5 ms·

Integers, fractions, and decimals are different things to kids

• gus_massa 6y ago
  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 6y ago
    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.
    • gus_massa 6y ago
      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.
      • jonsen 6y ago
        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?
        • gus_massa 6y ago
          Not here in Argentina, but I think it's the "standard" method for the kid.
• jonsen 6y ago
  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