Elementary POW, November 18-22, 1996
Elem POW Problems || Sept-Nov '96 Problems || Elem POW Main Page
The desks in a classroom are lined up in straight rows. Unless someone is sick, each desk is filled. Masaki is in the second row from the front and the fourth row from the back. She is also the third student from the left end of the row and the fifth student from the right. How many students are in the class? (Remember, a correct answer without an explanation will not be given credit.)
This week's mentors are the math education graduate students in Dr. Eileen Schoaff's class at Buffalo State College in Buffalo, NY.
Names: Nick Seibert & Jenny Somach Teacher: Mrs. Gutierrez School: Western Salisbury Hometown: Allentown, PA Grade: 5 Name: Zach Seibert Teacher: Mrs. Geschel School: Western Salisbury School Hometown: Allentown, PA Grade: 3 Name: Rosaura Butron, Tyler DeJong, Andrew Richardson Teacher: Mary Anne Davis School: Asheville Christian Academy Hometown: Asheville, NC Grade: 4 Names: Elizabeth Latham, Josh Neese, Daniel Wilcher, Jon Cole, Benjamin Upchurch, Beth Jones, Chandler Ditto, Bridget Purvis, Emily Roberts, Charlene Thompson and Jessica Westbrook Teacher: Ms. Perry School: Brandon Middle School Hometown: Brandon, MS Grade: 5 Names: Nicholson 4th grade with team leader Nick Ingram Teacher: Bill Richardson School: Nicholson Elementary Hometown: Crawfordsville, In Name: Rachel Forster School: Home School Hometown: Cygnet, Tasmania, Australia Grade: 3 Name: Huw Wilkins School: Home School Hometown: Cygnet, Tasmania, Australia Grade: 4 Name: Becca Glas, Adam Arens, Stephen Jerde, Sarah Kraft, Amanda Johnson Teacher: Mr. Bingea School: Delano Elementary Hometown: Delano MN. Grade: 4 Names: Steve, Katie, Tim, Daina, Lauren, and Claire Teacher: Mrs. Brennan School: Drexel Hill School of the Holy Child Hometown: Drexel Hill, PA Grade: 4 Name: Emily G., Rachel T., Kristi M., Kevin Mc., Kylene J., Rafael S., Diana M., Stephanie S., Zach B., Moon C., Shea M., Kevin M., and Lauren G., Monica R., Melanie B., and Colleen C. Teacher: Miss Colwell School: Oak View Elementary School Hometown: Fairfax, Virginia Grade: 6 Name: Daniel Kahn Teacher: Mrs. Berendsen School: Far Hills Country Day School Hometown: Far Hills, N.J. Grade: 3 Teacher: Savita Joshi's First Grade Class School: Germantown Academy Hometown: Fort Washington, PA Names: Sara Wyszomierski and Michael Lavner, Josh Aibel and TJ Jackson Teacher: Phy Chauveau School: Germantown Academy Hometown: Fort Washington, PA Grade: 5 Names: Kurt, Ben, Zach, Josh, Julie, Katie, Sobon and Andrew, Kevin, Mason, Katie Rose, Joe, Matt Shearon, Matt Conway, Alexandra, Deidre, Alexander Teacher: Mrs. Bennett School: Germantown Academy Hometown: Fort Washington, Pa Grade: 3 Names: Leah H. and Cathy T., Bryan B. and Kevin L., Jessi S., Chris C., Lauren K and Mike C., Pam K. and Patrick Z., Brian B. and John K., Amanda B. and Leah P., Kyle B. and Tom B., Laura B. and Katelyn R., Sarah S. and Jen M., Steven P. and Nick D., Katelyn E. and Katie S., Rick and Chris, Joshua M. and Bryan C., Jessica S. and Nicole C., Art, Peter and Curt Teacher: Mrs. Caruso School: Bagnall School Hometown: Groveland, MA Grade: 6 Names: Dan K, Elyse D, Meghan R, Kate D, Mark M, Katelyn W Teacher: Mrs. Crawford School: Bagnall School Hometown: Groveland, MA Grade: 5 Names: David G., Josh R., Ashley T., Katie B., Jake C., and Kerry B., Mariah L., John D., and Zack D., Sam R., Billie Jo C., and Brain A., Megan I., Mike B., Katy P., and Amy G., Katie L., Sara B., Kali S., and Billy, David H., Megan Teacher: Miss Lalumiere School: Bagnall School Hometown: Groveland, MA Grade: 6 Names: Francesca Ebba, Jeffrey R. Titus, Keith Farrell, Allison Bevelaqua, Mason Pelletier, Caitlyn Downey Teacher: Mrs. Galluzo Hamilton School: Bagnall School Hometown: Groveland, MA Grade: 4 Name: Sonia R. Teacher: Mrs. Sturtevant School: Bagnall School Hometown: Groveland, MA Grade: 4 Names: Connie and Philip B. Teacher: Miss Seager School: Bagnall School Hometown: Groveland, MA Grade: 3 Names: Jameson C., Michael B., Michael C., Kyle F., Chad B., Aliaa K., Antoinette D., and John Parker W. Teacher: Ms. Powell School: Trace Crossings School Hometown: Hoover, Alabama Grade: 4 & 5 Names: Mrs.Hayes Math students School: Shaffer Elementary Hometown: Littleton, CO Grade: Name: Francis Chung Teacher: Mrs. Taylor School: Stoneybrook P.S. Hometown: London, Ontario, Canada Grade: 4 Names: Cassie Mattie, Ashley Pina, Amanda Vinje, Lisa Erickson, Zachary Larson, Sarah Mueller, Carina Bailey, J.T. Turner Teacher: Mrs. Horton School: Emerson Elementary School Hometown: Madison, Wisconsin Grade: 5 Names: Shane Fedkenhauer, Ira Ochs, Andrea Olson, Grace McCants, Sarah Campbell, Emily Dodson, Mary Cass, Jesse Lueders, Ben Haynes, Devin Edmonds Teacher: Mrs. Dunlap School: Emerson Elementary School Hometown: Madison, Wisconsin Grade: 5 Name: Matt Angrisani, Brett Weaver, Shayna Hintze, Robert Gannon Teacher: Mrs. Bach School: Joyce Kilmer School Hometown: Mahwah, New Jersey Grade: 5 Names: Kayla Cappadocia, Daniel Brenner, Gabrielle Haberman, Jay Johnson and Christy Barbetto, Jake Cramer, Mrs. Cramer, Robert Lamber, Alison Johnston and Elain Fang, Gillian Powell, Patrick Johnson, Anthony Parmenter and Rebecca Martin, Allyson Mallick, Nikolia Demarinis, Michael Morrissey, Jesse Calderone Teacher: Marianne Blair School: George L. Hess Educational Complex Hometown: Mays Landing,NJ Grade: 3 Names: Kristin Began, Joey DeLescia and Sean Driscol School: Beebe school Hometown: Melrose Grade: 4 Names: Miss Varney's fourth grade School: Beebe school Hometown: Melrose Grade: 4 Name: Emily Farrington Teacher: Sally Farrington School: The Franklin Pierce School Hometown: Parkton, NC Grade: 5 Name: Anne Bozack Teacher: Elaine McMahon School: Murray Middle School Hometown: Ridgecrest CA Grade: 6 Name: Casey Gorish Teacher: Mr. Norton School: Murray Middle School Hometown: Ridgecrest CA Grade: 6 Names: Sheila Swedberg and Benjamin Stone Teacher: Mrs. Barbara Stone School: Calvary Christian School Hometown: Sacramento, California Grade: 5 Name: Silvije Lumani Teacher: Mr. Auckland Hometown: St. Thomas, Ontario Grade: 6 Names: Nick Beaudoin & RC Granger Teacher: Mrs Palmbach School: Center School Hometown: Stow MA Grade: 3 Names: Sam Hahn, Mitchell Samson Teacher: Mrs. Kelley School: Center School Hometown: Stow MA Grade: 5 Names: Ashley Wells, Alexandra Basilakos, Meghan Dailey, Kerry Hegarty Teacher: Thomas E. Taylor School: Brushy Creek Elementary School Hometown: Taylors, South Carolina Grade: 4 Names: Katrina Ross and Naomi Beuerlein Teacher: Mr. Hoops School: St. Mary's School Hometown: Ticonderoga, NY Grade: 4 Name: Benjamin Stoller Teacher: Mr.Welland School: Island Public Shool Hometown: Toronto Island in Canada Grade: 4 Names: Tim Schumann, Melissa Vitolo, Daniel Sullivan, Jill Smith Teacher: Mrs. O'Connor School: Titus Elementary School Hometown: Warrington, PA Grade: 4 Names: Henry, Andrew, & Ilya Teacher: Mrs. Seale School: St. Patrick's School Hometown: Washington, DC Names: Andrew Klepper, Nicko Margolies, Julia Tomasko, Udit Garg, Laura Mattison, Max Zinser, Vinay Aggarwal Teacher: Paul Nass School: Georgetown Day Hometown: Washington D.C. Grade: 4 Name: Harrison Miller, Alexander Berger, Andrew Migdail, Simone Levien, Michael Bilik, Mitchell Malasky, Becky Cisin Teacher: Paul Nass School: Georgetown Day School Hometown: Washington D.C. Grade: 5 Name: Tommy Grace Teacher: Carol Berenson School: Georgetown Day School Hometown: Washington DC. Grade: 6 Name: Rebecca Zeldin, Zachary Sandler, David Driscoll, Cyrus Karhas, Lauren McBride, Ry Henry, Kathrin Gilbert, Jon Huddleson, Courtney Jones, Collin Willis Teacher: Linda Prueter School: Georgetown Day School Hometown: Washington, DC Grade: 5 Correct answers were received from the following, as well, even though we don't know where you are located: Name: Danielle Teacher: Mrs.Schill Grade: 4 Name: Michael S. Teacher: Mrs. Fox School: Seventh District Elem School Grade: 3 Names: Willy Lopez, John Adamovich Teacher: Mr. Gebig School: Munsey Park Grade: 5 Names: Bethany and Stephanie Teacher: Mr.Dyer School: Sea Road School Correct answers were also received from the following, but no school or location was indicated: Jeffrey D. Hemming, Brian Scarbrough, Deanna Anderson, and ROOM 304
1. Submitted by Francis Chung: Since Masaki is in the second row from the front and the fourth row from the back, there are 5 rows. There is one row in front of him, three rows behind him, and his row (1 + 3 + 1 = 5). Since he is also the third student from the left end of the row and the fifth student from the right, there are 7 columns. There are two columns to his left, and four columns to his right, and of course, his own column (2 + 4 + 1 = 7). Therefore, there is a total of 35 desks, or children, because we multiply the number of rows by the number of columns (7 x 5 = 35). 2. Submitted by Savita Joshi's First Grade Class: In 1SJ we used blocks. We put one block for Masaki. Then we put - one block in front of Masaki so she will be 2nd in the row, - three blocks behind her so she is 4th from the back, - two blocks on her left, - four block on her right. - Then we filled in rest of the spaces. Each row had 5 kids (blocks). We counted by 5's - 5, 10, 15, 20, 25, 30, 35. Our answer was ... 35 students in Masaki's class! 3. Submitted by Tim Schumann, Melissa Vitolo, Daniel Sullivan, Jill Smith Our solution to this week's problem puts 35 students in the class. We solved the problem by drawing a diagram like this: ROW 1 2 3 4 5 6 7 ROW X X X X X X X 1 X X M X X X X 2 X X X X X X X 3 5 X 7 = 35 X X X X X X X 4 X X X X X X X 5 To be in the second desk from the front and the fourth desk from the back means that there are five rows of desks. To be in the third row from the left and the fifth row from the right means there are seven rows across the classroom. Masaki's desk is marked with an M. 4. Submitted by Mrs. Bennett's 3rd Grade Group 1...Kurt, Ben, Zach, Josh, Julie, Katie Sobon We used the strategies of Acting Out, Making a picture, and Look for a pattern. We used pieces of paper and we put an M for Masaki's name. We put the papers into equal rows. We counted the papers and came up with the answer of 35. Group 2...Andrew, Kevin, Mason, Katie Rose, Joe, Matt Shearon, Matt Conway, Alexandra, Deidre, Alexander We used the strategies of Acting Out and Using Objects. We used white rods as the desks. We read the problem and, as we went along, we filled in the other desks. We came up with the answer of 35.
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