How many pos integers less than 1000 are not multiples of 7?
Middle school problem?
Strategies you teach your students?
"Big Ideas" here?
Sketch of one possible method:
1000/7=142.857... ---> 142 multiples of 7 less than 1000 ---> 999-142 = 857 non-mult
The devil is in the details of course which I intentionally omitted! Why didn't I mention that the largest mult of 7 less than 1000 is 994? Would most solutions involve finding 994 first?
Someone out there is thinking about the repeating decimal expansion of 1/7 = 0.142857142857… and why the ans to our problem is 857. A coincidence?
Too bad we have no time in our classrooms to explore and go in depth. If we spend time doing that we'll never cover all the required topics in the Core Curriculum. Yes?
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