mentally. It really helped me to see which students struggled with .9 versus .09
It was amazing how many said 9.84 without reasoning the place value mentally. Very eye opening for me.
If we are teaching students that 0.3 is equal to 0.30 then how can we not accept either as a correct answer for rounding 0.34 to the nearest tenth?
My question would be are you grading on a standard based system or a point system based on correct/incorrect? I am not suggesting it is not an equivalent number but I would want to ask a follow-up question before I measured their progress toward the standard.
I am very interested in hearing more about your thoughts.
Rounding is a difficult concept for many students to understand, and it may be that it's usefulness in not clearly explained. For example; we always round money to the nearest cent, why? because we can't pay anything less than a cent.
Recent emphasis on estimating has made rounding much more important. It took me a while to figure out that using calculators made estimating more important so we know when an answer is clearly way off.
That is such an interesting question Mary Lou. My question (to myself) when asking students to round is "What is my purpose?" When we use rounding, as adults it is typically to make something a bit easier to deal with rather than using the original number or when we are estimating, right? In the CCSS, rounding is used as an estimation strategy to think about reasonableness of an answer: http://www.corestandards.org/Math/Content/4/OA/A/3/, so that is really interesting to me and makes me think that the answer 0.30 is absolutely correct. It is 3 tenths, which is 30 hundredths, which would be the same reasonable answer to a question that asked students to think about a reasonable answer to a question.
Hope that helps!
Yes I always tell my fourth graders the zero after the last digit is nothing.hope that helps.
Very interesting question indeed. I would say there are different answers to this question. Think in terms of real life context: what if you were talking about money? Rounding .34 dollar to the nearest tenth you would could say .3 dollars or 30 cents or $0.30 - all logical and correct ways to think about it in real life context. However if you are strictly evaluating the understanding of tenths place versus hundredths place then .3 seems like it demonstrates that understanding better.
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