Elementary POW, March 18-22, 1996
Elementary POW Problems || January-March, 1996 Problems || Elementary POW Main Page
****************************************************** Elementary Problem of the Week, March 18 - 22, 1996 This week's problem was submitted by Ryan Grace, Mrs. Brennan's 6th grade class, Drexel Hill School of the Holy Child, Drexel Hill, PA. Dan can throw a ball 5 meters. Joe can throw a ball 4 meters. Mike can throw a ball 3 meters. If they all throw a ball at the same time, as hard as they can, how far apart would they have to stand to have the ball land in the same spot? ******************************************************* Bonus Puzzler My husband, Mr. Wes Carver, enjoys doing the word jumble in the newspaper each day. He made up this one for you. Unscramble the letters in each of the four words below, one letter to each space. The letters in the space with the circle will be used along with the hint below to arrive at your answer. DDVIIE - O - O - O PLRTEI - - - O - O RFACOT O - O - O - RIAP O O - - Hint: What math students have for dessert each year on 3/14. Answer: - - - - - - - - - - ******************************************************
Amy Forster 11 Years Old 7th Grade Cygnet,Australia. **************************************************** Jamie Chan 6th Grade Mr. Len Hall West Beechboro Primary School Perth, West Australia **************************************************** Ryan Higgs 6th Grade Mr. Len Hall West Beechboro Primary School Perth, West Australia **************************************************** Edward Chau 6th Grade Mr. Len Hall West Beechboro Primary School Perth, West Australia **************************************************** Logan Gradison 4th Grade Teacher: Sue Jaggar Georgetown Day School Washington D.C. *************************************************** Liz Grade 4 Teacher: Priscilla Roehm Mandarin Oaks Elementary Jacksonville, FL *************************************************** Sarah P. and Melissa Grade 3 Teacher: Priscilla Roehm Mandarin Oaks Elementary Jacksonville, FL *************************************************** Evan Mossman, Matt Spindler, and Todd Feiler 4th Grade Mr. Fred Rimmel and Mr. Thomas Mueller Kerr Elementary Pittsburgh, PA ************************************************** Maite, Margrethe, and Emmalyn Colleen Brodie Leal School Urbana, IL ************************************************* Brittany Kress and Katie Kleppick Grade 5 Marzoff Elementary School Pittsburgh, PA **************************************************** Amanda Tumminelli,Kim Fugok, Christine McGowan, and Ryan Grace 6th grade Mrs. Brennan Drexel Hill School of the Holy Child Drexel Hill, PA **************************************************** Julie Grade 4 Teacher: Priscilla Roehm Mandarin Oaks Elementary Jacksonville, FL **************************************************** Anthony and Patrick Ms. Duggan Fourth grade **************************************************** Mike Bianchi, Jason Gullifer, and Kevin La France Grade 5 Miss Flynn Bagnall School Groveland, MA **************************************************** Meghan Lovett Grade 4 Ms. Hamilton Bagnall School, Groveland, MA **************************************************** Meghan Ramsey Grade 4 Ms. Hamilton Bagnall School, Groveland, MA **************************************************** Lindsay Bonfanti, Alan Weider, Talia Racca, Bill Mavroides, Rick Piatti, Donnie Aylward, Alexis Karavedas, Joe, Brent and Brian, Jeff Morse, Brian Q., Shauna, Brian, Jennifer Yuszkus, Colin and Justin Grade 6 Mrs. Caruso Bagnall School, Groveland, MA **************************************************** Kristin, Mike and Cory Grade 4 Ms. Arria-Lucey Bagnall School, Groveland, MA **************************************************** Jordan Gable 5th grader Ms. Smollon Lewisboro Elementary School South Salem, NY. **************************************************** Logan Gradison and Andrew Migdail 4th Grade Sue Jaggar Georgetown Day School Washington D.C. **************************************************** Sade Jimoh and Annie Bolotin Geogetown Day School Washington D.C. Joan's and Paul's 4th grade class **************************************************** Kevin Ohashi Fourth grade Teacher: Joan Foster Georgetown Day School Washington D.C. **************************************************** Mike,Christpher and Shane Mrs. Kaye's class **************************************************** Greg Grade 3 Mrs. Kaye **************************************************** Jessica 5th Grade St Joseph's School Seattle, Wa. Teacher: Kristin McNabb ****************************************************
Congratulations to everyone who attempted this problem. There were 40
answers submitted and 36 correct solutions. Thanks again to everyone for
submitting an answer.
*****************************************************************************
Amy Forster
11 Years Old
7th Grade
Cygnet,Australia.
-First I assumed that seperating the boys by 1 m side ways might be a
safe distance.
-To make the triangles easier to work out,I put Dan in the middle of the
other two.
#
T(target)
/|\
/ | \
/ | \
/ | \ 3 m
/ | \
4 m / | \
/ A | B \
/ |y__ \(Mike)
/ | \
/ | \
J (Joe) /_ _x | \
/ | \
/ | \
/ | D
(Dan)
To work out the distance of Joe to Dan.For triangle A,
Using pythagoras
4^2=1^2 + (TX)^2
TX^2= 4^2 -1
= 15
TX =*15
so DX =5-*15
For triangle C,
Using Pythagoras
((5-*15)^2 +1^2= (JD)^2
(5-*15) (5-*15)+1=(JD )^2
25-5*15-5*15+15+1=(JD)^2
*(41-10*15) =JD
JD =1.5067 m
Joe is 1.5 m to the left of Dan
To work out the distance from Mike to Dan
For triangle B
TY^2=3^2
TY^2=3^2 -1^2
TY^2=8
TY =*8
so,YD==5-*8
For triangle D,
DM^2=(5-*8)^2+1^2
=25-5*8-5*8+8+1
=34-10*8
so DM=*(34-10*8)
=2.4 m
so Mike is 2.4 m to the right of Dan.
To find the distance between Joe and Mike which is the length of line JM,
Let Q be the point where line JM crosses line TD.
JQ^2=1^2 +QX^2
=1^2+(TX-TY)^2
=1+[(*15-*8)/2]^2
=1+15/4 - (2*8*15)/4 +8/4
=(27-2*8*15)/4
JQ=*[(27-2*8*15)/4]
=1.128m
Since line JX=YM
and line XQ =QY
Then line JQ must equal QM
so the distance between J and M=2JQ
=2x 1.128
=2.245 m
So Joe and Mike are 2.3 m apart.
For the BONUS PUZZLER
my answer is
A PIECE OF PI.
****************************************************
My name: Jamie Chan
Grade: Year Six
Teachers Name: Mr Len Hall
School: West Beechboro Primary School
Location: Perth, West Australia
Answer: Dan, Joe and Mike stand a metre apart in a radius. The three of
them can move anywhere around the radius on the circumference and still
have the ball hit the hole/mark. The distances apart may vary when they
move. When they are in a line, they are a metre apart. The ball will also
be throuwn into the hole because the strenght of the boys are different as
is the distance.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++
My name: Ryan Higgs
Grade: Year Six
Teachers Name: Mr Len Hall
School: West Beechboro Primary School
Location: Perth, West Australia
Answer:If Dan, Joe and Mike stand in a line there would be metre between
Dan and Joe and Joe and Mike. Dan would be 2 metres from Mike. But it does
not matter if Dan stands 5 metres away from the spot the ball has to land
in. The same goes for Joe and Mike.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++
My name: Edward Chau
Grade: Year Six
Teachers Name: Mr Len Hall
School: West Beechboro Primary School
Location: Perth, West Australia
Answer: If the three of them stand in a straight line, the answer will always
be one metre. Dan is 2 metres apart from Mike and one metre apart from Joe
and Joe is one metre apart from Mike. But, if they all stand on a certian
circle Mike must have a radius of 3 metres, Joe's must have a radius of 4
Metres and Dan's must have a radius of 5 metres. The distance will vary as
they rotate around the circle.
The greatest distance Dan can be from Mike is 8 metres,The greatest
distance Dan can be from Joe is nine metres. The greatest distance Joe can
be from Mike is seven metres.
****************************************************
Logan Gradison
4th Grade
Teacher: Sue Jaggar
Georgetown Day School
Washington D.C.
Each person throws 1 meter further than the other so you put Dan
behind Joe and Joe behind Mike.
***************************************************
Liz
Grade 4
Priscilla Roehm
Mandarin Oaks Elementary
Jacksonville, FL
1 meter apart because 5, 4, 3 are only 1 number apart.
Bonus:
A piece of pie. In math pi = 3.14. It is a play on words.
***************************************************
Sarah P. and Melissa
Grade 3
Priscilla Roehm
Mandarin Oaks Elementary
Jacksonville, FL
Starting with Mike, he should move back two meters. Then Joe should move
back one meter. Then Dan should not move back at all.
***************************************************
Evan Mossman, Matt Spindler, and Todd Feiler
4th Grade
Mr. Fred Rimmel and Mr. Thomas Mueller
Kerr Elementary Pittsburgh, PA
Dan, Joe, and Mike would each have to stand 1 meter apart. The
order would be Mike in the front. Joe would be 1 meter behind Mike. And Dan
would be 1 meter behind Joe. We arrived at this answer when we made a
diagram on the marker board. Our reasoning was since each person was 1
meter apart in there throwing ability, they each had to stand 1 meter apart
from their starting point.
BONUS
What do math students have for dessert each year on 3/14 (3.14)?
The answer we came upon was, "A PIECE OF PI"
*************************************************
Maite, Margrethe, and Emmalyn
Colleen Brodie
Leal School
Urbana, IL
Dan, Joe, and Mike will have to stand 1 meter apart to throw the
same distance. Because their balls land 1 meter apart if they stand in the
same spot.
How we figured this out was we drew a chart in our notebooks
showing where they stood and how far apart their balls landed.
*************************************************
Brittany Kress and Katie Kleppick
Grade 5
Marzoff Elementary School
Pittsburgh, PA
To get each of them to throw to the five meter line, Dan must stand at
the 0 meter line, Joe must stand at the 1 meter line, and Mike must stand at
the 2 meter line.
Mike __________________________________
Joe _____________________________________________
Dan ________________________________________________________
0 1 2 3 4 5
Bonus:
Divide
Triple
Factor
Pair
A Piece of pi
****************************************************
Amanda Tumminelli,Kim Fugok, Christine McGowan, and Ryan Grace
6th grade
Mrs. Brennan
Drexel Hill School of the Holy Child
Drexel Hill, PA
First, we sketched the problem on the board like this. Dan = A, Joe = B,
Mike = C and the landing spot = D.
A B C D
Dan has to stand 1 meter further away than Joe. Joes has to stand 1 meter
further aways than Mike. Also, Dan and Mike are 2 meters apart. If they
stand in these positions and throw the ball at the same time the balls will
land at point D at the same time.
Bonus Problem
The words are: divide, triple, factor, and pair. The circled letters
unscrambled spell - A PIECE OF PI
****************************************************
Julie
Grade 4
Priscilla Roehm
Mandarin Oaks Elementary
Jacksonville, FL
They all have to stand 1 meter apart. Explanation - You know that if it is
3 meters, 4 meters, 5 meters that you would only have to stand 1 meter apart.
Bonus:
Answer: a piece of pie
Explanation: pi - the symbol that stands for the ratio of the
circumference of a circle to its diameter. Pi equals about 3.14159.
****************************************************
Anthony and Patrick
Ms. Duggan
Fourth grade
We figured out that each boy has to stand as many meters away as they
can throw. Because Dan can throw 5 meters, if he walked 5 meters back, he
would throw it 5 meters ahead. And it's the same for everybody, except for
how
many meters they can throw.
****************************************************
Mike Bianchi, Jason Gullifer, and Kevin La France
Grade 5
Miss Flynn
Bagnall School, Groveland, MA
We drew a picture to help solve the problem. Dan would stay there, Joe
would walk up one meter and Mike would walk up two meters. So Dan is 1 meter
from Joe and two meters from Mike. Joe is one meter from Mike.
Dan--------------------5m
Joe---------------4m
Mike---------3m
****************************************************
Meghan Lovett
Grade 4
Ms. Hamilton
Bagnall School, Groveland, MA
There would be 2 meters between Dan and Mike, 1 meter between
Dan and Joe, and 1 meter between Joe and Mike. First I drew the
finish line where all the balls will land. then off that, I drew 5
inches
( to take the place of meters) for Dan. Then below that I drew 4
inches for Joe. After that, I drew 3 inches for Mike. The answer I came
up with is that Dan stood 1 meter from Joe and 2 meters away from
Mike. Joe stood 1 meter away from both boys and Mike stood 1 meter
away from Joe and 2 meters away from Dan.
Dan--------------------5m
Joe---------------4m
Mike---------3m
Bonus: A piece of pi
****************************************************
Meghan Ramsey
Grade 4
Ms. Hamilton
Bagnall School, Groveland, MA
They would stand one meter apart. I drew a picture. I drew a line
from an even line in how hard the boys can throw. Then I subtracted
the boys meters of throwing. Dan is one meter from Joe and 2
meters from Mike while Joe is one meter from Mike.
Dan--------------------5m
Joe---------------4m
Mike---------3m
Bonus: A piece of pi
****************************************************
Lindsay Bonfanti, Alan Weider, Talia Racca, Bill Mavroides,
Rick Piatti, Donnie Aylward, Alexis Karavedas, Joe, Brent and Brian,
Jeff Morse, Brian Q., Shauna, Brian,
Jennifer Yuszkus, Colin and Justin
Grade 6
Mrs. Caruso
Bagnall School, Groveland, MA
Colin and Justin: They would both have to stand one meter in front
of the other person. I showed this by the diagram.
Dan--------------------5m
Joe---------------4m
Mike---------3m
Jennifer: They would both have to stand one meter apart to throw
the same length.
Dan --1m--Joe--1m--Mike----------3m-------------|
Brain Q.: 1 meter. Dan --1m--Joe--1m--Mike----------3m-------------|
Shauna: They would each have to stand one meter away from each
other.
Dan--------------------5m
Joe---------------4m
Mike---------3m
Jeff: Joe would have to move up one meter and Mike would have to
move up 2 meters.
Jon, Brent, Brian: Dan is one meter behind Joe and Joe is one meter
behind Mike.
Bonus: A piece of pi
Alexis: Joe needs to stand 1 meter ahead of Dan and Mike needs to
stand 2 meters ahead of Dan and 1 meter ahead of Joe.
Donnie: Dan should stand 1 meter behind Joe. Joe should stand 1
meter behind Mike. Then the balls would go the same distance.
Bill and Rick: One meter apart.
Talia: Joe needs to stand one meter ahead of Dan and Mike needs
to stand two meters ahead of Dan and 1 meter ahead of Joe.
Alan: 1 meter apart. I made a line of dots and pretended each dot
was 1 meter apart. I put Dan on the first dot and counted down 5 dots.
Then I put Joe on the second dot and counted down 4 dots. I did the
same for Mike.
Dan Joe Mike
- - - - - |
Lindsay: Dan would have to stand 1 meter behind Joe while Joe is standing
in his spot and Mike would stand one meter in front of Joe. I got this
answer by figuring Dan can throw 1 meter more than Joe, so he will take a
step back. Mike can throw 1 meter less than Joe so he takes a step forward.
When they throw their balls, they should all land in the same spot.
Dan--------------------5m
Joe---------------4m
Mike---------3m
****************************************************
Kristin, Mike and Cory
Grade 4
Ms. Arria-Lucey
Bagnall School, Groveland, MA
Kristin: They would have to stand one meter apart.
Mike and Cory: Joe would have to stand one meter above Dan. Mike
would stand one meter above Joe and 2 meters above Dan because
Joe and Mike throw shorter than Dan.
Dan--------------------5m
Joe---------------4m
Mike---------3m
****************************************************
Jordan Gable
5th grader
Ms. Smollon
Lewisboro Elementary School
South Salem, NY.
If Mike can throw the ball 3 meters and Dan can throw it 5 meters in
order to have it land in the same spot, Mike has to stand 2 meters ahead of
Dan. Joe has to stand 1 meter in front of Dan and 1 meter behind Mike. So
when Dan throws the ball, it travels 2 meters before it gets to Mike and then
3 meters further. When Joe throws the ball, it has to travel 1 meter before
it gets to Mike and then 3 meters further. When Mike throws the ball it
travels 3 meters and lands in the same spot as the other 2 balls.
****************************************************
Logan Gradison and Andrew Migdail
4th Grade
Sue Jaggar
Georgetown Day School
Washington D.C.
Each person throws 1 meter further than the other so you put Dan
behind Joe and Joe behind Mike.
****************************************************
Sade Jimoh and Annie Bolotin
Geogetown Day School Washington D.C.
Joan's and Paul's 4th grade math classes
Dan stands one meter behind Joe. Joe stands one meter behind Mike.
We figured this out by if Dan can throw a ball 5 feet then he must be in the
back and if Mike can throw the ball 3 meters he has to be in the front. Since
5 and 3 are a difference by two meters and Joe has to be in the middle it is
one meter.
Bonus Puzzler:
DIVIDE
TRIPLE
FACTOR
PAIR
A PIECE OF PI
We figured this out by guessing the last two words because they seemed
easier. The only two possible ones were "of" and "pi." Then using the rest of
the letters we figured out "piece" because the first word had to be "a".
****************************************************
Kevin Ohashi
Fourth grade
Teacher: Joan Foster
Georgetown Day School
Washington D.C.
Dan is five meters away from the spot. Joe is four meters away (one meter in
front of Dan). Mike is three meters away from the spot.
****************************************************
Mike,Christpher and Shane
Mrs. Kaye's class
If Dan could throw five meters away, then Joe who could throw four meters
would be one meter in front of Dan. Mike who could throw three meters would
have to be one meter in front of Joe.
Dan stays where he is. Joe moves up one meter from Dan. Mike has to go up
two
meters from Dan.
Mike
Joe
Dan
Bonus Puzzler
1. divide
2. triple
3. factor
4. pair
answer
A piece of pi.
****************************************************
Greg
Grade 3
Mrs. Kaye
Dan steps 2 meters behind Mike. Joe steps 1 meter behind Mike and Mike stays
where he is.
My strategy was thinking that Dan needed to step 2 meters behind Mike and Joe
needed to step 1 meter behind Mike. So Mike had to stay where he was and if
they did they would throw the ball and it would land in the same place.
****************************************************
Jessica
5th Grade
St Joseph's School
Seattle, Wa.
Teacher: Kristin McNabb
Mike stands 1 meter in front of Joe, and 2 meters in front of
Dan. Joe stands 1 meter in front of Dan. Then by the time all the balls
reach Mike they'll have 3 more meters they can each travel( in the air)
****************************************************
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