th
5 Grade
Math
Sample Items
Aligned to
CCSS
Created for Morehouse Parish Schools by Dr. Stacey Pullen
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5th Grade
Sample Math Items Aligned to CCSS
Table of Contents
CCSS Code
5.0A.A.1
5.0A.A.2
5.0A.B.3
5.NBT.A.1
5.NBT.A.2
5.NBT.A.3
5.NBT.A.3a
5.NBT.A.3b
5.NBT.A.4
5.NBT.B.5
5.NBT.B.6
5.NBT.B.7
5.NF.A.1
5.NF.A.2
5.NF.B.3
5.NF.B.4
5.NF.B.4a
5.NF.B.4b
5.NF.B.5
5.NF.B.5a
5.NF.B.5b
5.NF.B.6
5.NF.B.7
5.NF.B.7a
5.NF.B.7b
5.NF.B.7c
5.MD.A.1
5.MD.B.2
5.MD.C.3
5.MD.C.3a
5.MC.C.3b
Page #
3
4
6
7
10
11
13
14
15
16
17
19
21
22
25
26
27
28
29
31
32
33
34
35
36
37
38
39
40
42
43
CCSS Code
5.MD.C.4
5.MD.C.5
5.MD.C.5a
5.MD.C.5b
5.MD.C.5c
5.G.A.1
5.G.A.2
5.G.B.3
5.G.B.4
Key
Rubrics
Origination of Items
2
Page #
44
45
47
48
49
50
51
53
54
55
57
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
5th Grade
Sample Math Items Aligned to CCSS
5. OA.A.1
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with
these symbols. (Conceptual Understanding & Procedural Skill and Fluency)
What test questions look like:
Sample 1:
What is the value of 13 × [4 + (9 – 2)]?
Enter your answer in the box.
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by Dr. Stacey Pullen
5. OA.A.2
Write simple expressions that record calculations with numbers, and interpret numerical
expressions without evaluating them. For example, express the calculation "add 8 and 7, then
multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 +
921, without having to calculate the indicated sum or product. (Conceptual Understanding)
What test questions look like:
Sample 1:
Katie went to a craft store to purchase the supplies she needed to make two types of jewelry. This table
shows the costs of the supplies Katie needed. Costs of Supplies
Item
Cost per Item
bead
$0.05
charm
$0.45
This table shows the supplies needed to make each piece of jewelry.
Supplies Needed
Type of Jewelry
Beads
Charms
bracelet
25
4
necklace
48
1
Katie purchased the exact amount of supplies to make 1 bracelet and 2 necklaces.
Part A
Write an expression to determine the cost of supplies to make 1 bracelet.
Enter your expression in the box provided.
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by Dr. Stacey Pullen
Part B
Write an expression to determine the cost of supplies to make 2 necklaces.
Enter your expression in the box provided.
Sample 2:
Which expression matches the statement “the sum of 2 and 4 subtracted from 9”?
A
2+9–4
B
9–2+4
C
9 – (2 + 4)
D
(2 + 4) – 9
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. OA.B.3
Generate two numerical patterns using two given rules. Identify apparent relationships
between corresponding terms. Form ordered pairs consisting of corresponding terms from the
two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule
"Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0,
generate terms in the resulting sequences, and observe that the terms in one sequence are
twice the corresponding terms in the other sequence. Explain informally why this is so.
(Conceptual Understanding)
What test questions look like:
Sample 1:
Two number patterns are described below.
•
•
Pattern 1 starts at 4 and follows the rule “Add 5.”
Pattern 2 starts at 4 and follows the rule “Add 4.”
Which statement about the two number patterns is correct?
A
The difference between the corresponding terms in each pattern is always 1.
B
The difference between the corresponding terms in each pattern is never less than 1.
C
The difference between the corresponding terms in each pattern is always greater than 1.
D
The difference between the corresponding terms in each pattern continues to increase by 1.
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by Dr. Stacey Pullen
5. NBT.A.1
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it
represents in the place to its right and 1/10 of what it represents in the place to its left.
(Conceptual Understanding)
What test questions look like:
Sample 1:
The distance from Neptune's north pole to its center is about 24,341 kilometers.
24,341
The value of the underlined 4 is how many times as much as the value of the 4 that is not
underlined?
Enter your answer in the box.
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
Sample 2:
Leah incorrectly added the fractions
,
, and
. She said that to add fractions with different
denominators, you use the common denominator and add the numerators. Leah’s work is shown.
+
+
2 + 1 + 5 12
•
What is Leah's mistake?
•
Find the correct value of
•
Show your work or explain your answer.
.
Enter your answers and your work or explanation in the box provided.
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by Dr. Stacey Pullen
Sample 3:
Which statement correctly compares two values?
A. The value of the 6 in 26.495 is
the value of the 6 in 17.64.
B. The value of the 6 in 26.495 is 10 times the value of the 6 in 17.64.
C. The value of the 6 in 26.495 is
the value of the 6 in 17.64.
D. The value of the 6 in 26.495 is 100 times the value of the 6 in 17.64.
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by Dr. Stacey Pullen
5. NBT.A.2
Explain patterns in the number of zeros of the product when multiplying a number by powers
of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied
or divided by a power of 10. Use whole-number exponents to denote powers of 10.
(Conceptual Understanding)
What test questions look like:
Sample 1:
Two expressions are shown.
Expression A: 6 × 102
Expression B: 6 × 108
Each expression can be written in standard form.
Which statement best explains how the expressions are different when they are written in
standard form?
E
Expression A has 4 more zeroes than Expression B.
F
Expression A has 6 more zeroes than Expression B.
G
Expression B has 4 more zeroes than Expression A.
H
Expression B has 6 more zeroes than Expression A.
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. NBT.A.3
Read, write, and compare decimals to thousandths. (Conceptual Understanding)
What test questions look like:
Sample 1:
Leroy is learning to write decimals in various forms.
Part A
How should Leroy write eight hundred twenty-seven thousandths in numerical form?
Part B
How should Leroy write 0.445 in words?
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
Sample 2:
Anna put multi-digit numbers in a list from least to greatest, using her knowledge of the
place value system.
Which list shows the numbers correctly ordered from least to greatest?
A. 0.2; 0.02; 0.002; 0.202
B. 0.002; 0.202; 0.02; 0.2
C. 0.002; 0.02; 0.2; 0.202
D. 0.202; 0.2; 0.02; 0.002
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. NBT.A.3a
Read and write decimals to thousandths using base-ten numerals, number names, and
expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
(Conceptual Understanding)
What test questions look like:
Sample 1:
Lana is creating a video. Her computer shows that the video is 184.026 seconds long. She writes
the length of the video in expanded form.
Which expression represents the value of one of the digits in the length of Lana’s video?
A
1 × 1000
B
2×
C
4 × 10
D
6×
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. NBT.A.3b
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =,
and < symbols to record the results of comparisons. (Conceptual Understanding)
What test questions look like:
Sample 1:
Which inequality will be true when the > symbol is placed in the blank?
A. 0.009 _____0.1
B. 0.8_____0.777
C. 22.266 _____ 221.5
D. 321.253 _____ 321.258
Sample 2:
Shelly’s guinea pig weighs 0.2 kilograms. Leo’s hamster weighs 90 grams.
Express the weights of the two pets in kilograms in the box below. Then use place value
concepts to explain which weight is greater.
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. NBT.A.4
Use place value understanding to round decimals to any place. (Conceptual Understanding)
What test questions look like:
Sample 1:
Which number would be 4.875 when rounded to the nearest thousandth?
A
4.8755
B
4.8759
C
4.87409
D
4.87509
Sample 2:
What is 75.32 rounded to the nearest tenth?
Enter your answer in the box.
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by Dr. Stacey Pullen
5. NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm. (Procedural Skill and
Fluency)
What test questions look like:
Sample 1:
What is 402 × 365?
A
12,010
B
15,330
C
146,730
D
146,780
Sample 2:
Joshua planted carrots and peas in his garden.
Pea
1 yard
Carr ot
2 yards
Use the model to write and solve an equation that shows how much larger in square yards the pea
section of the garden is than the carrot section of the garden.
Enter your equation and your solution in the box provided.
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. NBT.B.6
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors,
using strategies based on place value, the properties of operations, and/or the relationship between
multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays,
and/or area models. (Conceptual Understanding & Procedural Skill and Fluency)
What test questions look like:
Sample 1:
A teacher drew an area model to find the value of 6,986 ÷ 8.
Teacher’s Model for 6,986 ÷ 8
800
N
P
M
560
Q
R
not to scale
•
•
•
Determine the number that each letter in the model represents and explain each of your
answers.
Write the quotient and remainder for 6,986 ÷ 8.
Explain how to use multiplication to check that the quotient is correct. You may show your
work in your explanation.
Enter your answers and your explanations in the box provided.
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
Sample 2:
Emilio is tiling a countertop with square tiles. Each tile covers 64 square inches. The total area of
the countertop is 5,184 square inches. What is the minimum number of tiles Emilio will need to tile
the entire countertop?
Enter your answer in the box.
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. NBT.B.7
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and
strategies based on place value, properties of operations, and/or the relationship between addition and
subtraction; relate the strategy to a written method and explain the reasoning used. (Conceptual
Understanding & Procedural Skill and Fluency)
What test questions look like:
Sample 1:
Sandra buys stamps that cost $0.65 each. She spends a total of $158.60 on the stamps. To
determine how many stamps she buys, she needs to divide 158.60 by 0.65.
How many stamps does Sandra buy?
A. 204
B. 244
C. 2,044
D. 2,440
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
Sample 2:
Katie went to a craft store to purchase the supplies she needed to make two types of jewelry. This table
shows the costs of the supplies Katie needed. Costs of Supplies
Item
Cost per Item
bead
$0.05
charm
$0.45
This table shows the supplies needed to make each piece of jewelry.
Supplies Needed
Type of Jewelry
Beads
Charms
bracelet
25
4
necklace
48
1
Katie purchased the exact amount of supplies to make 1 bracelet and 2 necklaces.
Part A
Write an expression to determine the cost of supplies to make 1 bracelet.
Enter your expression in the box provided.
Part B
Write an expression to determine the cost of supplies to make 2 necklaces.
Enter your expression in the box provided.
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. NF.A.1
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given
fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of
fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d =
(ad + bc)/bd.) (Procedural Skill and Fluency)
What test questions look like:
Sample 1:
Sarah and her dad are moving a pile of bricks from the front of their house to the back. Sarah
moves
of the pile. Her dad moves
of the pile. Which expression could be used to find
the total fraction of the pile that Sarah and her dad moved together?
A.
+
B.
C.
D.
+
+
+
Sample 2:
What fraction completes the equation?
–
=n
A.
B.
C.
D.
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. NF.A.2
Solve word problems involving addition and subtraction of fractions referring to the same whole,
including cases of unlike denominators, e.g., by using visual fraction models or equations to represent
the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess
the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing
that 3/7 < 1/2. (Conceptual Understanding & Application)
What test questions look like:
Sample 1:
Karla is mowing her lawn. She mows
of the lawn before stopping for a snack. She resumes
mowing after her snack and mows another of her lawn before stopping for lunch. What total
fraction of her lawn does Karla mow before lunch?
A
B
C
D
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
Sample 2:
Mika takes the same quiz two days in a row.
•
•
On the first day, she answers of the questions correctly.
On the second day, she answers all of the same questions correctly as she did on the first
day.
• On the second day, she also correctly answers another
of the questions.
What fraction of the questions on the quiz does Mika answer correctly on the second day?
A
B
C
D
Sample 3:
A community center has three swimming pools. The water level of each pool is measured at 8:00
p.m. each night. Two of the measurements from Saturday night are shown.
•
The water level in the first pool is 3
•
The water level in the second pool is 4
feet deep.
feet deep.
Part A
What is the difference in depth, in feet, between the water levels of the second pool and the first
pool?
A.
1
B.
1
C.
D.
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
Part B
The water level in the third pool is 2
feet deeper than the second pool.
What is the total depth, in feet, of the water level in the third pool?
A.
6
B.
6
C.
7
D.
7
Sample 4:
Jake has 2 containers of liquid soap that are the same size. He wants to pour all the liquid soap
from one container into the other. One container is full. The other container is
statement best explains whether all the liquid soap will fit into one container?
full. Which
A. All the soap will fit into one container because
+
=
, which is less than 1.
B. All the soap will fit into one container because
+
=
, which is less than 1.
C. All the soap will not fit into one container because one of the containers is more than half
full and the other is almost half full.
D. All the soap will not fit into one container because each container is more than half full.
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5. NF.B.3
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems
involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g.,
by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the
result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared
equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of
rice equally by weight, how many pounds of rice should each person get? Between what two whole
numbers does your answer lie? (Conceptual Understanding & Application)
What test questions look like:
Sample 1:
Eloise bought 30 pounds of sand to refill 4 sandboxes at a local park. She is going to put the same
amount of sand in each sandbox. Which statement about this situation is true?
A. The fraction
sandbox.
represents the amount of sand, in pounds, Eloise should put in each
B. Each sandbox should get a whole number of pounds of sand and Eloise will have no sand
left over.
C. Eloise cannot evenly divide 30 pounds of sand into 4 sandboxes because 30 is not a
multiple of 4.
D. The product of
each sandbox.
× 4 is equal to the amount of sand, in pounds, Eloise should put in
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by Dr. Stacey Pullen
5. NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a
fraction. (Conceptual Understanding)
What test questions look like:
Sample 1:
Maria has a pile of wooden cubes. Each edge of each cube is 1 unit long.
Which statement about Maria’s cubes is correct?
A. Each of Maria’s cubes is a unit cube.
B. Each of Maria’s cubes has a volume of 6 cubic units.
C. Maria can use her cubes to measure the area of a plane figure in cubic units.
D. A rectangular prism in which 8 of Maria’s cubes fit perfectly has a volume of 48.
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by Dr. Stacey Pullen
5. NF.B.4a
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result
of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3,
and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) ×
(c/d) = ac/bd.) (Conceptual Understanding)
What test questions look like:
Sample 1:
Solve.
×
A
B
C
D
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by Dr. Stacey Pullen
5. NF.B.4b
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate
unit fraction side lengths, and show that the area is the same as would be found by multiplying the side
lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as
rectangular areas. (Conceptual Understanding & Procedural Skill and Fluency)
What test questions look like:
Sample 1:
Bella sells jewelry at a market. She cuts out a rectangular piece of wood for a necklace display. The
length of the piece of wood is
foot. The width of the piece of wood is foot. What is the
area, in square feet, of the piece of wood Bella cuts out?
A
B
C
1
D
2
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by Dr. Stacey Pullen
5. NF.B.5
Interpret multiplication as scaling (resizing) (Conceptual Understanding)
What test questions look like:
Sample 1:
Use the expression to answer the question.
Complete this sentence:
The product of this expression will be ____ the size of a
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by Dr. Stacey Pullen
Sample 2:
Janie and Sylas are multiplying 7/10 x 4/10 .
Without performing the calculations, Janie said that the product would be less than 7/10
Without performing the calculations, Sylas said that the product would be less than 4/10
Part A:
Who is correct?
Part B:
Explain your reasoning.
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. NF.B.5a
Comparing the size of a product to the size of one factor on the basis of the size of the other factor,
without performing the indicated multiplication. (Conceptual Understanding)
What test questions look like:
Sample 1:
Which statement is true about the product below?
(1/2) (7/8)
A. (1/2) (7/8) is twice as large as (7/8)
B. ½ x 7/8 > 7/8
C. 7/8 is half of (1/2) (7/8)
D. 7/8 is twice as large as (1/2) (7/8)
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5. NF.B.5b
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than
the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case);
explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the
given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of
multiplying a/b by 1. (Conceptual Understanding)
What test questions look like:
Sample 1:
Tommy bought a baseball card in March. In August, he learned that the value of his card was
of
what he paid for it. Which statement best explains how the value of Tommy’s baseball card
changed from March to August?
A. The value has decreased because whenever you multiply a number by a fraction less
than 1, the product is less than the number you started with.
B. The value has decreased because whenever you multiply a number by a fraction
greater than 1, the product is less than the number you started with.
C. The value has increased because whenever you multiply a number by a fraction less
than 1, the product is greater than the number you started with.
D. The value has increased because whenever you multiply a number by a fraction
greater than 1, the product is greater than the number you started with.
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5. NF.B.6
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual
fraction models or equations to represent the problem. (Application)
What test questions look like:
Sample 1:
Mr. Hernandez made sandwiches for a picnic. Of the sandwiches he made, 1/6 of them were
turkey sandwiches. Mr. Hernandez added cheese to 1/2 of the turkey sandwiches he made.
What fraction of the sandwiches made by Mr. Hernandez had both turkey and cheese?
A. 1/12
B. 1/8
C. 2/8
D. 4/6
Sample 2:
At a football game, 8/15 of the fans wore team T-shirts. Of those wearing team T-shirts, 1/4 of
the fans also wore team hats. What equation and fraction model the amount of the fans, f, at the
football game who wore both a team T-shirt and a team hat?
Select the two correct answers.
A. 2/15
B. 9/19
C. 47/60
D. 8/15 x ¼ = f
E. 8/15 + ¼ = f
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by Dr. Stacey Pullen
5. NF.B.7
Apply and extend previous understandings of division to divide unit fractions by whole numbers and
whole numbers by unit fractions. (Conceptual Understanding)
What test questions look like:
Sample 1:
What is 0.75 × 6.5?
Enter your answer in the box.
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by Dr. Stacey Pullen
5. NF.B.7a
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For
example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use
the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 =
1/3. (Conceptual Understanding & Procedural Skill and Fluency)
What test questions look like:
Sample 1:
Cora has
hour to do 5 chores. She plans to spend the same fraction of an hour on each chore. She
wants to use the number line to help her determine what fraction of an hour she can spend on
each chore.
0
•
•
•
A
1 Hour
What is the correct number label for point A?
Explain how to use this number line to help Cora solve her problem.
What fraction of an hour will she spend on each chore?
Enter your answers and your explanation in the box provided.
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by Dr. Stacey Pullen
5. NF.B.7b
Interpret division of a whole number by a unit fraction, and compute such quotients. For example,
create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the
relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
(Conceptual Understanding & Procedural Skill and Fluency)
What test questions look like:
Sample 1:
Sample 1:
Cora has
hour to do 5 chores. She plans to spend the same fraction of an hour on each chore. She
wants to use the number line to help her determine what fraction of an hour she can spend on
each chore.
0
•
•
•
A
1 Hour
What is the correct number label for point A?
Explain how to use this number line to help Cora solve her problem.
What fraction of an hour will she spend on each chore?
Enter your answers and your explanation in the box provided.
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by Dr. Stacey Pullen
5. NF.B.7c
Solve real world problems involving division of unit fractions by non-zero whole numbers and division of
whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the
problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate
equally? How many 1/3-cup servings are in 2 cups of raisins? (Application)
What test questions look like:
Sample 1:
Kari’s grandmother has
pound of silver coins. She divides the coins evenly, by weight, among her
4 grandchildren, including Kari. What fraction of a pound of silver coins does Kari receive?
A
B
C
D
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by Dr. Stacey Pullen
5. MD.A.1
Convert among different-sized standard measurement units within a given measurement system (e.g.,
convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
(Conceptual Understanding & Application)
What test questions look like:
Sample 1:
Tom has a water tank that holds 5 gallons of water.
Part A
Tom uses water from a full tank to fill 6 bottles that each hold 16 ounces and a pitcher that holds
gallon.
How many ounces of water are left in the water tank?
Enter your answer in the box.
Part B
Tom drinks 4 pints of water a day.
How many full tanks of water will he drink in 30 days?
Enter your answer in the box.
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5. MD.B.2
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use
operations on fractions for this grade to solve problems involving information presented in line
plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid
each beaker would contain if the total amount in all the beakers were redistributed equally.
(Conceptual Understanding & Application)
What test questions look like:
Sample 1:
Elijah ate trail mix nine different times. Each X on the line plot represents an amount that he ate.
Amounts of Trail Mix
×
×
×
×××
×××
0
1
Cup
How much total trail mix, in cups, did Elijah eat?
A
B
C
D
39
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. MD.C.3
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
(Conceptual Understanding)
What test questions look like:
Sample 1:
Theresa, Jake, and Brittany have a small rectangular box. They want to find the volume of
the box.
Part A
Theresa says, “Let’s measure the length, width, and height of the box in centimeters using this
ruler.”
Explain how to find the volume of the box using Theresa’s idea.
Part B
Jake says, “Let’s pack the box neatly with these plastic cubes that are 1 centimeter on each
side.”
Explain how to find the volume of the box using Jake’s idea.
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Created for Morehouse Parish School System
by Dr. Stacey Pullen
Part C
Brittany says, “Why don’t we pack the box with these pieces of popcorn?”
Explain two reasons why popcorn would not work as well as centimeter cubes for finding the
volume of the box.
41
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. MD.C.3a
A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can
be used to measure volume. (Conceptual Understanding)
What test questions look like:
Sample 1:
Maria has a pile of wooden cubes. Each edge of each cube is 1 unit long.
Which statement about Maria’s cubes is correct?
A. Each of Maria’s cubes is a unit cube.
B. Each of Maria’s cubes has a volume of 6 cubic units.
C. Maria can use her cubes to measure the area of a plane figure in cubic units.
D. A rectangular prism in which 8 of Maria’s cubes fit perfectly has a volume of 48.
42
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. MD.C.3b
A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume
of n cubic units. (Conceptual Understanding)
What test questions look like:
Sample 1:
Ramon has 2 boxes. He packs the first box with 38 unit cubes. The unit cubes have no gaps or
overlaps. Then, he empties that box and uses the same 38 cubes to fill the second box. These unit
cubes also have no gaps or overlaps. There are 6 unit cubes left over.
What is the volume, in cubic units, of the second box?
A. 6
B. 32
C. 44
D. 228
43
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. MD.C.4
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
(Conceptual Understanding)
What test questions look like:
Sample 1:
Emily completely fills a container with 6 cubes. Each cube has an edge length of 3 centimeters. The
container is in the shape of a right rectangular prism. What is the volume of the container in cubic
centimeters?
Enter your answer in the box.
44
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. MD.C.5
Relate volume to the operations of multiplication and addition and solve real world and mathematical
problems involving volume. (Conceptual Understanding, Procedural Skill and Fluency, &
Application)
What test questions look like:
Sample 1:
The Candle Company makes candles in the shape of rectangular prisms. Each candle
has a height of 6 centimeters and a volume of 360 cubic centimeters. Which table
shows the possible dimensions for these candles?
A.
Length (cm)
Width (cm)
10
6
12
5
15
4
Length (cm)
Width (cm)
12
6
18
4
24
3
Length (cm)
Width (cm)
6
6
12
12
18
18
Length (cm)
Width (cm)
20
18
24
15
36
10
B.
C.
D.
45
Created for Morehouse Parish School System
by Dr. Stacey Pullen
Sample 2:
Use the diagram of a swimming pool to answer the question.
Brian wonders how much water it would take to fill the swimming pool to the top.
What is the total volume, in cubic feet, of the swimming pool?
46
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. MD.C.5a
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit
cubes, and show that the volume is the same as would be found by multiplying the edge lengths,
equivalently by multiplying the height by the area of the base. Represent threefold whole-number
products as volumes, e.g., to represent the associative property of multiplication. (Conceptual
Understanding)
What test questions look like:
Sample 1:
Use the picture to answer the question.
The picture shows how a solid shape made of cubes can be separated in two different ways to
find the volume of the solid shape.
Which equation is modeled by this picture?
A. 3 x 4 = 6 + 6 + 6 + 6
B. 12 + 6 + 8 = 6 + 6 + 6 + 6
C. 2 + (3 + 4) = (2 + 3) + 4
D. 2 x (3 x 4) = (2 x 3) x 4
47
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. MD.C.5b
Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular
prisms with whole-number edge lengths in the context of solving real world and mathematical
problems. (Procedural Skill and Fluency, & Application)
What test questions look like:
Sample 1:
Scott has an aquarium that is in the shape of a rectangular prism. He knows the aquarium has a
volume of 192 cubic feet. The height of the aquarium is 4 feet.
What are the possible dimensions for the base of the aquarium?
A. length = 6 feet, width = 8 feet
B. length = 8 feet, width = 16 fee
C. length = 12 feet, width = 12 feet
D. length = 12 feet, width = 16 feet
Sample 2:
Kim stacks 10 pieces of wood to form a rectangular prism. Each piece of wood is 2 inches thick,
with a base that is 25 inches long and 8 inches wide. What is the total volume, in cubic inches, of
Kim’s rectangular prism?
A. 132
B. 400
C. 1320
D. 4000
48
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. MD.C.5c
Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right
rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve
real world problems. (Conceptual Understanding, Procedural Skill and Fluency, & Application)
What test questions look like:
Sample 1:
There are two tanks at the aquarium, Tank A and Tank B. Each tank has two sections.
Part A
The volume of one section of Tank A is 24 cubic feet. The volume of the other section of Tank A is
96 cubic feet.
What is the total volume, in cubic feet, of Tank A?
A 4
B 72
C 120
D 2,304
Part B
Tank B has the same volume as Tank A.
The volume of one section of Tank B is 45 cubic feet. What is the volume, in cubic feet, of the other
section of Tank B?
Enter your answer in the box.
49
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. G.A.1
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the
intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the
plane located by using an ordered pair of numbers, called its coordinates. Understand that the first
number indicates how far to travel from the origin in the direction of one axis, and the second number
indicates how far to travel in the direction of the second axis, with the convention that the names of the
two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
(Conceptual Understanding)
What test questions look like:
Sample 1:
Select the three statements that correctly describe the point plotted on the coordinate plane.
y
10
9
8
7
6
5
4
3
2
1
0
x
1 2345678910
A. The point is located at the ordered pair (4, 6).
B. The point is located at the ordered pair (6, 4).
C. The x-coordinate is 6 and the y-coordinate is 4.
D. The x-coordinate is 4 and the y-coordinate is 6.
E. The point is 4 units to the right of the origin on the x-axis and 6 units up from the origin on the
y-axis.
F. The point is 6 units to the right of the origin on the x-axis and 4 units up from the origin on the yaxis.
50
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. G.A.2
Represent real world and mathematical problems by graphing points in the first quadrant of the
coordinate plane, and interpret coordinate values of points in the context of the situation. (Conceptual
Understanding, Procedural Skill and Fluency, & Application)
What test questions look like:
Sample 1:
Mia is playing several rounds of a word game. Each coordinate pair shows the number of a round
and Mia’s score for that round. She is keeping track of these coordinate pairs on a coordinate
plane.
• Round 1: (1, 3)
• Round 2: (2,
6)
• Round 3: (3, 3)
Part A
Which coordinate plane correctly shows Mia’s scores for the first three rounds of play?
(Answer options continued on next page)
0
1 2 3 4 5 6 7 8 9 10
Rounds of Play
0
y
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
Rounds of Play
y
10
9
8
7
6
5
4
3
2
1
x
51
x
Created for Morehouse Parish School System
by Dr. Stacey Pullen
y
10
9
8
7
6
5
4
3
20
1
y
1 2 3 4 5 6 7 8 9 10
Rounds of Play
10
9
8
7
6
5
4
3
20
1
x
1 2 3 4 5 6 7 8 9 10
Rounds of Play
Part B
In round 4, Mia scores the same number of points as in rounds 2 and 3 combined.
What is the coordinate pair that represents Mia’s score for round 4?
A. (4, 5)
B. (9, 4)
C. (5, 4)
D. (4, 9)
52
x
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. G.B.3
Understand that attributes belonging to a category of two-dimensional figures also belong to all
subcategories of that category. For example, all rectangles have four right angles and squares are
rectangles, so all squares have four right angles. (Conceptual Understanding)
What test questions look like:
Sample 1:
What is true of every rhombus that is also true of every parallelogram?
A. A rhombus has right angles
B. A rhombus has all equal sides.
C. A rhombus has no perpendicular lines.
D. A rhombus has two pairs of parallel sides.
Sample 2:
Which quadrilaterals appear to be parallelograms?
A. I, III, V
B. I, III, VI
C. I, III, IV, and VI
D. I, II, IV, and VI
53
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5. G.B.4
Classify two-dimensional figures in a hierarchy based on properties. (Conceptual Understanding)
What test questions look like:
Sample 1:
Which statement is true?
A. All squares are parallelograms.
B. All parallelograms are squares.
C. All rhombuses are rectangles.
D. All rectangles are rhombuses.
Sample 2:
Levi drew a shape with these properties.



more than 3 sides
exactly 1 pair of parallel sides
exactly 2 pairs of sides with equal lengths
Which shape could not be Levi’s shape?
A. Parallelogram
B. Pentagon
C. Hexagon
D. Octagon
54
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5th Grade
Sample Math Items Aligned to CCSS
CCSS Code
5.0A.A.1
5.0A.A.2
5.0A.B.3
5.NBT.A.1
5.NBT.A.2
5.NBT.A.3
Sample 1
143
See Rubric #11
D
100
D
Part A: .0827
Part B: four
KEY
Sample 2
Sample 3
Sample 4
C
See Rubric #23
B
C
hundred forty-five
thousandths
5.NBT.A.3a
5.NBT.A.3b
5.NBT.A.4
5.NBT.B.5
5.NBT.B.6
5.NBT.B.7
5.NF.A.1
5.NF.A.2
D
B
D
C
See Rubric #14
B
B
C
5.NF.B.3
5.NF.B.4
5.NF.B.4a
5.NF.B.4b
5.NF.B.5
A
A
C
A
5.NF.B.5a
5.NF.B.5b
5.NF.B.6
5.NF.B.7
5.NF.B.7a
5.NF.B.7b
D
D
A
4.875
See Rubric #42
See Rubric #42
1/4|a quarter or
one quarter or
quarter or a fourth
or one fourth or
fourth
See Rubric
75.3
See Rubric #28
81
See Rubric #11
C
D
Part A: Both
are correct
Part B: see
rubric
A&D
55
Part A: D
Part B: C
D
Created for Morehouse Parish School System
by Dr. Stacey Pullen
CCSS Code
5.NF.B.7c
5.MD.A.1
5.MD.B.2
5.MD.C.3
5.MD.C.3a
5.MC.C.3b
5.MD.C.4
5.MD.C.5
Sample 1
A
Part A: 480
Part B: 3
D
See Rubric
A
B
162
A
Sample 2
Sample 3
Sample 4
1,200 or 1200 or
1,200 cubic feet or
1200 cubic feet or
1,200 cu. ft. or
1200 cu. ft. or
1,200 cu ft or 1200
cu ft or 1200 ft^3
or 1,200 ft^3 or
1200 ft.^3 or 1,200
ft.^3
5.MD.C.5a
5.MD.C.5b
5.MD.C.5c
D
A
D
Part A: C
Part B: 75*
5.G.A.1
B, C, F
5.G.A.2
Part A: A
Part B: D
5.G.B.3
D
B
5.G.B.4
A
A
*Scorer should follow student work from part A to part B. Part B can receive
credit if an incorrect response in part A is used correctly in part B.
56
Created for Morehouse Parish School System
by Dr. Stacey Pullen
Grade 5 Math Items Aligned to CCSS
Scoring Rubrics
5.OA.B.3
Sample 1 Part B (Rubric #11)
Part A
Score Description
1
Student response includes the following element. x
Modeling component = 1 point o Correct expression
for the cost of the bracelet Sample Student Response:
0.05 x 25 + 0.45 x 4
Note: Any valid expression can receive credit.
0
Student response is incorrect or irrelevant.
Part B
Score Description
1
Student response includes the following element. x
Modeling component = 1 point o Correct expression for
the cost of the necklaces Sample Student Response:
(0.05 × 48 + 0.45 × 1) × 2
Note: Any valid expression can receive credit.
0
Student response is incorrect or irrelevant.
Part C
Score Description
1
Student response includes the following element. x Computation
component = 1 point o Correct amount of money Katie had
left after purchasing her supplies
Sample Student Response:
$31.25
0
Student response is incorrect or irrelevant.
57
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5.NBT.A.1
Sample 2 (Rubric #23)
Score Description
3
Student response includes each of the following 3 elements.
x Reasoning component = 2 points
o
Identification of Leah’s
1
5
mistake
o
Correct work shown for
2
12
adding 2
3
x Computation component = 1 point
o Correct value of 2 1 5 ,or equivalent
3
2
12
Sample Student Response:
Leah used the wrong numerators. To add fractions with different
denominators, you have to find the common denominator. Then
you convert each fraction to an equivalent fraction using the
common denominator. Then you add the numerators together
and put the result as the numerator.
2 1
5
3 2
12
8 6 5
12
12
12
2
Student response includes 2 of the 3 elements.
1
Student response includes 1 of the 3 elements.
0
Student response is incorrect or irrelevant.
58
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5.NBT.A.3b
Sample 2
Score Description
Exemplary Response
90 grams is equal to 0.09 kilograms.
0.2 kilograms is greater than 0.09 kilograms, because tenths
are larger than hundredths, so 2 tenths is greater than 9
hundredths. (or other valid response)
Points Assigned


1 point for expressing 90 grams as 0.09 kilograms
1 point for using place concepts to explain why 0.2
kilograms is greater than 0.09 kilograms.
2
2 points
1
1 point or minimal understanding of comparing decimals
0
The student’s response is incorrect, irrelevant, too brief to evaluate, or blank.
59
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5.NBT.B.5
Sample 2 (Rubric #28)
Score Description
3
Student response includes the following 3 elements. x Modeling
component = 2 points o Correct explanation of how to use the
model to find the size of each section of the garden. o Correct
use of common denominators to write an equation to find the
difference between the two sections of the garden. x
Computation component = 1 point o The student finds how
many square yards larger the pea section is than the carrot
section.
Sample Student Response:
Since there are 16 squares in the first half of the model and 3
are shaded, this means that the area of the carrot section is
square yard. Since there are 4 squares in the second half of
the model and 1 is shaded, this means that the area of the pea
section is
square yard.
square yard
Notes:
o A variety of explanations are possible. As long as the
explanation shows a clear understanding of using the model to
find the size of each section, credit should be awarded. o A
variety of equations are possible. As long as the equation can be
used to represent the problem, credit should be awarded. o If a
student uses the model for peas and divides it into sixteenths in
order to use the common denominator, the student should be
awarded both modeling points since the modeling for two steps
was completed in one step.
2
1
0
Student response includes 2 of the 3 elements.
Student response includes 1 of the 3 elements.
Student response is incorrect or irrelevant.
60
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5.NBT.B.6
Score
Sample 2 (Rubric #14)
Description
Student response contains the following 4 elements:
•
Computation component: Correct numbers for each letter in the
model
•
Reasoning component: Valid explanation for finding the numbers in
the model
•
Computation Component: Correct value for quotient, 873 remainder
2
•
Reasoning component: Valid explanation or work to show
multiplication check
4
Sample Student Response
The value of M is 6,400 because 8 × 800 = 6,400. The value of N is 70
because 8 × 70 = 560. Then 6,400 = 560 = 6,960. So there are 26 left.
Since 8 × 3 = 24, the value of P is 3 and the value of Q is 24. There are
2 left over, so R is 2.
The value of 6,986 ÷ 8 is 873 with a remainder of 2.
3
To check by multiplication, first multiply 873 by 8. Then add 2 to the product. 873
× 8 = 6,984
6,984 + 2 = 6,986
Student response includes 3 of the 4 elements. If a student has a computation
error, points can still be awarded for correct reasoning.
2
Student response includes 2 of the 4 elements. If a student has a computation
error, points can still be awarded for correct reasoning.
1
Student response includes 1 of the 4 elements. If a student has a computation
error, points can still be awarded for correct reasoning.
0
Student response is incorrect or irrelevant.
61
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5.NF.B.5
Sample 2
Score Description
Exemplary Response
Part A: Both are correct (or Janie and Sylas are correct.)
Part B: When multiplying by a fraction less than 1 whole, the
product will be less than the number we are multiplying the
fraction by.
Points Assigned:
 Part A: point for answering correctly
 Part B: 1 point for exhibiting understanding in the
concept of interpreting multiplication as scaling
(resizing).
2
2 points
1
1 point or minimal understanding of comparing the size of a product based on the factors
0
The student’s response is incorrect, irrelevant, too brief to evaluate, or blank.
62
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5.NF.B.7a & 5.NF.B.7b Sample 1 (Rubric #42)
Score Description
3
Student response includes each of the following 3 elements. x
Reasoning component = 2 points o Correct label for point
A,
hour or equivalent o Correct explanation of how to use
the number line to solve the problem x Computation
component = 1 point o Correct fraction of an hour spent
per chore,
or equivalent
Sample Student Response:
Point A should have the label
hour.
The number line is divided from 0 to
in 5 equal sections
because there are 5 chores. It would take 10 of these sections to
divide the number line from 0 to 1. Each section represents the
time she can spend on one chore. So she can spend
hour on each chore.
2
1
0
Student response includes 2 of the above elements.
Student response includes 1 of the above elements.
The response is incorrect or irrelevant.
63
of an
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5.MD.C.3
Sample 1
Score Description
Part A
The length times the width times the height in centimeters will equal the volume in cubic
centimeters. (other responses are possible)
Part B
The number of centimeter cubes that pack neatly into the box with no gaps will equal
the volume of the box in cubic centimeters (Other responses are possible.)
Part C
Pieces of popcorn do not fit together neatly with no gaps. Also, the pieces are different
sizes. So they are not as good as centimeter cubes for finding volume. (Other responses
are possible.)
For full credit, the student should mention any two of the following:
 Popcorn does not have a uniform size, unlike centimeter cubes.
 Popcorn can be squashed or compressed, unlike plastic cubes.
 Popcorn does not pack neatly with no gaps or overlaps, while centimeter cubes
do.
 Popcorn can break into smaller pieces, while plastic cubes generally break.
 Other valid factors that make popcorn a poor choice for measuring volume.
Points Assigned:
 1 point for explaining that volume can be found by multiplying the three
dimensions.
 1 point for explaining that volume can be found by counting the number of unit
cubes that pack neatly into the box.
 1 point for explaining one reason that popcorn makes a poor replacement for
unit cubes when finding volume.
 1 point for explaining a different reason that popcorn makes a poor replacement
for unit cubes when finding volume.
4
4 points
3
3 points
2
2 points
64
Created for Morehouse Parish School System
by Dr. Stacey Pullen
1
1 point of minimal understanding of ways to find volume
0
The student’s response is incorrect, irrelevant, too brief to evaluate, or blank
65
Created for Morehouse Parish School System
by Dr. Stacey Pullen
5th Grade
Sample Math Items Aligned to CCSS
CCSS Code
5.0A.A.1
5.0A.A.2
5.0A.B.3
5.NBT.A.1
5.NBT.A.2
5.NBT.A.3
5.NBT.A.3a
Origination of Sample Items
Sample 1
Sample 2
Sample 3
2016 Leap Practice
Test #1
2016 Leap Practice
Test #11
2016 Leap Practice
Test #18
2016 Leap Practice
Test #21
2016 Leap Practice
Test #37
Eagle
2016 Leap Practice
Test #39
2016 Leap Practice
Test #23
2016 Leap Practice
Test #2
Eagle
2016 Leap Practice
Test #15
2016 Leap Practice
Test #4
2016 Leap Practice
Test #14
2016 Leap Practice
Test #7
2016 Leap Practice
Test #16
2016 Leap Practice
Test #3
2016 Leap Practice
Test #34
2016 Leap Practice
Test #33
2016 Leap Practice
Test #31
2016 Leap Practice
Test #9
2016 Leap Practice
Test #29
2016 Leap Practice
Test #28
2016 Leap Practice
Test #35
2016 Leap Practice
Test #11
2016 Leap Practice
Test #30
2016 Leap Practice
Test #19
5.NF.B.5
5.NF.B.5a
5.NF.B.5b
Eagle
Eagle
5.NF.B.6
5.NF.B.7
Eagle
5.NBT.B.5
5.NBT.B.6
5.NBT.B.7
5.NF.A.1
5.NF.A.2
5.NF.B.3
5.NF.B.4
5.NF.B.4a
5.NF.B.4b
5.NF.B.7a
2016 Leap Practice
Test #36
Eagle
Eagle
5.NBT.A.3b
5.NBT.A.4
Sample 4
Eagle
2016 Leap Practice
Test #5
Eagle
2016 Leap Practice
Test #26
2016 Leap Practice
Test #42
66
2016 Leap Practice
Test #22
2016 Leap Practice
Test #32
Created for Morehouse Parish School System
by Dr. Stacey Pullen
CCSS Code
5.NF.B.7b
5.NF.B.7c
5.MD.A.1
5.MD.B.2
5.MD.C.3
5.MD.C.3a
5.MC.C.3b
5.MD.C.4
5.MD.C.5
5.MD.C.5a
5.MD.C.5b
5.MD.C.5c
5.G.A.1
5.G.A.2
5.G.B.3
5.G.B.4
Sample 1
Sample 2
2016 Leap Practice
Test #42
2016 Leap Practice
Test #25
2016 Leap Practice
Test #27
2016 Leap Practice
Test #8
Eagle
2016 Leap Practice
Test #33
2016 Leap Practice
Test #13
2016 Leap Practice
Test #24
Eagle
Eagle
Eagle
2016 Leap Practice
Test #6
2016 Leap Practice
Test #12
2016 Leap Practice
Test #17
2016 Leap Practice
Test #10
2016 Leap Practice
Test #20
Eagle
Eagle
2016 Leap Practice
Test #40
Eagle
67
Sample 3
Sample 4