Ohio Achievement Assessment
Grade 8 Mathematics
Spring 2011
Answer Key
and
Scoring Guidelines
Ohio Department of Education, Rev. October 2011
Page 1 of 8
Grade 8 Mathematics
Answer Key
Spring 2011
Item
No.
1
2
3
4
5
6
7
8
9
10
11
12-17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
Type
Multiple Choice
Multiple Choice
Multiple Choice
Multiple Choice
Multiple Choice
Short Answer
Multiple Choice
Multiple Choice
Multiple Choice
Multiple Choice
Short Answer
Multiple Choice
Multiple Choice
Multiple Choice
Extended Response
Multiple Choice
Multiple Choice
Multiple Choice
Multiple Choice
Short Answer
Multiple Choice
Multiple Choice
Multiple Choice
Multiple Choice
Short Answer
Multiple Choice
Multiple Choice
Multiple Choice
Multiple Choice
Short Answer
Multiple Choice
Multiple Choice
Multiple Choice
Multiple Choice
Multiple Choice
Multiple Choice
Multiple Choice
Multiple Choice
Content
Standard
Content Standard
Benchmark
Measurement
D
Data Analysis and Probability
F
Patterns, Functions, and Algebra
F
Data Analysis and Probability
D
Geometry and Spatial Sense
C
Measurement
E
Patterns, Functions, and Algebra
D
Data Analysis and Probability
G
Geometry and Spatial Sense
D
Measurement
B; C;
Number, Number Sense and Operations
I
Field Test questions not used for student score
Data Analysis and Probability
B
Number, Number Sense and Operations
I
Measurement
D
Patterns, Functions, and Algebra
C
Data Analysis and Probability
J
Measurement
E
Geometry and Spatial Sense
E
Number, Number Sense and Operations
H
Geometry and Spatial Sense
F
Number, Number Sense and Operations
C
Measurement
D
Data Analysis and Probability
I
Geometry and Spatial Sense
B
Number, Number Sense and Operations
G
Patterns, Functions, and Algebra
D
Geometry and Spatial Sense
B
Patterns, Functions, and Algebra
A
Number, Number Sense and Operations
I
Data Analysis and Probability
A
Patterns, Functions, and Algebra
C
Number, Number Sense and Operations
A
Data Analysis and Probability
A
Patterns, Functions, and Algebra
G
Number, Number Sense and Operations
B
Measurement
A
Data Analysis and Probability
B
Geometry and Spatial Sense
D
Key
Not for public release
B
A
B
Not for public release
2 pt rubric
Not for public release
Not for public release
Not for public release
Not for public release
2 pt rubric
A
Not for public release
C
4 pt rubric
Not for public release
Not for public release
Not for public release
C
Not for public release
Not for public release
Not for public release
Not for public release
Not for public release
2 pt rubric
C
Not for public release
Not for public release
Not for public release
2 pt rubric
Not for public release
C
C
Not for public release
Not for public release
Not for public release
B
C
Limited = 0-9; Basic = 10-15; Proficient = 16-27; Accelerated = 28-35; Advanced = 36-46
Multiple Choice = 1 point; Short Answer = 2 points; Extended Response = 4 points
Ohio Department of Education, Rev. July 2011
Page 2 of 8
6.
A contractor is installing a new concrete sidewalk. The sidewalk will be 580 feet
long, 9 feet wide and 6 inches deep.
Trucks will deliver 10 cubic yards of concrete in each truckload.
Determine how many truckloads of concrete the contractor will need to order. In
your Answer Document show or explain all steps you used to determine the
number of truckloads needed. (2 points)
Scoring Guidelines
Points
Student Response
Sample Response:
2 point
• 1 cubic yard = 3 × 3 × 3 = 27 cubic feet1 truck is 10 cubic yards = 270
cubic feet 580 × 9.5 × .5 = 2755 cubic feet 2755 ÷ 270 = 10.2 or 11
truckloads needed.
•
580 ft = 580 ÷3 =
9
ft ÷ 3 =
yards
yards
6 in. ÷12 = 0.5 ft ÷3 = yard
×
×
=
= 102.037
Therefore, 102 cubic yards of concrete are needed. 102 ÷10 = 10.2, so 11
truckloads of concrete need to be ordered.
NOTE: Credit for correct volume of the sidewalk will be given for answers in
cubic inches (4,760,640) or cubic feet (2,755).
1 point
0 point
The focus of this task is to find the volume of a rectangular prism. The
response provides the number of truckloads that need to be ordered and
shows the supporting work.
The response shows partial evidence of finding the volume of a rectangular
prism; however, the solution may be incomplete or slightly flawed.
Sample Response:
• Provide a slight calculation error in one of the unit conversions, but state
the correct answer of 11 truckloads.
• Provide one calculation error that is carried through to an incorrect
solution.
• Provide only the calculation for the volume of the sidewalk and not the
truckloads needed.
• State 11 truckloads with missing or incomplete supporting work.
The response provides inadequate evidence of finding the volume of a
rectangular prism.
Sample Response:
• State 10.2 truckloads with no work shown.
• Restate the information provided in the item.
• Be blank or state irrelevant information.
Ohio Department of Education, Rev. July 2011
Page 3 of 8
11.
In 2000, the population of the United States was about
of the United States is about 3,500,000 square miles.
. The land area
Find the average number of people per square mile in the United States in 2000.
In your Answer Document show or explain how you found the average.
(2 points)
Scoring Guidelines
Points
Student Response
Sample Response:
2 point
• I determined the number of people per square mile by dividing the
number of people by the number of square miles. 3,500,000 = 3.5
•
•
8
6
x
)=
.
83 × 102, or 83 people per square mile
8
) = 290,000,000 people3,500,000 square miles
people per square mile
82.86 people per square mile. I divided the number of people by
the number of square miles.
NOTE: Correctly approximated answers such as 82.86 or 83 and
appropriate answers such as 82 or 82.85 are acceptable.
1 point
0 point
The focus of this task is multiplying and dividing numbers written in
scientific notation. The response provides a correct average number of
people per square mile and an explanation of the process used.
The response shows partial evidence of multiplying and dividing numbers
written in scientific notation; however, the solution may be incomplete or
slightly flawed.
Sample Response:
• Provide a correct average number of people per square mile but
fail to describe the process or show supporting work.
• Show or explain the process accurately but include an error in the
calculations or state the incorrect units (e.g. millions or
thousands).
The response provides inadequate evidence of multiplying and dividing
numbers written in scientific notation. There are major flaws and
reasoning errors.
Sample Response:
• Fail to set up the problem correctly.
• Provide no accurate calculations.
• Restate the information provided in the item.
• Be blank or give irrelevant information.
Ohio Department of Education, Rev. July 2011
Page 4 of 8
21.
The brochure from Store-It-Yourself Storage shows the monthly cost for storage
units.
In your Answer Document create a line graph that shows the relationship
between unit size and cost per month. (4 points)
Write an equation that can be used to determine the per-square-foot cost of a
storage unit with any number of square feet. Show or explain how you found your
equation.
Then, use your equation to determine how much it will cost Tom to rent a 10-by12-foot storage unit from Store-It-Yourself Storage. Show or explain your work.
Scoring Guidelines
Points
Sample Response:
4 point
Student Response
•
I found the slope by calculating
y = 0.89x, where x is the
total number of square feet and y is the total cost. So, if x = 120, then
The focus of this task is relating representations of a relationship in a
table to a graph and symbolic form. The response provides an adequate
graph, a correct equation for determining the cost of the storage unit, the
correct cost for renting a 10-by-12-foot storage unit, and shows work or
provides an explanation.
Ohio Department of Education, Rev. July 2011
Page 5 of 8
3 point
2 point
1 point
0 point
The response provides evidence of relating representations of a
relationship in a table to a graph and symbolic form; however, the solution
may contain a slight error, a flaw or a vague explanation.
Sample Response:
• Provide a graph with major flaws and use the graph to write an
equation and correctly use that equation to find the cost of the 10by-12-foot storage unit, with correct work or an adequate
explanation.
• Provide an adequate graph, correct equation and correct cost of
the 10-by-12-foot storage unit but fail to show work or provide an
adequate explanation.
The response provides partial evidence of relating representations of a
relationship in a table to a graph and symbolic form; however, the solution
is incomplete and/or contains minor flaws.
Sample Response:
• Provide a correct equation but fail to graph the relationship or fail
to find the cost of the 10-by-12-foot storage unit.
• Provide a graph with major flaws, use that graph to write an
equation and to find the cost of the 10-by-12-foot storage unit, but
fail to show work or provide an explanation.
• Provide only an adequate graph and a correct cost of the 10-by12-foot storage unit without using an equation.
The response provides minimal evidence of relating representations of a
relationship in a table to a graph and symbolic form. The response
contains major flaws and the explanation is incomplete or missing.
Sample Response:
• Provide an adequate graph only.
• Write an incorrect equation but use the equation correctly to find
the cost of the 10-by-12-foot storage unit.
• State only $106.80.
The response provides inadequate evidence of relating representations of
a relationship in a table to a graph and symbolic form. The response
provides major flaws in explanations or irrelevant information.
Sample Response:
• Provide only a graph with major flaws.
• Restate the information provided in the item.
• Be blank or give irrelevant information.
Ohio Department of Education, Rev. July 2011
Page 6 of 8
31.
An auditorium has 5 sections of seats. Each section has between 190 and 210
seats. At a concert, 75% of the seats were occupied.
Estimate the number of occupied seats at the concert. In your Answer
Document show or explain your estimation strategy. (2 points)
Scoring Guidelines
Points
Student Response
2 point text Sample Response:
• 750 occupied seats. 5(200)(.75) = 750
NOTE: A whole number estimate between 712.5 and 787.5 is acceptable
for the number of occupied seats.
The focus of this task is estimating and computing problems involving
rational numbers. The response provides a reasonable estimate of the
number of occupied seats, with adequate supporting work.
1 point
0 point
NOTE: Answers in the range of 712.5 and 787.5 are acceptable.
The response provides partial evidence of estimating and computing
problems involving rational numbers; however, the solution may be
incomplete or slightly flawed.
Sample Response:
• Provide a reasonable estimate without adequate supporting work.
• Provide only a calculation that is an exact answer, such as
5(190)(.75) = 712.5 or 5(210)(.75) = 787.5, instead of using an
estimation strategy.
• Provide an estimation method but makes a calculation error and
carries it through such as 5(200)(75) = 75,000.
• Provide a whole number estimate for only one section of occupied
seats that is between 142.5 and 157.5.
The response provides inadequate evidence of estimating and computing
problems involving rational numbers. The response provides major flaws
in explanations or irrelevant information.
Sample Response:
• Provide calculations that cannot be used to find a reasonable
estimate.
• Restate the information provided in the item.
• Be blank or give irrelevant information.
Ohio Department of Education, Rev. July 2011
Page 7 of 8
36.
The table shows the batting averages for the Sousa Middle School baseball
team.
In your Answer Document create a box-and-whisker plot to represent the data
in the table. Be sure to identify the median, the lower and upper quartiles, and
the lower and upper extremes. (2 points)
Scoring Guidelines
Points
Sample Response:
2 point
Student Response
Lower Extreme: 0.150
Lower Quartile: 0.2125
Median: 0.250
Upper Quartile: 0.285
Upper Extreme: 0.300
1 point
0 point
The focus of this task is creating a box-and-whisker plot to represent
data. The response provides an accurate plot, with the median at 0.25;
the location of the lower quartile at 0.2125, and the location of the upper
quartile at 0.285. The lower extreme is located at 0.15, while the upper
extreme is located at 0.3.
The response provides partial evidence of creating a box-and-whisker
plot to represent data. However, the solution is incomplete or contains
flaws.
Sample Response:
• Provide misplaced or missing data or labels.
• Provide a correct graph for incorrect calculations.
• Provide all five key points and either do not attempt a box-andwhisker plot or provide a highly flawed plot.
The response provides inadequate understanding of creating a box-andwhisker plot to represent data.
Sample Response:
• Provide a graph other than a box-and-whisker plot.
• Provide a box-and-whisker plot with numerous flaws.
• Restate the information provided in the stem.
• Be blank or give irrelevant information.
Ohio Department of Education, Rev. July 2011
Page 8 of 8