Partitive vs. measurement division problems
kalanamak
http://www.bestwebbuys.com/books/compare/isbn/0130322741/isrc/b-search-other
stresses two kinds of division problems: partitive (fairsharing) and
measurement (repeated subtraction). Their examples of the two, in order,
is:
Maria has six oranges. She puts an equal number of oranges in 3 bags.
How many oranges in each one?
AND
Maria has six oranges. She puts oranges in each bag. How many bags does
she end up using?
The equation for both problems was identical: 6/3=2
I read on as it was a busy chapter, but now that I'm up to division with
fractions, they stress how important it is go to back over these two
types of division problems with the students before starting division
with fractions.
Having never taught kiddos division, does this distinction really help
or is it an oddity of this book? My adult mind sort of rolls right over
it, I don't recall any teaching on different kinds of story
problems...you were just thrown into them after the section with the
rote problems, and you sank or swam.
If this distinction is important, why, does anyone have a more riveting
way that some tired oranges and some paper bags as example, and finally,
in order to teach these types to children, do you use the
partitive/measurement names or the fairsharing/repeated subtraction.
Both sets seem a little "big", considering the book also devotes time to
having the teacher us "children's language" for operations.
TIA
blacksalt
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Guess who
wrote:
>The text I'm using to learn about teaching math to kids
>http://www.bestwebbuys.com/books/compare/isbn/0130322741/isrc/b-search-other
>
>stresses two kinds of division problems: partitive (fairsharing) and
>measurement (repeated subtraction). Their examples of the two, in order,
>is:
>Maria has six oranges. She puts an equal number of oranges in 3 bags.
>How many oranges in each one?
>AND
>Maria has six oranges. She puts oranges in each bag. How many bags does
>she end up using?
You have to say "how many" she put in each bag. I'll presume you mean
"two". If she put them all into one bag, the answer would be "1". If
she put one into each, it would be "6".
>The equation for both problems was identical: 6/3=2
Not really, and that's not an "equation", but a statement of
equivalence. To find the number of oranges, you'd have 6/3 = 2, but
to find the nunber of bags, again assuming two each, you'd have 6/2 =
3.
>I read on as it was a busy chapter, but now that I'm up to division with
>fractions, they stress how important it is go to back over these two
>types of division problems with the students before starting division
>with fractions.
They are possibly trying to stress the manipulative skills needed when
dealing wit hrational quantities, and how they can be learned at an
early age without actually mentioning them as such.
>If this distinction is important, why, does anyone have a more riveting
>way that some tired oranges and some paper bags as example, and finally,
>in order to teach these types to children, do you use the
>partitive/measurement names or the fairsharing/repeated subtraction.
Do you have any more "riveting" examples to offer yourself? You have
not indicated that you yet see the purpose of the exercise. Have you
talked to any of the teachers to see if you can see why they do this
in the way that they do? Either way, do not expect the teachers of
the young to be mathematicians. They do an awesome job, having to
teach the fundamentals in all subject areas. Math can be particularly
difficult, trying to please all of the people all of the time.
Perhaps you can offer them some advice and assistance.
I taught high school math, and at a much more advanced level than what
is being discussed here, and am here to tell you that I admire the
public school teachers for what they do, even if students did come
insufficiently unprepared at times. Some of the needs are not obvious
to them, and they must strictly follow the texts and curriculum
guidelines or face the wrath of a thousand parents. There is sense to
what they are doing here. The kids just wouldn't realise it until they
met me [and other HS math teachers], and my expectations.
Guess who
wrote:
>On Wed, 05 Jan 2005 14:44:15 GMT, kalanamak <kala...@qwest.net>
>I taught high school math, and at a much more advanced level than what
>is being discussed here, and am here to tell you that I admire the
>public school teachers for what they do, even if students did come
>insufficiently unprepared at times.
A typo: should be "insufficiently prepared." But that is still not a
derogatory remark against the generally great efforts of these
teachers of the very young.
kalanamak
> They are possibly trying to stress the manipulative skills needed when
> dealing wit hrational quantities, and how they can be learned at an
> early age without actually mentioning them as such.
Ah, that is possible, as the book stressed manipulative skills a great
deal.
> Do you have any more "riveting" examples to offer yourself? You have
> not indicated that you yet see the purpose of the exercise.
I thought I indicated that I don't see the purpose of differentiating
partitive division problems from measurement problems. The books seems
to spend a fair amount of time on them, but does not say why. They do,
e.g., explain why reciprocals of fractions can be useful ("helpful later
on for understanding division with fractions"), but not why this issue
is brought up more than once.
> Have you
> talked to any of the teachers to see if you can see why they do this
> in the way that they do? Either way, do not expect the teachers of
> the young to be mathematicians. They do an awesome job, having to
> teach the fundamentals in all subject areas. Math can be particularly
> difficult, trying to please all of the people all of the time.
> Perhaps you can offer them some advice and assistance.
I was speaking of the authors of the text I put a link to. There are no
live breathing teachers, only these print teachers who are the authors
of a book for people seeking to teach elementary and middle school
children math. Since I might, possibly, maybe, something of a long shot,
be in that position myself in the upscoming years, I'm trying to learn
how to teach children math, most specifically my son. I have discovered
that the journey shook loose alot of unpleasant memories on the math
education I had, and have found significant gaps in my understand, even
on the basic level. I can crank through the rules, but don't have a firm
grasp of what underlies them.
I am used to sounding all educated and grown up, but am stumbling along
rather clumsily on this group, not even sure if the questions I ask have
relevance, let alone an answer I can comprehend at my level of
knowledge.
Pardon my mathematical immaturity.
blacksalt
Worden
and multiplication is repeated addition begins to lose it's value when
you deal with fractions. If you want to discuss 3/8 divided by 1/2,
do you ask student to consider out how many times can they can
substract 1/2 from 3/8? When multiplying 2/3 times 3/4, do you want
to add 3/4 two-thirds of a time? Hopefully students have graduated to
more sophisticated concepts for multiplication and division by the
time you reach fractions. For multiplication, asking how many items
total do you have with n groups of m items works tolerably for
fractions. For division, asking how items are in each group when m
items divided into n groups also still works.
I favor servings of pizza as a model for multiplication and division
of fractions: 1) Two pizzas can be divided into how many servings if
a serving is one-fourth pizza each? (Dividing by 1/4 is the same as
multiplying by 4.) 2) Two pizzas can be divided into how many
servings if a serving of pizza is 3/4 of a pizza? (If you can serve 8
people in part 1) and you triple the serving size, now you can only
serve one third as many people or 2 2/3.) 3) For multiplication, 2/3
of 3/4 of a pizza is clearly 1/2 the pizza.
On Wed, 05 Jan 2005 14:44:15 GMT, kalanamak wrote:
>The text I'm using to learn about teaching math to kids
><a
href="http://www.bestwebbuys.com/books/compare/isbn/0130322741/isrc/b-search-other">http://www.bestwebbuys.com/books/compare/isbn/0130322741/isrc/b-search-other</a>