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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.

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  • Advanced regression (inference and transforming)
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  • Inference comparing two groups or populations
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  • More on regression
  • Prepare for the 2020 AP®︎ Statistics Exam
  • AP®︎ Statistics Standards mappings
  • Polynomials
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  • Derivatives: definition and basic rules
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  • Applications of derivatives
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  • 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.

Get Khanmigo

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

For learners     For teachers     For parents

ChiliMath logo 2024 updated

Free Math Lessons

Looking for free math tutorials online.

ChiliMath.com  is a place for you to learn math at your own pace for  FREE ! Allow me to help you solve math problems with a direct approach through the use of examples and diagrams.

New Lessons Added: June 10, 2024

Radical Equations Practice Problems with Answers

Determinant of 2×2 Matrix Quiz

Adding Integers Quiz

Subtracting Integers Quiz

Multiplying Integers Quiz

Identifying Function by its Graph Quiz

Writing Coordinates of a Point Quiz

Dividing Integers Quiz

Log Rules Quiz

Derivation of Pythagorean Theorem Formula

Absolute Value Equations Practice Problems with Answers

Literal Equations Practice Problems with Answers

LCM of Two Numbers Practice Problems with Answers

Quadratic Formula Practice Problems with Answers

literal equations

Whether you are a student studying algebra, a parent helping your kids with homework, or a teacher looking for additional learning resources then ChiliMath is the perfect free math help resource for you!

List of Algebra Lessons

Introductory Algebra

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Math can be challenging, but it is not difficult. As a math teacher, my goal is to encourage students just like you to solve as many problems as you can. With a lot of practice, you will build confidence, and in the process, develop your mathematical skills.

ChiliMath is a growing site created for students who need extra help in algebra/math. Since July 2011, I have added new topics on a regular basis with the goal of covering most lessons covered in an algebra class (Introductory Algebra, Intermediate Algebra, and Advanced Algebra).

I am also pleased to share that recently, I have started creating lessons for other math subjects as well such as Geometry, Number Theory, and Basic Math Proofs. Slowly but surely, and there’s more to come!

Please don’t forget to bookmark this page and reach out to me at contact(at)www.chilimath.com anytime if you found any typographical and/or content errors. I would greatly appreciate any support or help I can get to make this site better. Thank you very much for visiting my humble math website!

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English teachers tell their students explicitly how to format their papers: what fonts, what page margins, what style guides, etc. Math teachers, on the other hand, frequently just complain amongst themselves in the faculty lounge about how messy their students' work is. Meanwhile, their students wonder why they've lost points on homework and tests.

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Personalized Help ($): Investigate hiring a qualified tutor in your local area (US only), or try e-mail tutoring from Purplemath's author. But for in-depth, quality, video-supported, at-home help, including self-testing and immediate feedback, try MathHelp.com . MathHelp.com comes highly recommended by homeschoolers, military service members, and other practical people. If you're needing more intensive help, give MathHelp.com a try!

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Free help with your math—check your answers, quiz yourself, explore topics and more.

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Use the Wolfram|Alpha website for free to check answers, plot equations, balance chemical equations, visualize results, review interesting facts on a subject area and more.

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Use textbook notation to enter your math input and see it displayed in 2D. We've provided popular templates for you to use, as better visualization and quick editing mean faster results.

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Use Wolfram|Alpha how and where you want with our natively designed apps. From additional features to specially designed keyboards, we’ve made it easy to use Wolfram|Alpha on the go.

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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 .

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123 My Daughter loves these!
   
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100 Last-Day-of-School Activities Your Students Will Love!

80+ Awesome Websites for Teaching and Learning Math in 2023

Bookmark this list STAT!

Collage of math websites, including an online geoboard from Didax and still from a basketball video at Get the Math

The internet is full of incredible new ways to teach and learn math, from games and videos to lessons and even complete curricula. Teachers, students, and parents can all benefit from these online learning resources. This list of the best math websites has options for every skill level, from learning to count to advanced math like calculus. You’re bound to find a new favorite!

  • Comprehensive Math Programs
  • Interactive Tools to Use in Instruction
  • Games and Activities for Students
  • Resources for Teachers

Best math websites: Comprehensive math programs.

These are some of the best math websites that provide complete standards-based math curricula. Try them if you’re looking for a new way to teach math at your school. These can be good choices for homeschoolers too.

The littlest learners will benefit from ABCMouse’s complete online curriculum, including math. The progressive program builds on the math skills kids need to master. (Grades pre-K–2; monthly and annual subscriptions available)

Adventure Academy

From the same company that created ABCMouse, Adventure Academy is geared toward older elementary kids. It offers programs in math, language arts, science, and social studies. (Grades 3–8; monthly and annual subscriptions available)

Art of Problem Solving

Along with textbooks, Art of Problem Solving has a stable of robust online resources. You’ll find videos, math problems from math contests, and online classes. (Grades 5–12; pricing varies by program)

Buzzmath is one of the best math websites for middle schoolers. It helps them practice their math skills with high-quality problems, gives immediate and detailed feedback, and lets students progress at their own pace. Randomly generated values let students retry problems to obtain mastery. Teachers also receive detailed results that help them guide and monitor student progress. (Grades 1–9; free demo with subscription plans for students and families)

Make free detailed charts of all kinds, including bar graphs, pie charts, scatter plots, and more. (K–12; free)

Corbettmaths

This resource from England provides math videos with associated math practice questions and worksheets. It’s basic, but it’s a good way to get no-cost practice. (Grades K–12; free)

This National Science Foundation–funded program helps students strengthen math skills. Students will learn to solve problems and explain their thinking using mathematician George Polya’s four-step approach. (Grades K–12; priced per teacher or school, with free trial available)

Desmos Math

A blend of paper and technology puts student ideas at the center of learning. Lessons pose problems that invite a variety of approaches, engaging kids more fully. (Grades 6–8; contact them for pricing)

An adaptive learning platform designed to complement classroom instruction and deliver results. Includes resources for teachers, student data reports, and instructive insights. (Grades K–8; home users can sign up for individual or family subscriptions, schools pay per student or school)

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Take courses online from universities across the world, in math subjects ranging from statistics to calculus and many other options. (Grades 9+; audit courses are free, while courses for credit vary in cost)

Effortless Math

With dozens of online math courses, along with puzzles, worksheets, tips, and e-books, Effortless Math is a one-stop shop for math needs. (Grades K–12; cost varies by item)

eMathInstruction

This site provides e-textbooks, answer keys, video lessons, and printables. Topics include Algebra 1 and 2, geometry, and trigonometry. (Grades 6–12; free lessons plans, homework sets, and videos; paid subscriptions include answer keys, assessments, and more)

First in Math

We love the friendly competition and game-based content offered by First in Math. Kids gain skills practice and fluency as they play games targeted toward fact proficiency and logical thinking. (Grades K–8; subscriptions available for schools and parents, with 45-day free trial)

Freckle Education

This site allows kids to practice math at their own level and pace. It has more than 30,000 math questions, starting with a diagnostic that assigns material at just the right level. Freckles also features lessons, assessments, and reports for teachers. (Grades K–12; basic use is free for teachers; premium subscriptions available)

Illuminations

This site from the National Council of Teachers of Mathematics (NCTM) features complete lesson plans, mobile games for students, interactive activities, and brainteasers. (Grades pre-K–12; free)

Illustrative Mathematics

Get high-quality educational resources for teachers and students. Excellent math tasks, videos, lesson plans, and problem-based curriculum modules. (Grades K–12; free)

Imagine Learning

Formerly known as Edgenuity, Imagine Learning offers several online digital curricula for primary or supplementary instruction. Give students the support they need exactly when they need it. (Grades pre-K–12; priced per subject, per student)

Istation makes personalized learning easy with computer-adaptive instruction, assessments, personalized data profiles, and teacher resources. Includes digital lessons and face-to-face teaching strategies. (Grades pre-K–8; priced per student)

Make math about more than numbers with engaging items, real-world scenarios, and unlimited questions. Teachers choose the strand and then set up students to work independently. (Grades pre-K–12; free 30-day trial, pricing is per classroom or site)

Khan Academy

Khan Academy is on a mission to give a free, world-class education to anyone, anywhere. Their personalized learning resources make them one of the best math websites available for all ages, in a huge array of subjects. (Grades K–12; free)

Here’s an online learning space that is engaging, supportive, and designed to get kids interested in math. (Grades K–12; yearly subscription required; school and family pricing available)

MIND Research Institute

Through ongoing research, MIND Research Institute continues to investigate key questions about learning, mathematics, and how the brain works. ST Math is their pre-K–8 visual instructional program, helping teachers engage kids more deeply in math learning. (Grades pre-K–8; pricing based on total school enrollment)

This award-winning program finds and fixes learning gaps with the power of personalized learning. The three-pronged approach features personalized learning, pinpoint assessments, and an interactive classroom. (Grades K–8; pricing per student, school, and district)

Origo Education

Stepping Stones 2.0 from Origo is a unique and comprehensive curriculum that combines print and digital materials. It features problem-solving activities, strategies, and practice. (Grades pre-K–6; price varies by program)

PowerMyLearning

This organization is geared toward students, teachers, and families in low-income communities. The program features school workshops, instructional coaching, and professional learning communities. (Grades K–12; try limited Family Playlists for free, request consultation for pricing)

Prodigy Math

Join the 1 million teachers already using Prodigy Math in their classrooms at no cost. This fun and engaging curriculum-aligned game lets students engage in a fun wizarding world that motivates them to practice more math than ever. It contains 1,500+ standard-aligned skills. Plus you can track student progress with a teacher dashboard that provides instant feedback on areas of progress with no grading necessary. (Grades 1–8; free for teachers, monthly memberships available for parents)

Enter an interactive, game-based learning world that motivates kids through rewards. Features include a daily challenge, step-by-step lessons, and parent connections. (Grades K–5; 30-day free trial, then monthly subscription)

SplashLearn

Boost confidence, increase scores, and get ahead. Fun for enrichment or regular practice. (Grades K–5; free for teachers and schools, monthly subscriptions available for parents)

Math games make learning fun! Focus on specific skills, target interventions, and make assessment easy. (Grades K–8; teachers can try six games for free, subscription unlocks more games and features)

Tang Math strives to provide unparalleled math lessons for students as well as professional development for in-service teachers. Find games and puzzles, plus other resources like free downloads, worksheets/word problems, and math centers. (Grades K–5; free)

Woot Math offers adaptive practice for teaching rational numbers and related topics, such as fractions, decimals, and ratios. (Grades 3–7; free tier for teachers, additional features available for extra cost)

Personalized math curriculum that includes digital lessons and small-group instruction. Also has online modules, workbooks and answer keys, and professional development. (Grades K–5; free for individual teachers and classrooms)

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These are some of the best math websites that offer engaging videos and tools to use in your daily math instruction.

Engaging animated learning videos, games, quizzes, and activities to encourage kids on their unique learning path. (Grades pre-K–8; teacher, school, and district pricing available, as well as parent or homeschool options)

Teachers prep an assignment, students work on their devices, everybody gives feedback, and the teacher sees it all! (Grades K–12; free basic plan, Pro accounts unlock more features)

A website that allows teachers to assign math practice content to their students. Students get immediate feedback as they complete the problems. (Middle school+; free, with premium school and district plans available)

Desmos Graphing Calculator

An online graphing calculator that students can use for free. Includes a teacher-centric activity builder for creating digital math activities. (Grades 9–12; free)

Save money by using virtual math manipulatives like geoboards, base-10 blocks, 10-frames, pattern blocks, and more. (Grades K–12; free)

An award-winning series of math apps that harness the power of digital tools to create a better, deeper, more fun learning experience. Blogs such as “Making Math Social” and “Saying No to Math Anxiety” are included as resources for teachers and parents. (Grades K–6; priced per app, with free trials for teachers and bulk pricing for schools)

Flocabulary

Use hip-hop to teach math! Flocabulary offers songs, activities, and videos. (Grades K–12; teacher, school, and district pricing available)

Upload your own materials or build them from scratch, find something pre-made, act on live responses, and track student growth over time. (Grades K–12; free, premium subscription unlocks additional features)

Another graphing calculator for functions, geometry, algebra, calculus, statistics, and 3D math, along with a variety of math resources. (Grades 9–12; free)

You know it. Your kids love it. Why not use it to teach math? Engage your students with this game-based classroom-response system played by the whole class in real time. Multiple-choice questions are projected on the screen, then students answer with their smartphone, tablet, or computer. (Grades K–12; free, Kahoot+ AccessPass subscription offers premium content)

Math Central

Run by the University of Regina in Canada, this site offers free resources for math teachers and their students, including a database where users can search for the answers to math questions. Their “Mathematics With a Human Face” page includes information about careers in mathematics as well as profiles of mathematicians. (Grades K–12; free)

Teachers know that one of the best ways to make sure learning sticks is through song. Numberock features ad-free music videos of songs about math topics, like fractions, money, and integers, produced by an Emmy Award–winning studio. Numberock also has anchor charts, worksheets, comics, games, and more. (Grades K–5; limited free videos, monthly subscription offers six-month free trial)

Transform presentations into classroom conversations with Pear Deck for Google Slides. Effortlessly build engaging instructional content, formative assessments, and interactive questions. (Grades K–12; basic access is free, premium subscriptions unlock more features)

Take a photo of an equation, and this site will explain how to solve it, step-by-step. It even explains different options to get to the answer. Students can use it for help with homework, and teachers can incorporate it in their own lesson plans. (Grades 6+, free with premium options available)

TeacherTube

Think of this site like YouTube but specifically for teachers and schools. Find videos created by other teachers, and upload your own to share. (Grades K–12; free)

Best math websites: Games and activities for students.

These are some of the best interactive math websites and provide students with instruction and independent practice.

Arithmetic Four

Two users play a game in which each player tries to connect four game pieces in a row (like Connect 4). The players answer math questions to connect the pieces. The teacher chooses how much time each player has to answer, the level of difficulty, and the type of math problem. (Grades 2–8; free)

Coolmath Games

Yes, math games can be cool! Check out the hundreds of games on this site and on Coolmath4kids . (Grades K–12; free with ads, premium subscription removes ads and provides extra features)

Figure This!

Figure This is a site designed to encourage families to practice math together. It includes fun and engaging math games and high-quality challenges. It even offers challenges in Spanish. (Grades 6–8; free)

Funbrain has been helping students learn key math concepts and develop crucial skills since 1997. Students can choose from a slew of games. Why is it one of the best math websites? It’s all free! (Grades pre-K–8; free)

Get the Math

Get the Math is about algebra in the real world. Students see how professionals use math in music, fashion, video games, restaurants, basketball, and special effects. Then take on interactive challenges related to those careers. (Grades 6–12; free)

Your students will love fun math games like Speed Math Deluxe, Mystery Math, Place Value Game, and more. (Grades 3–12; free)

A popular game-based site for online math-learning resources. It covers algebra, geometry, statistics, and more. (Grades K–12; schools can contact them for a quote; parents pay per child)

Math Game Time

There are dozens of games to explore here, organized by grade and subject. (Grades pre-K–7; free)

MATHHelp.com

In-depth lessons with videos, guided practice, interactive self-tests, and more. (Grades 5–12; monthly or yearly subscription required)

Math Is Fun

Find general information along with games and practice for a variety of math subjects, including geometry, algebra, calculus, physics, and more. (Grades 6–12; free)

Math Playground

More than 425 math games, logic puzzles, and brain workouts for students to practice their math skills. (Grades 1–6; free with ads, Premium removes ads and provides extra features)

Most learners do best when they can see a problem walk-through, step-by-step. This site features multiple example problems, with walk-throughs by three separate instructors (including one in Spanish). They offer some basic math but are focused on advanced subjects from algebra on up. (Grades 6–12; free)

Thousands of original math games, workshops, and practice modules, as well as math printables. (Grades 1–6; monthly or yearly subscription required)

Multiplication.com

Need to master your multiplication facts? This is the site to try! Fun games and memory-building strategies will help students tackle this key skill. (Grades 2–6; free, with Premium membership available for extra features)

Numeracy Ninjas

This is a free intervention tool designed to fill gaps in students’ mental calculation skills and empower them with number fluency. Students can earn ninja belts of different colors for their skill level. (Grades 2–8; free)

PBS Math Club

From PBS Learning Media, this is one of the best math websites for middle schoolers. They love this entertaining video blog. Not only does each episode cover Common Core Standards, it makes math learning culturally relevant with pop-culture references. (Grades 6–9; free)

Students can create study flash cards, play educational games, practice skills, collaborate with other students, and more. (Grades 5–12; free, QuizletPlus provides additional features)

Another resource to help students build fact fluency. Each game is tailored to students’ ability levels. (Grades 2–6; school and home licenses available)

Sheppard Software

Tons of fun and educational online math games, from basic operations to algebra and geometry. (Grades K–6; free)

Simple math test activities for teachers and students, from beginning math operations to calculus. You set the skill level, number of problems, and time limit. A report, which tallies right and wrong answers, is provided after each quiz. (Grades 3–12; free)

Toy Theater

How would your students like to learn multiplication while shooting hoops? They can do that and more at Toy Theater, which teaches early math concepts through game-based learning. (Grades K–5; free)

Wolfram MathWorld

Upper-level math students will appreciate the no-frills information that’s easy to find on this site. Get overviews and see examples of advanced math subjects. (High school+; free)

XtraMath is like a daily math vitamin. An interactive online tool that helps students practice and master basic arithmetic facts, it’s quick and easy to use. Weekly emails provide progress reports for teachers and parents. (Grades K–8; free, with premium licenses that offer additional features)

Best math websites: Resources for teachers.

These are some of the best math websites that provide lesson-planning resources and professional-development materials.

Get differentiated, standards-aligned math practice problems that you can generate, assign, and evaluate online. (Grades 6–8; limited free plan with paid plans available)

Casio has a lot more to offer math teachers besides calculators. Their Worldwide Education Site is packed with free resources like worksheets, activities, teaching videos, how-to videos, font sets, and software options.

Citizen Math

Formerly known as Mathalicious, this site provides supplemental math lessons. Experience an immersive, participatory approach that makes learning and teaching more rewarding. (Grades 6–12; monthly or yearly subscriptions available)

Common Core Sheets

Find math worksheets for just about any area of study. Use them for planning lessons, review, and independent work. (Grades K–6; free)

Education.com

Here’s a reliable site for worksheets, games, and even lessons plans. They cover a variety of subjects, with lots of math options to choose from. (Grades K–8; limited free access, monthly subscriptions unlock all content)

This platform allows teachers to create technology-enhanced online math assessments from a huge question bank. (Grades K–12; free teacher accounts)

Kuta Software

For teachers of pre-algebra through calculus. Create the math worksheets you need, exactly how you want them, in minutes. You can also create customizable homework, quizzes, and tests. (Grades 8–12; free two-week trial, then single-user and site licenses available)

Mashup Math

A creative solution that aims to revive students’ passion and interest in math. Mashup Math has a library of 100+ math video lessons as well as a YouTube channel that features new math video lessons every week. A free e-book of math challenges is also available. (Grades K–8; free)

Math-Aids.com

Dynamically created math worksheets for students, teachers, and parents. (Grades K–10; free with ads, paid membership removes ads)

MathsBot.com

Tools for math teachers, including bell ringers and drills, math tools and manipulatives, question generators, printables, and puzzles. (Grades K–12; free with ads)

National Library of Virtual Manipulatives (NLVM)

This National Science Foundation–supported project provides a large library of uniquely interactive, web-based virtual manipulatives and concept tutorials for math instruction. (Grades K–12; free)

TeacherMade

Convert all of your paper assignments, quizzes, homework, etc., into digital activities delivered online. (Grades K–12; free basic version, Pro plan adds multiple extra features)

TeacherVision

For a very affordable monthly fee, gain access to thousands of resources created by teachers like you. They cover every topic and every grade level. (Grades K–12; monthly subscription)

Topmarks is one of the best U.K.-based math websites that provides a database of resources for teachers as well as online learning games for students. (Grades pre-K–8; free)

Varsity Learning

The Varsity Learning Online Math Management System is one of the best math websites because it provides course templates, assignments, an online teacher’s assistant, and thousands of practice problems so you can get organized, save assignments and videos on the web, share resources, and incorporate technology in your classroom. (Grades: 7–12; free)

Virtual Nerd

More than 1,500 video lessons ranging from middle-grade math through Algebra 2. (Grades 6–12; free)

What’s on your list of the best math websites? Come share your ideas in our We Are Teachers HELPLINE group on Facebook.

Plus, our favorite websites for teaching kids and teens to code ..

From learning numbers to advanced math like calculus, the best math websites offer something for everyone. All the top free and paid options!

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A soccer coach wants to know how many hours a week his players spend training at home. He has 20 players and he decides to ask the first 4 players to arrive at Monday's soccer practice how many hours they spend training per week. He then calculated that they spend an average of 10 hour per week. Therefore, he assumed that all the players train 10 hours per week. Is this an example of a simple random sample? 

A No, because each student did not have an equal chance of being selected. 

B Yes, because each student had an equal chance of being selected. 

C No, because he did not sample every soccer player. 

D Yes, the minimum number of students sampled need to be four for it to be a simple random sample. 

The figure shows the graph of f. 

(b) Which of the cx-values A, B, C, D, E, F and G appear to be inflection points of f? 

The diagram shows two rectangles, A and B. 

All measurements are in centimetres. 

The area of rectangle A is equal to the area of rectangle B. 

Find an expression for y in terms of w. 

George's page contains twice as many typed words as Bill's page and Bill's page contains 50 fewer words than Charlie's page. If each person can type 60 words per minute, after one minute, the difference between twice the number of words on Bill's page and the number of words on Charlie's page is 210. How many words did Bill's page contain initially?

 Bill's page initially contained        words. 

Simplify 2sin(5x)cos(3x) - sin(2x) to one an expression containing one trigonometric function. Then graph the original function and your simplified version to verify they are identical. Enclose arguments of functions in parentheses. For example, sin(2x). 

2sin(5x)cos(3x)-sin(2x)=

A health psychologist was interested in the effects of vitamin supplements on the immune system. Three groups of adults were exposed (in a highly ethical way) to the cold virus; one group took no supplements for a week before exposure, another had vitamin C supplements, and a third had multivitamins (excluding C). The severity of the cold was measured as a percentage (0% = not contracted, 100% very severe symptoms). The psychologist also measured the number of cigarettes that each person smoked per day, as smoking suppresses the immune system. The psychologist was interested in the differences in the severity of the illnesses across different vitamin groups accounting for cigarette usage. What technique should be used to analyse these data? 

A. Two-way repeated-measures ANOVA 

B. Two-way independent ANOVA 

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Opinion | Parental help with homework might solve student math woes | READER COMMENTARY

Baltimore City Public Schools Administrative Headquarters on E. North Avenue.

One thing glaringly absent from the article regarding efforts to change how students learn math in Baltimore’s public schools ( “Baltimore’s math scores consistently trail Maryland’s. Here’s city schools’ 5-year plan for improvement.” June 12) is the missing importance of a parent working with their child doing the homework.

The planners speak of individual teams arranged according to student progress, with such smaller teams providing attention where needed. But there will be no better team than the bond of a parent working with their child on homework.

Instead, the plan described is another rocket science approach — with percentage benchmarks and multiple teacher-pupil segments. They all amount to the latest high-cost dart throwing at the same basic target of teaching basic math that hasn’t changed for centuries. Algebra is the basic math of problem solving, which the planners themselves are having a problem with.

— Charles Herr, New Oxford, Pennsylvania

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