Method of Markers
Objectives:
1. Use the Method of Markers to divide a collection of discrete objects.
2. Given a value system, determine how to place the markers so that each
person receives a “fair” share.
EXAMPLE 1 (Whole Group)
Tech/Media/Ring/Cash Loot
EXAMPLE 2 (Small Group)
Trick or Treat Aftermath
(See “Markers 65” file)
Your task is to divide the candy from your bag so that every student gets a fair share.
Step 1 - Bidding
1. Without looking, remove the items from your bag one at a time and arrange them
from left to right in a line.
2. Without revealing to the others in your group, decide where to place your
markers so that the booty is divided into the same number of segments as the
number of people in your group. (So in a group of N, each person places N-1
markers.) The segments do not have to have the same number of items. You
should choose to place your markers so that you would be happy if you received
any of the segments. (In other words, you think each section represents a “fair
share” of the items in the bag.)
3. Once everyone has decided where to place his/her markers, you may reveal
them to the group by placing all of them on the array. (Write your name on the
tabs provided and place them in the spots on your line of items.)
Step 2 - Allocation
1. Now it is time to divide the items. Starting from the left-hand side, scan the
items until you come to the first marker. The player who has placed that marker
gets all the items up to that first marker. Now you can remove that player’s
remaining markers, and that player is finished.
2. Scan the items again until you come to the first second marker. That player gets
his/her second section only. (Any surplus from the first set of markers is set
aside and will be dealt with at the end.) Remove that player’s markers and that
player is also finished.
3. Repeat the process with the first third marker. That player will get his/her third
section only. (Again, remove any surplus left over between the second and third
markers.) Continue repeating the process until each player has gotten a share of
the items.
Step 3 – Divide the Surplus
At the end, there may be some items left over. Discuss a strategy for dividing
the leftovers. Once you decide, call your teacher over to approve.
Please do not go on until instructed to do so.
EXAMPLE 3 (Indiv
vidual)
Known
n Value Sysstem
p
(Katte, Manny, and Jerry) agree to diivide some candy usin
ng the meth
hod
Three players
of marke
ers. The ca
andy consis
sts of 3 Ree
ese’s Peanut Butter Cups, 6 Snicckers, and 6
M&M’s. The players’ value sy
ystems are as follows:
• Kate love
es Reese’s Peanut Bu
utter Cups, but does no
ot like Snicckers or M&
&M’s
at all.
oves Snicke
ers and Ree
ese’s Pean
nut Butter C
Cups equallyy well, but d
does
• Manny lo
not like M&M’s
M
at alll.
s and M and M’s equa
ally well butt is allergic to Reeses’s
• Jerry loves Snickers
Peanut Butter
B
Cups
s.
The
T candy is
s arranged as shown:
ut the method of marke
ers by inserting where
e the three w
would place
e their markers
Carry ou
based on their valu
ue system and
a determine who gets what. Be
e sure to exxplain clearly
and com
mpletely.
Addition
nal Though
hts:
1. Under
U
whatt conditions
s will this form of divisio
on work or not work?
2. How
H
could you
y change
e this proble
em so that it is not so “neat” and more realisstic?
ner)
Assessment (Partn
Names
s: ________
_________ _________
_________
__
t examplle from abo
ove with the
e same know
wn value syystem, but the candy
Repeat the
arranged
d as follows
s.