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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.

28 7th Grade Math Problems

28 7th grade math questions targeting the skills and knowledge needed for the four operations, order of operations, percentages, proportional relationships, one-step and two-step equations, geometry and word problems. Includes answers and explanations.

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.

Solution :        6

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

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
• 1st grade math problems
• 2nd grade math problems
• 3rd grade math problems
• 4th grade math problems
• 5th grade math problems
• 6th grade Math Problems
• 8th 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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28 Math Problems For 2nd Graders With Answers & Teaching Ideas

37 Math Problems For 3rd Graders: Answers With Worked Examples

3rd to 8th Grade Practice Tests

Get ready for your state math test with our 3rd to 8th grade practice assessments. These 6 multiple-choice tests, created by US math experts, cover essential topics and include detailed answers for effective test prep. Aligned with Common Core Standards, they’re the perfect tool to build student confidence.

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• 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.
• Videos provide instant help for students who are struggling with their assignments.

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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Free Mathematics Tutorials

Grade 7 math problems with solutions.

Grade 7 Maths questions and problems for deep understanding of Maths concepts and skills of students are presented. Solutions and answers to the questions are also provided.

Grade 7 Math

• Grade 7 Math Practice Test with detailed solutions and explanations.
• How to Solve Rate Problems? ; Grade 7 questions With Detailed Solutions are included.
• Find Ratio in Math ; Grade 7 questions With Detailed Solutions are included.
• Find Rate in Math ; Grade 7 questions With Detailed Solutions are included.
• Solve Maths Proportions ; grade 7 questions With Detailed Solutions are included.
• Grade 7 Maths word Problems With Answers . Also Solutions and explanations are included.
• Fractions and Mixed Numbers - Grade 7 Maths Questions and Problems With Answers . Also solutions and explanations are included.
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• Common Factors Calculator. An online calculator that computes the common factors and the GCF of two or more positive integers.
• Introduction to Polynomials
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• Video on Solving Linear Inequalities
• Graphing Functions
• What are Exponents in Math? ; examples and questions With Detailed Solutions are included.
• Algebra Questions and Problems with detailed solutions and explanations.
• Convert Yards, Feet and Inches
• Relations in Mathematics
• Functions in Mathematics
• Functions Represented by Equations
• Number to Words Converter
• What are Radicals in Math? ; examples and questions with detailed solutions are included.
• Prime and Composite Numbers ; examples and questions With Detailed Solutions are included.
• Greatest Common Factor (GCF) ; examples and questions With Detailed Solutions are included.
• Lowest Common Multiple (LCM) ; examples and questions With Detailed Solutions are included.
• How to Reduce Fractions ; examples and questions With Detailed Solutions are included.
• How is Cross Multiplication Used to Solve Equations? ; examples and questions With Detailed Solutions are included.
• Grade 7 Maths Questions on Set Theory With Answers . Also, the solutions and explanations are included.
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• Units Conversion and Calculators
• Convert Units of Measurements

Online Calculators to Practice and Understand Concepts

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7th Grade Math Worksheets

Ease into key concepts with our printable 7th grade math worksheets that are equipped with boundless learning to extend your understanding of ratios and proportions, order of operations, rational numbers, and help you in solving expressions and linear equations, in describing geometrical figures, calculating the area, volume and surface area, finding the pairs of angles, and getting an insight into statistics and probability and much more! Instantly evaluate with our answer keys. Give our free grade 7 math worksheets a try and head over for more!

Select Grade 7 Math Worksheets by Topic

Explore 3,600+ Seventh Grade Math Worksheets

Writing the Equivalent Ratios

Create equivalent ratios that express the same relationship by multiplying the first and second term of the ratio by the same number. Also, complete the table with equivalent ratios.

• Download the set

Adding Integers Using Number Lines

Open doors to adding integers with our grade 7 math worksheet pdfs. Students start with the first addend, draw as many hops as the other addend toward the right or left on the number line, and find the sum.

Exponents and Operations

Take your skills in applying the order of operations up a notch as you evaluate the expressions involving fractions with positive and negative exponents.

Solving for 'x' | Side Lengths of Rectangles

With this set of printable 7th grade math worksheets, your students are well-equipped to practice setting up an equation with the indicated lengths, rearranging the equation, making 'x' the subject, and solving.

Enlarging or Reducing Shapes Using the Scale Factor

Find the dimensions of the figures on the grid, sketch the shapes on the grid, enlarging or reducing the original shape as instructed, multiplying the dimensions with the given scale factor.

Finding the Area of a Circle Using the Radius

Prepare students in grade 7 in finding the area of a circle using this printable collection of worksheets offering oodles of practice. Plug in the radius in the formula A = π * r 2 to find the area of the circle.

Area of Rectangles | Unit conversion

Make the units in the dimensions uniform by converting them to the units specified in the answer, multiply the length and width, and calculate the area of each rectangle.

Surface Area of Rectangular Prisms | Unit Squares

Finding the surface area doesn't feel like a chore with our 7th grade math worksheet pdfs. Count the number of unit squares on each of the six faces of the rectangular prism, multiply by the scale and add.

Finding Complementary Angles

Two angles are complementary if they add up to 90°. Subtract the angle from 90° to find its complement, state whether each given angle pair is complementary and find the measure of the unknown angle.

Comparing Mean Absolute Deviations

Perfect for calculating the mean absolute deviation or MAD of the two data sets using the formula, ∑|x i - x̅|/n, and comparing them, these printable math worksheets are a must-have for your grade 7 learners.

Forming a Proportion

A proportion is nothing but two ratios equivalent to each other. Form a proportion by identifying the four numbers that can be set up as a pair of equivalent ratios from the given set of 5.

Adding Integers

Rich with scads of practice, this set of math worksheet pdfs for 7th grade learners helps them add two integers with the same sign and subtract those with different signs, and figure out the sum instantly.

Squaring Numbers | Fractions

Multiply the given fraction by the same fraction to obtain its square. Convert the product to mixed numbers if required, and also identify the square of the given fraction from a pool of options.

Finding Side Lengths of Triangles Using the Perimeter

Our printable grade 7 math worksheets are an add-on to your practice in computing the side lengths of a triangle by equating the sum of linear expressions with the given perimeter, and solving for x.

Scale Factor | Perimeter and Area of Similar Figures

Upgrade your skills in calculating the area or perimeter of the original or dilated image using the scale factor and comprehend the impact of the scale factor on the ratio of areas and perimeters with these pdfs.

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7th Grade Math Word Problems

Related Pages More Math Word Problems Algebra Word Problems More Singapore Math Word Problems 7th Grade Math Word Problems 2

In these lessons, we will look at some examples of 7th grade word problems with answers, solved using the Singapore Math block diagram method as well as using Algebra.

Printable Words to Equations Algebra Word Problems Angle Word Problems (6th Grade) Angle Word Problems (7th Grade)

Inequality Word Problems

Word Problems (Multiplication & Division) 2-Step Word Problems (Multiply/Divide/Add/Subtract) Multi-step Word Problems (using +, -, ×)

The following are some examples of 7th Grade Math Word Problems that deals with ratio and proportions.

These are Grade 7 word problems from a Singapore text. The problems are solved both using algebra (the way it is generally done in the US) and using block diagrams (the way it was shown in the Singapore text). You can then decide which one you prefer.

Singapore Math 2 (A Grade 7 Algebra Word Problem from a Singapore text)

Example: Mr. Rozario bought some apples and oranges. The ratio of the number of apples to the number of oranges are 2:5. He gave 3/4 of the apples to his sister and 34 oranges to his brother. The ratio of the number of apples to the number of oranges that he has now is 2:3. How many apples did Mr. Rozario buy? How many oranges did Mr. Rozario buy?

Example: At first, the ratio of Sam’s savings to Ray’s savings was 5:4. After each of them donated $45 to charity, the ratio of Sam’s savings to Ray’s savings became 13:10. What was Sam’s savings at first?

Example: Dan had 50% fewer stickers than Jeff. After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff (had after he gave away 20 of his stickers). How many stickers did Dan have at first?

Example: There are 8 more girls than boys in a particular class. 3/5 of the boys and 1/3 of the girls were born in Georgia. If the number of boys that were born in Georgia is equal to the number of girls that were born in Georgia, how many students (boys and girls together) in that class were born in Georgia?

Example: Ray and Omar collect stamps. Originally, 1/5 of Omar’s stamps were equivalent to 1/3 of Ray’s stamps. If Ray gave Omar 24 stamps, Omar would have 3 times as many stamps as Ray. Find the number of stamps each of them had in the beginning.

Example: Jim had 103 red and blue marbles. After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles. How many blue marbles did he have originally?

Example: The ratio of the amount of turkey to the amount of chicken at the grocery store was 8:3 in the morning. By the end of the day, 14 pounds of turkey had been sold. The ratio of the amount of turkey to the amount of chicken was now 3:2. a. How many pounds of turkey did the grocery store have in the morning? b. How many pounds of chicken did the grocery store have in the morning?

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Seventh grade math

IXL offers hundreds of seventh grade math skills to explore and learn! Not sure where to start? Go to your personalized Recommendations wall to find a skill that looks interesting, or select a skill plan that aligns to your textbook, state standards, or standardized test.

A. Integers

• 1 Understanding integers
• 2 Integers on number lines
• 3 Graph integers on horizontal and vertical number lines
• 4 Understanding absolute value
• 5 Absolute value and opposite integers
• 6 Quantities that combine to zero: word problems
• 7 Compare and order integers
• 8 Integer inequalities with absolute values

B. Operations with integers

• 1 Add integers using counters
• 2 Add integers using number lines
• 3 Integer addition rules
• 4 Add integers
• 5 Add three or more integers
• 6 Subtract integers using counters
• 7 Subtract integers using number lines
• 8 Integer subtraction rules
• 9 Subtract integers
• 10 Integer addition and subtraction rules
• 11 Add and subtract integers using counters
• 12 Add and subtract integers
• 13 Complete addition and subtraction equations with integers
• 14 Add and subtract integers: word problems
• 15 Understand multiplying by a negative integer using a number line
• 16 Integer multiplication rules
• 17 Multiply integers
• 18 Integer division rules
• 19 Equal quotients of integers
• 20 Divide integers
• 21 Integer multiplication and division rules
• 22 Multiply and divide integers
• 23 Complete multiplication and division equations with integers
• 24 Add, subtract, multiply, and divide integers
• 25 Evaluate numerical expressions involving integers

C. Decimals

• 1 Decimal numbers review
• 2 Compare and order decimals
• 3 Round decimals

D. Operations with decimals

• 1 Add and subtract decimals
• 2 Add and subtract decimals: word problems
• 3 Multiply decimals
• 4 Multiply decimals and whole numbers: word problems
• 5 Divide decimals
• 6 Divide decimals by whole numbers: word problems
• 7 Estimate sums, differences, and products of decimals
• 8 Add, subtract, multiply, or divide two decimals
• 9 Add, subtract, multiply, and divide decimals: word problems
• 10 Multi-step inequalities with decimals
• 11 Maps with decimal distances
• 12 Evaluate numerical expressions involving decimals

E. Number theory

• 1 Prime factorization
• 2 Greatest common factor
• 3 Least common multiple
• 4 GCF and LCM: word problems

F. Fractions

• 1 Understanding fractions: word problems
• 2 Equivalent fractions
• 3 Write fractions in lowest terms
• 4 Fractions: word problems with graphs and tables
• 5 Least common denominator
• 6 Compare and order fractions
• 7 Compare fractions: word problems
• 8 Convert between mixed numbers and improper fractions
• 9 Compare mixed numbers and improper fractions
• 10 Round mixed numbers

G. Operations with fractions

• 1 Add and subtract fractions
• 2 Add and subtract fractions: word problems
• 3 Add and subtract mixed numbers
• 4 Add and subtract mixed numbers: word problems
• 5 Inequalities with addition and subtraction of fractions and mixed numbers
• 6 Estimate sums and differences of mixed numbers
• 7 Multiply two fractions using models
• 8 Multiply fractions
• 9 Multiply mixed numbers
• 10 Multiply fractions and mixed numbers: word problems
• 11 Multiplicative inverses
• 12 Divide fractions
• 13 Divide mixed numbers
• 14 Divide fractions and mixed numbers: word problems
• 15 Estimate products and quotients of fractions and mixed numbers
• 16 Add, subtract, multiply, and divide fractions and mixed numbers: word problems
• 17 Maps with fractional distances
• 18 Evaluate numerical expressions involving fractions

H. Rational numbers

• 1 Convert fractions or mixed numbers to decimals
• 2 Convert decimals to fractions or mixed numbers
• 3 Convert between decimals and fractions or mixed numbers
• 4 Identify rational numbers
• 5 Classify rational numbers using a diagram
• 6 Classify rational numbers
• 7 Absolute value of rational numbers
• 8 Compare rational numbers
• 9 Put rational numbers in order
• 10 Classify real numbers

I. Operations with rational numbers

• 1 Add and subtract positive and negative decimals
• 2 Add and subtract positive and negative fractions
• 3 Add and subtract rational numbers
• 4 Rational numbers: find the sign
• 5 Apply addition and subtraction rules
• 6 Identify quotients of rational numbers: word problems
• 7 Multiply and divide positive and negative decimals
• 8 Multiply and divide positive and negative fractions
• 9 Multiply and divide rational numbers
• 10 Apply multiplication and division rules
• 11 Multi-step word problems with positive rational numbers

J. Exponents

• 1 Understanding exponents
• 2 Evaluate powers
• 3 Solve equations with variable exponents
• 4 Powers with negative bases
• 5 Powers with decimal and fractional bases
• 6 Powers of ten
• 7 Evaluate numerical expressions involving exponents
• 8 Scientific notation
• 9 Compare numbers written in scientific notation

K. Square roots

• 1 Square roots of perfect squares
• 2 Estimate square roots

L. Ratios, rates, and proportions

• 1 Understanding ratios
• 2 Identify equivalent ratios
• 3 Write an equivalent ratio
• 4 Equivalent ratios: word problems
• 5 Unit rates
• 6 Calculate unit rates with fractions
• 7 Compare ratios: word problems
• 8 Compare rates: word problems
• 9 Do the ratios form a proportion?
• 10 Do the ratios form a proportion: word problems
• 11 Solve proportions
• 12 Solve proportions: word problems
• 13 Estimate population size using proportions

M. Coordinate plane

• 1 Coordinate plane review
• 2 Quadrants and axes
• 3 Follow directions on a coordinate plane
• 4 Distance between two points

N. Proportional relationships

• 1 Find the constant of proportionality from a table
• 2 Write equations for proportional relationships from tables
• 3 Identify proportional relationships by graphing
• 4 Find the constant of proportionality from a graph
• 5 Write equations for proportional relationships from graphs
• 6 Identify proportional relationships from graphs and equations
• 7 Identify proportional relationships from tables
• 8 Complete a table and graph a proportional relationship
• 9 Graph a proportional relationship: word problems
• 10 Interpret graphs of proportional relationships
• 11 Write and solve equations for proportional relationships

O. Percents

• 1 What percentage is illustrated?
• 2 Convert between percents, fractions, and decimals
• 3 Compare percents to fractions and decimals
• 4 Estimate percents of numbers
• 5 Solve percent problems using strip models
• 6 Percents of numbers and money amounts
• 7 Percents of numbers: word problems
• 8 Solve percent equations
• 9 Solve percent equations: word problems
• 10 Percent of change
• 11 Percent of change: word problems
• 12 Percent of change: find the original amount word problems
• 13 Percent error: word problems

P. Consumer math

• 1 Add, subtract, multiply, and divide money amounts: word problems
• 2 Price lists
• 3 Unit prices
• 4 Unit prices with unit conversions
• 5 Unit prices: find the total price
• 6 Percent of a number: tax, discount, and more
• 7 Which is the better coupon?
• 8 Find the percent: tax, discount, and more
• 9 Sale prices: find the original price
• 10 Multi-step problems with percents
• 11 Estimate tips
• 12 Simple interest
• 13 Compound interest

Q. Units of measurement

• 1 Compare and convert customary units
• 2 Mixed customary units
• 3 Compare and convert metric units
• 4 Convert between customary and metric systems
• 5 Celsius and Fahrenheit temperatures

R. Expressions

• 1 Write variable expressions: one operation
• 2 Write variable expressions: two or three operations
• 3 Write variable expressions: word problems
• 4 Evaluate linear expressions
• 5 Evaluate multi-variable expressions
• 6 Evaluate absolute value expressions
• 7 Evaluate nonlinear expressions
• 8 Identify terms and coefficients
• 9 Sort factors of variable expressions

S. Equivalent expressions

• 1 Properties of addition and multiplication
• 2 Simplify expressions by combining like terms: with algebra tiles
• 3 Simplify expressions by combining like terms
• 4 Multiply using the distributive property: area models
• 5 Multiply using the distributive property
• 6 Write equivalent expressions using properties
• 7 Add and subtract linear expressions
• 8 Add and subtract like terms: with exponents
• 9 Factor linear expressions: area models
• 10 Factors of linear expressions
• 11 Identify equivalent linear expressions using algebra tiles
• 12 Identify equivalent linear expressions I
• 13 Identify equivalent linear expressions II
• 14 Identify equivalent linear expressions: word problems

T. One-variable equations

• 1 Which x satisfies an equation?
• 2 Write an equation from words
• 3 Solve equations using properties
• 4 Model and solve equations using algebra tiles
• 5 Write and solve equations that represent diagrams
• 6 Solve one-step equations
• 7 Solve two-step equations without parentheses
• 8 Solve two-step equations with parentheses
• 9 Solve two-step equations
• 10 Solve two-step equations with fractions
• 11 Choose two-step equations: word problems
• 12 Solve two-step equations: word problems
• 13 Solve equations involving like terms
• 14 Solve equations: complete the solution

U. One-variable inequalities

• 1 Solutions to inequalities
• 2 Graph inequalities on number lines
• 3 Write inequalities from number lines
• 4 Solve one-step inequalities
• 5 Graph solutions to one-step inequalities
• 6 One-step inequalities: word problems
• 7 Solve two-step inequalities
• 8 Graph solutions to two-step inequalities

V. Sequences

• 1 Identify arithmetic and geometric sequences
• 2 Arithmetic sequences
• 3 Geometric sequences
• 4 Sequences: mixed review
• 5 Sequences: word problems
• 6 Evaluate variable expressions for sequences
• 7 Write variable expressions for arithmetic sequences
• 1 Find the slope from a graph
• 2 Find the slope from two points
• 3 Find a missing coordinate using slope
• 4 Graph a line using slope
• 5 Constant rate of change
• 6 Rate of change: tables
• 7 Rate of change: graphs

X. Two-variable equations

• 1 Identify independent and dependent variables
• 2 Find a value using two-variable equations
• 3 Evaluate two-variable equations: word problems
• 4 Complete a table for a two-variable relationship
• 5 Write a two-variable equation
• 6 Identify the graph of an equation
• 7 Graph a two-variable equation
• 8 Interpret a graph: word problems
• 9 Write an equation from a graph using a table
• 10 Write a linear equation from a graph

Y. Lines and angles

• 1 Name, measure, and classify angles
• 2 Lines, line segments, and rays
• 3 Parallel, perpendicular, and intersecting lines
• 4 Identify complementary, supplementary, vertical, and adjacent angles
• 5 Find measures of complementary, supplementary, vertical, and adjacent angles
• 6 Write and solve equations using angle relationships
• 7 Identify alternate interior and alternate exterior angles
• 8 Transversals of parallel lines: name angle pairs
• 9 Transversals of parallel lines: find angle measures
• 10 Find lengths and measures of bisected line segments and angles

Z. Two-dimensional figures

• 1 Identify and classify polygons
• 2 Classify triangles
• 3 Triangle inequality
• 4 Identify trapezoids
• 5 Classify quadrilaterals I
• 6 Classify quadrilaterals II
• 7 Graph triangles and quadrilaterals
• 8 Find missing angles in triangles
• 9 Find missing angles in triangles using ratios
• 10 Find missing angles in quadrilaterals I
• 11 Find missing angles in quadrilaterals II
• 12 Interior angles of polygons
• 13 Parts of a circle
• 14 Central angles of circles

AA. Three-dimensional figures

• 1 Bases of three-dimensional figures
• 2 Nets of three-dimensional figures
• 3 Front, side, and top view
• 4 Cross sections of three-dimensional figures

BB. Perimeter and area

• 1 Perimeter
• 2 Area of rectangles and parallelograms
• 3 Area of triangles and trapezoids
• 4 Area and perimeter: word problems
• 5 Circumference of circles
• 6 Area of circles
• 7 Circles: word problems
• 8 Area of semicircles and quarter circles
• 9 Semicircles: calculate area, perimeter, radius, and diameter
• 10 Quarter circles: calculate area, perimeter, and radius
• 11 Area of compound figures made of rectangles
• 12 Area of compound figures with triangles
• 13 Area of compound figures with triangles, semicircles, and quarter circles
• 14 Area between two shapes

CC. Surface area and volume

• 1 Surface area of cubes and prisms
• 2 Surface area of pyramids
• 3 Lateral area of prisms and pyramids
• 4 Surface area of cylinders
• 5 Volume of cubes and prisms
• 6 Volume of cubes and rectangular prisms: word problems
• 7 Volume of prisms: advanced
• 8 Volume of pyramids
• 9 Volume of cylinders

DD. Scale drawings

• 1 Scale drawings of polygons
• 2 Scale drawings: word problems
• 3 Scale drawings: scale factor word problems
• 4 Perimeter and area: changes in scale

EE. Transformations

• 1 Identify reflections, rotations, and translations
• 2 Translations: graph the image
• 3 Translations: find the coordinates
• 4 Reflections over the x- and y-axes: graph the image
• 5 Reflections over the x- and y-axes: find the coordinates
• 6 Reflections: graph the image
• 7 Reflections: find the coordinates
• 8 Rotations: graph the image
• 9 Rotations: find the coordinates

FF. Congruence and similarity

• 1 Similar and congruent figures
• 2 Congruence statements and corresponding parts
• 3 Side lengths and angle measures of congruent figures
• 4 Side lengths and angle measures of similar figures
• 5 Similar figures and indirect measurement

GG. Data and graphs

• 1 Create line plots
• 2 Interpret line plots
• 3 Create and interpret line plots with fractions
• 4 Create stem-and-leaf plots
• 5 Interpret stem-and-leaf plots
• 6 Create bar graphs
• 7 Interpret bar graphs
• 8 Create histograms
• 9 Interpret histograms
• 10 Create frequency charts
• 11 Interpret circle graphs
• 12 Circle graphs and central angles
• 13 Box plots

HH. Statistics

• 1 Calculate mean, median, mode, and range
• 2 Interpret charts and graphs to find mean, median, mode, and range
• 3 Mean, median, mode, and range: find the missing number
• 4 Changes in mean, median, mode, and range
• 5 Calculate mean absolute deviation
• 6 Calculate quartiles and interquartile range
• 7 Identify an outlier
• • New! Populations and samples
• 8 Identify representative, random, and biased samples
• 9 Make inferences from multiple samples
• 10 Compare populations using measures of center and spread

II. Probability

• • New! Sample spaces of simple events
• 1 Probability of simple events
• 2 Probability of simple events and opposite events
• 3 Probability of mutually exclusive events and overlapping events
• 4 Experimental probability
• 5 Make predictions using experimental probability
• 6 Use collected data to find probabilities and make predictions
• 7 Make predictions using theoretical probability
• 8 Compound events: find the number of outcomes
• 9 Compound events: find the number of sums
• 10 Find the number of outcomes: word problems
• 11 Probability of compound events
• 12 Which simulation represents the situation?
• 13 Identify independent and dependent events
• 14 Probability of independent and dependent events

Seventh grade lessons

These lessons help you brush up on important math topics and prepare you to dive into skill practice!

• Absolute value
• Additive inverses
• Adding and subtracting integers
• Multiplying and dividing integers
• Adding decimals
• Subtracting decimals
• Multiplying decimals by powers of 10
• Multiplying decimals by whole numbers
• Multiplying decimals
• Dividing decimals by powers of 10
• Dividing decimals by whole numbers
• Dividing decimals
• Rational numbers
• Comparing rational numbers
• Adding and subtracting rational numbers
• Multiplying and dividing rational numbers

Exponents and powers of 10

• Powers of 10

Properties and mixed operations

• The distributive property
• Order of operations

Percents, ratios, and rates

• Unit rates with fractions
• Simple interest
• Percent change

Proportions and proportional relationships

• Proportions
• Proportional relationships
• Constant of proportionality
• Expressions and equations
• Writing algebraic expressions
• Evaluating expressions
• Equivalent expressions
• Simplifying expressions
• Expanding expressions
• Factoring expressions
• Solving equations
• Multi-step equations
• Independent and dependent variables
• Inequalities on a number line
• Solving inequalities
• Area of triangles
• Area of parallelograms
• Area of rhombuses
• Area of trapezoids
• Parts of a circle
• Area of circles
• Circumference of circles
• Complementary angles
• Supplementary angles
• Adjacent angles
• Vertical angles
• What is surface area?
• Surface area formulas
• Volume formulas
• Volume of rectangular prisms
• Volume of prisms
• Volume of cylinders
• Volume of pyramids
• Cross sections
• Triangle inequality theorem

Statistics and probability

• Mean, median, mode, and range
• Mean absolute deviation
• Box and whisker plots
• Statistical questions
• Probability
• Compound probability

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

Themed-problems and a weekly fun fact make it easy to keep learners engaged

MINIMAL PREP

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PRINT & DIGITAL

Includes both print and digital student options for added flexibility

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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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7th Grade Mathematics Worksheets: FREE & Printable

Looking for FREE printable 7th-grade math questions and exercises to help your students review and practice 7th-grade mathematics concepts?

Need Mathematics Practice questions to measure your 7th-grade student’s exam readiness? If so, then look no further.

Here is a comprehensive collection of free exercises and worksheets that would help your students for 7th Grade Math preparation and practice.

Download our free Mathematics worksheets for the 7th Grade Math.

You can download free 50+ 7th Grade Math Worksheets  from Bytelearn.

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7th grade mathematics concepts, fractions and decimals.

• Simplifying Fractions
• Adding and Subtracting Fractions
• Multiplying and Dividing Fractions
• Adding and Subtracting Mixed Numbers
• Multiplying and Dividing Mixed Numbers
• Adding and Subtracting Decimals
• Multiplying and Dividing Decimals
• Comparing Decimals
• Rounding Decimals
• Factoring Numbers
• Greatest Common Factor
• Least Common Multiple

Real Numbers and Integers

• Adding and Subtracting Integers
• Multiplying and Dividing Integers
• Order of Operations
• Ordering Integers and Numbers
• Integers and Absolute Value

Proportions, Ratios, and Percent

• Simplifying Ratios
• Proportional Ratios
• Similarity and Ratios
• Ratio and Rates Word Problems
• Percentage Calculations
• Percent Problems
• Discount, Tax and Tip
• Percent of Change
• Simple Interest

Algebraic Expressions

• Simplifying Variable Expressions
• Simplifying Polynomial Expressions
• Translate Phrases into an Algebraic Statement
• The Distributive Property
• Evaluating One Variable Expressions
• Evaluating Two Variables Expressions
• Combining like Terms

Equations and Inequalities

• One-Step Equations
• Multi-Step Equations
• Graphing Single–Variable Inequalities
• One-Step Inequalities
• Multi-Step Inequalities

Systems of Equations

• Systems of Equations Word Problems
• Quadratic Equation

Linear Functions

• Finding Slope
• Graphing Lines Using Line Equation
• Writing Linear Equations
• Graphing Linear Inequalities

Exponents and Radicals

• Multiplication Property of Exponents
• Zero and Negative Exponents
• Division Property of Exponents
• Powers of Products and Quotients
• Negative Exponents and Negative Bases
• Scientific Notation
• Square Roots

Geometry and Solid Figures

• Pythagorean Relationship
• Rectangular Prism
• Pyramids and Cone

Statistics and Probability

• Mean and Median
• Mode and Range
• Stem–and–Leaf Plot
• Probability Problems
• Combinations and Permutations

The Best Book to Ace 7th-Grade Math Concepts!

Mastering Grade 8 Math Word Problems The Ultimate Guide to Tackling 8th Grade Math Word Problems

7th grade math exercises, proportions and ratios, polynomials, solid figures.

Looking for the best resources to help your students review and practice Math topics?

The Best Books to Ace the Math Test!

Mastering Grade 6 Math Word Problems The Ultimate Guide to Tackling 6th Grade Math Word Problems

Mastering grade 5 math word problems the ultimate guide to tackling 5th grade math word problems, mastering grade 7 math word problems the ultimate guide to tackling 7th grade math word problems.

by: Effortless Math Team about 4 years ago (category: Blog , Free Math Worksheets )

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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 :

Reflection and 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.

●   Practical Geometry

• Practical Geometry
• Construction of a Circle

●  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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Math Wheels for Note-taking?

Teaching Problem Solving in the Middle School Classroom

I love teaching problem solving to my middle schoolers! By this stage in their math journey, they’ve already laid a foundation. Now, I get to show them all the different ways they can approach a problem. It’s so rewarding to see how unique each student is, especially when one strategy works great for one and another for someone else. In the end, though, they all reach the right answer, which is what really matters. This process also sparks some amazing, authentic math conversations in the classroom. Today, I’m excited to share all the posts I’ve written to help with teaching problem solving!

Helping our students develop problem solving skills can be difficult. It takes time and lots of opportunities to practice those skills. Over the years I’ve used a variety of teaching strategies and activities when it comes to problem solving. Some worked well and some not so much. So I’ve pulled together the things that worked well to share with you here. I hope that as you read through the posts you will find some nuggets that will help you make teaching problem solving easier and more effective.

Roundup of Posts for Teaching Problem Solving

Teaching math problem solving strategies.

This post is all about helping our students develop strong problem-solving skills through a variety of strategies. I highlight different approaches that can guide our students in breaking down math problems, making them more manageable and less intimidating. It also dives into why exposing our students to multiple strategies is important. It gives them the tools to find what works best for their individual learning styles.

My Problem Solving Doodle Notes resource is a fantastic tool for teaching problem solving in a way that’s interactive and visually engaging for students. In this blog post, I share how I’ve used this resource to teach a variety of problem solving strategies that make breaking down math problems easier. The doodle notes allow my students to keep track of various strategies like guessing and checking, working backward, drawing diagrams, and making organized lists. What I love most about this resource is how it encourages students to take ownership of their learning by keeping these notes as a reference all year long. It’s a fun and effective way to reinforce different methods for teaching problem solving!

To learn more about these problem solving strategies and the doodle notes read the full article here .

How to Teach Real Life Math Problem Solving Activities

My next post is all about building strong problem-solving skills in our students using real-life math activities. My experience in the classroom has led me to the conclusion that students love math when they see its relevance. There’s nothing more relevant than real-life examples of how problem solving skills are used in the day-to-day.

In this post, I explore different strategies that help students break down complex problems. This helps to make them feel less overwhelmed and more approachable. The post also explains why it’s important to introduce a variety of methods so that our students can discover what works best for them. By providing them with options, we empower them to choose strategies that fit their learning style.

5 Ways to Practice Problem Solving in Middle School

The next post emphasizes the importance of teaching students to break down complex problems into smaller, manageable steps. This one step helps them feel more confident and less overwhelmed. I also explore how teaching problem-solving approaches, such as drawing diagrams, working backward, and using logical reasoning, gives our students the flexibility to find the best method for their unique learning style.

The post also explains why building these skills is crucial for our students’ overall math success. It acknowledges that our students will face more challenging concepts. If you’re looking for ways to make teaching problem solving engaging and effective, this post offers a range of techniques that can be easily incorporated into your lessons!

Decimal Operations Math Problem Solving

Sometimes our problem solving skills change a little when it comes to specific skills and concepts. In this post, I share tips and ideas for teaching problem solving when it comes to decimals. I focus on helping students strengthen their problem solving skills through decimal operations.

This post dives into different strategies that guide our students in working through multi-step problems involving decimals. I share how I have taught problem solving skills that make the process feel less daunting. By including a variety of methods, our students can approach decimal problems from angles that make sense to them. Some of the problem solving skills I share in this post include teaching students how to use estimation, logical reasoning, or step-by-step calculations. This post highlights the importance of practicing these skills to build confidence and accuracy when tackling decimal operations. If your students are struggling with decimals and problem solving, this post is a must read!

Help Middle School Math Students Improve Problem Solving Skills

Ready to help your students expand their repertoire of problem solving strategies? This post will help! This post dives into effective ways to help middle schoolers improve their problem-solving skills in math. It covers different approaches that can simplify the process for our students. These approaches can break problems down step by step and make them more approachable.

By introducing a variety of strategies, our students gain the tools they need to navigate more complex math problems with confidence. The post also emphasizes the importance of consistency and practice in building these skills. If you’re looking for actionable ways to support your students’ growth in math while teaching problem solving, I share some great tips in this post!

Problem Solving Math Wheels

If you’ve been a follower, then you probably already know how much I loved using math wheels in the classroom. They are one of my absolute favorite tools for students. In this post, I dive into how you can use the Problem Solving Math Wheel to teach a variety of problem solving strategies.

These wheels allow our students to visually break down problems step by step. They also help them organize their strategies and make connections between different methods. By rotating through various approaches, such as guess and check, working backward, or drawing diagrams, our students can see how each technique plays a role in finding the solution. It’s a fantastic way to make abstract concepts more concrete. When we do, we are giving our students the tools to confidently approach math problems. Whether you’re working on basic operations or more complex equations, math wheels are a creative resource for teaching problem-solving skills.

Using Collaboration to Improve Math Problem Solving

If there is one thing our middle school students love it is collaboration. Any time we can add opportunities for our students to work together we have increased engagement. In this post, I explore the benefits of using collaborative problem-solving in middle school math. It emphasizes how working together allows our students to tackle challenging problems by sharing different strategies and perspectives.

Collaborative problem solving boosts critical thinking and fosters communication and teamwork skills. The post highlights how this approach encourages our students to explain their reasoning, ask questions, and build on each other’s ideas. This makes math more engaging and interactive. The post offers great strategies to use while teaching problem solving to your students!

How to Teach Problem of the Week in Middle School Math

We all know the saying “An apple a day keeps the doctor away.” But what if we applied this concept to helping our students improve their problem solving skills? In this post, I highlight the effectiveness of using a Problem of the Week to build strong problem-solving skills in middle school math.

In this post, I dive into how implementing a Problem of the Week can boost problem-solving skills in middle school math. This approach gives our students the chance to focus on one challenging problem each week. It allows them to explore various strategies and think critically about their solutions. I outline how this method promotes deeper understanding, persistence, and encourages student discussions around their problem-solving processes. If you aim to introduce a consistent and engaging routine for teaching problem solving in your classroom, this post is a great place to start.

Metric Conversions Free Problem Solving and Matching Activity

Similar to the post above on teaching problem solving with decimals, this post shares the specific problem solving strategies I used when my students were learning about metric conversions. In this post, I explore an engaging approach to teaching metric conversions through a matching activity that helps solidify problem-solving skills.

In this post, I share an activity that challenges students to pair conversion problems with their correct answers. It encourages them to think critically and work through the process step by step. This method makes learning metric conversions more interactive. It also helps students build confidence in their problem-solving abilities. The post also includes a free problem-solving activity that offers extra practice for our students. This ensures they get hands-on experience with these essential math concepts.

Teaching Problem Solving Made Easier

Teaching problem solving is about giving our students the tools they need to tackle any math problem that comes their way. Whether it’s through collaborative activities, hands-on resources, or weekly challenges, there are many ways to make problem solving effective. By exposing our students to a variety of strategies, we empower them to find what works best for their unique learning styles. I hope these ideas help you to incorporate more creative problem solving techniques into your classroom!

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Remember to save this post to your favorite math Pinterest board for quick access to these resources to help with teaching problem solving!

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Problem Solving Activities: 7 Strategies

• Critical Thinking

Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough. 

I was so excited!

We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies. 

It was a proud moment for me!

Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy. 

Genius right? 

After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name. 

What a crushing blow! Just when I thought I did something special, I find out I did it all wrong. 

I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom. 

When I Finally Saw the Light

To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students. 

Problem Solving Activities

Here are seven ways to strategically reinforce problem solving skills in your classroom. 

Seasonal Problem Solving

Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!

Cooperative Problem Solving Tasks

Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.

Notice and Wonder

Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it. 

Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.

Math Starters

Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here ! 

Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.

Calculators

Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!

Three-Act Math Tasks

Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons . 

Getting the Most from Each of the Problem Solving Activities

When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next. 

Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below. 

Which of the problem solving activities will you try first? Respond in the comments below.

Shametria Routt Banks

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2 Responses

This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.

Thank you, Scott! Best wishes to you and your pre-service teachers this year!

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