Thanks for the definitions. I still think it is an arbitrary and unnecessary way of trying to separate division into types of division. I cannot see that it helps with learning about division and it is certainly incomplete.
What about;
I suppose if, say, D = 20 miles and T = 5 hours, you could think of dividing 20 into 5 equal groups with 4 mph in each, but then
would have to involve making groups of 4mph until 20 is reached. It just doesn't seem to work for most of the maths I know.
And which classification is involved here:
In number theory, division is defined as the reverse of multiplication. As multiplication is commutative ( ab = ba ) I think all division of type 1 can be re-written as division of type 2. Hence, all problems can be done either way.
Bob
]]>Happy to hear suggestions.
]]>Conceptually, division describes two distinct but related settings. Partitioning involves taking a set of size a and forming b groups that are equal in size. The size of each group formed, c, is the quotient of a and b. Quotative division involves taking a set of size a and forming groups of size c. The number of groups of this size that can be formed, b, is the quotient of a and c.
If the number in each group is known, and you are trying to find the number of groups, then the problem is referred to as a quotative division problem. Quotative division may also be called measurement, or repeated subtraction. You are, in effect, counting or measuring the number of times you can subtract the divisor from the dividend.
If the number of groups is known, and you are trying to find the number in each group, then the problem is referred to as a partitive division problem. Partitive division may also be called equal groups, or sharing and distribution. You are, in effect, partitioning the dividend into the number of groups indicated by the divisor and then counting the number of items in each of the groups.
Why? Division is division; the rest is just 'examples in context'. I have taught maths for many years and have never even met the term 'measurement' division (I had to google it just to work out what you meant); nor the other one, the name of which I've managed to forget already (part....something ?).
I encourage my students/pupils to think about the problem and what maths they can bring to bear on it. If they conclude that division is needed then they either use a calculator or do the working on paper; but why burden them with an extra word that is just for (unnecessary?) classification purposes.
Bob
]]>I've read two pages on division, but none includes measurement division. It'll be nice if the author explains and mentions the two types of division.
Thanks...
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