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Assessment Model #2 Pre-Algebra Grade 8
- 1. Total Score: ______
Name: ________________________ ID: ________________ Date: ___________
Waterfront Junior High School
Quick Start ©
Mathematics – Grade 8
(Pre-Algebra)
Assessment
Training Demonstration 2014
- 2. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 2
Preparation
STEP 1. Establish the testing sessionthat will begin the Waterfront Junior High SchoolGrade 8test
administration window.Allow time in the schedule for make-up test sessions prior to the
end of the administration window. Keep in mind that the entire test is designed to be
administered in two (2) parts over several class periods. Makecopies of the test form and
reference sheetsbased upon the number of students on your rolls.
STEP 2. Review the test administration steps, understand the guidelines for administering the test,
and arrange for the material and equipment you will need.Prior to administering the test,
review the test form, answer key, and directions located within the test booklet.
STEP 3. Establish a controlled testing environment with appropriate testing accommodations.
Administration
STEP 1. Distribute the assessment to the students, while compiling a list of students who will need
to makeup the session. Say to the students: “If you have questions about any of the
instructions that I give you, please ask them before the test begins.”
STEP 2. Write and post in the classroom the “Start Time and Date” and “Completion Time and
Date” for each part of thetest. Ensure that the students complete the demographic
information on the test booklet cover. Say to the students: “This test will be administered
in two (2) parts. You will complete the first part today. The second part consists of
Extended Performance Tasks (EP) that you will complete over severalclass periods.”
STEP 3. Begin the testing session.
a) Multiple Choice (MC) and Short Answer (SA) Questions 1-12: Say to the
students: “Let‟s prepare to start the test. After you have completed the test, read
quietly at your desk until the testing period is over, and I will collect the tests at that
time. Remember to try your best on each question. If you need help during the test,
raise your hand and I will come to your work area. If you have no questions, begin
the test.”
b) Extended Performance (EP) Task Question 13: Say to the students: “Let‟s
prepare to start the performance portion of the test. Read the Extended Performance
(EP) Taskpreparation and begin working on Task #1, Part A. When you get to class
tomorrow and the next day, I will not give any further instructions. I will hand you
the testing materials you need for that day and you will begin work. Remember to try
your best on each assignment. If you need help during any part of the test, raise your
hand and I will come to your workarea. If you have no questions, you may begin the
task.”
End the testing session.
a)Say to the students: “This part of the testing period has ended; I will now collect the
tests and your responses to Question #13.” Explain the procedures for students who
need more time to complete the test. Pick up all test forms and secure all testing
materials.
- 3. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 3
After Testing
STEP 1. At the end of each testing period, ensure 100% accountability for all assessment materials
and store them in a secure area.
STEP 2. Use the scoring key and rubric to score theon-demand items and the performance task.
Enter the raw score (points earned vs. total points possible) on the test booklet cover for
each student. Determine if the student‟s score meets the performance standard.
NOTE: Mark as incorrect questions left blank or multiple choice questions with more
than one answer.
STEP 3. After all students have completed the test, including make-ups, collect and inventory all
scored tests. Report student results in accordance with the district‟s policy in terms of
percent (%) correct or achieving a specific performance level.
- 4. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 4
DIRECTIONS:
For Questions 1 through 10, read each question carefully, select the best answer from the four
provided. Circle the letter (A, B, C, or D) that corresponds with the best answer. Each question
is worth one (1) point towards your overall score.
1. Which of the following equations illustrates the inverse property of multiplication?
A. 6 ( ) = 1
B. 6 (1) = 6
C. 6 (n) = 36
D. 6 (0) = 0
(0001.MTH.GR8.MC-LV1-2.8.8.A)
2. Solve the following equation:
x = 18
A. 10.8
B. 30
C. 54
D. 270
(0002.MTH.GR8.MC-LV2-2.8.8.A)
3. The sum of a number (n) plus 12 is 87. Which equation shows this relationship?
A. 12 + n = 87
B. 87n = 12
C. 12 – n = 87
D. 87 + n = 12
(0003.MTH.GR8.MC-LV1-2.8.8.C)
- 5. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 5
4. The total cost (c) in dollars of renting a sailboat for n days is shown by the equation:
c = 120 + 60n
If the total cost is $360, how many days was the sailboat rented?
A. 4 days
B. 8 days
C. 540 days
D. 21,720 days
(0004.MTH.GR8.MC-LV1-2.8.8.C)
5. Kim has $70 to spend on CDs. The cost of buying CDs online is $15 per CD. The
shipping cost per order is $12. Let mequal the number of CDs Kim can buy. Which
algebraic sentence allows Kim to buy CDs without going over her budget?
A. $12m + $15 ≥ $70
B. $12m + $15 ≤ $70
C. $15m + $12 ≥ $70
D. $15m + $12 ≤ $70
(0005.MTH.GR8.MC-LV1-2.8.8.E)
6. Study the set of ordered pairs for a linear function of x in the table below.
x y
1 1
3 7
5 13
7 19
Which of the following equations was used to generate the set of ordered pairs?
A. y = 2x +1
B. y = 2x -1
C. y = 3x - 2
D. y = 4x -3
(0006.MTH.GR8.MC-LV2-2.8.8.D)
- 6. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 6
7. Kyle has a total of 58 DVDs and CDs. If the number of CDs is two more than three times
the number of DVDs, how many CDs does he have?
A. 12 CDs
B. 14 CDs
C. 42 CDs
D. 44 CDs
(0007.MTH.GR8.MC-LV2-2.8.8.E)
8. Which graph shows y = -x2
?
A. B.
C. D.
(0008.MTH.GR8.MC-LV2-2.8.8.D)
9. If 4(3x + 2) – (x + 5) = -3, then x = _______________.
A.
B.
C.
D.
(0009.MTH.GR8.MC-LV2-2.8.8.A)
- 7. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 7
10. Find the solution to the following equation:
3x + 4x = 196
A. x = 26
B. x = 28
C. x = 81
D. x = 87
(0010.MTH.GR8.MC-LV2-2.8.8.A)
DIRECTIONS:
For Questions 11 and 12, read each question carefully and write your complete answer in the
space provided. For full credit, be sure to show ALL of your work. Each question is worth two
(2) points towards your overall score.
11. Sheryl is choosing a new cellular phone plan. Horizon‟s plan offers $65 a month plus
$0.10 per gigabyte (GB) over the monthly limit. Spritely Phone‟s plan has a monthly fee
of $35 per month, plus $0.20 per GB over the monthly limit.How many gigabytesover the
monthly limit will the two plans charge the same amount?
(0011.MTH.GR8.SA-LV3-2.8.8.E)
12. An auditorium earned $25,000 in sold-out concert ticket sales. Front section tickets cost
$75 per seat and back section tickets cost $50 per seat. The number of front section seats is
twice the number of back section seats. How many seats are in the front section?
(0012.MTH.GR8.SA-LV3-2.8.8.E)
- 8. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 8
Question #13
Extended Performance Task
Task #1: Determining Rate of Change
Task#2: Creating Systems of Equations
Task #3: Graphing a System of Equations
DIRECTIONS FOR QUESTION #13:
You will have several class periods to complete the entire three-part Extended Performance (EP)
Task. The time allowed for each task is noted after its title in the test booklet. Use the space
provided in each section to complete your answers.For full credit, be sure to show ALL of your
work. The complete three-part task is worth 24 points towards your overall score. Use the Score
Rubric(Pages 13-14) to guide your responses.
Day 1. Task Preparation
Research was conducted on the germination and growth period for a variety of plants. The
following table details the information gathered on four (4) plants.
Plant
Germination Time
(sprouted from soil)
Plant Growth
(days AFTER sprouting)
Approximate
Growth Height
Basil 4 days/.5 inches 7 days 14 inches
Chives 3 days/1 inch 20 days 15 inches
Oregano 6 days/.5 inches 14 days 21 inches
Parsley 3 days/1.5 inches 14 days 7 inches
Select two (2) plants and use them to respond to the following questions.
For Plant A I chose __________. The germination is _______ after ______ days.
For Plant B I chose __________. The germination is _______ after ______ days.
- 9. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 9
Question #13 – Task#1: Rate of Change
Time: 45 minutes
Total Possible Score: 4 points
Determine the growth rate of each plantyou selected and explain how you established this rate
(including the applicable units).
Growth Rate:
Explanation:
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
- 10. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 10
Question #13 – Task#2: Creating Systems of Equations
Time: 45 minutes
Total Possible Score: 12points
Part A: Create a system of equations based on the germination height and growth rate of each
plant that you selected on Day 1. (4 points)
Use the germination height of each plant as a y-intercept.
Plant A: ________________
Plant B: ________________
Use the growth rate of each plant as the slope.
Plant A: ________________
Plant B: ________________
Using the height and growth rates, write an equation in slope-intercept form
(y=mx+b).
Plant A: ________________
Plant B: ________________
Part B:
Reflect: What does the equation of each of these plants really mean? In the space below,
briefly describe in your own words what these mathematical sentences are telling you
about each plant. (4 points)
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Connect: In the space below, briefly explain why the germination height would be a good
value to use for the y-intercept. Also, explain why the rate of growth would be an
appropriate value for the slope. (4 points)
______________________________________________________________________________
______________________________________________________________________________
- 11. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 11
______________________________________________________________________________
______________________________________________________________________________
Question #13 – Task #3: Graphing a System of Equations
Time: 45 minutes
Total Possible Score: 8 points
Part A: On the graphing paper provided, create a graph with a title, a labeledx-axis and y-axis,
and an appropriate scale. Graph and label the equation for each line that you created. (4
points)
Part B: In the space below ANDon a separate sheet of graphing paper, explain what could
happen if you chose to plant two seedlings of the SAME plant. Illustrate what these
equations would look like graphed. (4 points)
___________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
(0013.MTH.GR8.EP-LV4-2.8.8.B)
- 12. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 12
Scoring Rubric
Advanced (4 pts.) Proficient (3 pts.) Basic (2 pts.) Below Basic (1 pt.)
Task #1:
Rate of Change
(4 points)
The student clearly defines germination
time, in both inches and days, and the
rate of change for both plants. The
student gives a clear explanation and
supports it mathematically.
The student clearly defines
germination time, in inches and days,
and the rate of change for both plants,
but either the student‟s explanation
does not show a clear understanding
of the rate of change concept or the
student fails to support the explanation
mathematically.
The student clearly defines
germination for both plants. The
student defines the rate of change
but may commit minor errors.
The rate of change is inversed,
showing a minor
misunderstanding. The student
supports the explanation
mathematically but shows the
misconception in the rate.
The student fails to define
germination and defines the
rate of change poorly and
with major errors ORdefines
germination time but either
fails to define rate of change
or provides a completely
inaccurate definition, even
after checking for common
errors. The student provides
no explanation.
Task#2:
Equations
Part A
(6 points)
Based upon the germination data, the
student assigns each plant a y-intercept.
Based upon the growth rate or measured
height over time, the student assigns
each plant a slope Using these values,
the student writes an equation in slope
intercept form for each plant.
Based upon the germination data, the
student assigns each plant a y-
intercept. Based upon the growth rate
or measured height over time, the
student assigns each plant a slope.
Using these values, the student writes
an equation in slope intercept form for
each plant. One or both of the
equations may include minor flaws.
Based upon the germination data,
the student assigns each plant a y-
intercept. Based upon the growth
rate or measured height over time,
the student assigns each plant a
slope. Using these values, the
student writes an equation in
slope intercept form for each
plant. A major flaw occurs in rate
or slope in that the student
computes time over height or
mixes the y-intercepts between
plants.
Based upon the germination
data, the student assignseach
plant a y-intercept. Based
upon the growth rate or
measured height over time,
the student assigns each plant
a slope. The student fails to
attempt equations.
Task #2:
Equations
and Conceptual
Meanings
Part B
(6 points)
The written explanation is clear and
mathematically supported in the “Reflect
and Connect” section. The student
shows a clear understanding of the
meaning of the equation when applied to
a real life situation. The student also
explains the selection of germination and
rate for the respective positions in a
graph, showing further connection of the
equation and its application.
In the “Reflect and Connect” section,
the student explains briefly how the
equation is related to the real life
situation. The explanation shows an
understanding but with minor flaws or
misconceptions. The student may try
to explain the reason for the slope and
intercept choices but may not be able
to support the explanation
mathematically.
The student shows little or very
misconstrued conceptual
understanding of the equation the
real life meaning when writing
the mathematical sentence. The
student may also skip one part of
the “Reflect and Connect” written
portion or fail to support both
partswith mathematical
explanations.
The student answers only one
part of the “Reflect and
Connect” written portion and
either fails to support that
explanation at all or shows no
real conceptual
understanding of the
equations or their
components when related to
real life events.
- 13. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 13
Advanced (4 pts.) Proficient (3 pts.) Basic (2 pts.) Below Basic (1 pt.)
Task #3:
Graph
Part A
(4 points)
The student graphs each equation on a
coordinate plane. The graphed lines are
completely accurate and drawn with a
straight edge. The student labels the
graph with a title, both axes, and
appropriate scales.
The student graphs each equation on a
coordinate plane. The graphed lines
are accurate or very nearly accurate
and drawn with a straight edge. The
graph should label the graph witha
title, both axes, and appropriate scales;
however, one or two of these
components is missing.
The student graphs each equation
on a coordinate plane. The
graphed lines are accurate or
nearly accuratebutare not drawn
with a straight edge. The graph
includes a title, both axes, and
appropriate scales; however,
major flaws, such as the omission
of several parts of these
components or the inclusion of an
inappropriate scale, are evident.
The student graphs only one
equation on a coordinate
plane. The graphed line
seems accurate or nearly
accurate but is not drawn
with a straight edge. The
graph includes a title, both
axes, and appropriate scales;
however, major flaws, such
as the omission of several
parts or the inclusion of an
inappropriate scale, are
evident.
Task #3:
Application
and Extension
Part B
(4 points)
The responseis made up of complete
sentences with well thought out,
articulate answers that are
mathematically supported. The response
is accurate.
The responseismade up of complete
sentences. The response is accurate or
very nearly accurate but could use
additional mathematical support.
The response ismade up of
complete sentences. The response
includes only minor inaccuracies
but needs additional mathematical
support.
The student attempts the
response, but it is
neitherarticulate nor thought
out. The response is not
supported correctly by
mathematical concepts.
0 points The student writes “I don‟t know” ORmakes no attempt to respond.
- 14. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – Demo Page 14
Waterfront Junior High School
Quick Start ©
Mathematics – Grade 8
(Pre-Algebra)
Score Sheet
Training Demonstration 2014
- 15. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – DemoPage 15
NOTE: Targeted standards were extended form.
Assessment Name Grade/Course Administration
Total Possible
Points
Mathematics
Grade 8
Pre-Algebra
End of Course
(EoC)
38
Question
#
Item Tag Item Type Point Value Answer
1 0001.MTH.GR8.MC-LV1-2.8.8.A MC 1 A
2 0002.MTH.GR8.MC-LV2-2.8.8.A MC 1 B
3 0003.MTH.GR8.MC-LV1-2.8.8.C MC 1 A
4 0004.MTH.GR8.MC-LV1-2.8.8.C MC 1 A
5 0005.MTH.GR8.MC-LV1-2.8.8.E MC 1 D
6 0006.MTH.GR8.MC-LV2-2.8.8.D MC 1 C
7 0007.MTH.GR8.MC-LV2-2.8.8.E MC 1 C
8 0008.MTH.GR8.MC-LV2-2.8.8.D MC 1 A
9 0009.MTH.GR8.MC-LV2-2.8.8.A MC 1 B
10 0010.MTH.GR8.MC-LV2-2.8.8.A MC 1 B
11 0011.MTH.GR8.SA-LV3-2.8.8.E SA 2
See Short Answer
Rubric
12 0012.MTH.GR8.SA-LV3-2.8.8.E SA 2
See Short Answer
Rubric
13 0013.MTH.GR8.EP-LV4-2.8.8.B EP 24 See Scoring Rubric
- 16. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – DemoPage 16
11. Sample Work
Horizon: y = .10x + 65
Spritely Phone: y = .20x + 35
.20x + 35 = .10x + 65
.20x + 35 – 35 = .10x + 65 – 35
.20x = .10x + 30
.20x – .10x = .10x + 30 – .10x
30 = .10x
30 ÷ .1 = .10x ÷ .1
x = 300 gigabytes (GB)
“How many gigabytes over the monthly limit will the two plans charge the same amount?”
2 points
The student‟s response shows the correct inequalities for each of the phone services and the correct
number of gigabytes over the monthly limit for which the two (2) plans will be charged the same
amount. The response includes supporting evidence (work shown above) with no computational
errors.
1 point
The student‟s response shows the correct inequalities for each of the phone services, but, does not
contain the correct number of gigabytes over the monthly limit for which the two (2) plans will be
charged the same amount; OR, the number of gigabytes over the monthly limit for which the two (2)
plans will be charged the same amount is correct, but the inequalities are not correct.
0 points The student records no response, OR the response is completely incorrect or irrelevant.
12. Sample Work
25000 = 75x + 50y
Where x is the number of front section seats and y is the number of back section seats,
x = 2y
75(2y) + 50y = 25000
150y + 50y = 25000
200y÷ 200 = 25000 ÷ 200
y = 125 seats [back]
75x + 50(125) = 25000
75x + 6250 = 25000
75x + 6250 – 6250 = 25000 – 6250
75x = 18750
75x ÷ 75 = 18750 ÷ 75
x = 250 seats [front]
Answer: 250 seats [front]
- 17. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – DemoPage 17
“How many seats are in the front section?”
2 points
The student‟s response shows the correct number of front section seats with supporting evidence
(work shown on Page 3). All parts of the problem are correct and complete.
1 point
The student‟s response shows the correct number of front section seats, but the supporting evidence
contains one or more errors in conceptual understanding, OR, the student‟s work displays conceptual
understanding, but the student was not able to produce the correct answer.
0 points The student records no response, OR the response is completely incorrect or irrelevant.
- 18. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – DemoPage 18
Question #13
Extended Performance Task (Tasks 1-3)
Scoring Rubric
Advanced (4 pts.) Proficient (3 pts.) Basic (2 pts.) Below Basic (1 pt.)
Task #1:
Rate of Change
(4 points)
The student clearly defines
germination time, in both inches and
days, and the rate of change for both
plants. The student gives a clear
explanation and supports it
mathematically.
The student clearly defines
germination time, in both inches
and days, and the rate of change
for both plants, but either the
student„s explanation does not
show a clear understanding of
the rate of change concept or the
student does not support the
explanation mathematically.
The student clearly defines
germination for both plants. The
student defines the rate of
change but may commit minor
errors. The rate of change is
inversed, showing a minor
misunderstanding. The student
supports the explanation
mathematically but shows the
misconception in the rate.
The student fails to define
germination and defines the rate
of change poorly and with major
errors OR defines germination
time but either fails to define
rate of change or provides a
completely inaccurate definition,
even after checking for common
errors. The student provides no
explanation.
Task #2:
Equations
Part A
(6 points)
Based upon the germination data, the
student assigns each plant a y-
intercept. Based upon the growth rate
or measured height over time, the
student assigns each plant a slope.
Using these values, the student writes
an equation in slope intercept form
for each plant.
Based upon the germination
data, the student assigns each
plant a y-intercept. Based upon
the growth rate or measured
height over time, the student
assigns each plant a slope. Using
these values, the student writes
an equation in slope intercept
form for each plant. One or both
of the equations may include
minor flaws.
Based upon the germination
data, the student assigns each
plant a y-intercept. Based upon
the growth rate or measured
height over time, the student
assigns each plant a slope. Using
these values, the student writes
an equation in slope intercept
form for each plant. A major
flaw occurs in rate or slope in
that the student computes time
over height or mixes the y-
intercepts between plants.
Based upon the germination
data, the student assigns each
plant a y-intercept. Based upon
the growth rate or measured
height over time, the student
assigns each plant a slope. The
student fails to attempt
equations.
- 19. Quick Start ©
Mathematics-Grade 8 (Pre-Algebra) – DemoPage 19
Advanced (4 pts.) Proficient (3 pts.) Basic (2 pts.) Below Basic (1 pt.)
Task #2:
Equations
and Conceptual
Meanings
Part B
(6 points)
The written explanation is clear and
mathematically supported in the
“Reflect and Connect” section. The
student shows a clear understanding
of the meaning of the equation when
applied to the real life situation. The
student also explains the selection of
germination and rate for the
respective positions in a graph for the
germination and rate, showing further
connection of the equation and its
application.
In the “Reflect and Connect”
section, The student explains
briefly how the equation is
related to the real life events. .
The explanation shows an
understanding but with minor
flaws or misconceptions. The
student may try to explain the
reason for the slope and intercept
choices but may not be able to
support the explanation
mathematically.
The student shows little or very
misconstrued conceptual
understanding of equations and
the real life meaning when
writing the mathematical
sentence. The student may also
skip one part of the “Reflect and
Connect” written portion or fail
to support both parts with
mathematical explanations
The student answers only one
part of the “Reflect and
Connect” written portion and
either fails to support that
explanation at all or shows no
real conceptual understanding of
the equations or their
components when related to real
life events.
Task #3:
Graph
Part A
(4 points)
The student graphs each equation on
a coordinate plane. The graphed lines
are completely accurate and drawn
with a straight edge. The student
labels the graph with a title, both
axes, and appropriate scales.
The student graphs each
equation on a coordinate plane.
The graphed lines are accurate or
very nearly accurate and are
drawn with a straight edge.
Although the student should
label the graph with a title, both
axes, and appropriate scales, one
or two of these components is
missing.
The student graphs each
equation on a coordinate plane.
The graphed lines are accurate or
nearly accurate but are not
drawn with a straight edge. The
graph includes a title, both axes,
and appropriate scales; however,
major flaws, such as the
omission of several parts of
these components or the
inclusion of an inappropriate
scale, are evident.
The student graphs only one
equation on a coordinate plane.
The graphed line seems accurate
or nearly accurate but is not
drawn with a straight edge. The
graph includes a title, both axes,
and appropriate scales; however,
major flaws, such as the
omission of several parts or the
inclusion of an inappropriate
scale, are evident.
Task #3:
Application
and Extension
Part B
(4 points)
The response is made up of complete
sentences with well thought out,
articulate answers that are
mathematically supported. The
response is accurate.
The response is made up of
complete sentences. The
response is accurate or very
nearly accurate but could use
additional mathematical support.
The response is made up of
complete sentences. The
response includes only minor
inaccuracies but needs additional
mathematical support.
The student attempts the
response, but it is neither
articulate nor thought out. The
response is not supported
correctly by mathematical
concepts.
0 points The student writes “I don‟t know” OR makes no attempt to respond.