7th grade math problem solving worksheets

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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!

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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.

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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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TRY SOME FREE SAMPLE 7TH GRADE PRINTABLE MATH WORKSHEETS

7TH GRADE MATH WORKSHEETS

• Separate answers are included to make marking easy and quick.
• Over 200 pages of the highest quality 7th Grade math worksheets. Each worksheet is differentiated, including a progressive level of difficulty as the worksheet continues.
• Single user license for parents or teachers. Separate school licenses are available here
• Single digital pdf download, with worksheets organized into high level chapters of Algebra, Statistics, Number and Geometry, and further by subtopics. See below for the extensive range of sheets included.

List of Topics

Our 7th Grade printable math worksheets cover the full range of topics. See below the list of topics covered. See below the list of topics covered. All our math worksheets can be accessed here.

PEMDAS Expanding Brackets Factorising Indices Inequalities Linear Functions Real Life Graphs Rearranging Equations Sequences Simplification Solving Equations (linear equations) Substitution

Calculator Methods Decimals Fractions Fractions Decimals Percentages Mental Methods Negative Numbers Percentages Place Value Powers Proportion Ratio Rounding Time Types of Number Written Methods

2D Shapes 3D Shapes Area and Perimeter Bearings Scale and Loci Circles Compound Measures Constructions Coordinates Lines and Angles Polygons Pythagoras (Pythagorean theorem) Similarity and Congruence Transformations Volume and Surface Area

Histograms and Frequency Polygons Mean Median Mode Pie Charts and Bar Charts Probability Scatter Graphs Stem-and-Leaf Diagrams Two-Way Tables and Pictograms

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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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IMPORTANT: COPYRIGHT TERMS: These worksheets are for personal use. Worksheets may not be uploaded to the internet, including classroom/personal websites or network drives. You can download the worksheets and print as many as you need. You can distribute the printed copies to your students, teachers, tutors, and friends. 

You Do NOT have permission to send these worksheets to anyone in any way (via email, text messages, or other ways). They MUST download the worksheets themselves. You can send the address of this page to your students, tutors, friends, etc.

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The Absolute Best Workbook to Review 7th-Grade Math Concepts!

Mastering Grade 8 Math The Ultimate Step by Step Guide to Acing 8th Grade Math

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

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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.

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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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7 th Grade Math Worksheets

Free, Printable Math Worksheets for at-home Practice

A Parent’s Guide to Seventh Grade Math + Practice Worksheets

Download this informative guide to learn how to best support your seventh grader as they learn and master important seventh grade math concepts.

Free Practice Worksheets

Choose a Grade

Click on a concept below to try a sample question

Ratio & Proportion

Number system.

Probability

Why 7th grade math worksheets are important.

A stated objective of Common Core State Standards (CCSS) is to standardize academic guidelines nationwide. In other words, what Seventh Graders learn in math in one state should be the same as what students of the same age are learning in another state. The curricula may vary between these two states, but the general concepts behind them are similar. This approach is intended to replace wildly differing guidelines among different states, thus eliminating (in theory) inconsistent test scores and other metrics that gauge student success.

An increased focus on math would seem to include a wider variety of topics and concepts being taught at every grade level, including Seventh Grade. However, CCSS actually calls for fewer topics at each grade level. The Common Core approach (which is clearly influenced by “Singapore Math”—an educational initiative that promotes mastery instead of memorization) goes against many state standards. Many states mandate a “mile-wide, inch-deep” curriculum in which children are taught so much in a relatively short time span, that they aren’t effectively becoming proficient in the concepts they truly need to understand to succeed at the next level. Hence, CCSS works to establish an incredibly thorough foundation not only for the math concepts in future grades, but also toward practical application for a lifetime.

How Our Seventh Grade Math Worksheets Reflect Common Core Standards

In Seventh Grade, CCSS recommends that instructional time should focus on four critical skills. Thinkster worksheets for seventh grade have been designed to cater to these skills:

• Developing understanding of and applying proportional relationships
• Developing understanding of operations with rational numbers and working with expressions and linear equations
• Solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume
• Drawing inferences about populations based on samples

7th Grade Math Worksheets: Critical Areas of Focus

Seventh grade is very much a transition year for math. Much will be expected this year from students—after all, this is middle school, and the level of instruction, as well as the level of expectations, has increased. Yet, seventh graders will also discover that their hard work in previous years has left them well-prepared for this year’s math. For example, the concepts of ratio and unit rates introduced in seventh grade evolve into calculating the constant of proportionality in tables, graphs, equations, and diagrams in seventh. Here are four critical areas of focus, straight from Common Core, that will be emphasized in seventh grade:

Proportional Relationships

As already stated, ratios and proportions are a fluency requirement for seventh grade. Some of the focus will include real-world situations such as tax, discounts, tips, and other percentage problems. Students will solve problems about scale drawings, will graph proportional relationships and learn about slope, and distinguish proportional relationships from other relationships.

Rational Numbers, Expressions and Linear Equations

Students will understand that fractions, decimals, and percentages are different representations of rational numbers. Furthermore, they will extend their mastery of the four basic operations (addition, subtraction, multiplication, and division) to rational and negative numbers as well as expressions and equations involving one variable.

Scale Drawings, Informal Geometric Constructions, and Cross Sections of Twoand Three-Dimensional Shapes

Seventh graders will continue to work with area, including circumference and the surface area of three-dimensional objects. Congruence and similarity are on the horizon in Grade 8, and to prepare for that, students will reason about relationships using scale drawings and informal geometric constructions, as well as the relationship between angles and intersecting lines. They will also work with three-dimensional figures by examining two-dimensional cross sections, and they will solve real-world problems involving area, surface area, and volume.

Drawing Inferences on Populations Based on Samples

Having previously worked on single data distributions in Sixth Grade, seventh graders will compare two data distributions and answer questions about the differences of the populations. Also, they informally will work with random sampling to generate data sets and learn about drawing inferences based on representative samples. Seventh Grade : Introduction, Common Core State Standards Initiative. -->

Overview of Seventh Grade Math Topics

Though they may have seem detailed, the four areas of focus presented in the previous section are more just starting points of what seventh graders can expect during this crucial school year. From those areas, teachers and students will delve into more specific concepts that will prepare kids for eighth grade math and beyond. The five topics presented here, taken directly from CCSS 4 itself, include some details on what kids will be taught in seventh grade.

Ratios and Proportional Relationships

• Analyze proportional relationships and use them to solve realworld and mathematical problems. By the end of seventh grade, students will become experts in ratios and proportions. The concepts and activities in store for them include:

• Computing unit rates of ratios associated with fractions. For example, if you swim 1/4 of mile in 1/10 of an hour, a complex fraction of 1/4 / 1/10 miles, or 2.5 miles, per hour can be computed.
• Deciding whether two quantities are in a proportional relationship. This can be achieved by testing for equivalent ratios in a table or graphing on a coordinate plane and looking for a straight line through the origin.
• Identifying the constant proportionality—the unit rate—in tables, graphs, equations, diagrams, verbal descriptions, and word problems.
• Representing proportional relationships by equations. For example, if the total cost (t) of something is proportional to the number of items purchased (n) at one constant price (p), the relationship between the total cost and the number items can be described as t=pn.
• Explaining what a point (x,y) on a graph of a proportional relationship means in terms of the situation, especially to the points (0,0) and (1,r) in which r is the unit rate.
• Using proportional relationship to solve multi-step real-world problems. For example, if you paid $50 at a restaurant, and that total included a 20 percent tip, how much did you just pay for dinner itself before tipping?

Seventh Grade: Introduction, Common Core State Standards Initiative.

The Number System

• Apply and extend previous understandings of operations with fractions. Rational numbers also are emphasized with this topic, and students will understand how the additive property intertwines with this concept. Some areas taught include:

• Adding and subtracting rational numbers (any number that can be written as a simple fraction, in which the denominator is not 0), and, from students’ understanding of fractions, applying these operations by using a number line.
• Describing situations in which opposite quantities combine to make 0, which is an additive inverse. For example, spending $50 to pay off a negative account balance of -$50 to reach 0.
• The knowledge of absolute value is extended: Understanding that p+q as the number located a distance |q| from p in a positive or negative direction (depending on if q was positive or negative).
• Understanding that subtracting rational numbers is the same as adding the additive inverse. For example, 7 - 4 = 7 + (-4).
• Dividing and multiplying rational numbers, and understanding that (-1)(-1)=1 and that -(p/q) = (-p)/q = p/(-q).
• Converting a rational number to a decimal using long division, and the concept of repeating decimals.
• Solving real-world problems involving rational numbers using the four basic operations.

Expressions and Equations

• Use properties of equations to generate equivalent expressions. Students will apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. Also, they will discover that rewriting an expression or equation in a different form (for example, x + 0.1 = 1.1x is the same as increasing a number by 10 percent and is the same as multiplying by 1.1) can lead them to a better understanding of the problem at hand

• Solve real-life mathematical problems using numeric and algebraic expressions and equations. The algebra continues. Seventh graders will learn to:

• Solve multi-step word problems with positive and negative rational numbers in any form (fractions, decimals, and whole numbers), and convert between forms when necessary (for example, if a business saw its profits increase by 10 percent in a year, it made 1/10 more money than last year).
• Solve word problems that lead to equations such as px+q=r or p(x+q)=r, in which p, q, and r are rational numbers. Student s will also learn to compare the algebraic solution to an arithmetic solution and identify the series of operations in each approach—for example, if a rectangle has a perimeter of 30 inches and a length of 10 inches, what is the area?
• Solve word problems involving inequalities; for example, a word problem that leads to the equation 2x + 5 < 25, so x < 10. Also, seventh graders will graph solution sets for inequalities—for example, if a pizza delivery driver makes $100 a week plus $2 per pizza, a student could graph how many pizzas the driver would need to deliver to make $175

• Draw, construct, and describe geometrical figures and describe the relationship between them. Students will solve problems involving scale drawings of geometric figures, will draw geometric shapes (by hand, with a ruler and compass, and with technology) with given conditions, and will describe two-dimensional figures resulting from slicing three-dimensional figures such as pyramids and rectangular prisms.

• Solve real-life and mathematical problems involving angle measure, area, surface, and volume. Seventh graders will master the formulas for area and circumference of circles and use this knowledge to solve problems. They will also work with different types of angles (supplementary, complementary, vertical, and adjacent) and solve problems involving volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Statistics and Probability

• Use random sampling to draw inferences about a population. Students will understand that statistics can be used to gain information about a population, and they will also be taught about random sampling. Furthermore, seventh graders will gather data from a random sample to draw inferences about a population with an unknown characteristic. For example, if a classroom has three more girls than boys in it, make an estimate about how many more girls are at the entire school.

• Draw informal comparative inferences about two populations. Simply put, students compare two groups and arrive at conclusions, including inferences based on variability. For example, if one cross country team averages 9-minute miles during practice and a second team averages 10-minute miles, what will happen if a runner logging 7-minute miles switches from the first team to the second?

• Investigate chance processes, and develop, use, and evaluate probability models. Though it may not appear so at first glance, probability nicely ties in to many other topics seventh graders are being taught. Among the concepts explored:

• Understanding that the probability of an event lies somewhere between 0 and 1— with near 0 being unlikely, around 1/2 as about even odds, and near 1 as likely.
• Collecting data to approximate the probability of a chance event. For example, rolling a die 300 times and estimating a 6 will come up about, but likely not exactly, 50 times.
• Developing a model for probability and explaining its results and discrepancies.
• Using organized lists, tree diagrams, tables, and simulation to arrive at probabilities of compound events. For example, if half of the students in a classroom have brown eyes, what is the probability that if you pick a random eight kids, five will have that eye color?

Surviving Middle School Math

Junior high is a crazy time for many students. Many self-contained middle schools (schools that aren’t K-8) present unique challenges academically and socially. The homework load is greater, the routines are completely different, and kids that seemed so young just a couple years earlier are now ... teenagers. Moreover, 67 percent of middle school teachers feel that math is the toughest subject for students to re-engage in after summer break, and 50 percent added that kids' math skills regress more than any other school subject. Combining these factors creates a situation daunting for students and parents alike. And perhaps nowhere is the challenge more acute than with middle school math. However, there’s no reason why students can’t thrive during these two critical years. What follows are several tips for middle schoolers and their parents to help them through this part of their math education.

Middle School Study Tips

• Be cool If you have been looking through this guide at the topics you can expect to learn for this school year, you may be understandably intimidated. However, the way Common Core is designed, you will get plenty of instruction, practice, and reinforcement with one concept before moving on.

Furthermore, you will discover that becoming good at a certain topic sets you up to succeed at the next. In many previous math curricula, teachers would move onto the next concept before many students felt they had mastered the last one. With Common Core, you can be confident you’ll be ready for whatever lies ahead.

• Practice When You Are Not Tired The homework loads of many students increase in middle school. However, your math capabilities are better suited for when you are most alert and less tired. Therefore, try to work on math homework in the later afternoon or early evening when you are at your freshest after school. Getting all your homework completed is important, but reading a book for a literature class won’t require the computing power from your brain that math will.

• Read the Question You might encounter math problems that appear intimidating, both on first glance and after you’ve read the question. No need to worry: Almost everything being thrown at you is stuff you have learned or are currently learning. Clear your mind and read the question again. Break down the problem by writing all the given information and relevant numbers. From there, work your way through the question on your path to the answer. Once you master this process, all those intimidating problems won’t seem so frightening.

• Check Your Work One helpful aspect of solving algebraic equations is that checking your work is easy: Simply plug in the answer into the variable of the original problem and do the math. This is a good habit to start with your homework because if you made a mistake, you have time to figure out what went wrong, which will help you all the more in the future. Furthermore, once you are proficient in checking your work accurately and quickly with your homework, you will naturally do the same on tests, possibly (and hopefully!) resulting in better grades because you are catching your mistakes before handing the test in.

• Keywords, Keywords, Keywords! One math strategy you likely learned in elementary school is to look for keywords when solving word problems. Keywords are simply clues within a word problem that guide you toward a solution. This strategy is just as applicable in middle school as it was when you were younger, maybe even more so as you work to solve multi-step problems. Moreover, with new concepts you are learning, a new set of words will be entering your math vocabulary. Look for terms such as save, rate, per, proportion, percentage, and compare in middle school word problems.

• Skip the Calculator You will encounter plenty of math in the coming years (especially in trigonometry and pre-calculus) that will require the use of a calculator. At this level, however, you should know how to perform almost every required operation without technological help. Skipping the calculator and figuring out problems by hand (for example, computing circumference by multiplying by 3.14) keeps your skills sharp, shows the teacher you are taking time to solve problems instead of taking a shortcut, and prepares you for tests on which a calculator isn't allowed.

• Math Everywhere Much of the math you are learning now can extend to rest of your life. Look for opportunities to practice your skills outside of school. For example, if you are watching a football game and see that a quarterback has completed 15 of 24 passes, try converting that number to a fraction and a percentage. Or, figure out what percentage a $5 tip on a $27 haircut is. Your math skills will help your realworld skills that when sharp, will improve your in-school math skills in turn.

• Ask for Help If you find yourself struggling with a specific concept or with math in general, by all means, seek help from your teacher. Educators want you to succeed, and they will do whatever they can to help you do so … but sometimes, you have to ask. Also, don’t be afraid to tell your parents that you are having a rough time. Most adults remember how challenging middle school math was, and your parents can provide encouragement, work with you and your teacher, or explore other options to get the help you need to succeed.

Parent Tips

Parenting a 12, 13, or 14 year old is already quite a task. Navigating middle school math only increases the challenge, as well as your possible level of stress. Arguing with your child about school work is counterproductive, so staying calm and working positively with him or her is essential, no matter how frustrated you may get. The time parents get with their growing children is short enough; you don’t want to spend the middle school years in a constant battle with your kids. Take a deep breath—you will survive math during these years. Here are some tips to keep your sanity along the way:

• Be cool This is sage advice for parents as well as students. The level of math education you and your child encounter in middle school is unlike anything you may have experienced before. Yet, students this age are ready to take their learning to another level the curricula wouldn’t include such content if they weren’t capable. Though there may be bumps along the way, your child can still reach the destination.

• Relearn the Math One reason parents are apprehensive to engage their middle schooler with his or her math homework is that they might be a few decades removed from the math itself. Most parents remember how to multiply, but they might not have a clue how to solve two variable inequalities. Middle school math isn’t so difficult that adults can’t relearn the concepts. Many websites are available that describe a variety of math topics, or if you can sneak in 20 minutes here and there, read your student’s textbook (just don’t let your kids catch you!). Once you understand the math a little more, you will be better able to help your child when he or she is struggling.

• Understand Common Core Irrespective of your opinions about Common Core, more than likely, your kids are learning in a curriculum following the standards. Therefore, understanding the goals, guidelines, and structure of CCSS ultimately will help as you support your middle schooler through these years of math. For example, your child may be learning methods and strategies to solve a problem that you have never encountered. Your first inclination might be to dismiss these approaches and not offer any support. However, knowing that Common Core aims to provide multiple methods so that students achieve a well-rounded mastery will give you clarity on why your child is learning something a certain way … and it may inspire you to learn this new strategy as well.

• Drill for Skills Find opportunities for your middle schooler to practice math outside of his or her schoolwork. Challenge your daughter to compute tips. Direct your son to figure out what percentage of a gallon of gas is tax (the tax price is usually on the pump). If you are stuck in traffic or driving to an afterschool activity, rapid-fire some problems and equations, such as converting fractions to decimals. A couple extra minutes here and there keeps kids’ minds actively focused on math skills, which will be sharpened for when they are testing or doing homework.

• Become Involved If you are concerned with how Common Core is being implemented at your school, the amount of homework being given, or anything else in the math classroom, then you should absolutely get involved. Talk to teachers and administrators. Attend committee meetings. Research the subject that has you concerned. Parents naturally will have opinions about the quality of their children’s education. Those opinions can affect dialogue and solutions, but only if you take action. Your middle schooler is working hard to get the best education possible. There’s no reason you shouldn’t do the same for your child.

• Seek Help for Your Child If your middle-schooler is consistently struggling with math, your first step should be to talk to his or her teacher, who can provide guidance on how those struggles can be overcome. From there, another step you might consider is finding outside help your child. Several online resources provide math tutelage, including worksheets and sample tests that conform to Common Core standards. Tutoring might be an option, too. Innovative iPad-based math software has emerged that combines the personalized approach of a tutor with today’s technology. These revolutionary programs also may feature a curriculum based on Common Core, thus ensuring your child’s learning at home is aligned with what he or she is learning at school

Tips for Helping Your Seventh Grader with These Seventh Grade Math Worksheets

In addition to the grade-specific standards it sets forth, Common Core also emphasizes eight “Standards of Mathematical Practice” that teachers at all levels are encouraged to develop in their students. Here are descriptions of these eight practices—designed to improve student performance—and how they apply to middle schoolers:

Make sense of problems and persevere in solving them

Students explain the problem to themselves and determine ways they can reach a solution. Then, they work at the problem until it’s solved. By middle school, for example, many word problems are multi-step, requiring more than one operation on the way to an answer. Students must take care to determine what these steps are, decide what strategies (including correspondences between equations, verbal descriptions, graphs and tables, and looking for regularity and trends) will be necessary to solve the problem, and work toward the solution.

Reason abstractly and quantitatively

Students decontextualize and contextualize problems. By decontextualizing, they break down the problem into anything other than the standard operation. By contextualizing, they apply math into problems that seemingly have none. Middle-schoolers who are decontextualizing may envision a fraction or decimal into unit rates—for example, a student working with the fraction 3/8 might picture three squares across a chessboard—to help solve a problem. Students who are contextualizing might break a polygon into several smaller shapes in order to compute the total area.

Construct viable arguments and critique the reasoning of others

Students use their acquired math knowledge and previous results to explain or critique their work or the work of others, analyzing and using counterexamples as necessary. Most middle-schoolers have already learned how to work with classmates to achieve a goal. Students might be encouraged not only to work with a group to solve a particularly challenging math problem, but also to present and explain their solution to the teacher and the class.

Encourage them to show their work

This suggestion can be read two ways. First, students will be encouraged to show how they arrived at an answer, especially within Common Core. Second, ask your children to show you their homework, particularly the challenging stuff. Explaining how a problem is solved is a basic CCSS tenet, so if your kids can be confident in explaining their work to you, they will carry that confidence into the classroom when the teacher asks for those same explanations.

Model with mathematics

This is just like it sounds: Students use math to solve real-world problems. For example, a national department store chain offers sales either in the form of percentages off retail price and by a flat dollar amount savings (and sometimes both). Middle-schoolers can use their knowledge of ratios and percentages to determine from which sales method they will save more.

Use appropriate tools strategically

Another self-explanatory practice: Students learn and determine which tools are best for the math problem at hand. For older kids, the tools may seem obvious—pencil, paper, calculator, protractor, and so on—but knowing when to use what is important. For example, graph paper can be a big help when solving variable inequalities.

Attend to precision

Students strive to be exact and meticulous—period. The math vocabulary introduced to middle-schoolers rapidly expanding, so students must be precise in their words as well as their numbers. Consider this example: An equation (x=1) is different than an expression (x-1) and an inequality (x>1). Middle-schoolers who know these definitions will have an easier time when working with the corresponding concepts.

Look for and make use of structure

Students will look for patterns and structures within math and apply these discoveries to subsequent problems. Take the equation x +5=10; to get an answer, 5 must be subtracted from both sides. This basic algebraic structure will apply to almost all equations middle-schoolers will encounter, no matter the operation or the number of variables. Once students recognize and master this structure, they will automatically think about both sides of the equation when solving.

Look for and express regularity in repeated reasoning

Students come to realizations—“aha” moments is a good term for these realizations—about the math operations that they are performing and use this knowledge in subsequent problems. For example, middle-schoolers may discover that tipping 15 percent is an easy computation: Figure out 10 percent of the bill, then take half of that and add to get 15 percent. In no time, they will want to figure out the tip when you are at a restaurant. 6 Standards for Mathematical Practice, Common Core State Standards Initiative. -->

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7th Grade Online Math Worksheets

According to the Common Core Standards, in Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

7th Grade Domains

If you know a particular Common Core Domain that you'd like to practice, you can drill down to it here.

• Analyze proportional relationships and use them to solve real-world and mathematical problems.
• Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
• Use properties of operations to generate equivalent expressions.
• Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
• Draw, construct and describe geometrical figures and describe the relationships between them.
• Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
• Use random sampling to draw inferences about a population.
• Draw informal comparative inferences about two populations.
• Investigate chance processes and develop, use, and evaluate probability models.

All 7th Grade Online Math Worksheets

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Grade 7 Maths Problems With Answers

Grade 7 math word problems with answers are presented. Some of these problems are challenging and need more time to solve. The Solutions and explanatiosn are included.

• In a bag full of small balls, 1/4 of these balls are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
• In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
• If the length of the side of a square is doubled, what is the ratio of the areas of the original square to the area of the new square?
• The division of a whole number N by 13 gives a quotient of 15 and a remainder of 2. Find N.

• A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
• A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
• Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $200, what were her original savings?
• Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?
• 15 cm is the height of water in a cylindrical container of radius r. What is the height of this quantity of water if it is poured into a cylindrical container of radius 2r?
• John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $16, what was the price before the first discount?
• How many inches are in 2000 millimeters? (round your answer to the nearest hundredth of of an inch).
• The rectangular playground in Tim's school is three times as long as it is wide. The area of the playground is 75 square meters. What is the primeter of the playground?
• John had a stock of 1200 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?
• N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N? A) 1 1/2 B) 1 1/3 C) 5/3 D) 3/2
• In 2008, the world population is about 6,760,000,000. Write the 2008 world population in scientific notation.
• Calculate the circumference of a circular field whose radius is 5 centimeters.

Answers to the Above Problems

• 6 balls are blue
• 10 students are 10 years old
• x = 5/6 meter
• 20,000 square meters
• 368 square units
• 1250 meters per minute
• 78.74 inches
• 40 square meters
• 10π centimeters

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Real World Algebra by Edward Zaccaro

Algebra is often taught abstractly with little or no emphasis on what algebra is or how it can be used to solve real problems. Just as English can be translated into other languages, word problems can be "translated" into the math language of algebra and easily solved. Real World Algebra explains this process in an easy to understand format using cartoons and drawings. This makes self-learning easy for both the student and any teacher who never did quite understand algebra. Includes chapters on algebra and money, algebra and geometry, algebra and physics, algebra and levers and many more. Designed for children in grades 4-9 with higher math ability and interest but could be used by older students and adults as well. Contains 22 chapters with instruction and problems at three levels of difficulty.

7th Grade Math Worksheets

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Improve your students' math skills and help them learn how to calculate fractions, percentages, and more with these word problems. The exercises are designed for students in the seventh grade , but anyone who wants to get better at math will find them useful.

The sections below contain two-word problem worksheets for students, in section Nos. 1 and 3. For ease of grading, identical worksheets, including the answers, are printed in section Nos. 2 and 4. More detailed explanations of some of the problems are also provided within the sections.

Worksheet 1 Questions

Find out what birthday cakes, grocery stores, and snowballs have in common with these fun word problems. Practice calculating fractions and percentages with problems such as:

When the birthday cake was about to be served, you were told you could have 0.6, 60%, 3/5, or 6%.

Which three of the choices will give you the same size portion?

Explain to students that the correct answer is .6, 60%, and 3/5 because all of these equal 60 percent, or six out of 10, or 60 parts out of 100. By contrast, 6 percent means just that: only six pennies out of 100, six parts out of a 100, or six tiny slivers of cake out of 100.

Worksheet 1 Answers

Find the solutions to the word problems that students tackled in the first math worksheet. The second problem, and answer, state:

Problem: 4/7 of the birthday cake was eaten on your birthday. The next day your dad ate 1/2 of what was left. You get to finish the cake, how much is left?

Answer: 3/14

If students are struggling, explain that they can easily find the answer by multiplying fractions as follows, where "C" stands for the portion of cake that is left. They first need to determine how much cake was left after the birthday

• C = 7/7 - 4/7
• C = 3/7 

Then they need to see what fraction was left the next day after dad gobbled up some more of the cake:

• C = 3/7 x 1/2
• C = 3 x 1 / 7 x 2
• C = 3 / 14

So 3/14 of the cake was left over after dad had a snack the next day.

Worksheet 2 Questions

Have students learn how to calculate a rate of return and how to divide a large area into smaller lots with these math problems. To help students, go over the first problem as a class:

Sam loves basketball and can sink the ball in the net 65% of the time. If he takes 30 shots, how many will he sink?

Explain to students that they simply need to convert 65% to a decimal (0.65), and then multiply that number by 30.

Worksheet 2 Answers

Find the solutions to the word problems students have tackled in the second math worksheet. For the first problem, demonstrate how to work out the solution if students are still having difficulty, where "S" equals shots made:

• S = 0.65 x 30
• S = 19.5

So Sam made 19.5 shots. But since you can't make half a shot, Sam made 19 shots if you don't round up.

Normally, you'd round up decimals five and greater to the next whole number, which would be 20 in this case. But in this rare case, you'd round down because, as noted, you can't make half a shot.

• Popular Math Terms and Definitions
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• Free Math Word Problem Worksheets for Fifth-Graders
• Realistic Math Problems Help 6th-graders Solve Real-Life Questions
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• Quiz 8th-Graders With These Math Word Problems
• First Grade Math: Word Problems
• 4th-Grade Math Word Problems
• Multiplication Word Problems With Printable Worksheets
• Thanksgiving Math Worksheets and Activities for Kids
• Multiply Fractions With Common Denominators Worksheets
• 2nd Grade Math Word Problems
• Sixth Grade Word Problems
• Halloween Math Worksheets & Printable Activities
• Subtraction of Fractions With Common Denominators
• Free Christmas Math Worksheets

Free Printable Math Word Problems Worksheets for 7th Grade

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

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Explore printable Math Word Problems worksheets for 7th Grade

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

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

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7th Grade Inequalities Worksheets

7th grade inequalities worksheets help students understand a non-equal comparison. Inequality worksheets focus on comparisons between two numbers or operations. The concept of inequality can be a bit tricky. These worksheets also have detailed step-wise solutions for all the questions which help students get an in-depth understanding of the topics.

Benefits of Grade 7 Inequality Worksheets

7th grade inequalities worksheets provide students with a variety of problems based on inequalities like graphing inequalities, inequalities in one variable, inequalities in a number line, etc. These grade 7 math worksheets follow a step-wise pattern so that students can easily explore all the topics in detail. Inequality worksheets for 7th grade focus on core concepts and thus can be a great guide for grade 7 students.

Printable PDFs for Inequality Word Problems Worksheets 7th Grade

Students can download Grade 7 inequalities worksheets for free in pdf formats and download a variety of inequality questions.

• Math 7th Grade Inequalities Worksheet
• 7th Grade Inequalities Math Worksheet
• Seventh Grade Inequalities Worksheet
• Grade 7 Math Inequalities Worksheet

Explore more topics at Cuemath's Math Worksheets .

Rate Problems with Fractions

Grade 7 math worksheets.

Rate problems typically involve quantities changing over time or in relation to each other. When fractions are involved, it often means that the rates of change or comparison are not whole numbers.

Here’s a general approach to solving rate problems with fractions:

1. Identify the Rates : Determine what quantities are changing and at what rates. These rates might be given in fractions, percentages, or other forms.

2. Set Up Equations : Use the given information to set up equations that represent the relationship between the quantities and their rates. This might involve using proportions or ratios.

3. Solve for the Unknowns : Solve the equations to find the unknown quantities. This often requires basic algebraic manipulation, such as cross-multiplication or finding common denominators.

4. Check Your Solution : Once you have found the solution, check to ensure it makes sense in the context of the problem. Verify that the rates and quantities align with the given information.

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Rate Problems with Fractions - Grade 7 Math Worksheet PDF

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Steps to Follow to Solve Rate Problems with Fractions: 

To solve unit rate problems with fractions, you typically follow these steps:

• Understand the Problem: Read the problem carefully to understand what is being compared and what units are involved. Identify the quantities and units mentioned in the problem.
• Identify the Numerator and Denominator: Determine which quantity is the numerator (the top part) and which is the denominator (the bottom part) of the fraction in the unit rate.
• Set Up the Ratio: Create a ratio with the numerator representing the quantity of interest and the denominator representing the corresponding unit. Make sure the units in the ratio match.
• Simplify Fractions: Simplify any fractions in the ratio by finding their greatest common factor and dividing both the numerator and denominator by it if possible.
• Calculate the Unit Rate: Divide the numerator by the denominator to find the unit rate.
• Interpret the Result: Make sure you understand what the unit rate represents in the context of the problem.

Solved Example: Water Flow Rate: A water tank fills up in 5/6 hours when water flows at a rate of 4/5 gallons per hour. What is the unit rate of water flow in gallons per hour?

• Identify the Numerator and Denominator: The numerator is 4/5 gallons of water, and the denominator is 5/6 hours.
• Set Up the Ratio: Let x be the unit rate of water flow in gallons per hour. The ratio is (4/5) / (5/6).
• Simplify Fractions: The fractions (4/5) and (5/6) are already simplified.
• Calculate the Unit Rate: Divide (4/5) by (5/6): (4/5) / (5/6) = (4/5) * (6/5) = 24/25.
• Interpret the Result: The unit rate of water flow is 24/25 gallons per hour

Solved Example : Fuel Efficiency: A car travels 2/3 of a mile on 1/4 gallon of gasoline. What is the unit rate of fuel efficiency in miles per gallon?

• Identify the Numerator and Denominator: The numerator is 2/3 mile, and the denominator is 1/4 gallon.
• Set Up the Ratio: Let x be the unit rate of fuel efficiency in miles per gallon. The ratio is (2/3) / (1/4).
• Simplify Fractions: The fractions (2/3) and (1/4) are already simplified.
• Calculate the Unit Rate: Divide (2/3) by (1/4): (2/3) / (1/4) = (2/3) * (4/1) = 8/3.
• Interpret the Result: The unit rate of fuel efficiency is 8/3 miles per gallon.

These examples illustrate how to solve unit rate problems involving fractions by setting up the ratio, simplifying fractions if necessary, and calculating the unit rate.

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Practice Questions

Q1. Sarah can paint 3/4 of a wall in 2 hours. What is her painting rate per hour in square feet?

Q 2. A car can travel 7/8 of a mile on 1/4 gallon of gasoline. What is the car’s mileage rate in miles per gallon (mpg)?

Q3. Sam bakes cookies and can make 2/3 of a batch in 30 minutes. What is his baking rate per minute in batches?

Q4. Anna is baking cookies, and the recipe calls for 3/4 cup of sugar for every 2 dozen cookies. What is the unit rate of sugar required for one dozen cookies in cups?

Solution 1: Sarah’s painting rate per hour is 3/8 of a wall in square feet. This means she can paint 3/8 of a wall in one hour.

Solution 2 : The car’s mileage rate is 7/2 miles per gallon (mpg), which is equivalent to 3.5 mpg. So, the car’s mileage rate is 3.5 miles per gallon.

Solution 3 : Sam’s baking rate per minute is 1/45 of a batch. It means he can bake 1/45 of a batch in one minute.

So, the unit rate is 1/45 of a batch per minute.

Solution 4: Anna needs 3/8 cup of sugar for one dozen cookies. So, the unit rate is 3/8 cup of sugar per dozen cookies.

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What is a rate problem involving fractions?

A rate problem with fractions is a mathematical question that relates two quantities, such as distance and time, where one or both of the quantities are expressed as fractions or involve fractional parts.

How do I calculate the rate when dealing with fractions?

To calculate the rate, you can use the formula: Rate = Quantity / Time. If either the quantity or time involves fractions, make sure to perform the necessary operations to simplify and work with the fractions.

What are some common examples of rate problems with fractions?

Common examples include calculating the speed of a car in miles per hour (mph) when the distance is given in fractions of a mile or calculating the time it takes for a job to be completed when fractional parts of the job are done in each hour.

How do I convert mixed numbers to fractions when solving rate problems?

To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction and add the numerator. For example, 2 1/4 becomes (2 * 4) + 1 = 9/4.

What if the rate problem involves adding or subtracting fractions?

When adding or subtracting fractions in a rate problem, make sure the fractions have the same denominator. If not, find a common denominator, perform the operation, and simplify the result.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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Unit 9: Geometry

About this unit.

Geometric shapes are all around us. The world is built with them. In this series of tutorials and exercises you'll become familiar with Euclidean geometry and terms like scale drawings, parts of a circle, area, angles, and geometric figures.

Area and circumference of circles

• Geometry FAQ (Opens a modal)
• Radius, diameter, circumference & π (Opens a modal)
• Labeling parts of a circle (Opens a modal)
• Radius, diameter, & circumference (Opens a modal)
• Radius & diameter from circumference (Opens a modal)
• Relating circumference and area (Opens a modal)
• Area of a circle (Opens a modal)
• Partial circle area and arc length (Opens a modal)
• Circumference review (Opens a modal)
• Area of circles review (Opens a modal)
• Radius and diameter Get 5 of 7 questions to level up!
• Circumference of a circle Get 3 of 4 questions to level up!
• Area of a circle Get 5 of 7 questions to level up!
• Circumference of parts of circles Get 3 of 4 questions to level up!
• Area of parts of circles Get 3 of 4 questions to level up!

Area and circumference challenge problems

• Finding circumference of a circle when given the area (Opens a modal)
• Area of a shaded region (Opens a modal)
• Impact of increasing the radius (Opens a modal)
• Circumference and rotations Get 3 of 4 questions to level up!
• Area and circumference of circles challenge Get 3 of 4 questions to level up!
• Shaded areas Get 3 of 4 questions to level up!

Vertical, complementary, and supplementary angles

• Angles: introduction (Opens a modal)
• Complementary & supplementary angles (Opens a modal)
• Vertical angles (Opens a modal)
• Complementary and supplementary angles review (Opens a modal)
• Vertical angles are congruent proof (Opens a modal)
• Name angles Get 3 of 4 questions to level up!
• Identifying supplementary, complementary, and vertical angles Get 5 of 7 questions to level up!
• Complementary and supplementary angles (visual) Get 3 of 4 questions to level up!
• Complementary and supplementary angles (no visual) Get 5 of 7 questions to level up!
• Vertical angles Get 3 of 4 questions to level up!
• Finding angle measures between intersecting lines Get 3 of 4 questions to level up!

Missing angle problems

• Find measure of vertical angles (Opens a modal)
• Find measure of angles word problem (Opens a modal)
• Equation practice with complementary angles (Opens a modal)
• Equation practice with supplementary angles (Opens a modal)
• Equation practice with vertical angles (Opens a modal)
• Finding missing angles Get 5 of 7 questions to level up!
• Create equations to solve for missing angles Get 5 of 7 questions to level up!
• Unknown angle problems (with algebra) Get 5 of 7 questions to level up!

Constructing triangles

• Construct a right isosceles triangle (Opens a modal)
• Construct a triangle with constraints (Opens a modal)
• Triangle inequality theorem (Opens a modal)
• Triangle side length rules Get 3 of 4 questions to level up!

Slicing geometric shapes

• Slicing a rectangular pyramid (Opens a modal)
• Cross sections of 3D objects (basic) Get 3 of 4 questions to level up!

Volume and surface area word problems

• Volume word problem: gold ring (Opens a modal)
• Volume of triangular prism & cube (Opens a modal)
• Volume of rectangles inside rectangles (Opens a modal)
• Volume and surface area word problems Get 3 of 4 questions to level up!