LONE DIVIDER METHOD
(TXT: 3.3 & SOL: DM.7)
Classwork:
p. 107 (21, 25, 29)
Homework (day 22):
p. 107 (22, 26, 30) or
www.mathxlforschools
Introduction to Lone Divider
Method
◦ https://www.youtube.com/watch?v=xOZUKsA8pOo
Lone Divider
• One person divides and the others choose.
◦ 1. Division- divider divides the cake into specified
number of shares (𝒔𝟏 , 𝒔𝟐,… 𝒆𝒕𝒄)
◦ 2. Bidding- the choosers determine what they
consider to be a fair share. (Bid List)
◦ 3. Distribution- “Who gets what?”
(depends on which pieces are listed in the bids)
Ex: Four people want to
divide an island valued
at $100,000.
A
10,000
10,000
20,000
60,000
B
30,000
10,000
35,000
25,000
C
30,000
5,000
60,000
20,000
D
Divider
Divider
Divider
Divider
The chart lists the value of each section after
division per person.
1.Determine the fair share.
2.Declarations (what each person would
take- equal to or great than fair share)
3. What are the possible divisions?
Answers:
◦ 1. Fair Share:
100,000
4
◦ 2. Declarations
A = 𝑠4
= 25,000
B = 𝑆1 , 𝑆3 , 𝑆4
C= 𝑆1 𝑜𝑟 𝑆3
D = what is left
3. Possible Division
A = 𝑆4
B = 𝑆1
C = 𝑆3
D = 𝑆2
Only way everyone is happy.
Sometimes there is no solution.
Ex: Divider- Demi
Choosers – Chan, Chloe & Chris
◦ Demi divides the cake into four pieces: 𝑆1 , 𝑆2 , 𝑆3 , 𝑆 4
𝑺𝟏
𝑺𝟐
𝑺𝟑
𝑺𝟒
Chan
30%
20%
35%
15%
Chloe
20%
20%
40%
20%
Chris
25%
20%
20%
35%
Demi
25%
25%
25%
25%
1. What is the Bid List?
2. Distribution?
Chan {𝑆1 , 𝑆3 }
Chan - 𝑆1
Chloe {𝑆3 }
Chloe- 𝑆3
Chris {𝑆1 , 𝑆4 }
Chris- 𝑆4
Demi - 𝑆2
Answers HW day 20 p. 107 (22, 26, 30)