## 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!

## 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.

How to Integrate Which One Doesn’t Belong? in your classroom: My favorite part about this site is that there are multiple answers for each set. Students can see how perspective and which attributes you are looking at can change the answer. The site is a great catalyst for critical thinking and problem solving in math (or any) class. Put a problem set up on a projector as a math class starter and ask your students to independently choose their answer and be ready to justify it. Then, as a class, discuss answers. After students have done this once, challenge them to find as many possible answers as they can independently before sharing responses. This site would be a great tie-in with the humanities to discuss perspective and vantage point. Even in something that feels as static as math, perspective can actually make any problem quite dynamic.

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.

## 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!

How to integrate Woot Math into your classroom: To begin with Woot Math, decide how you will use it in your classroom. Do all of your students have access to a technology device? Do you have a bank of devices that they can rotate through? Do you have a projector/interactive whiteboard? If you are using Woot Math with limited technology access, beginning with the Interactive Problem Bank is best. Here you can quickly access thousands of hands-on fraction and decimal problems for students to work through together. You can project the problems on a whiteboard or use an interactive whiteboard. Problems can be selected by topic or standard and then by model type. Students can either work together in community solving problems, or as a center in a math rotation. If you have better access to technology, and students can work independently on a device, the Adaptive Practice is the place to start. Here you can print out student login cards, assign an initial topic, and the program will adaptively generate and assess thousands of interactive problems. This is also the place where you can track student progress and understanding through concepts and skills. The visual examples and leading through problems is fantastic, it is truly an engaging process for students to learn with! This is the best way (in my humble opinion) to use Woot Math, because it allows students to work in exactly the way they need to increase understanding and build a solid foundation of understanding. Be sure to go through Woot Math independently of your students to truly appreciate the interactive learning modules and visual representation of concepts…they are brilliant!

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

## 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!

## Post-it Plus: Digitize your Post-it Notes and take brainstorming with you!

What it is: Post-it Notes are among my very favorite office supplies. I use them for brainstorming, my calendar, to jot down reminders, and to collect the brilliant ideas that happen in the middle of the night. At Anastasis, we use Post It Notes constantly to help organize brainstorm sessions and lines of inquiry during an inquiry block. As you might imagine, we use TONS of Post-it Notes during any given week! They are hard not to love, brightly colored squares just waiting to collect brilliance and post it for the world to see. Recently, I stumbled on an app, Post-it Plus, that takes my love of sticky notes to a whole new level! Post-it Plus is an app that lets you snap pictures of a Post-it note brainstorm session, and then arrange, refine, and organize the notes on a virtual board. The newly organized digital board can then be shared out.  Students can capture 50 Post-it notes at a time and collect and combine ideas from multiple categories. Notes can be organized on a grid, or free form any way that you would like. Boards can be shared via email, PowerPoint, Excel, Dropbox, by PDF, etc. After the work has been shared, anyone can help contribute and arrange the notes to create a great idea! The app is free and optimized for iOS 8.

How to integrate Post-it Plus in your classroom: Post-it Plus is a great way for students to capture their brainstorms and group work so that they can take it with them.

Collaboratively brainstorm with your class or explore some different lines of inquiry and record each new thought on a sticky note. Students can then take a picture of the group on their iOS devices and arrange and group in a way that best makes sense to them. Now all of your students can manipulate the sticky notes individually and bring their learning with them.

As students are writing (either creative or informational), they can write each new idea or paragraph on a different sticky note. Then they can arrange their notes and take a picture. As they create different arrangements, they can use the digital version to compare with the original to make decisions about the flow of their writing.

Teach young students? Write down the different parts of a story (beginning, middle, supporting details, end) on several sticky notes. Students can snap a picture of the notes and practice sequencing the story. Each student has the digital version, so each can practice ordering and you can quickly assess their understanding.

Post-it Plus could also be used for phonics work. Write phonemes on individual sticky notes and ask students to take pictures of each phoneme with the app. Then call out words that students can create with their phonemes in the app.

Post-it Plus is also fantastic for students learning math processes (order of operations anyone?) and algebraic thinking. Write each part of an equation down and students can manipulate the digital sticky notes to show process.

Students can also use Post-it Plus to categorize and organize ideas and events in history, science, government, etc. How We Got to Now anyone? 🙂

Tips: I can’t tell you how many conferences I’ve been to that we used Sticky notes to brainstorm ideas. Post-it Plus makes it easy to take that thinking and learning with you in a very practical form that you can interact with later! Speaking of conferences, the 5 Sigma Edu Conference is a great one to test out this app!

## Math Class Needs a Makeover: videos, inquiry, math stories and more

What it is:  I’ve had the great fortune of time to go through my Google Reader favorites this week as I prepare for the shutdown (still bitter about that!).  The unexpected benefit I’ve had from Google Reader’s demise? The forced opportunity to go back through and be reminded of some of the truly amazing people and resources in education.  Dan Meyer is one of my all time favorite math geniuses.  He reminds us that math is more than computation, it is a frame of mind and an outlook on the world.  If your math program isn’t that…it is time to change!  As I went back through the resources of Dan’s that I had tagged, I re-watched his TEDx Talk: Math Class Needs a Makeover.  If you haven’t seen this TED Talk, or haven’t watched it in a while…now is the time.  I’ve embedded the talk above for your viewing pleasure…you don’t even have to go anywhere!  If you have watched it recently, be a friend and share it with someone else.

Dan also has some other really useful mathspiration.  His blog, dy/dan, is a source of math prompts and discussions that will have you thinking beyond computation. 101Questions is a project that encourages students to think about math through photo prompts and inquiry.  Graphing Stories is STINKING fantastic, Dan offers a printout for your students, they can then watch any video and graph the story.  AWESOME describes this resource. Three Act Math is a curricula that Dan developed, click on the links within the doc to get to the resources.  Again…AWESOME. Geometry curricula offers you Dan’s handouts, pdfs, powerpoint and keynote presentations.  Algebra curricula offers the same.

THANK YOU Dan for sharing your passion for mathematics, your inspiration for those of us who aren’t as naturally inclined to geek out about math, and for your openness of resources.

How to integrate Dan Meyer’s awesomeness into the classroom:  Dan makes it really easy for you to integrate his methods into your classroom.  Everything you need from inspiration, to mathematical story sets, to curricula materials is available.  If you teach math, the obvious place to start is with the type of math that you teach.  Dan’s resources are mostly intended for high school students use.  However, as I looked through his resources again, I think they could be appropriate for students in elementary school as well.

101Questions is a great way to have your kids enter an inquiry mindset as they approach math.  These are photos that ask your students what the first thing that comes to mind is.  Students can type in their answer and get a new prompt.  These would be a great way to start your class using a projector or interactive whiteboard.  Have your class inquire and come up with questions together.  Students can also do this as an independent activity and then share their questions with other students.

Graphing Stories speaks for itself.  Again, it is geared toward secondary students, but I think that given enough support, primary students would really enjoy engaging math this way too.  (Sometimes we don’t give students enough credit for where an interest can take their thinking.  Case in point: Anastasis 2nd and 3rd graders who know Fibonacci inside and out. Normally you wouldn’t see the concept until high school or later.)

The Three Act Math is also a favorite of mine.  Use Dan’s three acts, or use his as inspiration for creating your own!

Dan’s resources hit on every level of Bloom’s Taxonomy…that alone is good reason to stop reading this and go on your own exploration!

Tips: Dan is great to follow on Twitter...a constant stream of 140 character mathspiration!

## Dragon Box: a game for students to learn algebra…secretly

What it is: Dragon Box has got to be the most brilliant game for teaching a new concept I have seen in a LONG time.  I am SO impressed with this app, I can’t say enough about it!  This is a math game that teaches algebra without you really realizing that it is a math game teaching you algebra.  It feels more like a logic card game than anything else.  There are 200 puzzles that secretly teach kids to solve equations.  They unlock each level by figuring out how to balance an equation (you have to isolate the dragon on one side of the board in order for him to emerge). After each level, he grows a little until he is full-grown.  Students learn concepts such as elimination, fractions and isolating variables throughout the game.  This is the best math app I’ve seen. It is NOT a drill/skill type app. It is actually teaching students to think like mathematicians instead of just asking them to solve a bunch of problems.

How to integrate Dragon Box+ into the classroom: I cannot say enough about this app.  The way that it gets kids thinking is completely fantastic.  Students learn algebra and how to think like mathematicians without even realizing it.  The game gives minimal direction, and invites students to explore and try new things to isolate the dragon.  The best way to use this app in this classroom: just let students start playing with it!  I love that this app could be played by students as young as six years old successfully, but also used by high school students where they would get those “aha” moments of understanding how algebra works that they may have missed along the way.

Put your students in teams, or let them explore Dragon Box independently.  Dragon Box allows for multiple logins, so you could even use it as a classroom center rotation.

Because you can download Dragon Box on multiple device types, you could even use this on a classroom computer connected to an interactive whiteboard or a projector and take turns playing as a class.  There are plenty of levels for every child to participate multiple times.

Price: \$5.99

Devices: Compatible with iPhone 3GS, iPhone 4, iPhone 4s, iPhone 5, iPod Touch (3rd-5th generation) and iPad. Requires iOS4.0 or later

Tips:  Dragon Box is also available on the Mac App Store, Google Play, PC shop, Amazon Appstore for Android, and Windows Store.  Even if you don’t have iDevices, your students can play with Dragon Box!

I’ve been nominated for a Bammy Award for Educational Blogger.  I’d appreciate your vote to help spread the word about iLearn Technology.  Vote here.  Thank you for your continued support!!

What it is: Math Trail is a neat way for students to explore virtual trails that lead to a variety of locations connected by a theme.  Along the way, students put their math and geography skills to the test.  The trail list currently has eight trails to choose from, with varying degrees of difficulty.  Students can choose an Olympic trail, 7 Wonders, Towers, Rivers, Eminent Mathematicians, Famous Islands, Cricket or Ramanujan trails. To begin, students choose a trail and then click on the “start” button.  A list of instructions pops up.  In each trail, math questions are hidden around the map.  Students zoom in within the map to the location suggested by the clue.  There are little balloons located all over the map.  If students struggle to find the location, they can click the “show location” button at the bottom.  At the bottom of the page, there is a white box that holds clues.  When students reach a location, they are given a math challenge to complete.  At each location, students have the opportunity to earn a gold coin.

How to integrate Math Trail into the classroom:  I like the integration of history, geography, social studies and math in this game.  Students aren’t just going through a series of multiple choice math problems.  Instead, students are set forth on a journey and asked to locate various places according to the clues given.  This means that as their math skills are put to the test, they are exercising that geography muscle as well!  I don’t know what it is about maps, but they are just fun to explore.  The treasure hunt nature of Math Trail keeps it interesting.  Students get math practice and geography practice along the way.  This beats the practice set that is in the textbook!

I found some of the “low” and “medium” level questions to be challenging.  Before playing with students, go through the trails to find the challenge that is most appropriate for your students.  This could mean that you have students playing different trails.  The low end seems to be 6th-7th grade math with the Medium being middle school and the High being high school.

These trails are great for exploring on their own, but you could have students go through a trail together using the interactive whiteboard.  Give each student an opportunity help the class search for the location (the class can help or bring in a Google search for particularly difficult clues).  Each student can work out the math problem on their own and then come to a consensus of which answer to play in the game.

Tips: I wish that Math Trail provided a cheat sheet of all of questions in the game so that teachers could choose a trail for their students at-a-glance.  If anyone has done this, let us know where to find it!

## Media 4 Math: Math in the News

What it is: Media 4 Math: Math in the News helps students view current events through the “prism of mathematics.”  Every week features a new story that makes headlines and the underlying mathematical story gets extracted.  The Math in the News site is a little bit confusing to navigate at first (it isn’t really clear where to find each issue of Math in the News).  Scroll down to see an archive of stories.  Each entry has a Slideshare version of the presentation, a YouTube version or the Math in the News app version.  These presentations are full lessons with embedded background knowledge articles and videos, data  sets, current event explanations and a walk through of how to solve.

In addition to Math in the News, Media 4 Math also has Math Tutorials, Promethean Flipcharts, Powerpoint slideshows, Math Labs, Print Resources, a Video Gallery, Math Solvers and more.  I really like the Math Solvers, students can choose a problem type, input their own data and see a breakdown of how to solve the problem.  The Math Labs include PDF worksheets and YouTube Videos that lead them through real-math problem sets.

How to integrate Media 4 Math: Math in the News into the classroom: Media 4 Math: Math in the News is a fantastic way to help your students make the connection between the upper-level math they are learning and life. I’m fairly certain that every math teacher in history has heard “what are we ever going to use this for?”  This site helps students not only see that math is everywhere, but also walks them through how to think mathematically.  There are plenty of resources that walk students through common mathematical functions.  This site is a great supplement to any math curriculum!

With new content weekly, your curriculum will be fresh and relevant!  Share Math in the News using an interactive whiteboard or projector-connected computer, as a math center on classroom computers, individually with laptops or iPads, etc.   Flip your math class and have students explore a Math Tutorial to prepare them for the next day of learning.  Then they can test a few scenarios in Math Solvers and come up with their own explanation of the concept.  In class, students can work with you to solidify and practice the learning.

Tips: Sign up for the free weekly newsletter to have Math in the News delivered right to your inbox.  Do you have a classroom iPad?  Math in the News now has an app!