Grade 4 math arkansas 04 + answers

PART II

Released Mathematics Items

CALCULATOR NOT PERMITTED — ITEMS 1–8
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1. Which number will make the equation true?

2. Mr. Preddy put the chart below on the board.
He asked his students, “If the pattern
continues, which pair of numbers would come
next?” What answer should the students have
given?

(10 + n) – (2 × 3) = 8
* A.

4

B.

9

C.

10

D.

16

20

A.

55, 10

* B.

60, 12

C.

75, 15

D.

90, 18


PART II

Released Mathematics Items

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3. The school librarian made a graph showing the number of books checked out each month by students in
the fourth grade. In April, there were 45 books checked out. How many books should be displayed in the

graph?

A.

05

B.

06

* C.

09

D.

45

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4. Last week, Mark’s pet bunny weighed
12 ounces. This week, it had gained 4 more
ounces. How much does it weigh now?
* A.

1 pound

B.

8 ounces

C.

16 pounds

D.

48 ounces

5. Kisha visited the Aerospace Education Center
in Little Rock with her family. She bought a
toy airplane for $4.88 in the gift shop. She
gave the salesperson $5.00. How much change
should Kisha receive?

21

* A.

$0.12

B.

$0.22

C.

$1.12

D.

$1.88


PART II

Released Mathematics Items

Use the table below to answer question 6.

Use the figure below to answer question 8.

Hector’s Table
Approx. Miles From
Little Rock

State Park
Pinnacle Mountain
Woolly Hollow
Village Creek
Crater of Diamonds
Bull Shoals

10
40
90
100
120

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8. Which figure is the flip image of Figure A
above?

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*

6. Hector made the table above for his family to
compare the approximate distance from their
home in Little Rock to several state parks.
How many more miles is it to Village Creek
State Park than to Woolly Hollow State Park?
A.

40

* B.

50

C.

80

D.

90

Use the calendar below to answer question 7.
Sun

MAY
Wed Thu
3
4

Mon
1
S
8

Tue
2
9

10

16

21

15
S
22

28

29

7
14

Fri
5

Sat
6

11

12

13

17

18

19

20

23

24

25

26

27

30

31

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7. Jane has swim practice on the first and third
Monday of each month. What will be the date
of her first swim practice in June?
A.

1st

* B.

5th

C.

15th

D.

29th
22

PART II

Released Mathematics Items

CALCULATOR PERMITTED — ITEMS 9–40
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9. Cliff brought cupcakes to share with his
classmates. He brought 12 chocolate and
13 vanilla. What are Jane’s chances of getting
a chocolate cupcake?
A.

01 out of 25

B.

01 out of 12

* C.

12 out of 25

D.

12 out of 13

Use the figure below to answer question 12.

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12. Annie made a pattern block design using
1 hexagon and 2 trapezoids. How many
equilateral triangles will cover this design?
(You may use your pattern blocks to help you
find the answer.)

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10. Mrs. Andrew’s class collected canned food for
a local food drive. They wanted to sort the
cans before they donated them. Which of the
following is not a way they could group the
cans?
A.

size

B.

weight

C.

type of food

* D.

A.

3

B.

6

* C.

12

D.

14

Use the information below to answer question 13.

total number of cans

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SCHEDULE
FOR FEEDING SNAKES
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10:00 A.M.
12:00 P.M.
2:00 P.M.
4:00 P.M.

11. Marty is about to begin reading the 250-page
book she just checked out from the library.
She plans to read 25 pages per night. At this
rate, how many nights will it take her to finish
her book?
A.

1

B.

5

* C.

10

D.

20

13. Sandra’s fourth-grade class went to the Little
Rock Zoo on a field trip. Her group arrived at
the snake exhibit at 10:25 A.M. How long will
the group have to wait to see the next snake
feeding?
A.

2 hours

B.

35 minutes

* C.
D.

23

1 hour, 35 minutes
2 hours, 35 minutes


PART II

Released Mathematics Items

Use the figure below to answer question 14.

Use the chart below to answer question 15.

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Pattern Chart
A
B
6
12
12
24

24
48
?
?
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15. Mrs. Gordon put the chart above on the board.
What pair of numbers would come next in the
pattern?
14. The figure above is made with cubes which
are 1 cm3. What is its volume?
A.

6 cm3

B.

12 cm3

* C.

18 cm3

D.

21 cm3

24

A.

30, 60

B.

30, 96

C.

48, 60

* D.

48, 96


PART II

Released Mathematics Items

Use the figure below to answer question 16.
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16. How long is the rod above, to the nearest half inch?
* A.

4

1
in.

2

B.

5 in.

C.

11 cm

D.

11

1
cm
2
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18. A runner can burn 1,280 calories in
60 minutes. Which of the following number
sentences would you use to find out how
many calories can be burned in 30 minutes of
running?

Use the diagram below to answer question 17.

A.
* B.
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17. The basketball court above is 94 feet long and
50 feet wide. What is the perimeter of this
basketball court?

A.

0,144 ft

B.

0,188 sq ft

* C.
D.

1,280 × 30 =
1,280 ÷ 2 =

C.

21,380 − 30 =

D.

1,280 × 2 =

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19. Melissa is first in line to go on the pony ride at

the state fair. There are 2 brown ponies, 4 tan
ponies, and 3 black ponies. What is the
probability that she will get to ride on a black
pony?

0,288 ft
4,700 sq ft

25

A.

2
9

* B.

3
9

C.

1
9

D.

4
9

PART II

Released Mathematics Items

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20. Kathy is wearing a heavy coat, scarf, mittens,
and a hat. Which temperature is it most likely
outside?

23. What number comes next in the pattern?

1, 2, 4, 7, 11, __

A.

35°C

A.

15

* B.

35°F

* B.

16

C.

68°C

C.

18

D.

68°F

D.

22

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21. One morning it took Carlos 167 seconds to
brush his teeth. How many minutes and
seconds did it take him to brush his teeth?

24. Which of the following has the most lines of
symmetry?

* A.

2 minutes and 47 seconds

B.

3 minutes and 67 seconds

C.

4 minutes and 17 seconds

D.

16 minutes and 7 seconds

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22. Ashley is visiting her grandparents for the
weekend. Her mom packed 1 pair of black
pants, 1 pair of tan shorts, and 4 shirts: white,
blue, green, and yellow. How many different
outfits can she make from the clothes her
mom packed?

A.

2

B.

4

C.

6

* D.

8

26

A.

B.

C.

*D.


PART II

Released Mathematics Items
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27. Jim’s fish tank holds 40 quarts of water. How
many gallons of water does that equal?

Use the chart below to answer question 25.
The Population of Pulaski County, Arkansas
1960–2000

B.

20

Population

C.

40

1960

242,980

D.

60

1970

287,189

1980

340,613

1990

349,660

2000

361,474

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28. Mr. Taylor told his math students to guess
what pattern block he was holding. He gave
the following clues:
•
•
•

25. According to the table above, which of the
following is a true statement about the
population of Pulaski County, Arkansas?

* B.

10

Year

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A.

* A.

What is it?

It has remained the same.
It has increased every ten years.

C.

It has increased every five years.

D.

It has decreased every ten years.

It has 4 sides.
All of its sides are equal.
It has no right angles.

A.

triangle

B.

hexagon

* C.

rhombus

D.

trapezoid

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26. Mrs. Kramer wrote the following number on
the board:
9,463,187

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29. Ms. Smith wants to cover the floor of her sun
porch with tiles. Which of the following is the
correct formula for finding the area of the
porch?

What is the value of the 6 in this number?
A.

00,006

B.

06,000

* C.

60,000

D.

63,000

27

A.

l+w=A

* B.

l×w=A

C.

2l + 2w = A

D.

l+l+w+w=A


PART II

Released Mathematics Items
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32. I am Sam the Robot. My head is a hexagon.
My legs are right triangles. My body is a
trapezoid. Which robot am I?

Use the table below to answer question 30.
Lengths of Snakes at City Zoo
Black Rat Snake
72"
King Snake
48"
Worm Snake
11"
Scarlet Snake
15"
Brown Snake
13"
Ring-neck Snake
15"

*

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30. The table above shows the lengths of the
snakes at City Zoo. What is the mode of these
lengths?

A.

6"

* B.

15"

C.

29"

D. 57"

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31. What is the rule for the pattern below?

2

4

7

14

17

34

37

A.

Add 2, then add 3 in a repeating pattern.

B.

Double each number.

C.

Double the first number, then double the
next number, then subtract 1.

* D.

Double the first number, then add three
to the next number.

28


PART II

Released Mathematics Items

Use the table below to answer question 33.

Use the chart below to answer question 35.

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Super Cinema Theaters
Adult admission
Children
Large popcorn
Small popcorn
Large soda
Small soda
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33. Alicia took a survey of the fourth-graders in
her class to find out which of the four snacks
above they liked best. Which of the following
statements is true about the data Alicia
collected?

A.

35. Mr. Dunbar took his five-year-old daughter to
the movies. After paying for the admission for
each of them, he bought a large popcorn and
2 small sodas. How much did he spend?

No fourth-graders liked yogurt.

* B.

More fourth-graders like cheese and
crackers than chips.

C.

Fourth-graders like chips better than
yogurt.

D.

More fourth-graders prefer yogurt to
fruit.

$6.25
$3.75
$4.00
$3.00
$1.89
$0.99

A.

$14.98

* B.

$15.98

C.

$16.88

D.

$17.98

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36. Pinnacle Mountain has a height of 1,011 feet.
What would be its height in yards?
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34. Sandra brought a bottle of soda to share at her
class party. What is most likely the size of the
bottle?

* A.

2 liters

B.

20 liters

C.

2 milliliters

D.

20 milliliters

* A.

337 yards

B.

975 yards

C.

1,014 yards

D.

3,033 yards

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37. What number does n represent in order for the
statement below to be true?

6×3=2×n

29

A.

1

B.

3

C.

5

* D.

9


PART II

Released Mathematics Items

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38. Pat’s coach told the team to arrive at the
ballpark 45 minutes before their baseball
game. The game begins at 6:00 P.M. What
time should Pat arrive at the ballpark?

39.

Alex went to a movie. His ticket cost $5.75,
and he bought a popcorn and soda for $3.50.
His change was $10.75. What amount of
money did he take to the movie?

A.

4:45 P.M.

A.

$ 9.25

* B.

5:15 P.M.

B.

$10.00

C.

5:30 P.M.

* C.

$20.00

D.

6:45 P.M.

D.

$21.25

Use the chart below to answer question 40.

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40. Molly made the pictograph above to show how many books were read by all of the fourth-grade students
at Burton Elementary. Students in Ms. Jarrell’s class read a total of 250 books. How many books should
Molly display in the row representing Ms. Jarrell’s class?

* A.

10

B.

25

C.

250

D.

275

30


PART II

Released Mathematics Items

MATHEMATICS OPEN-RESPONSE ITEM A
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A. Each of the four counselors at Camp Lake View must choose one camper from his/her group to go
waterskiing. Each counselor will put the names of all his/her campers in a bag. One name will be drawn
from the bag to select the “winner.” Each group consists of the following:

●
●
●
●

Lonnie’s group: 10 boys and 8 girls
Maria’s group: 8 boys and 10 girls
James’s group: 9 boys and 9 girls
Tonya’s group: 6 boys and 12 girls

1.

Which of the four groups offers the best chance that a boy will win? Explain your answer using
words and/or numbers.

2.

Which of the four groups offers the best chance that a girl will win? Explain your answer using
words and/or numbers.

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. The response contains no incorrect work.
The student earns 3 – 3 ½ points.
The student earns 2 – 2 ½ points.
The student earns ½ – 1 ½ points or shows some minimal understanding.
No understanding is shown.
Blank – No response. A score of “B” will be reported as “NA” (No Attempt – Zero Score).

31


PART II

Released Mathematics Items

Solution and Scoring
Part 1:

(2 points possible)

1 point for correct answer of Lonnie’s group,
AND

1 point for correct and complete work or explanation.
● Give credit for the following explanations or equivalent:
o “Lonnie’s has more boys than any other group and all groups have the same number of
kids (or 18 kids),” or
o “They are the only group with more boys than girls,” or
o “They have the greatest number of boys and the fewest number of girls of any group,” or
o “10/18 are boys,” or “There are 10 chances out of 18.”
OR

½ point for correct, but incomplete work or explanation.
● Example: “Lonnie’s group has the most boys (or more boys) than any group.
Note: Do not give credit for the following incomplete explanation.
● “Lonnie’s group has more boys than girls.” (Doesn’t say “only group.”)
Part 2:

(2 points possible)
1 point for correct answer of Tonya’s group,
AND

1 point for correct and complete work or explanation.
● Give credit for the following explanations or equivalent:
o “Tonya’s has more girls than any other group and all groups have the same number of
kids (or 18 kids),” or
o “They have the greatest number of girls and the fewest number of boys of any group,” or
o “12/18 are girls,” or “There would be 12 chances out of 18.”
OR

½ point for correct, but incomplete work or explanation.
● Example: “Tonya’s group has the most girls (or more girls) than any group.”
Note: Do not give credit for the following incomplete explanation.
● “Tonya’s group has more girls than boys.” (So does Maria’s group.)

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PART II

Released Mathematics Items

MATHEMATICS OPEN-RESPONSE ITEM B

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B. A group of students is helping to paint the basketball court at their neighborhood recreation center. They
need to find the area of the court in order to buy enough paint. They measured the court and found the
length to be 80 feet and the width to be 50 feet.

1.

What is the area of the court? Explain your answer using words, numbers, and/or pictures.

2.

They need to tape the outer edges before painting. They need to find the perimeter so they will know
how much tape they need. How much tape will they need? Explain your answer using words and/or
numbers.

BE SURE TO LABEL YOUR RESPONSES 1 AND 2.

33


PART II

Released Mathematics Items

RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM B
SCORE
4
3
2
1
0
B

DESCRIPTION

The student earns 4 points – Answers must have correct labels.
The student earns 3 points.
The student earns 2 points.
The student earns 1 point or shows some minimal understanding.
Example: A and/or P are reversed with work shown or explained.
No understanding is shown.
Blank – No response. A score of “B” will be reported as “NA” (No Attempt – Zero Score).

Solution and Scoring
Part 1:

(2 points possible)
1 point for correct answer of 4,000 (with or without square feet),
AND

1 point for correct and complete procedure for finding area shown and/or explained.
● Give credit for the following explanations or equivalent:
o Area is found by multiplying the length by the width. The length is 80 feet and the
width is 50 feet. Therefore, the area is 4,000 (square feet), or
o A = 80 x 50 = 4,000 (square feet), or
o Correct procedure (l x w = A) to find area is used, but answer is incorrect due to a
calculation or copy error.

Note: Do not give credit for copying the formula l x w = A only.
Part 2:

(2 points possible)
1 point for correct answer of 260 (with or without feet),
AND

1 point for correct and complete procedure for finding perimeter shown and/or explained.
● Give credit for the following explanations or equivalent:
o Perimeter is found by multiplying the length and the width times two, then adding these
two numbers. Two times 80 is 160. Two times 50 is 100; therefore 160 added to 100 is
260 feet, or
o P = 2l + 2w = 2(80) + 2(50) = 160 + 100 = 260 (feet), or
o Diagram correctly labeled on all four sides (l = 80, w = 50), or
o Correct procedure (l + l + w + w = P) to find perimeter is used, but answer is incorrect
due to a calculation or copy error.

Note: Do not give credit for copying the formula l + l + w + w = P or 2l + 2w = P only.
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PART II

Released Mathematics Items

MATHEMATICS OPEN-RESPONSE ITEM C
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C. Barb and William are each growing sweet potato vines. Barb’s plant measures one-and-a-half feet long.
William’s plant measures 24 inches long.

1.

Whose plant is longer? Explain your answer using words and/or numbers.

2.

How much must William’s plant grow before it is one yard long? Explain your answer using words
and/or numbers.

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

0
B

DESCRIPTION

The student earns 4 points – Answers must have correct labels.
The student earns 3 points.
The student earns 2 points.
The student earns 1 point or shows some minimal understanding.
No understanding is shown.
Blank – No response. A score of “B” will be reported as “NA” (No Attempt – Zero Score).

Solution and Scoring
Part 1:

(2 points possible)
1 point for correct answer of William’s plant is longer.
● Note: Do not give credit if there is clear evidence of incorrect procedure.
AND

1 point for correct conversion of Barb’s 1 ½ foot plant into 18 inches or William’s 24 inch plant
into 2 feet shown and/or explained.
● Give credit for any of the following explanations or equivalent:
o 12 + 6 = 18 and 24 >18, or
o 24/12 = 2 and 2 >1 ½, or
o “Twenty-four inches equals two feet, so William’s plant is longer,” or
o “His plant is longer since a foot and a half would only be eighteen inches.”

● Do not give credit for the following incomplete explanations:
o “His plant is 6 inches longer,” or

o “His plant is longer since 24 inches is longer than 1 ½ feet.”

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PART II
Part 2:

Released Mathematics Items

(2 points possible)
1 point for correct answer of “12 inches” or “1 foot.” Label must be correct.
AND

1 point for correct procedure shown and/or explained.
● Give credit for any of the following explanations or equivalent:
o There are 36 inches in a yard. William’s plant is 24 inches long. The difference is
12 inches, or
o 1 yard = 3 feet and he has 2 feet. Therefore, it needs to grow 1 foot, or
o 1 yard = 36 inches. 36 - 24 = 12 inches.
OR

● Answer is incorrect due to a calculation or copy error, but correct procedure is used.
o Example: 36 - 24 = 11 inches.
♦ Note: Credit will be received for the procedure, but not for the answer.

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PART II

Released Mathematics Items

MATHEMATICS OPEN-RESPONSE ITEM D

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D. Dwight and his brother, Jim, decided what they would like to eat for breakfast every day for a month.
They each began filling in the calendar above with their favorite breakfast foods.

1.

If Dwight’s pattern on the calendar above continues, how many times during the month will he have
eggs? Explain your answer using words, numbers, and/or pictures.

2.

If both Dwight’s and Jim’s patterns continue, how many days during the month will both boys have
the same thing for breakfast? Explain your answer using words, numbers, and/or pictures.

BE SURE TO LABEL YOUR RESPONSES 1 AND 2.

37


PART II

Released Mathematics Items

RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM D

SCORE
4
3
2
1
0
B

DESCRIPTION
The student earns 4 points.
The student earns 3 points.
The student earns 2 points.
The student earns 1 point or shows some minimal understanding.
No understanding is shown.
Blank – No response. A score of “B” will be reported as “NA” (No Attempt – Zero Score).

Solution and Scoring
Part 1:

(2 points possible)
1 point for correct answer of Dwight eats eggs 10 times,
AND
1 point for correct and complete procedure shown and/or explained.
● Give credit for the following explanations or equivalent (Answer might not be “10.”):
o “He has eggs on the 2nd ,5th ,8th, 11th, 14th, 17th, 20th, 23rd, 26th, and 29th;” or
o “He has eggs on the 2nd and every third day after that;” or
o 31/3 = 10 r1; or
o Correct number of times eggs are eaten each week (1 + 3 + 2 + 2 + 2); or

o Calendar is correctly filled out indicating days when Dwight eats eggs. (Dates do not have to

be circled.)

Note: Do not give credit for incorrect or incomplete procedures:
● Student continues the pattern past May 31st. (Incorrect procedure. This usually follows an
answer of “He has eggs 11 times.”)
● “The pattern is CEW,” or “I did the pattern.” (Incomplete procedure.)

38


PART II
Part 2:

Released Mathematics Items

(2 points possible)
1 point for correct answer of they will eat the same things 11 times,
AND
1 point for correct and complete procedure shown and/or explained.
● Give credit for the following explanations or equivalent (Answer might not be “11.”):
o “They will both have –
♦ Cereal on the 1st, 7th, 13th, 19th, 25th, and 31st; and
♦ Waffles on the 6th, 12th, 18th, 24th, and 30th,” or
o “They will eat the same things on the following dates: 1, 6, 7, 12, 13, 18, 19, 24, 25, 30,
and 31,” or
o “They will both have cereal on the first day of the month and every sixth day after that.
They will both have waffles every sixth day,” or
o Correct number of times they have the same breakfast each week (1 + 2 + 3 + 3 + 2), or

o Calendar is correctly filled out indicating days when they eat the same thing. (Dates do not

have to be circled.)

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PART II

Released Mathematics Items

MATHEMATICS OPEN-RESPONSE ITEM E

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E. Jake used the 100’s chart above to solve a mystery number puzzle with the following clues:

● It is a two-digit number greater than 23, but less than 50.
● It is an even number.
● Two, four, and twelve are some of its factors.
● The sum of its digits is a two-digit number.
What is the mystery number?
Use words, pictures, and/or numbers to explain your answer.
RUBRIC FOR MATHEMATICS OPEN-RESPONSE ITEM E
SCORE
4

DESCRIPTION
Correct answer of 48. Work and/or explanation is correct and contains:
• Elimination Clue by Clue Method:
Numbers, charts, lists, calculations and/or words clearly show or explain the procedure of
elimination. Clues 1 and 2 may be combined. At a minimum, the numbers remaining after

performing Clue 3 (24, 36 and 48) or Clue 4 if reversed (28, 38, 46 and 48) are listed.
OR
• “48 is the number that fits the Clues” Method:
Four clues are addressed or repeated. Work is shown for Clue 3 AND Clue 4.
Elimination may be partial or missing.
o Example: “It’s 48 because it’s between 24 and 49, it’s even, 2, 4 and 12 are factors because
48/2 = 24 and 48/12 = 4, and the sum of its digits is a 2-digit number since 4 + 8 = 12.

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PART II

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3

Correct answer of 48. Work and/or explanation is incomplete, but is beyond repeating clues.
• Elimination Method is shown or explained (for at least Clues 1 and 2), but elimination using
other clues is missing or incomplete in some respect. Three to four clues are addressed or
repeated.
o Example: Verbal description of elimination clue by clue, but the numbers remaining after
performing Clue 3 (or Clue 4 if reversed) are not listed.
o Example: 23-50 are listed, with all numbers crossed out except 48 without differentiation
between clues or explanation.
o Example: Chart lists numbers between 23 and 50 and eliminates odd numbers. Clue 3 and/or
Clue 4 are addressed or repeated.
OR
• “48 is the number that fits the Clues.” Method is incomplete, but some work is shown for
either Clue 3 OR Clue 4. Three to four clues are addressed or repeated. Elimination of other

numbers is partial or missing:
o Example: “It’s 48 because it’s between 24 and 49, it’s even, 48/2 = 24 and 48/12 = 4.”

2

• Answer of 24, 36 and 48. Response explains process of elimination by going through Clues 1,
2 and 3, with 24, 36 and 48 remaining. (Does not proceed far enough – Clue 4 is not
addressed.)
OR
• Answer of 28, 38, 46 and 48. Response explains process of elimination by going through
Clues 1, 2 and 4, with 28, 38, 46 and 48 remaining. (Does not proceed far enough – Clue 3 is
not addressed.)
OR
• Correct answer of 48. Three to four clues are addressed or repeated with no supporting work
for Clue 3 and no supporting work for Clue 4.
o Example: “It’s 48 because it’s between 24 and 49, it’s even, 2, 4, and 12 are factors and the
sum of its digits is a 2-digit number.”
OR
• Correct answer of 48. One to two clues are addressed or repeated, with or without work or
elimination shown and/or explained.
o Example: “It’s 48 because it’s between 24 and 49 and it’s even.”

1

• Answer of 48. No clues are addressed, no work is shown or explained, or work contains
vague, but not incorrect, procedure.
OR
• Answer is an even number between 23 and 50 (≠ 48). At least one clue is addressed.
o Example: “It’s 44 because it’s greater than 23 and less than 50.”
o Example: “It’s 24 because 2, 4, and 12 are its factors.”

0

No understanding shown.
o Example: 48 with obvious use of incorrect procedure.
o Example: An even number (≠ 48) between 23-50 with no clues addressed: “It’s 44.”
o Example: Any odd number.

B

Blank – No response. A score of “B” will be reported as “NA” (No Attempt – Zero Score).

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PART II

Released Mathematics Items

Solution and Scoring

Answer: The mystery number is 48.
Explanations may be:
● Numerical –
o Clue 1: All numbers from 24 to 49 (or 23 to 50) are listed.
o Clue 2: All odd numbers are eliminated: 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48
remain.
o Clue 3: All numbers that do not have two, four and twelve as factors are eliminated: 24, 36
and 48 remain.
o Clue 4: All numbers whose digit sum is not a two-digit number are eliminated: only 48

remains.

Note: Some students perform Clue 4 before Clue 3 (after Clues 1 and 2).
♦ Example: 28, 38, 46 and 48 remain since the digit sum is a 2-digit number. Then, the only
number remaining with factors of 2, 4 and 12 is 48.
OR

● A chart – The numbers are listed and eliminated clue by clue. The clues are differentiated in
some way.

OR

● Verbal – The response contains a correct and complete verbal explanation of the procedure
using elimination clue by clue, with at least 24, 36, and 48 mentioned (or 28, 38, 46, and 48 if
Clue 4 is performed before Clue 3).
o Example: “First, I omitted all of the numbers that were not greater than 23 or less than 50.
Then I omitted all of the odd numbers, since it said the number was even. Then I crossed
out all of the numbers that 2, 4, and 12 did not go into, leaving 24, 36 and 48. Then I saw
which of these numbers had a 2-digit sum and it was 48.”

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PART II

Released Mathematics Items

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)

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