
Integers, fractions, and decimals are different things to kids - ColinWright
https://mikesmathpage.wordpress.com/2015/03/06/integers-fractions-and-decimals-are-totally-different-things-to-kids/
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jonsen
Shortcuts and insightful tricks should of course be encouraged, but learning a
standard way of translating assignments into a basic arithmetic reduction
would support the notion that it is all numbers of the same kind which can be
handled with the same basic operations:

    
    
      20% more than 70 =
      70 + 20% of 70 =
      70 + 20/100*70 =
      70 + 20*70/100 =
      70 + 1400/100 =
      70 + 14 = 84
    
      30% less than 1/5 =
      1/5 - 30% of 1/5 =
      1/5 - 30/100*1/5 =
      1/5 - 30*1/100/5 =
      1/5 - 30/(100*5) =
      1/5 - 30/500 =
      100/500 - 30/500 =
      (100 - 30)/500 =
      70/500 = 7/50 = 14/100 = 0.14
    
      10% more than 3.4 =
      3.4 + 10% of 3.4 =
      3.4 + 10/100*3.4 =
      3.4 + 10*3.4/100 =
      3.4 + 34/100 =
      3.4 + 0.34 = 3.73

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gus_massa
The approach for decimals and fractions is quite similar.

The approach for integers looks like a nice shortcut. They should try with the
30% of 410 to see how the kids solves the cases that are not easy.

~~~
jonsen

      30% of 410 =
      30/100*410 =
      30*410/100 =
      12300/100 = 123
    

How is this “not easy”?

I mean, this should be as easy as any percentage calculation of this kind.

Edit: Ah, you think the kid would find it difficult. My point is, that it’s a
shame if they don’t have a fall back to basics procedure when the tricks don’t
work.

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gus_massa
My guess is that he can use the fallback when the calculation is not easy.

The part that I find interesting is that for the 20% of an integer he uses a
"shortcut", but for the 10% of a decimal he uses the "standard" procedure.

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jonsen
What do you mean by “”standard””? Is introducing an unknown and solving an
equation for that unknown to calculate a percentage a kind of standard?

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gus_massa
Not here in Argentina, but I think it's the "standard" method for the kid.

