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50 math problems for 6th graders

Sixth graders tackle a variety of math concepts throughout the year. If you’re looking for ways to help your child practice their skills, check out this list of 50 math problems for 6th graders!

Author

Katie Wickliff

Published:

March 2025

Key takeaways

In 6th grade, students expand on foundational concepts introduced in earlier grades. While much of elementary school focuses on mastering basic operations and introducing concepts like measurement, geometry, and fractions, 6th graders move beyond concrete thinking to abstract reasoning, allowing them to tackle more complex and challenging material.

6th grade math focuses on five key areas: ratios and proportional relationships, the number system, expressions and equations, geometry, and statistics and probability. Sixth graders also strengthen their mathematical practices throughout the year, building habits and routines that will help prepare them for the future.

It’s also important to know that you can still support your 6th grader in math–even if the method of learning is different than when you were a student! Ways to support your student include:

Making math part of daily life. One way to do this is to encourage your 6th grader to help you budget and calculate discounts at the grocery store.
Encouraging a growth mindset. If your child gets frustrated, remind them that mistakes and challenges are part of learning and that even if they don’t understand something immediately, effort WILL lead to improvement.
Communicating with teachers. Establishing a strong partnership with your child’s teacher and school will help you understand where they might need more support.

Providing opportunities for your child to practice math problems in a low-stress environment. In addition to this worksheet, check out DreamBox— an engaging, interactive program that adapts to your child’s needs, helping them practice important math skills.

50 problems for 6th graders (and answers)!

In this article, we’ve provided a list of 50 math problems for 6th graders that will reinforce the concepts your child is learning at school. You’ll notice that the questions are divided into sections so your student can complete all the problems or focus on a specific topic. We’ve also included hard math problems for 6th graders if your child wants an extra challenge.

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Ratios and proportional relationships

Question 1: What is the ratio of triangles to circles?

Question 2: Reduce each ratio to its lowest form:

a) 6:18

b) 39:9

c) 14:14

Question 3: Fill in the blanks to make equivalent ratios:

a) 7:1=____:2

b) ___:5=16:20

c) 5:3=____:27

Question 4: Using the table below, determine if the relationship is proportional.

X Y

2	20
8	80
6	60
7	70

Yes, the relationship is proportional b) No, the relationship is not proportional

Question 5: Find the Unit Rate:

a) 24 copies in 6 minutes = ______ copies per minute

b) 4 movie tickets cost 56 dollars = _______ dollars per ticket

c) 54 pints of chocolate milk in 6 containers =_______pints per container

The number system

Question 1: Find the quotient of the following:

a) ⅔ ➗ 8/9

b) 7/10➗1/3

c) 3/8➗2/7

Question 2: List all of the factors for each number:

a) 42

b) 18

c) 60

Question 3: Convert the following fractions to decimals:

a) 3/10

b) 9/12

c) 6/5

Question 4: Add the following integers

a) -8+-5

b) 12+-23

c) 3+10+ -15

Question 5: Add the decimals using a number line

4.4 + 0.5=

Expressions and equations

Question 1: Solve for y

a) 5y+7=32

b) y-6=12

c) y/5=9

Question 2: Simplify the following expression:

6(3x+2)-2x

Question 3: Calculate the expressions. Write the expression that matches the statements. The first one has been done for you.

expression	when	value
15-m	m=6	15-6=9
3y + 5	y=5
4.5+h	h=2.7

Question 4: Which expression is equivalent to 3(x+7)

a) 3x+14

b) 7 (x+3)

c) 3x+21

Geometry

Question 1: A square has a side length of 5 cm.

a) Find the area of the square

b) Find the perimeter of the square

Question 2: A triangle has a base of 9 cm and a height of 5 cm.

Find the area of the triangle.

Question 3: A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm.

What is the volume of the rectangular prism?

Question 4: The radius of a circle is 5 inches. What is the circumference of the circle?

Math word problems for 6th graders

Statistics and probability

Question 1: Several schools won athletic awards. Find the median of the number of awards each school won:

3, 4, 4, 7, 8, 10, 13, 14, 15

Question 2: Find the mode for the following set of numbers:

21, 22, 22, 22, 23, 26, 27, 30

Question 3: Lee scored 76, 84, 92, and 89 on his math tests. What is the mean score of Lee’s tests?

Question 4: Which of the following is an example of a statistical question:

a) How many players are on the 6th grade volleyball team?

b) What color dress is Maeve wearing?

c) What are the favorite ice cream flavors of the girls in Ms. Cook’s 6th grade class?

Question 5: A school has 500 students. If 40% of the students are girls, how many girls are in the school?

Question 6: If you rolled the dice one time, what is the probability that it will land on a 4?

Question 7: If you rolled the dice one time, what is the probability that it will not land on a 1?

Extra challenge – tricky math problems for 6th graders

Question 1: Piper spends 25 minutes studying math, 35 minutes studying history, and 20 minutes studying grammar. What percentage of her time is spent studying grammar?

Question 2: David has 56 cookies. 1/4 are chocolate chip, 2/4 are oatmeal, and the rest are peanut butter. What is the ratio of chocolate chip to oatmeal to peanut butter?

Question 3: Solve ⅞ ➗3/4

Question 4: Sally’s fish tank has a height of 12 yards, a width of 6 yards, and a length of 24 yards. What is the volume of the fish tank?

Question 5: Solve (-18) – ____=(-34)

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