Division for kids

[Physou]

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 !

 

[Mark44]

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 ?

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.

 

[Physou]

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 !

 

[pbuk]

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 !

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.

 

[Physou]

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 ?

 

[pbuk]

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 ?

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.

 

[Physou]

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.

 

[mfb]

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

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.

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? ;)