Elementary POW, April 22-26, 1996
Elementary POW Problems || April-June, 1996 Problems || Elementary POW Main Page
****************************************************** Elementary Problem of the Week, April 22-26, 1996 You have a three-inch cube painted red (length, width and height are each 3 inches). See if you can answer the following questions about the cube: a. How many cuts will it require to divide the cube into one-inch cubes? b. How many cubes would you have? c. How many cubes would have four red sides? d. How many cubes would have three red sides? e. How many cubes would have two red sides? f. How many cubes would have one red side? g. How many cubes would have no red sides? As you answer parts c to f of the problem, try to think of a way of explaining where the cubes in your answer would be. You might devise a numbering system or another method so that the reader will understand which cubes you are refering to. ****************************
*********************** Carol Copeland, Kristen Dempsey, Fifth Grade George L. Hess Educational Complex Mays Landing, NJ ************************ Danny, Matt, Ashley and Willy Ms.Duggan's class in fourth grade Munsey Park School Manhasset, NY ************************ Megan Weeman, Ashley Baker, Brian Stuart, Brooke Desper, and Jeff Pardue Mr. Dyer's class sixth grade Sea Road School Kennebunk, Maine ************************** Rachel Forster, Age 8, Grade 3, Australia. Wilkins/Forster family Crooked Tree Point.Cygnet. Tasmania.Australia 7112. ************************* Sam Hahn Ms McCarthy's 4th grade Center School, Stow, MA ************************ Tricia Eisenberg, Meaghan Kroner, Alissa Glading, and Ember Swinton St. Mary's School Mr. Hoops Class Ticonderoga, NY ***************** Daniel Sussman, Lori Ruhl, and Sean Nolan Western Salisbury School, Allentown, PA ************************ Caitlin Davis Melville Primary School, Perth, Western Australia ********************** Chris Wade Mrs. Pensa's 3rd grade Center School - Stow MA ********************** Benedito Tadeu Freire Natal/ RN/ Brasil *********************** ************************ Partially Correct ********************** Kyle and Andrew from Mrs. Camp's class Naples, FL *********************
I didn't word this problem carefully. Most students gave the answer that
Danny, Matt, Ashley and Willy, in Ms.Duggan's fourth grade class in Munsey
Park School, Manhasset, NY gave. This was the answer I had in mind.
However, one very bright student, Carol Copeland, Fifth Grade - George L.
Hess Educational Complex, Mays Landing, NJ , realized that the problem
didn't specify "exactly 2 painted sides, etc" so she gave both the answer
for cubes with paint on 2 sides as well as those with paint on 3 or 4
sides. Her answer is highlighted below. Great job, Carol!
**************************
Hi! This is Danny, Matt, Ashley and Willy. We are in Ms.Duggan's class in
fourth grade class in Munsey Park school, Manhasset. We are responding to your
problem of the week. This weeks problem is hard to explain. But we wiil
explain it any way.
a.6 cuts,4 on the top (two horizontzally and 2 vertically), and 2 on
the sides.
b.27 one inch cubes (3x3x3)
c.0,4 sided cubes
d.8 three sided cubes all 8 corners
e.12 two sided cubes.4 on top,4 on the bottom and 4 in the middle.
f.6 one sided red cubes (the center on each of 6 sides)
g.1 cube with no red sides (in the very center of the cube)
TAKE CARE NOW BYE BYE THEN!!!!!!
****************************
Fifth Grade - George L. Hess Educational Complex, 700 Babcock Rd., Mays
Landing, NJ 08302
This problem led to a lot of lively discussion. Students gave their
reasoning for question a. and with the help of drawings and finally the
cutting up of a sponge, they decided on an answer.
Kristen Dempsey: I used graph paper to construct a cube and then I
numbered the cubes located in the same place on a side with the same
numbers.
a. 6 cuts
b. 27 cubes
c. no cubes are red because corners have the most sides showing and
they have three red sides.
d. 8 cubes with three red sides located on the corners of the box
e. 12 cubes with two red sides located between every two corners
f. 6 cubes with 1 red side located in the middle of each side
g. 1 cube with no red sides located in the middle of the cube
Carol Copeland: I counted all the cubes and remembered the one in
the middle.
a. 6 cuts
b. 27 cubes
c. The whole cube has at least 4 red sides or if you don't count that
0 have 4 red sides.
d. 8 cubes have three red sides.
e. There are 20. 12 that have only two red sides plus the 8 with
three sides because if they have three they also have two.
f. 26 using the same idea as in e. 6 with only one red side, plus
the cubes that have 2 and 3 sides also have one red side.
g. The one in the middle.
**************************
>Sam Hahn - Ms McCarthy's 4th grade - Center School, Stow, MA
>
>A = 6
>B =27
>C =0
>D =8
>E =12
>
>F =6
>G = 1, the number 14
>
>this is how I represent the cube
>
>top layer
>1 2 3
>4 5 6
>7 8 9
>
>middle layer
>10 11 12
>13 14 15
>16 17 18
>
>bottom layer
>19 20 21
>22 23 24
>25 26 27
**************************
A. six cuts- four vertically (in opposite directions) and two
horizontally
B. twenty-seven cubes- nine times three equals twenty-seven.
C. none
D. eight cubes- corners
E. twelve cubes- middle two sided corners
F. six cubes- outside middles
G. one cube- middle inside
We made a cube of twenty-seven multi-colored centimeter cubes. Every
step we took out the cubes that applied. Thank you for including us
in this problem. We hope to do more, as we have just discovered your
web page.
From, Megan Weeman, Ashley Baker, Brian Stuart, Brooke Desper, and
Jeff Pardue
Mr. Dyer's class, sixth grade
Sea Road School
Kennebunk, Maine 04043
**************************
a. 6 cuts
b. 27 cubes
c. none ( because each cube has four side and atleast one side of each cube
has to be connected to the larger cube)
d. 8 cubes ( all the corner cubes)
e. 12 cubes (all edge cubes, except the corner cubes)
f. 6 cubes (one cube in the middle of each side)
g. 1 cube (the cube in the center of the large cube)
Daniel Sussman, Lori Ruhl, and Sean Nolan from Western Salisbury School,
Allentown, PA 18103
**************************
Caitlin Davis
EMAIL Address: sthildas@iinet.net.au
I go to school at Melville Primary School, which is a government school
in Perth, Western Australia.
Solution:
a) 6 cuts - 2 along the top,the bottom and the side
b) 27
c) there are none
d) 8 - each of the corners
e) 12 - the middle of each edge
f) 6 - the middle of each face
g) 1 - in the middle
*************************
>Chris Wade - Mrs. Pensa's 3rd grade - Center School - Stow MA
>
> First I made a 3 by 3 box and while I was making it I figured out
>the first question, ' How many cuts will it require to divide cube into
>1-inch cubes? The answer is 6. Then I knew you had to solve
>9+6+6+6=27. So the answer is 27. Then I knew the answer for ' How many
>cubes would have four red sides must be 0 because the 3 by 3 cube would
>have 8 sides. Then there would be 8 cubes with 3 red sides. I got 8 by
>counting the corners on the bigger cube. Then I got 12 2 red sided
>cubes, by counting the cubes in between the corners. Then I knew there
>were 6 1 sided cubes, 1 on each side of the bigger cube( The bigger cube
>is the 3 by 3 cube). Then I got 1 no red sided cube. I double checked
>by adding up all the answers except the how many cuts question (8+12+6+1=27)
**************************
I have an answer to the Elementary POW April 22-26.
a)It took 6 cuts to divide the cube into 1" cubes.
b) You would have 27 cubes.
c) 0 cubes would have four red sides.
d) 8 cubes (which are on the corner) would have three red sides.
e) 12 cubes (which are in the middle of each edge) would have 2 red sides.
f)6 cubes( in the middle of each face) would have 1 red side.
g) 1 cube( which is the only one that doesn't touch the out side becaus it
is in the verry center) would have no red sides.
>From Rachel Forster, Age 8, Grade 3, Australia.
Wilkins/Forster family
Crooked Tree Point.Cygnet.
Tasmania.Australia 7112.
ph.[002] 951456
****************************
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