Des-blog

2024 Art Expo Gallery is Open for Viewing!

desmos — Mon, 03 Feb 2025 00:00:00 +0000

The 2024 Art Expo gallery is live! We recommend that you put this post down for a bit and check out the gallery first because the featured graphs are something special.

In this fifth year of the Art Expo, we took a new direction and explicitly centered learning. Every year, the graphs blow us away, which is a reflection not just of the new capabilities we’ve added but also of the Desmos community’s growing creativity, curiosity, and collaboration.

Art has been a surprising part of Desmos from our earliest days. Take this picture of a dog, which a student named Amy drew back when the Desmos Graphing Calculator was only a few weeks old:

“Untitled Graph”

by Amy

It was inspiring to us then – we even turned it into one of our first shirts! – and it still is today. But it’s even more inspiring to compare that graph to the works of creativity we see today. Not only has the math become more elaborate, but the breadth of topics, art styles, and perspectives has grown each year, too. This year’s gallery has a graph for almost every interest: nature, music, game design, fashion, architecture, advanced physics, and more.

Filter through the graphs using our new tagging system to find 3D examples or clever uses of features like tone and complex numbers. And be sure to check out the artist statements and graph notes to learn more about subjects ranging from astronomy to fiber arts.

We received a record number of submissions this year, and picking 80 graphs to highlight was agonizingly difficult. If we didn’t select your entry, please know that we could’ve filled this gallery ten times over with incredible graphs we wish we could’ve selected.

We’re so grateful to everyone who participated as well as everyone who shared their ideas in classrooms and living rooms and on social media. We learn from you every year, and we love watching you learn with each other. We can’t wait to see what you’ll create next.

View the gallery now!

–Team Desmos

P.S. Here are some quick stats about this year’s gallery:

Featured artists come from 22 different countries
Artists’ ages range from 13 to 65
62 of the graphs use lists
48 are animated
42 are interactive
38 use randomization
11 use tone
10 use the Geometry Tool
10 use the 3D Calculator
5 use recursion
3 use complex numbers

2024 Desmos Studio Math Art Expo

desmos — Fri, 15 Nov 2024 00:00:00 +0000

At Desmos Studio, we love learning and growth. Every year, we try to add new features to make Desmos more powerful, useful, and fun (check out our What’s New page!). And every year, we’re blown away by the new techniques and discoveries shared so generously across the Desmos community.

So, this year’s Math Art Expo is focused on learning and the journey it takes us on. That’s why we’re calling this an “Expo” – a celebration of creativity, growth, and community. We want to see how you use the capabilities we’ve added to express yourself. But even more than that, we want to see how you’ve grown, what you’ve learned about math and about creating art with Desmos in the last year.

For example, we were blown away by this anonymous participant’s two self-portraits, first in 2020 and then in 2021:

Or take a look at these two graphs from Diana A., both amazing, and together showing so much growth from 2022 to 2023:

If you’ve submitted in the past, we can’t wait to see what you’ve learned in the last year.

If this is your first time participating, we hope this is the first of many, and are just as excited to see what you create!

We’re also going to try something new this year, highlighting graphs in the gallery that make use of the following features:

Lists
Animation: sliders, the ticker
Interactivity: moveable points, the Geometry tool, 3D, clickable objects
Random
Tone
Complex numbers
Recursion

Pick one of these that you’re excited to learn more about, and explore how you might incorporate it into your submission.

As you’re working on your graphs, please reach out to us with any questions or suggestions at support@desmos.com or join our temporary Art Expo Discord Server to connect with our team and with each other. More details about this year’s Math Art Expo can be found below.

– The Desmos Studio Team

Who can enter?

Any individual from any country, aged 13+ may submit a Desmos graph to the competition via the Desmos Graphing, Geometry, and/or 3D tools. We’ll select graphs to feature from each of the four age groups listed below based on participant age as of January 1, 2025:

13–14 years old
15–16 years old
17–18 years old
19+ years old

Similar to last year, a parent or guardian over the age of 18 will be able to submit a graph on behalf of their student. This means that anyone over 13 can participate from anywhere in the world, even in countries where people under 16 aren’t allowed to submit graphs themselves.

What are we looking for?

Your original art, created in the Desmos Graphing, Geometry, and/or 3D tools. Participants may submit one entry on each of these tools, for a max of three entries in this year’s expo. Desmos Studio will be picking submissions to feature from across all three tools.

Submissions CANNOT contain copyrighted images or audio (Pokémon™, Among Us™, recently released songs, etc.), or non-original work. While you cannot submit graphs of copyrighted images or audio, you may submit graphs of works that are in the public domain.

As with last year, we’ll feature submissions that have some combination of the following:

Creativity and originality, including:
- A personal story or connection to the work
- Notes describing your process and your connection to the work
- Mathematical variety, including using some of the highlighted features for this year
Care and precision
- Beautiful visual design, including custom colors
- Subtle and surprising details
Performance
- Simplicity, including using fewer expressions to achieve the same goal
- Fast rendering and smooth animations, even on low-powered devices
Approachability
- Using familiar math where possible
- Graph organization & documentation

What prizes will be awarded?

Our panel of judges will select 20 featured graphs in each of the four age categories. Each of the 80 featured artists (20 in each age category) will receive:

$250 USD cash prize
Exclusive Desmos Studio merch
Artwork publicly displayed by Desmos Studio on our company website and social media channels.

How to submit your entry

Individuals submitting their own works will be able to submit their entries through the sparkle icon available in the Desmos Graphing, Geometry, and/or 3D tools. If you’re over 13 but live in a place where you aren’t allowed to submit a graph yourself, you may invite a parent or guardian to submit on your behalf at www.desmos.com/art. All submissions must be made on or before January 15th, 2025 at 8:59 p.m. PST / 11:59 p.m. EST.

The fine print

All contestants must be ages 13+ as of January 1st, 2025 to participate.
Complete the starter questions when submissions open in the Desmos Graphing, Geometry, and/or 3D tools to determine your eligibility to participate. Consider inviting a parent or guardian over the age of 18 to submit on your behalf if you’re over 13 but not eligible to participate based on geography via www.desmos.com/art.
We will only consider a contestant’s last submission, so you’re welcome to resubmit your graph(s) any number of times before the deadline, this includes via an adult submitting on your behalf at www.desmos.com/art.
All graphs must be the original work of the contestant and created using the Desmos Graphing, Geometry, and/or 3D tools. We cannot accept submissions that include copyrighted images and audio. Specifically, submitted graphs may not include the use of content that is not the intellectual property of the person who made the graph. This includes graphs of your favorite characters, logos, images, etc. that are not currently in the public domain.
Before distributing prizes, winners must complete our winner’s form. We reserve the right to verify a contestant’s eligibility and application information. It is the contestant’s responsibility to ensure that they are abiding by local data privacy laws.

Learn more about math art

Brand new to graphing with Desmos? Not so new, but want to learn more? Check out any of these links to get started.

Learn about bringing your graph to life with Animation and Interactivity in these videos.
Read about some favorite features in the Desmos Help Center:
- Lists, Tone, Complex Numbers, Recursion
Level up your Geometry skills with this Art with Transformations video.
Watch videos on go-to art strategies like Shading with Inequalities and using Custom Colors.
Check out our Desmos Math Art Teacher Guide if your’re interested in a class or organization-wide math art expo.
Explore more math art in the Help Center.

Questions? Contact us at contest@desmos.com or ask fellow artists for help and inspiration in the Desmos Art Expo Discord.

Our 4th Annual Global Math Art Contest is Here!

desmos — Thu, 16 Nov 2023 00:00:00 +0000

Update February 1, 2024: The gallery is live! Thank you to everyone who participated. We were blown away by the artistry, care, and ingenuity on display this year. Choosing just 100 graphs was nearly impossible, but we expect you’ll be as inspired by them as we are. As you explore the gallery, be on the lookout for the small details and bits of magic you’ll find scattered throughout artist statements and notes. You can find the graphs at www.desmos.com/art.

Our Global Math Art Contest is one of the highlights of our year. It reinforces the connection between math and art and creativity. It pushes our technical limits. And it inspires wild new features and products (see the 3D Calculator) in our quest to make tools worthy of the incredible people who use us around the world.

This year’s contest begins now! You’re welcome to get started, even though submissions won’t open for another two weeks. You’ll be able to submit anytime between December 1st and January 15th.

As you’re thinking about what you’ll create, we wanted to share a few themes to consider this year.

1. We have new tools!

Over the last year, we launched our new Desmos Geometry and 3D tools, and this year you can submit up to one graph from each of the tools (Graphing, Geometry, and 3D).

2. We want to welcome first time participants

We know that the gallery can be intimidating for folks who have never participated, so this year we’re expanding our galleries. We’ll be picking 25 graphs to feature in each age group, at least 5 of which will come from first-time participants.

3. We’re focusing on fast

This year we’re going to pay extra attention to the speed of your graph, especially in the 3D calculator (since it’s brand new, and not yet as fast as it will eventually be!). Remember that every year our tools get faster, computers get faster, and your techniques get more powerful. So if you have an idea that’s too slow this year, hopefully it won’t be for long.

4. We love approachable graphs

This year we’re seeking graphs that are as “approachable” as you can make them. The dream is that someone could open your graph and learn some math, or a new Desmos technique, from it. Think about using folders to organize, lists and functions to simplify, comments to explain.

5. We’re adding new audio capabilities

So often, our new capabilities are inspired by the incredible creativity of our community. The way folks have used “Audio trace” to make music is a great example. So this year, just in time for the art contest, we’re pleased to introduce a new (beta!) feature, Tone, which you can use to make music, sound effects, and generally highlight the connections between math, visual art and sound. We’ll be highlighting at least a few graphs that make use of this feature. Learn more about Tone.

As always, we just can’t wait to see what folks create. Please reach out to us with any questions or suggestions at contest@desmos.com! More details below.

– The Desmos Studio Team

Who Can Enter?

13–14 years old
15–16 years old
17–18 years old
19+ years old

This year we’re going to add a way for a parent or guardian over the age of 18 to submit a graph on behalf of their student. This means that anyone over 13 can participate from anywhere in the world, even in countries where people under 16 aren’t allowed to submit the graph themselves.

What Are We Looking For?

Your original art, created in the Desmos Graphing, Geometry, and/or 3D tools. Participants may submit one entry on each of these tools, for a max of three entries in this year’s contest. Desmos Studio will be picking submissions to feature from across all three tools.

Submissions that contain 1) copyrighted images or audio (Pokémon™, Among Us™, recently released songs, etc.), or 2) graphs or equations you did not create yourself will not be considered. While you cannot submit graphs of copyrighted images or audio, you may submit graphs of works that are in the public domain.

We’ll feature submissions that have some combination of the following:

Creativity and originality, including:
- A personal story or connection to the work
- Beautiful visual design (static or animated!)
- Varied mathematics
Delight. Delight comes in many forms, but some of our favorites include:
- Movement/animation
- Custom colors
- Subtle details and precision
- Sound effects using tone (beta!)
Performance
- Simplicity, including using fewer expressions to achieve the same goal
- Fast rendering, including on low-powered devices
Approachability
- Using familiar math where possible
- Graph organization & documentation
- Using simple techniques to create powerful things

What Prizes Will be Awarded?

Our panel of judges will select 25 featured graphs in each of the four age categories with at least 5 selections being from first time participants*. Each of the 100 featured artists (25 in each age category) will receive:

$250 USD cash prize
$100 gift code to the Desmos store
Artwork publicly displayed by Desmos Studio on our company website and social media channels.

*First time participation will be self-reported. Please be honest. We will disqualify folks from this and future competitions if we find out they were dishonest about previous participation using a different account.

How to Submit Your Entry

Individuals submitting their own works will be able to submit their entries through the trophy icon available on the Desmos Graphing, Geometry, and/or 3D tools. Submission portals will go live the first week of December 2023! If you’re over 13 but live in a place where you aren’t allowed to submit a graph yourself, you may invite a parent or guardian to submit on your behalf at www.desmos.com/art. All submissions must be made on or before January 15th, 2024 at 8:59 p.m. Pacific Time / 11:59 p.m. Eastern Standard Time.

We’ll update this blog post and announce on our website and on our social media channels when submission portals are open!

The Fine Print

All contestants must be ages 13+ as of January 1st, 2024 to participate.
Complete the starter questions when submissions open in the Desmos Graphing, Geometry, and/or 3D tools to determine your eligibility to participate. Consider inviting a parent or guardian over the age of 18 to submit on your behalf if you’re over 13 but not eligible to participate based on geography via www.desmos.com/art.
We will only consider a contestant’s last submission, so you’re welcome to resubmit your graph(s) any number of times before the deadline, this includes via an adult submitting on your behalf at www.desmos.com/art.
All graphs must be the original work of the contestant and created using the Desmos Graphing, Geometry, and/or 3D tools. We cannot accept submissions that include copyrighted images and audio. Specifically, submitted graphs may not include the use of content that is not the intellectual property of the person who made the graph. This includes graphs of your favorite characters, logos, images, etc. that are not currently in the public domain.
Before distributing prizes, winners must complete our winner’s form. We reserve the right to verify a contestant’s eligibility and application information. It is the contestant’s responsibility to ensure that they are abiding by local data privacy laws.

Resources

Brand new to graphing with Desmos? Not so new, but want to learn more? Check out any of these links to get started.

Getting started with our Graphing, Geometry, and 3D tools
Getting started with Desmos Art
Learn about Custom Colors - Article, Video, Graph Challenge
Learn about Transformations - Article, Video, Graph Challenge
Learn about Shading with Inequalities - Article, Video, Graph Challenge
Learn about Sliders and Animations
Learn about making Sounds using Tone
Learn about Polygons
Learn about Lists

Questions? Contact us at contest@desmos.com.

Español, 日本語, 简体中文, Pусский, Français

Introducing Desmos Studio's 3D Calculator (Beta)

desmos — Thu, 28 Sep 2023 00:00:00 +0000

Today, we’re excited to share the fruits of over a year of labor at Desmos Studio: our new 3D Calculator.

Why jump into this new dimension? 3D graphing doesn’t make all that many appearances in K-12 education. Few people today instinctively reach for a 3D calculator when trying to reason about a question.

But that’s exactly why this tool has felt so important to develop. The world we inhabit is three-dimensional. So much interesting mathematics lives there, from the abstract (e.g. conic sections) to the practical (volume, surface area), to the professional (movie & game design). Yet very few of us have built up a deep intuition for how points, curves, and surfaces behave in three dimensions.

We’re hoping that we can help to change that. Over and over we’ve seen the power that comes from matching a powerful tool with a curious mind. The products we strive to build make it possible to more easily explore new ideas, to develop them, and to share them. We’re eager to hear from you whether we’ve hit the mark with this first version — and also how it can improve from here!

Read on for some interactive examples of the 3D Calculator in action.

With the 3D calculator, you can take the parabola you know and love and turn it into a cup:

Explore this graph

Many of your favorite features will work just as they do in the Graphing Calculator. Try adjusting the sliders above, for example. What do you notice?

You can define functions in 3D as well. Here we draw a surface of revolution of the function $f$ by using the distance formula to plot circles around the x-axis so that $y^2+z^2$ equals the square of the radius, $f(x)$ :

Explore this graph

Some of the more powerful 2D features are here in 3D as well. For example, we can use lists to plot many values at once. Here’s a seemingly simple list of points. Change the orientation to reveal the secret shape:

Explore this graph

Most of all, we encourage you to just play around. You’ll be surprised, as we have been, by some of the shapes that will emerge:

Explore this graph

For more examples, head over to our new 3D Graph Gallery.

As part of this launch, we’re also excited to introduce a new approach to built-in learning that we call “quests.”

Each quest is a challenge to complete with a series of goals. There’s no one way to complete a quest, so get creative. Try to use as few equations as you can, or find a solution no one else has. Try a quest!.

It’s early days, and as a beta product we know that there will be rough edges to sand down. Please forgive us for any splinters. But please also complain loudly about any issues you run into (or praise us loudly as you find things you like). We are always immensely grateful for both. This product takes inspiration not just from all of the requests we’ve received over the years, but from the countless examples of people building their own 3d interfaces inside of the Graphing Calculator. We can’t overstate how lucky we feel to get to learn with and from the incredible, brilliant, generous, and creative Desmos community.

Building a 3D Calculator has been a goal of ours for years, and was one of the first things we chose to prioritize when we formed Desmos Studio PBC last year. Our mission at Desmos Studio is to help everyone learn math, love math, and grow with math. To succeed at that we need to continually grow with you. We hope this is one step of many to come in that direction.

– The Desmos Studio Team

Explore the 3D Calculator

Visit the 3D Help Center

Read the 3D User Guide

Try a 3D quest

Desmos Studio’s New Terms of Service

desmos — Tue, 22 Aug 2023 00:00:00 +0000

Desmos Studio PBC has a fresh new Terms of Service and Privacy Policy to match our fresh new homepage.

You might have a pit in your stomach anytime you see an update like this. You might worry, as we often do, that it’s actually a sneaky power or privacy grab (“surprise, we now have the right to listen to all of your conversations!”). Not so here – the primary motivation for these changes is to reflect last year’s split into Desmos Studio and Desmos Classroom. For example, we needed to change every instance of Desmos Inc (which no longer exists) to Desmos Studio PBC (our new name). We also needed to remove references to Desmos Classroom, which is now part of Amplify and governed by their Acceptable Use Policy and Privacy Policy.

While we were revising, we wanted to make a few other improvements based on questions and feedback we’ve gotten over the past year. For example, we added clarity about allowed use of images generated using Desmos Studio’s tools. No additional permission is required for these uses – just attribution – even when embedded in a commercial application. Similarly, we’ve gotten some questions about whether Desmos-generated images are compatible with the CC-BY requirements for inclusion on platforms like Wikipedia. The answer: an enthusiastic yes, and our terms now reflect that as well. If you ever have a question about collaborating with Desmos Studio, you can find us at partnerships@desmos.com.

As always, we try for maximum transparency with changes to our policies. You can see a line-by-line “diff” of all of the changes, and can see the history of past changes as well. If you’re familiar with GitHub, you can subscribe to any future changes.

In general, we recommend reading through any company’s terms of service instead of relying on a summary from them. If there’s anything in there that feels off with our Terms of Service, Privacy Policy, or any related docs, now or in the future, please let us know at feedback@desmos.com. We want these to be as straightforward and fair as possible, and will continue to refresh them as we hear from you, and as Desmos Studio PBC continues to grow and change in the years to come.

See the updated policies here:

Introducing the Next Generation Desmos Geometry Tool (Beta)

desmos — Thu, 11 May 2023 00:00:00 +0000

Today, we’re releasing a brand new tool from Desmos Studio PBC. It’s the successor to our Geometry Tool, built on top of the computational engine of the Graphing Calculator. If you want to try it out, we’ll take no offense if you stop reading and head to www.desmos.com/geometry-beta. We’ve also embedded some interactive examples that you can play with below.

We’re excited about this tool for three reasons.

First, Geometry is such a beautiful and universal subject. It starts with simple tools – just lines and circles – which, in combination, can be used to construct incredibly intricate and complicated things. Across all of mathematics, and much of science, geometric interpretations help things “make sense.”

Second, by building on top of the math engine of our graphing calculator, this new Geometry Tool gives power well beyond what the previous tool could. You can compute, plot on a coordinate plane, use sliders and lists, and even leverage advanced features like custom colors and actions, all integrated into the constructive geometry world.

Finally, this tool is the first major release of Desmos Studio PBC, and perfectly encapsulates why we formed this entity.

Just under a year ago, we made a huge change to Desmos. We split in half, and the curriculum business and teacher.desmos.com were acquired by Amplify Education, a long-time partner and collaborator. We chose Amplify because we wanted to find a trusted and respected home that could help expand the curriculum to cover all of K-12 while reaching more and more classrooms. That curriculum is cruising, including recently getting a perfect score(!) from EdReports.

As Desmos Studio PBC, we want to focus all of our energy on refining our tools and expanding their capabilities. We want to keep pushing the boundary of what’s possible with accessibility in mathematics. And we want to build new tools to unleash everyone’s inner mathematician.

This new Geometry Tool is the result of countless hours of work across our entire team, and we’re really excited to share beta access with you. Let’s see how it works.

You can construct using the tools at the top of the screen:

Explore this construction

But you also have access to the calculator so that you can, for example, measure the total angles of a polygon:

Explore this construction

…or hook a transformation up to a slider:

Explore this construction

You can even hook that transformation up to a list:

Explore this construction

… or to a list of dynamic colors.

Explore this construction

You can explore beautiful and surprising theorems, like the relationship between “centroid”, “orthocenter”, and “circumcenter” of a triangle:

Explore this construction

…or you can discover your own.

We’re just getting started with this tool. It’s beta, which means that it will have bugs. Please let us know if you stumble upon anything surprising, at feedback@desmos.com. It also means that we’ll be making many changes in the coming weeks and months. Some of these might break your constructions (though we’ll try not to!). We might remove features that you love. We might add features that you hate. Please forgive us for all of these transgressions, but please also let us know anything we can do to make it more useful or more intuitive.

The Desmos community is one of the most creative and collaborative that we’ve ever seen or been a part of. We feel so lucky to get to learn with you, build for you, and create with you, as together we explore new frontiers in math on computers. We can’t wait to see what you make.

– The Desmos Studio Team

Explore Geometry Beta

Visit the Geometry Help Center

Read the Geometry User Guide

Our 3rd Annual Global Math Art Contest is Here!

desmos — Tue, 15 Nov 2022 00:00:00 +0000

Update as of February 15, 2023: The 2022 Art Contest Gallery is live! You can find it at www.desmos.com/art.

Huge congratulations to everyone who participated. We’re so inspired by the effort, artistry, and creativity we saw across all of the age brackets and from around the world. It was nearly impossible to pick just 80.

We’re looking forward to seeing you again next year!

Last year we received more than 10,000 submissions from more than 100 countries for our 2nd annual Global Math Art Contest. Each year, we’ve been amazed by the creativity and artistry of people from around the world. The Art Contest has inspired new features, pushed our technical limits, and motivated us to improve our calculator to be worthy of the incredible people who use it.

We’re excited to announce our 3rd annual Global Math Art Contest, this year with some big changes.

First and foremost, we’re still going to select 20 graphs in each of 4 age brackets to feature on our website. But this year every single person featured will receive a prize. We found it nearly impossible to pick a “winner” from amongst the featured graphs. So we decided we want this to feel more like an Art Gallery than a prize contest. There’s just too much variety and ingenuity.

Secondly, we’re clarifying our evaluation criteria to prioritize some new characteristics, including performance. Part of our mission at Desmos Studio is to make sure that math is accessible to everyone, and so we prioritize performance—even on low-powered devices—in everything we build. We want to feature graphs that do the same!

Finally, we’ll have a few surprises this year, which we’ll share at the end.

We can’t wait to see what you’ll build.

Who Can Enter?

Any individual from any country, aged 13+ may submit a Desmos graph to the competition via the Desmos Graphing Calculator. We’ll select graphs to feature from each of four categories based on participants’ age as of December 31, 2022:

13–14 years old
15–16 years old
17–18 years old
19+ years old

Some international math artists may be ineligible due to various international age restrictions in online privacy laws. Complete the starter questions in the Desmos Graphing Calculator to determine your eligibility to participate.

What Are We Looking For?

Your original art, created in the Desmos Graphing Calculator. Submissions that contain 1) copyrighted images, or 2) graphs or equations you did not create yourself will not be considered. While you cannot submit graphs of copyrighted images, you may submit graphs of works that are in the public domain.

We’ll feature submissions that have some combination of the following:

Creativity and originality, including:
- A personal story
- Beautiful visual design
- Varied mathematics
Delight. There are lots of ways to show this, such as:
- Movement/animation
- Actions
- Sound using the audiotrace feature
- Custom colors
- Fine detail
Performance
- Simplicity, including using fewer expressions to achieve the same goal
- Performance, including on low-powered devices

How Will We Select Graphs to Feature?

We’ll select 20 featured graphs in each of the four age categories. Each of the 80 featured artists (20 in each age category) will receive:

$250 USD
Exclusive Desmos merch (worth $100)
Artwork publicly displayed by Desmos Studio on our company website and social media channels.

How to Submit Your Entry

Contestants can submit their entries through the Desmos Graphing Calculator at desmos.com/calculator. Just sign in and click on the trophy icon in the top right corner.

All submissions must be made on or before January 15th, 2023 at 11:59 p.m. Pacific Time.

The Fine Print

All contestants must be ages 13+ as of midnight on December 31, 2022 to participate. Age categories will be determined as of December 31st, 2022.
Some international contestants may be ineligible due to various international age restrictions in online privacy laws. Complete the starter questions in the Desmos Graphing Calculator to determine your eligibility to participate.
We will only consider a contestant’s last submission, so if you need to make any edits after you submit your graph, just submit it again.
All graphs must be the original work of the contestant and created using the Desmos Graphing Calculator. We cannot accept submissions that include copyrighted images. Specifically, submitted graphs may not include the use of content that is not the intellectual property of the person who made the graph. This includes graphs of your favorite characters, logos, images, etc. that are not currently in the public domain.
Before distributing prizes, we reserve the right to verify a contestant’s eligibility and application information. It is the contestant’s responsibility to ensure that they are abiding by local data privacy laws.

Resources

Brand new to graphing with Desmos? Not so new, but want to learn more? Check out any of these links to get started.

Getting started with the Graphing Calculator
Getting started with Desmos Art
Learn about Custom Colors
Learn about Polygons
Learn about Sliders and Moveable Points
Learn about Lists

Questions? Contact us at contest@desmos.com.

Español, 日本語, 简体中文, Pусский, Français

Introducing “Desmos Studio PBC” and “Desmos Classroom at Amplify”

desmos — Wed, 18 May 2022 00:00:00 +0000

We have some important news that we’re excited to share with all of you.

The Desmos you know is splitting into two entities: Desmos Studio, a Public Benefit Corporation that develops our free calculators, and Desmos Classroom, the creators of our curriculum and activity platform.

The curriculum part of Desmos is then joining forces with Amplify, an education company we’ve been proud to partner with for many years. The team developing everything at teacher.desmos.com (our free activities, the free Activity Builder, and Desmos Math 6-A1) will join Amplify as a division called Desmos Classroom.

For our community of teachers, learners, mathematicians, and creators, we are continuing to support all of our existing products, and everything that is free will remain free, now and always. Desmos Studio and Desmos Classroom will also remain tightly collaborative. We will continue doing the same work, committed to the same ideals, now with more resources to improve our products and serve more communities.

What does this mean for Desmos Classroom?

The Desmos Classroom + Amplify partnership will help us make Desmos Math 6-A1 available to more students and teachers. This means our shared vision of a creative and connected math education can become a reality for every student, rather than a select few, and that’s why we’re so incredibly excited about this work ahead.

Amplify and Desmos have been traveling on parallel paths for several years and we believe we can go farther together. We have both been creating math curricula based on the Illustrative Mathematics core curriculum. We have both been using core Desmos technology to do it. Both of our teams share the same unique understanding of the complexity of teaching, an appreciation for the brilliance of students, and a commitment to the inclusion of students who often feel pushed to the margins of math class.

Desmos has a proven model for helping students learn math and love learning math with technology. Amplify has a proven model for supporting students, teachers, schools, and districts at scale. We have decided we need each other’s strengths in order to help every student learn math and love learning math.

What does this mean for Desmos Studio?

By remaining independent, Desmos Studio will be able to focus all of its energy on building the most equitable, accessible, powerful, and delightful tools for exploring mathematics. Desmos Studio will continue to partner with the best publishers, platforms, and assessments around the world. The revenue from those partnerships will let us keep investing in our calculators and support our development of new tools.

Desmos Studio will reincorporate as a Public Benefit Corporation, formalizing our commitment to the people who use and rely on our tools, and formalizing our commitment to equity and accessibility as uncompromising values.

More than 75 million people use Desmos Studio tools today. The calculators are integrated into almost every state test and college entrance exam. Communities have sprung up on Reddit, Tiktok, and Discord, sharing ideas and exercising creativity beyond our wildest imagination. By forming Desmos Studio, we will be able to grow with and alongside this community for years to come.

What does this mean for you?

If you love tools like our graphing calculator, we have good news. The team at Desmos Studio is now 100% focused on their development, with lots of resources and a long list of your feature requests in front of them.

If you love Activity Builder and other free tools at teacher.desmos.com, we have good news. They will continue to be free, continue to power our curriculum, and continuously improve.

If you love our math curriculum, we have good news. Together with Amplify, we are continuing to sell and support it now and into the future. It will receive more attention and more resources than before, letting us develop learning supports we’ve always wanted to provide but couldn’t when we were operating independently. It’s a great time to get in touch with our team and learn more about our curriculum.

If you love people who work at Desmos, we have good news. We are all still working at either Desmos Classroom or Desmos Studio, all of us committed to the same mission that brought us to Desmos in the first place.

This is a new chapter in the Desmos story, and I hope you’ll keep turning pages with us. The action is just starting.

Note: In June 2025, Desmos Classroom became Amplify Classroom as the free teaching and learning platform expanded its offerings beyond math to include science and literacy.

2nd Annual Desmos Global Math Art Contest

desmos — Mon, 15 Nov 2021 00:00:00 +0000

Update as of February 4, 2022:

Thank you to the more than 10,000 participants from around the world who participated in the second annual Desmos Global Art Contest! The winners and finalists were chosen from countless examples of incredible effort, artistry, ingenuity, and creativity.

View the 2021 winners

Did you know the Desmos Graphing Calculator is a fantastic tool for making art? Using only graphed mathematical expressions, people around the world have created awe-inspiring masterpieces, from geometric patterns and architectural scenes to self-portraits, renderings of famous paintings, and beyond.

After the huge success of our 2020 Global Math Art Contest, featuring over 4,000 graphs from over 100 countries, we had to bring it back! Everyone from around the world can submit their entries for the 2nd Annual Desmos Global Math Art Contest and win prizes for their hard work. This year, we added more ways to submit and a category for ages 19+.

Who Can Enter?

Any student from any country, ages 13–18, plus individuals ages 19+ may submit a Desmos graph to the competition via the Desmos Graphing Calculator or a Desmos activity launched by a classroom teacher. Judging will be based on four categories for participants by their age as of December 31, 2021:

13–14 years old
15–16 years old
17–18 years old
19+ years old

What Are We Looking For?

Your original art created in the Desmos Graphing Calculator. Original means that a) you made it yourself and b) it doesn’t contain any copyrighted images. While you cannot submit graphs of copyrighted images, you may submit graphs of works that are in the public domain.

Want to impress our judges? We’re looking for submissions that have some combination of the following: Creativity and originality, including:

Visual content
How you use the math you know

Delight. There are lots of ways to show this, such as:

How Does Judging Happen?

10 finalists in each of the four age categories will be selected by our in-house panel of judges. All 40 finalists’ graphs will be featured on our website and will then proceed to a final round of judging.

The Prizes

In each age category, the following prizes will be awarded:

First Prize: $500
Second Prize: $250
Third Prize: $100

All 40 finalists, including the top three in each category, will get:

Desmos T-shirts.
Their work displayed publicly by Desmos on our company website and social media channels (with permission from the finalists).

How to Submit Your Entry

Individuals can submit their entries through the Desmos Graphing Calculator on desmos.com. In addition, teachers can launch a Desmos activity through which students can submit their entries. All submissions must be made on or before January 15th, 2022 at 11:59 p.m. Pacific Time. Desmos will follow up by email with teachers who submit graph entries through the Desmos Activity that are selected to be finalists to ensure that we can properly credit the student.

The Fine Print

All contestants must be ages 13+ as of midnight on December 31, 2021 to participate. Age categories will be determined as of December 31st, 2021.
Some international contestants may be ineligible due to various international age restrictions in online privacy laws. Complete the starter questions in the Desmos Graphing Calculator to determine your eligibility to participate.
We will only consider a contestant’s last submission, so if you need to make any edits after you submit your graph, just submit it again. All graphs must be the original work of the contestant and created using the Desmos Graphing Calculator. We cannot accept submissions that include copyrighted images. Specifically, submitted graphs may not include the use of content that is not the intellectual property of the person who made the graph.
Before distributing prizes, we reserve the right to verify a contestant’s eligibility and application information. It is the contestant’s responsibility to ensure that they are abiding by local data privacy laws.

Resources

Brand new to graphing with Desmos? Not so new, but want to learn more? Check out any of these links to get started.

Getting started with the Graphing Calculator
Getting started with Desmos Art
Learn about Custom Colors
Learn about Polygons
Learn about Sliders and Moveable Points

Questions? Contact us at contest@desmos.com.

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Rewriting Our List of Mathematicians

allison — Wed, 14 Jul 2021 00:00:00 +0000

When using Desmos activities, we want students to feel comfortable sharing their ideas with the teacher and the class. To support this, teachers can turn on anonymize mode swapping students’ names with the names of notable mathematicians.

Though our list of mathematician names was originally created for student safety, it is also a way we publicly amplify particular figures. By its nature, this list serves as a commentary on who is regarded as a mathematician. With that in mind, we recently inspected our list of names and chose to overhaul it. This blog post explains what prompted a change and how we crafted a new list.

What Prompted a Change

Our equity principles guide our work. The principles call us to make products that serve all students and teachers, and also to disrupt systemic inequities and conditions of marginalization in education.

Our first list of anonymous mathematicians contained 120 mathematicians. On that list, we identified fewer than 25% of the mathematicians as female or non-binary, and just over 10% as people of color. Inspired by people on Twitter, teachers who have reached out with suggestions, and folks who have bravely shared concerns about representation, we’ve updated the list over time.

After years of small updates, we still identified fewer than 40% of the mathematicians as female or nonbinary, and fewer than 34% as people of color. So this time, when a couple of teachers reached out about representation within our anonymized list, we decided that we’d reimagine the list from the ground up rather than making more small changes.

Dreaming Up a New List

Our goal was to create more opportunities for students to see aspects of themselves in math classrooms. Dr. Rudine Sims Bishop, Dr. Rochelle Gutierrez, and others use the analogies of windows and mirrors, where windows help you see into other parts of the world and mirrors help you see yourself.

We decided the new list should:

Overrepresent identities (race, gender, sexual orientation, etc.) that have been historically excluded in mathematical fields.
Showcase mathematicians in many different fields, including outside of academia.
Include people with easy-to-find information, including a picture.

Systemic & historical inequities mean that there aren’t equal opportunities for students to encounter mathematicians of all identities. This lack of diversity perpetuates narrow definitions of who mathematicians are and what they do. The first and second criteria intend to counteract that. The third criterion comes from the idea that we want students to be able to see and relate to the mathematicians they encounter.

Our Process

We researched each of the 200+ names on our existing list with these criteria in mind. We asked ourselves: What were identities we could find about each person? How easy was it to find information? How might different students see themselves in the information that was easily accessible about the person?

We selected some of the individuals from the existing list who met our criteria. Then, we did research on other folks who were not on the original list. Where we’ve landed for now is a list of about 110 mathematicians. We identified about 65% of the mathematicians on the list as female or nonbinary and nearly 80% as people of color.

We are so grateful for the work done by others, including but not limited to Annie Perkins, Talithia Washington, Ph.D, and Shelley M. Jones, Ph.D, who helped us learn about many wonderful mathematicians through their work.

What’s Next?

Rewriting our list of notable mathematicians is only one small part of living up to our equity principles, and our list will continue to evolve over time.

For this list, we focused on race, gender, and sexual orientation. We know these are not the only aspects of identity that are typically underrepresented in mathematics and hope to overrepresent additional excluded identity markers going forward. In addition, we are excited to add more individuals outside of academia who highlight the ways in which mathematical thinking is essential in so many fields.

We invite you to read our list of mathematicians. If you want to respond publicly, tag us @desmos. If you want to respond privately, feel free to email equity@desmos.com. We would love to hear your thoughts.

Updated July 16, 2021

Edited to include reference to Dr. Rudine Sims Bishop, who wrote Mirrors, Windows, and Sliding Glass in 1990.

The Desmos Guide to Building Great (Digital) Math Activities v2.0

faith — Thu, 11 Feb 2021 00:00:00 +0000

Desmos wants to help every student learn math and love learning math. To accomplish that goal, we build math activities for students, and we build them to the specifications in this document.

Our design code folds in our collective understanding of mathematics, identity, culture, curriculum, cognition, and pedagogy. Together, these ideas can increase the likelihood that a student will come to identify themselves as a “math person.”¹

We intend this document to be descriptive of choices we have already made and prescriptive for choices we will make in the future. When we have doubts about our design decisions, we use this document to settle them. We share these principles publicly in case they’re of use to you and, especially, so you’ll hold us accountable if we fail to meet them.

Create opportunities for students to be right and wrong in different, interesting ways.

We often ask students questions that have a single, correct answer. Those questions have value. More emblematic of our work are questions that lead to many interesting ways to be correct, and where even wrong answers offer a class something interesting to think about. In many of our activities, students create representations of their thinking that are so creative and interesting that labels like “right” and “wrong” feel inadequate.

In our curriculum, students create and share mosaics, turtles, robots, polygons, kaleidoscopes, transformations, water slides, card sorts, stories, problems for their classmates, and many other mathematical creations that point toward their brilliance.

When we anticipate and design for mathematical creativity, we make room for more kinds of mathematical brilliance and, by extension, more kinds of mathematical people.

Questions We Ask Ourselves

How can we provide opportunities for students to be creative?
How do we create space for answers that are wrong and brilliant?
What are different ways that people come to understand a particular mathematical idea?

Give feedback that attaches meaning to student thinking.

Whenever possible, we use computers to interpret rather than evaluate student thinking. Where evaluative feedback says, “You’re right” or “You’re wrong,” interpretive feedback says, “Here’s how we’re understanding your answer. What do you think now?” ^{2, 3} For example:

We don’t tell you whether or not your sketch is correct; we use it to control the path of the parachutist.
We don’t just tell you if your parabola is right or wrong; we show you whether or not it passes through the slaloms.
We don’t just tell you your paint ratio is right or wrong; we mix the colors for you.

We show students what their ideas mean in context, without judgment, giving them the freedom to revise their thinking and the incentive to build on their earlier ideas.

Questions We Ask Ourselves

How can we help students learn about their answer, beyond telling them it’s right or wrong?
What concrete, visual contexts can we build to help students make sense of this abstract idea?
What new ideas might students have as a result of our feedback?

Create a need.

We want students to experience math as power, rather than punishment; as purposeful, rather than pointless. We want students to experience mathematics as though it were aspirin for a headache. We want students to understand the power of the intellectual tools they bring from home, like estimation, their imagination, and their visual senses⁴. And we want them to experience a need for new tools. When we connect new tools to existing ones, we help students strengthen their understanding of both.

For example, in our lesson Make It Scale, we invite students to sketch a scaled figure without a grid before then inviting them to experience the precision that a grid offers them.

Questions We Ask Ourselves

Why did different groups of people invent this idea? What was its need?⁵
How can we help students experience that need?

Use a variety of resources.

Helping students learn math and love learning math is a huge, demanding task. It wants every resource we can offer it, so we try to offer as many as we can. We’re best known for connecting students to digital resources, but we also connect students to resources like paper, pencils, and other physical manipulatives. Jere Confrey has said that “students are the most underutilized resource in a classroom,” so we try to connect students to each other, creating opportunities for conversation and making visible every student’s experiences, strengths, and knowledge for the benefit of the entire class.

Questions We Ask Ourselves

Should students engage with this lesson on paper or on a computer?
Should we ask students to type a text response into the computer or ask them to discuss their thinking with a partner?
What early experiences, personal intuitions, or cultural knowledge will students make use of in this lesson⁶?
How can we get students out of their desks and moving?

Interrupt our biases.

When students use our activities, they’re experiencing the sum of the values and experiences of everyone involved in their creation. So we invest significant time in developing those values, especially in interrogating our own beliefs and interrupting our biases. We hone our values in internal reading and discussion groups, in our interactions with educators in the Desmos Fellowship, in our collaboration with external organizations, and by using our equity principles⁷ to guide our decisions, all so we can help every student experience the kind of mathematics education they deserve.

Questions We Ask Ourselves

What stereotypes might this lesson perpetuate?
What messages about math are we communicating through the questions we ask and the ways we give feedback to student responses?⁸
How might we ensure that every student will have access and opportunity to engage with grade level content?⁹
How can we help teachers invite, celebrate, and develop the brilliance in early student thinking?
How will a student’s identities affect their engagement with this activity?¹⁰

References

Finding Associations #Desmosify

dan — Tue, 17 Nov 2020 00:00:00 +0000

Welcome to a series of posts sharing how we #Desmosify the curriculum from Open Up Resources/Illustrative Mathematics. You can use this lesson for free, or sign up to get many more activities just like it in our core middle school curriculum!

Here’s how we #Desmosified an Open Up Resources/IM lesson to help students find associations in data..

Desmosification #1: Estimate, then calculate.

Two-way tables are a powerful way to represent data from the world. Associations that were invisible in a one-way table suddenly pop to the surface under the bright light of the two-way table, like the association between gender, age, and survival on the Titanic.

At Desmos, we try as often as possible to start with a student’s concrete and contextual knowledge before inviting them to develop more abstract and mathematical knowledge. Once a curriculum digests a context into numbers, certain contextual questions like “what do you think?” become harder to ask. So we chose to start this investigation without numbers, inviting as much contextual thinking from students as possible.

An advantage of the digital medium over print is that we can always add the numbers later.

Desmosification #2: Create connections.

We know that students learn more when they see connections between mathematical ideas. We love that our Activity Builder allows us to ask students a challenging question about associations and then let students choose the representation that best helps them answer it.

The bar graph might lead one to conclude that the second-class cabins had the fewest survivors. But the segmented bar graph makes the distribution of survivors and casualties much clearer.

Desmosification #3: Create conflict.

Once students are fully immersed in a context, it becomes easier to ask very pointed questions that draw out subtleties in the mathematics. By asking students to evaluate a claim that seems, at least from the perspective of a bar graph, pretty plausible, we’re very pointedly inviting the student to consider the affordances and limitations of each representation. (Again, with the representation switcher!)

Behind the Scenes

Desmos lesson developer Michael Fenton describes one of the core design dilemmas of the lesson and how our team found our way through it.

This is our second version of this lesson. The first was called “Headlines.” That original lesson probably received the most mixed reviews for any of the lessons we piloted in the 2018-2019 school year. And not in the sense that it was well-received by some students and teachers, and not by others. Rather, almost everyone offered strong positive feedback for some parts of the lesson, and strong negative feedback on other parts of the lesson. So we went back to the drawing board to redesign the lesson and tried to keep the strongest bit, namely, presenting students with data in two-way tables and asking whether there appears to be an association between one variable and another.

It’s also worth noting that the original contained several unrelated data sets from several different contexts. We wanted our rewrite to contain a more coherent storyline, so we wracked our brains to find a single scenario that we could explore several different data sets within. We considered grad school admission rates and gender, income and race, athletic achievement and birth month, driving and death rates, and several other contexts before settling on the Titanic.

What Did Teachers Think

The context made all the numbers feel serious and real.

I enjoyed the real world connection of using the story of the Titanic to help teach this lesson. I teach social studies and mathematics so it was nice to see a connection that allowed students to connect math to a real event from history.

What’s Next?

Overall, teachers in our 2019–20 pilot study really liked the Open Up Resources/Illustrative Mathematics curriculum . . . but they loved what we did to #Desmosify it. (Definition of the scale.)

Invite your students to learn with one of our curriculum’s activities: Finding Associations.
Get activities like this every day in our core middle school math curriculum.

Tortoise and the Hare #Desmosify

dan — Fri, 30 Oct 2020 00:00:00 +0000

Here’s how we #Desmosified an Open Up Resources/IM lesson to help students students interpret graphs of functions..

Desmosification #1: Create concrete connections.

In the original activity, Open Up Resources/Illustrative Mathematics starts with a context about temperature. We’re on board!

The activity immediately asks students to analyze the graph of a context precisely and numerically, but students have not yet had opportunities to develop and understand the context concretely.

One of our core commitments in designing curriculum is to invite students to use their voice, vision, touch, and intuition in mathematical analysis, all components of what Rochelle Gutierrez describes as “rehumanized mathematics.” If an activity invites students to access and apply their intuition about a context, it strengthens both their later numerical analysis and their sense of themselves as capable mathematicians with valuable ideas.

So in our activity, we chose acontext that has several advantages for students—a race between a tortoise and a hare.

We start by asking students to tell a story about what they see. This is an opportunity for teachers to learn what details are most salient for students. Are they noticing speed? The hare’s nap in the middle. The psychobiological conflict between two species?!

The hare is in the lead and and he stops and sleeps and the turtle wins.

It’s only much later in the activity, after the context has been enriched by the students’ own intuitions, that we ask for any precise, numerical analysis.

Desmosification #2: Give feedback that causes thinking.

Another advantage of this context is that because it’s a digital animation, we can invite students to control its different elements using their own thinking. We invite students to create a race between the tortoise and a dog using a graph. Students create a dog by graphing!

We ask students to create a specific dog—one with a head start that still loses the race, for example. And rather than give students binary feedback—right or wrong—which often fails to credit them for their abundant brilliant thinking even in a wrong answer, we just render the dog they created in the animation. Students can then decide if the dog did what they wanted it to do and make modifications accordingly.

Behind the Scenes

Desmos lesson developer Michael Fenton describes one of the core design dilemmas of the lesson and how our team found our way through it.

We agonized over the details of the race. How fast should each animal move? What distance should we use for the entire race? When and for how long should the hare rest? We wanted something that felt realistic if you look closely at the numbers. We also put a huge emphasis on the end of the race being suspenseful (will the hare catch up?!) while also having a clear-cut winner. And since it was nontrivial to change the parameters of the actual animation, we did most of our iterating with piecewise functions in a Desmos graph, making it easy to see important details from the entire race all at once.

What Did Teachers Think

Loved it! Students are really understanding how the graph tells a story. They know that the flat line means that there is no movement, negative slope means moving back towards the start and the steeper the line the faster the animal was moving. Great results on the cool downs!

My students loved this entire concept with the animals racing. They enjoyed creating the graphs for the tortoise and the dog because they were able to see how their graphs showed the story.

They knew immediately if they were right or wrong and that helped them work backwards to fix their graphs if necessary. My students were also confident in using their prior knowledge about what they know about lines and their steepness.

Students loved being able to tell their own story and give meaning to the graphs, awesome for some students’ creativity to shine through in writing. I appreciated the push for specific, detailed answers. It lent itself to stronger, clearer thinking practices.

What’s Next?

Overall, teachers in our 2019–20 pilot study really liked the Open Up Resources/Illustrative Mathematics curriculum . . . but they loved what we did to #Desmosify it. (Definition of the scale.)

Invite your students to learn with one of our curriculum’s activities: Tortoise and the Hare.
Get activities like this every day in our core middle school math curriculum.

Shira the Sheep #Desmosify

dan — Thu, 22 Oct 2020 00:00:00 +0000

Here’s how we #Desmosified an Open Up Resources/IM lesson to help students learn to solve inequalities..

Desmosification #1: Create concrete connections.

In the original lesson we #Desmosified, Open Up Resources/Illustrative Mathematics invites students to complete a series of exercises like the one below.

These exercises are likely to give students valuable experience with the subtleties of inequalities. The examples include inequalities that are strict and inclusive, inequalities that include negative and positive values, etc.

We worried, however, that students would spend too much time filling in tables to notice those subtleties. We also wanted to connect the solution of inequalities to a representation that’s more concrete for students than tables.

Enter Shira the Sheep!

Shira the Sheep likes eating grass and dislikes getting wet. She also provides us with a concrete and memorable metaphor for the solutions of inequalities.

Desmosification #2: Give feedback that causes thinking.

Imagine all the different inequalities students might enter in response to this situation. Our goal is to faithfully interpret all of them in Shira’s world, giving students more effective feedback than either a) a right/wrong evaluation or b) no feedback at all, which is common for paper-based curriculum.

The most straightforward interpretation of a solution like x > 3 is that Shira should land at x = 3 and run to the right. Deciding how to interpret strict inequalities when we asked for an inclusive inequality and vice versa was challenging for our team – and fun. In those instances, we decided Shira would leave a blade of grass behind or the ground would crumble beneath her.

We feel pretty confident that your students will anchor their discussions about inequalities on Shira the Sheep for months to come.

Desmosification #3: Create cognitive conflict.

We wanted to make sure students reflected on some of the same subtleties of the original lesson. We find that’s easier when students have a concrete context anchoring their thinking. Once students are immersed in the context, we can more easily ask them to settle a dispute between two contrasting ideas, or to explain why a method works.

Behind the Scenes

Desmos lesson developer Zack Miller describes one of the core design dilemmas of the lesson and how our team found our way through it.

Settling on the concept of a grass-eating sheep was tough! In an earlier draft, we had a sheep eating stars, and it wasn’t feeling right because stars are discrete and inequalities are continuous. But grass can be continuous!

Getting the interpretive feedback to feel right was also tricky. As is typical of our approach, we wanted to show, not tell; and we also wanted to be generous in the kinds of inequalities we’d accept. So what should happen in sheep world if a solution set is an inclusive inequality but students answer with a strict inequality, or vice versa? What should happen if the answer is x < 3 and a student answers x ≤ 2.99 (which has a very similar solution set)? What should happen if students enter an equation? Or an inequality that’s way off the screen?

I’m pleased with how we ended up handling every one of those cases.

What’s Next?

Overall, teachers in our 2019-20 pilot study really liked the Open Up Resources/Illustrative Mathematics curriculum . . . but they loved what we did to #Desmosify it. (Definition of the scale.)

Invite your students to play with Shira the Sheep!
Get activities like this every day in our core middle school math curriculum.

Paint #Desmosify

dan — Wed, 14 Oct 2020 00:00:00 +0000

Here’s how we #Desmosified an Open Up Resources/IM lesson introducing students to equivalent ratios.

Desmosification #1: Create concrete connections.

The original lesson we #Desmosified seeks to connect a student’s understanding of ratios to the taste of a drink. Helping a student connect their developing knowledge to some piece of concrete knowledge is a great way to strengthen both.

Contexts that students can touch and taste have lots of appeal. We chose a different context, however, one with several unique advantages.

In our lesson, students adjust the amount of green and white paint to create different color mixtures, some equivalent and others not, offering us two other unique #Desmosifications.

Desmosification #2: Give feedback that causes thinking.

A major challenge students experience in math class is getting zero feedback on their ideas or getting bad feedback. Kluger and DeNisi (1996) found that one third of feedback interventions have a negative effect on student learning.

When we ask students to make the same color with a different number of cups of paint, the student starts developing ideas. In a paper-based math lesson, they may not receive any feedback on those ideas. In many digital math lessons, students are told immediately that their idea is right or wrong. Dylan Wiliam writes that “feedback should cause thinking.” Neither of those kinds of feedback will cause much more thinking.

In our activity, students enter a number of cups and see the color they made. This lets students test conjectures in ways that would be much harder given the taste of a drink. Also, with the drink, the difference between equivalent and inequivalent ratios is perhaps more subtle than it is here, where you can see the difference between the colors. (We also describe the color difference in words for students who are vision-impaired.)

Desmosification #3: Create opportunities for students to experience themselves and their classmates as mathematicians.

In many math classes, the roles are well-defined. Teachers ask the questions and students answer them. We build technology that helps students understand that they can be authors and askers of questions just as much as any adult.

So at the end of this lesson, we invite students to create a color by mixing red, green, blue, and white paint, and then to specify how much of a color they want. That information becomes a question for their classmates to solve in the Class Gallery, making more visible everyone’s capacity for mathematical thought, not just the teacher’s.

Behind the Scenes

Desmos lesson developer Sean Sweeney describes one of the core design dilemmas of the lesson and how our team found its way through it.

One challenging part of creating Paint was balancing the on-screen feedback we provided for students. We really wanted to include text-based feedback on each color to help support students that could have difficulty telling those colors apart, but it became tough to provide that feedback without being too descriptive about exactly what students should do to get the right mix. We discussed and experimented quite a bit to strike the right balance between interpreting the colors on screen for every possible color combination and allowing students the room to think for themselves on the relationships between paint combinations. In the end, we made a system that attempts to describe the color the way a person might instead of just simply telling students what paints to add or remove.

What Did Teachers Think?

Students liked the ability to make up their own mixtures of paint.

The visual feedback of the mixed paint colors was great!

What Did Students Think?

I wish ALL subjects could use Desmos!

It’s like a game—like solving a puzzle!

This is my favorite Desmos lesson we’ve done so far this year.

What I get to make my own paint color!?!

Shouts Outs

Open Up Resources/Illustrative Mathematics for creating fantastic lessons we get to adapt. Also check out their own paint-mixing lesson in Grade 6.

What’s Next?

Invite your students to play with Paint!
Get activities like this every day in our core middle school math curriculum.

Flags #Desmosify

dan — Thu, 08 Oct 2020 00:00:00 +0000

Here’s how we #Desmosified an Open Up Resources/IM lesson about vertical intercepts.

Desmosification #1: Connect math to the world and back again.

A conviction we share with Open Up Resources/Illustrative Mathematics is that math learning is more durable and more interesting when students get opportunities to connect mathematical representations.

In their original lesson, OUR/IM invites students to connect together text and graphs.

So we were excited to use our digital technology to invite students to connect graphs and a dynamic animation.

We used our technology to let students make that connection in both directions. They turn our flag into a graph. But we also turn their graph into a flag.

Desmosification #2: Go further with fewer contexts.

The original OUR/IM lesson invites students to think about one context in its warm-up, six contexts in its card sort, and another context in a later activity. We originally had more contexts too, but teachers told us the lesson felt scattered and that students were doing too much reading and reorienting to focus in depth on the mathematical goals.

We decided to introduce more contexts in the rest of this unit on linear relationships, but we kept this lesson focused only on the flag. We explore this context in different ways throughout the lesson so students stay engaged. The result is that students know the context so well they can explore it using not just graphs, but numbers, tables, and equations as well.

Behind the Scenes

A word from Desmos lesson developer Michael Fenton on the development of the lesson:

Our original version of this lesson included three contexts. We kicked things off with a visual pattern (asking students, “How many tiles in the nth stage?”), spent five screens reasoning about flag scenarios, and then wrapped things up with several screens comparing social media followers vs. time. The consensus from our early classroom testing is that the lesson contained some promising ideas, but was generally scattered and unfocused. So in our revision of Grade 8 Unit 3, we pared everything back. We deleted the warm-up, dove directly into the flag scenarios, and lingered there for quite a bit longer. Our hope was that the tasks and prompts we built around the flags would be strong enough to carry the entire lesson, and that by focusing on a single core interaction, students would better grasp the main mathematical ideas in the lesson.

What Did Teachers Think?

The kids really connected the starting point and the speed to the equations in this lesson. Many “ah-ha” moments were had with very little prompting by myself. I don’t think that I have had kids connect to linear relationships so quickly through the equations.

Students that don’t typically feel successful in math class were shining today. They were making the connections as quickly as everyone else.

This lesson was one of the best I have seen at getting kids to grasp the idea of y = mx + b without ever providing the formula to them. It was a great day when I could watch them correctly come up with the equation on their own and have them truly having ahha moments.

Shoutouts

Shout out to Open Up Resources/Illustrative Mathematics for developing a fantastic print curriculum that inspired so much of our own work.
We’ve been working with connected representations since the second lesson we ever created, Function Carnival. Shout out to that little goofball, which celebrates its seventh birthday in January! 🎉
Decades ago, SimCalc developed a tool that connects representations in a similar way. They’re one of many giants whose shoulders we stand on.

Overall, teachers in our 2019-20 pilot study really liked the Open Up Resources/Illustrative Mathematics curriculum . . . but they loved what we did to #Desmosify it. (Definition of the scale.)

What’s Next?

Invite your students to play with Flags!
Get activities like this every day in our core middle school math curriculum.

Fit Fights #Desmosify

dan — Thu, 17 Sep 2020 00:00:00 +0000

Welcome to a series of posts sharing how we #Desmosify the curriculum from Open Up Resources/Illustrative Mathematics. You can use this lesson for free, experience it in a live show next week, or sign up to get many more activities just like it in our core middle school curriculum!

Here’s how we #Desmosified an Open Up Resources/IM lesson about fitting lines to data.

Desmosification #1: Collect and connect student creativity.

In the original lesson, students draw a line based on data that are tightly correlated and then loosely correlated. Ideally, they’d notice how the spread of the data makes fitting a line easier and harder.

“Compare [your lines] with a partner’s,” asks the lesson, a question which under really good conditions will result in useful learning. But what if your partner hasn’t drawn a line yet? What if you and your partner have a very similar or very different line? What if you’re learning virtually during a pandemic?!

On Desmos, we ask students to draw the two lines and then . . . we collect and connect all of them.

That’s both of your lines, along with all the lines from your classmates, all on the same screen!

It’s an image that helps students make the connection between the spread of the data and the fit of the line with incredible efficiency.

This is the Computation Layer code that powers this screen!

Desmosification #2: Give students interpretive feedback.

The original lesson then asks students to compare two lines that are fit to the same data and think about which one is a better fit. The lesson asks questions about how many points are above and below the line and how many points are less than a certain distance away from the line.

The lesson tries to help students develop an intuition for fitting lines to data, but paper limits the kinds of experiences students can have here.

Using digital technology, we ask students to draw a line to fit the data, and then we interpret their line with a meter that gives them feedback on their fit.

We’ll even let you know if you have the closest fit in your class!

Desmosification #3: Collect and connect student creativity.

Let’s run this #Desmosification again! In the paper lesson, the authors ask students to practice fitting lines to several prefabricated sets of data.

This felt like a useful opportunity for us to invite students to create their own data sets and practice fitting lines to data from their classmates.

We required a minimum of five data points and students went way above and beyond. They’re getting more than practice fitting lines here; they’re getting the realization that they are authors of math and math problems just as much as the grown-up authors of their curriculum are.

Check Out Our Brilliant Community

We asked our community how they would #Desmosify this kind of math and they did not disappoint.

Leandra Fernandez:

Give a graph of the data and ask students to draw a line that best predicts the data. Then do a class overlay of everyone’s lines… and that’s where I get stuck!

Michael Birkeland:

Create y=mx+b lines with sliders to move around to make a best estimate, overlay all the students’ responses (or show in summary) to find agreements and disagreements. Have a discussion about those. Refine and repeat until everyone is mostly in agreement!

John Brown:

A cool exploration could be to make a line with moveable points and show the “score” (SSR). Tell them it’s like golf – lowest score wins. Then let them play and ask what makes a line a good one. Bonus: have them hit a submit button before seeing the score, Marbleslides-style.

Behind the Scenes

A word from Desmos lesson developer Lisa Bejarano on the development of that meter:

I had the hardest time deciding how to provide feedback on the accuracy of a line of fit. I knew I wanted students to get interpretive feedback so that they knew: 1) How to improve their line of it and 2) why the new line had an improved fit.

In an early draft, we provided a numerical score for the accuracy of the line of fit, but it was not clear what the score meant or how it was calculated.

I wanted a way for students to see how accurate their line was while keeping this interaction focused on the line of fit and not on measures of variance that are not appropriate at this grade level.

The next idea was to draw a blob around the line and count how many points were inside the blob so that it was more obvious to students how they could improve their line, but that is not a very precise method for measuring the accuracy of a line of fit.

A third idea was to draw in the actual line of best fit and compare it to the student’s line, but that provides an answer, which would eliminate the opportunity for students to iterate on their own thinking.

Then we had the idea to add the meter instead of a numerical score. We decided to include the residuals as a visual indication of how students can adjust their line to improve their score.

What Did Teachers Think?

The “good line of fit - o - meter” for creating the line of fit was spectacular! SO POWERFUL!

The students were really able to see what is a good fit for the data with the meters.

I would change nothing about this lesson. I loved this lesson so much and that meter was so awesome for the kids! They love it when they get that okay on their own screen!

Overall, teachers in our 2019-20 pilot study really liked the Open Up Resources/Illustrative Mathematics curriculum . . . but they loved what we did to #Desmosify it. (Definition of the scale.)

What’s Next?

Invite your students to play with Fit Fights!
Get activities like this every day in our core middle school math curriculum.
Join me on Monday, Sept. 21 at 4 p.m. Pacific for #DesmosLive where we’ll discuss this activity and other exciting examples of Desmos technology.

What a Point in a Scatter Plot Means #Desmosify

dan — Thu, 10 Sep 2020 00:00:00 +0000

Several years ago, we realized that in order to have any kind of meaningful impact on a student’s math education, we needed to integrate ourselves into their daily math experience, especially their curriculum. At the same time, Illustrative Mathematics and Open Up Resources released their openly-licensed core middle school math curriculum. We loved the coherence of their curriculum, the way they told middle school mathematics like a story. We then asked 68 teachers how they liked their current curriculum using a tool called a Net Promoter Score, and Illustrative Mathematics was the clear winner.

A negative NPS means more detractors than promoters. Positive means more promoters than detractors. Anything positive is considered good. 50 is considered excellent. Illustrative Mathematics was the only curriculum in our sample with a positive NPS.

But Illustrative Mathematics was built for paper. It includes a few digital applets, but they’re supplementary, not core to the student experience. Meanwhile, at Desmos, we work with paper and computers. We get to decide on the best medium for whatever mathematics we’d like to help students learn.

So we built a Desmosified version of an Illustrative Mathematics unit, and later, all of Grade 8. Here is how those teachers responded to the same Net Promoter Score question.

We’re very proud of those results and want to share some of the labor and love we think they represent. So, periodically, we’re going to give you folks a look inside our digital mathematics playbook.

Our lesson “Robots” (use it for free!) is based on IM’s lesson “What a Point in a Scatter Plot Means.” Here’s what that means.

Desmosification #1: We use “progressive disclosure” to give students concrete experiences in math before abstract ones.

Here is how the lesson starts in the paper Illustrative Mathematics materials.

Math curricula often move students quickly to numerical precision before students have had a chance to experience mathematics in a more concrete, intuitive form first. That’s often a liability with paper. You need to put math in all of its forms on the same page.

With the digital medium, we’re able to ask students questions about the graph without numbers first, questions like, What do you notice and wonder here? and then later introduce numerical precision. This invites more learners to the mathematics.

Desmosification #2: We connect the concrete and abstract representations.

All too often, computer-based math—even other computer-based adaptations of Illustrative Mathematics—fails to take advantage of what makes computers special. Sometimes they offer the same paper material only in a digital worksheet or in digital presentation slides. Other times they use a dynamic medium only to evaluate students, to tell them that their ideas are right or wrong.

Meanwhile, we have seen over and over again the power of computers to connect concrete and abstract representations of mathematics, helping students understand both.

In the paper version of Illustrative Mathematics, the point (36, 82) just sits there, unchanging. In our adaptation, students move the point and make sense of a changing robot.

Desmosification #3: We give students interpretive feedback.

With paper-based math, students often don’t get timely feedback on their thinking at all.

With some computer-based math, students get immediate feedback, but it’s evaluative, a right/wrong judgment that isn’t very helpful for learning.

With the Desmos adaptation of Illustrative Mathematics, we give students interpretive feedback, showing them a) the robots they created with their points and b) how those robots compare to the robots we asked them to create. They can learn, change their work, and try again.

Desmosification #4: We support student creativity and connection.

We loved this question from the original Illustrative Mathematics lesson, which asks students to “tell the story” of a point. What a fantastic way to connect concrete and abstract representations!

Using the digital medium, we decided to a) let students choose from several contexts, b) invite students to share their stories with one another, and c) ask them to participate in one another’s story.

Students can choose from eight data sets.

They add a new point.

They tell a story about the point. Then, they submit the data set, their point, and their story into the “Class Gallery.”

Students then work on one another’s stories, trying to match a point to their classmate’s story before seeing their classmate’s responses. This a) gives students interesting practice and repetition and b) helps them understand that they can be the authors of math problems just as much as grown-ups can.

What Did Teachers Think?

Super funny student quote that I repeated in front of the whole class after screen 1. “Look! I made a really tall cyclops!” I asked students why it looked that way when dragging the point to where he did. Good discussion.

I think students (including the inclusion students) were able to make good realizations and had good comments with the notice and wonders. Being able to see the robot grow when you check your work, it was awesome to see / hear the students ooing and ahhing. The challenges are definitely a game changer–as expected. I was able to see the students write some pretty amazing questions, allowing them to be super creative.

My students are understanding the points better than they did on the paper/pencil Illustrative Mathematics work last year.

The animated robots kept students engaged. The diversity in topics for the challenge activity gave different students different access points.

My students kept saying how much they loved this lesson. With remote learning, this was a great way to introduce scatter plots.

Behind the Scenes

Desmos lesson developer Lisa Bejarano on “robot eye distance”:

I loved the idea that each point was connected to a unique individual, and knew I wanted to leverage our interpretive feedback to help students make sense of the meaning of each point. I started brainstorming more concrete variables to put on the axes that would intuitively connect to horizontal and vertical changes. Height seemed a pretty obvious choice on the y-axis. For the x-axis, I really wanted students to have a chance to consider what it would mean if the point was on the y-axis and x=0. I initially considered body width, but decided it was not a great option, because if the width was zero, the robot would disappear. After many brainstorming calls with colleagues, we decided to use eye distance because we could visually communicate what an eye distance equal to zero would mean in the context.

Shout Outs

Aside from Illustrative Mathematics and Open Up Resources, of course, we have to shout out Malcolm Swan and the Shell Centre’s Language of Functions and Graphs. Nearly 40 years old and still dazzling with tasks like this.

What’s Next?

Invite your students to play with Robots!
Get activities like this every day in our core middle school math curriculum.
Join me on Monday, Sept. 14 at 4PM Pacific to participate in Robots as a student.

Retiring Support for Internet Explorer

desmos — Wed, 01 Jul 2020 00:00:00 +0000

After July 31, 2020, Desmos’s tools and activities will no longer support Internet Explorer. If you’re using Internet Explorer, we recommend switching to Microsoft Edge, Chrome, or Firefox.

Why this change? Three reasons.

Microsoft recommends it!
While Internet Explorer is still being maintained, it’s no longer being actively developed. This means that Internet Explorer users are already not benefiting from the additional development that browser makers have invested over the last few years.
We have new features that we want to add, which rely on consistent browser implementation and standards. Part of the joy of building software for the web is that we can continually add new capabilities as browsers and devices evolve.

We try to balance our goal of continually improving our tools with our goal of supporting every user across different browsers and devices. We don’t make the decision to stop supporting a browser lightly. In this case, we believe that the time has come to thank Internet Explorer for its service and bid it farewell.

Welcoming Districts and Schools to the Desmos 2020-21 Middle School Math Program

desmos — Tue, 09 Jun 2020 00:00:00 +0000

In January, we announced our core middle school math program, which pairs the open-source middle school curriculum from OpenUp Resources/Illustrative Mathematics with powerful technology, humanizing pedagogy, and intuitive design from Desmos.

We were extremely grateful to receive interest from thousands of sites and teachers. In order to provide the best possible support for as many partners as possible, we’ve decided to limit participation this year to a small set of applicants.

We looked for partners who had:

Communities of teachers—people who love supporting one another and learning together.
A dedicated teacher-supporter at the district level who understands our vision for connected and creative mathematics.
A record of perseverance and problem-solving, both of which are necessary in a best-case school year, and especially necessary in this time of school closure.
Demographic diversity, particularly with respect to student race and gender so we can understand how to include and support students who have historically been excluded and undersupported.

We are excited to announce our partners for the upcoming school year.*

Acton-Boxborough Regional School District
Amesbury Middle School
Baltimore County Public Schools
Belmont-Redwood Shores School District
Bowling Green Independent School District
Braintree Public Schools
Brightworks
Brookline Public Schools
Berwyn South School District 100
Caesar Rodney School District
Calamus-Wheatland Community School District
Cedar Rapids Community School District
Chiefess Kamakahelei Middle School
Dayton Regional STEM School
Eagle County Schools
East Hartford Public Schools
East Sac County Schools
Evanston/Skokie School District 65
Evergreen Public Schools
Grand Prairie Independent School District
High Tech High
Holy Family Catholic Schools
Inland Lakes Schools
Iowa School for the Deaf
Lewiston Independent School District
Long Beach Public Schools
Midway Independent School District
Midwest Regional ESC
Milton Public Schools
Monroe Township Public Schools
Naugatuck Public Schools
New Hanover County Schools
Northside Independent School District
Oakland Unified School District
Parkway School District
Patterson Joint Unified School District
PS/IS 288 The Shirley Tanyhill School
Riverdale Kingsbridge Academy
Rocky Hill Public School
Springfield Public School District
St. Charles Community Unit School District 303
Sunnyvale School District
Temecula Valley Unified School District
Teton County School District #1
Tolland Public Schools
Warren County Public Schools
West Chester Area School District
William M. Meredith School

* Don’t worry if you’ve been accepted to this program and your site is not listed here—there may still be some remaining administrative tasks to finalize.

We expect to expand this program in 2021–2022 with the inclusion of Grade 6 curriculum. To stay up to date as we plan our 2021-2022 program, sign up for updates: