Download “Snake” Probability Dice Game

“Snake” Probability Dice Game
Math Standards Addressed (From the Colorado Department of Education)
http://www.cde.state.co.us/scripts/allstandards/COStandards.asp?glid=0&stid2=4&glid2=9
Standard 3 - Data Analysis, Statistics, and Probability
 6th Grade:
o Outcome 1: Visual displays and summary statistics of one-variable data
condense the information in data sets into usable knowledge.
th
 7 Grade:
o Outcome 1: Statistics can be used to gain information about populations by
examining samples.
o Outcome 2: Mathematical models are used to determine probability.
 8rd Grade:
o Outcome 1: Visual displays and summary statistics of two-variable data
condense the information in data sets into usable knowledge
Objective: Develop basic understanding of probability concepts
Materials:
2 dice
Paper or whiteboard for each student
Procedure:
1. Choose what game you are going to play; multiplication or addition.
2. Start under the column S. Roll the dice. If either die is a one, ignore this roll and roll
again.
3. Students will add or multiply the two numbers as determined above. They write the sum
or product under the S column.
4. Students may decide to go out of the game after each roll of the dice. After rolling, give
them a short amount to compute and write. Then give them five seconds to decide if
they want to go out of the game. Call out names of those who are out and keep track
in-case someone tries to sneak back in.
5. Continue to roll the dice. Students continue to write the sum or product under the S
column.
6. The round ends whenever a single 1 on the die is rolled.
7. Students who are sitting out when a 1 is rolled may keep their points for that round. Any
student still in the game loses all their points for that round.
8. If you roll SNAKE EYES (two 1's), students still in the game lose points from ALL the
rounds.
9. All students come back into the game for the next round. For the second round you
start in next column and so on for successive rounds.
10. At the end of the game students count up all the points they have collected from all of
the rounds in which they earned points. The student with the highest point total wins.
11. Make a graph of all of the sums rolled and discuss the distribution. Did any numbers
appear more or less often?
12. Explain that certain sums appear more often because there are more ways to achieve
that sum. Derive the chart below
13. Compare the actual sums to the chart below. Are they similarly distributed?
14. The red entries are sums that result in players losing their points, i.e. they contain a 1.
Find the probability that a roll will result in losing points. (11/36) What does the
distribution of the sums tell you about choosing a strategy?
# of
occurrences↓
6
5
4
3
2
1
1+1
Sum→
2
2+1
1+2
3
3+1
2+2
1+3
4
5+1
4+2
3+3
2+4
1+5
6
4+1
3+2
2+3
1+4
5
6+1
5+2
4+3
3+4
2+5
1+6
7
6+2
5+4
4+4
3+5
2+6
8
6+3
5+4
4+5
3+6
9
6+4
5+5
4+6
10
6+5
5+6
11
6+6
12
15. If playing with products rather than sums, consider the following tables instead. Notice
that the products are the “Fibonacci” sequence. Does the product distribution affect
your strategy? Notice that all numbers 1-36 are not in the chart.
products
1
2
3
4
5
6
1
1
2
3
4
5
6
# of ways
to roll
4
3
2
1
x
Product→ 1
2
2
4
6
8
10
12
x
X
2
x
X
3
3
3
6
9
12
15
18
x
X
X
4
x
X
5
4
4
8
12
16
20
24
x
X
X
X
6
x
X
8
5
5
10
15
20
25
30
x
9
x
X
10
6
6
12
18
24
30
36
x
X
X
X
12
x
X
15
x
16
x
X
18
x
X
20
x
X
24
x
25
x
X
30
x
36
Prepared By:
Clayton Thurmer
Bechtel K-5 Education Excellence Initiative
References
Brutlag, Dan. "Choice and Chance in Life: The Game of SKUNK," Mathematics Teaching in
the Middle School, Vol. 1, No. 1 (April 1994), pp. 28-33. As adapted here:
http://illuminations.nctm.org/LessonDetail.aspx?id=L248
Golden, John. “Math Games: For Skills and Concepts” GVSU
http://faculty.gvsu.edu/goldenj/GameshandoutHS.pdf
Mueller, Mary. “SNAKE – A Whole Class Math Dice Game.” Guided Math: A Teachers Guide
to Guided Math. http://www.guided-math.com/2011/03/snake-whole-class-dicegame.html
# of
occurrences↓
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Sum→
2
3
4
5
6
7
8
9
10
11
12
S N A K E
Round Totals:
Game totals: