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Interactive visualizations of fraction operations (fractions, ratios, proportions).

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Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math.

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Short animations to help students conceptualize ratio problems.

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When you visit any website, it may store or retrieve information on your browser, mostly in the form of cookies. This information might be about you, your preferences or your device and is mostly used to make the site work as you expect it to. The information does not usually directly identify you, but it can give you a more personalized web experience. Because we respect your right to privacy, you can choose not to allow some types of cookies. Click on the different category headings to find out more and change our default settings. However, blocking some types of cookies may impact your experience of the site and the services we are able to offer. More information

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Geometry visualization tools for dynamic understanding.

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Simulate fraction addition and subtraction with visual models.

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Explore fractions while you help yourself to 1/3 of a chocolate cake and wash it down with 1/2 a glass of water! Create your own fractions using fun interactive objects. Match shapes and numbers to earn stars in the fractions game. Challenge yourself on any level you like.

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Students manipulate ratios in real-time.

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Mental Math - simplify fractions
Problem Solving - create equivalent ratios

Common Core Connection for Grades 6 and 7

Understand ratio concepts and use ratio reasoning to solve problems.

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Play Dirt Bike Proportions at Math Playground! Practice solving proportions in this fast-paced math game.

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Personalized skills practice (limited free access).

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The exact skills you need

Planning a lesson or prepping for an exam?
We've custom-built IXL skills to reinforce each topic within your:

State standards

Virginia Standards of Learning (2016)

Textbooks

See skills that match every chapter of 80+ popular textbooks

Assessments

Use IXL for the NWEA MAP, ACT, SAT, and more

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IXL | Math, Language Arts, Science, Social Studies, and Spanish

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IXL is the world's most popular subscription-based learning site for K-12. Used by over 15 million students, IXL provides personalized learning in more than 10,000 topics, covering math, language arts, science, social studies, and Spanish. Interactive questions, awards, and certificates keep kids motivated as they master skills.

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Immediate feedback quizzes by standard.

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If you’re seeing this message, it means we’re having trouble loading external resources on our website.

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ThatQuiz.org: Fractions & Integers – Quick, focused practice.

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Math test activities for students and teachers of all grade levels

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Teacher-generated, student-paced quizzes.

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Absolute Value Quiz | Wayground (formerly Quizizz)

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Absolute Value quiz for grade students. Find other quizzes for and more on Wayground for free!

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Free, standards-aligned interactive e-text.

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Easily downloadable, comprehensive textbook.

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OpenStax | Free Textbooks Online with No Catch

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OpenStax offers free college textbooks for all types of students, making education accessible & affordable for everyone. Browse our list of available subjects!

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Illustrative Mathematics: Free Teacher Guide

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Illustrative Mathematics: Free Teacher Guide

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Lesson guides and resources.

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Illustrative Mathematics provides resources and support for giving their students an enduring understanding of mathematics.

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Lesson plans and interactive math activities.

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Georgia Standards of Excellence (Math 6–8)

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Georgia Standards of Excellence (Math 6–8)

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State-aligned documentation and guidance.

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GeorgiaStandards.org Sunset – Georgia Department of Education

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Tips for explaining mathematical reasoning in writing.

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Suggested Resources
Style Guide Overview MLA Guide APA Guide Chicago Guide OWL Exercises

This page is brought to you by the OWL at Purdue University. When printing this page, you must include the entire legal notice.

Copyright ©1995-2018 by The Writing Lab & The OWL at Purdue and Purdue University. All rights reserved. This material may not be published, reproduced, broadcast, rewritten, or redistributed without permission. Use of this site constitutes acceptance of our terms and conditions of fair use.

Tables, figures, and equations are the three categories of extra-textual items that require numbering and labelling. Each should be numbered consecutively throughout the paper - i.e., the numbering system does not start over in a new section or in an appendix, but simply continues on. For instance, if you have four figures in Section I, the first figure in Section II is simply Fig. 5, not Fig. II-1 or similar. The numbering of figures does not impact the numbering of tables or equations, but each category is numbered independently - e.g., if you have three figures and then a table, that table is still Table I, not Table IV.

Please note that tables, figures, and equations should always be introduced within the body of the paper before you show the actual table / figure / equation. If the data, or the figure itself, comes from an outside source, you should cite that source when you introduce the table / figure / equation. Moreover, you should follow the table / figure / equation with some form of explanation or connection to the broader point of your paper. In the case of equations, it is of primary importance to insure that, at some point in either the introduction or the explanation of the equation, you define the symbols used. No matter how self-explanatory an expression like φ²= 3*ξ may seem, if your reader doesn't know what φ and ξ signify, you may as well be typing nonsense.

Tables

In this context, "table" refers exclusively to data laid out in a grid format; if the data is rendered into a graph or other more visual format, that is a figure. In formatting tables, vertical lines are optional, and double horizontal lines may be used to signify the beginning and end of the table. Some horizontal lines may be removed if they are not necessary to understanding the table.

The table is labelled with the same format as a section or appendix heading, along with a title. Note that tables are enumerated with Roman numerals. Below the table, you may include explanatory notes as necessary; notes that apply to a specific part of the table should be marked in the same manner as a footnote, but notes that apply to the whole table are merely treated as captions.

See below for an example of what a table might look like in an IEEE paper. Note that this image (as well as the other ones on this page) have been zoomed in for clarity and detail.

Figures

"Figure" is a broad term that covers any image, graph, diagram, etc. that is neither a "table" nor an "equation". Please note that these should always simply be referred to as "figures" - IEEE format does not recognize labels such as "graph 1".

Unlike tables, the label for a figure goes below the figure. It is in sentence case, rather than small caps, and does not include line breaks. The format is as follows: "Fig.", followed by the number, then a period and an em space, followed by the title for the figure. It is recommended that figures be titled in an informative manner that includes what/where/when information. For instance, an effective title might be something like "Fig. 3. Number of citation errors in undergraduate papers at Purdue University, 2005-2015."

If parts of the figure are labeled specifically, this should be done with a lowercase letter within parentheses. The explanation of those labels should be included in the label for the overall figure. See the following example:

Equations

It is acceptable to use the built-in functions of your word processor to create equations, but there are a few elements of the process that require your attention. First, note that while variables and numbers should be italicized, the following elements of equations should be set in roman type: function names, units, words, and abbreviations thereof.

Equations are centered on the page and labeled with Arabic numerals, right-aligned, in parentheses, and referred to only by those numbers in the text - e.g., you should always say "as seen in (3)" rather than "as seen in Equation (3)". The only exception to this is if the equation number would begin a sentence, in which case you can say "Equation (3) shows..." in order to avoid the awkwardness of beginning a sentence with a numeral.

This page is brought to you by the OWL at Purdue University. When printing this page, you must include the entire legal notice.

Copyright ©1995-2018 by The Writing Lab & The OWL at Purdue and Purdue University. All rights reserved. This material may not be published, reproduced, broadcast, rewritten, or redistributed without permission. Use of this site constitutes acceptance of our terms and conditions of fair use.

Tables, figures, and equations are the three categories of extra-textual items that require numbering and labelling. Each should be numbered consecutively throughout the paper - i.e., the numbering system does not start over in a new section or in an appendix, but simply continues on. For instance, if you have four figures in Section I, the first figure in Section II is simply Fig. 5, not Fig. II-1 or similar. The numbering of figures does not impact the numbering of tables or equations, but each category is numbered independently - e.g., if you have three figures and then a table, that table is still Table I, not Table IV.

Please note that tables, figures, and equations should always be introduced within the body of the paper before you show the actual table / figure / equation. If the data, or the figure itself, comes from an outside source, you should cite that source when you introduce the table / figure / equation. Moreover, you should follow the table / figure / equation with some form of explanation or connection to the broader point of your paper. In the case of equations, it is of primary importance to insure that, at some point in either the introduction or the explanation of the equation, you define the symbols used. No matter how self-explanatory an expression like φ²= 3*ξ may seem, if your reader doesn't know what φ and ξ signify, you may as well be typing nonsense.

Tables

In this context, "table" refers exclusively to data laid out in a grid format; if the data is rendered into a graph or other more visual format, that is a figure. In formatting tables, vertical lines are optional, and double horizontal lines may be used to signify the beginning and end of the table. Some horizontal lines may be removed if they are not necessary to understanding the table.

The table is labelled with the same format as a section or appendix heading, along with a title. Note that tables are enumerated with Roman numerals. Below the table, you may include explanatory notes as necessary; notes that apply to a specific part of the table should be marked in the same manner as a footnote, but notes that apply to the whole table are merely treated as captions.

See below for an example of what a table might look like in an IEEE paper. Note that this image (as well as the other ones on this page) have been zoomed in for clarity and detail.

Figures

"Figure" is a broad term that covers any image, graph, diagram, etc. that is neither a "table" nor an "equation". Please note that these should always simply be referred to as "figures" - IEEE format does not recognize labels such as "graph 1".

Unlike tables, the label for a figure goes below the figure. It is in sentence case, rather than small caps, and does not include line breaks. The format is as follows: "Fig.", followed by the number, then a period and an em space, followed by the title for the figure. It is recommended that figures be titled in an informative manner that includes what/where/when information. For instance, an effective title might be something like "Fig. 3. Number of citation errors in undergraduate papers at Purdue University, 2005-2015."

If parts of the figure are labeled specifically, this should be done with a lowercase letter within parentheses. The explanation of those labels should be included in the label for the overall figure. See the following example:

Equations

It is acceptable to use the built-in functions of your word processor to create equations, but there are a few elements of the process that require your attention. First, note that while variables and numbers should be italicized, the following elements of equations should be set in roman type: function names, units, words, and abbreviations thereof.

Equations are centered on the page and labeled with Arabic numerals, right-aligned, in parentheses, and referred to only by those numbers in the text - e.g., you should always say "as seen in (3)" rather than "as seen in Equation (3)". The only exception to this is if the equation number would begin a sentence, in which case you can say "Equation (3) shows..." in order to avoid the awkwardness of beginning a sentence with a numeral.

# data[].attributes.attachment_link.description
Style Guide Overview MLA Guide APA Guide Chicago Guide OWL Exercises This page is brought to you by the OWL at Purdue University. When printing this page, you must include the entire legal notice. Copyright ©1995-2018 by The Writing Lab & The OWL at Purdue and Purdue University. All rights reserved.

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Full curriculum modules for self-paced learning.

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Learn sixth grade math—ratios, exponents, long division, negative numbers, geometry, statistics, and more. (aligned with Common Core standards)

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Coursera: Introduction to Mathematical Thinking

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Coursera: Introduction to Mathematical Thinking

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College-level enrichment (audit for free).

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About this Course

Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years.

Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world. This course helps to develop that crucial way of thinking.

Reset deadlines in accordance to your schedule.

Approx. 38 hours to complete

Subtitles: Arabic, French, Portuguese (European), Italian, Vietnamese, Korean, German, Russian, English, Spanish

Skills you will gain

Number Theory

Real Analysis

Mathematical Logic

Language

Reset deadlines in accordance to your schedule.

Approx. 38 hours to complete

Subtitles: Arabic, French, Portuguese (European), Italian, Vietnamese, Korean, German, Russian, English, Spanish

Instructor rating

4.81/5 (358 Ratings)

Offered by

Stanford University

The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is an American private research university located in Stanford, California on an 8,180-acre (3,310 ha) campus near Palo Alto, California, United States.

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Syllabus - What you will learn from this course

Content Rating 96% (19,094 ratings)

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Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years. Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system.

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Open access pre-algebra resources.

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Algebra I | Mathematics | MIT OpenCourseWare

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This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.

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Clear, visually engaging video lessons.

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Fun walkthroughs of grade‑appropriate math topics.

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Multiplying Fractions Word Problem Practice

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Numberphile – Interesting Math Concepts 

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Numberphile – Interesting Math Concepts 

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Deep dives into engaging mathematical ideas.

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Calculating Pi with Real Pies - Numberphile

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CK‑12 Foundation. (2024). CK‑12 Middle School Math Concepts. CK‑12. https://www.ck12.org/student/

Coursera. (2024). Introduction to mathematical thinking. Coursera. https://www.coursera.org/

Desmos. (2024). Desmos classroom activities. Desmos. https://teacher.desmos.com/

Khan Academy. (2024). Middle school math. Khan Academy. https://www.khanacademy.org/

PhET Interactive Simulations. (2024). Area builder. University of Colorado Boulder. https://phet.colorado.edu/