Elementary POW, January 29-February 2, 1996
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****************************************************** Elementary Problem of the Week, January 29- February 2, 1996 This week's problem was created by Meghan Ramsey, Meghan Lovett, Nick Stephenson, Mike Dennis, and Julia Colpitts, from Ms. Hillary Seager's 4th grade class, Bagnall School, Groveland, MA We have a large jar of jelly beans. The number of jelly beans is a 3 digit number. The sum of the digits is an odd number. If you divide this number of jelly beans between 2 kids, there will be 1 jelly bean left over. The sum of the ones digit and the tens digit is one less than the hundreds digit. If you divide this number of jelly beans between 10 kids, there will be 3 jelly beans left over. The ones digit is half the sum of the tens digit and the hundreds digit. The number of jelly beans is less than 800. How many jelly beans are there? *******************************************************
******************** 3rd Grade Math Masters Gage School Rochester MN 55901 Dan Frissora,advisor Students:Jill Eikenhorst, Adam Falk, Teresa Frissora, Susan Horsman, Ben Rattle, and Rachel Stroetz ************* Georgtown Day School Washington D.C. Joan's 4th Paul's Math Students: Cyrus Kharas, Annie Bolotin, David Driscoll ************** Andrew Oswald The Oldest Group Ellen Murphey's Class The School in Rose Valley Media, PA ************** Lincoln Elementary School Burlingame, CA Ms. Nancy Kaye's 3rd Grade Ashleigh and Rebecca ************* Drexel Hill School of the Holy Child Drexel Hill, PA Ms. Caroline Brennan's 6th grade Amanda Tuminelli, Christine McGowan, Kim Fugok, and Ryan Grace ************** Jefferson Rd. School, Pittsford, N.Y. Ms. Pat Gaborski Michelle and Sherr ************** Munsey Park School Manhasset, NY Mrs. Hirn's fourth grade class Matt Burke, Ryan Drago and Jesse McConnell, Greg, Anthony, Danny, Willy ***************** Underhill School Maidstone, Kent, England Mr. Grant Whitaker's Form 4 Set One Carly Crockford, Chloe Kerrigan, Angus Rouse, Ashley Phillips, Sophie Hutchinson, Victoria Higginson, Laura Gower, Caroline Court, Caroline Leaver, Elizabeth Ireland **************** Center School Stow MA Mrs Pensa's 3rd Grade Andrew Bawn, Chaz Rosenberg, Chris Wade, Kristin Squires, Riannon D, Ted Powers Center School, Stow MA Mr. Ellsworth's 4th grade class Rahul Jain *************** Bagnall School, Groveland, MA Ms. Arria-Lucey, Grade 4 Kyle Littrell, Alex Balford, Jenny Corso, Ashley, Kate Bagnall School, Groveland, MA Ms. Galluzzo-Hamilton, Grade 4 Rachel, Heather Quigley, Sarah, Marissa, Jeff York, Mike Murphy, and Cory Bagnall School, Groveland, MA Mrs. SturtevantGrade 4, Caitlin Stokes Bagnall School, Groveland, MA Ms.Lemieux, Grade 6 Brian Griffiths, Nicole, Talia Racca, Allison Foote, Alyson Christopher, Megan Danforth, Nisha Hughes, Chris Puopolo, Billy Mavroides, Alexis Karavedas, Ian Gugger, Rick Piatti, Donnie, Lindsay Bonfanti, Jason Saldi, Christine O'Malley, Scott Luken Bagnall School, Groveland, MA Mrs. Christopher, Grade 6 Jill Martel and Danielle Gugger *************** Name:Aneil Baron Grade: third Teacher: Paul Nash School: Georgetown Day School Washington,D.C. Naomi S. Baron Department of Language and Foreign Studies American University Washington, DC 20016-8045 202-885-2455 FAX: 202-885-1076 *******************
************** This week the 3rd Grade Math Masters at Gage School in Rochester MN 55901 decided to participate in the 'Problem of the Week'. Their answer is 513. The students are: Jill Eikenhorst, Adam Falk, Teresa Frissora, Susan Horsman, Ben Rattle, and Rachel Stroetz. Dan Frissora is the advisor for the once a week math enrichment program. The problem was solved as a team. In solving the problem (which they all thought was impossible at first) They first decided to represent the number of ABC, then after learning the sum was odd they ruled out sums of 1 and 3 because of some of the other rules. They all said 'duh' (direct quote) to the 1 left over rule, immediately recognizing that with odd numbers that would always be true! They quickly saw that the '3 left over' rule meant that 'C' was 3. We then represented the other rules as A=C+B+1 and 3 = 1/2 of A+B which they immediately saw to be 6 = A+B and that A= 3 + B +1 was A = 4 + B. Armed with those facts they quickly said A was 5 and B worked out to be one. I'm not sure if 5 was a lucky guess or if the actually figured it out somehow, but we tried the answer and it worked. I think the nearby office was wondering what the cheering was about! (and in a math class no less :) Thanks again for the problems, hope I'll 'see' you again next week! Dan Frissora ************* Amanda Tuminelli, Christine McGowan, Kim Fugok, and Ryan Grace - Grade 6 Caroline Brennan,Drexel Hill School of the Holy Child, Drexel Hill, PA Our answer is 513. We used trial and error and we also limited each digit with each clue. We knew our ones digit had to be either 1, 3, 5, 7, or 9. If you were dividing by 10 and having a remainder of 3 then the ones digit had to be 3. If the ones digit is three and the sum of the tens digit and hundreds digit is double the ones digit then their sum must be 6. So, we worked on combinations for 6. 513 is a three digit number. The sum of the digits is 9 and 9 is an odd number. If you divide 513 jelly beans between 2 kids each kid will get 256 jelly beans and you will have one left over. The sum of the ones digit and the tens digit is 4 which is one less than the hundreds digit 5. If you divide 513 jelly beans between 10 kids you will have 3 extra jelly beans. The ones digit - 3- is half the sum of the tens digit and the hundreds digit - 6-. 513 is less than 800. So there is 513 jelly beans in the jar. ******************* Kyle Littrell, Alex Balford, Jenny Corso, Ashley, Kate Grade 4 Ms. Arria-Lucey Bagnall School, Groveland, MA The answer is 513 jelly beans. Kyle, Alex, and Kate guessed and checked. Jenny used the sum of the ones and tens clue to figure out the last two digits were 1 and 3 and the hundreds digit was 5. Ashley used her fingers and the clues to figure it out. ********************* Rachel, Heather Quigley, Sarah, Marissa, Jeff York, Mike Murphy, and Cory Grade 4 Bagnall School, Groveland, MA Ms. Galluzzo-Hamilton The answer is 513. Rachel drew pictures based on the clues and used sample numbers and divided them into group to see howver. Mike listed odd numbers, used the divided by ten clue to find the last digit was 3 ans then guessing and checking to determine the other numbers. Heather, Sarah, Marissa, Jeff, and Cory guessed and checked. **************** Caitlin Stokes Grade 4 Mrs. Sturtevant Bagnall School, Groveland, MA First I read all the clues. Then I knew it had to be less than 800. Next I saw it was a 3 digit number. After that I added up the tens and the ones and saw it was one less than the hundreds. then I looked to see which ones were odd. All of them were. I looked to see if the ones digit was half of the sum of the tens and hundreds. There were only 2 numbers left. Then I divided those numbers by 2 and they both had one left. Last, I divided by 3 and 513 had 3 left and 201 had 1 left so the answer is 513. ****************** Chris Wade- Mrs. Pensa's 3rd Grade - Center School - Stow MA I got to the clue that said, The number is a three digit number. Then I got to the clue that said,If you divide this number of jelly beans between 10 kids,there will be 3 jelly beans leftover. So I knew the number ended in 3. Then I read the clue that said,The sum of the ones digit and tens digit is one less then the hundreds digit. So I came up with 423,243,and 513. So I added up the digits of the numbers because on clue it said. The sum of the digits is odd. So I got 513! ******************* Kristin Squires Mrs. Pensa's 3rd grade Center school. the way i got the answer to the problem of the week was by lining the possibilities of what the number could be under a line. And I had 'three lines because the first clue said that it was a three digit number. so this is how i set it up. Then I used the clues to exclude some numbers. for an example. clue number 3 was if you divide the number of jelly beans between 2 people you will have one left over. So that excluded all of the odd numbers from the ones column.and so i kept on using this method and got the answer 513! 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 ********* Rahul Jain - Mr. Ellsworth's 4th grade class - Center School - Stow MA There are 513 jelly beans. The way I found is first I read all the facts and started working with some numbers. One clue is the one that helped me the most is the one that said, If you divide this number by ten kids there would be 3 jelly beans left over. Then I knew that the ones digit was a three. Then this other clue the ones digit is half the sum of the tens and hundreds digit and the other clue the number of jellybeans is less then 8 hundred. Then I started trying some numbers. First I tried the number 733 but it didn't work because 7 plus three is ten and three isn't half of ten . So then I tried 623 But that didn't work Because 6 plus 2 is eight and two isn't half of eight. Then I tried 513, 5 plus one was 6 and three was half of six if you divide it by two kids one would be left over they all equal a odd number if you divide it by ten kids three jelly beans will be left over and it fits all the other facts. So then I knew that 513 is the number. ************ Riannon D - Mrs. Pensa's 3rd grade class - Center School - Stow MA The answer is 513. It is an odd number and the last digit (ones) is 3 because of the 10 kids and the "3" beans that are left over. All the digits are odd. The ones digit is half the sum of the tens digit and the hundreds digit when added together. It is less than 800 so it can't be 4 and 6 because they are even number. It can't be 7 because there's no two numbers to add together to get seven - you need at least one even number and you can't have an even number. So I tried 5. Now I needed the tens digit and I got it to be "1" because "when you add the hundreds and tens together it is twice as much as the ones digit" and "When you add the tens and ones together you get a number that is one less than hundreds" so 1 is perfect! ********************** Ted Powers - Mrs. Pensa's 3rd grade class - Center School - Stow MA Answer 513 I found that the answer is 513 because the ones digit is half the sum of the tens digit and the hundreds digit. You have to know the ones digit. You know the ones digit is three because it says "if you divide the number of jelly beans between 2 kids there will be 3 left over." Then using that information you know what the tens is because it would have to be "1" because the hundreds digit has to be less than eight and it can't be 733 or 623 so it has to be 513. ****************
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