fourth grade geometry question???
Diane
parallelogram.
Does this seem like 4th grade to anyone? I finally got the answer but
we have no book to use as a reference.
Walter Whiteley
playing with something like straws, or connectrix sicks and joints.
I imagine the answer they are looking for is the 'kite'.
This type of lateral thinking is appropriate at many levels.
Sometimes it is easier for younger children, who are not
as 'routinized'.
Interestingly, at the other end of experience, the first example
I thought of was the 'butterfly' - which is self-interesecting,
and probably further from what fourth grade students would image.
This I would find by making something like a parallelogram
from straws and strings, then playing with it into 3-space and
back into the plane. In that kind of kinematic play, you realize
the opposite sides are still equal in length, and only have to puzzle
over whether it ceased to 'be a quadrilateral' when it dropped
back into the plane with a crossing.
Walter Whiteley
karen
My daughter just presented this question as well. Only by looking at
the response generated from your question here on the net(from Walter
somebody who appears to be a mathematics statistician ) did I get it.
Now my 9 year old has assured me that she is smarter than me because
she actually had an answer that I didn't think was correct until I
read Mr. Math professor's answer. I also am having nightmarish
reminders of my 9th grade geometry teacher. thank you.
Alexander Bogomolny
>On 28 Aug 02 23:22:36 -0400 (EDT), Diane wrote:
>>Draw a quadrangle that has 2 pairs of equal sides but is NOT a
>>parallelogram.
>>Does this seem like 4th grade to anyone? I finally got the answer
but
>>we have no book to use as a reference.
>
>My daughter just presented this question as well. Only by looking at
>the response generated from your question here on the net(from Walter
>somebody who appears to be a mathematics statistician ) did I get it.
>Now my 9 year old has assured me that she is smarter than me because
>she actually had an answer that I didn't think was correct until I
>read Mr. Math professor's answer.
What I do not understand about this remark is that how is it possible
not to acknowledge an answer when it does solve the problem. The kite
does have two pairs of equal sides. If that's what your daughter
brought as an answer then, by inspection, you might have verified that
it was correct. Why would not it?
Alexander Bogomolny
http://www.cut-the-knot.org
GEIvey
Of course, if you DON'T KNOW what a "parallelogram" IS, you can't
"verify"it!
Melinda
I know you posted this last week but I am in the same boat. My 4th
grader as a geometry sheet for homework and I am lost. We do not have
a book to go by either. What is wrong with this system?? It has been
almost 20 yrs. since graduated much less did geometry. I am looking to
fing out what type of shape has four sides that are not equal.
Neal Silverman
>I know you posted this last week but I am in the same boat. My 4th
>grader as a geometry sheet for homework and I am lost. We do not have
>a book to go by either. What is wrong with this system?? It has been
>almost 20 yrs. since graduated much less did geometry. I am looking
to
>fing out what type of shape has four sides that are not equal.
The figure being described is generally called a "kite." In fact, it
looks like a kite (that a child would fly). It has 2 pairs of
congruent sides (let's say sides AB and BC are congruent, and sides CD
and DA are congruent). It is not a parallelogram because the opposite
sides are not parallel.
For an exact definition of kite, I give you what Prof. Moise uses: A
kite is a quadrilateral in which exactly one diagonal is the
perpendicular bisector of the other diagonal. (If both diagonals were
perpendicular bisectors of each other, the figure would be a rhombus,
and therefore a parallelogram. To add to the definitional confusion,
Prof. Conway would, in fact, call all rhombuses kites. Most writers
use the definition set forth by Prof. Moise, however.)
Hope this is of some help.
Walter Whiteley
student should approach this is with imagination and examples. Try
some shapes (with a drawing program, with some sticks, etc.) Look at a
variety of examples and find one that fits the properties listed.
Take a parallelogram and say -what if I take these edges in a different
order?
Do I still have pairs of sides of equal length? What changes, what is
the same?
Doing this kind of playing around, and asking what if, is good
mathematics. Giving examples in a reference book does little to assist
the essential learning which can happen here. In fact, it feeds a
misperception of what mathematics is, and what children can do in
mathematics.
There may be a gap in communicating this sense of play, and
experimentation to children (and parents) - but the goal is great and I
encourage this approach.
Walter Whiteley
leonora
My daughter just started 4th grade and the question you posted for your 4th grader is exactly the same homework she had for the weekend. I have the same problem as we do not have materials to refer. Thank you for posting the question. By the way we are from Hawaii.
Aloha,
Leonora
Dina
Thanks!
Dina
Steve Cooke
> On 28 Aug 02 23:22:36 -0400 (EDT), Diane wrote:
> > Draw a quadrangle that has 2 pairs of equal sides
> but is NOT a
> > parallelogram.
> > Does this seem like 4th grade to anyone? I finally
> got the answer but
> > we have no book to use as a reference.
>
Another take on this question since I am sure it will come up again:
Start with a pair of equal sides that share a common vertex. Imagine the two equal sides of an isosceles triangle without the base. Now creates a second pair but with the length different from the first.
Now that you have two pair of sides, each pair having the same length, how can you join them? You can set them so the open end of each has the same span and point them away from each other like this "<>" to make what is called a kite. Is that the only way? You can also turn them with the smaller pair inside the larger like this ">>" to make what is called a dart.
Are those the only combinations with those two pairs? If instead of two pair of equal length, what if you start with two pair of unequal length but having two common lengths between them. What figure is created by joining those pairs? Have you exhausted all possibilities?