Download 8dataa - Logan Elm Schools

Grade 8
Data Analysis, Statistics and Probability Answers
Open Response Question 12
An eighth-grade class will perform the first four acts in the annual talent show. Every
student is in exactly one of the four acts. The order in which the acts will be presented is
to be decided by a drawing so that each act has an equal chance of being drawn.
a. Chantal is a member of the eighth-grade class. What is the probability that her
act will be presented first?
b. Chantal's act was chosen to be presented first. Make a tree diagram, chart, or list
showing all the possible orders in which the other three acts could be
presented. Use the letters A, B, and C to represent these three acts.
c. Rory, Jesse, and Chantal are all members of the eighth-grade class who will each
perform an act. What is the probability that Rory's act will immediately follow
Jesse's? Explain how you found your answer.
Scoring Guide
Score
Description
4
The response demonstrates comprehensive understanding of the concepts of
probability and basic combinatorics by accurately describing outcomes and
events and determining the probability of those events.
3
The response demonstrates general understanding of the concepts of probability
and basic combinatorics by describing outcomes and events and determining the
probability of those events.
2
The response demonstrates basic understanding of the concepts of probability
and basic combinatorics by describing outcomes and events and/or determining
the probability of events.
1
The response demonstrates minimal understanding of the concepts of
probability and basic combinatorics by describing outcomes and events and/or
determining the probability of events.
0
The response is incorrect or contains some correct work that is irrelevant to the
skill or concept being measured.
Blank No response.
1
Open Response Question 23
An eighth-grade class took a survey and found that the most popular types of music in
their school were alternative rock, rap, and classic rock. They took a second survey to
find out the students' preference among these three types of music. These are the results
for 120 students.
2
Favorite Types of Music
Alternative Rock Rap Classic Rock
60
40
20
a. Make a rough sketch of a circle graph displaying these data. Tell how many
degrees should be in each sector of the graph.
b. Explain how you found the number of degrees for each sector.
Scoring Guide
Score
Description
4
Student makes reasonable sketch of circle graph and specifies correct number of
degrees for each sector. Explanation or work is clear and shows correct strategy.
3
Student makes reasonable sketch. Explanation or work shows correct strategy for
determining number of degrees. Errors are clearly careless.
OR
Student makes reasonable sketch and specifies correct number of degrees.
Explanation is vague but indicates correct strategy.
2
Student makes reasonable sketch and gives correct percent for each sector, but
no degrees. Explanation may or may not be included.
OR
Student specifies correct number of degrees for each sector. Explanation is
incomplete, hard to follow, or missing. Sketch may or may not be included.
OR
Student's explanation shows understanding of strategy that can be used for
determining number of degrees in a sector other than the 180° sector for
alternative rock. Sketch may or may not be included.
OR
Student makes reasonable sketch and gives clear explanation based on fractional
parts of circle. Answer has no conceptual errors regarding percents or degrees.
1
Student's sketch of graph shows some understanding of data.
OR
Response shows a minimal understanding of problem.
0
Response is incorrect or contains some correct work that is irrelevant to the skill
or concept being measured.
Blank No response.
3
4
5
6
Question 22
Lionel and Tracy are playing a game using two six-sided number cubes. The faces of
each cube are numbered as shown below.
7
Lionel has a red cube and Tracy has a green cube. To play the game they both roll their
cubes at the same time.


The numbers that show face up when the cubes stop rolling are used to make a
fraction.
The number on the red cube is used for the numerator and the number on the
green cube is used for the denominator.
1
For example, the results shown below would make the fraction
.
2



Lionel wins 1 point if the fraction formed has a value less than one.
Tracy wins 1 point if the fraction has a value greater than one.
No one gets a point if the fraction is equal to one.
a. Make a list or a table in your Student Answer Booklet of all of the fractions
possible from rolling 1 red and 1 green cube. How many total different fractions
are there?
b. If Lionel (red cube) rolls a 3, what is the probability that Tracy (green cube) wins
1 point? Show your work or explain how you obtained your answer.
c. Using your table, what is the probability of each player winning a point on a given
turn? Do you think this game is fair to both players? Show your work or explain
how you obtained your answer.
Scoring Guide
Score
4
Description
The response shows a comprehensive understanding of how to find the total
number of outcomes for a situation and calculate the probability of simple
compound events.
8
3
The response shows a general understanding of how to find the total number of
outcomes for a situation and calculate the probability of simple compound
events.
2
The response shows a basic understanding of probability.
1
The response shows a minimal understanding of probability.
0
The response is incorrect or contains some correct work that is irrelevant to the
skill or concept being measured.
Blank No Response.
2002 MCAS
Grade 8 Mathematics
Question # 22 - Score Point 4
9
10
11
Answer: G, 300,000
Answer: H, median = mode
Answer: J, 50%
12
Answer: Victoria would pick ten first then go to 5 or 15, depending on whether she was too high
or too low. She would continue to reduce her previous guess by half until she gets the number.
Answer: 15/31; There are 15 positive integers (natural numbers) and 15 negative integers and
then zero. So the chances are 15 out of 31 that you would get a positive number.
13
ANSWER: A
ANSWER: D
14
ANSWER: C
ANSWER: D
ANSWER: C
15