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Grade 6 Mathematics Sample Questions (CCSS)

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“We used this for SBAC through out the year. It may have helped the students to identify the skills and the level of difficulty of the exam.”

Grade 6 Math Sample Question 20

Which of the following measurements requires the highest degree of accuracy?

A) The distance a kindergarten student walks home every day

B) The dimensions of the window frame to replace a broken pane (Correct Answer)

C) The amount of time you spend completing each math problem, if twenty problems were assigned

D) The size and weight of your bicycle after you fill the tires with air

Explanation:
The size of a window frame would have to be measured with a high degree of accuracy to ensure that the glass fits securely. The other three choices listed do not need as high of a degree of accuracy.

Related Common Core State Standard: The Number System: 6.NS.5

6th-Grade-Mathematics-Books-and-eLearning-Products-Schools-Libraries-&-TeachersClick Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 19

Leonardo and six friends want to go mountain biking. They will all meet at Dale’s house, load the bikes into cars, and then drive to the trail. What information do they need to consider as they plan their trip?

A) The brand of bike owned by each rider

B) The number of bikes each car can carry (Correct Answer)

C) The top speed of each bike

D) The age of each member of the group

Explanation:
It would be most useful for them to know how many bikes each car can carry so that they know how many vehicles will be needed to haul the bikes to the trail.

Related Common Core State Standard: The Number System: 6.NS.5

6th-Grade-Mathematics-Books-and-eLearning-Products-Schools-Libraries-&-TeachersClick Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 18

Write an equivalent expression to 12x+3.

A) 12(x+1)

B) 3(4x + 1) (Correct Answer)

C) 6(2x-2)

D) 3(9x+1)

Explanation:
To determine if (3(4x + 1) expression is equivalent, first simplify the expression using the distributive property. 3*4x = 12x; 3*1 = 3. Therefore, the expression is equivalent to 12x+3.

Related Common Core State Standard: Expressions & Equations: 6.EE.3

6th-Grade-Mathematics-Books-and-eLearning-Products-Schools-Libraries-&-TeachersClick Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 17

Which one of these proportions is true?

A) 3/5 = 7/11

B) 9/6 = 15/10 (Correct Answer)

C) 3/4 = 9/16

D) 2/5 = 5/10

Explanation:
To determine if proportions are equivalent, cross multiply the numerator and
denominator across the equal sign. Here, 9 * 10 = 90, and 6 * 15 = 90. Therefore,
the proportions are equivalent. No other set of proportions allow the products
of cross multiplication to be equal.

Related Common Core State Standard: Ratios & Proportional Relationships: 6.RP.3

6th-Grade-Catalog-of-Mathematics-School-Library-Teacher-Books-and-eLearning-ProductsClick Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 16

If six cards were placed into a bag, what would be the
probability of randomly choosing a card with “F” or “N”?

A) 0.5 (Correct Answer)

B) 0.67

C) 0.17

D) 0.33

Explanation:
There is one “F” card and there are two “N” cards. Therefore, the chances
of pulling one of these cards is 3 out of 6, or 0.5.

Related Common Core State Standard: Statistics & Probability: 6.SP.2

Catalog-of-6th-Grade-Mathematics-School-Library-Teacher-Books-and-eLearning-ProductsClick Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 15

Solve: x – 4 < 5

A) x > 9

B) x < 9 (Correct Answer) C) x > 1

D) x < 1 Explanation:
To solve this inequality, you must add 4 to both sides to isolate the x. Thus, x < 9. Related Common Core State Standard: Expressions & Equations: 6.EE.8

Catalog-of-Grade-6-Mathematics-School-Library-Teacher-Books-and-eLearning-ProductsClick Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 14

Joyce is putting a decorative border below the ceiling of her
bedroom. The bedroom’s ceiling is a rectangle. The shorter
sides are 12 feet and the longer sides are 16 feet. What is the
perimeter of the ceiling?

A) 192 ft.

B) 28 ft.

C) 56 ft. (Correct Answer)

D) 768 ft.

Explanation:
To find the perimeter of the ceiling (a rectangle) the four sides must be totaled.
12 + 16 + 12 + 16 = 56. The perimeter of the ceiling is 56 feet.

Related Common Core State Standard: Geometry: 6.G.1

Catalog-of-Grade-6-Mathematics-School-Library-Teacher-eLearning-Products-and-BooksClick Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 13

What would be the next two numbers in the following sequence?

1600, 800, 400, ____ , ____

A) 500, 600

B) 200, 100 (Correct Answer)

C) 200, 0

D) 0, -400

Explanation:
Each number in this sequence is half of the number preceding it. Therefore, the next two
numbers would be 200 (half of 400), and 100 (half of 200).

Related Common Core State Standard: Expressions & Equations: 6.EE.3

Catalog of Grade 6 Math e-Learning Products and BooksClick Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 12

Simplify the following ratio:

4/22

A) 1/11

B) 2/11 (Correct Answer)

C) 8/44

D) 3/21

Explanation:
To simplify a ratio, first find the Greatest Common Factor (GCF) of the numerator and the denominator. Then, divide each by that number. Here, the GCF is 2. When the numerator and denominator are each divided by 2, the result is 2/11.

Related Common Core State Standard: CCSS: 6.RP.3

Catalog of Grade 6 Math e-Learning Products and BooksClick Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 11

The measure of an angle is approximately 105 degrees. What type
of angle is it?

A) Right

B) Acute

C) Obtuse (Correct Answer)

D) Oblong

Explanation:
By definition, an obtuse angle measures between 90 and 180 degrees. Therefore, the angle described
above (having a measure of about 105 degrees) must be an obtuse angle.

Related Common Core State Standard: CCSS: 6.G.1

Click Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 10

The city of Trenton hired a crew of 100 workers to clean up the streets
of the city. The crew worked for 14 days. Each worker was paid at a
rate of $90 per day. What was the total labor cost for the city?

A) $1,260

B) $126,000 (Correct Answer)

C) $11,400

D) $9,000

Explanation:
If each of the 100 workers worked 14 days, the city had to pay for the equivalent of 1,400
days worth of work. 100 x 14 = 1,400. At a rate of $90 per day, that would amount to
$126,000. 1,400 x $90 = $126,000.

Related Common Core State Standard: CCSS: 6.NS.3

Click Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 9

When the expression 3(n + 7) is evaluated for a given value of n, the
result is 33.

What is the value of n?

A) n = 4 (Correct Answer)

B) n = 5

C) n = 21

D) n = 120

Explanation:
Since 3(n + 7) is equal to 33, then (n + 7) must equal 11. (3 x 11 = 33) Therefore, n must equal 4,
since 4 + 7 = 11.

Related Common Core State Standard: CCSS: 6.EE.2

Click Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 8

Which of the following statements is not true?

A) The denominator is the bottom number in a fraction.

B) The multiples of 9 are 1, 3, and 9. (Correct Answer)

C) The factors of 12 are 1, 2, 3, 4, 6, and 12.

D) A mixed number consists of a whole number and a fraction.

Explanation:
The second statement is not true. The multiples of nine would be an infinite set, including such
numbers as 9, 18, 27, 36, 45, and so on.

Related Common Core State Standard: CCSS: 6.NS.1

Click Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 7

Which of the following sets below contains only prime numbers?

A) 7, 11, 49

B) 7, 37, 51

C) 7, 23, 47 (Correct Answer)

D) 2, 29, 93

Explanation:
A prime number is a whole number (greater than 1) which is divisible by only 1 and itself.
The set {7, 23, 47} contains three numbers which fit the definition stated above. Each
number is divisible by only 1 and itself.

Related Common Core State Standard: 6.NS.4

Click Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 6

Which of the following is not a quadrilateral?C) Trapezoid

D) Rhombus

Explanation:
By definition, a quadrilateral must have four sides. Therefore, a triangle is not a quadrilateral since it only has three sides.

Related Common Core State Standard: 6.G.1

Click Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 5

50 percent of 65 is approximately equal to ________.

A) 15

B) 25

C) 30 (Correct Answer)

D) 40

Explanation:
To find 50% of 65, 65 can be multiplied by 0.5. 65 x 0.5 = 32.5. The answer choice
which is the closest approximation of this result is 30.

Related Common Core State Standard: 6.RP.3

Click Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 4

Which fraction below is greater than 3/5 but less than 3/4?

A) 1/3

B) 5/8 (Correct Answer)

C) 1/2

D) 4/5

Explanation:
As decimals, 3/5 = 0.60 and 3/4 = 0.75. The fraction 5/8 would be found within this range,
since 5/8 = 0.625 as a decimal.

Related Common Core State Standard: 6.NS.6

Click Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 3

Which of the following statements is true?

A) Perpendicular lines must cross, but intersecting lines do not have
to cross.

B) Perpendicular lines never cross, but intersecting lines always cross.

C) Perpendicular lines must cross to form ninety degree angles, but
intersecting lines cross to form angles of varying measures. (Correct Answer)

D) Perpendicular lines must cross to form obtuse angles, whereas
intersecting lines must cross to form acute angles.

Explanation:
The third statement is true. By definition, perpendicular lines must cross to form ninety-degree angles,
whereas intersecting lines simply need to cross at a point regardless of the angles formed.

Related Common Core State Standard: 6.G.1

Click Here to See Our Grade 6 Math Resources

Grade 6 Math Sample Question 2

When two fractions with different denominators are to be added
using the standard procedure, which of these must first be found?

A) The GCF (Greatest Common Factor) of the fractions

B) The prime factorization of the fractions’ numerators

C) The LCD (Least Common Denominator) of the fractions (Correct Answer)

D) The mean value of the denominators

Explanation:
In order to add fractions with different denominators using the standard procedure,
the Least Common Denominator (LCD) must be found. That way only the numerators of
the fractions need to be added.

Related Common Core State Standard: 6.NS.1

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Grade 6 Math Sample Question 1

Which of these is the standard form of twenty and sixty-three thousandths?

A) 20.63000

B) 20.0063

C) 20.63

D) 20.063 (Correct Answer)

Explanation:
The standard form would be written 20.063, since the whole number part is 20 and the decimal part is written .063 (sixty three thousandths).

Related Common Core State Standard: 6.NS.6

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