Elementary POW, January 22-26, 1996
Elementary POW Problems || January-March, 1996 Problems || Elementary POW Main Page
****************************************************** Elementary Problem of the Week, January 22-26, 1996 There were 3 dogs and 3 cats on an island. They all wanted to go to the mainland because of flooding on the island. They had one boat that would take only 2 animals, but when there were more dogs than cats in a group, the dogs tormented the cats. Therefore, the cats would not let themselves be outnumbered by the dogs. How did they all get to the mainland? *******************************************************
Chaz Rosenberg Mrs. Pensa's 3rd grade class Center School Stow MA Chris Wade Mrs. Pensa's 3rd grade class Center School Stow MA Laura Fraser Ms. McCarthy's 5th grade class Center School Stow MA Alan Weider, Chris Puopolo, Nisha Hughes Miss Lemieux, Grade 6 Bagnall School, Groveland, MA *** Interesting Solution **** Allison Foote and Alyson Christopher Miss Lemieux, Grade 6 Bagnall School, Groveland, MA ****************************** Meghan L. and Meghan R. Miss Seager, Grade 4 Bagnall School, Groveland, MA Alan Weider, Chris Puopolo, Nisha Hughes Miss Lemieux, Grade 6 Bagnall School, Groveland, MA Nora Fabris and Andrew Markos Miss Lemieux, Grade 6 Bagnall School, Groveland, MA Aneil Baron 3rd grade Paul Nash (teacher) Georgetown Day School Washington,D.C. Blast Out Math Maniacs LaRon Hudson Grade 4 Miss Petty Olivehill Elementary Dayton, Ohio Emily Huelskamp Grade 6 Miss Petty Olivehill Elementary Dayton, OH Cecilia Ekperi 3rd grade Paul Nass Georgetown Day School Sherri Jefferson R.d School Pittsford NY Elizabeth Ahlers 5th grade Paul Nass Georgetown Day School Washington DC. Lisa Orenstein Paul Nass 3rd Grade Georgetown Day School Washington, D.C. Thomas A. Grace 5th grade Paul Nass Georgetown Day School Washington D.C. Matt, Dan,Eliz,Tony and Will Teacher's name: Paul Nass Benjie Achtenberg 5th grade Georgetown Day School, Washington D.C. U.S.A. Fifth grade at Rogers Elementary School District in Pittsburgh Pa. Dr. Slomer-teacher Students: Kirk Thompson, Brad Jadlowied
Chaz Rosenberg - Mrs. Pensa's 3rd grade class - Center School - Stow MA
(1) a dog sails the boat.
(2) the dog takes dog 2.
(3) the dog takes a cat.
(4) the dog takes cat 2.
(5) the dog takes dog 3.
(6) the dog takes cat 3.
Chris Wade - Mrs. Pensa's 3rd grade class - Center School - Stow MA
One animal has to drive the boat. The dogs wouldn't be out numbered so
I had a dog drive the boat. I had the dog take a cat. Then the dog
sailed back. Then the dog took a dog. Then the dog sailed back, again.
Then the dog takes a cat. Then the dog sailed back. Then the dog took
another dog. Then sailed back. Then the dog took the final cat. Then
the dog took the final dog.
Laura Fraser - Ms. McCarthy's 5th grade class - Center School - Stow MA
On the first round, a dog and a cat went to the mainland. the dog rode
back and got off.
For the second round, 2 cats got on and went to the mainland one cat
got off and the other cat rode back and picked up a dog for the 3rd round.
The dog got off at the mainland so there is now 1 dog on the mainland and 2
cats.
When the cat got back to the island it picked up a dog.
Now there are 2 dogs and 2 cats on the mainland and one dog on the island.
The cat went back and got the last dog and went to the mainland and the
animals were safe and sound.
Alan Weider, Chris Puopolo, Nisha Hughes
Miss Lemieux, Grade 6
Bagnall School, Groveland, MA
A dog and a cat got on the boat. The dog got off at the mainland.
The cat went back and picked up a dog. The cat got off and the
dog went back and picked up a cat. The cat off and the dog went
back to the island. The dog picked up the other dog and took
him to the mainland. One dog gets off and the other goes back
and picks up the last cat. They go to the mainland and both get off.
*** Interesting Solution ****
Allison Foote and Alyson Christopher
Miss Lemieux, Grade 6
Bagnall School, Groveland, MA
First, one dog and one cat went over in the boat.
Secondly, another cat and dog went over. Then, another
cat and dog went over in the boat. The boat was
computerized on the mainland so it could be controlled
by a remote. No one had to row or even steer.
******************************
Meghan L. and Meghan R.
Miss Seager, Grade 4
Bagnall School, Groveland, MA
There would be 9 trips. Two dogs go to the mainland. One dog
goes back and picks up a cat and takes it to the mainland. The dog goes
back and gets another cat and takes it to the mainland. The dog goes back
and picks up the last dog and takes it to the mainland. The dog goes back
one last time to pick up the last cat and take it to the mainland.
To solve this, we drew the mainland and the island. Then we drew
arrows from the island to the mainland and back, On each line, we drew
boats with cats and dogs on them. We made sure each side was even so each
animal couldn't gang up on each other. We had the dog in the boat to keep
it even.
Alan Weider, Chris Puopolo, Nisha Hughes
Miss Lemieux, Grade 6
Bagnall School, Groveland, MA
A dog and a cat got on the boat. The dog got off at the mainland.
The cat went back and picked up a dog. The cat got off and the
dog went back and picked up a cat. The cat off and the dog went
back to the island. The dog picked up the other dog and took
him to the mainland. One dog gets off and the other goes back
and picks up the last cat. They go to the mainland and both get off.
Nora Fabris and Andrew Markos
Miss Lemieux, Grade 6
Bagnall School, Groveland, MA
First 2 dogs go over and one comes back. The dog
takes a cat over. The dog goes back and picks up another
cat and takes it over. Then he goes back for the 3rd cat and
takes him over. Then the dog picks up the last dog and they
are all on the mainland.
A cat-1 and a dog-1 get in the boat and go to the mainland. Cat-1 gets off.
Dog-1 goes back. Dog-1 gets dog-2. They go to the mainland. Dog-1 gets off.
Dog-2 goes back. Dog-2 gets cat-2. They go to the mainland. Cat-2 gets off.
Dog-2 goes back. Dog-2 gets dog-3. They go to the mainland. Dog-2 gets off.
Dog-3 goes back. Dog-3 gets cat-3. They go to the mainland.
Aneil Baron
3rd grade
Paul Nash (teacher)
Georgetown Day School
Washington,D.C.
We are Anita and Jesse from Mrs. Hirn's 4th grade in the Munsey Park School,
Manhasset, NY. Here is our answer:
One dog took the cat to the mainland and then he went back to the
island and got another dog. He took him to the mainland and went back to the
island and got the other cat and brought her to the mainland. Then he went
back and got the other dog and went to the island and got the last cat and
they
went to the mainland. They all lived happily ever after! We used paper
models
to help us figure it out.
The following solutions were submitted by members of the Olivehill
Accelerated School Math Club -- "Blast Out Math Maniacs"...
#1
The dog rows the boat at all times. Blast Out Math Maniacs decided
that we were going to act out the problem. So the first thing we did
was send a cat over to the main land. Then came back and got a dog.
After that we came back and got a cat then took it over to the main
land. After the dog came back it doesn't matter who you take over.
Sincerely,
Blast Out Math Maniacs
LaRon Hudson
Grade 4
Miss Petty
Olivehill Elementary
Dayton, Ohio
#2
Our Math Club decided to act out the problem. We had enough to act
it out with the help from the teacher. A dog must always row or steer
the boat. First take a cat, then a dog, that way you have a cat and a
dog on the mainland, and two cats and a dog on the island. Third, take
a cat. The fourth and fifth trip doesn't matter if you take a dog or
cat because it will still be safe because there won't be more dogs than
cats.
Emily Huelskamp
Grade 6
Miss Petty
Olivehill Elementary
Dayton, OH
Cecilia Ekperi 3rd grade Paul Nass Georgetown Day School
1. There were 0 dogs and 0 cats on the Mainland.
2. A cat and a dog go to the Mainland,the cat drops off the dog.
3. The cat goes back to the Island, picks up a dog and they go back to the
Mainland.
4. The dog drops off the cat, goes back to the to island, picks up a cat and
the dog and the cat go to the Mainland.
5. The dog drops off the cat,goes back to the island, picks up a cat and
they go back to the Mainland.
6.The cat drops off the dog, goes back to the island,picks up the last dog
and they go to the Mainland.
Answer from Sherri(Jefferson R.d School, Pittsford NY)
The first trip is a dog and cat. The cat stays on the main land. The dog
returns to pick up another dog. One dog stays on the main land. The dog
returns to pick up a cat. The cat stays on the main land. The dog returns
to pick up another dog. One dog stays on the main land. The dog returns
to pick up a cat, and they both stay on the main land. This problem seemed
fairly easy.
Elizabeth Ahlers, 5th grade, Paul Nass, Georgetown Day School, Washington DC.
My answer:
1st trip 2 dogs/ one dog goes back.
2nd trip 1 dog and 1 cat/ 1 cat goes back
3rd trip 1 dog and 1 cat/1 cat goes back
4th trip 2 cats/ 1 dog goes back
5th trip 1 dog and 1 cat/ nobody goes back
How I got my answer: I used trail and error.
Lisa Orenstein-Paul Nass-3rd Grade-Georgetown Day School-Washington, D.C.
STEP ONE:two dogs go to the main land.
STEP TWO:one dog goes back again and picks up another cat and drops that cat
of at the main land.
STEP FOUR:one dog goes back again and picksup another cat and drops off that
cat.
STEP FIVE: dog goes back again and picks up the last dog and they both go to
the main land.
Thomas A. Grace, 5th grade, Paul Nass, Georgetown Day School, Washington D.C.
C=Cat
D=Dog
C+D go out, C comes back. 2D go out, 1D comes back. 2C go out, C+D come
back. 2C go out, 1D comes back. 2D go out, 1D comes back. 2D go out.
Hi this is Matt, Dan, Elizabeth, Tony and Will. We have the answer for the
problem of the week. The first thing we did was working with numbers and
trying to have the number of dogs not outnumber the number of cats. Then we
came up with this answer:
2 dogs went and 1 dog was left at the mainland. The other dog came back and
picked up a cat and the cat got left at the mainland.
The dog came back and got off.
The 2 cats got on and 1 was left at mainland. The other cat came back and
picked up a dog and the dog was left at the mainland.
The cat came back to the island and picked up a dog and they both got off
at the mainland.
Your math solvers,
Matt, Dan,Eliz,Tony and Will
P.S. We made a paper boat and used squares of paper to represent each cat
and dog. That really helped us!
Teacher's name: Paul Nass
Benjie Achtenberg
5th grade
Georgetown Day School, Washington D.C. U.S.A.
1. Send 1cat and 1dog over and have the dod drive the boat back. 2. Have
the dog take a dog over and hve the dog drive the boat back. 3. Have the
dog take another cat over and drive the boat back. 4. Have the dog take the
last dog over and drive the boat back. 5. Have th dog take the last cat
over and both animals get of at the mainland.
The following are all in fifth grade at Rogers Elementary School
District in Pittsburgh Pa. Dr. Slomer-teacher
Kirk Thompson
They all got to the mainland by taking two animals across,
one gets off, but the other one comes back. Then, another animal
comes on and the one that was on the first trip get off and the other
one comes back to get another. They keep doing this until all the
animals are off the island.
Brad Jadlowiec
There would be 1 dog, i cat on each boat trip and the boat
would have three trips to the mainland.
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