## Grade 5 Mathematics Sample Questions (CCSS)

### Grade 5 Math Sample Question 20

Given that a triangle can have at most one angle measuring more than 90 degrees, which of the following statements must be true?

A) A quadrilateral can have at most one angle measuring more than 90 degrees.

B) A triangle can have at most one angle measuring less than 90 degrees.

C) A scalene triangle can have at most one angle measuring more than 90 degrees (Correct Answer)

D) None of the above

Explanation:
Because a scalene triangle is a special type of triangle, then it must have the same attributes as any other triangle. It must have no more than one angle measuring more than 90 degrees.

Related Common Core State Standard: Geometry: 5.G.3

### Grade 5 Math Sample Question 19

The chairs in the front half of the school auditorium are arranged in 9 rows of 20. The chairs in the back half are arranged in 5 rows of 25. Which expression could be used to find how many chairs are set up in the auditorium altogether?

A) 9 + 20 + 5 + 25

B) 9 x 20 x 5 x 25

C) 9 x 20 + 5 x 25 (Correct Answer)

D) (9 + 5) x (20 + 25)

Explanation:
The number of chairs in the front of the auditorium can be expressed as 9 x 20. The number of chairs in the back of the auditorium can be expressed as 5 x 25. In total, the number of chairs is the sum of these two expressions: 9 x 20 + 5 x 25.

Related Common Core State Standard: Operations & Algebraic Thinking: 5.OA.2

### Grade 5 Math Sample Question 18

What is the volume of this figure?

A) 6 cubic feet

B) 8 cubic feet

C) 12 cubic feet

D) 24 cubic feet (Correct Answer)

Explanation:
The volume of a rectangular prism is found by multiplying its three dimensions (V = l x w x h.) The volume of this figure is 4 x 3 x 2 = 24 cubic feet.

Related Common Core State Standard: Measurement & Data: 5.MD.5b

### Grade 5 Math Sample Question 17

Which of the following equations could be used to calculate the volume of this rectangular prism?

A) V = 2 + 2 + 6

B) V = (2 + 2) x 6

C) V = (2 x 2) x 6 (Correct Answer)

D) V = (2 x 2) + 6

Explanation:
The volume of a rectangular prism can be found by multiplying its three dimensions. For this figure, V = l x w x h = 2 x 2 x 6. By applying the Associative Property to group the factors, V = (2 x 2) x 6.

Related Common Core State Standard: Measurement & Data: 5.MD.5b

### Grade 5 Math Sample Question 16

How many 4 inch long pieces of wood could be cut from a board
that is 2 yards long?

A) 18 pieces (Correct Answer)

B) 24 pieces

C) 12 pieces

D) 6 pieces

Explanation:
Using the conversion factor: 1 yard = 36 inches, then 2 yards = 72 inches.
Cutting a 72 inch board into pieces that are 4 inches long: 72 ÷ 4 = 18.
18 pieces could be cut from the board.

Related Common Core State Standard: Measurement & Data: 5.MD.1

### Grade 5 Math Sample Question 15

Complete the following statement with the correct number:

The number 17,000,000 is equal to ________ times the number 17,000.

A) 100

B) 1,000 (Correct Answer)

C) 10,000

D) 100,000

Explanation:
The correct value is 1,000. 17,000 x 1,000 = 17,000,000.

Related Common Core State Standard: Number & Operations in Base Ten: 5.NBT.1

### Grade 5 Math Sample Question 14

Evaluate the expression shown below:

[55 ÷ (5 + 6)] x [(80 – 65) ÷ 5]

A) 51

B) 85

C) 15 (Correct Answer)

D) 335

Explanation:
To evaluate the expression, follow this procedure:

[55 ÷ (5 + 6)] x [(80 – 65) ÷ 5] = [55 ÷ 11] x [15 ÷ 5] = 5 x 3 = 15

Related Common Core State Standard: Operations & Algebraic Thinking: 5.OA.1

### Grade 5 Math Sample Question 13

Match up corresponding elements in each pattern below to form
ordered pairs. If (0, 0) is the first ordered pair in the list, what
would the seventh ordered pair be?

Rule “Add 3”: 0, 3, 6, . . .

Rule “Add 8”: 0, 8, 16, . . .

A) (21, 56)

B) (18, 48) (Correct Answer)

C) (21, 54)

D) (18, 56)

Explanation:
The list of ordered pairs would be (0, 0), (3, 8), (6, 16), (9, 24), (12, 32), (15, 40),
(18, 48), (21, 56), . . . The seventh ordered pair in the list is (18, 48).

Related Common Core State Standard: Operations & Algebraic Thinking: 5.OA.3

### Grade 5 Math Sample Question 12

Which of the following comparison statements is true?

A) 3.909 = 3.990

B) 3.099 > 3.99

C) 3.990 = 3.99 (Correct Answer)

D) 3.09 < 3.009 Explanation:
3.990 (three and 990 thousandths) is equal to 3.99 (three and 99 hundredths). The fraction 990/1000 is
equivalent to the fraction 99/100, so the decimal representations are also equivalent.

Related Common Core State Standard: Number & Operations in Base Ten: 5.NBT.3b

### Grade 5 Math Sample Question 11

Find the product.

6.8 x 0.5

A) 0.034

B) 0.34

C) 3.4 (Correct Answer)

D) 34.0

Explanation:
Using the standard multiplication process, 68 times 5 is found to be 340. There are two decimal places
involved in the expression (one in each factor), so the decimal point is moved two places to the left in
our product. The final answer is 3.40 (or 3.4).

Related Common Core State Standard: Number & Operations in Base Ten: 5.NBT.7

### Grade 5 Math Sample Question 10

Find the sum.

2 1/3 + 3 1/2

A) 5 2/5

B) 5 5/6 (Correct Answer)

C) 5 1/3

D) 6 1/6

Explanation:
To find the sum of the mixed numbers, follow these steps: (Note: It is necessary to rewrite the
mixed numbers as improper fractions and to find a Least Common Denominator before adding.)

Related Common Core State Standard: 5.NF.1

### Grade 5 Math Sample Question 9

Evaluate this expression when h = 5:

{102 – [h x (2 + 7) + 3 x (21 – h)]} ÷ 3

A) 3 (Correct Answer)

B) 9

C) 15

D) 35

Explanation:
Follow these steps to evaluate the expression:

{102 – [h x (2 + 7) + 3 x (21 – h)]} ÷ 3
Replace every h with the value 5. The new expression is {102 – [5 x (2 + 7) + 3 x (21 – 5)]} ÷ 3 = {102 – [5 x 9 + 3 x 16]} ÷ 3 = {102 – [45 + 48]} ÷ 3 = {102 – 93} ÷ 3 = 9 ÷ 3 = 3

Related Common Core State Standard: 5.OA.1

### Grade 5 Math Sample Question 8

Which of these is a correct interpretation of this numerical expression?

90 x 5 + 16

A) Sixteen more than the product of 90 and 5

B) The product of 90 and 5, increased by sixteen

C) 16 added to the result of 90 times 5

D) All of the above (Correct Answer)

Explanation:
All three of the choices given are correct ways of interpreting the same numerical expression.
The terms “more than”, “increased by”, and “added to” can all imply addition. The terms
“product” and “times” imply multiplication.

Related Common Core State Standard: 5.OA.2

### Grade 5 Math Sample Question 7

Lonnie measured the volume of a large box. Which of the following
results could have been the volume of the box?

A) 2.5 yards

B) 2.5 square yards

C) 2.5 cubic yards (Correct Answer)

D) 2.5 Tons

Explanation:
The volume of a rectangular prism (box) would be represented in cubic units.
The only possible result for the volume of the box would be 2.5 cubic yards.

Related Common Core State Standard: 5.MD.3

### Grade 5 Math Sample Question 6

What is the expanded form of the number 2,305,780?

A) (2 x 1,000,000) + (3 x 100,000) + (5 x 10,000) + (7 x 100) + (8 x 10)

B) (2 x 1,000,000) + (3 x 100,000) + (5 x 10,000) + (7 x 100) + (8 x 1)

C) (2 x 1,000,000) + (3 x 100,000) + (5 x 1,000) + (7 x 100) + (8 x 10) (Correct Answer)

D) (2 x 1,000,000) + (3 x 10,000) + (5 x 1,000) + (7 x 100) + (8 x 10)

Explanation:
The third choice is correct. (2 x 1,000,000) + (3 x 100,000) + (5 x 1,000) + (7 x 100) + (8 x 10) = 2,305,780.

Related Common Core State Standard: 5.NBT.1

### Grade 5 Math Sample Question 5

What is the standard form of 9 and 15 hundredths?

A) 915

B) 9.15 (Correct Answer)

C) 9.015

D) 0.915

Explanation:
The word form tells us there are 9 ones and 15 hundredths. The decimal form
of 15 hundredths is .15, so 9.15 would be the correct standard form.

Related Common Core State Standard: 5.NBT.3

### Grade 5 Math Sample Question 4

Two sequences of numbers are created. They both start from 0.
The first sequence follows the pattern rule “Add 2”. The second
follows the pattern rule “Add 6”. Which of the following statements
is true?

A) Each number in the second sequence is 4 more than the
corresponding number in the first sequence.

B) Each number in the second sequence is 6 times as much as the
corresponding number in the first sequence.

C) Each number in the second sequence is 3 times as much as the
corresponding number in the first sequence. (Correct Answer)

D) Each number in the second sequence is double the corresponding
number in the first sequence.

Explanation:
The sequences would look like this:

First: 0, 2, 4, 6, 8, …; Second 0, 6, 12, 18, 24, . . . Matching up the corresponding elements
yields the pairs (0, 0), (2, 6), (4, 12), (6, 18), (8, 24), . . . The second element in each pair is
three times as much as the first element.

Related Common Core State Standard: 5.OA.3

### Grade 5 Math Sample Question 3

A grocery store scale is used to weigh a bag of vegetables. The scale
shows “13.456 oz”. What is this value rounded to the nearest tenth
of an ounce?

A) 13.4 oz

B) 13.5 oz (Correct Answer)

C) 13.45 oz

D) 13.46 oz

Explanation:
The tenths place is the decimal place immediately to the right of the decimal point. To round to the nearest tenth, use the hundredths digit.
In this number, the hundredths digit is a 5. Therefore, the tenths digit will round up to a 5. The rounded number is 13.5 oz.

Related Common Core State Standard: 5.NBT.4

### Grade 5 Math Sample Question 2

Which of the following expressions would have a value that is triple the
value of the expression shown here?

(88 + 17) ÷ 6 + 9

A) (88 + 17) ÷ 6 + 9 x 3

B) 3 x (88 + 17) ÷ 6 + 9

C) 3 x [(88 + 17) ÷ 6 + 9] (Correct Answer)

D) 3 x 88 + 17 ÷ 6 + 9

Explanation:
In order for the new expression to have a value that is triple the value of the original expression, the entire original expression has to be multiplied by 3. The only answer choice that works is the third choice. The other choices only triple part of the original expression, not the entire value.

Related Common Core State Standard: 5.OA.2

### Grade 5 Math Sample Question 1

Evaluate the following expression:
[25 x (8 + 4)] – (20 x 4 + 5)

A) 24

B) 225

C) 215 (Correct Answer)

D) 120

Explanation:
Follow these steps to evaluate the expression:
[25 x (8 + 4)] – (20 x 4 + 5) = [25 x 12] – (20 x 4 + 5) = 300 – (80 + 5) = 300 – 85 = 215

Related Common Core State Standard: 5.OA.1