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7th Grade Math Practice, Topics, Test, Problems, and Worksheets

  • Go Math Grade 7 Answer Key
  • Big Ideas Math Answers Grade 7
  • Big Ideas Math Answers Grade 7 Advanced
  • Eureka Math Grade 7 Answer Key
  • AUROPHARMA Pivot Point Calculator

In 7th Grade Math Practice, you will find all Kinds of Topics explained in a clear-cut way. Keeping in mind the Child’s Level of Understanding in Grade 7 we have outlined all the concepts in a simple language so that they understand them easily. Improve your knowledge by practicing the 7th Grade Topics regularly and understand the application of concepts.

Relations and Mapping

Relations and mapping – worksheets, numbers – worksheets, fractions – worksheets, bodmas/pemdas rule, profit, loss, and discount, profit, loss and discount – worksheets, ratios and proportions, ratios and proportions – worksheets, time and work, time and work – worksheets, unitary method, unitary method – worksheets, simple interest, simple interest – worksheets, algebraic expressions, algebraic expressions – worksheets, formula – worksheets, algebraic identities, equations – worksheets, inequations, inequations – worksheets, lines and angles, polygons – worksheets.

  • Quadrilateral

Symmetrical Figure

Coordinate system, mensuration, mensuration – worksheets, volume and surface area of solids.

We have compiled Practice Tests, Worksheets for the 7th Standard Math Concepts so that you can test your preparation levels. Identify the areas you are not comfortable with and allot time to them so that you can attempt them with confidence in the actual exam. After practicing from these 7th Grade Math Problems you will interpret and compute different types of topics and their problems easily.

Go Math Grade 7 Answer Key Free PDF Download

Students who wish to prepare the 7th Grade Math Concepts can check out the Chapterwise Go Math Grade 7 Answer Key available below. You just need to click on the quick links to access the concerned chapter of Go Math 7th Grade Solution Key. Clarify all your concerns easily by practicing the Step by Step Go Math Grade 7 Solutions on a daily basis.

HMH Go Math 7th Grade Answer Key

  • Chapter 1: Adding and Subtracting Integers
  • Chapter 2: Multiplying and Dividing Integers
  • Chapter 3: Rational Numbers
  • Chapter 4: Rates and Proportionality
  • Chapter 5: Percent Increase and Decrease
  • Chapter 6: Algebraic Expressions
  • Chapter 7: Writing and Solving One-Step Inequalities
  • Chapter 8: Modeling Geometric Figures
  • Chapter 9: Circumference, Area, and Volume
  • Chapter 10: Random Samples and Populations
  • Chapter 11: Analyzing and Comparing Data
  • Chapter 12: Experimental Probability
  • Chapter 13: Theoretical Probability and Simulations

Big Ideas Math Book 7th Grade Answer Key

Utilize the Big Ideas Math Book Grade 7 Answer Key for all the Chapters whenever you need Homework Help. The BIM Grade 7 Answer Key available ensures you achieve your learning targets and achieve success in your exams. To make your searching experience simple we have outlined all the Big Ideas Math Grade 7 Answer Key organized as per the Big Ideas Math 7th Grade Textbooks. Simply click on the respective chapter you wanted to prepare and learn all the underlying topics in it easily.

  • Chapter 1 Adding and Subtracting Rational Numbers
  • Chapter 2 Multiplying and Dividing Rational Numbers
  • Chapter 3 Expressions
  • Chapter 4 Equations and Inequalities
  • Chapter 5 Ratios and Proportions
  • Chapter 6 Percents
  • Chapter 7 Probability
  • Chapter 8 Statistics
  • Chapter 9 Geometric Shapes and Angles
  • Chapter 10 Surface Area and Volume

Big Ideas Math Book 7th Grade Answer Key

Big Ideas Math Book 7th Grade Advanced Answer Key

Big Ideas Math Book 7th Grade Advanced Answer Key available here covers all the concepts as per the latest syllabus guidelines. Develop a Conceptual Understanding of Grade 7 Math and improve your ability to apply mathematics to solve problems. To make it easy for you we have compiled all the Chapterwise 7th Standard Math Answer Key in a simple and understandable language. You just have to click on the concerned chapter you wish to prepare and allot time accordingly.

  • Chapter 1 Equations
  • Chapter 2: Transformations
  • Chapter 3: Angles and Triangles
  • Chapter 4: Graphing and Writing Linear Equations
  • Chapter 5: Systems of Linear Equations
  • Chapter 6: Data Analysis and Displays
  • Chapter 7: Functions
  • Chapter 8 Exponents and Scientific Notation
  • Chapter 9 Real Numbers and the Pythagorean Theorem
  • Chapter 10 Volume and Similar Solids
  • Chapter A: Equations and Inequalities
  • Chapter B: Probability
  • Chapter C: Statistics
  • Chapter D: Geometric Shapes and Angles
  • Chapter E: Surface Area and Volume

7th Grade Math Topics

On this page, you will learn all the Topics that a Grade 7 Student should learn. We have covered all the topics that a middle school student should learn as a part of the curriculum. You will find Chapters such as Integers, Fractions, Decimals, etc. Tap on the concerned chapter you wish to learn the concepts in it accordingly. You just need to tap on the direct links available and avail the topics easily.

  • Objects Form a Set
  • Elements of a Set
  • Properties of Sets
  • Representation of a Set
  • Different Notations in Sets
  • Standard Sets of Numbers
  • Types of Sets
  • Pairs of Sets
  • Subsets of a Given Set
  • Operations on Sets
  • Union of Sets
  • Intersection of Sets
  • Difference of Two Sets
  • Complement of a Set
  • Cardinal Number of a Set
  • Cardinal Properties of Sets
  • Venn Diagrams
  • Ordered Pair
  • Cartesian Product of Two Sets
  • Domain and Range of a Relation
  • Functions or Mapping
  • Domain Co-domain and Range of Function
  • Worksheet on Math Relation
  • Worksheet on Functions or Mapping
  • 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 Operations
  • Examples on Fundamental Operations
  • Uses of Brackets
  • Removal of Brackets
  • Examples on Simplification
  • Worksheet on Multiplication of Integers
  • Worksheet on Division of Integers
  • Worksheet on Fundamental Operations
  • Worksheet on Simplification
  • 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
  • Worksheet on Fractions
  • Worksheet on Multiplication of Fractions
  • Worksheet on Division of Fractions
  • Decimal Numbers
  • Decimal Fractions
  • Decimal Places
  • Decimal and Fractional Expansion
  • Like and Unlike Decimals
  • Conversion of Unlike Decimals to Like Decimals
  • Comparing Decimals
  • Adding Decimals
  • Subtracting Decimals
  • Simplify Decimals Involving Addition and Subtraction Decimals
  • Multiplying Decimal by a Whole Number
  • Multiplying Decimal by a Decimal Number
  • Dividing Decimal by a Whole Number
  • Dividing Decimal by a Decimal Number
  • Simplification of Decimal
  • Converting Decimals to Fractions
  • Converting Fractions to Decimals
  • Rounding Decimals
  • Rounding Decimals to the Nearest Whole Number
  • Rounding Decimals to the Nearest Tenths
  • Rounding Decimals to the Nearest Hundredths
  • Round a Decimal
  • H.C.F. and L.C.M. of Decimals
  • Terminating Decimal
  • Non-Terminating Decimal
  • Repeating or Recurring Decimal
  • Pure Recurring Decimal
  • Mixed Recurring Decimal
  • Conversion of Pure Recurring Decimal into Vulgar Fraction
  • Conversion of Mixed Recurring Decimals into Vulgar Fractions
  • BODMAS Rule
  • BODMAS Rules – Involving Integers
  • BODMAS/PEMDAS Rules – Involving Decimals
  • PEMDAS Rule
  • PEMDAS Rules – Involving Integers
  • PEMDAS Rules – Involving Decimals

BODMASPEMDAS Rule

  • 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
  • Practice Test on Profit Loss and Discount
  • Worksheet on Discounts
  • What is a Ratio?
  • What is a Proportion?
  • Worksheet on Ratios
  • Worksheet on Proportions
  • 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
  • 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
  • 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
  • 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
  • What is Simple Interest?
  • Calculate Simple Interest
  • Practice Test on Simple Interest
  • Simple Interest Worksheet
  • Division of Polynomial by Monomial
  • 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
  • Worksheet on Framing the Formula
  • Worksheet on Changing the Subject of a Formula
  • Worksheet on Changing the Subject in an Equation or Formula
  • Square of The Sum of Two Binomials
  • Square of The Difference of Two Binomials
  • Product of Sum and Difference of Two Binomials
  • Product of Two Binomials whose First Terms are Same and Second Terms are Different
  • Square of a Trinomial
  • Cube of The Sum of Two Binomials
  • Cube of The Difference of Two Binomials
  • Cube of a Binomial
  • Square of a Binomial
  • 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
  • Worksheet on Linear Equations
  • Worksheet on Word Problems on Linear Equation
  • 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
  • Worksheet on Linear Inequations

    Geometry

_   Geometry

  • 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
  • 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
  • Worksheet on Polygon and its Classification
  • Worksheet on Interior Angles of a Polygon
  • Worksheet on Exterior Angles of a Polygon
  • Perimeter of Quadrilateral
  • Angle Sum Property of a Quadrilateral
  • Missing Angle of a Quadrilateral
  • Angles of a Quadrilateral are in Ratio
  • Linear Symmetry
  • Lines of Symmetry
  • Point Symmetry
  • Reflection Symmetry
  • Nets of a Solids
  • Rotational Symmetry
  • Order of Rotational Symmetry
  • Types of Symmetry
  • Reflection of a Point in x-axis
  • Reflection of a Point in y-axis
  • Reflection of a point in origin
  • 90 Degree Clockwise Rotation
  • 90 Degree Anticlockwise Rotation
  • 180 Degree Rotation
  • 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
  • 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
  • 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 of Cubes and Cuboids
  • Worked-out Problems on Volume of a Cuboid
  • 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?

Grade 7 Math Goals and Objectives

Comprehensive 7th Grade Math Curriculum will concentrate on the below areas and ensure students are achieving these learning targets. They are as under

  • Understand Rational Number Operations
  • Representation of Rational Numbers with Decimals
  • Analyze Proportional Relationships to solve mathematical problems in the real world.
  • Construct and describe geometrical figures and the relationships between them.
  • Solve Problems involving Angle Measure, Area, and Volume.
  • Extend the use of 4 basic arithmetic operations on whole numbers, mixed numbers, decimals, and fractions.
  • Analyze and Interpret Data presented in various forms.
  • Solve Mathematical Problems involving numerical and algebraic expressions, equations and inequalities, etc.

Why Choose our 7th Grade Math Curriculum?

Master the concepts of Grade 7 Math and study advanced mathematics in a fun learning way. They are as follows

  • 7th Grade Math Practice helps you to achieve learning targets and master the concepts easily.
  • Our Preparation Material keeps students engaged irrespective of their learning method.
  • You can access the 7th Grade Math Topics 24/7 from anywhere for free of cost.
  • 7th Grade Math Worksheets and Practice Tests available make it easy for you to learn challenging concepts too even after school.
  • Learning Exercises and Simulated Assessments provide 7th Grade Standardized Test Practice.

We wish the knowledge shed regarding the 7th Grade Math Topics has enlightened you. If you have any suggestions do leave us your feedback so that we can look into them and add if necessary. Keep in touch with our site to avail latest updates on Gradewise Math Topics in no time.

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problem solving examples math grade 7

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.

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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problem solving examples math grade 7

Common Core - State Standards Initiative

  • Students learn about ratios, mixed properties, statistics and other seventh grade skills.
  • Teachers incorporate the use of the scratchpad to give students a visual representation.
  • Videos provide instant help for students who are struggling with their assignments.

Building Problem-solving skills for math

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

problem solving examples math grade 7

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

problem solving examples math grade 7

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

problem solving examples math grade 7

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

problem solving examples math grade 7

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

Communication is essential for building problem-solving skills for math

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

Building problem-solving skills for math involves solid understanding of mathematical concepts

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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problem solving examples math grade 7

Home / United States / Math Classes / Worksheets / 7th Grade Math Worksheets

7th Grade Math Worksheets

7th Grade Math Worksheets introduce students to new curriculum additions such as equations, use of expressions, probabil ity, statistics, number operations, algebra, geometry, measurements, spatial sense, probability, and data analysis. These printable math worksheets for grade 7 teach students through interactive activities such as learning games and assessments. They contribute to critical thinking and efficient problem-solving. With these worksheets, students can learn these topics in depth and apply them to the problems of the real world. ...Read More Read Less

Benefits of 7th Grade Math Worksheets

Comprehensive Curriculum

The Grade 7 Math worksheets provide extensive coverage of mathematical topics ranging from number theory, integers and operations with integers, decimals and operations with decimals, fractions and mixed numbers and related operations, ratio and proportion, rational numbers, powers and exponents, linear equations in one variable, and congruence and similarity of triangles.

Visual simulations

Grade 7 Math worksheets consist of appealing visuals, simulations, and colorful images. This helps your child visualize the mathematical concepts being taught. In addition, students can reinforce their learning by "seeing things in action."

Systematic Learning Process

7th Grade Math Worksheets for all topics follow a stepwise learning process. There is always a brief introduction to the topic, followed by solved examples and practice questions. This helps students understand concepts better, and they can easily transition from one difficulty level to the next.

Fun-based learning

Online worksheets for Grade 7 Math offer a fun learning environment for students. They include various activities, riddles, printable quizzes, and practice sets that encourage your child to ditch the traditional boring theoretical math learning.

Immersive learning experience

Grade 7 Math worksheets provide an immersive and engaging learning experience for your child both online and offline. They get to activate their thinking and reasoning skills and learn more than one way to solve a problem.

  • Interactive Worksheets
  • Printable Worksheets

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  • 7th Grade Geometry Worksheets
  • 7th Grade Ratio And Proportions Worksheets

7th Grade Solving Inequalities Worksheets

  • 7th Grade Mathematical Structure of Word Problems Worksheets

7th Grade Graphing Worksheets

  • 7th Grade Unit Rate in Graph Worksheets
  • 7th Grade Proportional Graphs

Choose Math Worksheets by Grade

Choose math worksheets by topic, grade 7 math worksheets explained.

Number Theory

Grade 7 Math worksheets help your child master the concepts of various elements of number theory.  They will learn, practice, and solve prime or composite numbers, multiplication inverses, rules of divisibility, HCF and LCM, and classification of numbers.

Integer Worksheets 

Grade 7 worksheets introduce students to integers. There are various difficulty levels for practice sums and word problems on integers, plotting integers on graph paper, the absolute value of integers, and the comparison of integers. In addition, your child will learn how to add, subtract, multiply, divide, and solve numerical expressions that have integers.

Grade 7 Math Worksheets provide a detailed discussion of decimal numbers and number lines, ordering and comparing, and rounding numbers to various digits levels. In addition, the worksheets include exercises on operations and different decimal numbers.

Fractions Worksheets

Online Grade 7 Worksheets for fractions cover the understanding of basic concepts for types of fractions, comparing fractions, and arranging them in an ascending or descending order. Students also learn to perform various operations on fractions, including addition, subtraction, multiplication, division, conversion to other forms, and estimation and evaluation of numeric expressions.

Understanding Rational Numbers

Grade 7 math worksheets for rational numbers teach students to identify, order, and compare rational numbers, convert decimals or fractions to rational numbers, and perform the four basic arithmetic operations on them.

Powers and Exponents

Grade 7 math worksheets provide comprehensive information about powers and exponents, and solving equations with variable exponents. They cover negative, fractional, and decimal bases. In addition, your child will learn how to evaluate numerical expressions.

Problem Solving & Estimation

Online Grade 7 worksheets include problem-solving and estimation questions with different variants, like word problems with multiple steps, elapsed time word problems, and Venn diagrams.

Number Sequences

Here you will find a range of printable Grade 7 worksheets for all kinds of arithmetic, geometric sequences, and number sequences of various types. You can teach your child to write and evaluate variable expressions for number sequences.

Congruence and similarity of triangles

Your child can ease through challenging topics like congruence and similarity of triangles. There are plenty of exercises in these printable worksheets for Grade 7. For example, students can practice angle and side measurement for similar and congruent figures and congruence statements and corresponding parts.

Are these 7th grade math worksheets suitable for middle school students?

These 7th grade interactive math worksheets have been designed for seventh grade students at three different levels – easy, medium and hard. The students are always encouraged to take up worksheets from all levels to strengthen their understanding of math concepts.

What are the topics covered in these grade 7 math worksheets?

The topics included in the 7th grade math worksheets are addition, subtraction, multiplication and division of rational numbers, algebraic expressions and their addition and subtraction, equations and inequalities, ratio and proportions, percent, discount, simple interest, probability, statistics, geometrical shapes and surface area and volume of 3D shapes.

Are there any levels of difficulty for the 7th grade math worksheets?

The seventh grade math worksheets are categorized into three levels – easy, medium and hard. Every student can easily choose among the levels based on their understanding of the math concepts and how confident they are. We always encourage students to attempt all three levels for getting a clear understanding of the math concepts which will eventually result in math learning and confidence.

Are the grade 7 math worksheets timed?

Yes, the seventh grade interactive math worksheets are timed. This will motivate the students more to participate in such time-bound activities and self-regulate their learning to get a better understanding on how prepared they are with the math concepts.

In what all formats are the seventh grade math worksheets available?

The 7th grade interactive worksheets are presented to the children in two different formats. The pdf based printable worksheets can be completed offline once downloaded while the others are tech based interactive or online math worksheets which are solved to get real time feedback and step wise solutions.

Who prepares the questions for grade 7 math worksheets?

The questions for seventh grade math worksheets are prepared by highly qualified subject matter experts who are adept with the subject. Each and every question is made online after several checks to ensure that the questions are authentic and unique enough for every level.

Can the 7th grade worksheets be solved more than once?

Yes, children can practice different math concepts using the BYJU’s free online math worksheets for seventh grade by attempting them more than once. In fact, for every new submission, a fresh set of questions appear for the students to practice and enhance their knowledge.

7th Grade Math Problems

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

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

●  Set Theory

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

● Relations and Mapping

Ordered Pair

Cartesian Product of Two Sets

Domain and Range of a Relation

Functions or Mapping

Domain Co-domain and Range of Function

● Relations and Mapping - Worksheets

Worksheet on Math Relation

Worksheet on Functions or Mapping

● Numbers - Integers

Multiplication of Integers

Properties of Multiplication of Integers

Examples on Multiplication of Integers

Division of Integers

Absolute Value of an Integer

Comparison of Integers

Properties of Division of Integers

Examples on Division of Integers

Fundamental Operation

Examples on Fundamental Operations

Uses of Brackets

Removal of Brackets

Examples on Simplification

● Numbers - Worksheets

Worksheet on Multiplication of Integers

Worksheet on Division of Integers

Worksheet on Fundamental Operation

Worksheet on Simplification

● Fractions

Types of Fractions

Equivalent Fractions

Like and Unlike Fractions

Conversion of Fractions

Fraction in Lowest Terms

Addition and Subtraction of Fractions

Multiplication of Fractions

Division of Fractions

● Fractions - Worksheets

Worksheet on Fractions

Worksheet on Multiplication of Fractions

Worksheet on Division of Fractions

● Story about the Decimal Number

Decimals : Concept for decimals in derails.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Rounding Decimals : Learn to round off decimals

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

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

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

Round a Decimal : Problems for rounding off decimals

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

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

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

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

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

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

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

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

BODMAS/PEMDAS rule:

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

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

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

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

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

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

● Profit, Loss and Discount

Concept of Profit and Loss

Calculate Profit and Profit Percent

Calculate Loss and Loss Percent

Calculate Cost Price using Sell Price and Loss Percent

Calculate Cost Price using Sell Price and Profit Percent

Calculate Selling Price using Cost and Loss Percent

Calculate Selling Price using Cost and Profit Percent

Calculating Profit Percent and Loss Percent

Word Problems on Profit and Loss

Examples on Calculating Profit or Loss

Practice Test on Profit and Loss

Practice Test on Profit Loss and Discount

● Profit, Loss and Discount - Worksheets

Worksheet to Find Profit and Loss

Worksheets on Profit and Loss Percentage

Worksheet on Gain and Loss Percentage

Worksheet on Discounts

● Ratios and Proportions

What is a Ratio?

What is a Proportion?

● Ratios and Proportions - Worksheets

Worksheet on Ratios

Worksheet on Proportions

● Time and Work

Calculate Time to Complete a Work

Calculate Work Done in a Given Time

Problems on Time required to Complete a Piece a Work

Problems on Work Done in a Given Period of Time

Problems on Time and Work

Pipes and Water Tank

Problems on Pipes and Water Tank

● Time and Work - Worksheets

Worksheet on Work Done in a Given Period of Time

Worksheet on Time Required to Complete a Piece of Work

Worksheet on Pipes and Water Tank

● Unitary Method

Problems Using Unitary Method

Situations of Direct Variation

Situations of Inverse Variation

Direct Variations Using Unitary Method

Direct Variations Using Method of Proportion

Inverse Variation Using Unitary Method

Inverse Variation Using Method of Proportion

Problems on Unitary Method using Direct Variation

Problems on Unitary Method Using Inverse Variation

Mixed Problems Using Unitary Method

● Unitary Method - Worksheets

Worksheet on Direct Variation using Unitary Method

Worksheet on Direct variation using Method of Proportion

Worksheet on Word Problems on Unitary Method

Worksheet on Inverse Variation Using Unitary Method

Worksheet on Inverse Variation Using Method of Proportion

● Simple Interest

What is Simple Interest?

Calculate Simple Interest

Practice Test on Simple Interest

● Simple Interest - Worksheets

Simple Interest Worksheet

● Algebraic Expressions

Division of Polynomial by Monomial

● Algebraic Expressions - Worksheets

Worksheet on Dividing Polynomial by Monomial

Formula and Framing the Formula

Change the Subject of a Formula

Changing the Subject in an Equation or Formula

Practice Test on Framing the Formula

● Formula - Worksheets

Worksheet on Framing the Formula

Worksheet on Changing the Subject of a Formula

Worksheet on Changing the Subject in an Equation or Formula

● Algebraic Identities

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cube of a Binomial :

Square of a Binomial :

● Equations

What is an Equation?

What is a Linear Equation?

How to Solve Linear Equations?

Solving Linear Equations

Problems on Linear Equations in One Variable

Word Problems on Linear Equations in One Variable

Practice Test on Linear Equations

Practice Test on Word Problems on Linear Equations

● Equations - Worksheets

Worksheet on Linear Equations

Worksheet on Word Problems on Linear Equation

● Inequations

What are Linear Inequality?

What are Linear Inequations?

Properties of Inequation or Inequalities

Representation of the Solution Set of an Inequation

Practice Test on Linear Inequation

● Inequations - Worksheets

Worksheet on Linear Inequations

● Lines and Angles

Fundamental Geometrical Concepts

Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Supplementary Angles

Complementary and Supplementary Angles

Adjacent Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines

● Congruence

Congruent Shapes :

Congruent Line-segments :

Congruent Angles :

Congruent Triangles :

Conditions for the Congruence of Triangles :

Side Side Side Congruence :

Side Angle Side Congruence : 

Angle Side Angle Congruence :

Angle Angle Side Congruence :

Right Angle Hypotenuse Side congruence :

Pythagorean Theorem :

Proof of Pythagorean Theorem :

Converse of Pythagorean Theorem :

Word problems on Pythagorean Theorem :

Polygon and its Classification

Terms Related to Polygons

Interior and Exterior of the Polygon

Convex and Concave Polygons

Regular and Irregular Polygon

Number of Triangles Contained in a Polygon

Angle Sum Property of a Polygon

Problems on Angle Sum Property of a Polygon

Sum of the Interior Angles of a Polygon

Sum of the Exterior Angles of a Polygon

● Polygons - Worksheets

Worksheet on Polygon and its Classification

Worksheet on Interior Angles of a Polygon

Worksheet on Exterior Angles of a Polygon

● Quadrilateral

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

Angles of a Quadrilateral are in Ratio :

●   Symmetrical Figure

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

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

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

Reflection Symmetry :

Nets of a Solids :

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

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

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

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

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

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

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

Rotation :  Explanation of rotation using an image.

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

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

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

●  Coordinate System

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

●  Mensuration

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

●  Mensuration - Worksheets

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

●   Volume and Surface Area of Solids

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

●  Statistics

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

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Unit 2: Rates and percentages

About this unit, rate problems with fractions.

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problem solving examples math grade 7

How to Solve Rate Problems - Grade 7 Math Questions With Detailed Solutions

How to solve questions on rates in math? Grade 7 math questions are presented along with detailed Solutions and explanations included.

What are rates in math and where are they needed? The rate is a ratio of two quantities having different units. Where are they needed? Example 1: Car A travels 150 kilometers in 3 hours. Car B travels 220 kilometers in 4 hours. We assume that both car travels at constant speeds. Which of the two cars travels faster? Solution Car A travels 150 kilometers in 3 hours. In one hour it travels \( \dfrac{150 \,\, \text{kilometers}}{3 \,\, \text{hours}} = \dfrac{50 \,\, \text{km}}{1 \,\, \text{hour}} \) = 50 km / hour Car B travels 220 kilometers in 4 hours. In one hour it travels \( \dfrac{220 \,\, \text{kilometers}}{4 \,\, \text{hours}} = \dfrac{55 \,\, \text{km}}{1 \,\, \text{hour}} \) = 55 km / hour The quantities 50 km / hour and 55 km / hour are called unit rates because the denominator is one unit of time: 1 hour. In this case the unit rates can be used to find out which car travels faster because we now know how many kilometers are traveled by each car in one hour and we can therefore compare the speed (or rates) and say that car B travels faster.

Example 2: A car travels 150 kilometers in 3 hours. We assume that the car travels at a constant speed. How many hours are needed for this car to travel 250 kilometers at the same speed? Let t be the number of hours needed to travel 250 kilometers. Since the car travels at a constant rate (speed), we can write that the unit rate is the same whatever values for distance and time we use. Hence we write \( \dfrac{150 \,\, \text{km}}{3\,\,\text{hour}} = \dfrac{250 \,\, \text{km}}{\text{t}} \) , t in hours The above equation in t has the form. \( \dfrac{a}{b} = \dfrac{c}{d} \) Multiply both terms of the above by the product of the denominators \(b \times d\). \( b \times d \times \dfrac{a}{b} = b \times d \times \dfrac{c}{d} \) Simplify \( \cancel{b}\times d \times\dfrac{a}{\cancel{b}} = b \times \cancel{d} \times \dfrac{c}{\cancel{d}} \) to obtain \( a \times d = b \times c \) Hence the equations \( \dfrac{a}{b} = \dfrac{c}{d} \) and \( a \times d = b \times c \) are equivalent and have the same solution. This method of changing an equation from fractions on each side to products on each side is called "cross muliply" method which we will use to solve our problems. We now go back to our equation \( \dfrac{150 \,\, \text{km}}{3\,\,\text{hour}} = \dfrac{250 \,\, \text{km}}{\text{t}} \) and use the "cross multiply" method to write it as follows. \( 150 \,\, \text{km} \times t = 250 \text{km}\times 3 \text{hours} \) Since we need to find t, we then isolate it by dividing both sides of the above equation by \( 150 \,\, \text{km} \). \( \dfrac{150 \,\, \text{km} \times t}{150 \,\, \text{km}} = \dfrac{250 \text{km}\times 3 \text{hours}}{150 \,\, \text{km}} \) Simplify. \( \dfrac{\cancel{150 \,\, \text{km}} \times t}{\cancel{150 \,\, \text{km}}} = \dfrac{250 \cancel{\text{km}}\times 3 \text{hours}}{150 \,\, \cancel{\text{km}}} \) \( t = \dfrac{250 \times 3}{150} \, \, \text{hours} = 5 \,\, \text{hours}\)

The exercises below with solutions and explanations are all about solving rate problems.

Solve the following rate problems.

  • The distance between two cities on the map is 15 centimeters. The scales on the map is 5 centimeters to 15 kilometers. What is the real distance, in kilometers, between the two cities?
  • A car consumes 10 gallons of fuel to travel a distance of 220 miles. Assuming a constant rate of consumption, how many gallons are needed to travel 330 miles?
  • Ten tickets to a cinema theater costs $66. Wha is the cost of 22 tickets to the same cinema theater?
  • Cans of soda are packaged in boxes containing the same number of cans. There are 36 cans in 4 boxes. a) How many cans are there in 7 boxes? b) How many boxes are needed to package 99 cans of soda?
  • Joe bought 4 kilograms of apples at the cost of $15. How much would he pay for 11 kilograms of the same apples in the same shop?
  • It takes a pump 10 minutes to move 55 gallons of water up a hill. Using the same pump under the same condition; a) how much water is moved in 22 minutes? b) how long does it take to move 165 gallons of water?
  • A container with 324 liters of water, leaks 3 liters every 5 hours. How long does it take for the container to become empty?
  • Twenty one cans of tomato paste of the same size have a weight of 7300 grams. What is the weight of 5 cans?
  • An empty container is being filled with water at the rate of 5 liters every 45 seconds and leaks water at the rate of one liter every 180 seconds. What is the quantity of water in the container after one hour?

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problem solving examples math grade 7

Problem Solving Activities: 7 Strategies

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problem solving examples math grade 7

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. 

This is an example of seasonal problem solving activities.

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.

This is an example of a math starter.

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.

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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.

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Education Standards

Maryland college and career ready math standards.

Learning Domain: Statistics and Probability

Standard: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Standard: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Standard: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"ť), identify the outcomes in the sample space which compose the event.

Standard: Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Common Core State Standards Math

Cluster: Investigate chance processes and develop, use, and evaluate probability models

Standard: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

Project Rubric: Making Connections

Project rubric: putting math to work, project rubric & criteria.

Project Rubric & Criteria

Students design and work on their projects in class. They review the project rubric and, as a class, add criteria relevant to their specific projects.

Key Concepts

Students are expected to use the mathematical skills they have acquired in previous lessons or in previous math courses. The lessons in this unit focus on developing and refining problem-solving skills.

Students will:

  • Try a variety of strategies to approaching different types of problems.
  • Devise a problem-solving plan and implement their plan systematically.
  • Become aware that problems can be solved in more than one way.
  • See the value of approaching problems in a systematic manner.
  • Communicate their approaches with precision and articulate why their strategies and solutions are reasonable.
  • Make connections between previous learning and real-world problems.
  • Create efficacy and confidence in solving challenging problems in a real-world setting.

Goals and Learning Objectives

  • Create and implement a problem-solving plan.
  • Organize and interpret data presented in a problem situation.
  • Use multiple representations—including tables, graphs, and equations—to organize and communicate data.
  • Articulate strategies, thought processes, and approaches to solving a problem and defend why the solution is reasonable.

Project Rubric

Lesson guide.

Have students view the project rubric. Give students a minute to study the rubric. Then have students take turns saying one thing about the rubric without looking at it.

When students are finished, tell them that today they will add any specifics to the rubric that they think are needed for evaluating their projects.

SWD: Students with disabilities may have a more challenging time identifying areas of improvement to target in their projects. Teach your students how to review a project using the rubric and a sample project. Model for students how to evaluate their project to ensure they are completing all components needed and identifying any areas that need to be addressed that are not in the rubric.

Work with a partner to review the project rubric.

  • Take a few minutes to study the rubric by yourself.
  • Without looking at the rubric, take 1 minute to describe the rubric as completely as possible to your partner (who can look at the rubric). Your partner should listen carefully to your description.
  • Briefly look at the rubric again. Your partner should now take 30 seconds to add to your description of the rubric—without repeating any of your description and without looking at the rubric.

Math Mission

Discuss the Math Mission. Students will work on their projects and evaluate their progress using the project rubric.

Work on your project, and evaluate your progress using the project rubric.

Organize and Analyze Project Data

Make sure students understand that the best use of this in-class project work day is to accomplish what they can't easily do later outside of class. Big, beautiful displays are a last step; now is the time for groups to decide how they will go about completing their project. Today's work is messy and preliminary; some of it may be devoted to finding resources (Internet-based and elsewhere).

Circulate among the working pairs and groups—listening to what they say and watching what they do. Ask clarifying questions:

  • What mathematical concepts can you use to investigate your question?
  • What materials are necessary?
  • How will you investigate your question?
  • How can you use units to clarify your results?
  • How will you communicate your results to your audience?

SWD: Some students with disabilities may struggle with time management, create a timeline and “to do list” for students so they know where their progress should be regarding project completion. Hang this information in a prominent location in your classroom.

Today you will:

  • Conduct research to gather information or collect data.
  • Organize your information or data.
  • Analyze your information or data in order to answer your question.

As you work on your project, consider these questions:

  • What mathematical concepts do you need to use in order to investigate your question?

Examples: Numerical reasoning, probability, statistics, geometry, ratios and proportional relationships, expressions, and equations

  • How will you communicate your conclusions to the class?

Examples: Diagrams and graphs, equations, verbal explanations, and models

As you work, use the project rubric to evaluate your progress and make sure you are on the right track.

Your Completed Project

Go over the list of what the presentations should include.

Your completed project should include:

  • The information or data you researched.
  • Graphs or diagrams that communicate your findings.
  • Expressions, equations, or formulas that you used to make your conclusions.
  • A summary of your findings.
  • Your conclusions regarding your specific question.

Make Connections

Have students return to the project rubric. Tell them that, as a class, they can agree to add to—but not subtract from—the general rubric to improve the fit with their problem-solving projects.

There are two main ways to add to the rubric:

  • Add detail to one or more of the descriptions of score 4.
  • See the column “Specific to This Project.”
  • Add a new criterion for scoring, and then describe the score 4 for that criterion. See the blank, last row.

Give students a couple of minutes to talk with their partner or group. Then let individuals propose any specific additions. You or a student may record these additions, and after the class discussion, adopt whichever criteria have the support of the class.

Note that this is a brief, focused opportunity for students to take ownership of the rubric. They may make several additions or none. The objective is their buy-in.

Performance Task

Ways of thinking: make connections.

Look at the rubric again.

  • Notice the blank column with the heading “Specific to This Project.” Is there anything that you think should be added to this column?
  • Next, look at the bottom row that is blank. Is there any scoring criterion for the project that you think should be added here?

Take a few minutes to discuss these questions with a partner.

  • Write down any ideas you have.
  • Discuss your ideas as a class. As you propose an idea make sure to explain why you think it is important. After all ideas are discussed the class will decide as a group whether to adopt any of the suggestions.

Reflect on Your Work

Give students a few minutes to respond individually to two simple prompts, focused on what they accomplished today and what their next steps are. These reflections can be quite skeletal—very short lists are fine.

Then give partners and groups a few more minutes to share their individual reflections.

Make sure students realize that their reflections now serve as their starter for the work they will do outside of class to complete their problem-solving project.

ELL: The “Reflect on Your Work” section provides opportunities for ELLs to develop literacy in English and proficiency in mathematics. Make sure students use both academic and specialized mathematical language when reflecting on their project. Give students time to discuss the summary before they write, and make sure students create a task list for completing their project based upon the rubric.

Write a reflection about the ideas discussed in class today. Use the sentence starters below if you find them to be helpful. After you have finished, share your reflections with your group.

Today my group accomplished…

Our next steps are…

Version History

COMMENTS

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