Elementary POW, March 25-29, 1996
Elementary POW Problems || January-March, 1996 Problems || Elementary POW Main Page
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Elementary Problem of the Week, March 25-29,1996
This week's problem was submitted by Michael Murphy, Cory Styrczula, and
Brian Parks, Grade 4, Ms. Arria-Lucey, Bagnall School, Groveland, MA.
In basketball there are three kinds of shots. A foul shot is worth
1 point, a shot taken inside the three point line is worth 2 points,
and a shot taken outside the three point line is worth 3 points.
During one game Magic Johnson and Michael Jordan both scored
20 points. Use the information below to figure out how many foul
shots, 2 point shots, and 3 point shots each player scored.
Magic didn't score any foul shots.
Magic scored more 2 point shots than Michael.
Both players scored the same number of 3 point shots.
Michael scored 1 less foul shot than Magic has 2 point shots.
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Correct Solutions submitted by:
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>From Amy Forster,age 11,grade 7
Cygnet,Tasmania,Australia,Home school.
E-mail
Wilkins/Forster family
Crooked Tree Point.Cygnet.
Tasmania.Australia 7112.
*******************
Sam Ravelson, 9 years old
fourth grade
Underwood School
Newton, MA
*******************
Name: Ravi, Matt, Robert, and Alesha
School: Leal
Teacher: Colleen Brodie
State: IL
City: Urbana
Grade: 4th
****************
Chris Wade
Mrs.Pensa's 3rd grade class
Center School - Stow,MA
******************
Martha Powers
Mrs. Walton's 5th Grade
Center School, Stow, MA
******************
Kristin Squires
Mrs.Pensa's 3rd grade class
Center School - Stow,MA
******************
Matt, Tony, Danny, Kate and E.P
Miss Duggan's fourth grade class
Munsey Park School
Manhasset, NY
******************
Brittany Kress
Grade 5
Marzoff Elementary School
Pittsburgh, PA
******************
John McGill and Eileen Ward
Mrs. Moran - Third Grade
Munsey Park School
Manhasset, NY
*****************
Meagan R., Nick, Meagan L., Mike, Julia,
Grade 4
Ms. Arria-Lucey
Bagnall School, Groveland, MA
*****************
Mike, Peter, Mark, Sam, Cathy
Mrs. Crawford
Grade 5
Bagnall School, Groveland, MA
*****************
Arthur Clausnitzer, Mike Bianchi, Bobby Tucker
Grade 5
Miss Flynn
Bagnall School, Groveland, MA
**********************
Rudianne Subtach, Chris Belkas
Grade 4
Mrs. Sturtevant
Bagnall School, Groveland, MA
****************
Brent, Jon, and Nick; Colin and Justin; Craig and Brian G;
Mrs. Caruso
Bagnall School, Groveland, MA
********************
Rebecca
Grade 3, Mrs. Kaye
Lincoln Elementary
Burlingame, CA
**************
Brandon H.
Grade 4
Priscilla Roehm
Mandarin Oaks Elementary
Jacksonville, FL
*************
Emily Y.
Grade 4
Priscilla Roehm
Mandarin Oaks Elementary
Jacksonville, FL
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Thanks again to Michael Murphy, Cory Styrczula, and Brian Parks, Grade 4,
Ms. Arria-Lucey, Bagnall School, Groveland, MA. for submitting this week's
problem.
I'd also like to share with you a note from Amy Fosrter in respone to my
students interest in learning more about Australia.
Dear Ruth,
Thankyou for your E-mail. I get a lot of pleasure out of doing your
problems.I think it is great that you and your students show interest in
people in other places and offer a chance for other people who are
interested in maths to communicate. It is not other wise easy to find
people who really enjoy problem solving.
Aboriginal Dancers from Mornington Island (Australia) visited Cygnet last
week. Their Dances were about fishing, collecting fruit hunting wallabies.
They also made fire by spinning one stick on top of another stick. They
carefully blew the fire to make the flames bigger, and carried it in a
shell bigger than their heads while they did a fire dance.
>From Amy Forster,age 11,grade 7
Cygnet,Tasmania,Australia,Home school.
E-mail
Wilkins/Forster family
Crooked Tree Point.Cygnet.
Tasmania.Australia 7112.
***********************
Kristin Squires, Stow MA Center school.
the way that I solved this problem was by making a graph like the one below,
then one the three column I knew that they had to be the same number of 3
pointers so I Put the number 1 under the 3 for both of the players. I
found out that that didn't work so I tried two and I got it to work and
here is how.
Magic scored 7 2 pointer shots. and then 2 ,3 pointer shots.
and then Michael cored 6 one pointer shots.4 two pointer shots, pointer
shots, and then 2 3 pointer shots.
Magic 1 2 3
Michael 1 2 3
- 7 2
6 4 2
-
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Martha Powers - Mrs. Walton's 5th Grade Center School Stow MA
I figured out these answers by making a graph. On the top of the grid , I
put 1 point,2 points and 3 points. On the side of the grid I put Michael
and Magic. All of these things that I just said,were on seperate lines.
Then I used the clues that you gave me,and here is my solution.Michael
got 2 baskets for the 3 pointers,4 baskets for the 2 pointers and 6
baskets for the 1 pointers. Magic got 2 baskets for the 3 pointers, 7
baskets for the 2 pointers and 0 1 pointers.
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Chris Wade - Mrs.Pensa's 3rd grade class-Center School - Stow,MA
First I knew Magic scored an odd number of 2-point shots because
Jordan would have to have an even number of foul shots. So the only way
that would work is to have 2 3-point shots each. Also for Magic to have 7
2-point shots and for Jordan to have 4-point shots. For Jordan, he has 4
2-point shots, 2 3-point shots, and 6 foul shots. For Magic, he has 7
2-point shots, 2 3-point shots, and 0 foul shots.
**************************
Answer: Magic scored 7 2point shots and 2 3point shots.
Michael scored 6 1point shots,4 2point shots,and 2 3point shots.
Solution:Let x= the number of foul shots
Let y = number of 2 point shots by Magic
Let Y ="" """
" Michael
Let z ="" 3 point shots.
I was able to write these equations from the given facts:
2 y + 3 z = 20- Magic - equation1.
y-1+2Y+3z=20
so, y+2Y+3z=21- Michael -equation 2.
y>Y-equation 3.
Equation 1. is true when y=1 & z=6
or y=4 & z=4
or y=7 & z=2
I substituted
y=4 and z= 4 into 2. to find Y
y+2Y+3z= 21
4+2Y+3(4)=21
2Y=21 -6-7
Y =5/2 & You can't have half a point
so I tried
y=7 and z=2
y+2Y+3z=21
7+2Y+3(2)=21
2Y=21-6-7
2Y=8
Y=4
y must be greater than Y,and 7 is greater than 4.So Y & y values must be
correct.
So Magic scored 7 2point shots & 2 3point shots
Michael scored 6 1point shots,4 2point
shots&2 3point shots.
>From Amy
Forster,age 11,grade 7,Cygnet,Tasmania,Australia,Home school.
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Hi! This is Matt, Tony, Danny, Kate and E.P.. We are responding to this math
problem of the week. At first we were stumped, but then we got the idea.
First
we played around with numbers, after a lot of thinking Matt came through with
the answer. The answer is: Magic scored:
2, 3 point shots
7, 2 point shots
Michael scored:
2, 3 point shots
4, 2 point shots
6, Foul shots
Take care now, Bye ,Bye then!!!!!!!!
Matt, Tony, Danny, Kate and E.P
Miss Duggan's fourth grade class
Munsey Park School
Manhasset, NY
******************
Meagan R., Nick, Meagan L., Mike, Julia,
Grade 4
Ms. Arria-Lucey
Bagnall School, Groveland, MA
Magic had 7 shots inside
the foul line and 2 shots outside the foul line. Michael had 6 foul
shots,
4 shots inside the foul line, and 2 shots outside the foul line.
Meagan R.: The way I solved this was by shuffling the different combin-
ations of foul shots, inside shots and outside shots around. I also used
the clues to find the answer.
Nick: First I made a chart showing Magic and Michael and the
number of points for each person. After that I used guess and check.
That's how I got my answer.
Meagan L: First I categorized points and the players names.
>From the clues, I started eliminating possibilities. From the clues, I
got Magic's score. Then I worked on Michael's. From each clue I
got the number of Micheal's shots.
Mike: On the POW, I made a chart and on the left side from top to
bottom I labeled: 2PT, 3PT, FT, and TOTAL PT. Then I figured out
ways to make 1, 2, and 3 points equal 20 points. Then I changed
the amounts that equal 20 points and made them fit the clues.
Julia: In clue 1, I noticed that Magic didn't score any foul shots so
I put down a zero. In clue 2, Magic scored more two point shots
than Michael so I started plugging in numbers until I got the answer.
********************
Mike, Peter, Mark, Sam, Cathy
Mrs. Crawford
Grade 5
Bagnall School, Groveland, MA
Magic had 7 shots inside the foul line and 2 shots outside the foul line.
Michael had 6 foul shots, 4 shots inside the foul line, and 2 shots outside
the foul line.
Mike: I gave Micheal 6 one points, 4 two points and 2 three points
and if you add them up together, he has 20 points. Magic has 7
two pointers and 2 three pointers and that equals 20. So it gave
them 20 points each.
Peter: I said to myself, what are the numbers for Michael that add
up to 20. I got 2, 3 pointers equals 6. Therefore, Magic also had 2,
3 pointers. Then I subtracted 6 from 20 and got 14. Magic didn't >score
any foul shots so he scored 7, 2 point shots. But Michael >scored 1 less
foul shot than Magic did 2's. So Michael had 6 foul
shots and 4 2's which adds up to 20.
Mark: I started with all 3'2 and I did the 2 and 1's and eventually
figured it out.
Sam: Magic-I added two 3 point shots which gave me 6 points. I added 7,
two point shots which gave me 14 points. Then I added >14 and 6 which is
20 points. Michael- I added up two 3 point shots
which gave me 6. Then I did 4 two point shots which gave me 8. >Then I
did 6 foul shots. I did 6 + 6 = 12 then 12 + 8 = 20 and that's >how many
shots he took of every kind.
Cathy: I mostly did trial and error and using what I knew.
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Arthur Clausnitzer, Mike Bianchi, Bobby Tucker
Grade 5
Miss Flynn
Bagnall School, Groveland, MA
Arthur, Mike and Bobby said Magic had 7 shots inside the foul line
and 2 shots outside the foul line. Michael had 6 foul shots, 4 shots
inside the foul line, and 2 shots outside the foul line.
Arthur: First I figured out Magic's shots. Then I filled in Michael's
according to what I needed.
Mike: I used guess and check and a table to help me.
Bobby: I made a chart to show how many of each were made. I did
it by multiplying and changing the numbers around until I got an
answer.
*****************
Rudianne Subtach, Chris Belkas
Grade 4
Mrs. Sturtevant
Bagnall School, Groveland, MA
Both students said Magic had 7 shots inside the foul line and 2
shots outside the foul line. Michael had 6 foul shots, 4 shots
inside the foul line, and 2 shots outside the foul line.
Rudianne: I made a graph like the one above. Then I used the
clues to figure out the problem and I kept trying until I got it.
Chris: Well Magic didn't score any foul shots. I guess 2, 3 point shots,
added Michael's one point shots and both their 2 point shots
to come up with this.
*******************
Brent, Jon, and Nick; Colin and Justin; Craig and Brian G;
Mrs. Caruso
Bagnall School, Groveland, MA
Magic had 7 shots inside the foul line and 2 shots outside the foul line.
Michael had 6 foul shots, 4 shots inside the foul line, and 2 shots outside
the foul line.
Craig and Brian G: I got this answer by giving Magic all 2 point shots
and Michael 9 foul shots and 5 two point shots and changed the
numbers around and got Magic with 7 shots inside the foul line and
2 shots outside the foul line. Michael had 6 foul shots, 4 shots inside
the foul line, and 2 shots outside the foul line.
***********************
I used a chart.I don't know how to explain it but here's the
answer.Michael got
6 foul points,4 two points,and 2 three points.And Magic got 0 foul points,7
two
points,and 2 three points.My dad helped me by asking me what this number is
x
what another number is.I wrote down the answer
from,Rebecca
Lincoln Elementary, Grade 3, Mrs. Kaye
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1 point foul 2 points 3 points
Magic Johnson 0 7 2
Michael Johnson 6 4 2
I knew that Magic had no foul shots. I figured out how 3-point shots you
could get and add all two-point shots to equal 20. Then I took one shot
away from the 2-point shots and Michael had that many foul shots. Michael
had the same amout of 3-pointers as Magic. Then I added free throw shots
with foul shots and came out with the two-point shots.
Brandon H.
Grade 4
Priscilla Roehm
Mandarin Oaks Elementary
Jacksonville, FL
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Michael Jordan scored 4 - 2 pts., 2 3pts., and 6 fouls. Magic Johnson
scored 7 2pt. shots, 2 3pt. shots, and 0 fouls. I just started playing
around with numbers and got this. First, I did Michael's score and I had it
so he got a total of 20. Then I worked on Magic's score and I did the same
3 pt., 0 fouls, and 1 more 2 pt. than Michael had fouls and it worked out so
they both had 20 pts.
Emily Y.
Grade 4
Priscilla Roehm
Mandarin Oaks Elementary
Jacksonville, FL
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