Model #2-Grade 8 Pre-Algebra-DEMO-FINAL

Total Score: ______

Name: ________________________ ID: ________________ Date: ___________

Waterfront Junior High School

Quick Start ©

Mathematics – Grade 8

(Pre-Algebra)

JUNE 2014

Model #2-Grade 8 Pre-Algebra-DEMO-FINAL Page 2

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.


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 (1

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:

𝟑

𝟓x = 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. 6

11

B. −6

11

C. 11

6

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.

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.


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)


Performance Task

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.


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.


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:

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

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.


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:

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.


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)

JUNE 2014

Score Sheet

Model #2-Grade 8 Pre-Algebra-DEMO-

FINAL

Page 15

Assessment Name Grade/Course Administration Total Possible

Points

Mathematics Grade 8/

Pre-Algebra

End-of-Course

(EoC) 36

Item # Item Tag Item Type Point Value Answer

1 0001.MTH.GR8.EOC.MC-LV1-2.8.8.A MC 1 A

2 0002.MTH.GR8.EOC.MC-LV2-2.8.8.A MC 1 B

3 0003.MTH.GR8.EOC.MC-LV1-2.8.8.C MC 1 A

4 0004.MTH.GR8.EOC.MC-LV1-2.8.8.C MC 1 A

5 0005.MTH.GR8.EOC.MC-LV1-2.8.8.E MC 1 D

6 0006.MTH.GR8.EOC.MC-LV2-2.8.8.D MC 1 C

7 0007.MTH.GR8.EOC.MC-LV2-2.8.8.E MC 1 A

8 0008.MTH.GR8.EOC.MC-LV2-2.8.8.D MC 1 C

9 0009.MTH.GR8.EOC.MC-LV2-2.8.8.A MC 1 C

10 0010.MTH.GR8.EOC.MC-LV2-2.8.8.A MC 1 D

11 0011.MTH.GR8.EOC.SA-LV3-2.8.8.E SA 2 See Sample Work &

Rubric on Page 3

12 0012.MTH.GR8.EOC.SA-LV3-2.8.8.E SA 2 See Sample Work &

Rubric on Page 4

13 0013.MTH.GR8.EOC.EP-LV4-2.8.8.B EP 22 See Sample Work &

Rubric on Pages 5-8


FINAL

Page 16

11. Sample Work:

Horizon: y = .10x + 65

Spritely: 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

Sample Response for: “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 2 plans will be charged the same amount with

supporting evidence (work shown above).

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 2 plans will be charged the same

amount; OR, the number of gigabytes over the monthly limit for which the 2 plans will be charged the

same amount is correct, but the inequalities are not correct.

0 points There is 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

75x + 50(125) = 25000

75x + 6250 = 25000

75x + 6250 – 6250 = 25000 – 6250

75x = 18750

75x ÷ 75 = 18750 ÷ 75

x = 250

Answer: 250


FINAL

Page 17

Sample Response for: “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 above).

1 point The student’s response shows the correct number of front section seats, but the students work to get to that

answer contains one or more errors in conceptual understanding; OR, the student’s work displays

conceptual understanding, but was not able to identify the correct answer.

0 points There is no response, or the response is completely incorrect or irrelevant.

13. Sample Work – Task 1

Task 1.1: Rate of Change

Part A

Plant Rate of Change

Basil 2 inches/day

Chives ¾ inch/day

Oregano 1 ½ inches/day

Parsley ½ inch/day

Rate is height over time (in/day) or speed of growth.

Task 1.2: Creating Systems of Equations

Part A

Plant Equations

Basil y = 2x + .5

Chives y = 3/4x + 1

Oregano y = 1.5x + .5

Parsley y = 1/2x + 1.5


FINAL

Page 18

Task 1.3: Graphing a System of Equations

Part A

Part B

Plant Combination Intersection Solution

Actual Estimate

Basil/Chives (0.4,1.3) (0.5,1.5)

Basil/Oregano No Solution They will never meet

Basil/Parsley (0.67,1.84) (0.5,2), (1,2)

(1,2), (0.5,1.5)

Chives/Oregano (0.67,1.5) (0.5,1.5), (1,1.5)

Oregano/Parsley (1,2) Estimates should be very

close

Chives/Parsley (2,2.5) Estimates should be very

close


Performance Task

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.


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.


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)


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.


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:

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

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

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

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


graph, showing further connection of the

equation and its application.

to support the explanation

mathematically.

parts with mathematical

explanations.

components when related to

real life events.


Task #3:

Graph

Part A

(4 points)


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.


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:

Application

and Extension

Part B

(4 points)


sentences with well thought out,

articulate answers that are

mathematically supported. The response

is accurate.


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.

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Model #2-Grade 8 Pre-Algebra-DEMO-FINAL

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