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I am teaching at the remedial level in college and I am trying to put together an argument on why we should explain the notations for mixed fractions and the terms proper/improper fractions before we test to see if students can skip the class. My theory of the case is that it has been some time since they have ever used these terms/concepts and we should give a brief reminder of the concepts before we test them (That way students who are capable should be able to do it).

However, I'm having trouble with my google-fu figuring out just when do students stop using these terms. Answers would ideally be in order of preference: Florida, United States, International.

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    $\begingroup$ When you say "give a brief reminder", are you thinking of putting some definitions at the top of the test? $\endgroup$
    – Nick C
    Sep 4 at 14:01
  • $\begingroup$ Aren't things like $5\frac14$ sufficiently widespread in ordinary life usage to not require explanation, or is the concern whether students know what the phrase "mixed number" (or "mixed fraction") means? The second canned food item I looked at in my kitchen cabinet, Campbell's SpaghettiOs with meatballs, has under the microwave cooking instructions "... on HIGH $1\frac12$ to 2 min. or until hot". (continued) $\endgroup$ Sep 5 at 17:07
  • $\begingroup$ Mixed numbers appear in recipes and blueprints and carpentry (at least, when English measuring units are used), in stock market values (apparently until maybe the last 15-20 years or so, according to a quick google search to double check stock market stuff), business texts and writings, and many other places I could list if I decided to write down all the places I see them (which I haven't, and don't plan to, so I'm only mentioning what first came to my mind). $\endgroup$ Sep 5 at 17:07
  • $\begingroup$ @DaveLRenfro I'm not questioning their use in real life or the idea that its worth teaching them, I just want to know how long it has been between a student last encountering them academically and entering college. If there is a significant gap I can argue for a brief terminology refresher before we give them a high stakes placement test. $\endgroup$
    – Alan
    Sep 6 at 6:09
  • $\begingroup$ @Alan, so you think it is acceptable that college freshmen have never made pancakes or baked cookies? What about filling up a car - gas prices in the U.S. are always in a mixed fraction form. We don't use floppy disks anymore, but screws and lumber and plywood and pipes are the same. It is not just a portion of math that they miss, it is a whole chunk of everyday life and chores. Did someone say snowflakes? $\endgroup$
    – Rusty Core
    Sep 6 at 18:31
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In parts of the UK and Commonwealth countries, mixed numbers (aka mixed fractions) are commonly used till about 16 years old. So, mark schemes typically specify $5\frac14$ instead of $\frac{21}4.$

For example, do a keyword search for “mixed”:
    https://www.cambridgeinternational.org/Images/597037-2023-2024-syllabus.pdf
    https://www.cambridgeinternational.org/Images/557161-2022-2024-syllabus.pdf

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