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Common Core - State Standards Initiative

• Students learn about ratios, mixed properties, statistics and other seventh grade skills.
• Teachers incorporate the use of the scratchpad to give students a visual representation.
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28 7th Grade Math Problems With Answers And Worked Examples

Linda Bortnick

7th grade math problems build on students’ reasoning skills and understanding of key mathematical concepts.

We’ve created 28 7th grade math problems for your classroom, suitable for use as additional practice before an assessment, as a Do Now activity, or for an Exit Slip to check for understanding after a lesson. Math teachers designed these problems to build on students’ math skills and help to prepare them for the rigor expected ahead in 8th grade and in high school courses like Algebra, Geometry, and Statistics.

What are 7th grade math problems?

7th grade math problems combine 7th grade math concepts with grade-level appropriate reasoning and problem solving skills.

7th grade math content includes computing with all rational numbers in all four operations, using the correct order of operations  to simplify expressions, solving problems involving percentages, using proportional reasoning, solving 1 and 2 step equations, multi-step inequalities and extending knowledge of geometry.

Why focus on problem solving in 7th grade?

Excelling at computation is great; excelling at computation but not understanding application is pointless. The purpose of mathematics is to learn to reason, find patterns, and use logic, so solving math problems  that are rich, deep, and complex is necessary to meet those purposes.

Mathematics today has advanced beyond just computation and evolved into a marriage of numbers and words – not only do students need to get to a numerical answer they also need to be able to communicate their thinking and processes along the way. They need repeated practice in reasoning, perseverance, and rational thinking to solve problems throughout their lives.

7th grade is a perfect time to extend problem solving activities in the classroom. The curriculum moves away from much of the memorization required in elementary school of basic addition facts and times tables , and builds on 6th grade content to focus on making connections between mathematical reasoning , logic, and numbers.

Math Games For 7th Grade

13 fun math games and activities for 7th grade students to complete independently or with a partner. Includes ready to go math games with minimal prep required. The perfect lesson starter or finisher.

The 7th grade math curriculum

This article focuses on problems for 7th grade students, especially concepts taught in pre-algebra. Pre-algebra includes concepts of proportional relationships, algebraic expressions, equivalent expressions, equations, rational numbers, graphs, and extension of knowledge of the number system, including whole numbers and mixed numbers. The problems align with common core standards.

Seventh grade math can be considered a turning point in mathematics. It bridges the concepts taught in elementary school, including the foundations of arithmetic and number sense, with the rigor expected ahead in high school courses like Algebra, Geometry, and Statistics.

7th grade math problems

We’ve designed 28 7th grade math problems to use as a whole class or in a Tier 2  or Tier 3 intervention  to help develop and secure students’ mathematical knowledge.  

7th grade math problems: Four operations

• Solve -4 + 10. Use the number line.

2. Solve: -8 – 12. Use the number line.

Solution :        6

Solution :         -20

3. Solve: 4(-3)(-2)

Solution :          24

4. Bill said the answer to -3 – 12 is 9. What mistake did he make? What is the correct answer?

Solution : Bill knows that the opposite of subtraction is addition, but he forgot to take the opposite of 12, so he re-wrote the problem as -3 + 12. Since we are subtracting 12 from -3, the answer is the same as -3+-12, which is -15.

7th grade math problems: Order of operations

5. Solve: 2(10-8) ÷ 2 + 4

    Solution : 2(10-8) ÷ 2 + 4

                    2(2) ÷ 2 + 4

                    4  ÷ 2 + 4

                    2 + 4

                    6

6. Solve: (3 + 10 ÷ 2 – 6) x 6

     Solution : (3 + 10 ÷ 2 – 6) x 6

                    (3 + 5 – 6) x 6

                    (8 – 6) x 6

                     2 x 6

                     12

7. Solve: -5(8) ÷ 2 + 6

    Solution : -5(8) ÷ 2 + 6

                    -40 ÷ 8

                     -5

8. Solve: (-2)3 – 2 + 6 ÷ 3

    Solution : (-2)3 – 2 + 6 ÷ 3

                     -8  – 2 + 6 ÷ 3

                     -8 – 2 + 2

                     -10 + 2

                     -8

7th grade math problems: Percentages

9. Isabella got 16 out of 40 questions wrong on her quiz. What percent did she get correct?

Solution : \frac{16}{40} can be simplified to \frac{2}{5} , which is equivalent to \frac{40}{100} or 40%. If Isabella got 40% incorrect, she got 60% correct (100-40=60).

10. Without doing any computation, explain whether \frac{38}{72} is greater than or less than 50%.

Solution: \frac{38}{72} is greater than 50%. \frac{36}{72} is equivalent to \frac{1}{2} , which is equivalent to 50%. Since 38 is a little greater than 36, \frac{38}{72} is a little greater than 50%.

11. Put the following in order from least to greatest: \frac{3}{4} , 76%, 0.68, \frac{3}{5} , \frac{35}{50} , 0.702

Solution: \frac{3}{5} , 0.68, \frac{35}{50} , 0.702, \frac{3}{4} , 76%

12. A store marked all shoes on sale for 30% off. What percent will Sam pay for shoes? Explain your answer.

Solution: Sam will pay 70% for shoes. The full price is 100%, so if 30% is saved, the remaining 70% will be the sales price.

7th grade math problems: Proportional relationships

13. \frac{5}{6}  = \frac{x+2}{15}

      Solution: 6( x +2) = 5(15)

                     6 x + 12 = 75

                  -12   -12

                    \frac{6x}{6} = \frac{63}{6}

      x =   10.5

14. Three out of every five students are wearing jeans. If there are 20 students in total, how many are wearing jeans?

Solution: \frac{3}{5}  = \frac{x}{20}

                3 (20) = 5 x

                60 = 5 x

                12 = x

15. Three out of every five students are wearing jeans. If there are 20 students in all, how many are not wearing jeans?

Solution: From the last problem, we saw that \frac{3}{5} is the same as the 12 students wearing jeans. If there are 20 students total, we can subtract the 12 wearing jeans from the 20 total to find that 8 are not wearing jeans. We could also set up this proportion and solve to get 8.

                \frac{2}{5}  = \frac{x}{20}

16. A museum requires 12 chaperones for the 60 students attending the field trip. How many students are assigned to each chaperone?

         \frac{12}{60} = \frac{1}{x}

        12 x = 60(1)

        12 x = 60

          x = 5

Each chaperone will have a group of 5 students.

7th grade math problems: One-step equations and two-step equations

17. Solve: x + 7.1 = 15.9

         Solution:   x + 7.1 = 15.9

                           -7.1      -7.1

                         x = 8.8

18. Solve: x – 63 = 106.75

         Solution: x – 63 = 106.75

                       +63     +63

                         x  = 169.75

 19. Solve: 6( x + 3) = -6

         Solution: 6 x + 18 = -6

                     – 18    -18

                          \frac{6x}{6} = \frac{-24}{6}

                         x = -24

20. Solve: 0.5 x + 10 = 36

         Solution: 0.5 x + 10 = 36

                           -10    -10

                        0.5 x = 26

                        x = 52

7th grade math problems: Geometry

21. Madison measured this angle with her protractor and said “It is 60°.”

Without measuring the angle, Bella said she could tell Madison’s answer was incorrect. How did Bella know this?

Solution : Bella knew this angle could not be 60° because this angle is obtuse

but a 60° angle is acute.

22. Find the circumference of the circle.

Solution: C = πd

            C =  15π

23. Use the figure to fill in the blanks:

Angles A and B are _________________ angles so their measures are _______________________________.

Solution: Angles A and B are vertical  angles so their measures are equal.

24. Find the value of x .

         Solution: 5 x + 4 x =90

                      9 x = 90

                        x = 10

7th grade math problems: Math word problems

25. The 7th Graders at Marxville Middle School voted for their student council representatives. There were 200 votes cast in all. How many votes did the winner get?

Solution: Alexandra won the election with 30% of the votes. To find 30% of the 200 total votes, we can multiply 0.3 (200) to discover that she got 60 votes in all.

26. Brian runs every 12 days and Stella every 8 days. Both Brian and Stella ran today. How many days will it be before they both run on the same day again?

Solution: This is a Least Common Multiple problem. Brian runs on days 12, 24, 36, 48… and Stella runs on days 8, 16, 24, 32…, so they will both run again on Day 24.

27. Mr. Orlando is planting his vegetable garden this summer. He plants \frac{3}{4} of the garden with peppers and \frac{1}{4} with tomatoes. Of the peppers, \frac{1}{3} are red peppers. What fraction of the entire garden will be red peppers?

Solution: Red peppers will make up \frac{1}{3} of \frac{3}{4} (the pepper section) of the garden. \frac{1}{3} x \frac{3}{4} = \frac{1}{4} , so \frac{1}{4} of the entire garden will consist of red peppers.

28. Will the product of -45(96) be positive or negative? Without solving, how do you know?

Solution: The answer will be negative. Multiplying a negative number by a positive one always leads to a negative product.

Challenges in teaching 7th grade mathematics

Let’s face it, most 7th graders don’t wake up every morning excited to get to math class that day to expand on their mathematical knowledge and thinking! Often, there are much more pressing matters in the mind of a 12 year old. However, with the right mindset and classroom climate, we can support our students to help them put forth their best effort every day.

• Praise effort:  Developing a growth mindset in the classroom  is key. Even if a student struggles to come to an answer, it is critical to praise the effort. We must make the thinking part of mathematics something to treasure rather than solely focus on correct numerical answers.
• Include low threshold high ceiling activities: These go a long way in piquing the interest level of most students.
• Have fun:  Don’t be afraid to have some fun math activities  and silliness in your lessons, whether that’s through funny estimation activities  or videos to get students interested, engaged and willing to try.

How can Third Space Learning help with 7th grade math?

STEM-specialist tutors help close learning gaps and address misconceptions for struggling 7th grade math students. One-on-one online math tutoring sessions help students deepen their understanding of the math curriculum and keep up with difficult math concepts. Each student works with a private tutor who adapts instruction and math lesson content in real-time according to the student’s needs to accelerate learning.

4 top tips for teaching 7th grade math problems

Here are some teaching tips to overcome common challenges and support problem solving in your classroom:

• Focus on effort, not accuracy:  Students come into 7th grade with many ideas about math. Many of these ideas are likely negative and may result in some math anxiety . They’ve heard math is hard, you’re never going to use it, it’s confusing. Be excited about what you’re teaching and learning! Praise kids for trying their best, not for always being correct. Consider establishing effort-based reward systems, such as publicly nominating students for Mathematician of the Month.
• Check for understanding:  Be sure students understand questions before they attempt to answer them. Have them rephrase the question or explain what they’re looking for to solve the problem.
• Ask for wrong answers: Students may feel a lack of confidence in math but if you ask them for a wrong answer, they may feel more inclined to answer. It can also prompt students to engage with and make sense of the information given in the problem in a less pressured environment.

Alternatively, as teachers, you can give some suggestions. For example, “3/10 of students got an A on the last test. There are 20 students in the class. How many got an A?” Could 20 of the students have gotten an A? No? Why not? Could 8.5 of the students have gotten an A? Why not? Then get more specific. Did more or less than 10 of the students get an A? How do you know?

• Use relatable, real-world problems:  Sometimes, problem solving uses questions about gas mileage or building fences that kids either don’t relate to or don’t care about. Find out what your students’ interests are and incorporate that into your math instruction. Alternatively, use seasonal and relatable contexts such as Thanksgiving math activities , summer math  or mardi gras math .

7th grade math worksheets

Looking for more resources? Please see our selection of seventh grade math worksheets covering 7th grade key math topics and more. Each includes printable resources and step-by-step answer keys:

• Surface Area Of Rectangular Prisms Worksheet
• Fraction to Decimal Worksheet
• Adding and Subtracting Integers Worksheet
• Adding and Subtracting Scientific Notation Worksheet
• Distributing Exponents Worksheet
• Simplifying Expressions Worksheet

READ MORE :

• 25 Fun Math Problems For Elementary School
• Math Questions For 5th Graders
• 4th Grade Math Problems

7th grade math problems FAQ

What math should a 7th grader know?

A 7th grader should be able to compute using all four operations with positive and negative rational numbers. They should be able to simplify expressions, solve one- and two- step equations, and solve proportions. Additionally, 7th graders can work with probability of simple and compound events, as well as study concepts of geometry, including finding angle measurements and solving for area and perimeter of regular and irregular polygons and circles.

What does 7th grade math focus on?

Seventh grade math focuses on working with positive and negative rational numbers in simplifying expressions and equations as well as solving one- and two-step equations. Additionally, extensive work is done in solving proportions and ratios.

Is 7th grade math hard?

Seventh grade math is always achievable! Students who find it hard usually come into the grade without having mastered basic concepts and facts. Be sure students are automatic with facts across addition, subtraction, multiplication, and division and have the ability to work with fractions and decimals. It will make the new concepts in 7th grade easier to learn.

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Algebra Questions and Problems for Grade 7

Grade 7 algebra questions and problems with detailed solutions are presented. Questions on simplifying expressions, solving equations, factoring expressions,....are included.

• 12 x 3 + 5 x 2 + 4 x - 6 for x = -1
• 2 a 2 + 3b 3 - 10 for a = 2 and b = -2
• (- 2 x - 1) / (x + 3) for x = 2
• 2 + 2 |x - 4| for x = - 4
• - 2( x - 8) + 3 (x - 7)
• 2 (a + 1) + 5b + 3(a + b) + 3
• a (b + 3) + b (a - 2) + 2 a - 5 b + 8
• (1 / 2) (4x + 4) + (1 / 3)(6x + 12)
• 4 ( - x + 2 - 3(x - 2) )
• x / y + 4 / y
• (2 x / 4 ) × (1 / 2)
• (3 x / 5 ) ÷ (x / 5)
• 3 x 2 × 5 x 3
• [ (2 y) 4 9 x 3 ] ÷ [ 4 y 4 (3 x) 2 ]
• 24 x + 18 y
• 2 x + 5 = 11
• 3 x = 6 / 5
• 3 (2 x + 2) + 2 = 20
• Rewrite the expressions 3 × a × a × a - 5 × b × b using exponential.
• A rectangle has a length given by 2 x + 3 units, where x is a variable. The width of the rectangle is given by x + 1 units. Find the value of x if the perimeter of the rectangle is equal to 32.
• A rectangle has a length given by 2x - 1 units, where x is a variable. The width of the rectangle is equal to 3 units. Find the value of x if the area of the rectangle is equal to 27.
• 45% of the students in a school are male? Find the ratio of the number of female to the total number of male students in this school.
• A car travels at the speed x + 30 kilometers in one hour, where x is an unknown. Find x if this car covers 300 kilometers in 3 hours?
• Solve the proportion : 4 / 5 = a / 16
• Find a if the ordered pair (2 , a + 2) is a solution to the equation 2 x + 2 y = 10?
• Find the greatest common factor of the numbers 25 and 45.
• Write the number " one billion, two hundred thirty four million, seven hundred fifty thousand two " using digits.
• Write the number 393,234,000,034 in words.
• Find the lowest common multiple to the numbers 15 and 35.
• Find x if 2 / 3 of x is 30?
• What is 20% of 1 / 3?
• Order 12 / 5 , 250% , 21 / 10 and 2.3 from the smallest to the largest.
• The sum of 3 positive consecutive integers is equal to 96. Find the largest of these numbers.
• Dany scored 93 in physics, 88 in mathematics, and a score in chemistry that is double his score in geography. The average score of all 4 courses is 79. What were his scores in chemistry and geography?
• Linda scored a total of 265 points in mathematics, physics and English. She scored 7 more marks in mathematics than in English and she scored 5 more marks in physics than in mathematics. Find her scores in all three subjects.
• There are bicycles and cars in a parking lot. There is a total of 300 wheels including 100 small wheels for bicycles. How many cars and how many bicycles are there?
• The difference between two numbers is 17 and their sum is 69. Find the largest of these two numbers.

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Building Problem-solving Skills for 7th-Grade Math

Mathematics is a subject that requires problem-solving skills to excel. In 7th grade, students begin to encounter more complex math concepts, and the ability to analyze and solve problems becomes increasingly important. Building problem-solving skills for math not only helps students to master math concepts but also prepares them for success in higher-level math courses and in life beyond academics. 

In this article, we will several key skills that are needed for success in 7th-grade math, and also explore how they can benefit students both academically and personally. We will also provide tips and strategies to help students develop and improve their problem-solving skills. Let’s dive in!

Building Analytical Skills

The first of seven important skills to build is that of analytical skills. These allow students to analyze a problem and break it down into smaller parts. From there, they’re able to identify the key components that need to be addressed. Analytical skills also hone students’ abilities to identify patterns. Students should be able to identify patterns in mathematical data, such as in number sequences, geometric shapes, and graphs. Importantly, students should not just be able to recognize the pattens, but they should be able to describe them (more on that in communication) and use them to make predictions and solve problems.

We alluded to this earlier, but breaking down problems is an essential component of analytical skills. Students with strong analytical skills can break problems down into smaller and more manageable parts. They are then able to identify key components of a problem and use this information to develop a strategy for solving it. 

Along with identifying patterns comes identifying relationships. Students with good mathematical analytical skills can identify relationships between different mathematical concepts, such as the relationship between addition and subtraction, or the relationship between angles and shapes. Through strengthening this skill, students will be able to describe these relationships and use them to solve problems. 

An important part of analytical skills is the ability to analyze data. Students should be able to analyzeand interpret data presented in a variety of formats, such as graphs, charts, and tables. They should be able to use this data to make predictions, draw conclusions, and solve problems.

Speaking of conclusions, reaching sound conclusions based on mathematical data is a fundamental skill needed for making predictions based on trends in a graph, or drawing inferences from a set of data.

Another skill students should master is the ability to compare and contrast mathematical concepts, such as the properties of different shapes or the strategies for solving different types of problems. Through this, they’ll be able to use the information they gather to solve problems. 

With all these skills at play comes arguably the most important: Critical thinking. This is an indicator that a student really grasps the concepts and it’s just repeating them back to you on command. Critical thinking is the ability to evaluate information and arguments, and make judgements and decisions based on evidence, and apply logic and reasoning to solve problems.

Building Creative Thinking

This is the ability for students (or anyone, really) to think outside the box and come up with innovative solutions to problems. This involves being able to approach problems from different angles and to consider multiple perspectives. For a 7th-grader, this skill can be exercised through the following:

• Thinking Outside the Box: Students should be encouraged to think creatively and come up with innovative solutions to problems. This involves thinking outside the box and considering multiple perspectives.
• Finding Multiple Solutions: Students should be able to come up with multiple solutions to a problem and evaluate each one to determine which is the most effective.
• Developing Original Ideas: Students should be able to develop original ideas and approaches to solving problems. This involves being able to come up with unique and innovative solutions that may not have been tried before.
• Making Connections: Students should be able to make connections between different mathematical concepts and apply these connections to solve problems. This involves looking for similarities and differences between concepts and using this information to make new connections.
• Visualizing Solutions : Students should be able to visualize solutions to problems and use diagrams, charts, and other visual aids to help them solve problems.
• Using Metaphors and Analogies: Students should be able to use metaphors and analogies to help them understand complex mathematical concepts. This involves using familiar concepts to explain unfamiliar ones and making connections between different ideas.

Building Problem-Solving Strategies

It may sound like the same thing, but building problem-solving strategies is not the same as building problem-solving skills. Building strategies for problem-solving lends itself to actual problem-solving. Let’s expand on this: Say your student is presented a problem that they’re struggling with, these are some of the problem-solving strategies they may use in order to solve the puzzle.

• Identify the problem: The first step in problem-solving is to identify the problem and understand what is being asked. Students should carefully read the problem and make sure they understand the question before attempting to solve it.
• Draw a diagram: Students can draw a diagram to help visualize the problem and better understand the relationships between different parts of the problem.
• Use logic: Students can use logic to identify patterns and relationships in the problem. They can use this information to develop a plan to solve the problem.
• Break the problem down: Students can break a complex problem down into smaller, more manageable parts. They can then solve each part of the problem individually before combining the solutions to get the final answer.
• Guess and check: Students can guess and check different solutions to the problem until they find the correct answer. This method involves trying different solutions and evaluating the results until the correct answer is found.
• Use algebra: Algebraic equations can be used to solve a variety of mathematical problems. Students can use algebraic equations to represent the problem and solve for the unknown variable.
• Work backward: Students can work backward from the final answer to determine the steps required to solve the problem. This method involves starting with the end goal and working backward to determine the steps needed to get there.

Building Persistence and Perseverance

In an increasingly instant-gratification world with apps, searches and AI chatbots just a click away, this is an important skill not just in the math classroom, but for life in general. Problem-solving, whether that’s a math problem or a life challenge, often requires persistence and perseverance. Student need to learn to be able to stick with a problem even when it seems challenging, difficult, or seemingly impossible. Here are ways you can encourage your students to stick it out when working on problems:

• Trying multiple approaches: When faced with a challenging problem, students can demonstrate persistence by trying multiple approaches until they find one that works. They don’t give up after one attempt but keep trying until they find a solution.
• Reframing the problem: If a problem seems particularly difficult, students can demonstrate perseverance by reframing the problem in a different way. This can help them see the problem from a new perspective and come up with a different approach to solve it.
• Asking for help: Sometimes, even with persistence, a problem may still be difficult to solve. In these cases, students can demonstrate perseverance by asking for help from their teacher or classmates. This shows that they are willing to put in the effort to find a solution, even if it means seeking assistance.
• Learning from mistakes: Making mistakes is a natural part of the problem-solving process, but students can demonstrate persistence by learning from their mistakes and using them to improve their problem-solving skills. They don’t get discouraged by their mistakes, but instead, they use them as an opportunity to learn and grow.
• Staying focused: In order to solve complex math problems, it’s important for students to stay focused and avoid distractions. Students can demonstrate perseverance by staying focused on the problem at hand and not getting distracted by other things.

Building Communication Skills

We alluded to this earlier, but a central part of building problem-solving skills is building the ability to articulate a problem or a solution. This isn’t just for the sake of personal understanding, but critical for collaboration. Students need to be able to explain their thinking, ask questions, and work with others to solve problems. Here are some examples of communication skills that can be used to build problem-solving skills:

• Clarifying understanding: Students can ask questions to clarify their understanding of the problem. They can seek clarification from their teacher or classmates to ensure they are interpreting the problem correctly.
• Explaining their reasoning: When solving a math problem, students can explain their reasoning to show how they arrived at a particular solution. This can help others understand their thought process and can also help students identify errors in their own work.
• Collaborating with peers: Problem-solving can be a collaborative effort. Students can work together in groups to solve problems and communicate their ideas and solutions with each other. This can lead to a better understanding of the problem and can also help students learn from each other.
• Writing clear explanations: When presenting their solutions to a math problem, students can write clear and concise explanations that are easy to understand. This can help others follow their thought process and can also help them communicate their ideas more effectively.
• Using math vocabulary: Math has its own language and using math vocabulary correctly is essential for effective communication. Students can demonstrate their understanding of math concepts by using correct mathematical terms and symbols when explaining their solutions.

Building Mathematical Knowledge

This would seem like a no-brainer, since you’re a math educator clicking on an article about building math problem-solving skills. However, it’s worth being explicit that problem-solving in math requires a solid understanding of mathematical concepts, including arithmetic, algebra, geometry, and data analysis. Students need to be able to apply these concepts to solve problems in real-world contexts.

7th-grade math covers a wide range of mathematical concepts and skills. Here are some examples of mathematical knowledge that 7th-grade math students should have:

• Algebraic expressions and equations: Students should be able to write and simplify algebraic expressions and solve one-step and two-step equations.
• Proportional relationships: Students should be able to understand and apply proportional relationships, including identifying proportional relationships in tables, graphs, and equations.
• Geometry: Students should have a solid understanding of geometry concepts such as angles, triangles, quadrilaterals, circles, and transformations.
• Statistics and probability: Students should be able to analyze and interpret data using measures of central tendency and variability, and understand basic probability concepts.
• Rational numbers: Students should have a solid understanding of rational numbers, including ordering, adding, subtracting, multiplying, and dividing fractions and decimals.
• Integers: Students should be able to perform operations with integers, including adding, subtracting, multiplying, and dividing.
• Ratios and proportions: Students should be able to understand and use ratios and proportions in a variety of contexts, including scale drawings and maps.

In conclusion, problem-solving skills are essential for success in 7th grade math. Analytical skills, critical and creative thinking, problem-solving strategies, persistence, communication skills, and mathematical knowledge are all important components of effective problem-solving. By developing these skills, students can approach math problems with confidence and achieve their full potential.

If you enjoyed this read, be sure to browse more of our articles . More importantly, if you want to save yourself hours of preparation time by having full math curriculums, review guides and tests available at the click of a button, be sure to sign up to our 7th Grade Newsletter . You’ll receive loads of free lesson resources, tips and advice and exclusive subscription offers!

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Build Confidence with Math Problem Solving

Daily Problem Solving will help your 7th grade students master the skills they need to be successful with challenging word problems...and have fun doing it .

What you'll get with this download:

Your download includes a full week of Daily Problem Solving for Grade 7 to try out in your own classroom. Developed with the brain in mind, these multi-step word problems will challenge your learners without overwhelming them. Best of all, you'll be able to watch their skills and confidence grow as they begin to internalize strategies for conquering this difficult math skill.

FUN & ENGAGING

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MINIMAL PREP

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PRINT & DIGITAL

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STUDENT PRINTABLES

You'll receive a full week of printable Daily Problem Solving practice for your students. This format includes:

• Paper-saving format that fits a full week on one page
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• Themed problems & weekly fun fact to engage

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Daily digital slides offer your remote or online learners the opportunity to build problem-solving skills in a structured format designed for success.

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Free Printable Math Word Problems Worksheets for 7th Grade

Math Word Problems: Discover a vast collection of free printable worksheets for Grade 7 students, created by educators to enhance mathematical skills and problem-solving abilities. Dive into Quizizz's resources today!

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Explore printable Math Word Problems worksheets for 7th Grade

Math Word Problems worksheets for Grade 7 are an essential resource for teachers looking to challenge their students and help them develop critical thinking skills. These worksheets cover a wide range of topics, including fractions, decimals, percentages, algebra, geometry, and more. By incorporating real-life scenarios and engaging themes, Grade 7 Math Word Problems worksheets not only make learning math more enjoyable but also help students understand the practical applications of the concepts they are learning. Teachers can easily find and download these worksheets online, making it simple to integrate them into their lesson plans and customize them to suit the needs of their students. With Math Word Problems worksheets for Grade 7, teachers can ensure their students are receiving a well-rounded math education that prepares them for future success.

Quizizz is an innovative platform that offers a variety of resources for teachers, including Math Word Problems worksheets for Grade 7, interactive quizzes, and engaging games. This platform allows teachers to create customized quizzes and activities that align with their lesson plans, making it easy to assess student understanding and track progress. In addition to Math Word Problems worksheets, Quizizz also offers a vast library of other math resources, covering topics such as number sense, measurement, data analysis, and more. Teachers can easily search for and access these resources, making Quizizz a one-stop-shop for all their Grade 7 Math needs. By incorporating Quizizz into their teaching strategies, educators can provide their students with a fun, interactive, and effective way to learn and practice essential math skills.

Fractions Worksheets Grade 7

Fractions worksheets 7th grade can be used to give students a better understanding of how to solve questions involving fractions numbers. These grade 7 math worksheets incorporate problems based on the application of arithmetic operators on fractions, word problems, and other questions associated with the concept of fractions.

Benefits of 7th Grade Fractions Worksheets

Fractions can sometimes be a confusing topic for young minds. To ensure that students have crystal clear concepts, they can solve the problems available in the fractions worksheets 7th grade. The well-curated questions are organized in an increasing level of difficulty and give students the flexibility to work at their own pace.

Printable PDFs for Grade 7 Fractions Worksheets

The 7th grade fractions worksheets is interactive, easy to use, and has several visual simulations that help students in assimilating the topic in a more effective manner. This worksheet is also available in PDF format that is free to download

• Math 7th Grade Fractions Worksheet
• 7th Grade Fractions Math Worksheet
• Seventh Grade Fractions Worksheet
• Grade 7 Math Fractions Worksheet

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7th Grade Math Problems

In 7th grade math problems you will get all types of examples on different topics along with the solutions.

Keeping in mind the mental level of child in Grade 7, every efforts has been made to introduce new concepts in a simple language, so that the child understands them easily. The difficulty level of the problems has been reduced and mathematical concepts have been explained in the simplest possible way. Each topic contains a large number of examples to understand the applications of concepts. If student follow math-only-math they can improve their knowledge by practicing the solutions step by step which will help you to score in your exam.

●  Set Theory

Sets : An introduction to sets, methods for defining sets, element of set and use of set notations.

Objects Form a Set : State, whether the following objects form a set or not by giving reasons.

Elements of a Set : Learn how to find the elements of a set with the help of various types of problems on the basic concepts of sets.

Properties of Sets : Using the basic properties to represent a set learn to solve various basic types of problems on sets.

Representation of a Set : Definition with examples of statement form, roster form or tabular form, set builder form cardinal number of a set and the standard sets of numbers.

Different Notations in Sets : Some of the familiar notations used in sets which are generally required to solve various types of problems on sets.

Standard Sets of Numbers : Learn to represent the standard sets of numbers using the three methods i.e. statement form, roster form and set builder form.

Types of Sets : Definition with examples of empty set or null set, singleton set, finite set, infinite set, cardinal number of a set, equivalent set and equal sets.

Pairs of Sets : Definition with examples of equal set, equivalent set, disjoint sets and overlapping set.

Subset : Definition with examples of subset and its types, super set, proper subset, power set and universal set.

Subsets of a Given Set : How to find the number of subsets of a given set and number of proper subsets of a given set.

Operations on Sets : Learn the meaning. What are the four basic operations on sets? How the operations are carried out in union of sets and intersection of sets?

Union of Sets : Definition of union of sets with examples. Learn how to find the union of two sets and worked-out examples.

Intersection of Sets : Definition of intersection of sets with examples. Learn how to find the intersection of two sets and worked-out examples.

Difference of two Sets : Learn how to find the difference between the two sets and worked-out examples.

Complement of a Set : Definition of complement of a set and their properties with some worked-out examples.

Cardinal number of a set : Definition of a cardinal number of a set, the symbol used for showing the cardinal number, worked-out examples.

Cardinal Properties of Sets : Learn how to solve the real-life word problems on set using the cardinal properties.

Venn Diagrams : Learn to represent the basic concepts of sets using Venn-diagram in different situations.

● Relations and Mapping

Ordered Pair

Cartesian Product of Two Sets

Domain and Range of a Relation

Functions or Mapping

Domain Co-domain and Range of Function

● Relations and Mapping - Worksheets

Worksheet on Math Relation

Worksheet on Functions or Mapping

● Numbers - Integers

Multiplication of Integers

Properties of Multiplication of Integers

Examples on Multiplication of Integers

Division of Integers

Absolute Value of an Integer

Comparison of Integers

Properties of Division of Integers

Examples on Division of Integers

Fundamental Operation

Examples on Fundamental Operations

Uses of Brackets

Removal of Brackets

Examples on Simplification

● Numbers - Worksheets

Worksheet on Multiplication of Integers

Worksheet on Division of Integers

Worksheet on Fundamental Operation

Worksheet on Simplification

● Fractions

Types of Fractions

Equivalent Fractions

Like and Unlike Fractions

Conversion of Fractions

Fraction in Lowest Terms

Addition and Subtraction of Fractions

Multiplication of Fractions

Division of Fractions

● Fractions - Worksheets

Worksheet on Fractions

Worksheet on Multiplication of Fractions

Worksheet on Division of Fractions

● Story about the Decimal Number

Decimals : Concept for decimals in derails.

Decimal Numbers : Learn reading decimal numbers, writing decimal numbers etc,.

Decimal Fractions : Learn reading decimal fractions, writing decimal fractions.

Decimal Places : Learn reading and writing the place values of a decimal number in words.

Decimal and Fractional Expansion : Learn how to expand the decimal numbers and the decimal numbers in fractions

Like and Unlike Decimals : Learn to identify like decimals and unlike decimals.

Conversion of Unlike Decimals to Like Decimals : Learn to convert unlike decimals in like decimals

Comparing Decimals : Learn to order and compare decimal numbers, arranging decimals in ascending order and arranging decimals in descending order

Adding Decimals : Learn to add decimals in the correct order, word problems.

Subtracting Decimals : Learn to subtract decimals in the correct order, word problems

Simplify Decimals Involving Addition and Subtraction Decimals : Examples for simplifying decimals for adding and subtracting.

Multiplying Decimal by a Whole Number : Learn to multiply decimals by a whole number in the correct order, word problems

Multiplying Decimal by a Decimal Number : Learn to multiply decimals by a decimal number in the correct order, word problems

Dividing Decimal by a Whole Number : Learn to divide decimals by a whole number in the correct order, word problems

Dividing Decimal by a Decimal Number : Learn to divide decimals by a decimal number in the correct order, word problems

Simplification of Decimal : Examples for simplifying decimals, operation on decimals.

Converting Decimals to Fractions : Learn to express decimal number into fraction

Converting Fractions to Decimals : Learn to express fraction into decimal number

Rounding Decimals : Learn to round off decimals

Rounding Decimals to the Nearest Whole Number : Learn to round off decimals to the nearest whole number

Rounding Decimals to the Nearest Tenths : Learn to round off decimals to the nearest tenths

Rounding Decimals to the Nearest Hundredths : Learn to round off decimals to the nearest hundredths

Round a Decimal : Problems for rounding off decimals

H.C.F. and L.C.M. of Decimals : Learn to find the highest common factor, lowest common multiple of more than two decimal numbers

Terminating Decimal : Definition of terminating decimals, examples to identify terminating decimals

Non-Terminating Decimal : Definition of non-terminating decimal, examples to identify non-terminating decimals

Repeating or Recurring Decimal : Definition of recurring decimals, examples to identify recurring decimals

Pure Recurring Decimal : Definition of pure recurring decimal, examples to pure recurring decimal

Mixed Recurring Decimal : Definition of mixed recurring decimal, examples to identify mixed recurring decimal

Conversion of Pure Recurring Decimal into Vulgar Fraction : Learn to express pure recurring decimals to vulgar fractions with examples.

Conversion of Mixed Recurring Decimals into Vulgar Fractions : Learn to express mixed recurring decimals to vulgar fractions with examples.

BODMAS/PEMDAS rule:

BODMAS Rule : Learn how to follow the BODMAS rules to simply the order of operations.

BODMAS Rules - Involving Integers : Learn how to follow the BODMAS rules to simply the order of operations involving integers.

BODMAS/PEMDAS Rules - Involving Decimals : Learn how to follow the BODMAS rules to simply the order of operations involving decimals

PEMDAS Rule : Learn how to follow the PEMDAS rules to simply the order of operations.

PEMDAS Rules - Involving Integers : Learn how to follow the PEMDAS rules to simply the order of operations involving integers.

PEMDAS Rules - Involving Decimals : Learn how to follow the PEMDAS rules to simply the order of operations involving decimals.

● Profit, Loss and Discount

Concept of Profit and Loss

Calculate Profit and Profit Percent

Calculate Loss and Loss Percent

Calculate Cost Price using Sell Price and Loss Percent

Calculate Cost Price using Sell Price and Profit Percent

Calculate Selling Price using Cost and Loss Percent

Calculate Selling Price using Cost and Profit Percent

Calculating Profit Percent and Loss Percent

Word Problems on Profit and Loss

Examples on Calculating Profit or Loss

Practice Test on Profit and Loss

Practice Test on Profit Loss and Discount

● Profit, Loss and Discount - Worksheets

Worksheet to Find Profit and Loss

Worksheets on Profit and Loss Percentage

Worksheet on Gain and Loss Percentage

Worksheet on Discounts

● Ratios and Proportions

What is a Ratio?

What is a Proportion?

● Ratios and Proportions - Worksheets

Worksheet on Ratios

Worksheet on Proportions

● Time and Work

Calculate Time to Complete a Work

Calculate Work Done in a Given Time

Problems on Time required to Complete a Piece a Work

Problems on Work Done in a Given Period of Time

Problems on Time and Work

Pipes and Water Tank

Problems on Pipes and Water Tank

● Time and Work - Worksheets

Worksheet on Work Done in a Given Period of Time

Worksheet on Time Required to Complete a Piece of Work

Worksheet on Pipes and Water Tank

● Unitary Method

Problems Using Unitary Method

Situations of Direct Variation

Situations of Inverse Variation

Direct Variations Using Unitary Method

Direct Variations Using Method of Proportion

Inverse Variation Using Unitary Method

Inverse Variation Using Method of Proportion

Problems on Unitary Method using Direct Variation

Problems on Unitary Method Using Inverse Variation

Mixed Problems Using Unitary Method

● Unitary Method - Worksheets

Worksheet on Direct Variation using Unitary Method

Worksheet on Direct variation using Method of Proportion

Worksheet on Word Problems on Unitary Method

Worksheet on Inverse Variation Using Unitary Method

Worksheet on Inverse Variation Using Method of Proportion

● Simple Interest

What is Simple Interest?

Calculate Simple Interest

Practice Test on Simple Interest

● Simple Interest - Worksheets

Simple Interest Worksheet

● Algebraic Expressions

Division of Polynomial by Monomial

● Algebraic Expressions - Worksheets

Worksheet on Dividing Polynomial by Monomial

Formula and Framing the Formula

Change the Subject of a Formula

Changing the Subject in an Equation or Formula

Practice Test on Framing the Formula

● Formula - Worksheets

Worksheet on Framing the Formula

Worksheet on Changing the Subject of a Formula

Worksheet on Changing the Subject in an Equation or Formula

● Algebraic Identities

Square of The Sum of Two Binomials : Using the formula of (a + b) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + 2ab, learn to evaluate the square of the sum of two terms.

Square of The Difference of Two Binomials : Using the formula of (a - b)\(^{2}\)  = a \(^{2}\) + b \(^{2}\) - 2ab, learn to evaluate the square of the difference of two terms.

Product of Sum and Difference of Two Binomials : Using the formula of a \(^{2}\) - b \(^{2}\) = (a + b) (a - b), learn to evaluate the product of sum and difference of two terms.

Product of Two Binomials whose First Terms are Same and Second Terms are Different : Learn to use the given formulas to evaluate the product of the two terms whose 1 \(^{st}\) terms are same and 2 \(^{nd}\) terms are different.

• (x + a) (x + b) = x \(^{2}\) + x(a + b) + ab

• (x + a) (x - b) = x \(^{2}\) + x (a – b) – ab

• (x - a) (x - b) = x \(^{2}\) – x (a + b) + ab

• (x - a) (x + b) = x \(^{2}\) + x (b – a) – ab

Square of a Trinomial : Learn to use the formula for the expansion of the square of a trinomial.

• (a + b + c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) + 2ab + 2bc + 2ca

• (a + b - c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) + 2ab – 2bc - 2ca

• (a - b + c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) – 2ab – 2bc + 2ca

• (a - b - c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) – 2ab + 2bc – 2ca

Cube of The Sum of Two Binomials : Learn the formula to determine the cube of the sum of two terms.

(a + b) \(^{3}\) = a \(^{3}\)   + 3a \(^{2}\) b + 3ab \(^{2}\)   + b \(^{3}\)

             = a \(^{3}\) + b \(^{3}\) + 3ab (a + b)

Cube of The Difference of Two Binomials : Learn the formula to determine the cube of the difference of two terms.

(a - b) \(^{3}\) = a \(^{3}\)   – 3a \(^{2}\) b + 3ab \(^{2}\)   – b \(^{3}\)

           = a \(^{3}\) – b \(^{3}\) – 3ab (a - b)

Cube of a Binomial :

Square of a Binomial :

● Equations

What is an Equation?

What is a Linear Equation?

How to Solve Linear Equations?

Solving Linear Equations

Problems on Linear Equations in One Variable

Word Problems on Linear Equations in One Variable

Practice Test on Linear Equations

Practice Test on Word Problems on Linear Equations

● Equations - Worksheets

Worksheet on Linear Equations

Worksheet on Word Problems on Linear Equation

● Inequations

What are Linear Inequality?

What are Linear Inequations?

Properties of Inequation or Inequalities

Representation of the Solution Set of an Inequation

Practice Test on Linear Inequation

● Inequations - Worksheets

Worksheet on Linear Inequations

● Lines and Angles

Fundamental Geometrical Concepts

Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Supplementary Angles

Complementary and Supplementary Angles

Adjacent Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines

● Congruence

Congruent Shapes :

Congruent Line-segments :

Congruent Angles :

Congruent Triangles :

Conditions for the Congruence of Triangles :

Side Side Side Congruence :

Side Angle Side Congruence : 

Angle Side Angle Congruence :

Angle Angle Side Congruence :

Right Angle Hypotenuse Side congruence :

Pythagorean Theorem :

Proof of Pythagorean Theorem :

Converse of Pythagorean Theorem :

Word problems on Pythagorean Theorem :

Polygon and its Classification

Terms Related to Polygons

Interior and Exterior of the Polygon

Convex and Concave Polygons

Regular and Irregular Polygon

Number of Triangles Contained in a Polygon

Angle Sum Property of a Polygon

Problems on Angle Sum Property of a Polygon

Sum of the Interior Angles of a Polygon

Sum of the Exterior Angles of a Polygon

● Polygons - Worksheets

Worksheet on Polygon and its Classification

Worksheet on Interior Angles of a Polygon

Worksheet on Exterior Angles of a Polygon

● Quadrilateral

Quadrilateral : Perimeter of Quadrilateral : Angle Sum Property of a Quadrilateral : Missing angle of a Quadrilateral :

Angles of a Quadrilateral are in Ratio :

●   Symmetrical Figure

Linear Symmetry :  Identify symmetric and non-symmetric figures and also identify shapes having horizontal line of symmetry, vertical line of symmetry, both horizontal and vertical lines of symmetry, infinite lines of symmetry and no line of symmetry.

Lines of Symmetry :  Identify the geometrical shapes having 1, 2, 3, 4, 0 and so on or infinite lines of symmetry.

Point Symmetry :  How to find the point symmetry of letters of the English alphabet and the different geometrical figures. Learn the important points to find the conditions that satisfy centre of symmetry.

Reflection Symmetry :

Nets of a Solids :

Rotational Symmetry :  Learn what is rotational symmetry and types of rotation i.e. clockwise rotation and anticlockwise rotation. 

Order of Rotational Symmetry :  Learn the different orders of rotation of the shapes through 360° in clockwise direction and anticlockwise direction.

Types of Symmetry :  Learn the various symmetries i.e. linear symmetry, point symmetry and rotational symmetry of the geometrical shapes. 

Reflection :  Learn how reflection is related to math, define reflection using an image and worked-out examples on math reflection. 

Reflection of a Point in x-axis :  Learn how to draw the image on the graph paper to find the reflection of a point in x-axis.

Reflection of a Point in y-axis :  Learn how to draw the image on the graph paper to find the reflection of a point in y-axis.

Reflection of a point in origin :  Learn how to draw the image on the graph paper to find the reflection of a point in origin. 

Rotation :  Explanation of rotation using an image.

90 Degree Clockwise Rotation :  Learn with the help of solved examples to rotate a figure 90 degrees clockwise direction around the origin on a graph paper.

90 Degree Anticlockwise Rotation :  Learn with the help of solved examples to rotate a figure 90 degrees anticlockwise direction around the origin on a graph paper.

180 Degree Rotation :  Learn with the help of solved examples to rotate a figure 180 degrees clockwise direction and anticlockwise direction around the origin on a graph paper.

●  Coordinate System

• Coordinate Graph
• Ordered pair of a Coordinate System
• Plot Ordered Pairs
• Coordinates of a Point
• All Four Quadrants
• Signs of Coordinates
• Find the Coordinates of a Point
• Coordinates of a Point in a Plane
• Plot Points on Coordinate Graph
• Graph of Linear Equation
• Simultaneous Equations Graphically
• Graphs of Simple Function
• Graph of Perimeter vs. Length of the Side of a Square
• Graph of Area vs. Side of a Square
• Graph of Simple Interest vs. Number of Years
• Graph of Distance vs. Time

●  Mensuration

• Area and Perimeter
• Perimeter and Area of Rectangle
• Perimeter and Area of Square
• Area of the Path
• Area and Perimeter of the Triangle
• Area and Perimeter of the Parallelogram
• Area and Perimeter of Rhombus
• Area of Trapezium
• Circumference and Area of Circle
• Units of Area Conversion
• Practice Test on Area and Perimeter of Rectangle
• Practice Test on Area and Perimeter of Square

●  Mensuration - Worksheets

• Worksheet on Area and Perimeter of Rectangles
• Worksheet on Area and Perimeter of Squares
• Worksheet on Area of the Path
• Worksheet on Circumference and Area of Circle
• Worksheet on Area and Perimeter of Triangle

●   Volume and Surface Area of Solids

• Volume of Cubes and Cuboids
• Worked-out Problems on Volume of a Cuboid

●  Statistics

• Real Life Statistics
• Terms Related to Statistics
• Frequency Distribution of Ungrouped and Grouped Data
• Use of Tally Marks
• Class Limits in Exclusive and Inclusive Form
• Construction of Bar Graphs
• Mean of the Tabulated Data
• Construction of Pie Chart
• How to Construct a Line Graph?

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Seventh Grade (Grade 7) Problem Solving Strategies Questions

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Grade 7 Mathematics Module: Solving Problems Involving Side and Angle of a Polygon

This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.

Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.

Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.

Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.

This module was designed and written with you in mind. It is here to help you learn solving problems involving side and angle of polygons. The scope of this module may be used in many different learning situations. The language used recognizes your vocabulary level. The lessons are arranged to follow the standard sequence of the course. But the order in which you study can be rearranged to correspond with the textbook you are now using.

The lesson presented in this module is:

1. Sides and angles of a polygons

After going through this module, you are expected to:

1. Solve problems involving sides and angle of a polygons.

Grade 7 Mathematics Quarter 3 Self-Learning Module: Solving Problems Involving Side and Angle of a Polygon

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