Download statistics and probability items

STATISTICS AND PROBABILITY ITEMS:
OVERVIEW
Resources:
Attached you will find practice items for Statistics and Probability. These practice items are packaged so
that you will have weekly items to use in your classroom as bell ringers or engagement items. Three items per
day have been provided for this domain and should take no more than fifteen minutes of classroom
instruction.
The purpose of using these practice items daily is to be able to formatively assess student understanding and
any misconceptions they may have in this domain. Being able to gather evidence of student learning and
misconceptions in the moment, will give you the flexibility to change your instruction to meet their needs.
As the instructional decision-maker, you are able to adjust your methods for whole class or small groups to
address student misconceptions and move them toward proficiency.
The practice items represent a variety of standards from the Statistics and Probability domain. Two weeks
of practice items have been selected for this domain. Because there is only two weeks, every standard may
not be addressed.
The goal is for you to have a total of 10 weeks of practice items that represent the 5 domains in 8th grade. We
would like for you to use these items for a 10 week period between the time you receive them and the end of
January. If used daily for student and teacher practice, in accordance with our recommendations or tips, the
outcome will be an improvement in ACT ASPIRE test scores.
At the end of each weekly packet, you will find an answer key for your use. Although answer keys are
provided, students should explain their thinking during the discussion of the practice item.
A separate resource available to you is tasks addressing each of the domains. These tasks require students to
think about an efficient strategy to solve the problem, show their work and justify their reasoning. This is the
ultimate goal for what we want students to be able to do.
Recommendations or Tips:
When administering the practice items, please allow students to read through the daily items to see if they
have any questions about vocabulary or what the problem is asking them to do prior to engagement. Taking
the time to do these things now, will help to ensure that students are familiar with vocabulary and the
different question types before the actual test.
Providing Feedback to Students:
Since the purpose of the test practice items is to assess student understanding, it is not enough just to give the
practice items as bell ringers or engagement items. A key part of the process for advancing student
thinking, is to debrief the practice items and provide specific feedback on the student thinking and
performance. This can be done during the sharing out process by asking effective questions. It is difficult to
make student thinking and understanding visible by just giving multiple choice questions and determining
whether their response is correct or incorrect. Asking questions similar to the ones below can help students
verbalize the reasoning for their choices:
•
•
To get the correct solution, what concept do you have to be aware of?
Why are the answer choices you did not choose incorrect?
•
•
What strategy did you use to solve the problem? Why did you use that particular strategy?
Is there another strategy that you could use to solve the problem?
The above questions can be used with short response and constructed response also. Other questions to
consider when prompting students to verbalize or justify their thinking are:
Monitoring as students work:
• What is the problem asking you to find?
• How would you start the problem? How did you start the problem?
• What else do you need to do?
During debriefing:
• What did the problem ask you to do?
• What information do you see in the problem?
• What did you do first to solve this problem?
• Who else started this same way?
• What did you do next?
• Who started a different way?
• What are some strategies that you heard today that you would like to try when solving a similar
problem in the future?
Answer Key:
The information above is intended to help teachers assess student understanding of the mathematical idea(s)
in each problem. Also provided is an Answer Key for each set of items. While it is important for students to
get the answer correct, it is equally important for them to understand how their thinking leads or does
not lead to a correct solution. Incorrect solutions set the stage for teachable moments!!!!
Name______________________________________
Set 2 - Standard(s): 8.SP.1, 8.SP.2
Massachusetts, Minnesota
Day 1 Items
Date______________________
1. The scatterplot below shows the relationship between the height, in inches, and the shoe
size of each of 10 students in a class.
Based on the scatterplot, what ordered pair represents the outlier in the data?
2. The scatterplot shows the heights of Ferris wheels and the years they were built.
Which statement is true about the scatterplot?
a. All Ferris wheels built before 1980 must have been less than 60 meters high.
b. Based on the line of best fit, Ferris wheel heights increase about 25 meters every 10
years.
c. Each Ferris wheel is taller than all Ferris wheels that were built earlier.
d. Each year, more Ferris wheels were built than the year before.
•
•
http://www.doe.mass.edu/mcas/ - Massachusetts Department of Elementary and Secondary Education, Permission is
hereby granted to copy for non-commercial educational purposes any or all parts of this document. Please credit the
“Massachusetts Department of Elementary and Secondary Education.”
http://minnesota.pearsonaccessnext.com/resources/item-samplers/math/itemsamplers/grade8/G8_Math_MCA_12_point_Accommodated_Item_Sampler.pdf Minnesota Department of Education.
Set 2 - Standard(s): 8.SP.1, 8.SP.2
Massachusetts, Minnesota
Day 1 Items
3. The scatter plot below shows the points scored and the points allowed by the Bulldogs
football team for several games.
Which association (correlation) best describes the data?
a.
b.
c.
d.
•
•
no association (correlation)
positive association (correlation)
negative association (correlation)
nonlinear association (correlation)
http://www.doe.mass.edu/mcas/ - Massachusetts Department of Elementary and Secondary Education, Permission is
hereby granted to copy for non-commercial educational purposes any or all parts of this document. Please credit the
“Massachusetts Department of Elementary and Secondary Education.”
http://minnesota.pearsonaccessnext.com/resources/item-samplers/math/itemsamplers/grade8/G8_Math_MCA_12_point_Accommodated_Item_Sampler.pdf Minnesota Department of Education.
Name______________________________________
Set 2 - Standard(s): 8.SP.2
Engage NY, Massachusetts
Day 2 Items
Date______________________
1. Which line represents the best fit for the scatter plot data?
2. The scatter plot shows the sizes and annual rents of some office spaces in the downtown
area of a city.
What would the line of best fit reveal about these data?
a. There is a strong negative relationship between the cost of rent and the size of the
office space.
b. There is a strong positive relationship between the cost of rent and the size of the office
space.
c. There is a weak positive relationship between the cost of rent and the size of the office
space.
d. There is a weak negative relationship between the cost of rent and the size of the office
space.
•
•
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
http://www.doe.mass.edu/mcas/ - Massachusetts Department of Elementary and Secondary Education, Permission is
hereby granted to copy for non-commercial educational purposes any or all parts of this document. Please credit the
“Massachusetts Department of Elementary and Secondary Education.”
Set 2 - Standard(s): 8.SP.2 (continued)
Engage NY, Massachusetts
Day 2 Items
3. A scatterplot is shown below.
Which of the following most closely approximates the line of best fit for the data in the
scatterplot?
•
•
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
http://www.doe.mass.edu/mcas/ - Massachusetts Department of Elementary and Secondary Education, Permission is
hereby granted to copy for non-commercial educational purposes any or all parts of this document. Please credit the
“Massachusetts Department of Elementary and Secondary Education.”
Name______________________________________
Set 2 - Standard(s): 8.SP.3
Engage NY
Day 3 Items
Date______________________
1. The scatter plot below shows the numbers of customers in a restaurant for four hours of
the dinner service on two different Saturday nights. The line shown models this
relationship, and x = 0 represents 7 p.m.
What does the value of the y-intercept represent?
a.
b.
c.
d.
the average number of customers at 7 p.m.
the average number of customers at 11 p.m.
the average change in the number of customers each hour
the average change in the number of customers during four hours of the dinner service
2. The winning time for the men’s 400-meter race in each of the Olympic Games from 1976 to
1996 can be modeled by the equation y = −0.054x + 44.54, where x is the number of years
after 1976 and y is the winning time in seconds. If the relationship continues, which
equation could be used to predict the winning time in the year 2020?
a.
b.
c.
d.
y = −0.054(1976) + 44.54
y = −0.054(2020) + 44.54
y = −0.054(24) + 44.54
y = −0.054(44) + 44.54
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
Set 2 - Standard(s): 8.SP.3 (continued)
Engage NY
Day 3 Items
3. A researcher studied the eyesight of people at different ages. She calculated a vision score
for each person in the study and plotted the data on the graph below.
The researcher used the line y = −0.1x + 110 to model the data. When she substituted the value
x = 65 into this equation, what did the result tell her?
a.
b.
c.
d.
the exact value for the vision score of a 65-year-old
the predicted value for the vision score of a 65-year-old
the minimum possible value for the vision score of a 65-year-old
the maximum possible value for the vision score of a 65-year-old
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
Name______________________________________
Set 2 - Standard(s): 8.SP.1, 8.SP.2, 8.SP.3
Engage NY, Massachusetts
Day 4 Items
Date______________________
1. Line k is the line of best fit for a set of data on a scatter plot. The data show a strong linear
association. Which scatter plot best represents the data and line k?
2. In a citywide survey, bicycle owners were asked how many bicycles they owned, and
whether any had been stolen during the previous year. The results indicated that people in
the city owned 9017 bicycles and, of these, 450 had been stolen. Based on this information,
which conclusion is most reasonable?
a. No bicycle owners will have their bicycles stolen this year.
b. All bicycle owners will have their bicycles stolen this year.
1
c. The probability that any one bicycle will be stolen is about 5 .
1
d. The probability that any one bicycle will be stolen is about 20 . *
•
•
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
http://www.doe.mass.edu/mcas/ - Massachusetts Department of Elementary and Secondary Education, Permission is
hereby granted to copy for non-commercial educational purposes any or all parts of this document. Please credit the
“Massachusetts Department of Elementary and Secondary Education.”
Set 2 - Standard(s): 8.SP.1, 8.SP.2, 8.SP.3
Engage NY, Massachusetts
Day 4 Items
3. The results of four games played by a school’s baseball team are shown in the table below.
In which game was the positive difference in scores the least between the winning team
and the losing team?
a.
b.
c.
d.
•
•
Game 1
Game 2
Game 3
Game 4 *
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
http://www.doe.mass.edu/mcas/ - Massachusetts Department of Elementary and Secondary Education, Permission is
hereby granted to copy for non-commercial educational purposes any or all parts of this document. Please credit the
“Massachusetts Department of Elementary and Secondary Education.”
Name______________________________________
Set 2 - Standard(s): 8.SP.4
Engage NY, Massachusetts
Day 5 Items
Date______________________
1. Mr. Wallace surveyed 75 students at Poole Middle School to find out the students’ favorite
place to eat lunch. The results are shown below.
2. The Ecology Club was planning to take a field trip either to the seacoast or the mountains. The club
president surveyed all the member to determine the preferred trip. The results are displayed in the
table below.
Which statement is true about the results of the survey?
a. 20% of eighth grade students preferred the seacoast
b. 32% of seventh grade students preferred the mountains
c. 40% of students preferred the mountains
d. 48% of students preferred the seacoast
•
•
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
http://www.doe.mass.edu/mcas/ - Massachusetts Department of Elementary and Secondary Education, Permission is
hereby granted to copy for non-commercial educational purposes any or all parts of this document. Please credit the
“Massachusetts Department of Elementary and Secondary Education.”
Set 2 - Standard(s): 8.SP.4
Engage NY, Massachusetts
Day 5 Items
3. The histogram below shows the relationship between the price of a used car and the
number of used cars sold.
Based on the histogram, which statement must be true?
a.
b.
c.
d.
•
•
No used car sold for $7,000.
Exactly 5 of the used cars sold for $4,000.
The most expensive used car sold for $11,999.
Most of the used cars sold for less than $6,000.
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
http://www.doe.mass.edu/mcas/ - Massachusetts Department of Elementary and Secondary Education, Permission is
hereby granted to copy for non-commercial educational purposes any or all parts of this document. Please credit the
“Massachusetts Department of Elementary and Secondary Education.”
Set 2 - Standard(s): 8.SP.1, 8.SP.2
Massachusetts, Minnesota
Day 1 Items - KEY
1. (7,67)
2. B
3. A
Set 2 - Standard(s): 8.SP.2
Engage NY, Massachusetts
Day 2 Items - KEY
1. A
2. B
3. D
Set 2 - Standard(s): 8.SP.3
Engage NY
Day 3 Items - KEY
1. A
2. D
3. B
Set 2 - Standard(s): 8.SP.1, 8.SP.2, 8.SP.3
Engage NY, Massachusetts
Day 4 Items - KEY
1. D
2. D
3. D
Set 2 - Standard(s): 8.SP.4
Engage NY, Massachusetts
Day 5 Items - KEY
1. B
2. D
3. D