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Grade 8 "Question of the Day" Ideas
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A decent source of questions is the AMC 8 math competitions that are held yearly. The competition consists of 25 questions in roughly increasing order of difficulty. There are also 10th and 12th grade ...

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Good resources for coaching for mathematics competitions (Highschool Level)
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You could have them work through problems on aops. It contains AMC questions as well as video lectures on the problems. Furthermore it has books and other resources you may be interested in.

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Using joke / song / film / pop culture to exhibit a new mathematical concept
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This may be known already but "The Simpsons" has many (advanced) math and physics references. Here is a relevant link.

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