Name:
Period:
Lone Divider – Worksheet 1 – Divide and Declare
Date:
A very thin rectangular piece of sterling silver is divided into twelve
equal squares, each square is 1 cm in length and 1 cm in width.
Use the Lone Divider Method to answer the following problems.
1.
If you were the lone divider, show three different ways that you could make a fair division of the
rectagle of silver if there were three players. Label each share, S1, S2, or S3.
2.
Determine whether each of the following divisions are fair or unfair.
3.
a.
b.
c.
d.
answer:
answer:
answer:
answer:
For each answer of unfair in #2, explain why the cut is unfair.
If the divider were to cut the silver as follows, show the declarations that should be made by the two
choosers.
4.
5.
Declarations:
7.
Declarations:
8.
Declarations:
10.
6.
Declarations:
9.
Declarations:
What is the minimum number of squares needed to make a share fair?
Declarations:
11.
Three brothers (or sisters) are to share a bedroom. Usig the Lone
Divider Method, the divider separated the area of the room as
shown in the diagram. If you were one of the choosers, which
share(s) of the room would you declare to be fair? Explain?
12.
The second floor of a home is under construction. The only
work left to complete is the addition of two walls that will divide
the floorplan into three fair bedrooms. Draw the two walls and
explain why you think each room would be a fair share of living
space. (Note: The hallway is shared by all.)
A recently discovered island, sketched in the figure, is made up
of a large rocky (mountainous) area in the middle, surounded by
fertile soil. There is a large beach area on the southwest side of
the island with rocky areas separating it from two smaller beach
areas. There is also a small beach area on the northeast side of
the island. The island will be shared by three real estate
developers. Use the Lone Divider Method to answer the
questions below.
13.
If you were selected to be the divider. Divide the island into what you consider to be three fair
sections. Label each section S1, S2, or S3.
14.
Find two classmates. Have each make independent (secret) declarations as to which shares they
consider fair. Write each classmates name and declaration(s) below.
Chooser 1:
Name:
Declaration(s):
Chooser 2:
Name:
Declaration(s):