Elementary POW, December 16, 1996 - January 10, 1997
Elem POW Problems || Dec '96 - Feb '97 Problems || Elem POW Main Page
Number Puzzles
- 123456789 = 100
Insert mathematical symbols between the digits on the left side to make the equation correct.
- 123456789 = 100
Can you make the equation true by inserting only three plus or minus signs?
- Use five 3's to make 37.
- Use five 4's to make 55.
- Use four 9's to make 20.
- Use six identical digits to make 100.
This week's mentors are from Ms. Overholt's 9th grade honors geometry class, Franklin County High School, Rocky Mount, Virginia.
The following students sent in all 6 correct responses: Steve young, grade 5 Western Salisbury School, Allentown, PA Brad Gorg fourth grader Titus Elementary School, Mrs. O'Connor's class Warrington, PA. Tim Schumann, Siena Frank, Jamielynn Miller, Melissa Vitolo Titus Elementary School in Mrs. O'Connor's class Christine Mortimer fourth grader Titus Elementary school, Mrs. O'Connor's class Robbie Vogt. Age:10 Grade:5 Prince George B.C. Canada Mrs. Dunn's class Mitchell Malasky Paul Nass's fifth grade math class Georgetown Day School in Washington D.C. Zach Larson Emerson Elementary School Madison, WI Mrs. Horton's 5th grade Samantha Ruth Grade 6, Pat Rieker (teacher), York Avenue Elementary School Lansdale, PA John Consorti Grade: 3 Teacher's Name: Judy DiMaio Glenwood Elementary, Media, PA Nathan Strauss, Nate Litz, Justin Weiss, Brian Powers bcoulter@teaparty.terc.edu Laura Meadows Mrs. Davis's 4th Grade Asheville Christian Academy Asheville, NC Andrew Richardson Mrs. Davis's 4th Grade Asheville Christian Academy Asheville, NC Lina Reed 4 grade Mrs.Ford Chantry Malvern Iowa Joseph Cross school: Maret grade: 3rd, Ms. Broach location: D.C. Christopher Sigmund and Matthew Gilstrap 5th graders in Paul Wezeman's class Enterprise Elementary, Federal Way, WA Fifth Grade Dillon Muth found the pattern for #6 Teachers: Anne Lynagh and Paul Schuman Collegiate School New York, NY Conrad Kirby Grade 5 (Ms. Williams) Burton Geo-World Elementary Durham NC Allison North Kingstown,Rhode Island Stony Lane School Grade 4 Diana M. Miss Colwell's 6th grade class Oak View Elementary School Fairfax, Virginia Sonja Riley Grade 4 Mrs. Sturtevant Bagnall School, Groveland, MA Scott Sacra Mrs. Trudell - 3rd Grade Center School, Stow, MA Brian Holman, Jennifer Cooke, Nathan Adam, Ashley Al-Darraji, Bryan Berry, and Nick Dobroski fifth graders, Garrison Elementary, Mrs. Hamilton Dover, NH Casey Gorish Mrs. McMahon 6th Grade Murray Middle School Ridgecrest CA Katie, Lauren, Steve, Claire, and Daina Mrs. Brennan, Grade 4 Drexel Hill School of the Holy Child, Drexel Hill, PA Andrew Dang, grade 5 Western Salisbury School (Mrs. Geschel) Allentown, PA The following students sent in answers to some of the six problems: Dean Tye Germantown Academy Fort Washington, PA Grade 4 Mrs. Rubinfield's Class Lewy,Ivan,Jack,Brennan,Max,Chris,Ben,Tamar (3) Fourth Grade, Ms.DeMaroney Edmunds Elementary school Burlington,VT Frankie Jachetta, Misty Dickerson, Caleb Andrea, Nina York, Chris Briggs (5) Grade: 5th/6th Teacher's Name: Kari Williams School: Idaho Hill Elementary Location: Oldtown, Idaho Bri Clow and Carrie Weber (5) Grade: 6th grade Teacher's Name: Kari Williams School: Idaho Hill Elementary Location: Oldtown, Idaho Deanna Anderson (1) Greg (4) 3rd grade Ms.Jane Keyes' Math class Zach Smith (1) 3rd grade Ms. Hacik Swarthmore Rutledge School Swarthmore, PA 19081 Keona Rivers (1) grade 4 teacher: Piccino School #26 1 E. 32nd and 11th Ave. Paterson, NJ 07514 Jamie Pruitt (5) Grade 6, Pat Rieker (teacher), York Avenue Elementary School Lansdale, PA Becca Glas and Melissa Carlberg (5) Grade:4 Teacher's Name: Mr. Bingea Delano Elementary, Delano, MN Ben Clements (5) bcoulter@teaparty.terc.edu Robbie Birge-Osborne (4) bcoulter@teaparty.terc.edu Rebecca (5) Erik (4) Eric (2) Thomas, Tyler, Emily, Sarah, Nick, and Joey (1) 3rd grade, room 12, Monfort Elementary, Greeley, CO John Davitt (3) third grade, Ms.Broach Maret School, Washington D.C. Leah H. (4) Grade 6 Mrs. Caruso Bagnall School, Groveland, MA Jeffrey T. (4) Grade 4 Mrs. Hamilton Bagnall School, Groveland, MA Jason (5) Stony Lane School Grade 4 North Kingstown, RI Josh Hewitt (1--but unique!) Stuart Wyss, Teacher, 4th grade Kutz, Central Bucks, PA, Mrs. Hayes 4th Grade Students (5) Shaffer Elementary Littleton CO Mr. Gunderson's 5th/6th math class (1) David Michael Pekarsky 5th grade--Mrs. Springfield, Mr. Swift and Ms. Dorn Underwood school Newton, Massachusetts
These are the solutions we chose to be highlighted. We
included one of the first to show all the different ways #6 could
be done. A first-time fifth grade class sent a wide variety of
answers. And a younger student was the only one to use factorials
in his answer.
-------------------------------------------------------
1. 1+2+3+4+5+6+7+(8X9) = 100
2.[123-(4+5)-(6+7)+8]-9=100
3. [(333/3)/3=37
4.(44/4) + 44 = 55
5. (99/9) +9 = 20
6. Number six can work with any number:
(999-99)/9 = 100
(888-88)/8 = 100
(777-77)/7 = 100
(666-66)/6 = 100
(555-55)/5 = 100
(444-44)/4 = 100
(333-33)/3 = 100
(222-22)/2 = 100
(111-11)/1 = 100
Steve young, grade 5
Mary Geschel, teacher
Western Salisbury School,
Allentown, PA 18103
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This is our first set of problems. Our 5th grade classes
worked on these problems on Monday and Tuesday of this week.
We used guess and check strategies for most of the problems,
but one student also found a pattern for problem # 6.
1) 123 - 45 - 67 + 89 = 100
[(1 x 2) + 3] x (4 x 5) + 6 - 7 - 8 + 9 = 100
123 + 45 - 67 + 8 - 9 = 100
(1 x 2) + 3 x (4 x 5) + 6 - 7 - 8 + 9 = 100
(1 + 2 + 3 + 4 + 5 + 6 + 7) + ( 8 x 9) = 100
12 + 34 + (5 x 6) + 7 + 8 + 9 = 100
(1 + 2 + 3 + 4) x 5 + 67 - 8 - 9 = 100
(1 + 2) x 3 x 4 + 5 + (6 x 7) + 8 + 9 = 100
2) 123 - 45 - 67 + 89 = 100
3) 333 / 3 / 3 = 37
33 + 3 + 3 / 3 = 37
333 / (3 x 3) = 37
4) 44 / 4 + 44 = 55
5) 99 / 9 + 9 = 20
6) (5 + 5) (5) + (5 + 5) (5) = 100
[ (5 x 5) - 5 ] x 5 - 5 + 5 = 100
55 + 55 - (5 + 5) = 100
55 - 5 + 55 - 5 = 100
99 - 9 + 9 + (9 / 9) = 100
(111 - 11) / 1 = 100
(222 - 22) / 2 = 100
(333 - 33) / 3 = 100
(444 - 44) / 4 = 100
(555 - 55) / 5 = 100
(666 - 66) / 6 = 100
(777 - 77) / 7 = 100
(888 - 88) / 8 = 100
(999 - 99) / 9 = 100
The boy who thought of the pattern in #6 is Dillon Muth.
Fifth Grade
Teachers: Anne Lynagh and Paul Schuman
Collegiate School
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Just thought I'd share one of my student's more unique
way of solvingt the problem: Use five 3's to make 37...
Josh Hewitt submitted this answer:
He did this: (3+3)x(3!)+(3 / 3)=37
6 x 6 + 1 =37
All of the other children used basic operations. Only
he used "factorials". Just FYI!
- Stuart Wyss, Teacher, 4th grade, Kutz, Central Bucks, PA,
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