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Free Math Worksheets — Over 100k free practice problems on Khan Academy

Looking for free math worksheets.

You’ve found something even better!

That’s because Khan Academy has over 100,000 free practice questions. And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun!

Just choose your grade level or topic to get access to 100% free practice questions:

Kindergarten, basic geometry, pre-algebra, algebra basics, high school geometry.

  • Trigonometry

Statistics and probability

High school statistics, ap®︎/college statistics, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra.

  • Addition and subtraction
  • Place value (tens and hundreds)
  • Addition and subtraction within 20
  • Addition and subtraction within 100
  • Addition and subtraction within 1000
  • Measurement and data
  • Counting and place value
  • Measurement and geometry
  • Place value
  • Measurement, data, and geometry
  • Add and subtract within 20
  • Add and subtract within 100
  • Add and subtract within 1,000
  • Money and time
  • Measurement
  • Intro to multiplication
  • 1-digit multiplication
  • Addition, subtraction, and estimation
  • Intro to division
  • Understand fractions
  • Equivalent fractions and comparing fractions
  • More with multiplication and division
  • Arithmetic patterns and problem solving
  • Quadrilaterals
  • Represent and interpret data
  • Multiply by 1-digit numbers
  • Multiply by 2-digit numbers
  • Factors, multiples and patterns
  • Add and subtract fractions
  • Multiply fractions
  • Understand decimals
  • Plane figures
  • Measuring angles
  • Area and perimeter
  • Units of measurement
  • Decimal place value
  • Add decimals
  • Subtract decimals
  • Multi-digit multiplication and division
  • Divide fractions
  • Multiply decimals
  • Divide decimals
  • Powers of ten
  • Coordinate plane
  • Algebraic thinking
  • Converting units of measure
  • Properties of shapes
  • Ratios, rates, & percentages
  • Arithmetic operations
  • Negative numbers
  • Properties of numbers
  • Variables & expressions
  • Equations & inequalities introduction
  • Data and statistics
  • Negative numbers: addition and subtraction
  • Negative numbers: multiplication and division
  • Fractions, decimals, & percentages
  • Rates & proportional relationships
  • Expressions, equations, & inequalities
  • Numbers and operations
  • Solving equations with one unknown
  • Linear equations and functions
  • Systems of equations
  • Geometric transformations
  • Data and modeling
  • Volume and surface area
  • Pythagorean theorem
  • Transformations, congruence, and similarity
  • Arithmetic properties
  • Factors and multiples
  • Reading and interpreting data
  • Negative numbers and coordinate plane
  • Ratios, rates, proportions
  • Equations, expressions, and inequalities
  • Exponents, radicals, and scientific notation
  • Foundations
  • Algebraic expressions
  • Linear equations and inequalities
  • Graphing lines and slope
  • Expressions with exponents
  • Quadratics and polynomials
  • Equations and geometry
  • Algebra foundations
  • Solving equations & inequalities
  • Working with units
  • Linear equations & graphs
  • Forms of linear equations
  • Inequalities (systems & graphs)
  • Absolute value & piecewise functions
  • Exponents & radicals
  • Exponential growth & decay
  • Quadratics: Multiplying & factoring
  • Quadratic functions & equations
  • Irrational numbers
  • Performing transformations
  • Transformation properties and proofs
  • Right triangles & trigonometry
  • Non-right triangles & trigonometry (Advanced)
  • Analytic geometry
  • Conic sections
  • Solid geometry
  • Polynomial arithmetic
  • Complex numbers
  • Polynomial factorization
  • Polynomial division
  • Polynomial graphs
  • Rational exponents and radicals
  • Exponential models
  • Transformations of functions
  • Rational functions
  • Trigonometric functions
  • Non-right triangles & trigonometry
  • Trigonometric equations and identities
  • Analyzing categorical data
  • Displaying and comparing quantitative data
  • Summarizing quantitative data
  • Modeling data distributions
  • Exploring bivariate numerical data
  • Study design
  • Probability
  • Counting, permutations, and combinations
  • Random variables
  • Sampling distributions
  • Confidence intervals
  • Significance tests (hypothesis testing)
  • Two-sample inference for the difference between groups
  • Inference for categorical data (chi-square tests)
  • Advanced regression (inference and transforming)
  • Analysis of variance (ANOVA)
  • Scatterplots
  • Data distributions
  • Two-way tables
  • Binomial probability
  • Normal distributions
  • Displaying and describing quantitative data
  • Inference comparing two groups or populations
  • Chi-square tests for categorical data
  • More on regression
  • Prepare for the 2020 AP®︎ Statistics Exam
  • AP®︎ Statistics Standards mappings
  • Polynomials
  • Composite functions
  • Probability and combinatorics
  • Limits and continuity
  • Derivatives: definition and basic rules
  • Derivatives: chain rule and other advanced topics
  • Applications of derivatives
  • Analyzing functions
  • Parametric equations, polar coordinates, and vector-valued functions
  • Applications of integrals
  • Differentiation: definition and basic derivative rules
  • Differentiation: composite, implicit, and inverse functions
  • Contextual applications of differentiation
  • Applying derivatives to analyze functions
  • Integration and accumulation of change
  • Applications of integration
  • AP Calculus AB solved free response questions from past exams
  • AP®︎ Calculus AB Standards mappings
  • Infinite sequences and series
  • AP Calculus BC solved exams
  • AP®︎ Calculus BC Standards mappings
  • Integrals review
  • Integration techniques
  • Thinking about multivariable functions
  • Derivatives of multivariable functions
  • Applications of multivariable derivatives
  • Integrating multivariable functions
  • Green’s, Stokes’, and the divergence theorems
  • First order differential equations
  • Second order linear equations
  • Laplace transform
  • Vectors and spaces
  • Matrix transformations
  • Alternate coordinate systems (bases)

Frequently Asked Questions about Khan Academy and Math Worksheets

Why is khan academy even better than traditional math worksheets.

Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.

Math WorksheetsKhan Academy
Math worksheets take forever to hunt down across the internetKhan Academy is your one-stop-shop for practice from arithmetic to calculus
Math worksheets can vary in quality from site to siteEvery Khan Academy question was written by a math expert with a strong education background
Math worksheets can have ads or cost moneyKhan Academy is a nonprofit whose resources are always free to teachers and learners – no ads, no subscriptions
Printing math worksheets use up a significant amount of paper and are hard to distribute during virtual learningKhan Academy practice requires no paper and can be distributed whether your students are in-person or online
Math worksheets can lead to cheating or a lack of differentiation since every student works on the same questionsKhan Academy has a full question bank to draw from, ensuring that each student works on different questions – and at their perfect skill level
Math worksheets can slow down student learning since they need to wait for feedbackKhan Academy gives instant feedback after every answer – including hints and video support if students are stuck
Math worksheets take up time to collect and take up valuable planning time to gradeKhan Academy questions are graded instantly and automatically for you

What do Khan Academy’s interactive math worksheets look like?

Here’s an example:

What are teachers saying about Khan Academy’s interactive math worksheets?

“My students love Khan Academy because they can immediately learn from their mistakes, unlike traditional worksheets.”

Is Khan Academy free?

Khan Academy’s practice questions are 100% free—with no ads or subscriptions.

What do Khan Academy’s interactive math worksheets cover?

Our 100,000+ practice questions cover every math topic from arithmetic to calculus, as well as ELA, Science, Social Studies, and more.

Is Khan Academy a company?

Khan Academy is a nonprofit with a mission to provide a free, world-class education to anyone, anywhere.

Want to get even more out of Khan Academy?

Then be sure to check out our teacher tools . They’ll help you assign the perfect practice for each student from our full math curriculum and track your students’ progress across the year. Plus, they’re also 100% free — with no subscriptions and no ads.

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The best way to learn and teach with AI is here. Ace the school year with our AI-powered guide, Khanmigo. 

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  • Solve equations and inequalities
  • Simplify expressions
  • Factor polynomials
  • Graph equations and inequalities
  • Advanced solvers
  • All solvers
  • Arithmetics
  • Determinant
  • Percentages
  • Scientific Notation
  • Inequalities

Download on App Store

What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

  • The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
  • The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
  • The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
  • The calculus section will carry out differentiation as well as definite and indefinite integration.
  • The matrices section contains commands for the arithmetic manipulation of matrices.
  • The graphs section contains commands for plotting equations and inequalities.
  • The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

Math Topics

More solvers.

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Get Started Learning With MathGames!

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  • Candy Stacker
  • King of Math
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  • P Pre-Kindergarten 34 skills
  • K Kindergarten 70 skills
  • 1 Grade 1 83 skills
  • 2 Grade 2 128 skills
  • 3 Grade 3 91 skills
  • 4 Grade 4 126 skills
  • 5 Grade 5 120 skills
  • 6 Grade 6 151 skills
  • 7 Grade 7 184 skills
  • 8 Grade 8 113 skills
  • Measurement
  • Mixed Equations
  • Multiplication
  • More Skills

Area of Complex Figures

Acute, right, obtuse, and straight angles

Positions - Left, Middle, Right

Counting and number patterns: Writing numbers in words

MathGames Video Tutorials

  • Instant setup using Google Classrooms, Remind or Office 355
  • Create printable worksheets for offline practice
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  • Skills Aligned to the Common Core Standards
  • Tablet, Chromebooks, iPads and mobile phone ready -no downloads needed
  • Trusted and used by over 5 million students in homes and classrooms

Math Games offers online games and printable worksheets to make learning math fun. Kids from pre-K to 8th grade can practice math skills recommended by the Common Core State Standards in exciting game formats. Never associated learning algebra with rescuing animals or destroying zombies? Time to think again!

Kids learn better when they're having fun . They also learn better when they get to practice new skills repeatedly . Math Games lets them do both - in school or at home .

Teachers and parents can create custom assignments that assess or review particular math skills. Activities are tailored so pupils work at appropriate grade levels . Worksheets can be downloaded and printed for classroom use , or activities can be completed and automatically graded online .

Best of all? It's completely free! Click on any of our games above to get started.

Get updates on what we do by following us on Twitter at @mathgames . Send us your comments, queries or suggestions here .

To get additional practice, check out the sample problems in each of the topic above. We provide full solutions with steps for all practice problems. There's no better way to find math help online than with Cymath, so also make sure you download our mobile app for and today! Learn more than what the answer is - with the math helper app, you'll learn the steps behind it too.

Even simple math problems become easier to solve when broken down into steps. From basic additions to calculus, the process of problem solving usually takes a lot of practice before answers could come easily. As problems become more complex, it becomes even more important to understand the step-by-step process by which we solve them. At Cymath, our goal is to take your understanding of math to a new level.

If you find Cymath useful, try today! It offers an ad-free experience and more detailed explanations. In short, goes into more depth than the standard version, giving students more resources to learn the step-by-step process of solving math problems.

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Category: Practice Questions

Vertical Line Charts Practice Questions

Vertical Line Charts Practice Questions

Real Life Linear Graphs Practice Questions

Real Life Linear Graphs Practice Questions

Misleading Graphs Practice Questions

Misleading Graphs Practice Questions

Dual Bar Charts Practice Questions

Dual Bar Charts Practice Questions

Composite Bar Charts Practice Questions

Composite Bar Charts Practice Questions

Tally Charts Practice Questions

Tally Charts Practice Questions

Pictograms Practice Questions

Pictograms Practice Questions

Bar Charts Practice Questions

Bar Charts Practice Questions

Splitting the Middle Practice Questions

Splitting the Middle Practice Questions

Invariant Points Practice Questions

Invariant Points Practice Questions

Factorising Brackets Practice Questions

Factorising Brackets Practice Questions

Combined Mean Practice Questions

Combined Mean Practice Questions

Money Coins Practice Questions

Money Coins Practice Questions

Identities, Formulae, Equations Practice Questions

Identities, Formulae, Equations Practice Questions

Cost per Metre Practice Questions

Cost per Metre Practice Questions

Equating Coefficients Practice Questions

Equating Coefficients Practice Questions

Compass Directions Practice Questions

Compass Directions Practice Questions

Profit Practice Questions

Profit Practice Questions

Money (Paying) Practice Questions

Money (Paying) Practice Questions

Quartiles from a List Practice Questions

Quartiles from a List Practice Questions

Money – Midpoint Practice Questions

Money – Midpoint Practice Questions

Money (Estimation) Practice Questions

Money (Estimation) Practice Questions

Reading Tables Practice Questions

Reading Tables Practice Questions

Greatest Number (Money) Practice Questions

Greatest Number (Money) Practice Questions

Midpoint of Two Fractions Practice Questions

Midpoint of Two Fractions Practice Questions

Mode from a table practice questions, multipliers practice questions, range from a frequency table practice questions, cost per litre video.

Cost per Litre Practice Questions

Cost per Litre Practice Questions

Turning Points using Completing the Square Practice Questions

Turning Points using Completing the Square Practice Questions

Mean from a Frequency Table Practice Questions

Mean from a Frequency Table Practice Questions

Population Density Practice Questions

Population Density Practice Questions

Odd and Even Numbers Practice Questions

Odd and Even Numbers Practice Questions

Fibonacci Practice Questions

Fibonacci Practice Questions

Ordering Fractions Practice Questions

Ordering Fractions Practice Questions

VAT Practice Questions

VAT Practice Questions

Questionnaires Practice Questions

Questionnaires Practice Questions

Reciprocals Practice Questions

Reciprocals Practice Questions

Wages Practice Questions

Wages Practice Questions

Discounts Practice Questions

Discounts Practice Questions

Capture Recapture Practice Questions

Capture Recapture Practice Questions

Regular Payments Practice Questions

Regular Payments Practice Questions

Cost per Kg Practice Questions

Cost per Kg Practice Questions

Income Tax Practice Questions

Income Tax Practice Questions

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Math Worksheets

Test your math skills! Ace that test! See how far you can get! You can view them on-screen, and then print them, with or without answers.

Every worksheet has thousands of variations, so you need never run out of practice material.

Choose your Subject !

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÷ (includes the correct spaces to help you get it right)
   
123 My Daughter loves these!
   
0.1 + − × ÷, and conversion from fractions
/ , / + − × ÷, and conversion
/ , / + − × ÷, and conversion
   
     
  Example: 12 + 8 × (5 − 4)
     
  Example: 2x + 8 = 16
     
3:30 "Tell the time" and "Draw the hands"

* Note: the worksheet variation number is not printed with the worksheet on purpose so others cannot simply look up the answers. If you want the answers, either bookmark the worksheet or print the answers straight away.

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AI Math Calculator Reviews

This tool combines the power of mathematical computation engine that excels at solving mathematical formulas with the power of artificial intelligence large language models to parse and generate natural language answers. This creates a math problem solver that's more accurate than ChatGPT, more flexible than a math calculator, and provides answers faster than a human tutor.

Sign up for free here .

Problem Solver Subjects

Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects.

  • Math Word Problems
  • Pre-Algebra
  • Geometry Graphing
  • Trigonometry
  • Precalculus
  • Finite Math
  • Linear Algebra

Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.

Basic Math Solutions

Below are examples of basic math problems that can be solved.

  • Long Arithmetic
  • Rational Numbers
  • Operations with Fractions
  • Ratios, Proportions, Percents
  • Measurement, Area, and Volume
  • Factors, Fractions, and Exponents
  • Unit Conversions
  • Data Measurement and Statistics
  • Points and Line Segments

Math Word Problem Solutions

Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 �� b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

Pre-Algebra Solutions

Below are examples of Pre-Algebra math problems that can be solved.

  • Variables, Expressions, and Integers
  • Simplifying and Evaluating Expressions
  • Solving Equations
  • Multi-Step Equations and Inequalities
  • Ratios, Proportions, and Percents
  • Linear Equations and Inequalities

Algebra Solutions

Below are examples of Algebra math problems that can be solved.

  • Algebra Concepts and Expressions
  • Points, Lines, and Line Segments
  • Simplifying Polynomials
  • Factoring Polynomials
  • Linear Equations
  • Absolute Value Expressions and Equations
  • Radical Expressions and Equations
  • Systems of Equations
  • Quadratic Equations
  • Inequalities
  • Complex Numbers and Vector Analysis
  • Logarithmic Expressions and Equations
  • Exponential Expressions and Equations
  • Conic Sections
  • Vector Spaces
  • 3d Coordinate System
  • Eigenvalues and Eigenvectors
  • Linear Transformations
  • Number Sets
  • Analytic Geometry

Trigonometry Solutions

Below are examples of Trigonometry math problems that can be solved.

  • Algebra Concepts and Expressions Review
  • Right Triangle Trigonometry
  • Radian Measure and Circular Functions
  • Graphing Trigonometric Functions
  • Simplifying Trigonometric Expressions
  • Verifying Trigonometric Identities
  • Solving Trigonometric Equations
  • Complex Numbers
  • Analytic Geometry in Polar Coordinates
  • Exponential and Logarithmic Functions
  • Vector Arithmetic

Precalculus Solutions

Below are examples of Precalculus math problems that can be solved.

  • Operations on Functions
  • Rational Expressions and Equations
  • Polynomial and Rational Functions
  • Analytic Trigonometry
  • Sequences and Series
  • Analytic Geometry in Rectangular Coordinates
  • Limits and an Introduction to Calculus

Calculus Solutions

Below are examples of Calculus math problems that can be solved.

  • Evaluating Limits
  • Derivatives
  • Applications of Differentiation
  • Applications of Integration
  • Techniques of Integration
  • Parametric Equations and Polar Coordinates
  • Differential Equations

Statistics Solutions

Below are examples of Statistics problems that can be solved.

  • Algebra Review
  • Average Descriptive Statistics
  • Dispersion Statistics
  • Probability
  • Probability Distributions
  • Frequency Distribution
  • Normal Distributions
  • t-Distributions
  • Hypothesis Testing
  • Estimation and Sample Size
  • Correlation and Regression

Finite Math Solutions

Below are examples of Finite Math problems that can be solved.

  • Polynomials and Expressions
  • Equations and Inequalities
  • Linear Functions and Points
  • Systems of Linear Equations
  • Mathematics of Finance
  • Statistical Distributions

Linear Algebra Solutions

Below are examples of Linear Algebra math problems that can be solved.

  • Introduction to Matrices
  • Linear Independence and Combinations

Chemistry Solutions

Below are examples of Chemistry problems that can be solved.

  • Unit Conversion
  • Atomic Structure
  • Molecules and Compounds
  • Chemical Equations and Reactions
  • Behavior of Gases
  • Solutions and Concentrations

Physics Solutions

Below are examples of Physics math problems that can be solved.

  • Static Equilibrium
  • Dynamic Equilibrium
  • Kinematics Equations
  • Electricity
  • Thermodymanics

Geometry Graphing Solutions

Below are examples of Geometry and graphing math problems that can be solved.

  • Step By Step Graphing
  • Linear Equations and Functions
  • Polar Equations

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Math Practice

Geogebra math practice.

Math Practice is a tool for mastering algebraic notation. It supports students in their step-by-step math work, let's them explore different solution paths, and helps build confidence, fluency, and understanding.

Getting started as a teacher or student

person with long dark hair sit at a table working at a laptop. 3x+2 and x² equations float in the air signifying that she is working on math problems

Enhance your skills

Immerse yourself in the world of algebraic problems to fine-tune your mathematical abilities and elevate your skillset

Linear equations

a+9=60

Order of Operations

4+2\times 3-5

Algebraic Expressions

2x+6(x+1)

Polynomials

1-2x+x^2

Unlocking the key elements

Use interactive notation to build comfort and fluency with algebraic transformations

Get adaptive hints and in-the-moment feedback to explore different solution paths

Get comprehensive help and guidance focused on improving understanding of basic concepts

Explore features

If you require any guidance on how to use GeoGebra Math Practice, explore the articles in our help center.

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Math Word Problems

Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.

There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:

  • Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
  • Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
  • Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
  • Calculate : Use your strategy to solve the problem.
  • Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.

Most Popular Math Word Problems this Week

Easy Multi-Step Word Problems

Arithmetic Word Problems

math problem solving questions free

  • Addition Word Problems One-Step Addition Word Problems Using Single-Digit Numbers One-Step Addition Word Problems Using Two-Digit Numbers
  • Subtraction Word Problems Subtraction Facts Word Problems With Differences from 5 to 12
  • Multiplication Word Problems One-Step Multiplication Word Problems up to 10 × 10
  • Division Word Problems Division Facts Word Problems with Quotients from 5 to 12
  • Multi-Step Word Problems Easy Multi-Step Word Problems

Copyright © 2005-2024 Math-Drills.com You may use the math worksheets on this website according to our Terms of Use to help students learn math.

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Free Math Printable Worksheets with Answer Keys and Activities

Other free resources.

Feel free to download and enjoy these free worksheets on functions and relations. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

  • Long Division with Remainders
  • Long Division with Remainders #2 (Zeros in the Quotient)
  • Long Division with 2 Digit Divisors
  • Whole Number by Unit Fraction
  • Equation of Circle
  • Simplify Imaginary Numbers
  • Adding and Subtracting Complex Numbers
  • Multiplying Complex Numbers
  • Dividing Complex Numbers
  • Dividing Complex Number (Advanced)
  • End of Unit, Review Sheet
  • Distance Formula
  • Simplify Rational Exponents (Algebra 2)
  • Solve Equations with Rational Exponents (Algebra 2)
  • Solve Equations with variables in Exponents (Algebra 2)
  • Exponential Growth (no answer key on this one, sorry)
  • Compound Interest Worksheet #1 (No logs)
  • Compound Interest Worksheet (Logarithms required)
  • Factor Trinomials Worksheet
  • Factor by Grouping
  • Domain and Range (Algebra 1)
  • Functions vs Relations (Distinguish function from relation, state domain etc..) (Algebra 2)
  • Evaluating Functions (Algebra 2)
  • 1 to 1 Functions (Algebra 2)
  • Composition of Functions (Algebra 2)
  • Inverse Functions Worksheet (Algebra 2)
  • Operations with Functions (Algebra 2)
  • Functions Review Worksheet (Algebra 2)
  • Logarithmic Equations
  • Properties of Logarithms Worksheet
  • Product Rule of Logarithms
  • Power Rule of Logarithms
  • Quotient Rule of Logarithms
  • Solve Quadratic Equations by Factoring
  • Quadratic Formula Worksheets (3 different sheets)
  • Quadratic Formula Worksheet (Real solutions)
  • Quadratic Formula (Complex solutions)
  • Quadratic Formula (Both real and complex solutions)
  • Discriminant and Nature of the Roots
  • Solve Quadratic Equations by Completing the Square
  • Sum and Product of Roots
  • Radical Equations
  • Mixed Problems on Writing Equations of Lines
  • Slope Intercept Form Worksheet
  • Standard Form Worksheet
  • Point Slope Worksheet
  • Write Equation of Line from the Slope and 1 Point
  • Write Equation of Line From Two Points
  • Equation of Line Parallel to Another Line and Through a Point
  • Equation of Line Perpendicular to Another Line and Through a Point
  • Slope of a Line
  • Perpendicular Bisector of Segment
  • Write Equation of Line Mixed Review
  • Word Problems
  • Multiplying Monomials Worksheet
  • Multiplying and Dividing Monomials Sheet
  • Adding and Subtracting Polynomials worksheet
  • Multiplying Monomials with Polynomials Worksheet
  • Multiplying Binomials Worksheet
  • Multiplying Polynomials
  • Simplifying Polynomials
  • Factoring Trinomials
  • Operations with Polynomials Worksheet
  • Dividing Radicals
  • Simplify Radicals Worksheet
  • Adding Radicals
  • Multiplying Radicals Worksheet
  • Radicals Review (Mixed review worksheet on radicals and square roots)
  • Rationalizing the Denominator (Algebra 2)
  • Radical Equations (Algebra 2)
  • Solve Systems of Equations Graphically
  • Solve Systems of Equations by Elimination
  • Solve by Substitution
  • Solve Systems of Equations (Mixed Review)
  • Activity on Systems of Equations (Create an advertisement for your favorite method to Solve Systems of Equations )
  • Real World Connections (Compare cell phone plans)
  • Identifying Fractions

Trigonomnetry

  • Law of Sines and Cosines Worksheet (This sheet is a summative worksheet that focuses on deciding when to use the law of sines or cosines as well as on using both formulas to solve for a single triangle's side or angle)
  • Law of Sines
  • Ambiguous Case of the Law of Sines
  • Law of Cosines
  • Vector Worksheet
  • Sine, Cosine, Tangent, to Find Side Length
  • Sine, Cosine, Tangent Chart
  • Inverse Trig Functions
  • Real World Applications of SOHCATOA
  • Mixed Review
  • Unit Circle Worksheet
  • Graphing Sine and Cosine Worksheet
  • Sine Cosine Graphs with Vertical Translations
  • Sine, Cosine, Tangent Graphs with Phase Shifts
  • Sine, Cosine, Tangent Graphs with Change in Period, Amplitude and Phase Shifts (All Translations)
  • Tangent Equation, Graph Worksheet
  • Graphing Sine, Cosine, Tangent with Change in Period
  • Cumulative, Summative Worksheet on Periodic Trig Functions - period, amplitude, phase shift, radians, degrees,unit circle
  • Ratio and Proportion
  • Similar Polygons
  • Area of Triangle
  • Interior Angles of Polygons
  • Exterior Angles of Polygons

math problem solving questions free

  • Identifying Fractions Worksheet
  • Associated Powerpoint
  • Simplify Fractions Worksheet (Regular Difficulty)
  • Associated PowerPoint
  • Simplify Fractions Worksheet (Challenging Difficulty level for advanced learners)
  • System of Linear Equations Worksheet
  • System of Linear Equations - Real World Application
  • Compositions of Reflections. Reflections Over Intersecting Lines as Rotations

All of these worksheets and activities are available for free so long as they are used solely for educational, noncommercial purposes and are not distributed outside of a specific teacher's classroom.

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120 Math Word Problems To Challenge Students Grades 1 to 8

Written by Marcus Guido

  • Teaching Tools

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  • Subtraction
  • Multiplication
  • Mixed operations
  • Ordering and number sense
  • Comparing and sequencing
  • Physical measurement
  • Ratios and percentages
  • Probability and data relationships

You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.

A jolt of creativity would help. But it doesn’t come.

Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.

This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes . ( See our entire list of back to school resources for teachers here .)

There are 120 examples in total.

The list of examples is supplemented by tips to create engaging and challenging math word problems.

120 Math word problems, categorized by skill

Addition word problems.

A teacher is teaching three students with a whiteboard happily.

Best for: 1st grade, 2nd grade

1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?

2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?

3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?

5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?

6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?

7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?

8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?

Subtraction word problems

Best for: 1st grade, second grade

9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?

10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?

11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

Five middle school students sitting at a row of desks playing Prodigy Math on tablets.

Practice math word problems with Prodigy Math

Join millions of teachers using Prodigy to make learning fun and differentiate instruction as they answer in-game questions, including math word problems from 1st to 8th grade!

12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?

13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?

14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?

15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?

16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?

Multiplication word problems

A hand holding a pen is doing calculation on a pice of papper

Best for: 2nd grade, 3rd grade

17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?

18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?

19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?

20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?

21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?

Division word problems

Best for: 3rd grade, 4th grade, 5th grade

22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?

23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?

24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?

25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?

26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?

Mixed operations word problems

A female teacher is instructing student math on a blackboard

27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?

28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?

29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?

30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?

Ordering and number sense word problems

31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?

32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?

33. Composing Numbers: What number is 6 tens and 10 ones?

34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?

35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?

Fractions word problems

A student is drawing on a notebook, holding a pencil.

Best for: 3rd grade, 4th grade, 5th grade, 6th grade

36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?

37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?

38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?

39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?

40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?

41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?

42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?

43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?

44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.

45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?

46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.

Decimals word problems

Best for: 4th grade, 5th grade

47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?

48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?

49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?

50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?

51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?

52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?

Comparing and sequencing word problems

Four students are sitting together and discussing math questions

Best for: Kindergarten, 1st grade, 2nd grade

53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?

54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?

55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?

56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?

57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?

58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?

59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?

Time word problems

66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?

69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?

70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?

71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?

Money word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade

60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?

61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?

62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?

63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?

64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?

65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?

67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.

68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?

Physical measurement word problems

A girl is doing math practice

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade

72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?

73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?

74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?

75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?

A tablet showing an example of Prodigy Math's battle gameplay.

76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?

77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?

78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?

79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?

80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?

81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?

Ratios and percentages word problems

Best for: 4th grade, 5th grade, 6th grade

82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?

83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?

84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?

85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?

86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?

87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?

88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?

Probability and data relationships word problems

Two students are calculating on a whiteboard

Best for: 4th grade, 5th grade, 6th grade, 7th grade

89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?

90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?

91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.

92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?

93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?

94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?

95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .

Geometry word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade

96. Introducing Perimeter:  The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?

97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?

98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?

99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?

100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?

101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?

102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?

103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?

104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?

105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?

106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?

107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?

108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?

109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?

110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?

111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?

112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?

113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?

114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?

Variables word problems

A hand is calculating math problem on a blacboard

Best for: 6th grade, 7th grade, 8th grade

115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?

116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.

117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.

118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.

119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.

120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?

How to easily make your own math word problems & word problems worksheets

Two teachers are discussing math with a pen and a notebook

Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:

  • Link to Student Interests:  By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
  • Make Questions Topical:  Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
  • Include Student Names:  Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
  • Be Explicit:  Repeating keywords distills the question, helping students focus on the core problem.
  • Test Reading Comprehension:  Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
  • Focus on Similar Interests:  Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
  • Feature Red Herrings:  Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.

A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.

Final thoughts about math word problems

You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.

Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.

The result?

A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.

Try Prodigy

There's no cost to you or your students and Prodigy is fully aligned with state standards for grades 1-8 math.

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Discover Frequently Asked Math Questions and Their Answers

  • How do you write the quadratic function #y=x^2+14x+11# in vertex form?
  • How many points does #y=-2x^2+x-3# have in common with the vertex and where is the vertex in relation to the x axis?
  • How do you solve #4x^4 - 16x^2 + 15 = 0#?
  • How do you solve #2x^2+3x-2=0#?
  • How do you solve #7(x-4)^2-2=54# using any method?
  • How do you solve #x^2 + 5x + 6 = 0# algebraically?
  • How do you use factoring to solve this equation #3x^2/4=27#?
  • What is the vertex of # y = (1/8)(x – 5)^2 - 3#?
  • How do you solve #| x^2+3x-2 | =2#?
  • How do you solve #2x²+3x=5 # using the quadratic formula?
  • How do you find the derivative of #y=tan(3x)# ?
  • How do you differentiate #f(x)= 1/ (lnx)# using the quotient rule?
  • How do you differentiate #(3+sin(x))/(3x+cos(x))#?
  • What is the derivative of this function #sin^-1(x/4)#?
  • What is the derivative of this function #y=sin^-1(2x)#?
  • What is the derivative of this function #arcsec(x^3)#?
  • What is the derivative of #y=sin(tan2x)#?
  • How do you differentiate #cos(pi*x^2)#?
  • What is the derivative of #f(x)=(x^2-4)ln(x^3/3-4x)#?
  • What is the derivative of #y=3sin(x) - sin(3x)#?
  • A triangle has corners at #(5 ,1 )#, #(2 ,9 )#, and #(4 ,3 )#. What is the area of the triangle's circumscribed circle?
  • How can we find the area of irregular shapes?
  • A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/3 #, and the triangle's area is #24 #. What is the area of the triangle's incircle?
  • An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(7 ,1 )# to #(8 ,5 )# and the triangle's area is #27 #, what are the possible coordinates of the triangle's third corner?
  • A triangle has corners at #(7 , 9 )#, #(3 ,7 )#, and #(4 ,8 )#. What is the radius of the triangle's inscribed circle?
  • Circle A has a center at #(2 ,3 )# and a radius of #1 #. Circle B has a center at #(0 ,-2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
  • A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 7 #. If the angle between sides A and C is #pi/4 #, what is the area of the parallelogram?
  • What is a quadrilateral that is not a parallelogram and not a trapezoid?
  • Your teacher made 8 triangles he need help to identify what type triangles they are. Help him?: 1) #12, 16, 20# 2) #15, 17, 22# 3) #6, 16, 26# 4) #12, 12, 15# 5) #5,12,13# 6) #7,24,25# 7) #8,15,17# 8) #9,40,41#
  • A triangle has corners A, B, and C located at #(3 ,5 )#, #(2 ,9 )#, and #(4 , 8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
  • What is the GCF of the set #64, 16n^2, 32n#?
  • How do you write the reciprocal number of 5?
  • Jeanie has a 3/4 yard piece of ribbon. She needs one 3/8 yard piece and one 1/2 yard piece. Can she cut the piece of ribbon into the two smaller pieces? Why?
  • How do you find the GCF of #25k, 35j#?
  • How do you write 132/100 in a mixed number?
  • How do you evaluate the power #2^3#?
  • How do you simplify #(4^6)^2 #?
  • How do you convert 3.2 tons to pounds?
  • How do you solve #\frac { 5} { 8} + \frac { 3} { 2} ( 4- \frac { 1} { 4} ) - \frac { 1} { 8}#?
  • What are some acronyms for PEMDAS?
  • How do you find all the asymptotes for function #y=(3x^2+2x-1)/(x^2-4 )#?
  • How do you determine whether the graph of #y^2+3x=0# is symmetric with respect to the x axis, y axis or neither?
  • How do you determine whether the graph of #y^2=(4x^2)/9-4# is symmetric with respect to the x axis, y axis, the line y=x or y=-x, or none of these?
  • How do you find the end behavior of #-x^3+3x^2+x-3#?
  • How do you find the asymptotes for #(2x^2 - x - 38) / (x^2 - 4)#?
  • How do you find the asymptotes for #f(x) = (x^2) / (x^2 + 1)#?
  • How do you find the vertical, horizontal and slant asymptotes of: #(3x-2) / (x+1)#?
  • How do you find the Vertical, Horizontal, and Oblique Asymptote given #s(t)=(8t)/sin(t)#?
  • How do you find vertical, horizontal and oblique asymptotes for #(x^3+1)/(x^2+3x)#?
  • How do you find vertical, horizontal and oblique asymptotes for #y = (4x^3 + x^2 + x + 5 )/( x^2 + 3x)#?
  • What is a pooled variance?
  • What is the mean, mode median and range of 11, 12, 13, 12, 14, 11, 12?
  • What is the z-score of sample X, if #n = 81, mu= 43, St. Dev. =90, and E[X] =57#?
  • The camera club has five members, and the mathematics club has eight. There is only one member common to both clubs. In how many ways could a committee of four people be formed with at least one member from each club?
  • How many permutations are there of the letter in the word baseball?
  • How do you evaluate 6p4?
  • What is the probability of #X= 6# successes, using the binomial formula?
  • A lottery has a $100 000 first prize, a $25 000 second prize, and five $500 third prizes. A total of 50000 tickets are sold. What is the probability of winning a prize in this lottery?
  • When a event is reported, the probability that is a negative event is 30%. What is the probability that 3 out of 5 reported events are negative?
  • What is the median of 5, 19, 2, 28, 25?
  • How do you solve this trigonometric equation?
  • What is the frequency of #f(theta)= sin 3 t - cos2 t #?
  • How do you evaluate #Sin(pi/2) + 6 cos(pi/3) #?
  • How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=9, b=40, c=41?
  • How do you express (5*pi)/4 into degree?
  • Solve for θ on the interval [90°,180°]:2tanθ +19 = 0?
  • Prove that #((cos(33^@))^2-(cos(57^@))^2)/((sin(10.5^@))^2-(sin(34.5^@))^2)= -sqrt2# ?
  • A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/3# and the angle between sides B and C is #pi/6#. If side B has a length of 26, what is the area of the triangle?
  • How do you write the following in trigonometric form and perform the operation given #(sqrt3+i)(1+i)#?
  • A triangle has sides A, B, and C. The angle between sides A and B is #(2pi)/3#. If side C has a length of #32 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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30 8th Grade Math Problems: Answers With Worked Examples

Erin Schumacher

8th Grade math problems build upon the basic algebraic reasoning and number system knowledge formed in prior grades. They help prepare students for more challenging math concepts that lay ahead of them in high school. 

In this blog, middle school math teacher, Erin, provides educators with 30 8th grade math problems to use in the classroom to strengthen learners’ math skills. Teachers can use these 8th grade math problems as warm-ups, competitive partner games, individual practice, or review before a test.

What are 8th grade math problems?

8th grade math problems are math problems specifically for 8th grade students focusing on the math skills and concepts learned in 8th grade. 

Many 8th grade math problems typically focus on algebraic reasoning to strengthen the foundations of solving for an unknown variable early on in the year. The majority of 8th grade math builds upon this skill. 

For example, when learning geometric concepts such as angle measures, surface area, volume, arc length, and sector area, formulas with an unknown variable are used to solve for measurement quantities.

Math Games For 8th Grade

Math Games For 8th Grade

15 fun math games and activities for 8th grade students to complete independently or with a partner.

8th grade math problems: Math curriculum

6th grade math problems and 7th grade math problems build the foundations for the 8th grade math curriculum. In 7th grade, students work with rational numbers and are introduced to simplifying algebraic expressions and solving algebraic equations. 

As students progress to 8th grade, a quick review of 7th grade material leads to a deeper dive into Algebra at a much faster pace.

The math curriculum in 8th grade hones in on linear functions and systems of equations where there are two variables rather than one. 

Perhaps, one of the biggest reasons 8th grade students struggle with the Common Core Math Standards is that they don’t have strong algebraic knowledge before introducing more than one variable.

30 8th grade math problems 

Here are 30 8th grade middle school math problems to help students practice and secure their knowledge of the core math concepts needed to succeed in high school and beyond. 

8th grade math problems: Rational number operations

Question 1 .

Add the values, then keep the negative sign when adding two negative numbers .

Question 2 

Answer:   -1\frac{11}{72} \text{ or } -\frac{83}{72}

This is another example of adding two negative numbers. Students must add the two fractions and then keep the negative sign.

Question 3 

Answer: \frac{53}{320}

Squaring a fraction means both the numerator and denominator are squared. Therefore: 

Show students how to enter fractions and exponents on their calculators. Calculators automatically reduce answers to the lowest terms and can help save students time.

READ MORE : What Is A Square Number?

8th grade math problems: Quotients of exponents, decimals, roots, and scientific notation

Question 4 .

Approximate the non-perfect root \sqrt{10} to the nearest tenth without using a calculator.

Answer: 3.2

The non-perfect root of 10 falls between the two perfect roots of 9 and 16.

Question 5 

Write the product of   \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} using the exponential form.

Answer: (\frac{2}{3})^{4}

Question 6 

Apply the Product of Powers Rule to simplify 4^{2} \times 4^{6} without using a calculator.

Answer: 4^{8}

The Produce of Powers Rule states that when the operation between to like bases raised to different powers is multiplication, keep the base and add the exponents.

8th grade math problems: Combining like terms and distributive property

Question 7 .

Answer: -4x-3

For struggling learners, circling one term and boxing the other works well. Additionally, using color to separate the terms is effective when several terms are used.

8th grade math problems combining like terms and distributive property answer

Answer: x+13

8th grade math problems visual answer

Explain to students that answers should often be reported with the variable listed before the constant.

Answer: -9x+27

8th grade math problems worked example

Drawing arrows to visualize which terms are multiplied together can be very effective.

Teach students they can use negative signs and subtraction signs interchangeably in algebra. 

For example, 14-2 x means the 14 is positive and the 2 x is negative, even though the operation before the 2 x is a subtraction sign.

8th grade math problems: Solving one-step and two-step equations

Question 10 .

-4 + x = 10

Answer: x =14 

Visual aids and drawings of a vertical line through the equal sign improve some students’ understanding. This clearly indicates the “left” and “right” sides and the need to balance them. 

Other students do not like the vertical line, and I typically leave it off when showing my work.

8th grade math problems multi-step problem

Question 11

\frac{x}{120} =3

Answer: x= 360

8th grade math problems multi-step problem answer

Question 12 

Answer: x=\frac{1}{2}

8th grade math problems two-step problem

8th grade math problems: Solving multi-step equations with the variable on both sides

Question 13 .

Answer: x = -6 

8th grade math problems multi-step equations with the variable on both sides

Question 14 

Answer: x= -4

Choose a side to move the x term to. I often told students to try and avoid working with negative numbers if they can, but it’s not necessary.

8th grade math problem and answer for a multi-step equations with the variable on both sides

Question  15 

Answer: x = 44

Problem and answer for a multi-step equations with the variable on both sides

When starting, it is helpful if all answers result in an integer. Students can then determine that something has gone wrong if they receive a fraction or decimal answer. 

For high-level learners, incorporate square roots of perfect squares and cube roots where applicable.

8th grade math problems: Special cases and determining the number of solutions

Question 16 .

Answer: All real numbers; infinite solutions

When the resulting statement is true (24=24) , any number can be used for x .

8th grade math problems determining the solution

Question 17 

Answer: Undefined; no solution

When the resulting statement is false (-12=2) , this means no number can be used for x

8th grade math problems no solution

Question 18 

-3(x+5)= -(3x+15) Answer: All real numbers; infinite solutions

8th grade math problems infinite solutions

Explain to students they should treat a negative sign (sometimes a subtraction sign) outside parentheses as a negative value that needs to be distributed.

8th grade math problems: Applying linear equations to word problems and real-world application

Question 19 .

Susie spent 2.75 hours on homework last night. She spent \frac{1}{4} hour longer on math than she did on reading. How much time did she spend studying both subjects?

Answer: Susie spent 1.25 hours reading and 1.5 hours on math.

8th grade math problems linear equations

Question 20 

In 5 years, Johnny will be twice as old as he is now. How old is Johnny now? Answer: Johnny is 5 years old.

8th grade math problems linear equations worked example

Challenge students to read simpler word problems and write their own equations to represent the scenarios.

8th grade math problems: Linear functions

Question 21.

Is there a proportional relationship in this table of values? If so, find slope.  

Answer: Yes; slope = -1

8th grade math problems linear functions problem

The definition of slope is the change in y (dependent variable) divided by the change in x (independent variable).

Question 22

Graph the function y=3x+4

8th grade math problems linear functions graph problem

Have students use a t-chart to help identify coordinates before graphing. Later on, show students how to graph simply using the rules of y-intercepts and slopes.

Question 23

Write the equation of the line that passes through (1, -19) and (-2, -7)  in slope-intercept form.

Answer: y= -4x-15

8th grade math problems slope intercept

8th grade math problems: Scatter plots

Question 24.

Give a possible scenario to relate the data in the graph provided.

8th grade math problems scatter plots

Answer: There are many possible solutions to this question. Here is one possible answer: 

8th grade math problems scatter plots answer

Question 25

Make a scatter plot from the data chart provided. Then, describe the correlation, if any.

8th grade math problems scatter plots information

The correlation shows a positive linear relationship between the x and y axis as both variables increase.

Question 26

Both graphs display the same data points. Write the equation of the trend line in the graph on the left, as it fits the data better than the trend line in the graph on the right.

8th grade math problems scatter plots comparison

Answer: y= -0.37x+7.46 

Extension: After students write the equation of the line of best fit on paper, challenge the students to plot the points on an online graphing calculator . 

Then, have students type y_{1} \sim mx_{1}+b  to see how close their equation matches the true linear regression.

8th grade math problems: Pythagorean Theorem, angles of triangles, surface area, volume

Question 27 .

Solve for the missing dimension in the right triangle.

8th grade math problems right angle triangle problem

Answer: x=8.1 \text{ feet} 

Question 28 

Calculate the measure of exterior angle A by solving for x . Use algebraic reasoning and apply the Exterior Angle Theorem.

8th grade math problems finding the exterior angle

Answer: A=108^{\circ}

Question  29

Calculate the surface area and volume for the given triangular prism .

8th grade math problems finding the area

Answer: \text{Surface area } = 68cm^2 ; \text{ Volume } = 30cm^3

Question 30 

Calculate the surface area and volume for the given cone. Round to the nearest hundredth.

8th grade math problems finding the surface area of a cone

Answer: \text{Surface area } = 75.40cm^2 ; \text{ Volume } = 37.70cm^3  

Top Tips for Teaching 8th Grade Math Problems

For success in teaching 8th grade math problems, educators should incorporate:  

  • Rote skills
  • Real-world application

Combining these teaching strategies is crucial for young learners. In my 15 years of experience as a math educator, students are more motivated to pay attention and power through lectures, note-taking, assignments, projects, and assessments if the educator figures out how to make the learning relevant and special to individuals. 

Simple things such as having students hand-write notes made a huge impact. Switching assignments between digital and paper frequently helped reduce groaning about the mundane. Incorporating art into math projects brought joy and opened students’ eyes to all the ways and places math is used in everyday life.

How can Third Space Learning help with 8th grade math?

STEM-specialist tutors help close learning gaps and address misconceptions for struggling 8th grade math students.

One-on-one online math tutoring sessions help students deepen their understanding of the 8th grade math curriculum and keep up with difficult math concepts before transitioning to high school.

Each student works with a private tutor who adapts instruction and math lesson content in real-time according to the student’s needs to accelerate learning.

8th grade middle school math tutor preparing for high school

8th grade math worksheets

Looking for more resources? Please see our selection of eighth grade math worksheets covering grade 8 key math topics and more:

  • Solve Equations With Fractions Worksheet
  • Adding and Subtracting Scientific Notation Worksheet
  • Solving Inequalities Worksheet
  • Ratios Problem Solving Worksheet
  • Negative Exponents Worksheet

READ MORE :

  • 2nd Grade Math Problems  
  • Math Problems For 3rd Graders
  • 4th Grade Math Problems
  • Math Questions for 5th Graders
  • Pythagorean theorem practice problems

Frequently asked questions

What math should an 8th grader know?

Upon completing the 8th grade, students should be well-prepared to enter Algebra 1. They should have a strong understanding of rational and irrational numbers, graphing, solving, and writing linear equations in standard form, slope-intercept form, point-slope form, inequalities, and functions including scatter plots, and geometry.

What grade is Algebra 1?

Algebra 1 typically starts in high school with 9th grade students.It is a high school math course that uses letters and mathematical symbols to solve math problems.

Do 8th grade students use a calculator?

8th grade students typically use calculators to help them solve most problems. Sometimes, an educator will ask students to think critically about an answer rather than relying on a device. However, many current educators understand that technology (including calculators) is readily available at any moment, and embrace using technology in everyday life.

Is 8th grade math hard?

8th grade math presents its challenges to many students. However, all students can succeed if using the tools accessible at their fingertips.

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

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[FREE] Ultimate Math Vocabulary Lists (K-5)

An essential guide for your Kindergarten to Grade 5 students to develop their knowledge of important terminology in math.

Use as a prompt to get students started with new concepts, or hand it out in full and encourage use throughout the year.

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Breaking’s Olympic Debut

A sport’s journey from the streets of new york all the way to the paris games..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

From “The New York Times,” I’m Sabrina Tavernise. And this is “The Daily.”

So my name is Gabriel “Kwikstep” Dionisio.

Rokafella, R-O-K-A-F-E-L-L-A.

I go by Kid Glyde. I represent Dynamic Rockers. I’m from Queens, New York.

This year at the Olympic Games, there’s one sport that’s on stage for the first time — breakdancing.

I’m excited that people are going to be exposed to it on that kind of stage.

They’re going to see breaking. They’re going to see hip-hop. They’re going to feel it. They’re going to — you know what I’m saying? So it’s going to be an experience.

Today, my colleague, Jonathan Abrams, tells the story of how it went from the streets of New York all the way to the Paris games.

But I’m also concerned that it’s not being represented at its fullest cultural capacity.

People are clueless to what this even is. And people are going to be really surprised.

And the debate that journey has inspired about whether treating breakdancing as just another sport might be a mistake.

This comes from a culture that had to go through so much just to exist. So are you going to do right by us?

[MUSIC PLAYING]

It’s Friday, August 9. Jonathan, welcome to the show.

Thank you so much, Sabrina.

So, Jonathan, we’re going to talk today about the Olympics. And I think something that catches people’s attention is when the Olympics adds new sports. The Olympics is this ancient thing. So, I find that kind of surprising when new things pop up. And you’ve been writing specifically about the new event that is debuting this year in Paris, and that is breakdancing.

Yeah, a lot of people in the community refer to it as “breaking.” Breakdancing is kind of a term that they have said was created by mainstream media and not a term that they use. So it’s almost frowned upon.

Ah. OK, breaking. Got it.

So it’s been a little bit of a journey these last few years to get it to the Olympics. And this is such a special watershed moment. It’s kind of crazy to think that breakdancers are going to be at the Olympic Games. They’re going to be mixing along with LeBron James, with Kevin Durant, with Simone Biles, all these athletes you historically think of being involved and intertwined with the games. You’re going to have a component of hip-hop right there alongside with them.

And it’s joining a class of new sports recently added to the Olympics, like skateboarding and rock climbing and surfing. And if you look at these sports, what they all have in common is that they’re trying to get a younger audience to watch the games.

And what the International Olympic Committee — they’ve been frank about what they’re trying to do — is that they’re trying to go for that younger audience because viewership has been way, way down. And so these ancient games are trying to modernize themselves by changing the rules and welcoming these new events to have a newer, younger, more diverse viewership.

OK, so breakdancing — oh, sorry, breaking — is here to try to breathe some new life into the Olympic Games — expand the audience, as you say. But I don’t really think of breaking as a sport, I mean, never mind a competitive Olympic sport.

Lots of people make that argument, Sabrina, but competition has been part of breaking since its inception in the Bronx in the 1970s. At that time, New York City is basically in this state of disrepair. The construction of the Cross Bronx Expressway cuts through the heart of the South Bronx, and it displaces thousands of residents. Crime levels rise, unemployment increases. These large buildings are sitting vacant because of white flight. And property owners, some are facing default, and they start burning their buildings in order to cash in on the insurance value. And people, especially the Black and Brown people in the Bronx, they’re feeling this sense of utter hopelessness. And the culture of hip hop grows out of that despair. It was a way for these marginalized communities to take something back and to have something for themselves.

And breaking is a key component of hip-hop, because when hip-hop first formed and came along, it was presented as this vivacious, multifaceted gem, where you had four distinct tenants and components. One was lyricism, the artists words going along a track of music. One is turntablism, or being a DJ, and that’s scratching records. The other one is graffiti, or writing. And then the last one is breaking. And that’s the physical expression of hip-hop, dancing to the music.

And so these latchkey kids in the Bronx would throw these massive parties where breaking was born. And people, they came together, and they formed crews. And they competed against one another. And they danced to make a name for themselves. They danced to earn respect in their street, in their neighborhood, and in their city. And that was how they cultivated self-esteem and made something of themselves when they really had nothing else.

OK, so in these poor neighborhoods in the Bronx, in this very turbulent time, kids were finding themselves finding inspiration in breaking. Why exactly did they call it breaking? Why that word?

Breaking comes from these pioneering DJs being able to figure out how to extend the breaks for songs. So say there’s a drum break in a famous song where it’s a snippet, and then the song will continue.

And they were the most popular parts of the songs, where kids would dance for 10, 15 seconds and then stop.

DJ’s like DJ Kool Herc and Grandmaster Flash. They were innovators and engineers because they figured out how to extend those breaks.

And once they were able to loop them endlessly, then kids were able to extend their dances and be able to dance and be creative with it and form the circles. And that’s where breaking came from.

So what did it actually look like?

There is no way I can accurately describe breaking just through words. I can try to say that it’s graceful or powerful or athletic, and all those words seem to fall flat. Breaking is a call and response. It’s a back and forth conversation. It’s almost like trumped up jazz.

Picture this. You’re going into a crowded party. There’s people everywhere. Music is thumping. If you’re walking to the cypher, which is the circle where breakers perform and compete in, you finally get to the front and what you see is people doing these most amazing moves, moves that you don’t think are possible with the human body.

They’re spinning, contorting their bodies into pretzels, stopping on a dime, bending backwards, and doing windmills and airflares. And then the next person is going to come in and challenge them. And what breaking is, it’s attitude. It’s an expression of yourself. It’s energy balled up.

And when did breaking go beyond the streets of the Bronx and really kind of emerge as a sport?

Well, before it got to that level, it had to become part of the mainstream culture. And breaking started to hit that level around the early to mid 1980s. And at this point, people may know “Rapper’s Delight.” They can maybe say “a hip hop, the hippie to hippie, hip hop.” Everybody knows that song by then.

But these movies, like “Flashdance” and “Wild Style,” are also starting to come out, and they’re starting to capture hip-hop’s infancy. And one of the main ones that comes out in 1984 is “Beat Street,” and that’s pivotal.

Bronx rockers. Gino, hey, come on.

Yo. Let’s serve.

There’s a scene of the movie with these crews coming together in a club.

And there’s anticipation. There is adrenaline. It looks like they may fight. But no, instead of fighting, a dance battle breaks out.

And if you’ve never seen this, like I said earlier, about words and being able to describe it, if somebody described breakdancing to you and you had never seen it in person, you wouldn’t have a good clue as to what it was.

But now, for the first time, in movie theaters from LA to New York, you can actually see what it is. And then you have these pioneering groups, like Rock Steady Crew and Dynamic Rockers, Zulu Kings, New York City Breakers, they all start to be in these movies and do these demonstrations globally. And that inspires a whole generation of kids to get into breakdancing.

This is the newest craze. It’s called breakdancing.

So as the popularity of breakdancing continues, experts say it’s OK to dance, as long as you just watch your step.

It’s the Big Breakdance Contest from the Roxy, with host Leslie —

And at this point, we’re starting to see judges and prizes be introduced into breaking. Then in 1990, a German breaker set up a breakdance competition in Germany known as Battle of the Year. And 2001 was a pivotal year because it’s the first year that Red Bull has its Lord of the Floors competition.

History in the making, y’all.

And that, again, convened all the best breakers to be able to compete against one another to measure themselves up. But there’s also the carrot at the end of the stick.

The runner-up of the 2001 Red Bull Lords of the Floor is —

There’s a multi-thousand dollar cash prize that’s awarded to the top talent.

The winners, Los Angeles Breakers. Come and get your checks.

So you start to see the trappings of this thing that was created in New York City in the Bronx in the 1970s start to leave its beginnings a little bit and become more of a competition and more of a sport through Red Bull and these other entities that are sponsoring it.

Y’all loving it or what? Give a big round of applause to all the contestants.

We’d like to thank Jaimeson Keegan and the whole Red Bull crew.

OK, so breaking is going mainstream in a very big way. But in my mind, there’s a big difference between a Red Bull event and the Olympics. So how do we get from here to there?

It’s actually a bit of a wild story. So nearly three decades ago, this global governing body of dance, International Dance Sport, is recognized by the International Olympic Committee, and they want to bring dance to the Olympics. So they want to have ballroom dancing. And they suggest that, and they get rebuffed.

So they eventually rebrand themselves as World Dance Sport Federation, and they find out that it’s not foxtrot or salsa or ballroom that the Olympic thinks could have a shot. It’s breaking. Breaking is highly watchable, easily viewable on social media. And it comes along as the Olympics is reevaluating what they’re going to use as a sport to try and gain that younger audience.

There was a testing period in 2018.

Winter Olympic Games just got a little more exciting. Breakdancing will now be part of the Youth Olympic Games. And there’s still a search for —

They debuted breaking at the Youth Olympics in Buenos Aires.

3, 2, 1! It’s battle time!

And what happens is that it exceeds almost every expectation by every metric possible. There was more than 50,000 people who attended the two-day event in 2018. There was over 2.5 million social media impressions, according to the International Olympic Committee. I mean, it seems like it aligns itself perfectly with the Olympics mission of trying to skewer to a younger audience. And once you see those numbers, that pretty much locked up breaking for the 2024 Olympic Games in Paris.

The Olympic Games are changing, and the future of breaking is coming.

We’ll be right back.

OK, so now we’re at the Games. Everybody’s watching how this is going to go, which must be pretty exciting for breakers.

You would think so. But there’s a lot of skepticism and tension from many of these veterans and pioneers and purists of breaking.

And what do they say? Why do they not feel excited about this?

Well, I think anytime you take something and strip it away from its roots — and let’s be honest, Paris 2024 is very, very, very far away from Bronx 1970s.

[LAUGHS]: That is true.

It is not going to be the same thing or presented in the same thing. I think that’s what the purists and the pioneers are afraid of.

But Jonathan, couldn’t you also make the case that skateboarding is also a specific kind of culture and that it also has all of its own peculiarities and is also potentially hard to judge by a bunch of Olympic judges?

To some extent, yeah. But breaking, it’s just different in a lot of ways. The pioneers and the purists, the ones who invented this thing will argue that it’s more than just a hobby or even a sport. It’s a lifestyle. It’s the product of a culture. It’s something that was born from Black and Brown people’s struggles in a deeply turbulent time in American history and is a way for people to express themselves, to tell their stories, to build self-confidence.

And on top of that, there’s a lot of breakers who just aren’t happy with how this arrived at the Olympics in the first place. It arrived in the hands of the World Dance Sport Federation. And remember, that’s an organization that wasn’t even associated with breaking. They were trying to put ballroom dancing into the Olympics way before they ever thought about breaking.

So back in 2017, a bunch of breakers, they got together and they signed a petition essentially protesting this organization. And they were saying, you don’t represent us. You’re not from our community, but you’re taking our art form and using it to advance your own goals. And all of this has left a lot of breakers really worried and concerned about what exactly this weekend is going to look like for breaking.

OK, let’s dig into that. What will breaking look like on stage in Paris? What can we expect?

Right, so there’s a lot of questions about how it’s going to actually look. In Paris, you’re going to have some of the crucial components of breaking. You’re going to have attitude. You’re going to have breakers. They’re going to be challenging each other. There’s going to be athleticism. [MUSIC PLAYING]

But there’s also going to be judges. A breaker is going to go get a score. Then the next breaker is going to go and get a score. So you can kind of see those seeds of the origin of this thing that was born in New York in the 1970s. But it’s definitely something different, and it’s more sterile and sanitized.

There’s going to be 16 men and 16 women who will go across two days of competition. There’s going to be nine judges, and they’re going to score the breakers based on five criteria — vocabulary, technique, execution, originality, and lastly, musicality.

And break those down for me. What do they actually mean?

The vocabulary is not how many words somebody can say. It’s the array of moves that a breaker deploys. And technique covers the breaker’s body control and their use of space. Execution consists of the cleanliness of one’s moves.

Then originality is improvising during their rounds, being able to react to what their opponent is doing. And then musicality is staying on beat with the music. They’re not going to know the music beforehand, so they’re going to have to really tune their moves to what’s going on to the beat.

OK, so this is how the judges are actually going to do it. But what about kind of what we know about breaking, the spirit of competition, the kind of outdoing each other, the attitude it brings, like the showboating? Is that taken into account in how it’s going to go with the Olympics?

Yeah, I can guarantee you this, Sabrina, that this is going to be the only Olympic sport with the misbehavior button.

What’s that?

The judges will be able to hit a misbehavior button if competitiveness crosses into crassness, if they deem that to be the case.

What’s an example of something that would get a misbehavior button?

Say if you finish off a move with the freeze and stick up your middle finger at your opponent.

[LAUGHS]: OK, fair enough. Got it. OK, misbehavior button. So this sport, of course, started here in the US. I have to ask, who are the Americans competing this year? Tell me about them.

Yeah, somebody that I’ve talked to a lot leading up to the Games is Sunny Choi, who was the first American woman to qualify for the Games.

All right, switching it up, all the way to USA, first entry, Sunny.

She’s Korean-American. She’s from Tennessee. She’s ironically the only New Yorker — she now lives in New York — who is competing in Paris at the Games.

All right, Sunny slay. Oh, you started as a gymnast? Is that true?

Yeah, so I actually, I watched the Olympics growing up.

She has a background in gymnastics, and she was working at Estée Lauder when she decided to go into breaking full-time.

Some people have been like, you’re a very unlikely Olympian. And I’m like, yeah, kind of. I had always envisioned myself going to the Olympics as a gymnast, and then I never thought I would have the chance again. And so it coming back full circle is amazing.

Woo! Victor.

OK, Victor.

What you got?

On the men’s side, you have Victor Montalvo, who goes by “B-Boy Victor.” And he’s a two-time Red Bull World One champion. He’s from Florida.

So my dad and his twin brother used to break back in Mexico. And they actually taught me, my brother, and my cousin.

His father was a pioneer in the Mexican breaking scene.

I was introduced into breaking at the age of six years old. And I took it serious at the age of 10.

Oh, my gosh.

Yeah, yeah.

So breaking is really in Victor’s blood. And he’s definitely a favorite to medal on the men’s side.

Heavy round.

Still go where the action is.

Victor, what you got?

Victor with the eye contact, going straight into it. He’s like, I see you, and I got you.

OK, so I’m assuming these Americans are poised to win this fundamentally American sport.

Eh, not necessarily, Sabrina.

Breaking is such a global entity now that I feel like America has really fallen behind some of these other countries and when it’s more popular and when people do it more often. So you look at this field and there’s breakers from Japan, from the Netherlands, from France, from Kazakhstan, from all over the world. On the women’s side, there’s B-Girl Nika from Lithuania.

And last year, she won the 2023 world title at the age of 16.

Wow, amazing. A Lithuanian girl has the world title, actually.

Yeah, and she’s an amazing story. And I think she’s emblematic of breaking and its evolution because she discovered breaking on YouTube at the age of five and within just about a decade is one of the world’s best breakers in the world and will be heavily favored to win a gold medal at the first Olympic breaking competition.

Just to go back to the tension around breaking in the Olympics that we started with, Jonathan, and the question of it leaving its roots, becoming detached from the place and the culture it sprung from, is there an argument that that’s already happened, that as people are kind of wanting to pull it back toward where it came from, it’s already gone. It already went out there. Is there any going back?

Yeah, that’s a great question. And I think we’re at this crossroads where you have breaking’s authenticity at stake. And breaking is about that expression from the heart. It’s about being able to show your attitude, your charisma, who you are as a person through your dance. And the pioneers and the purists are going to be watching this to see what part of the soul and the struggle exists as this thing that they invented, nurtured, and cultivated reaches its biggest stage ever.

But it is out there. And for somebody to be able to be in a foreign country and just study the art form on YouTube and be able to become world class leaders in it, it says something, one, about the art form and how wide-ranging and impactful it can be. And it also just says that this isn’t just New York’s anymore. This is global.

And perhaps the people performing on that stage are what breakdancing is now, right, in some ways?

Yeah, and we’re going to see people, men and women from different countries all over the world represented in Paris. And in some ways, it’s very, very far away from what was invented in New York in the 1970s.

But at the same time, seeing people from different countries and men and women be the best at breaking that they can possibly be is also exposing breaking to a whole new generation. And exposing breaking at the Olympics could be the vessel that keeps it alive for the next generation.

Jonathan, thank you.

Sabrina, anytime.

Here’s what else you should know today. On Thursday, former President Donald Trump held a news conference at Mar-a-Lago. It was his first public appearance since Vice President Kamala Harris became the Democratic presidential nominee.

And I look forward to the debates because I think we have to set the record straight.

In his remarks, Trump proposed three dates in September for debates with the vice president.

I haven’t recalibrated strategy at all. It’s the same policies — open borders, weak on crime.

Trump insisted that little had shifted in the contest, despite polling showing a tightening race.

Listen, I had 107,000 people in New Jersey. You didn’t report it. I’m so glad you asked. What did she have yesterday? 2,000 people? If I ever had 2,000 people, you’d say my campaign is finished.

It was an effort by the former President to recapture some political momentum, as the new Democratic ticket has continued to dominate the news coverage. During his remarks, ABC confirmed that it would host the two candidates for a debate on September 10th.

A quick reminder to catch a new episode of “The Interview” right here tomorrow. This week, Lulu Garcia-Navarro talks with Republican Senator James Lankford, including about Republicans who turned on him when he tried to pass bipartisan immigration reforms.

I did have several folks saying, I’ll destroy you if you do this, because although I like you, I like President Trump better. And he’s got to be elected for the future of the country. And you can’t take this issue off the table.

Today’s episode was produced by Sydney Harper and Luke Vander Ploeg, with help from Shannon Lin and Will Reid. It was edited by Lexie Diao and MJ Davis Lin, with help from Ben Calhoun, contains original music by Dan Powell, Marion Lozano, and Diane Wong, and was engineered by Alyssa Moxley. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

That’s it for “The Daily.” I’m Sabrina Tavernise. See you on Monday.

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Hosted by Sabrina Tavernise

Featuring Jonathan Abrams

Produced by Sydney Harper Luke Vander Ploeg Shannon M. Lin and Will Reid

Edited by Lexie Diao MJ Davis Lin and Ben Calhoun

Original music by Dan Powell Marion Lozano and Diane Wong

Engineered by Alyssa Moxley

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music | YouTube

More than 50 years after its inception, “breaking” — not “break dancing,” a term coined by the media and disdained by practitioners — will debut as an Olympic sport.

Jonathan Abrams, who writes about the intersection of sports and culture, explains how breaking’s big moment came about.

On today’s episode

math problem solving questions free

Jonathan Abrams , a Times reporter covering national culture news.

A person practicing breaking balances with his head and one hand on a concrete floor; his other hand and his legs extend into the air at various angles.

Background reading

The Olympic battles in breaking will be a watershed moment for a dance form conceived and cultivated by Black and Hispanic youth in the Bronx during the 1970s.

Breakers are grappling with hip-hop’s Olympic moment. Will their art translate into sport?

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Michael Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Maddy Masiello, Isabella Anderson, Nina Lassam and Nick Pitman.

Jonathan Abrams writes about the intersections of sports and culture and the changing cultural scenes in the South. More about Jonathan Abrams

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