7 Math Manipulatives for your Digital Toolkit

Happy New Year… seven FREE math apps for your digital toolkit!! 
Geoboard by The Math Learning Center (a nonprofit organization dedicated to K – 12 education) is a FREE app that turns your iPhone/iPad into a virtual geoboard. Geoboards can be used as tools to teach mathematical concepts such as polygons, perimeter, area, line segments, angles, congruent shapes, symmetry, fractions, etc. Shapes are created by stretching bands on the geoboard’s pegs. There are 5 colors of bands in the iPhone version and 8 in the iPad version. There is also a tool to fill in shapes. On the iPad version, you can switch from the standard 25 peg board to a 150 peg board to create more complex shapes. This is a great app with the potential to be used in so many ways.

Geoboard, by The Math Learning Center - Clarity Innovations

FREE for the iPad, Virtual Manipulatives contains math manipulatives for teaching fractions, decimals, and percents. Included are tiles/circles divided into halves, thirds, fourth, fifths, sixths, eighths, tenths, and 12ths AND their corresponding decimals and percentages! The manipulatives are color coded across the settings so that 1/2 is blue as is .50 and 50%. Kids drag tile pieces onto the work area to compare fractions/decimals/percentages. In the settings you can change from tiles to circles, make the pieces transparent, and hide the numbers on the pieces. Completed work can be easily saved to photos. Finding equivalent fractions has never been so slick – WOW!!

Common Core Standards met:

  • 3.NF.3 – Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
  • 4.NF.1 – Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Virtual Manipulatives! - ABCya.com

equivalent fractions

From the National Council of Teachers of Mathematics comes a FREE app called Equivalent Fractions. Kids create equivalent fractions by dividing and shading squares or circles. Circles can be divided into 24ths. Squares can be divided into 144ths. In the play mode, a fraction is shown and kids must create 2 additional fractions that are equivalent. All 3 fractions must have different denominators. The app also places the fractions on a number line – a great visual for comparing! There is also a “build your own” mode which would be fabulous to use for guided exploration & practice. Kids could also use this section as a virtual manipulative when working independently. This app is an excellent resource for the classroom !!

Common Core Standards met:

  • 3.NF.3 – Explain equivalence of fractions and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Equivalent Fractions - National Council of Teachers of Mathematics

counting board

Another FREE app is Counting Board HD, a colorful number grid that can be used to help kids learn basic number concepts. The app is advertised as being suitable for 2 to 4 year olds but it can also used with older students. I frequently used number grids with third graders. Number grids help kids see patterns and visualize math concepts. With younger children, the app can be used for counting to 100 – by ones, fives, tens. Younger kids can also learn basic addition and subtraction by using the app to count up or count back. With older kids, number grids can be used to teach: greater than and less than, how to find missing addends, place value concepts, skip counting, and more! The app can be used with the numbers showing or hidden and the pronunciation can be on or off. The app simple to use, visually appealing, and useful for so many math lessons. I love this app! It’s so much easier than dragging out the laminated number grids and counters. 🙂

Common Core Standards met:

  • K.CC.1. Count to 100 by ones and by tens.
  • K.CC.2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
  • 1.NBT.5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
  • 1.NBT.6. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
  • 3.OA. 9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

Download link: https://itunes.apple.com/us/app/counting-board/id450751745?mt=8&uo=4

number lineNumber Line, by the Math Learning Center is a fantastic FREE app that will help kids visualize number patterns and understand number operations. The app is well-designed with several useful features. The number line can be set by ones, twos, fives, tens, twenty-fives, and hundreds. It can also be customized to show multiples of any whole number from 1 to 100. This feature is perfect for skip counting and/or for visualizing multiplication. The app permits kids to add and manipulate forward & backward jumps – a great feature for teaching addition & subtraction. This feature also helps kids visualize multiplication as repeated addition of the same number and division as repeated subtraction of the same number. Teachers are able to hide or reveal numbers on the number line. This feature can be used to challenge kids to apply what they know in order to figure out the missing number/numbers. Teachers can also use this feature to teach kids how to solve more difficult patterns that are missing several numbers; such as 4, __, __, 16.  Kids can use the drawing tools to show what they know. They can write equations and expressions with the text tool. They can screen shot their work and use it as an exit slip after a lesson. Add this one to your virtual toolkit today – “seeing math” helps kids understand it. 🙂

Download Link: https://itunes.apple.com/us/app/number-line-by-math-learning/id751816884?mt=8&uo=4


Free Protractor from Pongo Soft is another tool that you may want to add to your digital toolbox. The angle can be set in two ways: by touching the pointer or by entering the angle on a keypad. Once the angle has been set, it can be locked to avoid movement of the pointer when taking readings. Kids can also use this tool to see how many degrees are in a straight angle and a right angle or to discover the difference between an acute angle and an obtuse angle. They can easily see what combinations of angles are equal to a straight angle.  Since the app is free, there is some advertising across the top. Check out this FREE educational app for your geometry students.

Download link: https://itunes.apple.com/us/app/free-protractor/id555590467?mt=8&uo=4

number pieces

FREE educational app – Number Pieces from Math Learning Center. This educational app is the digital version of place value manipulatives, hands-on tools used to help students understand place value. Using the place value models within this app, kids can visualize the process of adding and subtracting ones, tens, and hundreds. The app has a function that permits kids to break apart pieces or join them together. This feature is fabulous for kids who need concrete examples. The app also includes expanding edge pieces which can be used to introduce arrays. Other features of the app include: three colors for identifying groups, drawing tools for labeling, a text tool for writing number sentences, zooming & scrolling for larger numbers. Thanks to the Math Learning Center, teachers & their students have another great app to add to their digital toolkits!

Common Core Standards:

  • 1.NBT.6. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
  • 2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens — called a “hundred.” b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

Download link: https://itunes.apple.com/us/app/number-pieces-by-math-learning/id605433778?mt=8&uo=4


Santa’s Home

Santa's home
“He sees you when you’re sleeping. He knows when you’re awake.”
FREE again, just in time for the start of the Christmas season. Now you can see what Santa is doing with Santa’s Home. The app is a “LIVE” feed of Santa’s house – the bedroom, the kitchen, the living room, his office/workshop, and the outside grounds. Kids can keep track of what Santa is doing up at the North Pole. I checked in on Santa a few times – first he was in the kitchen washing his dishes, then he was on the computer checking his list, and a little after 11 PM he was in bed snoring. The app even displays the correct date and time to make it seem more realistic. The app also gives adults the option of can subscribing to Santa’s newsletter. Adults can also help kids send Santa one of their drawings that he will display in his workshop. Super cute!!
Teachers – This would be a fun one to use for creative writing!! It would also be fun for teaching prediction. :)

gFlash+ Flashcards & Tests

GFlash+ Flashcards & Tests is currently FREE. This educational app allows you to create, download, and manipulate flashcards for everything that you can imagine. You can create your cards in a Google docs spreadsheet and download it into the app or you can create your cards within the app. There is no limit on how many card sets you can have. Card sets created by leading educational publishers (Kaplan, Barron’s, McGraw-Hill, Wiley Publishing, etc.) are available as in-app purchases. You can also download and share sets from the gWhiz catalog. You must have an active wireless connection to download card sets or to use card sets with videos.

Once you have your cards ready, studying becomes simple. First choose box configuration or classic configuration. Both configurations keep track of the cards that are known & unknown. The box configuration has an unknown box, a known box, and a mastered box. As you go through the cards, the app keeps track of how many cards are in each box. In the classic mode, there is line of small cards on the right side of the screen. If you know a card, the little card turns green and if you do not know it, it turns read. It’s a nice visual for younger kids. A study score (percentage) is also given. Teachers of younger students could create the cards in Google docs for kids to download and study. This app is such a valuable tool for students of all ages to use in so many ways. I wish it would have been available when my kids were studying for the SAT and GRE. 🙂

Highly recommended!

gFlash+ Flashcards & Tests - gWhiz, LLC




Happy Birthday Wonderopolis – Here’s to 5 great years of wondering. 🙂

FREE – Wonderopolis, a fabulous educational app. Now you can explore Wonderopolis (the website) with your mobile device.

Wonderopolis (Wonderopolis | Where the Wonders of Learning Never Cease) is a fantastic website that provides a daily Wonder of the Day®.  A fun & intriguing question is featured every day. The website/app includes a written explanation of the answer, vocabulary words, and a gallery of images & videos – all to foster learning and inspire curiosity about the Wonder of the Day®. Other daily features include a “Try It Out” section which suggests activities based on the day’s question, a “Still Wondering” section which gives additional/related information, and a quiz. There is even a section for teachers/parents called the “Educator Sandbox” with additional resources and opportunities to connect with the Wonderopolis community. It’s such a fascinating and wonderful resource – I enjoy reading it myself!

Using this website/app would be a fabulous addition to a daily classroom routine. Kids could read (or listen to) the daily Wonder of the Day® as part of their independent work time. They could journal about what they learned and/or what they are still wondering about. A class discussion could be scheduled for later. What a great way to encourage THINKING! Wonderopolis is a fabulous resource to ignite the natural curiosity and imagination of kids!

Download link: https://itunes.apple.com/us/app/wonderopolis/id505247028?mt=8&uo=4


Smart Whiteboard HD

super white boardFREE – Smart Whiteboard HD, an educational app that is super simple to use! One finger writes, 2 fingers erase, 3 fingers clears all. Press the save button or shake your device to save an image. Writing can be done in black, blue, or red with 3 width choices. The app also includes a simple voice recorder. Just press record, talk, stop & name your file, and it is saved to a list. You can then email your recording if you wish to share it. Teachers can get rid of their classroom whiteboards, markers, and erasers! Have kids show their work, explain their thoughts, etc. with this simple educational app!

Smart White Board HD - Pad read


This Day in History

This Day in History

One of my favorite FREE resources…

WORLD BOOK  – This Day in History for iPad is a great FREE resource for the classroom. Historical events for the day are displayed on a calendar page. You can click on links to related media such as articles, photos/illustrations, music, speeches and more! When I was teaching, I had students  do “morning work” (correct punctuation, capitalization, & spelling in two sentences) while I took attendance, did lunch count, etc. This educational app would have been perfect for that daily assignment because I always used information about something interesting that happened that day. After correcting the sentences, the kids and I would discuss the history of that day. I was always amazed at how well kids retained what we had discussed during the opening minutes of every day. Throughout the year they would often remark, “We learned about that in our morning work.” You may want to try making this educational app part of your classroom’s morning routine. 🙂

WORLD BOOK - This Day in History for iPad - Software MacKiev



ClassDojo is a FREE & fabulous tool that helps improve classroom behaviors. Rewarding good behavior in real-time is easy – all it takes is a click. To use ClassDojo, you only need one device (computer, smart phone, a laptop, or a tablet) and an internet connection. It is very easy to set up. Each student on your class list is assigned a cute, monster-like avatar. Kids earn points for positive behaviors and lose points for negative behaviors. ClassDojo is also fully customizable so you can delete behaviors from the original list and/or add your own behaviors. As you use it, it automatically logs any data that you input. This data can be used to generate behavior reports to share with parents and administrators. How awesome is that? You can go into a meeting/conference with reports in hand! And now, parents can check online to see what kind of day their child is having.

And, ClassDojo just keeps getting better. FREE messaging has been added to the app. Teachers can now send “direct” messages and/or photos to individual parents or they can “broadcast” a message to all parents. Sending reminders, assignments, homework, permission slips, etc. just became easier! Another newer addition to ClassDojo the option of creating groups. Teachers can now put students into groups – making it simple to award table points, team points etc. Fostering a collaborative classroom culture is simple with ClassDojo.

If I was still in the classroom, I would enter my class list twice – once for data on work/study habits and the other for data on behaviors. I would make my habits/behaviors match exactly what was on my report cards. Then as I used the app, I would also be gathering data for my report cards. At the end of the grading period, I would just print out the date and enter it on the report cards – how easy!  I would also have the data (in a printed report) to be able to back up any grade on the card.  “As you can see Mrs. Doe, Jane only turned in her homework 56% of the time.”  Instant data would also be available for the RTI process, IEPs or any other team meeting on a child. What a powerful tool for teachers! An educational app that has the ability to positively impact the learning environment – LOVE it!!

Check out the website for more information: www.classdojo.com

ClassDojo - Class Twist Inc