## DragonBox Math Apps: Teaching students to think like mathematicians

What it is: I adore the DragonBox math apps! I was first introduced to DragonBox through their Algebra app. The app takes away all math anxiety by teaching algebraic concepts without numbers or algorithms. It is genius! You can read my review of that app here. DragonBox Numbers is for kids who are new to numbers, counting, addition, and subtraction. DragonBox BIG Numbers is the next level app of Dragon Box Numbers. As they play, children learn about how big numbers work, and how to perform long addition and subtraction. In DragonBox Elements, students will secretly learn geometry. By playing 100+ puzzles, kids will gain a deep understanding of the logic of geometry. As they play, students will actually be recreating the mathematical proofs that define geometry. What I love about the DragonBox suite of math games is that they are unlike any other math apps. You won’t find mindless repetitions and quizzes of math facts, instead, these games help teach students how to think like mathematicians. This is learning math through exploration.

How to integrate Dragon Box math apps into your classroom: The DragonBox math apps take advantage of a student’s innate curiosity through play and exploration of math concepts. Each game engages students through exploration, reflection, and application.  If you have a 1:1 iPad classroom, use these apps daily! Students can play a game, and then come together as a class to reflect and write down the rules they have learned in that “chapter.” Then, take an equation from the game and solve it on paper. See if students can connect the cards and rules of the game to the equations on paper. Solve the equations using strategies and rules from the game.

In a one or two device classroom, play DragonBox as a class by connecting your device to a projector. Explore the rules together and let students take turns being in charge of a chapter. Review rules and make connections as a class. Set up DragonBox as a math center that students can visit in a rotation where one center is interacting with the game, the next is an opportunity to record rules learned and reflect, and the last is application of the rules to an equation.

Be sure to check out the DragonBox for educators where you can download teachers guides and printable resources for each game in the DragonBox math suite. You’ll also find a great “rules” guide for the algebra and geometry games.

These are seriously my favorite math apps of all time! They encourage kids who can think and apply like mathematicians rather than kids who simply memorize a formula. DragonBox creates a deep understanding of mathematical concepts and number relationships.

Tips: While the DragonBox suite of math apps aren’t free, you can purchase them at a deep discount for educational institutions and bulk purchases. Teachers, you can get access for free to make sure that the apps are right before committing to a purchase for your students. You can also purchase apps in bundles.

## Mathigon: engage, play, and explore math

What it is: Today I was working on our inquiry block framework for the 2017/2018 school year and, as often happens with inquiry, fell down a wonderful rabbit hole that led me to this site. Mathigon is a fantastic *newish* math site (it’s still being built and added to) that brings textbooks to life. I know you’ve probably seen this claim before, but this is unlike the other online interactive textbooks I’ve seen. It’s more…alive. It’s like a personalized tutor, combined with story, and exploration. Really, textbook is the wrong word, because this is something totally new. A chat bot tutor makes Mathigon like having an additional team of teachers in the room, ready to answer questions and support your learners in real time. Real life application and narrative is part of the Mathigon DNA. This means that beyond learning the “rules” of math, learners are actually invited to engage the concepts, play with them, explore them in context, and find out what other concepts they are linked to. Rather than a linear approach, Mathigon lets students explore math in a more organic way through interest, linked ideas/concepts, and in a ‘down the rabbit hole’ approach. There are very few math sites that I’ve come across that truly support an inquiry approach to learning math, Mathigon is one such site.

How to integrate Mathigon into your classroom:  There are several ways to use Mathigon. Students can get a personalized math curriculum that adapts to them and offers recommendations based on what they are interested in and their understanding of different concepts. They can begin from several places: exploring the applications of math in every day life, the link between math and origami, Eureka Magazine (published by Cambridge University), through problems and puzzles, through fractal fiction, or through courses for grades 6-college.

The Treasure Hunt is a complete PDF Kit that can be downloaded and printed out. Split your students into teams and send them on an epic math treasure hunt through your school (available in primary and secondary levels) where each of the clues leads them to another.

Fractal fiction is particularly cool because it lets students explore mathematical concepts through interactive narrative of popular films including Alice in Wonderland, Oceans 11, and Harry Potter (the latter two are coming soon). You really have to go experience these to really understand the brilliance of how Mathigon has combined story with math exploration.  From the site: “The key to successful teaching is captivating storytelling – through real life applications, curious examples, historic background, or even fictional characters. These interactive slideshows combine an engaging narrative with beautiful graphics – explaining mathematical ideas in the context of popular stories and movies. They can be watched individually or be presented in classrooms.”

I cannot say enough about how impressed I am with the vastness of what this site brings to the classroom. Even if you don’t have the capacity for each of your students to have an account with Mathigon, the site can be easily adapted for the one computer classroom (as a center activity). Much of the content could also be explored as a whole class with a projector-connected computer.

Tips: I’ve found that really well done content for grades 6-12 (and beyond) in math to be severely lacking. This is a welcome addition to the math teachers tool box of resources!

## Photomath: Scan math problems for immediate step-by-step instructions

What it is: Photomath is an app available on the App Store and Google Play. With Photomath, students can scan a math problem and learn how to solve it with step by step instructions and an answer. The app includes a photo calculator (take a photo of a math problem, it gets solved in an instant), handwriting recognition, step-by-step instructions, and a smart calculator. For added features, Photomath+ includes complete step-by-step instructions, colorful explanations of the math, and extra math knowledge.

How to integrate Photomath into the classroom: On the surface, the Photomath app might look like the ultimate way for students to “cheat” their learning. After all, they can snap a picture of any math problem, get step-by-step “show your work” instructions, and the answer in an instant. When I look at Photomath, I see each device with the app as another teacher in the classroom. When students get stuck, or need to check their work/understanding, not only do they have access to the answer, but also to the process. They can see exactly where a mistake has been made, and even get an explanation about why the process is what it is. It also changes the math class from being procedures-based, and empowers teachers and students to engage math from a problem-based, practical aspect. Since students have help with the procedure of how to solve a problem, they can engage math as a mathematician, identifying the problem that needs to be solved, using number sense to understand the problem, and with Photomath ensuring that the procedure they apply has been solved correctly. It definitely could change the goal of your math class, rather than just finding the answer, assignments may become more practical application in nature.

Consider using Photomath as a check-in station where students can go through their own work and identify where they may need support. The app offers immediate step-by-step guidance, when students don’t understand the guidance, you know instantly that more teaching is needed.

Tips: If your school has homework, this would be a great app to recommend to parents! When they get stumped, the app can be a sanity saver.

## Which One Doesn’t Belong? K-12 Critical Thinking and Problem Solving

What it is: Which One Doesn’t Belong? is a site I learned about from @TeamBaldwin today. This math site is for students of all ages and challenges them to look at a set of four images and determine which image doesn’t belong and justify their answer. The best part of this site is that each problem has multiple correct responses that can be justified. Students have to think through the differences that they see and then make logical decisions and be able to explain it to others. There are three different categories for Which One Doesn’t Belong including: Shapes, Numbers, Graphs and Equations.

Yesterday, @TeamBaldwin used the site this way:

This is a class of kindergarten and first grade students! @michellek107 will be blogging more about the class experience on the class blog, Architects of Wonder if you’d like to read more.

Tips: The graphs and equations appear quite challenging, but even young students can begin making observations about the types of graphs that could lead to some higher-level math discussions.

## YouCubed: Think like a Mathematician

What it is: Do you know about Stanford’s YouCubed? If you are a math teacher (and even if you aren’t) you need to know about this awesome resource! It is packed full of goodness for teachers and parents alike. Fantastic (and approachable) articles about brain science, mathematical thinking, and mindset. Outstanding ideas that you can use RIGHT NOW! Links to really wonderful math apps and games, videos and radio shows, tasks (also known as mathematical brain teasers), and visual mathematics resources. My favorite portion of YouCubed is the Week of iMath. There are 5 days of lessons, each one comes with a lesson plan, video, and list of materials needed.

How to integrate YouCubed into your classroom: There are SO many resources that can transform your classroom! I love the articles and research as references to send parents throughout the year. These are also great for reading with your older students who may assume that math is not their gig. The articles and research included show that math is for all of us, but our mindset may need a bit of a shift! What I love about the articles is the way they quickly dispel so many myths about maths, I guarantee you’ve heard all of this from parents over the years and now you have research to share to help them understand the truth about mathematical thinking and brain science.

The links to math games and apps is really helpful. You’ll find some old favorites, but likely be introduced to something new to use with your class. One of my very favorites listed is an app called Dragon Box…it is truly so brilliant for teaching students algebraic concepts and math thinking without any numbers or mathematical symbols at all!

The iMath section gives you a wonderful inspirational math lesson for each day of the week. These lessons go far beyond your typical math drill/skill/learn-a-new-formula. Instead, they are all about helping your students develop a growth mindset when it comes to math, and arming them with the necessary tools to think like a mathematician. Depth of learning! The approach in each lesson is playful and inquiry driven, it encourages risk taking and mistake making as they work with numbers, patterns, and relationships between concepts. I cannot say enough about this section of YouCubed! Each lesson is broken down into grade ranges so that no matter what age you teach, you can find the fit for your class.

Tips: This is an ideal site to start the year with, and then use as a reference all year long! You should also be sure to check out Jo Boaler’s books and articles. If you’ve ever felt under prepared/qualified to teach math, Jo will help you shift your own mindset and equip you to teach math like a master!

What it is: Find Your Pi Day is a simple site from Wolfram where students can type in any number (like a birth date) and the site will tell you where that number falls within the Pi sequence. All dates fall somewhere within the first 10 million digits in the sequence. The place in the sequence is depicted by a spiral that goes in and out to display the beginnings and ends of such long digit sequences.

How to integrate Find Your Pi Day in your classroom: Find Your Pi Day is a neat site to generate conversation and inquiry into Pi. This is a fantastic place to begin exploration of Pi. Students can learn about the mathematical sequence and the science of Pi in this background Wolfram blog post.

Tips: For some extra fun and discussion, have a look at Vi Hart’s lighthearted “rants” about Pi.

## Woot Math: Adaptive learning for fractions and decimals

What it is: Woot Math uses adaptive technology to personalize the math learning experience in new ways for 3rd-6th grade students. With a focus on fractions and decimals, Woot Math allows students many inroads to understanding. Flexible implementation options mean that Woot Math can be used in any classroom configuration whether it be 1:1 devices, shared devices, whole-class, or as intervention. The Woot Math system works on the web, iPads, or Chromebooks seamlessly…it truly is a great option for any classroom! It is super user-friendly, and gives teachers the ability to customize for each student in the class as a starting point. Woot Math is adaptive, as students use it, it gets “smart” and creates learning pathways based on the specific needs of the student. Beginning with foundational rational math concepts, Woot Math makes these necessary foundational skills accessible for all students. It is like having a personal tutor sitting beside them as they work through new learning. If a student doesn’t understand a problem, the program adapts to approach the learning in a new way. The illustration of concepts is brilliant! Woot Math gives students a solid understanding of fractions, laying the necessary ground work for algebra, geometry, physics, chemistry, and statistics. Sign up TODAY, Woot Math is totally free for the 2015-2016 school year!

Hat Tip to @yourkidsteacher for sharing this awesome resource with me!

## World Education Games 2015! Math, Literacy, Science

What it is: You guys, the World Education Games is back again, taking place around the world October 13-15, 2015! More than 5 million students from over 200 countries and territories will participate in the games for 2015. This is an exciting online challenge for students around the world. The competition begins tomorrow and continues through October 15. The World Education Games includes World Literacy Day, World Math Day (which has been around since the first World Education Games), and World Science Day. Just by participating through the answering of questions, students will be earning UNICEF points which are converted into money that goes directly toward supporting UNICEF education programs where class and school resources are desperately needed.

In World Literacy Day, students will enter the Spellodrome to compete with students from around the world. A sentence will be read aloud and it is the student’s job to spell the missing word.

For World Maths Day, students will enter Mathletics, to compete with students around the world. This is a place for students to practice and work on math fluency speed and accuracy.

World Science Day will bring students to the IntoScience dashboard where students will test their knowledge with a panel containing 16 question boxes, split into four categories of science. Each question is worth one, two or thee points based on the difficulty. In this game, you must answer faster than your opponents.

How to Integrate World Education Games into your classroom: I love the World Education Games for the fun way that it helps students (k-12) practice facts in math, spelling, and science knowledge. This makes drill/skill infinitely more fun. Students can practice with their own classmates and with those around the world. When I was still in the classroom, World Math Day was a time of year that students looked forward to. They ASKED for homework (can I keep playing at home?). True story. The kids loved finding out which country they would be paired with. It was always very motivating to see someone half way around the world playing the same game at the same time. My students worked hard to see if they could be paired with someone on every continent before the Games were over. Keep track of the countries  that your students get matched with on a Google Map or on the printable maps offered on the World Education Games Website.

For at least one week, ditch the worksheets (or do it like we do at Anastasis and ditch them every day!) and practice math facts and spelling with fun games instead. This is a few days of fun, friendly competition for your students. The adjacent learning opportunities during the World Education Games is great (similar to what the Olympic games brings!). Geography, math, spelling, and science investigations are the obvious adjacent possible. This year, UNICEF is partnering in on the Games and the points that your students earn goes toward a very worthy cause, for every point your students earn, money is being donated to UNICEF for education. In addition to the drill/skill, your students can inquire into the Power of One (as our students at Anastasis Academy are doing), or can inquire into organizations that make a difference in the world (like UNICEF) and explore the social issues that these types of organizations are working to solve.

## SumBlox: explore number relationships through visual/kinesthetic play

** This is not a sponsored post, I’m just super excited about this product and can’t wait to see what our students do with it!

What it is: Why yes, this is a technology blog. But no, this manipulative is not a technology product. I’m writing about SumBlox here anyway because technology led to the happy discovery of SumBlox and is a great reminder of why it is important to be a connected educator! I learned about SumBlox just a few weeks ago on Twitter as a share from ISTE from @michellek107 and @sumblox. This also isn’t a free tool (like I normally share), but I’m already so impressed by the brilliance of this tool, that I’m sharing it anyway!

SumBlox are a wooden block set of numbers 1-10. What makes those blocks and numbers super amazing: each block size corresponds to the number that it represents. (1 being the smallest and 10 the biggest). Even more super amazing, when the blocks are stacked, they represent the equivalent number. For example, when the 2 and 3 blocks are stacked, they are the same height as a 5 block! GENIUS!! These blocks are a visual and kinesthetic representation of our base-ten number system.

I purchased the Educational Set for our classrooms which comes with 100 solid hardwood blocks including: Thirty 1 blocks; twelve 2 blocks; eight each of the 3, 4, 5, 6, 7, 8, and 9 blocks; two 10 blocks and four teaching manuals. The purchase was right around the \$300 mark with free shipping and a 10% discount with the code “sumfun.”

How to use SumBlox in the classroom: These blocks allow students to visually represent and discover math relationships. Students can stack blocks to explore and visualize addition equations, if the stacks are the same height, they also have equivalent values. Students can stack multiples of a number to represent abstract math concepts like multiplication grouping or addens of ten. Students can also explore the concept of fractions and of the mathematics behind adding fractions with different denominators by stacking and scaling fractions. SumBlox also are a fantastic introduction to algebra concepts.

The educational set comes with 4 guides that lead you (the teacher) through exercises and lessons to do with your students. While these are extremely well done, because we are inquiry based, my excitement comes in seeing how students will explore these independently first. I’m excited to see students discover the number/size relationships and number patterns.

At Anastasis, we have a 1:1 iPad program. I anticipate that students will use these blocks for stop-motion animation projects as they explore (iMotion HD is the app they use), capture their discoveries of number relationships in their eportfolio (we use Evernote), and even in Explain Everything videos.

Tips: If you are an administrator purchasing these for your school, go ahead and purchase a few of the educator kits. I only purchased one and am already going back to order one for each classroom. These are going to be popular!

## Monster Math: Build Mental Math Skills and Fact Fluency

******Update July 25, 2016: Monster Math Now available on Android! Check it out here!*******

What it is: Monster Math is an app that helps build kids mental math skills through a fun game. When students begin their journey in Monster Math, they are introduced to monster Maxx who is working to save his friend Dextra. What makes Monster Math different from most math practice apps, is the narrative and journey that they go on that keeps them wanting to play. Each “level” has them working to defeat a monster with math. This sends them to the Hall of Math where they get challenged to collect candies to defeat a monster. The challenge is to collect only the candies that are equal to the target number. As they play the game, students build fluency in addition, subtraction, multiplication, and division. Choosing the correct equations earns candies which are then used to defeat the other monsters. Additional challenge is thrown into the game throughout and soon students are not only challenged to find equations to match the target number, but also to do it before the other monster gets to it.

How to integrate Monster Math in your classroom: Monster Math is a great way for students who are building math fact fluency to practice their math facts. It is especially great for students at the 3rd-4th grade level who have learned addition, subtraction, multiplication, and division since the levels default to combine all 4. You can go in and toggle the skills that you want kids to practice. Monster Math is a fantastic alternative to flash cards for building mental math and is sure to be a favorite for kids who are working on mental math skills.

Use Monster Math as a center activity in the one or two device classroom. Students can each create their own account so that they can save their individual progress. You can go into the app and choose the skills to practice so that it is more tailored to each students needs. Building mental math and fact fluency is always important…this is one I like to keep ongoing every week regardless of what else students are working on. I’ve found the best way to build this fluency is to keep the practice regular.

Monster Math is a great app for students with individual devices. This allows them to track their own progress at home or school. Monster Math is a great app to recommend to parents who are looking for alternatives to flash card practice. Monster Math definitely takes the battle out of math practice because the storyline keeps it feeling fresh and challenging.

Teachers get reporting on where students are doing well, what skills they are struggling with, and what skills haven’t been started yet.

Tips: Monster Math is available for the iPhone and iPad. There is a free version and a \$2.99 paid version of the app.

Save