Elementary POW, September 16-20,1996
Elem POW Problems || Sept-Nov '96 Problems || Elem POW Main Page
***************************************************************** Elementary Problem of the Week, September 16-20, 1996 This week's problem involves folding a two-dimensional drawing or "net" into a cube. You might want to copy the net onto heavier paper such as stock paper. Cut out the net (including the tabs) and fold it into a cube. If you glue the tabs it should hold together nicely. This activity is best done in a group. Notice that each "face" of the cube has a word, a number in the lower left and upper right corner, and a letter in the lower right and upper left corner. One of the faces is blank. Your challenge is to determine what should be on the blank face based on the patterns that you see on the other faces. You should *justify* each part of your answer by explaining how it fits the pattern on the other faces. (Hint: You might want to look at patterns on opposite faces.) This week's Visiting Math Mentors are from Germantown Academy in Fort Washington, Pennsylvania. They are 9th, 10th and 11th graders from Mrs. Ruth Carver's Algebra II Honors class. *****************************************************************
Well, we're off to a good start after our first week. Sixty-four students sent in solutions in addition to several classses that worked on the problem as a group. Thirty-one students correctly solved this week's problem. We chose 5 solutions to highlight this week that we thought had clear explanations. Be sure to take time to look at them. Keep up the great work! ------------------------------------------------------------------------ Conrad Kirby 5th Grade, Ms. Williams Burton Geoworld Elementary School Durham, NC ------------------------------------ Drexel Hill School of the Holy Child, Drexel Hill, PA Grade 4 - Mrs. Brennan's class Students: Daina Andries, Katie Devlin, Lauren DiGirolamo, Stephen DiJulia, Tim Stumm, and Claire Viggiano ------------------------------------ Ithan Elementary School, Bryn Mawr, PA. Students: Goup 1: Heming, Claire, Peter, George and Mike; Group 2: Eric, Yiqiong, Jimmy and Samantha; Group 3: Yuki, Zack, Scott P., Scott C. and Caley ------------------------------------- Zach Seibert, grade 3 Western Salisbury School 3201 Devonshire Road Allentown, PA 18103 Mrs. Geschel's class ------------------------------------- Students: Stephanie,Sara,Bethany,Laura Mr. Dyer's Class Grade 6 Sea Road School, Kennebunk, Maine ------------------------------------- Solved by: Nate Litz, Nathan Strauss, and Alex Tuchel-Veyhl Bob Coulter's 3rd grade class Forsyth School St Louis, Missouri ------------------------------------- Students: Kinzie, Jonathon, Chris B. and Kathleen: 4th grade Teacher's name: Colleen Brodie Leal School 312 W. Oregon St., Urbana, IL 61801 ------------------------------------ Students: Erika Lamanna, Michael Mijuskovic, Peter Woods 4th grade Mrs. Bowerman's class Kyrene de la Mariposa ------------------------------------ Students name: Christine Grade: 5 Teacher:Pat Gaborski Jefferson Road Elementary School Pittsford, New York ------------------------------------ Katie Lynch Mrs. O'Connell 5th Grade Center School - Stow MA ------------------------------------- ------------------------------------- Alternate Solution ------------------------------------- ------------------------------------- Mrs. Jameson's fifth grade Heights Elementary School Sharon, MA. 02067 This week's problem solvers: Danielle, David, Amal, Kara, Kristina, Greg, Mike, Kandice,Elizabeth, Elisha,& Heather
We chose 5 of the solutions that we felt were particularly well thought out
and clear in their explanations.
We also included an alternate solution because we thought they made a good
case for it.
Germantown Academy Visiting Math Mentors
Fort Washington, PA
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Zach Seibert, grade 3
Western Salisbury School
3201 Devonshire Road
Allentown, PA 18103
Mrs. Geschel
mgeschel@prolog.net
I looked at the cube, and I saw a pattern. I noticed the letters in the
corner on each side of the cube were the same as the amount of sides of the
shape written in the middle. The number on the bottom left hand corner is
the same as the number of sides of the shape. The number in the upper right
hand corner is the same as the number of sides of the shape written on the
opposite side of the cube. I got the letter by the amount of sides of the
name of the shape in the middle.
I 7
nonagon
9 I
The letters in the other corners are I's because I is the ninth letter of
the alphabet and a nonagon has nine sides.
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Drexel Hill School of the Holy Child, Drexel Hill, PA
Grade 4 - Mrs. Brennan (caroline@mathforum.org)
Daina Andries, Katie Devlin, Lauren DiGirolamo, Stephen DiJulia, Tim Stumm,
and Claire Viggiano
Solution: The number in the lower left corner equaled the number of sides
of the figure mentioned on each face. The letter in the lower right corner
and upper left corner equals its numerical place in the alphabet. Example:
A = 1, B = 2, etc. The difference between the numbers on each face always
equaled two. The blank face had the word nonagon in the center because it
also had the number nine in the lower left hand corner. The number in the
upper right hand corner was 7 because it represented the number in the
center of the opposite face. The letter on this face is "i" because "i" is
the ninth letter in the alphabet.
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Mr. Dyers class got this answer by studying the other squares and finding out
what each letter and number meant and how it connected to the box .We found
out that the face opposite of each other had the same numbers but they were
switched around. Also we found out that each letter in the bottom right hand
corner ment that thats how many sides each figure has.
EXAMPLE If one figure has 9 sides then the 9th letter of the alphabet will be
in the bottom right hand corner and top left hand corner. It would also have
the number of the figure opposite of it. ANSWER The name of the shape would
be nonagon. The number in the lower left hand corner would be 9. The upper
right hand corner would be 7. The letter in the lower right hand corner and
the upper left hand corner would be an i
. Mr. Dyer's Class Sea Road School Kennebunk, Maine
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>
>Katie Lynch - O'Connell 5th Grade - Center School - Stow MA
> I think the answer is nonagon. I think this because if you look
>in the box with the square in the bottom left hand corner it says 4, and a
>square has 4 sides. when the square is in a cube if you look on directly
>on the opposite side it says 6 in the bottom left hand corner. It says
>hexagon and a hexagon has 6 sides. On the top where it says septagon it
>has 7 in the bottom left hand corner and a septagon has 7 sides.On the
>empty space it should say 9 in the bottom left hand corner and the shape
>that has 9 sides is the nonagon. The letter I goes in the upper left
>hand corner and the lower right hand corner because it is the ninth
>letter of the alphabet and all the other sides have the letter of the
>alphabet that is the same as counting in the alphabet: c=3, d=4, e=5....
>The number in the upper right hand corner is the seven because it is the
>reverse of the septagon side...otherwise the pattern wouldn't work out.
--------------------------------------------------------------------
Student: Michael Mijuskovic
4th grade
Mrs. Bowerman's class
Kyrene de la Mariposa
If you look at the number in the lower left hand corner it is the number of
sides of the shape. The number on the upper right hand corner is the number
of sides of the shape written on the opposite of the cube. The letters on
the top left hand corner and the bottom right hand corner are the letters of
the alphabet that match the number of sides that the shape has. So the shape
on the opposite side is a nonagon. The letter is I. The number on the
bottom left is 9 and the number on the upper right is 7.
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Alternate Solution
------------------------
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We rewrote the problem in our own words:
We thought the problem said...What
letters, numbers and shapes are on the empty face? And it told us they go in
special places.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This was our strategy:(We tried to think of more than one way)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We looked at all the different faces to see if there was a pattern.
!!!!!!!!!!!!!!
We solved it! We'll show you how we did:
"Octagon" is in the middle because it's the next shape. The number of sides
on
ther shapes increases by one on each side of the cube. It starts with 3 then
4, then 5 then 6,&7, next would be a shape with eight sides. So, we wrote
octagon.
On the bottom left corner, there should be an 8, because that's the number
of sides an octagon has.
In the upper right hand corner, there is a 6 because there are three numbers
that go up two(from the bootm corner) but only two on the cube that go down
two. So the there needs to be a third going down.
In the top right hand corner there is a "h" that's because it is the 8th
number in the alphabet and an octagon has 8 sides.
Our answer makes sense because...
it fits in with all the other sides of the cube.
:):):):):):):):):):):):):):):):):):):):):):):):):):):):):):):):):):):):):):):):
):):):):):):):):):):):):):):):):):):):):):):):):):):):):)Thank you for
checking our work!
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