Be amazed on the equations that were created to design graphics on this free online graphing calculator! Desmos set out to re-imagine the graphing calculator from the ground up, building on the best technologies available. They are driven by a few core beliefs:

> "every student deserves access to the best tools for learning > it's a travesty that educational tools have fallen so far behind as technology in general has catapulted forward > learning is a process of exploration and discovery, not a series of answers > everyone can learn and enjoy math, given the right environment > math is beautiful and surprisingly fun."

Do you want to find the best math resources to support your universally-designed lessons and student learning? Explore the data base of resources aligned to the CCSS, save your them online in MY Toolkit and particpate in the communities.

Mathlanding was developed by team of math experts who reviewed and evaluated each Mathlanding resource and collection to populate the site with thousands of engaging, high-quality lessons, interactives, games, activities, videos and articles. A handy advanced search feature makes it easy to explore and retrieve the right resources for your needs.

Sumdog offers over 100 K-8 math activities that teachers can assign to students to improve math fact fluency.

"In these activities, Sumdog learns about you as you work, and adapts its questions to suit." Here are the details about this feature:

> If you keep getting the questions right, they'll get harder automatically.

> If you have problems with a topic, Sumdog will help you practice by asking more questions. This means that you can use these activities with students of varying abilities, safe in the knowledge that each receives questions suited to his or her needs.

"The Equation Editor is an ideal tool for students with dysgraphia, allowing them to write math equations on the computer. The Equation Editor is built right into Microsoft Word and is free."

Why UDL?

The equation editor supports the UDL principle: multiple means of expression.

"With Sketchpad™, you can give your students a tangible, visual way to explore and understand core concepts—from numbers and operations, algebraic thinking, and geometry and measurement in elementary and middle school to algebra, geometry, trigonometry, precalculus, and calculus in high school and college. Concepts that students frequently find difficult become very clear when they see visual representations on the screen and interact with them using Sketchpad.

Why UDL?

> Geometer's Sketchpad allows students to visually represent math concepts and ideas in powerful ways and supports the notion of multiple means of representation.

> Geometer's Sketchpad allows students to demonstrate their knowledge using the computer ans supports the notion of multiple means of expression."

Google Sketch-up is an online program where you can create 3D models. There is a searchable repository, Google 3D Warehouse where you can explore models.

Why UDL?

>"Google SketchUp 7 is a great tool for students to help them to better visualize spatial concepts and supports multiple means of representation.

> Google SketchUp is also ideal for students who may have poor fine motor skills but need an alternative way to demonstrate their understanding of a concept or an idea and supports the notion of multiple means of expression."

Shuttle Mission Math App is well-designed with visual representation for solving algebraic problems. Here is what makes this a great app:

> Shuttle Mission Math introduces students to the fundamentals of algebraic thinking. The goal at each of the 24 levels is to find the weight of the Zogs.

> Students are given the weight of groups of Zogs. The challenge is to find their individual weights.

> To accomplish this, students must apply ideas such as equality, proportional reasoning, variables, and combining groups of objects.

> Each puzzle is a visual representation of one or more algebra problems.

> Many of the puzzles can be solved in more than one way. Students can explore various problem solving approaches without consequence.

Vi Hart has introduced a whole new way to understand and express mathematical concepts with doodling, food, balloons, paper instruments and through music. She calls herself a Mathemusician. She now works at Khan Academy.

In the video series, Vi outlines complex math concepts in a creative and easy to understand way. Make sure to check out her blog and the other creative ways for understanding math.

Nearly every math concept has explanations written out, one or two short video tutorials, and interactive applets (written with GeoGebra). Use this site as your math resource to help you learn math.

"Here's how to use this site:

> Choose a math topic from the list on the left. > Click the specific math concept you are looking for or just browse through the "book". > Read the examples and then watch the math video tutorial. > Play with the interactive math applet to further deepen your understanding."

Why UDL?: In general it offers multiple means of representation and engagement.

The Educreations iPad app launched in December as a free download in the App Store. This app transforms your iPad into an interactive whiteboard that records a teacher’s voice and handwriting as they explain a concept or work through an example problem. Teachers can add photos to their lessons from the iPad’s Photo Library or camera and they can animate the photos by tapping and dragging. Finished lessons can be hosted on educreations.com, where they can be shared privately with a class of students or publicly with everyone.

It’s the only app out of there that allows you to move and resize photos while you’re recording to create animations. Although other apps have the whiteboard feature, Educreations lets you create multiple pages, so you don’t have to erase the screen to give yourself more room.

Why UDL?

> Multiple Means of Representation: Use of photos, illustrations, audio or animations to present information in different ways.

> Multiple Means of Engagement: Teachers can present information with different mediums (visual, audio, animations) in addition to making the file accessible online.

> Multiple Means of Expression: Students have the ability to express what they know through the range of tools with multiple slides included.

Check out this web site for really engaging your middle and high school students in algebra!!

Get The Math uses videos and online interactive challenges from the music, fashion and video game industries to help students realize the importance of understanding algebra concepts and have fun while they learn. Help in solving problems is available if the students need it. The site also has support for teachers with lesson objectives, learning materials, and samples of evaluation questions.

Getting students to WANT to learn algebra is always difficult, but Get The Math does it by making algebra applicable to things kids like!

Why UDL? This site provides multiple means to engage students in algebra.

Math Pickle brings challenges and support to every learner in the math class. Dr. Gordon Hamilton proposes that elementary math be abolished and to replace it with problem solving that he sees is at the heart of quality math education. With the use of video, problems are proposed for every grade level along with a set of teacher resources.

Here is a testimonial that describes what students experienced with math with Dr. Gord.

"Dr. Gord worked full time with us for three years. In reflecting on what he brought to our school, I think of the joy the students experienced in working with him. He met groups of students with a wide range of abilities, but he never “watered down” a single challenging thought. Struggling students thrived and those who wanted the most difficult challenges were not disappointed. He teaches the way children learn – through inquiry and tenacious, self-directed thinking! When it comes to innovative approaches to teaching and learning, Dr. Gord is exemplary."

Doreen Grey Research & Development Master’s Academy and College

"Taking math education into the 21st century, and bringing my students and visionary teachers along for the ride!"

This blog from Sue Glascoe includes a variety of tools and apps that empowers the learner to understand math. These examples that Sue illustrates and describes here exemplify the application of the 3 UDL principles: multiple means of represenation, expression and engagement.

Share this far and wide to teachers of math everywhere!

The Talking Calculator app can be used to support math comprehension, assist students with math-related learning difficulties, as well as students with visual challenges. The audio can also reinforce student comprehension of numeric elements.

"Ideal for the vision impaired, blind, or anyone looking for an easy to read calculator, with optional speech. This calculator speaks answers, button names and formulas aloud with its built in voice, or with a custom voice recorded directly into the iPad, iPhone or iPod Touch!"

WebMath has been around for over a decade and it is a site that contains explanations and tools for learning and practicing dozens of math-related exercises, from simple functions to complex calculus. Composed of forms to fill-in it returns analysis of a problem and in many cases provides a step-by-step solution. This can support students in understanding math processes.

The only downside is that kids could potentially put in problems and get their answers (and work shown) without actually doing the legwork.

Parent or teacher involvement is key when kids use this site for homework.

BrainingCamp includes math interactives for all grade levels that supports the UDL principles of multiple means of representation and engagement and is aligned to State and CCSS. Each includes:

> Lessons using visual models and audio narration

> Interactive to explore and experiment with math concepts

> Application to apply and connect these math concepts to the real world

A Vanderbilt grad student, Jenna Gorlewicz, wants the visually impaired to be able to use one of their strongest senses--touch--to better visualize algebra, geometry, and more. 18 months ago she decided to develop a tablet app that uses haptic (or tactile) technology to help the visually impaired learn math and other subjects that are visually rich.

"Gorlewicz sees haptic tech being an important educational tool for a wide variety of students, given that it appeals to visual, auditory, and kinesthetic learners. In addition to those who are completely blind and partially visually impaired, it may also benefit those who are deaf and can take advantage of the haptic and visual feedback, as well as children with autistic and attention deficit disorders who interact more easily with tablets and tactile feedback."

Wolfram Alpha is one of the best kept secrets in education! It is a new search engine that can solve any type of mathematical equation. This is a essential tool for all learners to help them solve and check their work. Results of these problems are shown in different ways so that every learner can understand.

Why UDL?

Students could use Wolfram site to gain a better understanding of various math concepts and supports the notion of multiple means of representation.

Brightstorm has over 2,500 free math videos from Pre-Algebra through Calculus that offer actual teachers explaining and demonstrating math concepts. What is unique about Brightstorm is that with each concept, a set of 2-3 problems that demonstrates the concept is included.

Why UDL? This type of online tool offers multiple means of representation and engagement of math concepts that students often miss. Having the problems explained furthers the understanding for many students who need to see and hear several examples.

One of the first studies on a math app was conducted by USC Professor Michelle Riconscente on Motion Math. The results indicated that game play can boost kids’ confidence in and enthusiasm for academic subject matter. Here is the research design and some of the findings.

"The study evaluated whether playing Motion Math led to increases in children’s fractions knowledge and attitudes. Over 120 participants played the game for 20 minutes daily for five days, for a total of 1 hour and forty minutes of game play. Among the main findings were that fractions knowledge increased an average of 15%, and participants gained confidence in their fractions ability and reported liking fractions more after playing the game.

With hundreds of educational iPad apps on the market, it is important to know whether they help children learn, and whether iPad apps like Motion Math also contribute to children’s positive attitudes toward academic subject matter. Though much more research is needed to test learning apps, and to discover ways to use them most effectively with a broad range of learners, this study marks an important step toward testing educational technologies with stringent research designs.

In less than two hours of game play distributed over five days, the app shifted the needle on participants’ understanding of a topic that has long eluded most learners."

Math Open Reference provides interactive simulations that can be used for teaching Plane Geometry, Coordinate Geometry and Trigonometry. Because the illustrations are interactive and animated, the teacher can use this effectively in teaching all students with this library of 'digital manipulatives'. At the same time, students could use these interactive simulations to gain a better understanding of geometry concepts, vocabulary and topics. Most importantly. the interactive tools permit better visualization for learners that have challenges in this area.

Why UDL? (From the UDL Center)

Math Open Reference is organized into pages that highlight the critical features of geometry concepts. Topics are separated to clarify distinct features. Critical terms are linked directly to a glossary so as not to hinder the viewer based on lack of vocabulary knowledge.

UDL principle: Multiple Means of Representation - Checkpoint 2.5: Illustrate through multiple media

A great website that offers different simulations that can be used to illustrate geometric ideas. The website is organized by grade so that teachers can differentiate and use to teach geometry at all levels of education.

The Mind Institute has taken a spatial temporal approach with ST Math and the results have been outstanding for a broad range of learners in trials. This is an example of a math program that was universally-designed that reached the maximum amount of learners. Thank you Mind Institute!

"MIND Research Institute, an southern California nonprofit, developed an innovative way to teach math—and it works. Trials involving almost 60,000 students indicate that it typically doubles math gains.

They use visual games that all involve moving a penguin named Jiji across the screen. It’s all done without a word of instruction. The visual approach works for visual learners, students new to English, or students experiencing reading difficulties—in other words, it works for most kids.

MIND notes, that “Schools below 50% proficiency to begin with have averaged 15 to 20 point gains in proficiency within two years.” And remember, students in these trials just use the software twice a week for a bout 45 minutes."

"Mathematics 4.0 enables the user to “do” math on the computer. This is helpful for anyone who has difficulty using pencil and paper. In the context of UDL (Universal Design for Learning) the program is also helpful because it offers powerful visual alternatives for representing information to learners, as well as options for action and expression. For example, the graphing calculator can animate graphsof 2D and 3D equations. Below is a list of what Microsoft says the program will do:

The Microsoft Mathematics Add-in can help you with the following tasks:

> Compute standard mathematical functions, such as roots and logarithms > Compute trigonometric functions, such as sine and cosine > Find derivatives and integrals, limits, and sums and products of series > Perform matrix operations, such as inverses, addition, and multiplication > Perform operations on complex numbers > Plot 2-D graphs in Cartesian and polar coordinates > Plot 3-D graphs in Cartesian, cylindrical, and spherical coordinates > Solve equations and inequalities > Calculate statistical functions, such as mode and variance, on lists of numbers > Factor polynomials or integers > Simplify or expand algebraic expressions"

Thank you Paul for sharing this information on MS Math 4.0 and how it can be used to support UDL principles.

From CAST's UDL Spotlight, Shodor Interactivate is featured. Learn how this virtual manipulative tool for math supports these two UDL principles: multiple means of representation and multiple means of action and engagement.

"The Interactivate website has over 150 java-based interactive tools and activities (aka, applets) categorized by topic, that allow students to explore mathematics. It’s a free (donations accepted) resource developed and maintained by Shodor Educational Foundation and it’s as useful for teachers as it is engaging for students. All the tools and activities have explanations of how to use them in the classroom and most are aligned with common math texts. All are aligned to the National Council of Teachers of Mathematics (NCTM) standards."

Discover how math can be taught without words in this TED talk. Be inspired by the fact that Matthew is dyslexic and because of it, he discovered how to teach math to diverse learners like himself.

"In school, the dominant way of conveying ideas is through words. Words can be great barriers to learning. Matthew Petersen shows and explains how we can learn without words.

Matthew Peterson, Ph.D., is Co-Founder, Senior Institute Scientist, and Chief Technical Officer of the MIND Research Institute. He is the creator of MIND's Math instructional software that teaches math to students using a unique non-language-based approach. Matthew was recently featured on Discovery Channel's "Profile Series." His focus is on developing math learning environments that initially convey sophisticated concepts visually, enabling students to gain a solid conceptual understanding of mathematics regardless of language proficiency. Matthew's cutting-edge teaching methods are currently benefiting over 300,000 students. He is the author of "MIND's Algebra Readiness" textbook, adopted in California in 2008, in addition to other technical and scientific publications."

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