Download ITEM 11

SCORING GUIDE AND
TRAINING MANUAL
11.
ITEM 11
HIGH SCHOOL MATHEMATICS
Joseph and Cindy made up a game in their mathematics class. To earn points
in the game, each player rolls a six-sided cube with numbers 1 through 6 on the
sides and then flips a coin. When the coin lands “tails up,” the player gets a total
number of points equal to the number at the top of the cube. When the coin lands
“heads up,” the player’s points are doubled for that turn.
In the box below, list all the possible outcomes for each turn. Then indicate the
probability of a player getting 6 points in one turn.
6-88
SCORING GUIDE AND
TRAINING MANUAL
ITEM 11
HIGH SCHOOL MATHEMATICS
Scoring Rubric
High School Mathematics WASL Practice Test Item 11
Strand: Probability and Statistics
PS01
Learning Target (Probability) Demonstrate understanding of the concepts
of compound, dependent, and independent events; determine and use
probabilities of compound, dependent, and independent events (1.4.1, 1.4.2)
A 2-point response: The student shows an understanding of determining the size of a
sample space and/or listing all possible outcomes of an experiment to determine the
probability of a certain outcome by doing the following:
• shows all 12 coin/number cube combinations (1 H, 1 T, 2 H, 2 T, …) OR all the correct
possible game point totals: 1, 2, 3, 4, 5, 6, 8, 10, and 12
1
• indicates that the probability of getting 6 points is 2 or
12
6
NOTE: If the student doubles the tails column instead of the heads column, that alone
will not affect the student’s score.
A 1-point response: The student does one of the following:
• correctly lists at least nine of the possible outcomes or totals and no more than three
additional outcomes or totals that are incorrect. The response also gives a probability
that agrees with the possible outcomes or totals shown
• indicates the correct probability but fails to list all the possible outcomes or totals
• lists all the possible outcomes or totals but gives an incorrect or no probability.
A 0-point response: The student shows little or no understanding of determining the
size of a sample space and/or listing all possible outcomes of an experiment to determine
the probability of a certain outcome.
6-89
SCORING GUIDE AND
TRAINING MANUAL
11.
PR AC T I C E T E S T I T E M
11 - Anchor 1
HIGH SCHOOL MATHEMATICS
Joseph and Cindy made up a game in their mathematics class. To earn points
in the game, each player rolls a six-sided cube with numbers 1 through 6 on the
sides and then flips a coin. When the coin lands “tails up,” the player gets a
total number of points equal to the number at the top of the cube. When the
coin lands “heads up,” the player’s points are doubled for that turn.
In the box below, list all the possible outcomes for each turn. Then indicate the
probability of a player getting 6 points in one turn.
Score:
2
Annotation:
The student shows understanding of determining the size of a sample space and/or listing all possible
outcomes of an experiment to determine the probability of a certain outcome by showing all 12
coin/number cube combinations and all the correct possible game point totals; and indicating that the
probability of getting 6 points in one turn is “2 in 12 or 1 in 6.” This response earns two points.
6-90
SCORING GUIDE AND
TRAINING MANUAL
11.
PR AC T I C E T E S T I T E M
11 - Anchor 2
HIGH SCHOOL MATHEMATICS
Joseph and Cindy made up a game in their mathematics class. To earn points
in the game, each player rolls a six-sided cube with numbers 1 through 6 on the
sides and then flips a coin. When the coin lands “tails up,” the player gets a
total number of points equal to the number at the top of the cube. When the
coin lands “heads up,” the player’s points are doubled for that turn.
In the box below, list all the possible outcomes for each turn. Then indicate the
probability of a player getting 6 points in one turn.
Score:
2
Annotation:
The student shows understanding of determining the size of a sample space and/or listing all possible
outcomes of an experiment to determine the probability of a certain outcome by showing all the correct
possible game point totals and indicating that the probability of getting 6 points in one turn is “2/12.”
This response earns two points.
6-91
SCORING GUIDE AND
TRAINING MANUAL
11.
PR AC T I C E T E S T I T E M
11 - Anchor 3
HIGH SCHOOL MATHEMATICS
Joseph and Cindy made up a game in their mathematics class. To earn points
in the game, each player rolls a six-sided cube with numbers 1 through 6 on the
the sides and then flips a coin. When the coin lands “tails up,” the player gets a
total number of points equal to the number at the top of the cube. When the
coin lands “heads up,” the player’s points are doubled for that turn.
In the box below, list all the possible outcomes for each turn. Then indicate the
probability of a player getting 6 points in one turn.
Score:
2
Annotation:
The student shows understanding of determining the size of a sample space and/or listing all possible
outcomes of an experiment to determine the probability of a certain outcome by showing all 12
coin/number cube combinations and indicating that the probability of getting 6 points in one turn is
“2:12” (which is unacceptable notation for probability) but then demonstrates understanding of the
correct notation for probability by stating “2 out of 12” later in the response. This response earns two
points.
6-92
SCORING GUIDE AND
TRAINING MANUAL
11.
PR AC T I C E T E S T I T E M
11 - Anchor 4
HIGH SCHOOL MATHEMATICS
Joseph and Cindy made up a game in their mathematics class. To earn points
in the game, each player rolls a six-sided cube with numbers 1 through 6 on the
sides and then flips a coin. When the coin lands “tails up,” the player gets a
total number of points equal to the number at the top of the cube. When the
coin lands “heads up,” the player’s points are doubled for that turn.
In the box below, list all the possible outcomes for each turn. Then indicate the
probability of a player getting 6 points in one turn.
Score:
1
Annotation:
The student shows partial understanding of determining the size of a sample space and/or listing all
possible outcomes of an experiment to determine the probability of a certain outcome by indicating the
correct probability of getting 6 points in one turn is “2/12 = 1/6.” The list of possible combinations (1=T,
1=H ...) has only 11 correct combinations due to the repeat of 6T, and omission of 6H, at the end of the
list. This response earns one point.
6-93
SCORING GUIDE AND
TRAINING MANUAL
11.
PR AC T I C E T E S T I T E M
11 - Anchor 5
HIGH SCHOOL MATHEMATICS
Joseph and Cindy made up a game in their mathematics class. To earn points
in the game, each player rolls a six-sided cube with numbers 1 through 6 on the
sides and then flips a coin. When the coin lands “tails up,” the player gets a
total number of points equal to the number at the top of the cube. When the
coin lands “heads up,” the player’s points are doubled for that turn.
In the box below, list all the possible outcomes for each turn. Then indicate the
probability of a player getting 6 points in one turn.
Score:
1
Annotation:
The student shows partial understanding of determining the size of a sample space and/or listing all
possible outcomes of an experiment to determine the probability of a certain outcome by listing all 12
coin/number cube combinations, all the correct game point totals, and indicating an incorrect
probability of getting 6 points in one turn is “1/12.” This response earns one point.
6-94
SCORING GUIDE AND
TRAINING MANUAL
11.
PR AC T I C E T E S T I T E M
11 - Anchor 6
HIGH SCHOOL MATHEMATICS
Joseph and Cindy made up a game in their mathematics class. To earn points
in the game, each player rolls a six-sided cube with numbers 1 through 6 on the
sides and then flips a coin. When the coin lands “tails up,” the player gets a
total number of points equal to the number at the top of the cube. When the
coin lands “heads up,” the player’s points are doubled for that turn.
In the box below, list all the possible outcomes for each turn. Then indicate the
probability of a player getting 6 points in one turn.
Score:
1
Annotation:
The student shows partial understanding of determining the size of a sample space and/or listing all
possible outcomes of an experiment to determine the probability of a certain outcome by showing all 12
coin/number cube combinations. The listing of game point totals includes an error (1 -T - 1 should be 1 T - 2) and cannot receive credit. The probability “1/6” listed in the explanation is for “chance of rolling a
6” and is not the final answer for the probability of getting six points in one turn. This response earns
one point.
6-95
SCORING GUIDE AND
TRAINING MANUAL
11.
PR AC T I C E T E S T I T E M
11 - Anchor 7
HIGH SCHOOL MATHEMATICS
Joseph and Cindy made up a game in their mathematics class. To earn points
in the game, each player rolls a six-sided cube with numbers 1 through 6 on the
sides and then flips a coin. When the coin lands “tails up,” the player gets a
total number of points equal to the number at the top of the cube. When the
coin lands “heads up,” the player’s points are doubled for that turn.
In the box below, list all the possible outcomes for each turn. Then indicate the
probability of a player getting 6 points in one turn.
Score:
1
Annotation:
The student shows partial understanding of determining the size of a sample space and/or listing all
possible outcomes of an experiment to determine the probability of a certain outcome by showing all 12
coin/number cube combinations and all the correct possible game point totals in a chart format. An error
was made in reading the chart and the probability was incorrectly determined as “3/18 = 1/6.” Because
the probability was found in a incorrect manner, the 1/6 does not get credit as the probability of getting 6
points in one turn. This response earns one point.
6-96
SCORING GUIDE AND
TRAINING MANUAL
11.
PR AC T I C E T E S T I T E M
11 - Anchor 8
HIGH SCHOOL MATHEMATICS
Joseph and Cindy made up a game in their mathematics class. To earn points
in the game, each player rolls a six-sided cube with numbers 1 through 6 on the
sides and then flips a coin. When the coin lands “tails up,” the player gets a
total number of points equal to the number at the top of the cube. When the
coin lands “heads up,” the player’s points are doubled for that turn.
In the box below, list all the possible outcomes for each turn. Then indicate the
probability of a player getting 6 points in one turn.
Score:
0
Annotation:
The student shows little or no understanding of determining the size of a sample space and/or listing
all possible outcomes of an experiment to determine the probability of a certain outcome by showing
only 8 coin/number cube combinations; and indicating no probability of getting 6 points in one turn.
This response earns zero points.
6-97
SCORING GUIDE AND
TRAINING MANUAL
11.
PR AC T I C E T E S T I T E M
11 - Anchor 9
HIGH SCHOOL MATHEMATICS
Joseph and Cindy made up a game in their mathematics class. To earn points
in the game, each player rolls a six-sided cube with numbers 1 through 6 on the
sides and then flips a coin. When the coin lands “tails up,” the player gets a
total number of points equal to the number at the top of the cube. When the
coin lands “heads up,” the player’s points are doubled for that turn.
In the box below, list all the possible outcomes for each turn. Then indicate the
probability of a player getting 6 points in one turn.
Score:
0
Annotation:
The student shows little or no understanding of determining the size of a sample space and/or listing
all possible outcomes of an experiment to determine the probability of a certain outcome by showing a
drawing of a number cube and coin (heads and tails), listing only two coin/cube combinations and game
point totals; and not indicating the probability of getting 6 points in one turn. This response earns zero
points.
6-98
SCORING GUIDE AND
TRAINING MANUAL
11.
PR AC T I C E T E S T I T E M
11 - Anchor 10
HIGH SCHOOL MATHEMATICS
Joseph and Cindy made up a game in their mathematics class. To earn points
in the game, each player rolls a six-sided cube with numbers 1 through 6 on the
sides and then flips a coin. When the coin lands “tails up,” the player gets a
total number of points equal to the number at the top of the cube. When the
coin lands “heads up,” the player’s points are doubled for that turn.
In the box below, list all the possible outcomes for each turn. Then indicate the
probability of a player getting 6 points in one turn.
Score:
0
Annotation:
This student shows very little or no understanding of determining the size of a sample space and/or
listing all possible outcomes of an experiment to determine the probability of a certain outcome by
stating “the possible outcomes is 12,” and by indicating the probability of getting 6 points in one turn is
“6.” This response earns zero points.
6-99
6-100