Download Grade 3 – 2005 Practice Test – Problem # 36

Mathematics Benchmarks & Indicators
with Ohio Achievement Test Questions
Grades 3 – 4
Includes questions from the released
2008, 2007, 2006, and 2005 Ohio Achievement Tests
and the 2005 Practice Tests
Far East Regional Partnership
for Conceptually Based Mathematics
Youngstown State University
Compiled by A. Crabtree, 2006
Revised by A. Crabtree and L. Holovatick, 2007
Revised by A. Crabtree, J. Lucas, and T. Cameron, 2008
FERPCBM
Data Analysis and Probability
Standard
Data Analysis and Probability
Grades 3 - 4
A. Gather and organize data from surveys and classroom experiments, including data
collected over a period of time.
3-1. Collect and organize data from an experiment, such as recording and classifying
observations or measurements, in response to a question posed.
4-1. Create a plan for collecting data for a specific purpose.
Grade 4 – 2006 OAT – Problem # 2
Alan will be gathering data about the temperature.
Which part of Alan’s data collection plan should come first?
A. create a graph to display the data
B. record the data
C. choose a place and time to collect the data each day
D. interpret the data
B. Read and interpret tables, charts, graphs (bar, picture, line, line plot), and timelines
as sources of information, identify main idea, draw conclusions, and make
predictions.
3-4. Support a conclusion or prediction orally and in writing, using information in a table
or graph.
3-5. Match a set of data with a graphical representation of the data.
3-7. Analyze and interpret information represented on a timeline.
4-2. Represent and interpret data using tables, bar graphs, line plots and line graphs.
4-5. Propose and explain interpretations and predictions based on data displayed in
tables, charts and graphs.
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Data Analysis and Probability
Grades 3 - 4
Grade 3 – 2006 OAT – Problem # 39
The list shows the ages of all the players on
Miguel’s baseball team.
Which line plot shows this information
correctly?
Grade 3 – 2005 OAT – Problem # 26
How many goldfish are there?
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A. 12
B. 18
C. 24
July 2006 (Rev. July 2008)
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Data Analysis and Probability
Grades 3 - 4
Grade 3 – 2005 Practice Test – Problem # 7
The graph shows the favorite flavors of ice cream for
Stephanie’s class.
A. Chocolate
B. Strawberry
C. Vanilla
Which flavor is the mode of the data?
Grade 3 – 2005 Practice Test – Problem # 14
Use the data in the chart.
A. 5
B. 7
C. 8
How many more children picked the swings than the
slides as a playground activity?
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Data Analysis and Probability
Grades 3 - 4
Grade 4 – 2007 Test – Problem # 28
Ken goes grocery shopping once a week and keeps track of how much money
he spends. He made a bar graph and a line plot to display these data.
What information can be found only on the bar graph?
A. the number of weeks he shopped
B. the week he spent the least money
C. the most money he spent in one week
D. the least money he spent in one week
Grade 4 – 2005 Practice Test – Problem # 3
The bar graph shows the total number of jelly beans that
Greta has each day. The pattern for the number of jelly
beans will continue.
A. 15
B. 25
C. 30
D. 35
How many jelly beans will Greta have on Friday?
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Data Analysis and Probability
Grades 3 - 4
Grade 4 – 2005 Practice Test – Problem # 12
The Venn diagram shows the number of students in a class who have
brothers and sisters.
Which statement is true?
A. Exactly 6 students in the class have brothers.
B. Exactly 10 students in the class have brothers.
C. Exactly 16 students in the class have brothers.
D. Exactly 23 students in the class have brothers.
C. Construct charts, tables and graphs to represent data, including picture graphs,
bar graphs, line graphs, line plots and Venn diagrams.
3-6. Translate information freely among charts, tables, line plots, picture graphs and bar
graphs; e.g., create a bar graph from the information in a chart.
4-2. Represent and interpret data using tables, bar graphs, line plots and line graphs.
4-3. Interpret and construct Venn diagrams to sort and describe data.
4-4. Compare different representations of the same data to evaluate how well each
representation shows important aspects of the data, and identify appropriate ways to
display the data.
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Data Analysis and Probability
Grades 3 - 4
Grade 3 – 2006 OAT – Problem # 44
The chart below shows the kinds of pets owned by students in Mr. Grady’s class.
Which graph shows these data?
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Data Analysis and Probability
Grades 3 - 4
Grade 4 – 2007 Test – Problem # 35
Mrs. Allen has 15 students. Eight students belong to the drama club and 10
students belong to the computer club. Some students belong to both clubs.
Which Venn diagram represents these data?
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Data Analysis and Probability
Grades 3 - 4
Grade 4 – 2005 Practice Test – Problem # 10
Twelve students wrote their names and the number of letters in their names on
cards as shown.
Use the line to construct a line plot of the information on the students’ cards. Use
X to show the data.
Find the median, mode and range of the data on the cards.
Median: __________
Mode: ____________
Range: ___________
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Data Analysis and Probability
Grades 3 - 4
D. Read, interpret and construct graphs in which icons represent more than a single
unit or intervals greater than one; e.g., each  = 10 bicycles or the intervals on an
axis are multiples of 10.
3-2. Draw and interpret picture graphs in which a symbol or picture represents more than
one object.
3-3. Read, interpret and construct bar graphs with intervals greater than one.
Grade 3 – 2007 Test – Problem # 41
Mrs. Jones’ students made a picture graph of their favorite ice cream cones.
How any students chose vanilla ice cream cones as their favorite?
A. 3
B. 6
C. 18
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Data Analysis and Probability
Grades 3 - 4
Grade 3 – 2005 OAT – Problem # 30
This table shows the number of students in four classes.
Directions:
Use the grid on the next page to create a bar graph to show the data in the table.
Be sure to show a scale for your graph.
Write two different facts about the information in the graph.
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Data Analysis and Probability
Grades 3 - 4
Grade 3 – 2005 Practice Test – Problem # 4
The school store had fancy pencils for sale as shown in this table.
Make a picture graph showing the number of each type of pencil. Let each
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Data Analysis and Probability
Grades 3 - 4
Grade 4 – 2006 OAT – Problem # 27
The bar graph shows the number of people who visited
the first-aid station at Holden Creek State Park each
month last summer.
A. 15 people
B. 20 people
C. 40 people
D. 110 people
How many more people visited the first-aid station in July
than in May?
E. Describe data using mode, median and range.
3-8. Identify the mode of a data set and describe the information it gives about a data set.
4-6. Describe the characteristics of a set of data based on a graphical representation,
such as range of the data, clumps of data, and holes in the data.
4-7. Identify the median of a set of data and describe what it indicates about the data.
4-8. Use range, median and mode to make comparisons among related sets of data.
Grade 3 – 2006 OAT – Problem # 24
Nine students gathered data about their fathers’ shoe
sizes.
A. size 8
B. size 9
C. size 10
Shoe size: 8, 8, 8, 9, 9, 9, 9, 10, 10
What is the mode for the data they collected?
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Data Analysis and Probability
Grades 3 - 4
Grade 3 OAT 2005 – Problem # 3
Johnny asked his classmates to name their favorite food. The mode of this data
was pizza. Which statement tells what the mode means?
A. The greatest number of students said pizza.
B. The least number of students said pizza.
C. None of the students said pizza.
Grade 3 – 2005 Practice Test – Problem # 7
The graph shows the favorite flavors of ice cream for
Stephanie’s class.
A. Chocolate
B. Strawberry
C. Vanilla
Which flavor is the mode of the data?
Grade 4 – 2007 Test – Problem # 8
Fred recorded the heights, in inches, of the students in his class. The range of
the data was 15.
Which statement is true about Fred’s data?
A. Fred found that 15 students are all the same height.
B. The height of the shortest student is 15 inches.
C. Fred recorded the heights of 15 students in his class.
D. The tallest student is 15 inches taller than the shortest student.
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Data Analysis and Probability
Grades 3 - 4
Grade 4 – 2006 OAT – Problem # 20
Reuben recorded the heights of 7 boys and 7 girls in his class in the table
shown.
Calculate the range, the median and the mode for the height of the boys and for
the height of the girls.
Range:
Boys
Girls
Median:
Boys
Girls
Mode:
Boys
Girls
________
________
________
________
________
________
Use the range, median or mode to compare the heights of the boys and the girls
and tell which group you think is taller.
Explain how you made your choice.
Grade 4 – 2006 OAT – Problem # 37
Andrea made a line plot of the ages of children at
summer camp.
A. The data are
spread out evenly.
B. The data have a
hole between 10
and 13.
C. There is a clump
of data between 10
and 13.
D. The range and
the median are the
same.
Which is true about the data in the line plot?
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Data Analysis and Probability
Grades 3 - 4
Grade 4 – 2005 Practice Test – Problem # 10
Twelve students wrote their names and the number of letters in their names on
cards as shown.
Use the line to construct a line plot of the information on the students’ cards. Use
X to show the data.
Find the median, mode and range of the data on the cards.
Median: __________
Mode: ____________
Range: ___________
F. Conduct a simple probability experiment and draw conclusions about the
likelihood of possible outcomes.
3-9. Conduct a simple experiment or simulation of a simple event, record the results in a
chart, table or graph, and use the results to draw conclusions about the likelihood of
possible outcomes.
4-9. Conduct simple probability experiments and draw conclusions from the results; e.g.,
rolling number cubes or drawing marbles from a bag.
4-10. Represent the likelihood of possible outcomes for chance situations; e.g.,
probability of selecting a red marble from a bag containing 3 red and 5 white
marbles.
4-11. Relate the concepts of impossible and certain-to-happen events to the numerical
values of 0 (impossible) and 1 (certain).
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Data Analysis and Probability
Grades 3 - 4
4-12. Place events in order of likelihood and use a diagram or appropriate language to
compare the chance of each event occurring; e.g. impossible, unlikely, equal, likely,
certain.
Grade 3 – 2006 OAT – Problem # 21
Which spinner has the best chance of landing on a shaded space?
Grade 3 – 2005 OAT – Problem # 12
Monica pulls one block from each bag. Which bag is the least
likely to have a white block pulled from it?
Grade 4 – 2006 OAT – Problem # 30
The table shows the number of different-colored tiles Anita placed in a bag.
Anita picked one tile from the bag without looking.
Which shows the colors listed in order from the least likely to be picked to the
most likely?
A. green, red, yellow, blue
B. green, red, blue, yellow
C. yellow, blue, green, red
D. red, blue, yellow, green
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Data Analysis and Probability
Grades 3 - 4
G. Identify and represent possible outcomes, such as arrangements of a set of up to
four members and possible combinations from several sets, each containing 2 or 3
members.
3-10. Use physical models, pictures, diagrams and lists to solve problems involving
possible arrangements or combinations of two to four objects.
4-13. List and count all possible combinations using one member from each of several
sets, each containing 2 or 3 members; e.g., the number of possible outfits from 3
shirts, 2 shorts, and 2 pairs of shoes.
Grade 3 – 2005 OAT – Problem # 20
José has a red shirt, a blue shirt and a white shirt. He also has an orange hat
and a green hat.
Use words or pictures to show all the different ways José can wear one shirt and
one hat.
Grade 3 – 2005 Practice Test – Problem # 19
Steve has the three groups of objects shown below.
He picks one object from each group. Which is one possible way Steve could
have picked the three objects?
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Data Analysis and Probability
Grades 3 - 4
Grade 4– 2007 Test – Problem # 15
Raymond has these notebooks and pens in his backpack.
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Data Analysis and Probability
Grades 3 - 4
Grade 4 – 2006 OAT – Problem # 46
Calvin plans to plant one type of flower and one type of vegetable in his garden.
He chooses the plants from the table shown.
Which list shows all the different combinations of one flower and one vegetable
that Calvin can plant?
A. roses and carrots, roses and peas
B. roses and carrots, roses and peas, tulips and carrots, tulips and peas
C. roses and carrots, tulips and peas, roses and tulips, carrots and peas
D. roses and carrots, roses and peas, roses and tulips, tulips and carrots,
tulips and peas, carrots and peas
Grade 4 – 2005 Practice Test – Problem # 2
Ramón’s uncle is buying an automobile. He needs to choose an outside
color and an inside color.
What are all the possible combinations of one outside color and one
inside color that he could choose?
A. blue and gray, blue and tan, red and gray, red and tan
B. blue and red, blue and gray, blue and tan, blue and blue
C. gray and tan, red and blue
D. gray and red, gray and blue
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Data Analysis and Probability
Grades 3 - 4
H. Use the set of possible outcomes to describe and predict events.
4-10. Represent the likelihood of possible outcomes for chance situations; e.g.,
probability of selecting a red marble from a bag containing 3 red and 5 white
marbles.
4-11. Relate the concepts of impossible and certain-to-happen events to the numerical
values of 0 (impossible) and 1 (certain).
Grade 3 – 2005 Practice Test – Problem # 36
Morgan spins both spinners shown.
A. possible but not
certain
B. impossible
C. certain
He adds the two numbers on which the spinners land.
How likely is it that Morgan’s sum will be an odd
number?
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Data Analysis and Probability
Grades 3 - 4
Grade 4 – 2006 OAT – Problem # 8
Which spinner has a probability of 0 for landing on a star,
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?
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Data Analysis and Probability
Grades 3 - 4
Mathematical Processes:
A. Apply and justify the use of a variety of problem-solving strategies; e.g., make an
organized list, guess and check.
B. Use an organized approach and appropriate strategies to solve multi-step problems.
C. Interpret results in the context of the problem being solved; e.g., the solution must be a
whole number of buses when determining the number of buses necessary to transport
students.
D. Use mathematical strategies to solve problems that relate to other curriculum areas and
the real world; e.g., use a timeline to sequence events; use symmetry in artwork.
E. Link concepts to procedures and to symbolic notation; e.g., model 3 x 4 with a geometric
array, represent one-third by dividing an object into three equal parts.
F. Recognize relationships among different topics within mathematics; e.g., the length of an
object can be represented by a number.
G. Use reasoning skills to determine and explain the reasonableness of a solution with
respect to the problem situation.
H. Recognize basic valid and invalid arguments, and use examples and counter examples,
models, number relationships, and logic to support or refute.
I.
Represent problem situations in a variety of forms (physical model, diagram, in words or
symbols), and recognize when some ways of representing a problem may be more
helpful than others.
J. Read, interpret, discuss and write about mathematical ideas and concepts using both
everyday and mathematical language.
I.
Use mathematical language to explain and justify mathematical ideas, strategies and
solutions.
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Data Analysis and Probability – Answer Key
Grades 3 - 4
Multiple Choice:
OAT – Grades 3 & 4
Data Analysis and Probability
A
B
C
D
E
F
G
H
*
Grade
4
3
3
3
3
4
4
4
4
4
3
3
3
4
3
3
4
4
4
4
3
4
3
3
4
4
4
3
4
Test
Year
2006
2006
2005
2005*
2005*
2007
2005*
2005*
2007
2005*
2007
2005
2005*
2006
2005
2005*
2007
2006
2006
2005*
2005
2006
2005
2005*
2007
2006
2005*
2007
2006
No.
2
39
26
7
14
28
3
12
35
10
41
30
4
27
3
7
8
20
37
10
12
30
20
19
15
46
2
36
8
Answer
C
A
B
A
B
B
B
C
D
**
C
E.R.
**
C
A
A
D
E.R.
B
**
B
B
S.A.
C
S.A.
B
A
A
C
Half-Length Practice Test
** Scoring Guidelines Not Released
(Short Answer/Extended Response)
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Data Analysis and Probability – Answer Key
Grades 3 - 4
Short Answer & Extended Response Rubrics:
Grade 3
DAP – Benchmark G
2005 OAT – Grade 3 – Problem # 20 Scoring Guidelines:
Points
Student Response
2
The response shows six different combinations of shirts and hats using pictures or
words.
Examples of correct responses:
red shirt - orange hat
G and W
red shirt - green hat
G and R
blue shirt - orange hat OR G and B
blue shirt - green hat
O and W
white shirt - orange hat
O and R
white shirt - green hat
O and B
1
The response shows one to five correct combinations of shirts and hats.
0
The response indicates no understanding of the task or the underlying skills,
concepts tasks or processes.
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Data Analysis and Probability – Answer Key
Grades 3 - 4
DAP – Benchmark D
2005 OAT – Grade 3 – Problem # 30 Scoring Guidelines:
Points
4
Student Response
The response creates the bar graph with a correct scale and bar heights and
writes two different, correct facts based on the table or graph.
For example:
Acceptable facts:
• Any reference to the bar heights or numbers used in the table are ok
• Repetition of the information in the table is not correct
3
The response creates the bar graph with a correct scale and bar heights and
writes one correct fact based on the table or graph.
OR
The response creates the bar graph with no more than two errors (scale and/or
bar height(s)), and writes two different, correct facts based on the table or graph.
NOTE:
Multiple unrelated bar height errors = # of errors
One error in bar heights that is consistently carried through = 1 error
Scale and bar height error = 2 errors
2
The response creates the bar graph with a correct scale and bar heights OR
writes two different, correct facts based on the table or graph.
OR
The response creates the bar graph with no more than two errors (scale and/or
bar heights) AND writes one correct fact based on the table or graph.
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Data Analysis and Probability – Answer Key
Grades 3 - 4
1
The response creates the bar graph with no more than two errors (scale and/or
bar heights) OR writes one correct fact based on the table or graph.
0
The response indicates no understanding of the task or the underlying skills,
concepts or processes.
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Data Analysis and Probability – Answer Key
Grades 3 - 4
Short Answer & Extended Response Rubrics:
Grade 4
DAP – Benchmark G
2007 OAT – Grade 4 – Problem #15 Scoring Guidelines:
Points
Student Response
2
The focus of this task is to show all possible outcomes using one member
from each of two sets; each set contains three members. The response
includes a list of all 9 combinations of one notebook and one pen with no
incorrect combinations. Science and blue, Science and green, Science and
red, Reading and blue, Reading and green, Reading and red, Writing and
blue, Writing and green, Writing and red Note – Letters or symbols may be
used to represent colors, i.e., b – blue. Tables with outcomes are also
acceptable.
1
The response provides partial evidence of understanding how to list all
possible combinations using one member from each of two sets; however, the
response is incomplete or slightly flawed.
1 point sample answer:
For example, the response may:
• Include 5, 6, 7 or 8 correct combinations and may include additional
incorrect combinations.
• Include at least five correct combinations.
0
The response provides evidence of inadequate understanding of listing
possible outcomes. The response will provide major flaws in explanations or
irrelevant information.
0 point sample answer:
For example, the response may:
• Include 4 or fewer correct combinations.
• Only list the combinations shown adjacent on the chart.
• Be blank or state unrelated statements.
• Recopy information from the stem.
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Data Analysis and Probability – Answer Key
Grades 3 - 4
DAP – Benchmark E
2006 OAT – Grade 4 – Problem # 20 Scoring Guidelines:
Points
Student Response
4
The focus of the task is calculating relevant statistics for two sets of data and
making and explaining a conclusion based on the statistics. The response
provides a correct range for the girls and the boys, a correct median for the girls
and the boys, a correct mode for the girls and the boys, and an accurate
explanation of which group is taller.
Sample correct response:
Range: boys 58 – 47 = 11, girls 58 – 49 = 9
Median: boys = 53, girls = 55
Mode: boys = 53, girls = 56
The girls are taller because the tallest girl is just as tall as the tallest boy and the
range is smaller for the girls.
OR
The median height of the girls is higher, so half of the girls are taller than 55
inches and half of the boys are taller than 53 inches.
3
The response provides evidence of calculating relevant statistics for two sets of
data and making and explaining a conclusion based on the statistics; however,
the solution may contain a slight error, a flaw or a vague explanation.
For example, the response may:
• Provide two out of the three correct statistics and provide an accurate
explanation of the tallest group based on the statistics as provided.
• The response correctly determines the range, median, and mode, but
does not give an explanation, or uses a flawed reasoning to explain which
group is taller.
2
The response provides partial evidence of calculating relevant statistics for two
sets of data and making and explaining a conclusion based on the statistics;
however, the solution is incomplete and/or contains minor flaws.
For example, the response may:
• Incorrectly determine two of the statistics but provides a reasonable
explanation for which group is taller.
• Have multiple calculation errors in determining the range, median and
mode but includes an explanation that uses only slightly flawed reasoning.
1
The response provides minimal evidence of calculating relevant statistics for two
sets of data and making and explaining a conclusion based on the statistics. The
response has major flaws and errors in reasoning.
For example, the response may:
• Incorrectly determine 2 out of the 3 statistics and provide an explanation
based on flawed reasoning or omit an explanation.
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Data Analysis and Probability – Answer Key
Grades 3 - 4
DAP – Benchmark E
2006 OAT – Grade 4 – Problem # 20 Scoring Guidelines:
0
The response provides inadequate evidence of calculating relevant statistics for
two sets of data and making and explaining a conclusion based on the statistics.
For example, the response may:
• Incorrectly determine all of the statistics OR make multiple errors and
provide a completely flawed or unrelated explanation.
• Provide unrelated statements.
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