Grade 4 math arkansas 06 + answers

PART II

Released Mathematics Items – 2006 Benchmark Grade 4
CALCULATOR NOT PERMITTED — ITEMS 1–8

AR4M04A0403Y166-166D

1. What is the missing operation in the pattern below?
Input

n

10

11

12

13

14

15

Output

?

3

4

5

6

7

8

A.

add 7

B.

add 10

C.

subtract 3

* D.

subtract 7

AR4M04M1311Y052-052C

2. Jamie built a block structure with a volume of 9 cubic units. Which of the structures below did he build?

A.

Figure 1

B.

Figure 2

* C.

Figure 3

D.

Figure 4

21


PART II

Released Mathematics Items – 2006 Benchmark Grade 4

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3. How many yards of fencing would it

6. Mrs. Smith and Mr. Jones are taking their
classes on a field trip. Each school van holds

8 people. If there are 48 people going on the
trip, how many vans do they need?

take to surround a dog’s play area that is a
1
square measuring 4 yards per side?
2

A.

16 yards

B.

1
16 yards
2

* C.

18 yards

D.

25 yards

A.

5

* B.

6

C.

40

D.

56

7. Ashley has a 43-page sticker album. Each
page will hold about 20 stickers. About how
many stickers can she place in the album?

4. What is the value of the underlined digit
below?

218,036,097

A.

2

B.

20

A.

three thousand

C.

60

* B.

thirty thousand

* D.

800

C.

thirty-six thousand

D.

three hundred thousand

8. Based on the data collection below, how
many more fourth-grade students preferred
chocolate chip than preferred vanilla?

5. Zach created the secret code below to write
messages to his friends.
My Secret Code

1=B
2=C
3=D
4=E
etc.
What numbers will Zach write to represent the
word “HE”?
A.

4, 7

* B.

7, 4

C.

4, 8

D.

8, 4

22

A.

4

B.

5

* C.

19

D.

27


PART II

Released Mathematics Items – 2006 Benchmark Grade 4
CALCULATOR PERMITTED — ITEMS 9–40

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9. Jean made the chart below to record the
number of pencils sold at the school store for
the last four months.

12. Randy has 3 bags of marbles. Each bag has
86 marbles. About how many marbles does
Randy have in all?

Pencil Sales
Month
# of Pencils Sold
September
1,543
October
1,867
November
1,290
December
1,789

Which of the following is a true statement
about the number of pencils sold?

A.

83

B.

89

C.

240

* D.

270

13. What is the rule for the number pattern below?

1,125 225 45 9

A.

1,789 < 1,543

B.

1,290 > 1,867

A.

add 900

* C.

1,543 > 1,290

B.

divide by 2

D.

1,867 = 1,789

* C.

divide by 5

D.
10. Mr. Carter’s class has 30 students. Which
mathematical sentence shows how many
5-player basketball teams the class will be
able to make at recess?

subtract 900

14. Joey covered a hexagon pattern block using
3 triangles and 1 other shape. What is the
other shape? You may use your pattern blocks
to help you.

* A.

30 ÷ 5 = n

B.

30 × 5 = n

A.

square

C.

30 – 5 = n

B.

triangle

D.

30 + 5 = n

C.

rhombus

* D.

trapezoid

11. Felton weighed 8 apples and found that they
weighed 2 pounds. Approximately how much
does 1 apple weigh?

A.

2 oz

* B.

4 oz

C.

16 oz

D.

32 oz

23


PART II

Released Mathematics Items – 2006 Benchmark Grade 4

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15. How many triangle pattern blocks are needed to cover the figure below? You may use your pattern blocks
to help you.

A.

3

B.

4

* C.

12

D.

13

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16. Carl has a bag of fruit-flavored candy that
contains the following pieces:

17. Sean has 36 baseball cards. Tom has
25 baseball cards. Which of the following is a
true statement about their baseball card
collections?

•
•
•
•

3 grape
5 strawberry
1 cherry
2 watermelon

Carl pulls a piece of candy from the bag
without looking. What is the probability that

he picks a watermelon-flavored piece?
A.

1 out of 11

* B.

2 out of 11

C.

3 out of 11

D.

5 out of 11

24

A.

25 > 36

B.

25 × 36

* C.

36 > 25

D.

36 = 25


PART II

Released Mathematics Items – 2006 Benchmark Grade 4

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AR4M04D1501Y139-139D

18. Patty is playing a shape game with the spinner
below.

21. Jim and his friends made the table below to
show how many seashells they have in their
collections.

What is the probability that the pointer will
land on a hexagon on her next spin?
A.

1 out of 10

B.

2 out of 10

C.

3 out of 10

* D.

4 out of 10

How many seashells do they have in all?

19. Mrs. Rodriguez will use 54 square feet of tile
to cover her bathroom floor. What are the
dimensions of her bathroom?

* A.

6 ft by 9 ft

B.

7 ft by 8 ft

C.

5 ft by 4 ft

D.

8 ft by 8 ft

soda can

B.

stop sign

C.

cereal box

D.

front door of a house

13

B.

14

C.

52

* D.

54

1

2
1
2

22. Sheila is making beaded necklaces that are
10 inches long. She has a piece of string that is
78 inches long. How many necklaces can she
make from the string?

20. Which of the following is most like a
cylinder?

* A.

A.

25

* A.

7

B.

8

C.

780

D.

800


PART II

Released Mathematics Items – 2006 Benchmark Grade 4

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AR4M03G1102Y081-081D

23. On the cube below, the shapes on the faces
not showing are triangles.

Use the shapes below to answer question 25.

25. When the shapes above are combined with no
empty spaces left over, what new shape is
formed? (You may use your pattern blocks to
help you.)

What are the chances the cube will land on a
triangle when rolled?
A.

1 out of 3

B.

2 out of 6

* C.

4 out of 6

D.

6 out of 4

*

24. How many more vertices does a cube have
than a triangular prism?

* A.

2

B.

6

C.

8

D.

14

26. It is 150 miles between Little Rock and
Ashdown. Driving at 50 miles per hour, how
many hours will the trip take?

26

* A.

3

B.

2

C.

2

D.

3

1
2
1
2

PART II

Released Mathematics Items – 2006 Benchmark Grade 4

AR4M04M1308Y098-098A

27. Which length, rounded to the nearest

1
inch, best describes the toy cheetah below? Use your ruler to help
2

you.

* A.
B.

4 inches
4

C.
D.

1
inches
2
5 inches

5

1
inches
2

AR4M04M1307Y094-094C

28. What is the length, measured to the nearest

A.
B.

4 inches
4

* C.
D.

1
inch, of the plastic fork below? Use your ruler to help you.
2

1
inches
2
5 inches

5

1
inches

2

27


PART II

Released Mathematics Items – 2006 Benchmark Grade 4

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AR4M04A0403NXXX-163A

29. What symbol can replace the
in the
number sentence below to make it true?

31. When Ashley says “13,” the answer is 113.
When she says “36,” the answer is 136. When
she says “94,” the answer is 194. What is the
rule for Ashley’s pattern?

1,840

1,804

* A.

>

* A.

add 100

B.

=

B.

add 117

C.

<

C.

divide by 100

D.

+

D.

divide by 117

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30. There are 124 jelly beans in a bag. The table
below lists the colors and number of jelly
beans. Which fraction represents Katie’s
chances of picking out a pink jelly bean on her
first try?

32. Jacob drew the map below to show the
distance he drives from his house to the mall.

Jelly beans in the Bag
Color
Number
black
16
orange
17
pink
24
purple
12
red
14
yellow
24
white
17

A.

16
124

B.

Based on Jacob’s scale, what is the distance?
Use your ruler to help you.
* A.

3 miles

12
124

B.

4 miles

C.

7 miles

* C.

24
124

D.

8 miles

D.

124
24

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PART II

Released Mathematics Items – 2006 Benchmark Grade 4

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33. Toshio asked 55 fourth-grade students about their favorite after-school activity. He created the graph
below to display the results of his survey.

How many students chose riding their bike as their favorite activity?
A.

15

* B.

25

C.

30

D.

55

AR4M04D1702Y125-125B

34. Brad has a bag containing the shapes below.

Which statement best describes the outcome if Brad chooses a shape from the bag without looking?
A.

He is most likely to choose a triangle.

* B.

He is most likely to choose a rectangle.

C.

He is least likely to choose a rectangle.

D.

He is equally likely to choose triangles and circles.
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PART II

Released Mathematics Items – 2006 Benchmark Grade 4

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35. Mr. Booth put the two groups of numbers
below on the board.

37. I am a polygon. I have 6 sides. What is my
name?

A.

square

B.

octagon

* C.

hexagon

D.

quadrilateral

AR4M02N0102Y036-036B

38. The chart below shows the number of calories
consumed by a group of students in one week.

What is the rule he used when forming the two
groups?

Student Calorie Chart
Student
Number of Calories

Tony
James
Kendra
Sophia

15,285
14,768
14,876
15,852

A.

Group X: Multiples of 5
Group Y: Even Numbers

* B.

Group X: Odd Numbers
Group Y: Even Numbers

C.

Group X: Odd Numbers
Group Y: Multiples of 3

Which student consumed the least number of
calories?

D.

Group X: Odd Numbers
Group Y: Multiples of 6

A.
* B.

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36. Mrs. Berini used 18 yards of fabric to make
her living room curtains and 16 yards to make
her bedroom curtains. How much more fabric
did she use in the living room than in the
bedroom?

Tony
James

C.

Kendra

D.

Sophia

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39. Craig’s little brother weighed 5 pounds and
8 ounces when he was born. How many
ounces did he weigh?

A.

2 feet

* B.

6 feet

A.

40

C.

34 feet

B.

44

D.

72 feet

C.

80

* D.

88

30


PART II

Released Mathematics Items – 2006 Benchmark Grade 4

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40. Which of the following fractions identifies the part of the dozen eggs shown below that has been used?

A.

1
8

B.

1
4

C.

4
12

* D.

8
12

31


PART II

Released Mathematics Items – 2006 Benchmark Grade 4
MATHEMATICS OPEN-RESPONSE ITEM A

AR4M04M1310Y100-100CR

A. Cameron drew the rectangle below.

The length of Cameron’s rectangle is 3 times its width.
1.

What is the length of Cameron’s rectangle? Explain your answer using words, numbers, and/or
pictures.

2.

What is the area of Cameron’s rectangle? Explain your answer using words, numbers, and/or
pictures.

BE SURE TO LABEL YOUR RESPONSES 1 AND 2.
RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM A
SCORE
4
3
2
1
0
B

DESCRIPTION

The student earns 4 points. Correct units of “cm” in Part 1. Correct units of “Sq. cm.” in
Part 2. The response contains no incorrect work.
The student earns 3 points.
The student earns 2 points.
The student earns 1 point. Some minimal understanding is shown:
Ex. Student uses formula for area in Part 1 AND perimeter in Part 2 with all
calculations correct.
The student earns 0 points. No understanding is shown.
Blank – No Response. A score of “B” will be reported as “NA.” (No attempt to answer the
item. Score of “0” assigned for the item.)

32


PART II

Released Mathematics Items – 2006 Benchmark Grade 4

Solution and Scoring
Part
1

2

Points
2 points possible
1 point:
Correct answer: 9 (cm).
Note: Do not give credit for answer if incorrect procedure is evident.
AND
1 point:
Correct procedure shown and/or explained.
Work may contain a calculation error.
Give credit for the following or equivalent:
• 3 x 3 = L (uses fact that length is 3 times the width and w = 3 cm.)
• “If the width is 3, just multiply that by 3.” or
• 3 + 3 + 9 + 9 = 24 (Finds length based on perimeter, uses Guess & Check) or
• 3 + 3 = 6, 24 – 6 = 18, 18 ÷ 2 = L.
Note: Do not give credit for incomplete procedure:
Ex: L = 9 because 24 – 6 = 18.

2 points possible
1 point:
Correct answer: 27 (square cm) or
correct answer based on incorrect answer to Part 1.
AND
1 point:
Correct procedure shown and/or explained.
Work may contain a calculation error and/or may be based on an incorrect answer
given in Part 1.
Give credit for the following or equivalent:
• “3 x 9 = Area.”
or
• “I multiplied the width of 3 by the length of 9.”
or
• “I multiplied the length times the width, and the length is 9 and the width is 3.” or
• Drawing of a 3 x 9 rectangle that is divided into 27 squares.
Note: Do not give credit for only repeating the formula LW = Area only.

33


PART II

Released Mathematics Items – 2006 Benchmark Grade 4
MATHEMATICS OPEN-RESPONSE ITEM B

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B. Karen wants to make a bookmark out of leather. She is planning the design above on paper before she
starts cutting the leather.

1.

Using Karen’s pattern, complete the design for the bookmark.

2.

How many of each shape will she need to cut out to make her bookmark?

3.

Use the same number of squares, circles, and rhombuses to design a new bookmark that follows a
regular pattern.

BE SURE TO LABEL YOUR RESPONSES 1, 2, AND 3.
RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM B
SCORE

DESCRIPTION

4
3
2

The student earns 4 points. The response contains no incorrect work.
The student earns 3 points.
The student earns 2 points.
The student earns 1 point. Some minimal understanding is shown:
Ex. Part 1: 1 row is completed correctly with no other credit.
The student earns 0 points. No understanding is shown.

Blank – No Response. A score of “B” will be reported as “NA.” (No attempt to answer the
item. Score of “0” assigned for the item.)

1
0
B

34


PART II

Released Mathematics Items – 2006 Benchmark Grade 4

Solution and Scoring
Part
1

2

3

Points
1 point possible
1 point:
The last 4 top and bottom sections of the bookmark (positions 7-10) are correctly
completed, as shown in the diagram below:

Note: Top and bottom row do not have to be aligned.
1 point possible

1 point:
Correct number of shapes: 10 squares, 5 rhombuses, 5 circles
(shapes may be named or drawn).
Or
Correct # of squares, rhombuses and circles based on Part 1 answer.
2 points possible
Note: Design may be in a single row or a continuous pattern.
Note: If design is in a double row, both rows must have a repeating pattern
the 2nd row is a repeat of the 1st row.
Note: Design must be different from the original bookmark.
2 points:
Or
1 point:

or

Correct and complete design that contains all of the following:
• 10 squares, 5 rhombuses, 5 circles OR Equal #’s of each shape.
• The pattern is repeating horizontally, repeats at least once and has no errors.
Partially correct design:
• Design uses 10 Squares, 5 rhombuses, 5 circles or equal #’s of each.
(Repeats correctly at least once, proceeds with something incorrect.)
or
• The #’s of squares, rhombuses and circles ≠10, 5, and/or 5, and there are not
equal #’s of each shape, but the design repeats correctly at least once.

35


PART II

Released Mathematics Items – 2006 Benchmark Grade 4
MATHEMATICS OPEN-RESPONSE ITEM C

AR4M04N0303NXXX-032CR

C. Mrs. Grey wrote the following two numbers on the board.

12

4

1.

What is the sum of the two numbers that Mrs. Grey wrote on the board? Write a number sentence
using Mrs. Grey’s numbers and your sum.

2.

If 12 is the dividend and 4 is the quotient, what is the divisor? Write a number sentence using
Mrs. Grey’s numbers and your divisor.

BE SURE TO LABEL YOUR RESPONSES 1 AND 2.
RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM C
SCORE

DESCRIPTION

4
3

2

The student earns 4 points. The response contains no incorrect work.
The student earns 3 points.
The student earns 2 points.
The student earns 1 point. Some minimal understanding is shown:
Ex. 3 x 4 = 12 with no other credit.
The student earns 0 points. No understanding is shown.
Blank – No Response. A score of “B” will be reported as “NA.” (No attempt to answer the
item. Score of “0” assigned for the item.)

1
0
B

36


PART II

Released Mathematics Items – 2006 Benchmark Grade 4

Solution and Scoring
Part
1

2

Points
2 points possible

1 point:
Correct answer: 16 (sum).
Note: Do not give credit if incorrect procedure is used:
Ex: 4 x 4 = 16
AND
1 point:
Correct equation given.
Work may contain a calculation error.
Give credit for the following:
• 12 + 4 = #
or
• 4 + 12 = #
Give credit for the following only with an answer of 16:
• 16 – 4 = 12 (Guess & Check)
• 16 – 12 = 4 (Guess & Check)
Note: Do not give procedure credit for work that is not in the form of an equation:
Ex: 12
or
+ 4
16
Ex: “I added 12 and 4 and got…”
2 points possible
1 point:
Correct answer: 3 (divisor).
Give credit if the answer is stated “The divisor is 3.” or if 3 is shown as the

4
divisor in a division operation: Ex: 3 12
Note: Do not give credit if incorrect procedure is used:
Ex: 4 ÷ 12 = 3.

AND
1 point:

Correct equation given.
(Divisor may be incorrect.)
Give credit for the following:
• 12 ÷ 3 = 4
or
• 12 ÷ (divisor) = 4.
or
Give credit for the following only with an answer of 3:
• 3 x 4 = 12 (Guess & Check)
• 4 x 3 = 12 (Guess & Check)
• 12 ÷ 4 = 3 (Give credit except at “4” level).
Note: Do not give procedure credit for work that is not in the form of an equation:

4
Ex: Shows short division: 3 12
Ex: “I divided 12 by 3 and got…”

37

or


PART II

Released Mathematics Items – 2006 Benchmark Grade 4
MATHEMATICS OPEN-RESPONSE ITEM D

AR4M04G1102Y070-070CR

D. Casey used four pattern blocks to create the design below.

1.

Name the four pattern blocks Casey used. You may use your pattern blocks to help you find the
answer.

2.

What is another way that Casey’s design could have been created if he had used more than four
blocks? Explain your answer using words, numbers, and/or pictures.

BE SURE TO LABEL YOUR RESPONSES 1 AND 2.
RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM D
SCORE

DESCRIPTION

4
3
2

The student earns 4 points. The response contains no incorrect work.
The student earns 3 points.
The student earns 2 points.
The student earns 1 point. Some minimal understanding is shown:
Ex. Part 1: 2 correct names and #’s, 3rd name incorrect (with no drawing)
(Square, Trapezoid, 2 Octagons).

Ex. Part 1: correct drawings of Hexagon, Trapezoid, and Square.
The student earns 0 points. No understanding is shown.
Ex. 4 different polygons named – Octagon, Hexagon, Square, Trapezoid.
Ex. Part 1: 2 Octagons, 1 Square, and 1 Quadrilateral.
Blank – No Response. A score of “B” will be reported as “NA.” (No attempt to answer the
item. Score of “0” assigned for the item.)

1

0
B

38


PART II

Released Mathematics Items – 2006 Benchmark Grade 4

Solution and Scoring
Part
1

2

Points
2 points possible
2 points:
Answer is correct and complete: 2 Hexagons, 1 Trapezoid and 1 Square.
(Shapes are correctly named with correct # of each.)

Note: Rhombus, rectangle, parallelogram or quadrilateral may be used for the square.
Quadrilateral may be used for trapezoid.
But do not give credit if quadrilateral is used for both the trapezoid & square.
Or
1 point:
Partially correct answer.
Give credit for the following:
• Hexagon, Trapezoid and Square (correct shapes, no #’s)
Or
• 2 names & #’s are correct, 3rd has correct drawing of remaining shape,
but name may be incorrect or missing.
2 points possible
2 points:
Correct and complete answer.
Give credit for the following:
Note: If incorrect name(s) are given in Part 1, do not penalize again.
Credit can be given if answer is “correct” based on Pt. 1 answer.
• Correct shapes and # of shapes (> 4) needed to make new design with
support explaining or showing why they will work:
Ex: 1 hexagon, 3 trapezoids and 1 square with given diagram correctly divided.
Ex: “4 trapezoids, 3 triangles and one square because 2 trapezoids could
make up each hexagon and 3 triangles could make up one trapezoid.”
Ex: “2 hexagons, 1 square, 1 triangle, 1 rhombus since a trapezoid can be
made up of 1 triangle and 1 rhombus.”
Ex: 5 trapezoids and 1 square with given diagram correctly divided.
Ex: “15 triangles and 1 square because 6 triangles make up 1 hexagon and
3 triangles make up 1 trapezoid so 6 + 6 + 3 = 15 triangles, + 1 square.”
Or
• Correct and complete drawing of given design divided up into more than
4 pattern blocks.

Or
1 point:
Partially correct answer.
Give credit for the following:
• Correct shapes and #’s of each shape needed to make new design with missing,
incomplete or contradicting support. or
• Correct and complete new drawing with contradicting support. or
• Description of how to divide one of the figures in the given drawing, but
no reference is made to the rest of the given figure.

39


PART II

Released Mathematics Items – 2006 Benchmark Grade 4
MATHEMATICS OPEN-RESPONSE ITEM E

AR4M04D1501Y148-148CR

E. Joseph made the pictogram below to show the number of hits he had in his last four baseball games.

1.

How many hits did Joseph have in Game 2? Explain your answer using words and/or numbers.

2.

How many more hits did Joseph have in Game 4 than in Game 3? Explain your answer using words
and/or numbers.

BE SURE TO LABEL YOUR RESPONSES 1 AND 2.
RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM E
SCORE

DESCRIPTION

4
3
2

The student earns 4 points. The response contains no incorrect work.
The student earns 3 points.
The student earns 2 points.
The student earns 1 point. Some minimal understanding is shown:
Ex. Part 2: 9 minus any # (≠ 3) = answer with no credit in any other part.
Ex. Part 2: # (≠ 9) – 3 = answer with no credit in any other part.
Ex. Part 2: correct # of hits (identified) in Game 3 and/or 4.
The student earns 0 points. No understanding is shown.
Blank – No Response. A score of “B” will be reported as “NA.” (No attempt to answer the
item. Score of “0” assigned for the item.)

1
0
B

40


PART II

Released Mathematics Items – 2006 Benchmark Grade 4

Solution and Scoring
Part
1

2

Points
2 points possible
1 point:
Correct answer: 8 (hits).
Note: Do not give credit if incorrect procedure is evident.
AND
1 point:
Correct and complete procedure shown and/or explained.
Work may contain a calculation error.
Give credit for the following or equivalent:
• 4 x 2 = # of hits
or
• “I multiplied 4 and 2.”
or
• 2 + 2 + 2 + 2 = # of hits
or
• 4 + 4 = # of hits
or
• “I skip counted by 2 four times.”
or
• Draws four baseballs and accumulates hits.

With the correct answer of 8, give credit for the following:
• “I counted (skip counted) by 2’s.”
2 points possible
1 point:
Correct answer: 6 (more hits).
Note: Do not give credit if incorrect procedure is evident.
Ex: 10 – 4 = 6
AND
1 point:
Correct procedure shown and/or explained.
Work may contain a calculation error.
Give credit for the following or equivalent:
• Game 4: (2 x 4) + 1 = 9 Game 3: 2 + 1 = 3
9–3=6
• “He has 9 hits in game 4 and 3 hits in game 3 so minused 3 from 9.” or
• 9–3=#
or
• 4½ – 1½ = 3 baseballs, 3 x 2 = #
or
• “I subtracted 3 from 9.” or “I subtracted 9 and 3.”
Note: Do not give credit for incomplete procedure:
Ex: “He had 9 hits in Game 4 and 3 hits in game 3.” and stops.
Note: Do not give credit for vague procedure or procedure stated incorrectly:
Ex: “I subtracted 3 and 9.” (order implies 9 is subtracted from 3)
Ex: “I subtracted 9 from 3.” (incorrectly stated)

41


PART II

Released Mathematics Items – 2006 Benchmark Grade 4

Mathematics Reference Sheet
Grade 4
Use the information below, as needed, to answer questions on the Mathematics test.

1 foot = 12 inches

1 cup = 8 ounces (oz)

1 kilogram = 1000 grams

1 yard = 3 feet

1 pint = 2 cups

1 liter = 1000 milliliters

1 quart = 2 pints
1 gallon = 4 quarts
1 pound (lb) = 16 ounces (oz)

42