Elementary POW, October 9-13, 1995
Elementary POW Problems || October-December, 1995 Problems || Elementary POW Main Page
****************************************************** Elementary Problem of the Week, October 9-13, 1995 This week's problem was submitted by Lisa Varner and Candice Pennington, Ridgeview High School, Bakersfield, California. Your neighbor who is in the second grade is just now learning her times tables. She is having a problem understanding what multiplication means. Explain to her 5x6 as simply as possible. ***************************************************** This week's Bonus Puzzler was submitted by Krista Mignoni, Mount St. Joseph Academy, Flourtown, Pennsylvania. Divide a clock into three parts with two straight lines so that the sum of the numbers in each of the three parts are equal. ******************************************************
Great job this week! Your explanations were terrific! With your help, I'm sure all second graders will now understand the meaning of multiplication. Lamar Scott's explanation was particularly interesting. Tim, Jenny, Dan, and Katie from Pat Comerford-Haley's class Lancaster,NY gave a very interesting analysis of the Bonus Puzzler and Suzanne LeBarron of Grade 4, St. Mary's School, Ticonderoga, New York USA used a digital clock in her solution to this question. Very interesting! ****************************************************** Correct solutions to the first question were submitted by: Pat Hagan's Sixth Grade Class Students: Lamar Scott, Mike Schueftan, Bill Van Ess Mr. Miller's Intermediate Class, The Rice School, La Escuela Rice Students: Chase Boles and Eric Rachlin Pat Comerford-Haley's class Lancaster,NY Students: Lora, Kim, Greg, and Mike, Kurt, Kevin, Sam, and Lynne, Ken, Kyle, Carlene, and Bethany, Lynne, Sam, Kevin, and Kurt, Tim, Jenny, Dan, and Katie Theresa Perreault class from Wickford Elementary School, Grade 4 Students: Alexandra, Joe H, Ray. Mrs. Bahm's 4th grade class at Minster School in Minster, Ohio Mrs. Palmbach's 3rd grade class at Center School in Stow, MA Students: Joanna Brench, Jonathan LaRosee, Danny Glover & Garrett Jones, Robert Golder Standard Elementary School Bakersfield, CA Students: Thomas Tucker, Fourth Grade and Chris Brown Third Grade Mrs. Trudell's 3rd grade class - Center School - Stow MA Students: Cameron Kerr, Joshua De Benedetto Ms. Nancy Reid's Class Student: Trevor Hogan St. Mary's School, Ticonderoga, New York USA Students: Alex Michalak, grade five, Suzanne LeBarron of Grade 4, Kaitlyn Pote Cathy Weir's Class Students: Amy Lee and Morgan Nelson. ************************************************* Correct solutions to the Bonus Puzzler were submitted by: Lynne, Sam, Kevin, and Kurt Tim, Jenny, Dan, and Katie Pat Comerford-Haley's class Lancaster,NY: Suzanne LeBarron of Grade 4. St. Mary's School, Ticonderoga, New York USA Chase Boles and Eric Rachlin. MR. MILLER'S INTERMEDIATE CLASS THE RICE SCHOOL/ LA ESCUELA RICE Jamard Smith, 4th Grade School of Rose Valley, PA Trevor Hogan Nancy Reid's Class
Pat Hagan's Sixth Grade Class:
1. Once there lived a couple who lived in a cave. They have never seen a
math problem or number in their whole life. I tried to teach them, but
they kept on asking me all these questions, like," What is the "X" for?" I
said that the "X" stands for multiplication. They asked," What is
multiplication?" I said multiplication is like addition. They said, "What
is addition?" I said additions is a number you add, like, for instance, 2 +
2. Hold 2 fingers and another 2 and what do you get? They said they got 4.
Muliplication is the same way , but a little different, I said, but you
still add, but, for instance, 6 X 8 is the same way as saying 6 + 6 + 6 + 6
+ 6 + 6 + 6 + 6. Now you know how to do math. Now they are both math teachers.
This is my story from Lamar Scott.
2. Multiplication is very easy. 6 X 8 = 48. Think of 8 as 8 apples. Same
thing with 6. Now 8 apples and someone gives him 8 more apples, then
another and 8 then another 8 then another 8 then another 8. But an easy way
to do this is saying 6 X 8. That's all you have to do. Mike Schueftan
3. 6 X 8 is six, eight times or eight, six times. The answer is 48,
because
6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 48 or 8 + 8 + 8 + 8 + 8 + 8 =48. The "x"
means if you had 6 X 8 you would do 6, 8 times or 8, 6 times. You could do
that by adding (the +) 6 rocks 8 times or 8 rocks 6 times.
* * * * * * * * * * * * * *
* * * * * * * * * * * * * *
* * * * * * * * or * * * * * *
* * * * * * * * * * * * * *
* * * * * * * * * * * * * *
* * * * * * * * * * * * * *
* * * * * *
* * * * * *
>Bill Van Ess
******************************************************
FROM MR. MILLER'S INTERMEDIATE CLASS, THE RICE SCHOOL/ LA ESCUELA RICE
First you draw 6 circles aand put 5 dots in each circle. Then you count all
the dots together and that's your answer.Because
multiplication talks about groups of numbers.
CHALLENGE:Draw a clock with all of the numbers. If you draw a line above
the 10 and 3 and another line over the 8and 5, each section equals 26.
-ANSWEReD BY CHHASE BOLES and ERIC RACHLIN.
******************************************************
From the class of Pat Comerford-Haley's class Lancaster,NY:
This week we worked again in small groups but could not come to a concensus
so we are sending all our responses followed by the names of group members.
OK, multiplication is kind of like adding. 5x6 is like counting by five 6
times like 5,10,15,20,25,30.
-from Lora,Kim,Greg, and Mike
Take six cups and put five pennies in each cup. Then count how many pennies
are in all. That's what 5x6 means.
-from Kurt, Kevin, Sam, and Lynne
Say you have 6 groups of candy. Each group should have 5 pieces of candy.
Add all the groups together and your answer will be 30. That's what 5x6
means.
-from Liz, Dana, Ben, and Tony
Multiplication means to add the first number as many times as the second
number. Example: 5x6 : add 5 six times and your answer is 30. Or you can
add the second number as many times as the first number. Whichever is easy
for you.
-from Tim, Dan, Jennifer, and Kaitlin
All you have to do is count by 5's six times or count by 6's five times and
your answer is 30.
-from Ken, Kyle, Carlene, and Bethany
BONUS
After much pulling of hair, all groups arrived at the same answer. The
following two explanations show two different strategies:
We added all the numbers in the clock and got 78. Then we found a way to
get the numbers equal 3 ways and that was 26. We tried about 9 ways and
kept adding the numbers until we got the first part with 11,12,1,and 2 the
second part with 10,9,3, and 4 and the last part is 8,7,6, and 5. The lines
go across the clock from between 10 and 11 to between 2 and 3. The other
line goes across from between 9 and 8 to between 4 and 5.
-from: Lynne, Sam, Kevin, and Kurt
Our table found out that if you take 12+1 and 11+2 and 10+3 and 9+4 and 8+5
and 7+6 all the numbers add up to 13 in each group. So, that's how we got
our answer.Draw lines connecting those numbers. Then draw the two lines to
separate 12,1,2,11 and 10,3,9,4 and 8,5,7,6. And that's how we got our
answer.
-from: Tim, Jenny, Dan, and Katie
Once again, thanks to the fine mathemeticians for their creations!
******************************************************
Problem of the week Answers from Wickford Elementary School, Grade 4
>From Alexandra: Use something you can move
Tell your neighbor to put some beans or small stones on the table. Count
out five and put them in a group.
Count out five again and put them in a different group. Do this for a total
of six times.
Look at the groups and tell your neighbor that there are six groups of five
and that makes thirty.
>From Joe H: Draw a picture
Tell them to draw five lines on a piece of paper and circle them. Count 5
Then they draw five more lines, circle them and count 10 Draw five more
lines and that's 15
Draw five more and that's 20. Draw five more and that's 25, draw five more
and that's 30. When you are done you have 5 down there 6 times and that
counts to thirty.
>From Ray: Make a Chart
Tell them to draw a big box and make it into a chart.(Lines down and Lines
across to form little boxes)
In each box, write a number. Stop the row when you come to five. Do six
rows. When you are done numbering them you should be at thirty.
We decided on these after sharing all the possibilities with our class.
******************************************************
The 4th grade students at Minster School in Minster, Ohio hereby submit
this answer to the problem of the week:
Multiplication is repeated addition. So in order to solve this problem you
could have done one of two things. You could add 5 six times or you could
add 6 five times. Either way you will get an answer of 30.
See the diagram below:
5+5+5+5+5+5=30OR 6+6+6+6+6=30
If you like pictures it would look like this:
xxxxx+xxxxx+xxxxx
xxxxx+xxxxx+xxxxx
= xxxxx xxxxx xxxxx
xxxxx xxxxx xxxxx
Respectfully submitted,
Mrs. Bahm's 4th grade class
******************************************************
Mrs. Palmbach's 3rd grade class at Center School in Stow, MA
Joanna Brench -
1.Sent a drawing of five groups of six objects.
2.No answer given
Jonathan LaRosee -
1.Count to five, six times!
2.He had a drawing of a clock with a line under the 10 and the 2
and a perpendicular line up to the 12.
Danny Glover & Garrett Jones
1.Count to five, six times.
2.10, 11, 12, 1, 2 = 36. Plus they had the same drawing of a clock
with a line under the 10 and across to the 2 with a perpendicular line in
the middle of this line up to the 12.
Robert Golder
1.It's when you have five groups of six things.
2.No answer given
******************************************************
If the kid knows how to skip by fives then she just needs to skip by fives
six times.
-Thomas Tucker Fourth Grade student at Standard Elementary School
Bakersfield, CA
You just add five six times and see what you come up with.
-Chris Brown Third Grade student at Standard Elementary School Bakersfield,
CA
******************************************************
From Mrs. Trudell's 3rd grade class - Center School - Stow MA
Cameron Kerr
1.You just count to five, six times.
2.no answer given
Joshua De Benedetto
1.Me:Can you count by 5s?
Her: Yes
Me;All you have to do is count by 5s, six times!
2.No answer given
******************************************************
From: Nancy Reid
>by Trevor Hogan
1)You should tell her 5x6 is just 5 added to itslef 6 times. Or it is 5
groups of 6, in diagram form.
2) Put the numbers, 11, 12, 1, 2, in a group. 10, 9, 3, 4 in another. 8, 7,
6, 5 in another. They all equal 26.
>From Alex Michalak, grade five.
For the kid in the second grade having trouble with multiplying 5 x 6,
well, in the first place multiplication means times. And if she is having
trouble with 5 x 6 just ask her if she knows adding. Just tell her to add 5
six times or six five times. Five is probably easier to add. That would
equal 30.
******************************************************
St. Mary's School, Ticonderoga, New York USA
This solution provided by Suzanne LeBarron of Grade 4.
you can add like this 5 +5+5+5+5+5=30 or 6+6+6+6+6=30 or 5x6=30 or you have
five fingers count 6 dots on each finer and then you just add them up or
you have 6 fingers put 5 dots on each finger then you just add them up and
you have your anwser.Which is 30.
you have a digital clock so 2:22 and 2 lines between the first 2 and the
second 2 and then you have a line between the sceond 2 and the third 2 so
you have 2+0 in each box.
I hope it's right.
This solution devised by and typed by Kaitlyn Pote. For the problem 5 x 6
just count by fives six times like this 5,10,15,20,25,30!so the ansewer is
30!
*********************************************
If you had 5 as the first number and 6 as the second number, you
would do
6+6+6+6+6 which is five (6's) or sometimes it's easier to change the problem
around to 6x5 which would be 5+5+5+5+5+5. However, this gives the same
answer
but is a different problem. It's a quick way of adding. The answer is 30.
We also answered the clock problem. You would do a line through the
clock at the top so that the 11, 12, 1, and 2 are in the first section. Then
put a line through the bottom so that 10, 9, 3, 4 are in the middle. The
bottom section would have 8, 7, 6, and 5. Each section equals 26.
John McGill and Eileen Ward
Munsey Park School
Manhasset N.Y.
3rd grade
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