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B Division for kids

  1. Mar 4, 2016 #1
    I am following up my 8 years old daughter's homework, and want to show her how division and multiplication work together , such as in division by a fraction : am I right if I say " we divide chocolates by boxes and 6 chocolates divided by half a box means 6 x 2 half boxes = 12 in one box ? " or is it "forbidden" to divide things that don't have the same name, i.e. chocolate and box , as I read in an arithmetic course for kids ? Thank you !
     
  2. jcsd
  3. Mar 5, 2016 #2

    Mark44

    Staff: Mentor

    It might "forbidden" in a third-grade math course, to keep things simple, but in the real world, there is no problem with dividing or multiplying quantities that have different units. "Miles per hour" is a ratio (i.e., a quotient) that involves distance units and time units. To calculate your average speed when you drive 120 miles in 2 hours, you get ##\frac{120 \text{ miles }}{2 \text{ hours }} = 60 \frac{\text{ miles }}{ \text{ hour }}##, are as it's usually written, 60 mph.

    The same goes for multiplication of different kinds of units. If you apply a force of 50 lb on a lever that is 2 ft long, you are applying a torque of 50 * 2 lb-ft, or 100 ft-lbs.
     
  4. Mar 5, 2016 #3
    Thank you for your interest ! there seems to be indeed 2 ways and 2 different results : with the realistic way of chocolates divided by boxes we are closer to the idea of speed and other things with 2 dimensions; the "forbidden" way doesn't but seems more tempting to use, easier to understand by children : 6 chocolates divided by 1/2 ( not by a half box ) can be immediately seen as what that means : 12 halves as we cut the chocolates in 2, and we don't need to think of 6 chocolates in a half box and multiply by 2 half boxes and get 12 full chocolates. But all this is confusing : divided boxes, divided chocolates .. this is not so easy, even less for kids I presume !
     
    Last edited: Mar 5, 2016
  5. Mar 5, 2016 #4
    It is forbidden to add or subtract things that don't have the same name, usually when we multiply or divide we have things that are different. 12 chocolates per box is meaningful, 1 chocolate per chocolate, or 1 square chocolate is not.
     
  6. Mar 5, 2016 #5
    1 chocolate per chocolate is not meaningful, but saying " 6 chocolates divided by halves give 12 halves but divided by 1/2 box give 12 chocolates " is correct ?
     
  7. Mar 5, 2016 #6
    I think these analogies are only useful for integers. I also think that introducing division by fractions too early is a mistake: 8 years old is too early for most kids.
     
  8. Mar 5, 2016 #7
    Thank you for your insight; division by halves and thirds with a knife has gone ok, I will wait more time to introduce the divided box and the different meaning. Talking about analogies , in south east Asian agglutinative languages the active / passive voice is often not used in spoken practice, so that trying to distinguish " divide " and " divided by " with the help of the active / passive analogy from the real world is difficult with kids.
     
  9. Mar 7, 2016 #8

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    6 chocolate per half a box means 12 chocolates per box, I don't see anything wrong in dividing chocolates by boxes.

    You always have 1 chocolate per chocolate. If you do not own any chocolate, you also have 2 chocolate per chocolate you own.

    1 square chocolate - well, if it is not round? ;)
     
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