*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.

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.

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.

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 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

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

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