Elementary POW, October 30 - November 3, 1995
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****************************************************** Elementary Problem of the Week, October 30 - November 3, 1995 This week's problem was submitted by Kathleen McGrath, Mount St. Joseph Academy, Flourtown, Pennsylvania. In the year 97 B.C., a man is born in a small village. At the age of 14 he marries, and 1 year later, his first son is born. This son marries at the same age his father did, and his first daughter is born 3 years later. This daughter marries when her grandfather is 47 years old. How old is she and what year is it? ***************************************************** This week's Bonus Puzzler was submitted by Nicole Aurello, Mount St. Joseph Academy, Flourtown, Pennsylvania. There are two moms and two daughters out to dinner, but there are only 3 people there. How can that be? ******************************************************
The Rice School La Escuela Rice, Houston Texas Mike Miller's Class Amanda Dodd (POW & Bonus) The School in Rose Valley Rose Valley, PA Leigh Stefanik (POW & Bonus), Lauren McCarthy (Bonus) Center School Stow, Mass. Miss McCarthy's 4th Grade Class Sam Hahn (POW & Bonus), Todd Nicholas (POW & Bonus), Jacob Smith (Bonus) Jefferson Road School Pittsford, NY Greg I., Peter Z., Dan H., Sherri B., & Michelle G. (POW & Bonus) Center School Stow, Mass. Mrs. O'Connell's 5th Grade Class Jeanette Kurian (POW & Bonus), Center School Stow, Mass. Mrs. Kelley's 5th Grade Class Michael Farrar (Bonus) Springton Lake Middle School Media, PA Pat Hagan's 6th Grade Class Mike Skarbeck, Magaly Britt, Carl Haner, Casey Evans, Alex Price, Mike Schueftan,and Pearce Bolton (POW) St. Mary's School Ticonderoga, New York John Olsen ( POW & Bonus), Theresa Howard (POW), Shylah Ross (Age but not year of POW), Suzanne LeBarron & Amanda Yaw (Bonus) Lincoln Elementary School Burlingame, CA Nancy Kaye's Class (Bonus) Alvarado Elementary School Albuquerque, New Mexico Grades 4 & 5 Shawn Keith, Taylor Grisham & Jason Cox (POW) Munsey Park School Ms. Duggan's 4th Grade Class Elizabeth Pavlovich, Matthew Horne, Patrick Kelly & Todd Conis (Bonus) Standard Elementary School Bakersfield, CA Debbi Cairn's Class Elizabeth Veloz (Bonus)
LVARADO ELEMENTARY SCHOOL
ALBUQUERQUE, NEW MEXICO
FOURTH AND FIFTH GRADE
SHAWN KEITH, TAYLOR GRISHAM,
JASON COX
The way we found this out was that first made a time line of the years in
B.C. The time line went from 97 to 0. Then we took away 14 from 97 because
the man was 14 when he married. After that we took away 1 from 97 because
one year later the son was born. Then we took away another 14 from 97
because the first son married at the same age his father did. After that we
took away 3 from 97 because that is when the first daughter was born. When
we were done with the subtraction we got 65. Then we found out that now the
grandfather was 47 now and he was 32 when the daughter was born so we took
32 from 47 and got 15 which was the daughter age. Then we took 15 from 65
because the year had changed by 15 years and got 50 which was the year so
we were done.
97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80
Man Son Born
Marries
79 78 77 76 75 74 73 72 71 70 69 68 66 65 64 63 62 61
The Son The Daughter
Marries Is Born
60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45
Old Man Is 47 and
The Daughter Gets Married.
********************************************************
>From Miss McCarthy's Fourth grade class at Center School, Stow, Mass.
Sam Hahn:
1. The man was born in 97 BC
His son was born in 82 BC
The son marries in 68 BC
His daughter is born in 65 BC and
His daughter marries in the year 50 BC at the age of 15 2. There is
one grandmother (who is a mother)
One mother (who is both a mother and a daughter) and one daughter (who is
only a daughter)
Todd Nicholas:
1. Todd drew a timeline and marked off the years to find out the
correct date....
Man is born in 97 BC - He marries in 83 BC at the age of 14. He has his son
in 82 BC. The son marries and has the daughter 17 years later or in 65 BC
and the daughter marries in the year 50 BC when she is 15 and her
grandfather is 47 years old. 2. There is a grandma, a mother, and a
daughter.
********************************************************
>From Pat Hagan's sixth grade class at Springton Lake Middle School in
Media, Pennsylvania:
This was a tough one for my students. I knew the concept of BC time would
throw them, since ancient history is taught in 7th grade, so I found a time
line showing the years 200 B.C. to 100 A.D. I suggested that they look at
the time line to understand what B.C. meant, but it didn't really hit them.
Finally, one student(Rob LePard) made a connection with positive and
negative degrees on a thermometer, how numbers counted down toward zero
below zero. That was the big break. I further helped the process along by
suggesting that they draw a number line to chart births, marriages, etc. The
first solution came from a group of students who were working together with
a teaching aid.
Mike Skarbeck, Magaly Britt, Carl Haner, Casey Evans, Alex Price, Mike
Schueftan,and Pearce Bolton.
We figured out how to do this by drawing a time line and labeling certain
dates. We think that the daughter as 15 in the year 50 B.C.
>
********************************************************
From: MARILYN TAHL
Hi. We are from Munsey Park School. Our names are Elizabeth Pavlovich,
Matthew Horne,Patrick Kelly,Todd Conis.This problems answer is - she is 15
and the year was 47A.D. We also did the bonus,the answer was theres a
Grandma who is a mom,and her daughter is a mom to her daughter that makes
the Grandma and the mom both mothers,and the daughter to the Grandma and
the little child both daughters.I hope you understand that,bye. We are in
Ms. Duggan's 4th grade class.
>From One of our "Math Mentors"
Dear Elizabeth,
In this weeks POW, you are asked to use years in B.C. not A.D.
Counting in years B.C. is similar to counting on a number line, B.C. being
the negative numbers, and A.D. being the positive numbers.
-97-birth|97-14=83|83-1=82 |82-14=68|68-3=65 |50
of grand-|grand- |first son|son |daughter|year
father |father |born |marries |born |daughter
|marries | | | |marries
| | |
-----------------------------------------------------------------
BC
The grandfather is born in 97 b.c.. subtract 14 years to get the year of
his marriage.
97-14=83 bc
In one year he has a son. Subtract another year.
83-1=82
The son marries in 14 years. Subtract 14 years
82-14=68
The son has a daughter in three years. Subtract 3 years.
68-3=65
If the grandfather is 47 years old when the daughter marries,you subtract
47 years from the year he was born, 97
97-47=50
To get how old the daughter is in the year 50 bc, subtract 50, the year she
marries, from 65, the year she was born.
65-50=15
The girl was fifteen years old when she married in the year 50 BC.
Your bonus was good and your explanation was clear enough to explain
why you came to your answer.
Great job! Hope to hear from you again- ask your teacher for help if
you still don't understand counting years in B.C.
Jackie Mattera
Grade 9
Mount Saint Joseph Academy
Flourtown, PA
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