*The following applications contain more advanced math activities.*

**Most Highly Recommended**

Math Doodles: Children can play four different math games. (1) The “Sums Stacker” game has children move blocks around to make stacks. The sum of the blocks on each stack must match the number below. (2) The “Connect Sums” game shows a screen with many tiles on it. Children select two or more numbers that, if added together, would equal the number at the top of the screen. (3) The “Unknown Square” game is more puzzle-like. Numbers are presented in a three-by-three grid. At the ends of each row and each column, the sum of the numbers is given. Children have to fill in the missing number(s) in the grid. (4) The “Splat GoRound” game has children figure out how far around a clock-like circle to make a fly swatter move in order to swat the fly. For example, to move the swatter directly across the circle, you would have to select 6 hours. Other options for what to show on the circle are: minutes, angles, fractions, percents, and radians. Each game has many options. The types of items given can be: blocks with dots, hands with fingers up, “holes”, dots inside “ten frames”, tally marks, number words, and many others, including numbers in many languages. This app is well conceived, beautifully designed, and engaging. It requires children to think abstractly. Its activities are pretty challenging for most young children, so you may want to wait until closer to first grade. But preschoolers and kindergartners with an outstanding aptitude for math can benefit greatly from this app. The “Sums Stacker” and “Connect Sums” games are probably the best starting points.

Number Pieces and Number Pieces Basic: These two apps are very open ended. Children can drag single squares, groups of 10 squares, and groups of 100 squares onto the screen. They can be rotated, the colors can be changed, and the groups can be broken apart (i.e., from 100 into 10s, or from 10 into 1s). There is also a writing tool that children can use to write numbers or draw. There is only one difference between the two apps: the Number Pieces app also has a ruler that is 10 blocks long and can can be moved around to help children see how many blocks they have. These are great, simple apps that can be used with students at various skill levels and for a variety of types of learning. You could use blocks to solve addition and subtraction problems, or to learn about place value in two and three-digit numbers. However, the app does not have any bells or whistles. It is a tool that you will have to teach a child to use, and it will not likely keep a child engaged without some external support and/or added context. I have one constructive criticism. I wish there was a button that would save a images of what children create.

Motion Math: Hungry Fish: A fish with a number on it swims around the screen. Bubbles with numbers come out and children have to find or make the number on the fish. They can push the bubbles together to form new numbers. In the “Addition” game, children push number bubbles together to form new bubbles representing the sums of those numbers. In the “Subtraction” games, some bubbles have numbers with a minus in front of them. When those bubbles are combined with others, it subtracts the number. This is a great app. Children love it and it supports math skills in a creative way. However, it does not do much to help with the concepts of addition and subtraction, so I suggest using it with children who have a pretty strong grasp of those concepts. The difficulty level advances after children complete a level. I wish there were a way to freeze the game at the simplest levels, so children can get lots of practice with the simplest arithmetic. There is a very similar app called Motion Math: Hungry Guppy, which I also recommended.

Battle Station: A number line is presented with a starting number, an ending number, the number half way between them, and perhaps other numbers. Then a target number is shown on the bottom of the screen. Children have to touch the number line at the approximate location of the target number. A missile is dropped at the chosen location which, when correct, lands on a monster that had been hiding there. This app is fun for young children who are ready for a bit of a challenge. However, the levels become difficult rather quickly. Younger children will likely benefit mainly from the first few levels.

Symmetry Shuffle: Children must drag, flip, and rotate complicated shapes to match the shapes on a grid. The size of the grid, the type of shape, and the difficulty level can all be easily adjusted from the home screen. This app’s concept is simple, its design is beautiful, and it provides endless exercise for spatial reasoning skills. It’s pretty challenging, however, even for adults. My only constructive criticism is that it could benefit children of broader skill levels if simpler shapes were included as additional options.

Todo Number Matrix: Children are presented a matrix (a grid) with some kind of information on the top row and some kind of information on the side row. Some of the places in each matrix have already been filled in. They must figure out the meaning of those hints and fill in the rest of the matrix. (This is difficult to describe in words—follow the link and look at some images.) The simplest matrices contain numbers. They get much more complicated, incorporating pictures, shapes, addition and subtraction problems, multiplication problems, and fractions. This app is a great way to foster some analytical thinking. Most young children will be able to handle a few of the easier matrices, but from that point on they will probably need support. My only criticism is that it’s too easy to guess with this app. The correct answers snap into place. In fact, if you’re trying to drag something to an incorrect spot but inadvertently pass over the correct spot, it will snap into that correct spot. There’s no incentive for getting the correct answer without mistakes. Considering how challenging some of the matrices are, the temptation to guess is quite significant.

Math Word Problems – Addition and Subtraction for Kindergarten and First Grade: A simple addition or subtraction word problem is presented at the top of the screen. If you touch the speaker icon, the problem is read aloud. Below are different tools children can use to find the solution: there is a small space where they can draw what’s happening; there’s a number line; there’s a ten frame (two rows of five boxes) in which the objects from the story problem will appear if touched; and there’s an area where children can write out the problem. Answers are selected at the bottom right side of the screen. Although this app doesn’t have the most attractive design or the most user-friendly interface, I find it very useful. Children have the freedom to choose how they’d like to solve problems. As such, it’s a more open app than many other math apps. However, because there are so many tools squeezed onto the screen, they are all a little cramped for space. Children can become frustrated by how little room they have to work with.

Number Line: This is a very useful, simple app that helps children learn to work with numbers using a number line. A number line is presented, with integers or with multiples of 2, 5, 10, 25, or 100 (depending on the selected setting). Bars with arrows can be added to the line that show a leap between two numbers. Numbers can be shown or hidden both on the number line and on the leaps. A typing function allows children to type numbers and functions. A drawing function allows them to draw or write on the screen. This open-ended app is a great tool for helping children better understand numbers in the context of a number line. It can be used to solve addition and subtraction problems in a way that helps clarify the relationship between those concepts. However, most children will need support using it well, at least at first, and it is probably best used in conjunction with some other materials.

Math Bingo: Children are given a five-by-five bingo card with numbers on it. At the top of the screen, there is a problem. Children have to find the answer on their bingo card. The type of problem is adjustable (addition, subtraction, multiplication, or division), as is the difficulty level (easy, medium, hard). This is a very simple but very well-designed app. It provides good practice with addition and subtraction, and it will be useful later on, when children are ready for multiplication and division. Children are not rewarded for guessing randomly in this app. They get only one chance to find the correct answer to each problem. If they choose incorrectly, a different problem comes up.

Magic 10: Children find and touch two number cards, the sum of which is ten. The game can be played with one player or two players, and the cards can show numbers, numbers with stars, or numbers with stars inside of a tens box. This is a simple app that fosters a very specific but important skill. It’s not terribly exciting, but some students become pretty engaged. The two-player feature is nice, as it allows young children to engage in a more social experience while using tablet technology, and they learn from each other, of course.

Montessori 1st Operations: There are many different games in this app, divided into three different types: addition, subtraction, and evens/odds/halves/doubles. (1) In the main addition and subtraction sections, problems are presented with cubes next to each number. Children select from the answers below, which also have the appropriate number of cubes next to them. (2) Two more games have children move little dots to solve the addition and subtraction problems. (3) A third pair of games simply present a problem for which children find the correct answer in one of the moving bubbles. (4) The main odd/even section has children move the correct number of little balls into place under each number. When the balls are in place, the app tells whether the number is even or odd. A second game in this same section has children slice groups into two. The odd numbers it does not allow you to break into two (it says, “Three is odd”), but when children slice an even number, it tells what half of that number is and then doubles that half to return it to the original number. (5) Another game shows children bubbles with numbers and asks them to either pop the odds or the evens. (6) A third evens/odds game shows a number at the top of the screen. Children have to make that number by popping the numbered bubbles below, which break into half the numerical value when popped. (7) One final game asks children to create half of a number on each side of a line. This is a good app. The main addition and subtraction games are not my favorite. Children will often try to count the blocks to find the answers, but when they touch a group of blocks the app says the number aloud. I prefer the games that have children children move dots to solve problems. There are many different ways for children to learn about evens vs. odd and halves, which is valuable.

Pet Bingo: Children play bingo with math problems. A problem appears on the left side of the screen (addition, subtraction, multiplication, or division, depending on the type of game selected). The solution to the problem must be found on the bingo card to the right. There are three levels of difficulty to choose from. This is a very well-designed app. The concept is simple, but it is attractive and engaging. However, even the easiest addition and subtraction levels are challenging for almost all young children. This is an app that parents might want to try out with bright and curious youngsters. If it is too tough, then tuck it away and save it for later; it will still be valuable in a couple of years.

**Somewhat Recommended**

Math Concentration: Children play “Concentration” (a.k.a. “Memory”) with various math activities. At the simplest levels, they must match cards with the same number, which can be represented by a number of dots, a number of squares filled in on a “Ten Frame” (two rows of five squares), or the numbers, or number words. You can also play with complicated shapes, multiplication problems, fractions, and percents. The options allow you to with the cards hidden or shown, and you can play with one player or two players. This is a pretty good, simple app that will present some pretty big challenges for most young children, although it’s not all that engaging. I like to use the number setting with two players and the cards showing.

Word Problems: Children are given the text of a story problem at the top of the screen. If they touch the text, the problem is read aloud in a computer voice. They can solve the problem by dragging shapes onto the screen, or by drawing on a small white board. The choices (0-10) are then selected at the bottom of the screen. Each of the following types of story problems can be turned on or off: (X + Y = ?); (X + ? + Y); (? + X = Y); (X – Y = ?); (X – ? = Y); (? – X = Y). This is a good app to use to help introduce young children to story problems. It doesn’t look great or sound great, but its basic functions are well designed. The computer voice is hard to understand, so it is probably used best either with adult support, or with children who can read most of the words. Also, children tend to guess randomly with this app. They can guess as many times as they wish, and they can do so very quickly, which is much easier than solving problems. Adult interaction helps motivate children to figure out the answers with the tools provided.

Math Facts Express Card Matching Game: This is a memory game, wherein children must match problem cards (e.g., 4+3) to number cards (e.g., 7). The number of cards on the screen can be adjusted to six, twelve, or eighteen. You can play alone, with a friend in two-player mode, or against the computer. This is a simple but solid app for helping children memorize basic math facts. I would suggest that it is best suited for children who already have a solid grasp of the concepts of addition and subtraction, because it does not do anything to teach the meaning of those concepts. As a note, the basic app includes single-digit addition and subtraction. Those are the only two that I use with young students, so I have had no need for making the in-app purchases which open up more challenging math skill levels.

Math Series: Children see a series of numbers with one missing. They select the correct missing number from four choices on the bottom of the screen. The type of groups included can be adjusted. Numbers can be in increasing and/or decreasing order, the maximum can be 20, 50, or 100, and numbers can go in sequential order, or they can get larger or smaller in increments of 2, 3, 4, or 5. This is a simple app that requires some pretty complex mathematical thinking. Children have to figure out what kind of sequence is being presented (i.e., what the difference is between each number), and figure out what the missing number would be based upon that. A larger degree of customizability would greatly benefit this app. For example, I would like to be able to include sets that count by twos, but there is no way to do that without also including sets that have a difference of four or five between each number.

Everyday Mathematics Addition Top It: This is a game designed for two players, although one child could easily play alone. Two cards with numbers are dealt to each player. Next, children are asked to figure out the “sum” of the two numbers dealt to each player. Then, they have to figure out which of the two sums is larger, or if they are a “tie.” This is a pretty good app. It is a fun game to play with children who have a good understanding of the concept of addition and are able to compare numbers. With some children you may want to have toys or a piece of paper available to help them figure out the sums. I have only two criticisms. First, the word ‘sum’ is not usually a word that we use with young children. I wish it would use language like ‘plus’ or ‘add’ instead. Second, it pretty hard to tell whose turn it is at any given time.

Sushi Monster: Children see a monster with a number in the middle of the screen. Then they are given plates of food with numbers on them. They have to combine plates to make the numbers on the monster. The monster’s number changes each time it eats. There are addition levels and multiplication levels. This is a good app for helping children memorize math facts. However, it does not help teach the concept of addition, so I do not recommend trying it until children have a good grasp of that concept. You should also note that this app becomes pretty challenging pretty quickly. The first level or two are appropriate for some younger children, but anything beyond that may be too challenging for even the brightest young children.

Math Board Addition: Children are given a series of math problems and have to choose the correct answers. As they answer them, their past problems show up on the side of the screen. The types of problems and size of numbers can be adjusted. This is a good, simple app for practicing math facts. But its goal is to get children to memorize basic math functions, so it will not help much with the underlying concepts. For that reason, I suggest holding off on using this type of app with most children at least until they have mastered the concepts of addition and subtraction.

Telling Time- Photo Touch: Children see a screen with clocks on it and hear a time. They touch the clock that shows that time. The times included can be adjusted. For example, you can turn on just the times that are on the hour, or you can also include times that are half past the hour, and so on. This is a good simple app for helping children learn how to read clocks. However, children tend to guess randomly with this app. There is no reward for choosing the correct answer in the first or second try, and it is often easier to try all of the options than it is to figure out the answer.

**Not Recommended**

Dexteria Dots: Children see dots on the screen representing numbers. They are told to form a dot of a certain number, which they can do by breaking dots apart, putting them together, or both. The number for each dot is represented by its diameter. In the “Beginner” level, the dots have their number and that number of smaller circles inside of them. In the “Intermediate” level, each dot only has the smaller circles inside, no number. In the “Advanced” level, the dots differ only in diameter and color. In the “Expert” level, the dots are only distinguishable by their diameter. This app is engaging and fun. However, I do not think the way it presents numbers is helpful for young children. The diameter of a circle is not a very intuitive way to understand a number. It has the potential to confuse children on the concepts of size and area. For example, because diameter is the varying factor, the 10 dot has an area that is much more than 10 times the area of the 1 dot. I would suggest that combining lengths of bars or sticks would be a more valuable experience. As it stands, this app is really more like a brain teaser than an activity that fosters important early math skills. If I were to use this app, I would only use the beginner level, so that children can at least practice adding numbers.

Butterfly Math: Children solve different types of math problems by dragging butterflies into cages. For example, if children are given the problem 1+2, then they have to drag three butterflies into the cage after the equals sign and press the “Check” button. There are sections for addition, subtraction, multiplication, division, comparisons (<, =, >), and (a challenging type of) sequencing. This app could help foster some good math skills, but I would not count on it helping much. It is not very well designed. The way that butterflies are dragged into the cages to answer the questions is unnatural. As an example, if children want to use the butterflies to help them solve the problem “6-3”, then they have to drag 6 butterflies into the cage and then take 3 back out. It would make much more sense to have the butterflies up top, available for children to use if they need it, and have them use numbers to complete the problems. For addition problems, I would suggest that there be two cages to put numbers into, so that children can see that there are two numbers being put together. The subtraction problems I think ought to start with butterflies in one cage. Children could then remove the appropriate number.

Math Puppy: There are a few activities in this app, but it is primarily a math bingo game. Children see a problem at the top of the screen and have to select the solution on the bingo card. You can play with addition, subtraction, multiplication, or division problems. Other sections of the app include a “Math Challenge,” which has children select the answers to problems, and a “Math Calculator.” This app could be used to help children with math facts. However, it’s not the best app for what it is, and there are a couple of features that I think could use some improvement. First, the problems are not very prominently shown. It would help if they were more visible. Second, there is a time limit, which cannot be turned off. I would be able to use this app with younger children, in conjunction with manipulative toys to help them find the answers. But the app doesn’t allow enough time for that. Third, the calculator has a glaring omission; negative answers show up without the negative symbol.