5th Grade Number and Operations
Name
Core and Extended Core Items
1. Draw a picture that proves each of the following:
20 divided by 4 = 5
33 divided by 5 = 6 r 3
2. Which number sentence would you write for this problem:
How many cookies would each friend get if 15 cookies were shared among
5 friends?
a. 15 + 5 = ?
b. 15 ÷ 5 = ?
c. 15 x 5 = ?
d. 15 – 5 = ?
3. Which number shows 24 divided by 8
8
24
24
b.
8
a.
c. 2
4
8
d. 2
8
4
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4. Which mathematical statement correctly represents this situation:
There are 30 minutes until lunchtime. It takes Jacob 6 minutes to read each
page in his book. How many pages will he read before lunch?
a. 30 x 6
b. 30 ÷ 6
c. 30 – 6
d. 30 + 6
5. 42 divided by 5 is 8, with 2 left over. This can be written as:
42 ÷ 5 = 8 r 2.
Which math sentence means the same thing?
a. 8 x 5 + 2 = 42
b. 2 x 5 + 8 = 42
c. 5 + 8 x 2 = 42
d. 5 x 8 x 2 = 42
6. What is the greatest number you can get as a remainder when you
divide by 6?
a. 6
b. 5
c. 4
d. any number
Explain your answer:
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Select the correct mathematical sentence for each problem in #7 and #8.
7. How many people can share 20 cookies, if each person gets 4 cookies?
a. 20 ÷ 4 = ?
b. 20 – 4 = ?
c. 4 x 20 = ?
d. 4 + 20 = ?
8. How many buses would be needed for a group of 90 people, if each bus
holds 30 people?
a. 30 + 90 = ?
b. 90 – 30 = ?
c. 30 x 90 = ?
d. 90 ÷ 30 = ?
9. Jennie was assigned this problem:
146
x 25
She worked out the problem in this way:
146 x 5 = 730 and
146 x 2 = 292
Then she added 292 + 730. She thought that her answer was probably wrong
because it seemed too small. What should she have done differently?
a. 146 x 50
b. 146 x 20
c. 146 x 200
d. 140 x 2
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10. Find the answer without using a calculator. Show your work.
3241 multiplied by 37 =
11. Philip solved the following problem incorrectly. Explain his mistake.
1659
x 21
1659
+3318
4977
12. Suzy has 12 cousins. She received $15.00 from each cousin for her
birthday. How much money did she receive in all?
a. $180
b. $ 27
c. $ 45
d. $120
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13. Pablo has collected 1,225 marbles. He decides to share them equally with
the students in his class. There are 25 students including Pablo. How many
marbles will each student get?
a. 1250 marbles
b. 409 marbles
c. 48 marbles
d. 49 marbles
14. Solve the following problems without using a calculator:
4806 ÷ 15 =
a. 32
b. 320 r 6
c. 320 r 4
d. 320
15. Find 647 ÷ 21
a. 3 r 17
b. 30 r 8
c. 30 r 17
d. 308
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Show which is larger, smaller or equal using the less than symbol ( < ), the
greater than symbol ( > ), or the equal sign ( = ) for each of the following.
16. 0.02 __ 0.20
____ (Put a, b or c here. See the key below.)
17. 0.03 __ 0.003
____
18. 0.040 __ 0.004
____
19. 0.500 __ 0.005
____
Use a for less than ( < ), b for greater than ( > ) and c for equal ( = )
20. 0.1 = _______ hundredths
a.
b.
c.
d.
1 hundredth
10 hundredths
100 hundredths
0.01 hundredths
21. What percent is shown in this picture?
a. 4%
b. 40%
c. 44%
d. 14%
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22. What percent is shown in this picture?
a. 40%
b. 42%
c. 24%
d. 18%
23. What percent is shown in this picture?
a. 60%
b. 15%
c. 35%
d. 25%
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24. Thirty-five percent can also be written as:
a. 3.5%
b. 30.5%
c. 35%
d. 350%
25. 40 out of 50 can be written as a percent like this:
a. 10%
b. 40%
c. 60%
d. 80%
26. If you have
1
of a pizza, what percent of the pizza do you have?
4
a. 40%
b.50%
c. 25%
d. 30%
27. 1.0 = _________ tenths
a. 0.1 tenths
b. 1 tenth
c. 10 tenths
d. 100 tenths
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28. Sixty percent can be written using the percent symbol as
a. 6%
b. 30%
c. 60%
d. 160%
29. Solve each problem & explain any patterns you see.
6 x .01 = ______________
6 x 0.1 = ______________
6 x 1.0 = ________________
6 x 10 = _______________
6 x 100 = ______________
6 x 1000 = ______________
Patterns?
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30. Explain how to divide by 10, 100, & 1000 without using a calculator.
31. Solve the following: 15 x 0.2 =
a. 0.3
b. 0.35
c. 3.0
d. 30.0
3
1
pounds of jellybeans and Sarah has pounds. Write a math
8
2
sentence you could use to find how many pounds they have together.
32. Jim has
a.
1 3
x
2 8
b.
1 3
2 8
c.
1
3
+
8
2
d.
1
3
÷
2 8

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33. In problem 32 above, would Jim and Sarah have more than one pound all
together, or less than one pound?
a. more
b. less
34. Use the math sentence you selected in #32 to find how many pounds they
have together.
a. 3/16 pounds
b. 1/8 pounds
c. 7/8 pounds
d. 4/3 pounds
7
1
yard of wood. She uses yard to build a birdhouse. Which
8
3
math sentence shows how much wood is left over.
35. Beth has
 7 1
a. ÷
8

1 7
–
3 8
c.
7 1
x
8 3
d.
7 1
–
8 3

 
3
b.
 

 
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36. Solve the following:
3 x 0.65 =
a. 0.195
b. 0.95
c. 1.95
d. 19.5
37. Don has $12.32 in his piggy bank. He collects and returns pop cans for
$3.70. How much money does he have together? (Round answer to the
nearest whole dollar.) Explain why your answer makes sense.
a. $15
b. $16
c. $8
d. $17
38. Express
36
as a decimal and a percent. decimal:
100
percent:
39. 
Express 0.65 as a fraction and a percent. fraction:
percent:
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40. Express 7% as a fraction and a decimal. fraction:
decimal:
41. Express
7
as a decimal and a percent. decimal:
20
percent:
42.Suzi wanted to buy a new shirt that cost $24. It was on sale for 20% off. To
figure out how much she would save, she changed 20% to a fraction.
Which calculation did she use to figure out how much she would save?
a. 24 x
1
20
b. 24 x 20
1
 c. 24 x 2
d. 24 x

1
5
43. Mr. Moeckle buys 5 pizzas for 18 people. Express the ratio of pizzas to
people in the following ways:
in ratio form with a colon: ____________________
as a fraction: __________________
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44. A recipe uses 3 cups of flour for 2 dozen cookies. Which ratio shows how
many cups of flour would be needed for 8 dozen cookies?
a. 3:2
b. 12:8
c. 5:8
d. 11:10
45. Find an equivalent ratio for 7 boys to 10 girls:
a. 49:70
b. 10:7
c. 10:13
d. 17:20
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Item
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Correct Answer
First picture should show either 20 objects divided into 4
groups of 5 or 20 objects divided into 5 groups of 4, or a
whole (e.g. an area model) divided into 20 parts, then
fourths or fifths shaded. Same for 2nd picture, but showing 3
left over.
b
b
b
a
b Explanations will vary. An acceptable explanation is that
if you get a remainder greater than 5 (that is, if the
remainder is 6 or 7) that means that the remainder is still
divisible by 6, so the division problem is not “finished.”
a
d
b
Answer is 119917. Students may use several different ways
to calculate this multiplication. Check their work to look for
common computational errors if they don’t get the right
answer.
When Philip multiplied by the 2 in 21, he didn’t show that
he was actually multiplying by 20. When he lined up 3318
directly below 1659, he was only multiplying by 2, not by
20. The correct answer is 34,839.
a
d
b
c
a (<)
b (>)
GLCE
N.MR.05.01
b (>)
b (>)
b
b
c
a
c
d
c
c
c
.06, 0.6, 6.0, 60, 600, 6000
Pattern: Each successive answer increases by 10 times.
Several answers are possible. One would be to make the
N.ME.05.08
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N.ME.05.09
N.ME.05.09
N.ME.05.09
N.ME.05.09
N.ME.05.09
N.ME.05.09
N.ME.05.08
N.ME.05.09
N.MR.05.15
N.MR.05.01
N.MR.05.01
N.MR.05.01
N.MR.05.02
N.MR.05.02
N.MR.05.03
N.MR.05.03
N.FL.05.04
N.FL.05.04
N.FL.05.04
N.MR.05.05
N.MR.05.05
N.FL.05.06
N.FL.05.06
N.ME.05.08
N.ME.05.08
N.FL.05.16 NASL
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31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
number smaller by one (or two, or three) decimal places.
c
c
b
c
d
c
b Answer makes sense because $3.70 and $12.30 is $16 (or
similar reasoning).
0.36, 36%
65/100 (or 13/20), 65%
7/100, 0.07
0.35, 35%
d
5:18
5 pizzas to 18 people (or 5 to 18)
5/18
b
a
50 = 25 * 2 = 5 * 5 * 2 or 50 = 10 * 5 = 2 * 5 * 5
50 = 2 * 52
43 = 43 * 1
Every whole number (except 1) is a product of prime
numbers, at least a product of itself and 1.
a
d
a
d
Picture could show a whole object (like a pizza or a
rectangle) divided into 8 equal pieces, with 5 of the pieces
shaded. Or it could show 8 objects, with 5 circled. Or it
could show the number 5/8 on the number line (between ½
and 1). All of these are equivalent representations for the
fraction 5/8. Other drawings are possible, for example, 5
objects divided into 8ths, with one of the 8ths shaded on
each object. A corresponding problem would be If you had
5 candy bars and wanted to share among 8 people, how
much would each person get?
Rectangle should be divided into 1/4ths in one direction and
1/3s in the other direction, making 12 equal pieces. One of
the pieces should be shaded. Students might label one
column as 1/3 and one row as ¼, or vice versa, although the
labeling would not be critical if they showed one piece
shaded.
Multiple choice answer is c
a
c
N.MR.05.17
N.FL.05.18; N.FL.05.20
N.FL.05.18; N.FL.05.20
N.FL.05.20
N.MR.05.18
N.MR.05.17
N.FL.05.20
N.MR.05.22
N.MR.05.22
N.MR.05.22
N.MR.05.22
N.MR.05.22
N.ME.05.23
N.ME.05.23
N.ME.05.23
N.MR.05.07
N.MR.05.07
N.MR.05.07
N.ME.05.10
N.ME.05.11
N.ME.05.10
N.ME.05.12
N.FL.05.13
N.FL.05.13
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55
56
57
58
59
60
61
d
a
d
d
b
c
a
N.FL.05.14
N.FL.05.14
N.ME.05.11
N.MR.05.19
N.MR.05.19
N.MR.05.21
N.MR.05.21
GLCEs in grey are designated as “future core” by MEAP. Those items are on the
following pages.
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5th Grade Number and Operations Assessment
Items sorted according to GLCE (core and extended core GLCEs only)
Item
1
GLCE
N.MR.05.01
12
13
14
15
16
17
Correct Answer
First picture should show either 20 objects divided into 4
groups of 5 or 20 objects divided into 5 groups of 4, or a
whole (e.g. an area model) divided into 20 parts, then
fourths or fifths shaded. Same for 2nd picture, but showing 3
left over.
b
b
b
a
b Explanations will vary. An acceptable explanation is that
if you get a remainder greater than 5 (that is, if the
remainder is 6 or 7) that means that the remainder is still
divisible by 6, so the division problem is not “finished.”
a
d
b
Answer is 119917. Students may use several different ways
to calculate this multiplication. Check their work to look for
common computational errors if they don’t get the right
answer.
When Philip multiplied by the 2 in 21, he didn’t show that
he was actually multiplying by 20. When he lined up 3318
directly below 1659, he was only multiplying by 2, not by
20. The correct answer is 34,839.
a
d
b
c
a (<)
b (>)
18
19
20
27
21
22
23
24
25
26
28
29
b (>)
b (>)
b
c
b
c
a
c
d
c
c
.06, 0.6, 6.0, 60, 600, 6000
N.ME.05.08
N.ME.05.08
N.ME.05.08
N.ME.05.08
N.ME.05.09
N.ME.05.09
N.ME.05.09
N.ME.05.09
N.ME.05.09
N.ME.05.09
N.ME.05.09
N.MR.05.15
2
3
4
5
6
7
8
9
10
11
N.MR.05.01
N.MR.05.01
N.MR.05.01
N.MR.05.02
N.MR.05.02
N.MR.05.03
N.MR.05.03
N.FL.05.04
N.FL.05.04
N.FL.05.04
N.MR.05.05
N.MR.05.05
N.FL.05.06
N.FL.05.06
N.ME.05.08
N.ME.05.08
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30
31
36
35
32
33
34
37
38
39
40
41
42
43
44
45
Pattern: Each successive answer increases by 10 times.
Several answers are possible. One would be to make the
number smaller by one (or two, or three) decimal places.
c
c
d
c
b
c
b Answer makes sense because $3.70 and $12.30 is $16 (or
similar reasoning).
0.36, 36%
65/100 (or 13/20), 65%
7/100, 0.07
0.35, 35%
d
5:18
5 pizzas to 18 people (or 5 to 18)
5/18
b
a
N.FL.05.16 NASL
N.MR.05.17
N.MR.05.17
N.MR.05.18
N.FL.05.18; N.FL.05.20
N.FL.05.18; N.FL.05.20
N.FL.05.20
N.FL.05.20
N.MR.05.22
N.MR.05.22
N.MR.05.22
N.MR.05.22
N.MR.05.22
N.ME.05.23
N.ME.05.23
N.ME.05.23
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5th Grade Number and Operations
Name
Future Core Items
46. Find all factors of the following numbers and write the final answer using
exponential notation (powers).
50
43
47. Which of the following shows the correct prime factorization for 48?
a. 24 x 3 = 48
b. 33 x 2 = 48
c. 62 x 2 = 48
d. 42 x 32 = 48
48. Which of the following shows the correct prime factorization for 27?
a. 3 x 9 = 27
b. 32 = 27
c. 32 x 2 = 27
d. 33 = 27
49. Which of the following shows 2 ÷ 3 as a fraction?
a.
2
3
b.
3
2
c.
2
2
3
d.
3
3
2
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50. Choose an equivalent fraction for
1
3
and an equivalent fraction for
that
2
4
both use the same denominator:
equivalent
fraction for
equivalent
fraction for
1
2
3
4
a.
1
3
3
4
b.
3
2
3
4
c.
4
8
3
8
d.
4
8
6
8
51. Make a picture to show 5 ÷ 8
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52. Show how you would find the product of these fractions using the rectangle
as an area model. Then circle the correct answer.
1 1
x
4 3
a.
1
7
b.
2
7
c.
1
12
d.
2
12
=
53. Solve the following: 2 ÷
1
=
4
a. 8
b.
1
2
2
4
d. 2
c.
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54. Solve the following:
a.
4
3
b.
1
7
c.
1
12
1
÷4=
3
d. 12
55. Solve the following:
a.
7
11
b.
12
28
c.
1
3
d.
37
28
56. Solve the following:
a.
11
60
b.
5
7
c.
9
17
d.
5
60
3
4
+
=
7
4
7 2
=
12 5
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57. Which of these pairs shows
a.
3
6
and
4
4
b.
2
1
and
2
2
c.
3
6
and
8
8
d.
6
4
and
8
8
1
3
and
with common denominators?
2
4
1
3
of a cake to class, and Joe brought of a cake on the
2
4
same day. How much cake did the class have altogether? Show your work.
58. Patty brought
a.
1
cake
4

b. 1 cake

c.
4
cake
6
d. 1
1
cakes
4


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7
3
cups of milk. He gave 1 cups of milk to his cat. How much
8
4
milk did he have left? Show your work.
59. Paul had 3
a. 2 cups

1
b. 2 cups

8
4
c. 2 cups
4

7
d. 1 cups
8
5
1
60. In the equation + x =
, what does x = ?
12
3

a.

4
9

5
b.
4
c.
1
12
d.
3
12

61. Solve for x:
9
a.
16



13
1
-x =
16
4
12
b.
 12

c.
1
4
d.
5
16

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