quickguide_gr8

7/30/2019 QuickGuide_GR8

1/107

Measurements of Student Progress

Grade 8

MathematicsMathematicsAssessmentAssessment

Quick GuideQuick Guide


2/107

ThisdocumentmaybereproducedforeducationalpurposesbypermissionoftheWashingtonStateOfficeofSuperintendentofPublicInstruction

TableofContentsGrade62008ReleasedItemsItemNumber PE PageNumber

#2 8.2.D 3Grade6PracticeTestItemNumber PE PageNumber

#12 8.2.D 5#23 8.2.D 6#28 8.2.D 7

Grade72006ReleasedItemsItemNumber PE PageNumber

#2 Partialalignmentto

8.1.B8

Grade72007ReleasedItemsItemNumber PE PageNumber

#5 8.3.G 25Grade72008ReleasedItemsItemNumber PE PageNumber

#2 Partialalignmentto

8.2.D34

Grade82007ReleaseditemsItemNumber PE PageNumber

#2 8.2.F 36#4 Partial

alignmentto8.2.D

38

Grade8PracticeTestItemNumber PE PageNumber

#4 8.3.F 47#14 8.2.D 48#20 8.3.F 49#25 8.3.F 50#39 8.5.G(8.2.F) 51

2006HighSchoolPracticeTestItemNumber PE PageNumber

#1 8.5.C(8.2.E) 52#11 8.5.C(8.3.F) 53#15 8.2.A,C 65#19 8.2.D 66#26 8.2.D 67#29 8.5.G(8.4.A) 68#35 8.4.C 69#41 8.3.F 82

#42 8.3.F 822007HighSchoolReleasedItemsItemNumber PE PageNumber

#1 8.4.A 83#2 8.5.C(8.3.G) 84#3 8.4.B 85#8 8.3.F 86#15 8.5.C(8.2.E) 87

2008HighSchoolReleasedItemsItemNumber PE PageNumber

#1 8.4.A 96#4 8.2.D 97#5 8.3.F 98#9 8.3.G 99


3/107

2008 Mathematics Released Items

2 Look at the figure on the grid.

Which grid represents a 90 clockwise rotation (turn) of the figure about

point P?

A. C.

B. D.

10595

1

2

3

4

5

6

7

8

9

10

100 1 2 3 4 5 6 7 8 9

P

12

3

4

5

6

7

8

9

0

P

1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

0

P

1 2 3 4 5 6 7 8 9 100

12

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 100

P

1

2

3

4

5

6

7

8

9

10

0

P

1 2 3 4 5 6 7 8 9 100

11

11

3


4/107


Item Information

Score Points: 1

Tools: X

Strand and Target GS02 (Locations and Transformations): Describe the relative location

of points and objects on a positive-negative number line; recognize or draw a translation (slide)

or reflection (flip) of a 2-dimensional shape or figure; rotate (turn) a simple 2-dimensionalfigure 90 or 180 about the center or a vertex of the figure (1.3.3, 1.3.4)

Performance Data

(Use this space to fill in student performance information for your school and district.)

Percent Distribution

School District State Responses (* = correct response)

A*

B

C

D

NR

58.4%

8.7%

4.8%

27.9%

0.2%

4


5/107

Mathematics

NON-SECURE MATERIALS MAY BE COPIED BY WASHINGTON STATE EDUCATORS FOR INSTRUCTIONAL USE

12 Barett does not understand what an object looks like after a translation

(slide). His sister showed him by moving a picture into different positions.

Which picture shows an example of a translation?

A. *

B.

C.

D.

LM06GS0205M10594

1

1

1

1

5

Key: A


6/107

Mathematics


23 Alissa framed a picture for her mother. She placed the picture as shown in

the frame. She wants the top of the head in the picture to be at the top of

the frame.

How many degrees counterclockwise will she need to rotate (turn) the

picture so that the top of the picture is at the top of the frame?

A. 90

B. 180*

C. 270

D. 360

LM06GS0205M10602

1

1

1

1

6

Key: B


7/107

Mathematics


28 Jackson is looking at a picture.

He sees another picture and notices the same bus is facing in the oppositedirection.

How would Jackson describe the change in position of the bus from the

first picture to the next?

A. A reflection (flip) *

B. A translation (slide)

C. A 90 rotation (turn)

D. A 180 rotation (turn)

LM06GS0205M10614

1

1

1

1

7

Key:A


8/107

2006 Mathematics Released Items2006 Mathematics Released Items2006 Mathematics Released Items2006 Mathematics Released Items2006 Mathematics Released Items

2 Write the inequality below in words.

a 2

Graph the inequality on the number line. Label the intervals.

02754

0

8


9/107

2006 Mathematics Released Items2006 Mathematics Released Items2006 Mathematics Released Items

2 (continued)

Item Information

Score Points: 2

Tools: X

Strand: Makes Connections

MC01 (Connect within Mathematics) Apply concepts and procedures from two or more of the

mathematics content strands in a given problem or situation; relate and use different

mathematical models and representations of the same situation (5.1.1, 5.1.2)


School District State Points

0

1

2

NR

Mean

63.92%

12.91%

09.41%

13.76%

00.4


9


10/107

2006 Mathematics Released Items2006 Mathematics Released Items

Scoring guide for question number 2:

A 2-point response: The student demonstrates understanding of writing inequalities in words

and representing them graphically by:

writing the inequality in words as a is less than or equal to 2 or 2 is greater than or

equal to a

graphing the inequality as follows:

draws a ray pointing left on the number line starting at 2. The endpoint of the ray

must start at 2 or the marking for 2 on the number line

shows a closed representation of 2 on the number line.

NOTE: Unlabeled intervals will be assumed to be intervals of 1.

Example:

a is less than or equal to 2 or 2 is greater than or equal to a

A 1-point response: The student does one of the following:

writes the inequality in words and the graph is missing or incorrect

writes a is greater than or equal to 2 or 2 is less than or equal to a and graphs the

inequality 2 a

writes a is less than 2 or 2 is greater than a and graphs the inequality for a < 2

graphs the inequality a 2 but the words are incorrect, flawed or missing.

A 0-point response: The student demonstrates very little or no understanding of writing

inequalities in words and representing them graphically.

0 1

10


11/107


2 (continued)

Annotated example for a 2-point response for question number 2:


a 2

11


12/107


2 (continued)

Annotated example for a 2-point response for question number 2 (continued):

Annotations:

The student shows understanding of writing inequalities in words and representing them

graphically by writing the inequality in words as a is less then or equal to two and graphingthe inequality with a ray pointing left on the number line starting at 2. This response earns

two points.

12


13/107


2 (continued)



a 2

13


14/107


2 (continued)


Annotations:


graphically by writing the inequality in words as a is less then or equal to two and graphingthe inequality with a ray pointing left on the number line starting at 2. This response earns

two points.

14


15/107


2 (continued)



a 2

15


16/107


2 (continued)


Annotations:


graphically by writing the inequality in words as a is less than or equal to 2 and graphing theinequality with a ray pointing left on the number line starting at 2 spaces from zero. The

intervals are not labeled (see rubric NOTE), and therefore are assumed to be intervals of one.

This response earns two points.

16


17/107


2 (continued)



a 2

17


18/107


2 (continued)


Annotations:

The student shows partial understanding of writing inequalities in words and representing

them graphically by writing the inequality in words as a is less than or equal to two but notgraphing the inequality on the number line. This response earns one point.

18


19/107


2 (continued)



a 2


19


20/107


2 (continued)


Annotations:


them graphically by graphing the inequality with a ray pointing left on the number linestarting at 2 but writing the inequality in words as 2 is bigger than a, which is incomplete.

This response earns one point.

20


21/107


2 (continued)



a 2


21


22/107


2 (continued)


Annotations:


them graphically by writing the inequality in words 2 is greater than or equal to a but graphsthe inequality with a line segment between 2 and 3 on the number line which is incorrect. This

response earns one point.

22


23/107


2 (continued)



a 2

23


24/107


2 (continued)


Annotations:

The student shows little or no understanding of writing inequalities in words and representing

them graphically by writing the inequality in words as a is less than two, which isincomplete, and not graphing the inequality on the number line. This response earns zero

points.

24


25/107


5 Ms. Parker conducted a survey of the students in her class to see how

many liked rock or country music. The results of her survey are shown

below:

25 students took the survey.

22 students said they liked rock.14 students said they liked country.

How many students said they liked both rock and country music? Explain

your reasoning. Be sure to clearly label any diagrams or work included in

your explanation.

00792

How many students said they liked both rock

and country music? _____________

25


26/107


Item Information for item number 5

Score Points: 2

Tools: X

Strand and Target SR04 (Conclude): Draw conclusions and support them using evidence,

evaluate procedures and conclusions in various situations (3.2.1, 3.2.2)

Performance Data


Scoring Guide for item number 5

A 2-point response: The student shows understanding of how to draw and support a conclusion

by doing the following:

concludes that 11, 12, 13, or 14 students liked both country and rock music

supports the conclusion by using an explanation or clear labeling. (If they do not label

the 36, then they must label the 22 rock plus 14 country or they must label the 3.)

Example: Explains that there were a total of 36 votes for rock and/or country (22 for rock and

14 for country) from 25 students. Therefore, 11 students answered both rock and country.

Example: Explains that since 22 of 25 like rock, 3 like country only. Therefore, 11 of the 14 who

like country also like rock.

Example: Shows either of the above using a diagram that shows an overlap of 11 students.

A 1-point response does one of the following:

indicates that 11, 12, or 13 students liked both, but the explanation or work is

incomplete, flawed, or missing; indicates that 14 students liked both, but the explanation or work is incomplete or

flawed

shows appropriate reasoning with an incorrect or missing conclusion.

A 0-point response: The student shows very little or no understanding of how to draw and

support a conclusion.



0

1

2

NR

Mean

27.8%

40.2%

29.9%

2.0%

1.0

26


27/107




below:





your explanation.

Annotation for example 2-point response:

The student shows understanding of drawing and supporting a conclusion by concluding

11 students liked both country and rock and supporting the conclusion with an explanation.


27


28/107




below:





your explanation.



11 students liked both country and rock and supporting the conclusion with an explanation

including a Venn diagram. This response earns two points.

28


29/107




below:





your explanation.

00792



11 students liked both country and rock and supporting the conclusion with clearly labeled

work. This response earns two points.

29


30/107




below:





your explanation.

00792


The student shows partial understanding of drawing and supporting a conclusion by

concluding 14 students liked both country and rock. The explanation is incomplete. This


30


31/107




below:





your explanation.

00792



concluding 11 students liked both country and rock. The explanation so 25 subtract from 14 is

elevenis incorrect. This response earns one point.

31


32/107




below:





your explanation.



concluding 11 students liked both country and rock. The work consists of a run-on equation

14 Plus 22 = 36 25 = 11which is mathematically incorrect and does not earn credit for

supporting work. This response earns one point.

32


33/107




below:





your explanation.


The student shows little or no understanding of drawing and supporting a conclusion by

concluding 8 and supporting the conclusion with incorrect work. This response earns zero

points.

33


34/107


2 Sylvia and Alex are playing tic-tac-toe on their game board.

Which picture shows how the game board would look after being rotated

(turned) 90 clockwise?

A.

B.

C.

D.

13484

1

1

1

1

34


35/107

Item Information

Score Points: 1

Tools: X

Strand and Target GS02 (Locations and Transformations): Describe locations of points

on a coordinate grid in any of the four quadrants; rotate a simple 2-dimensional figure 90 or

180 about the center or a vertex of a figure; use combinations of translations and/or reflectionsto draw simple congruent figures (1.3.3, 1.3.4)

Performance Data



School District State Responses (* = correct response)

A

B*

C

D

NR

8.0%

74.0%

13.1%

4.6%

0.3%


35


36/107


2 The state wants to build a straight road so there is a direct route from

North Town to East Town.

How long will the road be between North Town and East Town?

A. 13 miles

B. 15 miles

C. 54 miles

D. 63 miles

10857

North Town

East Town9 miles

12 miles

South Town

1

1

1

1

36


37/107


Item Information

Score Points: 1

Tools: Y

Strand and Target ME03 (Procedures): Use formulas, including the Pythagorean Theorem,

to determine measurements of circles, triangles, rectangular prisms, and right cylinders; use

systematic procedures to measure and describe angles angle measurements as the attributeto be measured, select an appropriate unit for angle measurement, select and use a tool that

matches the unit chosen, use the selected tool to determine the number of units, record and

label the measurement (1.2.5)

Performance Data



School District State Responses (* = correct response)A

B*

C

D

NR

9.8%

76.0%

12.1%

1.7%

0.5%

37


38/107


4 Mary is making a maple leaf quilt. The directions in her quilt book state:

Rotate maple leaf M 90 clockwise around the tip of the stem and then

translate the rotated leaf down 4 inches.

Draw the resulting leaf on the grid.

06778

1 inch

M

Stem

38


39/107


Item Information

Score Points: 2

Tools: Y

Strand and Target GS02 (Locations and Transformations): Describe the location and/or

the relative positions of points on a coordinate grid; use translations, reflections, and/or

rotations to draw or locate congruent 2-dimensional figures (1.3.3, 1.3.4)

Performance Data


Scoring Guide for item number 4

A 2-point response: The student shows understanding of drawing a combination of translation

and rotation by doing the following:

shows the new location of the tip of the stem

shows the new orientation of the entire leaf

NOTE: Showing both the rotation and translation is acceptable.

NOTE: Showing a leaf with correct orientation and translated down 2 units (a result of

rotating around the tip closest to the leaf) earns full credit.


shows the new location of either tip of the stem

shows the new orientation of the leaf by drawing the stem and two segments from the

stem (adjacent and/or consecutive) or shows the new orientation of the body of the leaf.

A 0-point response: The student shows very little or no understanding of drawing a

combination of translation and rotation.



0

1

2

NR

Mean

32.9%

34.3%

28.6%

4.2%

1.0

39


40/107






06778

Annotation for example 2-point response:The student shows understanding of drawing a combination of a translation and rotation by

showing the new location of the tip of the stem and showing the new orientation of the leaf.

Both the rotated and translated leaf are shown. This response earns two points.

40


41/107






06778




41


42/107






06778



Both the rotated and translated leaf are shown. This response earns two points.

42


43/107






06778

Annotation for example 1-point response:The student shows partial understanding of drawing a combination of a translation and

rotation by showing the new orientation of the stem and the body of the leaf. The location of

the leaf is not correct. This response earns one point.

43


44/107






06778


rotation by showing the new orientation of the leaf by drawing the stem and two segments

from the stem (adjacent and/or consecutive). The location of the leaf is not correct. This


44


45/107






06778


rotation by showing the new location of one of the stem tips. The orientation of the leaf is not

correct. This response earns one point.

45


46/107






06778

Annotation for example 0-point response:The student shows little or no understanding of drawing a combination of a translation and

rotation by drawing more than one maple leaf from which to choose. This response earns zero

points.

46


47/107

Mathematics


4 A store at the mall is giving a Spring Break prize to a randomly selected

student and a randomly selected teacher at a middle school.

Faye predicts the prizes will go to a female student and a male teacher.

What is the probability that Faye is correct?

A.

B. *

C.

D.

LM08PS0104M07558

12

25

8

25

3

25

2

25

Population at a Middle School

Students Teachers

Female

Male

Total

360

240

600

24

6

30

1

1

1

1

47

Key: B


48/107

14 Look at the triangle in the graph.

First reflect the isosceles triangle across the x-axis. Then translate it

12 units to the left.

Which ordered pair represents the new coordinate for vertex S?

A. (3, 2) *

B. (9, 2)

C. (9, 2)

D. (3, 2)

LM08GS0204

3

9

8

7

6

5

4

2

1

3 98765421

-3

-9

-8

-7

-6

-5

-4

-2

-1-3-9 -8 -7 -6 -5 -4 -2 -1

R

Q S

y

x

1

1

1

1

Mathematics


48

Key: A


49/107

Mathematics


20 Mrs. Bartilottas mathematics class has 7 girls and 3 boys. She will

randomly choose two students to do a problem in front of the class.

What is the probability that she will choose 2 boys?

A. *

B.

C.

D.

LM08PS0104M09345

5

19

3

7

2

5

1

151

1

1

1

49

Key: A


50/107

Mathematics


25 Darin played a game with two spinners. The game is played by spinning

each spinner and then adding the two resulting numbers. The goal is to

spin two numbers that add up to eleven.

What is the probability that Darin will spin two numbers that add up

to eleven?

A.

B. *

C.

D.

LM08PS0104M09342

3

10

3

5

1

10

1

3

1

2 3

4

5

6

78

9

10

1 2

3

Spinner 1 Spinner 2

1

1

1

1

50

Key: B


51/107

Mathematics


39 Meara is making a food-guide pyramid for health class. She needs the

measurements of this picture to enlarge it for a poster.

Which expression represents the length of line segment AB?

A. (5 8)2

B. 52 82 *

C. 52 82

D. 2 5 2 8

LM08GS0205M10891

5

5 10

10

0

A

CB

Mearas Food-Guide Pyramid

Bread:

Fat:

Vegetables:

Protein:

2-4 servings

6-11 servings

Use very little

2-3servings

1

1

1

1

51

Key: B


52/107

High School Mathematics WASL Practice Test

Reminder: Use a No. 2 pencil only. Do not use a mechanical pencil or pen.

1 Henrietta is stacking soup cans for a display in the grocery store where she works.The bottom level of the display has 100 cans arranged in a square. The next level uphas 81 cans in a square. The level above that has 64 cans in a square. Shecontinues this pattern until she has just one can at the top.

How many cans does she have altogether in this display?

{ A. 246

{ B. 385

{ C. 450

{ D. 550

52

Key: B


53/107


11 Joseph and Cindy made up a game in their mathematics class. To earn points inthe game each player rolls a six-sided cube with numbers 1 through 6 on the sidesand then flips a coin. When the coin lands tails up, the player gets a total numberof points equal to the number at the top of the cube. When the coin lands headsup, the players points are doubled for that turn.

In the box below list all the possible outcomes for each turn. Then indicate theprobability of a player getting 6 points in one turn.

53


54/107

High School Mathematics WASL Practice Test Item 11

Strand: Probability and Statistics

PS01 Learning Target (Probability) Demonstrate understanding of the concepts

of compound, dependent, and independent events; determine and use

probabilities of compound, dependent, and independent events (1.4.1, 1.4.2)

A2-point response: The student shows an understanding of determining the size of a

sample space and/or listing all possible outcomes of an experiment to determine the

probability of a certain outcome by doing the following:

shows all 12 coin/number cube combinations (1 H, 1 T, 2 H, 2 T, ) OR all the correct

possible game point totals: 1, 2, 3, 4, 5, 6, 8, 10, and 12

indicates that the probability of getting 6 points is or

NOTE: If the student doubles the tails column instead of the heads column, that alone

will not affect the students score.

A1-point response: The student does one of the following:

correctly lists at least nine of the possible outcomes or totals and no more than three

additional outcomes or totals that are incorrect. The response also gives a probability

that agrees with the possible outcomes or totals shown

indicates the correct probability but fails to list all the possible outcomes or totals

lists all the possible outcomes or totals but gives an incorrect or no probability.A0-point response: The student shows little or no understanding of determining the

size of a sample space and/or listing all possible outcomes of an experiment to determine

the probability of a certain outcome.

SCORING GUIDE AND

TRAINING MANUAL

Scoring Rubric

HIGH SCHOOL MATHEMATICSITEM 11

2

12

1

6

54


55/107

PRAC TIC E TEST ITEM

Score:

2

Annotation:The student shows understanding of determining the size of a sample space and/or listing all possible

outcomes of an experiment to determine the probability of a certain outcome by showing all 12

coin/number cube combinations and all the correct possible game point totals; and indicating that the

probability of getting 6 points in one turn is 2 in 12 or 1 in 6. This response earns two points.

SCORING GUIDE AND

TRAINING MANUAL11 - Anchor 1

HIGH SCHOOL MATHEMATICS

11. Joseph and Cindy made up a game in their mathematics class. To earn points

in the game, each player rolls a six-sided cube with numbers 1 through 6 on the

sides and then flips a coin. When the coin lands tails up, the player gets a

total number of points equal to the number at the top of the cube. When the

coin lands heads up, the players points are doubled for that turn.

In the box below, list all the possible outcomes for each turn. Then indicate the

probability of a player getting 6 points in one turn.

55


56/107


Score:

2


outcomes of an experiment to determine the probability of a certain outcome by showing all the correct

possible game point totals and indicating that the probability of getting 6 points in one turn is 2/12.


SCORING GUIDE AND










56


57/107


Score:

2


outcomes of an experiment to determine the probability of a certain outcome by showing all 12

coin/number cube combinations and indicating that the probability of getting 6 points in one turn is

2:12 (which is unacceptable notation for probability) but then demonstrates understanding of the

correct notation for probability by stating 2 out of 12 later in the response. This response earns two

points.

SCORING GUIDE AND





the sides and then flips a coin. When the coin lands tails up, the player gets a





57


58/107


Score:

1

Annotation:The student shows partial understanding of determining the size of a sample space and/or listing all

possible outcomes of an experiment to determine the probability of a certain outcome by indicating the

correct probability of getting 6 points in one turn is 2/12 = 1/6. The list of possible combinations (1=T,

1=H ...) has only 11 correct combinations due to the repeat of 6T, and omission of 6H, at the end of the

list. This response earns one point.

SCORING GUIDE AND










58


59/107


Score:

1


possible outcomes of an experiment to determine the probability of a certain outcome by listing all 12

coin/number cube combinations, all the correct game point totals, and indicating an incorrect

probability of getting 6 points in one turn is 1/12. This response earns one point.

SCORING GUIDE AND










59


60/107


Score:

1


possible outcomes of an experiment to determine the probability of a certain outcome by showing all 12

coin/number cube combinations. The listing of game point totals includes an error (1 -T - 1 should be 1 -

T - 2) and cannot receive credit. The probability 1/6 listed in the explanation is for chance of rolling a

6 and is not the final answer for the probability of getting six points in one turn. This response earns

one point.

SCORING GUIDE AND










60


61/107


Score:

1


possible outcomes of an experiment to determine the probability of a certain outcome by showing all 12

coin/number cube combinations and all the correct possible game point totals in a chart format. An error

was made in reading the chart and the probability was incorrectly determined as 3/18 = 1/6. Because

the probability was found in a incorrect manner, the 1/6 does not get credit as the probability of getting 6

points in one turn. This response earns one point.

SCORING GUIDE AND










61


62/107


Score:

0

Annotation:The student shows little or no understanding of determining the size of a sample space and/or listing

all possible outcomes of an experiment to determine the probability of a certain outcome by showing

only 8 coin/number cube combinations; and indicating no probability of getting 6 points in one turn.

This response earns zero points.

SCORING GUIDE AND










62


63/107


Score:

0

Annotation:The student shows little or no understanding of determining the size of a sample space and/or listing

all possible outcomes of an experiment to determine the probability of a certain outcome by showing a

drawing of a number cube and coin (heads and tails), listing only two coin/cube combinations and game

point totals; and not indicating the probability of getting 6 points in one turn. This response earns zero

points.

SCORING GUIDE AND










63


64/107


Score:

0

Annotation:

This student shows very little or no understanding of determining the size of a sample space and/or

listing all possible outcomes of an experiment to determine the probability of a certain outcome by

stating the possible outcomes is 12, and by indicating the probability of getting 6 points in one turn is

6. This response earns zero points.

SCORING GUIDE AND










64


65/107


15 Each letter in the diagram represents an angle.

Which of the following statements is true?

{ A. x+ z= y+ z

{ B. w+x> y + z

{ C. w + x + y = y + z

{ D. w + x + y < y + z

65

Key: C


66/107


19 Look at the graph. The figure will be reflected over the y-axis.

What will be the new coordinates of point D?

{ A. (6, 2){ B. (-6, -2){ C. (2, 6){ D. (-2, -6)

66

Key: B


67/107


26 Look at the figure on the grid.

When the figure is translated so that point C is moved to the origin, and point D ismoved to the x-axis, what are the new coordinates of point A?

{ A. (-9, -6){ B. (-4, -8){ C. (-3, -9){ D. (-8, -4)

67

Key: D


68/107


29 Look at the chart.

Planet Mass

Mercury 3.30 x 1023 kg

Venus 4.87 x 1024 kg

Earth 5.97 x 1024 kg

Mars 6.42 x 1023 kg

Which planet has the largest mass?

{ A. Mercury{ B. Venus{ C. Earth{ D. Mars

68

Key: C


69/107


35 Naomi and Dana did the following computation.

3 x 42 + 7

Naomis answer was 55. Danas answer was 151.

Which students answer is correct? Describe the other students error.

Which students answer is correct? ___________________

69


70/107

SCORING GUIDE AND

TRAINING MANUAL

Scoring Rubric

High School Mathematics Practice Test Item 35

Strand: Number Sense

NS03 Learning Target: (Conceptual Understanding of Operations) Demonstrate

understanding of the meaning of operations with rational numbers

including whole number powers and square roots (1.1.5)

A 2-point response: The student demonstrates an understanding of order of operations

by doing one of the following:

indicates that Naomi got the correct answer of 55 and explains that Dana

multiplied 3 by 4 first, then squared the number 12

gives a full explanation of why Danas answer is incorrect indicates that Naomi got the correct answer with a full explanation of how she got

55 and gives a partial explanation of why Danas answer is incorrect.

A1-point response: The student does one of the following:

indicates that Naomi got the correct answer with a full or partial explanation of

how she got 55

indicates that Naomi is correct and gives a partial explanation of why Danas

answer is incorrect.

A0-point response: The student shows very little or no understanding of the order of

operations.

ITEM 35 HIGH SCHOOL MATHEMATICS

70


71/107

PRACTICE TEST ITEM

Score:

2

Annotation:

SCORING GUIDE AND



35. Naomi and Dana did the following computation.

3 x 42

+ 7


Which students answer was correct? Describe the other students error.

The student shows understanding of order of operations by indicating that Naomi got the correct

answer of 55 and explainingDana did (34)2 + 7, instead.This response earns two points.

71


72/107

PRACTICE TEST ITEM

Score:

2

Annotation:

The student shows understanding of order of operations by indicating the correct answer of 55 (3 x 42

+ 7, 3 x 16 + 7, 48 + 7 = 55) and explaining, She x 3 x 4 then squared it then added 7.This responseearns two points.

SCORING GUIDE AND




3 x 42

+ 7



72


73/107

PRACTICE TEST ITEM

Score:

2

Annotation:

The student shows understanding of order of operations by statingNaomis was correctandexplainingShe (meaning Dana) forgot to do her power numbers before everything else.The explanationfor Danas error implies that exponents come first in solving the expression. The response earns two

points.

SCORING GUIDE AND




3 x 42

+ 7



73


74/107

PRACTICE TEST ITEM

Score:

2

Annotation:

The student shows understanding of order of operations by statingNaomi was correctand explaining

She (meaning Dana) did 122 + 7. This response earns two points.

SCORING GUIDE AND




3 x 42

+ 7



74


75/107

PRACTICE TEST ITEM

Score:

1

Annotation:

The student shows partial understanding of order of operations by statingNaomis answer is correctand

partially explaining Danas error. Danas multiplied the 42 wrong.addresses the exponents but never fully

addresses what Dana did wrong.Did she multiply 4 x 2 instead of squaring, did she multiply 4 x 7 before

squaring, did she multiply 3 x 4 before squaring? There are too many different ways that multiplied the 42

wrongcan be interpreted so the statement is considered a partial explanation. This response earns one point.

SCORING GUIDE AND




3 x 42

+ 7



75


76/107


Score:

1

Annotation:The student shows partial understanding of order of operations by writing that Naomis answer isrightwith a full explanation of how she got 55. The student demonstrates mathematically how to get55 as an answer and also gives a written explanation of how to correctly use order of operations. The

student does not address Danas error. This response earns one point.

SCORING GUIDE AND




3 x 42

+ 7



76


77/107

PRACTICE TEST ITEM

Score:

0

Annotation:

The student shows little or no understanding of order of operations by indicating Naomi is correct butgives no explanation of how she got 55 and giving an explanation for Danas error (...she used thewrong procedures) that does not address exponents or the order of operations. This response earns zeropoints.

SCORING GUIDE AND




3 x 42

+ 7



77


78/107

PRACTICE TEST ITEM

Score:

0

Annotation:

The student shows little or no understanding of order of operations by indicating Naomi is correct but

gives no explanation of how she got 55 and giving an incorrect explanation for Danas error, Danas

answer is incorrect because she multiplied the answer.This response earns zero points..

SCORING GUIDE AND




3 x 42

+ 7



78


79/107

PRACTICE TEST ITEM

Score:

0

Annotation:

The student shows little or no understanding of order of operations by indicating Naomi is correct but

gives no explanation of how she got 55. The student does not address Danas error. This response earns

zero points.

SCORING GUIDE AND




3 x 42

+ 7



79


80/107

PRACTICE TEST ITEM

Score:

0

Annotation:

The student shows little or no understanding of order of operations by giving an incorrect explanation

of how to find 55 and never stating whether Naomi or Dana is correct. This response earns zero points..

SCORING GUIDE AND




3 x 42

+ 7



80


81/107


Score:

0

Annotation:The student shows little or no understanding of order of operations by indicating Dana is correct and

giving a full explanation of Naomis error. This response earns zero points.

SCORING GUIDE AND




3 x 42

+ 7



81


82/107


41 Anita and Ajay play a game of chess. The probability that Anita will win is 48%,and the probability that Ajay will win is 42%. What is the probability that thisgame will end in a stalemate (tie)?

{ A. 6%

{ B. 10%{ C. 52%{ D. 58%

42 J eremiah is doing an experiment in his mathematics class. He flips four

pennies in the air. What is most likely to happen?

{ A. Two of the pennies will be heads and two will be tails.{ B. Three of the pennies will be heads and one will be tails.{ C. All four pennies will be heads.{ D. None of the pennies will be heads.

82

Key: B

Key: A


83/107

Item Information

Score Points: 1

Key: D

Tools: N

Strand and Target NS01 (Number and Numeration): Demonstrate understanding of the

concepts and symbolic representations of rational numbers including whole number powers,

square roots of perfect squares, and numbers written in scientific notation; demonstrate

understanding of the relative values of rational numbers including whole number powers and

square roots of perfect squares; demonstrate understanding of and use the distributive

property and properties of addition and multiplication with rational numbers including

integers (1.1.1, 1.1.2, 1.1.3)

2007 Mathematics Sample Items

1 The park biologist reported the deer tick population in the park wasestimated at .

What was the population estimate in standard notation?

A. 0.0000965

B. 0.000965

C. 96,500

D. 965,000

12277

9 65 105

.

1

1

1

1

83


84/107


2 Jeremy wanted to determine how many of the 972 students at East HighSchool have dogs. Jeremy surveyed 54 students.

East High School / Pet Ownership Society

Based on the survey results, which is the best prediction of the total

number of students in the school who have dogs?

A. 144

B. 216

C. 360

D. 432

12912

Dogs Cats

Birds

8 8

4 3

5

10

0

16

1

1

1

1

Item Information

Score Points: 1

Key: C

Tools: Y

Strand and Target NS02 (Ratio and Proportion): Demonstrate understanding of and

apply the concepts of ratio, percent, and both direct and inverse proportion (1.1.4)

84


85/107


86/107


8 Vance graphed the relation between fund-raising profits for the chess cluband the number of members.

Which equation represents the data displayed on the graph?

A.

B.

C.

D.

27870

y n= +200

3180

y n= +2

3180

y n= +60 180

y n= +29 180

0 2 4 6 8 10 12 14 16 18 20

800

700

600

500

400

300

200

100

0

Number of Members

Profit(dollars)

Chess Club Fund-raising

n

y

1

1

1

1

Item Information

Score Points: 1

Key: A

Tools: X

Strand and Target PS03 (Data Representation and Interpretation): Draw a reasonable

line to describe the data represented by a scatter plot and determine whether a straight line is

an appropriate way to describe the trend in the data; read and interpret data presented in

tables of ordered pairs and scatter plots and make predictions based on the given data; use

statistics to support different points of view or evaluate a statistical argument based on data

(1.4.5, 1.4.6)

86


87/107


15 Ms. Parker gave her students this picture of a rectangular prism:

What is the surface area of the rectangular prism?

Show your work using words, numbers, and/or diagrams.

11369

What is the surface area of the rectangular prism? __________

4 cm 36 cm2

108 cm2

Item Information

Score Points: 2

Tools: N

Strand and Target ME03 (Procedures): Use formulas, including the Pythagorean Theorem,

to determine measurements oftriangles, prisms, or cylinders (1.2.5)

87


88/107

2007 Mathematics Sample ItemsScoring Guide for item number 15

A 2-point response: The student shows understanding of determining surface area of a

rectangular prism by doing the following:

shows work to determine surface area of the prism

writes 384 square centimeters.

NOTE: Allow one computation or one transcription error with an answer that follows from

the error.


shows 2(108) + 2(36) + 2(x), or equivalent, to show an addition of six faces

shows 48 as the area of the front face and sums three or more face areas labeled

square centimeters

writes 384.

A 0-point response: The student shows very little or no understanding of determining the

surface area of a rectangular prism.

88


89/107





4 cm 36 cm2

108 cm2


The student shows understanding of determining surface area of a rectangular prism by

showing work that uses 12 as the length of the prism and 48 as the area of the front face. The

student determines the area of the faces that show in the picture and then doubles that area.

The student writes a correct answer of 384 cm2.This response earns two points.

89


90/107





4 cm 36 cm2

108 cm2



showing work that uses 12 as the length of the prism and 48 as the area of the front face. The

student doubles the area of each face that shows in the picture. The student writes a correct

answer of 384 cm2.This response earns two points.

90


91/107





4 cm 36 cm2

108 cm2



showing work to determine the total area of six surfaces. The student writes an answer of

374 cm2.This incorrect answer follows from one computation error. This response earns two

points.

91


92/107





4 cm 36 cm2

108 cm2


The student shows partial understanding of determining surface area of a rectangular prism by

showing work to sum six faces of the prism (bullet 1). This response earns one point.

92


93/107





4 cm 36 cm2

108 cm2



showing work to sum three faces of the prism (bullet 2). This response earns one point.

93


94/107





4 cm 36 cm2

108 cm2



showing work to sum six faces of the prism. The response shows two faces as 108and four

faces as 36(bullet 1). This response earns one point.

94


95/107





4 cm 36 cm2

108 cm2


The student shows little or no understanding of determining surface area of a rectangular. The

student is attempting to find volume of the prism. This response earns zero points.

95


96/107

Item Information

Score Points: 1

Key: B

Tools: N

Strand and Target NS01 (Number and Numeration): Demonstrate understanding of the

concepts and symbolic representations of rational numbers including whole number powers,

square roots of perfect squares, and numbers written in scientific notation; demonstrate

understanding of the relative values of rational numbers including whole number powers and

square roots of perfect squares; demonstrate understanding of and use the distributive

property and properties of addition and multiplication with rational numbers including

integers (1.1.1, 1.1.2, 1.1.3)

2008 Mathematics Sample Items1 A tissue can be 0.000075 meters thick.

Which expression represents 0.000075 in scientific notation?

A.

B.

C.

D.

27089

75 106

75 106

7 5 105

.

7 5 105

. 1

1

1

1

96


97/107

2008 Mathematics Sample Items4 When the figure below is rotated 90 counterclockwise about the origin,

what would be the new coordinates of point C?

A. (5, 3)

B. (3, 5)

C. (5, 3)

D. (5, 3)

00896

1

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-1

-2

-3

-4

-5

-6

-7

-8

-9

2

3

4

5

6

7

8

9

y

x

B C

DA

1

1

1

1

Item Information

Score Points: 1

Key: A

Tools: X

Strand and Target GS02 (Locations and Transformations): Use geometric properties to

describe or identify the location of points on coordinate grids; use multiple transformations

including translations, reflections, and/or rotations to create congruent figures (1.3.3, 1.3.4)

97


98/107

2008 Mathematics Sample Items5 In a certain game, the contestants shut their eyes and draw either a

shaded cube or a white cube from a box. A contestant cannot return the

cube after drawing it from the box. The box contains the cubes shown in

the diagram.

What is the probability that a contestant will draw a shaded cube on

2 consecutive draws?

A.

B.

C.

D.

03516

7

15

1

2

1

4

3

14\

\

\

\

Item Information

Score Points: 1

Key: A

Tools: X

Strand and Target PS01 (Probability): Demonstrate understanding of the concepts ofcompound, dependent and independent events; determine and use probabilities of compound,

dependent, and independent events (1.4.1, 1.4.2)

98


99/107


9 A certain school has 12 mathematics teachers and only 3 types ofmathematics coursesalgebra, geometry, and calculus. Two of the

teachers teach only algebra. Eight teachers teach geometry, and six teach

calculus.

How many teachers teach both geometry and calculus?

Clearly explain or show how you arrived at your answer.

01066

How many teachers teach both geometry and calculus? _________

Item Information

Score Points: 2

Tools: X

Strand and Target SR02 (Construct Solutions): Select and organize relevant information;

use appropriate concepts and procedures from number sense, measurement, geometric sense,

probability and statistics, and algebraic sense; use a variety of strategies and approaches;

determine whether a solution is viable, mathematically correct; and answers the question(s)

asked (2.2.1, 2.2.2, 2.2.3, 2.2.4)

99


100/107

2008 Mathematics Sample ItemsScoring Guide for item number 9

A 2-point response: The student demonstrates understanding of selecting and using relevant

information and an appropriate strategy to determine an answer by doing the following:

indicates 4 teachers teach both geometry and calculus

provides an explanation (written, algebraic, or diagrammatic) for the answer.

NOTE: Allow for one computation or transcription error that does not affect the answer.


indicates 4 teachers teach both geometry and calculus, but the explanation is flawed,

incomplete, or missing

provides work showing either 2 calculus teachers do not teach geometry or

4 geometry teachers do not teach calculus

demonstrates an appropriate procedure to determine how many teachers teach both

geometry and calculus, but an error in the process results in an incorrect answer.

A 0-point response: The student demonstrates very little or no understanding of selecting and

using relevant information and appropriate strategy to determine an answer.

100


101/107




calculus.



01066



The student demonstrates understanding of selecting and using relevant information and an

appropriate strategy to determine an answer by writing 4 teachers teach both geometry and

calculus and providing a diagram to show 2 teachers teach algebra, 8 teach geometry, 6 teach

calculus and the overlap of 4 teachers who teach both geometry and calculus. This response

earns two points.

101


102/107




calculus.



01066



The student shows understanding of selecting and using relevant information and an


calculus, and providing an algebraic explanation (8 x) + (6 x) + x = 10 and solving the

equation correctly. This response earns two points.

102


103/107




calculus.



01066



The student demonstrates understanding of selecting and using relevant information and an


calculus, and providing a strategy showing that there are 16 classes and only 12 teachers. This

response earns two points.

103


104/107




calculus.



01066



The student demonstrates partial understanding of selecting and using relevant information

and an appropriate strategy to determine an answer by writing the correct number of teachers

as 4 but the strategy is flawed. The explanation 2, 8, and 6 is a repeat of the prompt

while 6 2 = 4 8 = 4 is an incorrect run-on equation. This response earns one point.

104


105/107




calculus.



01066




and an appropriate strategy to determine an answer by showing an appropriate strategy to

determine how many teachers teach both geometry and calculus, but an error in the process

results in an incorrect answer of 5. The diagram incorrectly shows that 7 teach calculus

rather than the 6 stated in the problem. This response earns one point.

105


106/107




calculus.



01066




and an appropriate strategy to determine an answer by showing an appropriate strategy to

determine how many teachers teach both geometry and calculus, but an error in the process

results in an incorrect answer of 2. The student writes that there are ten geometry and

calculus teachers and the equations 8 + 6 = 14 and 14 10 = 4 show the correct answer but

the student does not use it. Instead the interpretation is using two instead of 4 accounts for

the doubling up. The algebraic equation omits +x for the teachers who teach both geometry

and calculus so the algebraic strategy is incorrect. This response earns one point.

106


107/107




calculus.



01066



The student demonstrates very little or no understanding of selecting and using relevant

information and an appropriate strategy to determine an answer by incorrectly writing 1

teacher teaches both geometry and calculus with no strategy to determine the answer. The

quickguide_gr8

Documents