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 1 - Standard(s): 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4
NAEP Questioning Tool
Day 1 Items
Date______________________
1. Rick has earned a total of 581 points on all of his science tests. His overall test average
(mean) is 83. How many tests has Rick taken?
a.
b.
c.
d.
e.
6
7
8
9
10
2. Last month Bonnie recorded the weights of 11 dogs. Statistics for these weights are given
below.
This month, Bonnie weighed the 11 dogs again. The weight of one dog changed from 31
pounds to 27 pounds. The weights of all the other dogs stayed the same.
Which of the following statistics changed from last month to this month?
a. Maximum
b. Mean
c. Mode
d. First Quartile
e. Median
NAEP Questioning Tool - http://nces.ed.gov/nationsreportcard/nqt/, SOURCE: U.S. Department of Education, Institute of
Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009, 2011,
2013 Mathematics Assessment.
Set 1 - Standard(s): 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4
NAEP Questioning Tool
Day 1 Items
3. The stem-and-leaf plot below shows the number of seconds it took each student in a class
of 18 to complete a word search. 4. How many students took more than 25 seconds to
complete the word search?
a.
b.
c.
d.
e.
4
5
6
7
10
NAEP Questioning Tool - http://nces.ed.gov/nationsreportcard/nqt/, SOURCE: U.S. Department of Education, Institute of
Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009, 2011,
2013 Mathematics Assessment.
Name______________________________________
Set 1 - Standard(s): 7.SP.2, 7.SP.3
Engage NY
Day 2 Items
Date______________________
1. Laticia randomly selected 25% of the seventh-grade students in her school and asked them
their favorite season. Of the students surveyed, 51 chose summer as their favorite season.
Based on the data, what is the most reasonable prediction of the number of seventh-grade
students in her school who would choose summer as their favorite season?
a.
b.
c.
d.
15
75
150
200
2. Ms. Andrews made the line plots below to compare the quiz scores for her first-period math
class and her second-period math class. She gave the same quiz to each class.
What conclusion can Ms. Andrews make about the performance of her first- and second-period
classes?
a.
b.
c.
d.
The first-period class had a higher median score than the second-period class.
The second-period class scores had a higher mean than the first-period class scores.
The first-period class scores had a greater range than the second-period class scores.
The second-period class scores had a greater mean absolute deviation than the firstperiod class scores.
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
Set 1 - Standard(s): 7.SP.2, 7.SP.3 (continued)
Engage NY
Day 2 Items
3. To select a new school mascot, 20 randomly selected students in each grade were asked to
choose between the two finalists: tiger and eagle. The results are shown below.
Which statement is best supported by the results?
a. The preferred mascot is a tiger.
b. The preferred mascot is an eagle.
c. Fifth and sixth grade students at the school preferred an eagle mascot.
d. Seventh and eighth grade students at the school preferred an eagle mascot.
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
Name______________________________________
Set 1 - Standard(s): 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8
NAEP Questioning Tool
Day 3 Items
Date______________________
1. Each of the 6 faces of a fair cube is painted red, yellow, or blue. This cube is rolled 500
times. The table below shows the number of times each color landed faced up.
Color
Red
Yellow
Blue
Total
100
340
60
Based on these results, what is the most likely number of yellow faces on the cube?
a.
b.
c.
d.
e.
One
Two
Three
Four
Six
2. Ken has a box that contains 12 marbles. The table below shows the number of marbles of
each color that are in the box.
Ken randomly selects 2 marbles from the box and keeps them. If Ken then randomly selects a
third marble from the box, the probability that he will select a green marble is . Which of the
following statements could be true about the first 2 marbles Ken selected?
a.
b.
c.
d.
e.
One was yellow and one was green.
One was orange and one was yellow.
One was orange and one was blue.
Both were green.
Both were yellow.
NAEP Questioning Tool - http://nces.ed.gov/nationsreportcard/nqt/, SOURCE: U.S. Department of Education, Institute of
Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009, 2011,
2013 Mathematics Assessment.
Set 1 - Standard(s): 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8
NAEP Questioning Tool
Day 3 Items
3. The circular spinner shown below is divided into 6 congruent sectors. The sectors are yellow
or blue.
Label each of the sectors either yellow (Y) or blue (B) so that the probability of spinning
the arrow once and landing on yellow is .
NAEP Questioning Tool - http://nces.ed.gov/nationsreportcard/nqt/, SOURCE: U.S. Department of Education, Institute of
Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009, 2011,
2013 Mathematics Assessment.
Name______________________________________
Set 1 - Standard(s): 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8
NAEP Questioning Tool, Engage NY
Day 4 Items
Date______________________
1. How many different three-digit whole numbers can be written using each of the digits 4, 5,
and 6 exactly once?
a.
b.
c.
d.
e.
3
6
9
24
27
2. The spinner below is divided into 6 congruent sectors.
If the arrow is spun once, what is the probability that the arrow will land on either Red or
Blue?
a.
b.
c.
d.
e.
3. Sara is playing a board game. The probability that Sara will score a point on her next turn is
1
.
3
Which statement describes the probability that Sara will score a point on her next turn?
a. likely
b. certain
c. unlikely
d. impossible
•
•
NAEP Questioning Tool - http://nces.ed.gov/nationsreportcard/nqt/, SOURCE: U.S. Department of Education, Institute
of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP),
2009, 2011, 2013 Mathematics Assessment.
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
Name______________________________________
Set 1 - Standard(s): 7.SP.5, 7.SP.6, 7.SP.7
Engage NY
Day 5 Items
Date______________________
1. The school bus Evie rides is scheduled to arrive at her stop at 8:20 a.m. each day. The table
below shows the actual arrival times of the bus for several days that were randomly
selected over the past few months.
Based on these data, what is the probability that the bus will arrive at Evie’s stop before 8:20
a.m. tomorrow?
a.
b.
c.
d.
3
10
1
3
7
20
13
20
2. Cassie rolls a fair number cube with 6 faces labeled 1 through 6. She rolls the number cube
300 times. Which result is most likely?
a.
b.
c.
d.
Cassie will roll a 1 or a 2 about 50 times.
Cassie will roll a 1 or a 2 exactly 50 times.
Cassie will roll an even number about 150 times.
Cassie will roll an even number exactly 150 times.
3. Which tree diagram shows all of the possible outcomes for tossing a coin and rolling a fair
number pyramid that has four sides labeled 1 through 4?
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
Set 1 - Standard(s): 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4
NAEP Questioning Tool
Day 1 Items - KEY
1. B
2. B
3. C
NAEP Questioning Tool - http://nces.ed.gov/nationsreportcard/nqt/, SOURCE: U.S. Department of Education, Institute of
Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009, 2011,
2013 Mathematics Assessment.
Set 1 - Standard(s): 7.SP.2, 7.SP.3
Engage NY - https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
Day 2 Items - KEY
1. D
2. B
3. D
Set 1 - Standard(s): 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8
NAEP Questioning Tool
Day 3 Items - KEY
1. D
2. A
3. A Sample Correct Response:
NOTE: A correct response is any spinner with 6 sectors having any 2 sectors labeled yellow (Y)
and any 4 sectors labeled blue (B).
NAEP Questioning Tool - http://nces.ed.gov/nationsreportcard/nqt/, SOURCE: U.S. Department of Education, Institute of
Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009, 2011,
2013 Mathematics Assessment.
Set 1 - Standard(s): 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8
NAEP Questioning Tool, Engage NY
Day 4 Items - KEY
1. B
2. A
3. C
•
•
NAEP Questioning Tool - http://nces.ed.gov/nationsreportcard/nqt/, SOURCE: U.S. Department of Education, Institute
of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP),
2009, 2011, 2013 Mathematics Assessment.
https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
Set 1 - Standard(s): 7.SP.5, 7.SP.6, 7.SP.7
Engage NY - https://www.engageny.org/resource/new-york-state-common-core-sample-questions, Engage NY
Day 5 Items - KEY
1. C
2. C
3. D