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We have Clock arithmetic in grades 5 , 6 and thereafter nothing related to the Modular arithmetic is taught until students enter to the universities. Since this is very important topic in Number theory what would you have to say about introducing this to students as an extra activity? If you are going to teach basics with some applications for selected group of students who have interest,what are the textbooks or any resources available in pdf form for this purpose?

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    $\begingroup$ Since this is very important topic in Number theory --- Since probably less than $0.2 \%$ of students in these grades would later take an undergraduate number theory course (U.S. based, where about $1.5 \%$ of undergraduate degrees are in math, and relatively few undergraduate math majors take an undergraduate course in number theory), this doesn't provide much support for what you would like. That said, I think additional examples of modular arithmetic would be nice, at least for students in faster-paced classes who might be expected to later attend university and also major in a STEM area. $\endgroup$ Commented May 12 at 14:28
  • $\begingroup$ @DaveLRenfro One of the reasons for not choosing Number theory may be students are not given enough opportunity to feel the importance of it. In that case what I'm suggesting can be helpful for students to make a decision with having some kind of knowledge related to the topic. $\endgroup$ Commented May 12 at 16:06
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    $\begingroup$ Would you consider angles in trigonometry an extra activity related to modular arithmetic? For example, $\pi/2$ and $5\pi/2$ are equivalent mod $2\pi$. Or 90 degrees and 450 degrees are equivalent mod 360. $\endgroup$
    – user52817
    Commented May 12 at 16:46
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    $\begingroup$ One of the reasons for not choosing Number theory --- It's also not offered at many colleges (U.S.) despite more advanced courses (e.g. analytic number theory and algebraic number theory) being common in graduate programs, although usually not as primary courses that Ph.D. qualifying exams are based on. I think standard undergraduate number theory courses began getting squeezed out by the late 1950s (even more so, courses in theory of equations) with the increase in linear algebra and abstract algebra, then even more so in the 1980s with the rise in discrete and numerical math offerings. $\endgroup$ Commented May 12 at 17:22

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