Assessment Model #2 Pre-Algebra Grade 8

Total Score: ______

Name: ________________________ ID: ________________ Date: ___________

Waterfront Junior High School

Quick Start ©

Mathematics – Grade 8 (Pre-Algebra)

AssessmentTraining Demonstration 2014

Preparation

STEP 1. Establish the testing session that will begin the Waterfront Junior High School Grade 8 test 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. Make copies of the test form and reference sheets based 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 make up 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 the test. 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 several class 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) Task preparation 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 work area. 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.

Quick Start © Mathematics-Grade 8 (Pre-Algebra) – Demo Page 2

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 the on-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.


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 (16

) = 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:

35

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)


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 m equal 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)


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.611

B.−611

C.116


D.−11

6 (0009.MTH.GR8.MC-LV2-2.8.8.A)


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 gigabytes over 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)


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.

PlantGermination Time

(sprouted from soil)Plant Growth

(days AFTER sprouting)Approximate

Growth HeightBasil 4 days/.5 inches 7 days 14 inchesChives 3 days/1 inch 20 days 15 inchesOregano 6 days/.5 inches 14 days 21 inchesParsley 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.


Question #13 – Task #1: Rate of Change

Time: 45 minutes

Total Possible Score: 4 points

Determine the growth rate of each plant you selected and explain how you established this rate

(including the applicable units).

Growth Rate:

Explanation:

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________


Question #13 – Task #2: Creating Systems of Equations

Time: 45 minutes


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)

______________________________________________________________________________

______________________________________________________________________________


______________________________________________________________________________

______________________________________________________________________________

Question #13 – Task #3: Graphing a System of Equations

Time: 45 minutes


Part A: On the graphing paper provided, create a graph with a title, a labeled x-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 AND on 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)


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 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:EquationsPart 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.

Task #2:Equationsand Conceptual MeaningsPart 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 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:GraphPart 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 with a 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 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: Applicationand ExtensionPart 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.


Waterfront Junior High School

Quick Start ©

Mathematics – Grade 8 (Pre-Algebra)

Score Sheet

Training Demonstration 2014


Assessment Name Grade/Course AdministrationTotal Possible

Points

MathematicsGrade 8

Pre-AlgebraEnd 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 2See Short Answer

Rubric

12 0012.MTH.GR8.SA-LV3-2.8.8.E SA 2See Short Answer

Rubric

13 0013.MTH.GR8.EP-LV4-2.8.8.B EP 24 See Scoring Rubric

NOTE: Targeted standards were extended form.


11. Sample WorkHorizon: y = .10x + 65Spritely Phone: y = .20x + 35

.20x + 35 = .10x + 65

.20x + 35 – 35 = .10x + 65 – 35

.20x = .10x + 30

.20x – .10x = .10x + 30 – .10x30 = .10x30 ÷ .1 = .10x ÷ .1x = 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 Work25000 = 75x + 50yWhere x is the number of front section seats and y is the number of back section seats, x = 2y

75(2y) + 50y = 25000150y + 50y = 25000200y÷ 200 = 25000 ÷ 200y = 125 seats [back]

75x + 50(125) = 2500075x + 6250 = 2500075x + 6250 – 6250 = 25000 – 625075x = 1875075x ÷ 75 = 18750 ÷ 75x = 250 seats [front]


Answer: 250 seats [front]


“How many seats are in the front section?”

2 pointsThe 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 pointThe 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.


Question #13

Extended Performance Task (Tasks 1-3)

Scoring Rubric


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:EquationsPart 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.



Task #2:Equationsand Conceptual MeaningsPart 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:GraphPart 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: Applicationand ExtensionPart 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.


Education

Assessment Model #2 Pre-Algebra Grade 8