30 math problems for 7th graders
Math in 7th grade can leave students and parents scratching their heads. These 30 math problems can help clarify the key concepts in 7th-grade math and boost students’ confidence in the classroom.
Author
Tess Loucka
Published:
March 2025
Key takeaways
- • Math curriculum in 7th grade begins to prepare students for high school.
- • Key math concepts studied in 7th grade include proportions, the order of operations, basic geometry, 2-step equations, and beginning statistics and probability.
- • With plenty of structured practice, all 7th graders can excel in math class.
In 7th grade, students start learning how to visualize abstract concepts and create mathematic models to express ideas. Students must be able to prove their reasoning with viable arguments, too, requiring confidence in their work.
Key topics in 7th grade math
In 7th grade, students are expected to master the four operations of addition, subtraction, multiplication, and division, and be able to use the order of operations or PEMDAS. Students should also be able to simplify expressions, convert fractions, decimals, and percents, solve 1- and 2-step equations, and more.
The shift from math problems in 6th grade to math problems for 7th graders can be hard for some students, especially as the curriculum starts preparing students for high school. However, thorough practice and assistance with complicated concepts can help any student succeed.
For students interested in practicing math problems for 7th graders, DreamBox’s math program offers structured and immersive math problems, thorough explanations, and detailed answer keys to ensure you’re always on the right track.
For further study, this article offers 30 math problems for 7th graders with answers. Read through this article for practice on everything from simple problems to tricky math problems for 7th graders and everything in between.
Faces connect to form edges and vertices.
Table of contents
Ratios and proportional relationships
Students should be able to analyze proportional relationships and apply their knowledge to real-world situations.
Question 1: Sean can read 8 pages every 3 minutes. How long, in minutes, would it take him to read 336 pages?
Question 2: If Gordie takes 54 minutes to draw 9 pictures, how many minutes does it take him to draw 1 picture?
Question 3: Evie is making bracelets with beads. The arts and crafts store charges $1.25 for two bags of beads. How much will Evie need to pay for 18 bags of beads?
Question 4: If a pet store pays its employees $22 per hour of work, how much would an employee make if they worked for 45 minutes?
Question 5: Casey can organize ⅛ of her room in ¼ of an hour. If she continues organizing at this rate, how much of her room can she organize in 1.5 hours?
Question 6: Johnny can finish ⅕ of his homework every ½ of an hour. If he continues doing his homework at this rate, how long will it take him to finish his homework?
The number system
Students should understand the number line and be able to work confidently with both positive and negative numbers.
Question 7: -10 – (-8) – (-2) + 14
Question 8: -6 + (-11)
Question 9: What value, when substituted for x, makes the following equation equal 0?
-9 + x = 0
Question 10: What value, when substituted for x, makes the following equation equal 0?
12 – x + 2 = 0
Question 11: Mark your thought process and answer the following question using the number line provided.
-2 – 7
Question 12: -8 x 8
Expressions and equations
Question 13: Simplify the following expression:
3x + 5y – 2x + 7y
Question 14: Simplify the following expression:
136y + y
Question 15: Simplify the following expression:
18x – 4(x + 2)
Question 16: Simplify the following expression:
5(x – 3) – 7(x + 15)
Expressions and equations word problems
Word math problems for 7th graders can be tricky. Just remember to take notes, draw pictures, and do whatever else you can to better visualize the questions being asked.
Question 17: When 12 is added to ⅕ of another number, the result is 14. What is the other number?
Question 18: Write out an equation that represents the following situation:
Abby takes a karate class every week. The first week she spent 10 hours practicing alone with her instructor. Every week after that, Abby only practices with her instructor for 4 hours. She will take her belt test after a total of 22 hours of practice.
Geometry
Question 20: What is the area of this circle?
Question 21: What is the area of this triangle?
Question 22: Find the surface area of this rectangular prism.
Geometry word problems
Question 23: If a rectangular prism has a length of 5, a width of 8, and a height of 14, what is its area? Write your answer in inches squared.
Question 24: If a circle has a radius of 7, what is its circumference? Do not simplify your answer.
Statistics and probability
At this grade level, students should know how to make simple inferences about samples based on the rules of statistics and probability.
Question 25: Sally spun a spinner with red, green, and blue portions 20 times and recorded her results. During this experiment, the spinner landed on red 9 times, green 6 times, and blue 5 times.
What is the experimental probability of the spinner landing on the red section?
Question 26: Robert has a bag of marbles containing 3 blue marbles, 5 purple marbles, 8 red marbles, 11 yellow marbles, 2 clear marbles, and 1 green marble.
What is the probability that Robert will pick a purple marble out of the bag? Simplify your answer.
Question 27: Steve flips two coins and rolls one 6-sided die. What is the probability he will get two heads and will roll a 5?
Question 28: A juice company wants to find out what their customers’ favorite flavor of juice is. What population should the company study to get an answer?
- All of their customers
- The entire population of New York
- A portion of their customers
- Everyone in the US
Question 29: A children’s clothing company wants to find out if kids in the United States like their new clothing designs. What population should the company study to get an answer?
- Every adult in the US
- Every child in the US
- All of their customers
- A portion of children in the US
Question 30: A middle school basketball coach wants to figure out the average height (in inches) of the players on his basketball team. Use the provided dot plot to find the average height of the basketball players.
Answer sheet
Once you’ve worked on the questions above, check your answers with the following answer key! Don’t peek at the answers until you’ve done your best to find the answer yourself. The problems offered above are hard math problems for 7th graders, but for the best results, challenge yourself to answer them even if you aren’t sure how!
Ratio and proportional relationships
- 1. 126 minutes
- 2. 6 minutes
- 3. $11.25
- 4. $16.50
- 5. 6/8 or 3/4
- 6. 5/2 hours or 2.5 hours
The number system
- 7. 14
- 8. -17
- 9. 9
- 10. 14
- 11. -9
- 12. -64
Expressions and equations
- 13. x + 12y
- 14. 137y
- 15. 14x – 8
- 16. -2x – 120
- 17. 10
- 18. 4x + 10 = 22
Geometry
- 19. 91
- 20. 100 𝛑 in^2
- 21. 20
- 22. 124
- 23. 560cm^3
- 24. 2 𝛑 7
Statistics and probability
- 25. 9/20
- 26. 5/30 or 1/6
- 27. 1/24
- 28. A
- 29. B
- 30. 60.8
