*The following applications focus primarily on fostering early math skills such as: counting, number recognition, patterns, number comparisons, basic addition, and basic subtraction.*

**Most Highly Recommended**

The Math Tree: Children are presented with a mix of addition and subtraction problems. For each addition problem, there are birds in the tree (representing the first number in the problem) and some birds on the ground (representing the numbering being added). Children touch the birds to make them fly up into the tree. For subtraction problems, there are fruits in the tree. Children touch the number being subtracted to make those fruits fall down. The app walks children through the steps of addition and subtraction. It reads the problem with them, highlighting each part as it is read, before it offers solutions. This is a great app for introducing children to addition and subtraction. It has an attractive design and it teaches the ideas in a way that help build a strong early understanding of math concepts. Many of its characteristics are well thought out. For example, when children answer incorrectly, it tells them whether the number they chose is too many or too few. However, children who are a little further along with addition and subtraction skills sometimes find this app to be a little too slowly paced. Also, children are a little bit inclined to guess in this app. I wish it would provide some kind of reward for answering correctly in the first or second try.

Montessori Numbers- Math Activities For Kids: This app uses blocks that are grouped as single cubes, lines of 10, and sheets of 100 to help children recognize, find, and create numbers or varying sizes. There are a number of different activities included. In (1) the “1 to 20” and (2) the “Quantity” sections, children move the correct number of blocks up to form the numbers. (3) In the “Numerals” section, children hear a number and have to drag numbers up to form that number. For example, if they hear “38” then they have to drag a 3 into the tens place and an 8 into the ones place. (4) In the “Numerals from Quantity” section, children are given cubes in groups of one, ten, or one hundred. They count how many of each there and drag numbers to fill in the place values accordingly. Each section has three difficulty levels, corresponding to which numbers are included: 1 to 9, 10-99, or 100-999. This is a great app. I recommend it highly. It does a very good job of teaching place value, helping children understand what two and three-digit numbers represent. Many young children are not ready to fully grasp the idea of place values in numbers, but this app does a good job of introducing it. I like the way it says the numbers as they’re being formed. For example, if you drag two groups of ten into the tens box, it will say “20.” Then, if you add a single block to the ones box, it will say “21.” It gives this constant feedback until a child has created the correct number. And if you put ten single blocks into the ones box, it will form a new group of ten and move that group over to the tens section. Moving blocks around is easy and natural. They make a little sound when picked up or let go, which helps children who are still developing one-to-one correspondence.

Todo K-2 Math Practice; There are many games to choose from in this app. For each game, children can write numbers in the answer box (the app recognizes written numbers) or they can drag numbers into the answer box. (1) A “Counting” game shows foods. As children touch the foods to count them, the numbers briefly appear in order and bites are taken out of the foods already touched. (2) A “Tracing” game has children count balls and then follow an arrow to write the corresponding number. (3) A gamed called “Tallies” has children add or take away little characters in order to match the number on the top of the screen. (4) A “Cookies” game presents addition and subtraction problems. There is a brief animation of a hand bringing cookies for the first number in the problem. Then another hand either adds more cookies or takes some away. Children solve the problems with the support of the animations. (5) A game called “Little Farm” practices subtraction-like reasoning without numbers. A number of animals enter a barn. The animals are out of sight once inside the barn. Then some number of animals leaves. Children have to figure out how many animals are still inside of the barn. (6) The “Falling Blocks” game shows children a series of addition and subtraction problems with dots below to help find the answers. (7) The “Quick Facts” game presents addition and subtraction problems without dots for support. (8) The “Equation Maker” game has children put puzzle pieces together. The completed puzzles show addition or subtraction equations with a corresponding number of animals by each number. Additional games have been added regularly with app updates (although with an increase in price, as well). I am a big fan of this app. It has many great features. The counting game does a great job supporting one-to-one correspondence, by having the fruits change when they are touched. The “Cookies” game does a great job of showing children a process for solving addition and subtraction problems, and it does so in quickly enough that children do not spend much time passively watching the animation. The “Little Farm” game offers a remarkably creative way to support simple mental math skills without even presenting numbers. My one criticism is that children can guess as much as they want with this app. I would prefer that solutions be provided after two or three incorrect responses, to discourage random guessing.

Quick Math Jr.: Children are guided through a variety of math activities involving little round creatures. The activities focus on counting, subitizing (knowing how many are in a small group without having to count), quantity matching, number ordering, number writing, and other skills. This is an outstanding app. The characters are cute and engaging, and the educational content is very well thought out. There are a couple of features that I particularly appreciate. There is an activity that has children keep track of how many creatures go into and out of a house, which helps foster very simple mental math. Another nice feature: sometimes, creatures hold hands and move together in groups, which is a great way to teach skip counting and adding small numbers. I have a few constructive criticisms, however. First, this app is not very well suited for classroom use; I can’t control which activities are presented, and it takes far too long to allow each child to start from the beginning. Second, there is music in the intro screen—I wish I could turn it off. Third, there are no voices in the app. While that gives it an international appeal (students who speak any language can learn from it), it’s a missed opportunity for English speakers. Children who don’t recognize all of the numbers don’t get any support.

Monster Squeeze: This is a game designed for two players, though one child could play it just as easily. An octopus comes up with a “secret number” and children take turns trying to guess it by touching a number on a number line. When they guess, the octopus tells them if the secret number is larger or smaller, and it shrinks the number line accordingly, leaving fewer options. You can choose from the following number lines: 0 to 10, 5 to 15, 10 to 20, 15 to 25, 20 to 30, or all of them. This is a great app. It is fun, and it helps children learn how to compare numbers. My only criticism is that I wish there was a way to play with a broader range of numbers. If it was possible to play with numbers 0 to 100, then this app would present more of a challenge to students who are a bit further along.

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.

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, if you will, 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. And 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, as with the two “Number Pieces” apps reviewed above (which were made be the same developers), this app has no bells and whistles. Most children will need support using it well, at least at first, and it is probably best used in conjunction with other materials.

10 Frame Fill: This app presents one type of problem. It shows a tens frame (two rows of five spaces). Then some of the spaces are filled with circles. Children must figure out how many more circles are needed to get to ten. Optional math problems can be presented along with each item (e.g., 7 + ? = 10). While there are no bells and whistles—in fact, there’s no sound at all—this app gives children an opportunity to practice an important skill.

Moose Math: Children navigate between five different math games. (1) A smoothie-making game has children put the correct number of different fruits into a blender, based on a menu card that has fruits with numbers next to them. At higher levels, the recipes with more than one fruit are presented as addition problem, i.e. the number of one fruit plus the number of another. (2) A connect-the-dots game has children touch numbers in order. Higher levels start with higher numbers and/or count by multiples of two, five, etc. (3) Another counting game has children add dots to animals to match the number of dots (or to match a number, in higher levels) on a second animal animal. (4) A counting bingo game has children count dots and then touch the corresponding number. Higher levels have children solve addition and subtraction problems. (5) One more type of counting game instructs children to select a certain number of objects of a particular color and/or shape. The instructions are increasingly complicated in higher levels. This app offers some good early math skills practice. I find the smoothie-making game and the dot-drawing game to be particularly useful. However, I recommend this app with some hesitation. It is not customizable at all. You cannot select the levels that you want a child to work on. The app decides for you, based on a child’s prior successes. I like to have more control over the content. Also, some of the games make big leaps in difficulty level as a child moves into new levels. For example, in the counting/bingo game, children simply have to count a small number of dots in level 1, whereas in level 2, they must solve both addition and subtraction problems with dots or numbers in the problem.

Park Math: There are seven different games that children are free to move between. (1) The “Swing and Count With Me” game counts while children watch a swing go back and forth, or make it move back and forth (2) The addition game has children solve basic addition problems. Children figure out the solution by making ducks climb to the top of the slide, joining the other ducks already up there. (3) In the “Balance the See Saw” game, children make mice jump on or off of the see saw to make the number on both sides the same. (4) The subtraction game gives children a subtraction problem, which they solve by making apples fall out of a tree. (5) A “Sorting” game has children put dogs in order, based on size, number, or shade. (6) A patterns game has children complete patterns comprised of different objects. (7) The “Feed the Hippo” game has children feed a certain number of foods to a hippo. It counts the objects children put them in front of the hippo. For each game, you can choose between three levels of difficulty. The patterns game and the ordering game get more challenging by adding slightly different types of activities (e.g., sort the dogs from light to dark). The other games get more challenging simply by having larger numbers. This is a very good app for fostering early math skills, although it may not be challenging for children who are further along with their math skills (i.e., children who recognize all of the numbers, count well, and can making patterns).

Hundred Board: Children find numbers in order, up to 100. The numbers are scattered on the right side of the screen. When the next number is touched, the child hears the number and the number moves into place on the “Hundred Board” on the left. There are different ways to play. You can have the numbers shown on the board, so that children just have to match the numbers, or you can have them find the numbers without a guide. You can also choose whether to start with 50 choices, or only 25. The game keeps track of how many correct and incorrect numbers are selected at the bottom of the screen. This is a very good simple app for supporting number recognition and number sequencing. I recommend it. There isn’t much to it, but it is quite entertaining to many children.

Line ‘Em Up: Children see a number line with only some number tiles in place. Then the numbers missing from the line are either scattered or presented one at a time (depending on the settings) and children place them in the correct spots. The number of tiles on each screen and the starting number are adjustable. This is a very simple app, but a good one for practicing number recognition and ordering. Many apps that practice ordering are much too simple. This one is more challenging, but in a way that does not overwhelm children. The biggest improvement I would suggest for this app would be to include optional sounds. Doing so would help teach children the numbers.

What’s Hiding?: Children see a number of shapes on the screen, which they are to count. Next, a rectangle covers the shapes. Then, some of the shapes slide out from under the rectangle. Children have to figure out how many shapes are still remaining under the rectangle. They select the correct answer from the numbers on the bottom of the screen. The settings can be adjusted to show starting groups of 1-5, or 1-10, or 1-20. This is a very simple but well-conceived application. It requires children to hold mental representations of what is under the rectangle, thereby fostering a more abstract understanding of number concepts. There is some room for improvement, however. First, verbal cues could help clarify what is happening at each step. Second, a subtraction problem could be shown after or while each problem is solved, thereby giving children more experience with a simple math notation and its meaning. Third, children could be offered only one or two guesses for each problem. As it is, they are rewarded for guessing randomly, which is often much quicker than working to figure out the answer.

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.

Motion Math: Hungry Guppy: This is very similar to the “Hungry Fish” app, which I have recommended in the Advanced Math section of this website. The “Hungry Guppy” app is intended to foster more basic skills. A fish with either a number or a group of dots on it (depending on which game you select) swims around the screen. Bubbles with numbers or dots come out and children have to find or make the number on the fish. They can push the bubbles together to form new numbers. For example, a child could push two bubbles with one dot each together and form a new bubble with two dots. If there are also two dots on the fish, then the fish will eat that bubble. This is a great app. Children love it and it supports math skills in a creative way. I use the levels with dots until children have a good basic understanding of addition. When they understand what it means to put two numbers together, then I introduce the levels with numbers.

Montessori Math City: Children are guided through lessons that introduce the concept of place value in numbers 1 to 1,000. They practice counting single units, groups of ten, and groups of one hundred. First, they are introduced to the concept using small yellow circles. Later, they build towers: skinny tower pieces represent ones, wider towers pieces represent tens, and the widest tower pieces represent hundreds. This app is engaging, and it does a great job of introducing a difficult concept. I recommend it. However, it’s a little difficult to use in the classroom. The quiz section is the best way to practice skills with this app—it takes quite a bit of practice to master the concept of place value. This app presents questions of all difficulty levels in the quizzes, and I think introducing tens and hundreds simultaneously is too much at once for most young children. Also, unlocking each level takes quite a bit of time. I don’t like wasting time doing that for each of my classroom iPads, and I don’t have enough classroom time to let each student do so independently.

**Somewhat Recommended**

Montessori Board: There are five different sections in this app. (1) In the “Ordering” section, children place rods in order from shortest to longest. (2) In the “Counting” section, children practice counting the squares on rods and are asked to find rods with certain numbers. (3) In the “Numbers” section, children find numbers. (4) The “Association” section has children match numbers to rods. (5) The “Addition” section has children put rods together to match a rod at the top. For example, a child might use the 4 rod and the 2 rod to match the 6 rod. This app provides some good practice with counting and number recognition. I recommend using the “Addition” section. It presents addition in a way that I think is very valuable in my classroom, and I have not seen any other apps teach addition that way. But I have a number of criticisms of this app’s design. First, children have to complete all of the most basic levels before they can reach the more difficult levels. It is a pretty tedious process. Many students do not need to be taught how to count to three, but they must sit through it if they want to open the levels that are appropriate for them. Second, children cannot count the squares on rods by touching them with a finger (which is how almost all children count things). As soon as you touch a rod, the game says the number and/or counts it for you. Third, you have to complete all of the counting levels before being introduced to the numbers themselves. I think that is a missed opportunity. It would be beneficial to introduce children to the numbers while teaching them how to count. And lastly, the rods are sometimes so close together that it is hard to point to the correct one. Even I occasionally miss.

Moofy Pattern: This app includes sequencing activities and pattern activities. In the “Sequencing” section, children drag the correct missing numbers or letters (out of three choices) up into sequences. The type of sequences included can be adjusted to include letters, small numbers, large numbers, backwards numbers, and number skipping (counting by 10s, 2s, 5s). In the pattern games, children drag one of three shapes up from the bottom to fill in the missing shape in the pattern above. Most of the shapes missing are missing somewhere in the middle of the pattern. There are three different sections with pattern games, and they vary only in their difficulty level. When children touch the numbers, letters, or shapes in a pattern, the game says what they are. There is also a “Challenge” section that has patterns of varying difficulty. This is a pretty good app for practicing with patterns. I like the way the game says the items when they are touched. When children touch the items in order and hear them spoken aloud, it often helps them figure out what is missing. The customizability of this app allows it to be continually useful as children’s skills develop (e.g., counting by twos, fives, and tens). Random guessing is discouraged. If children guess incorrectly, then the game provides the answer for them. It also says the pattern for children, whether they got it correct or not, so that they can see and hear what pattern is being repeated. I have two criticisms. First, I would like for the simplest level to include only patterns that are missing a shape at the end. It is a bit more challenging to figure out what is missing in the middle of a pattern. Second, some of the patterns included are pretty hard to recognize because they have such a short setup (e.g., step patterns, like ABBCCCDDDD). I think it would be more beneficial to have a longer pattern for children to look at.

Little Digits – Finger Counting: Children use their fingers to touch the screen. The app shows the number of fingers that are touching the screen and it says the number aloud. Addition and subtraction sections of the app ask children to solve problems. Solutions are given by touching the screen with the correct number of fingers. This app is very creative. It has the potential to be a very useful tool. However, it moves very quickly. It is stressful using it, in part because of the loud music which, frustratingly, cannot be turned off. Children do not often use this app for long. It might benefit from the inclusion of some slightly slower, more guided activities. Another criticism: it is very easy to guess the solutions to addition and subtraction problems. Sometimes children inadvertently touch the screen with the right number of fingers while they are working their way toward the solution.

A Preschool Pattern Recognition Game: Children see a pattern with pictures and one picture missing. They have to choose the correct missing picture from four options below. The settings can be adjusted so that it provides easier patterns or more difficult patterns. This is a very simple app that provides some good practice with pattern recognition. The main criticism I have concerns the way it handles incorrect answers. When a child places the wrong picture in the pattern, the screen turns red briefly, then it replaces the picture with the correct choice and quickly moves on to the next question. If children are not watching closely, they do not notice what the correct answer is, and they do not have time to figure out why that answer is the correct choice.

Measure This: Various activities are presented in staggered order. (1) Some activities have children choose groups of objects with the most or least; (2) some have them order objects from longest to shortest; (3) some have them choose objects that are largest or smallest; (4) and some have them use a moveable ruler to measure objects. This app has nice features. I particularly like the activities wherein children have to use a ruler to measure objects. However, despite being attractive and easy to use, it is not the most engaging app. Also, it could benefit from a greater degree of customizability. For example, I would like it if a setting would allow me to present my students only with measurement activities. Third, the range of measurements is rather small. All of the items fall between 3 and 8 units (perhaps centimeters, but it is unclear and it likely varies depending on your device). Better use of screen space could allow for a greater variety of lengths and heights.

Adding Apples and Subtracting Sardines: Children see a very basic calculator with numbers 1-9 and only one function. In “Adding Apples,” they touch a number and that many apples roll onto the top of the screen. Next they touch another number and that many more apples appear. A voice narrates the math concepts (e.g., “8…plus 3… equals…”). Then they can count the apples. The apples can be moved around, and when they are touched, they change colors. After that, children have to select the new total (the sum) from three options. The “Subtracting Sardines” app follows the same steps, but with sardines instead of apples. When the second numbers is selected, that many sardines change into skeletons. If more are subtracted than there were to begin with, thereby creating a negative answer, then red fish appear on the screen. These two apps are attractive, fun, and easy to use. They have to potential to help foster early understandings of addition and subtraction. However, I have a number of criticisms. First, children can only select each number once, until almost all of the numbers have been used. As a result, you cannot add 1+1, 2+2, 3+3, etc. Second, I believe it would be helpful if children could see the problems they create written out somewhere on the screen, so that they can remember what they did, and so they become more accustomed to the notation. I think that’s a missed opportunity. Third, the sardines are somewhat difficult to count. Because they’re long and skinny, it’s hard to touch the one you want to count next. Fourth, I wish there were a way to turn off negative numbers. A setting could be introduced that would prevent children from subtracting numbers that are larger than their starting number. The concept of negative numbers is too advanced for many children who would benefit from this app. They consequently become confused. Fifth, zero has been left off of the calculators, which is another missed opportunity. The concept of zero is certainly more basic, and perhaps more important, than the concept of negative numbers.

GazziliMath: There are six sections in this app. (1) A “Numerals” section has children match numbers to groups of animals and then match numbers of food baskets to groups of animals so that each animal gets one basket. (2) In the “Counting” section, children first add blocks one at a time to an igloo and then count to see how many there are. Later, they take block away one at a time and count them again. (3) The “Adding One” game shows a group of animals which children are to count. Next it adds another animal and has the children count again. Then an addition problem is seen and heard, describing what the child has just done. (4) A section called “Ten” shows a lily pad with some number of frogs on it. Then two more lily pads with frogs appear. Children must select the group of frogs that can combine with the first group to make 10 frogs. (5) The “Subtraction” game has children count balloons and then pop a certain number of them. Children hear a subtraction problem corresponding to what happened with the balloons. (6) The “A Half” section has children practice cutting picnic items in half by slicing them horizontally or diagonally. This app is cute and engaging. However, I have a number of criticisms. First, the “Ten” section addresses a much more advanced skill than any of the other sections; the younger children that this app targets likely aren’t prepared for it. Second, if you touch the frogs to count them, as many children do when they count, the app treats it like selecting an answer and responds accordingly. Dragging would work better. Third, in the “Subtraction” section, the “Purple” character sometimes swings in and pops an extra balloon, thereby adding an unnecessary level of confusion. For example, a child might start with 5 balloons, pop 1 balloon, watch “Purple” pop another balloon and then see the problem “5-2=3”. The child could be confused because nobody popped 2 balloons. To understand, he or she must quickly add 1+1 and realize that it’s the same thing as 2 and therefore 2 can be inserted in the equation. Although that’s the sort of thinking we eventually want to foster, I expect that at this level and in this context it only fosters confusion. Fourth, this app pesters you a bit. Whenever you wait a few seconds, it prompts you to answer, which can be bothersome and distracting to a child who is working toward a solution.

Splash Math Kindergarten: This app guides children through various math activities, including the following. (1) Count the objects on the screen and select the correct number. (2) Which color has more counters? (3) Make the number of counters in both boxes the same. (4) Complete sentences about whether one number is greater than, smaller than, or equal to another number. (5) Fill in numbers or symbols to create the addition or subtraction sentence heard read aloud. (6) Choose correct comparative sentences out of multiple options. (7) Drag shapes to create a picture. (8) Drag the longest object into the box. (9) What number comes next? (10) Which pictures shows what is happening in the subtraction sentence? This app covers a lot of different math skills, and its approach to many of them is unique. However, there are a few reasons I don’t recommended it highly. First, some of the activities are too drill-like. For example, there are many activities that have children put together or choose math sentences based on what they hear. These activities don’t actually give children any visual representation of what the math problems represent. Perhaps the goal is to teach math vocabulary, but I think doing so in isolation of its meaning is a missed opportunity. Second, there are some activities that require children to count groups of objects. But if children touch the objects to count them, as they often do, the app treats it as having selected that group as an answer. In these cases, it would be better to have a drag function than a simple touch function for selecting answers. Third, there are some problems that rely on reading skills that young children may not have. For example, one type of activity asks whether there are more red dots or green dots. In order to answer, children have to select the word ‘red’ or the word ‘green’. Including reading skills in math lessons can be valuable, but in this case I think it is more likely to confuse than teach.

Mermaid Waters HD: Children move through levels sequentially and are presented with a variety of math activities including the following (1) Which group has more fish? (2) Solve simple addition problems, with pictures for support (3) Match similar shapes. (4) Choose objects that are biggest/smallest or order them according to their size. (5) Fill in the missing numbers in a sequence. (6) Fill in missing animals in patterns. (7) Find the bubbles with a certain number in them. This app does a pretty good job of introducing basic math skills. It is the type of app that many children will be able to use independently. However, it moves quickly through its various activities and therefore likely does little to foster a really strong understanding of the concepts. Also, there is no way to control which activities are presented, so for most children, it is likely that some activities will be too easy and some will be too difficult. And finally, children tend to guess randomly on this app, as there is no incentive for choosing the correct answers on the first or second try.

123 Number Magic Line Matching: Children count the dots on dominoes, pictures on playing cards, or beads on a string. In one section, they drag a line to match groups to other groups with the same number. In the other section, they drag a line to match them to numbers. This is a very simple but good app for practicing counting and number recognition. However, it is not terribly exciting, so it does not tend to hold a child’s attention for very long. I recommend turning the sounds off. Otherwise, the game will say the number in each group when touched, so children will not need to count the objects. Children are somewhat encouraged to guess in this game. There is no reward for getting the correct answer on the first or second try, so I often see children trying to match groups and numbers randomly.

IXL – Math and English: This app has loads of math content, from preschool level all the way to pre-calculus. Every item is presented as question that must be read, so very few young children will be able to use this app independently. Answers are selected as words from a list of options and submitted with a ‘submit’ button. There are many different kinds of questions. If you’re looking for an app full of drill-and-kill worksheets, this is the one. But if you want something that will keep children engaged, or if you want something that uses the technology in more unique ways, then you should definitely look elsewhere. I am tempted not to recommend this app at all. (I have no use for it in my practice.) But I acknowledge that some parents and teachers may want to use it with some children.

Caboose- Learn Patterns and Sorting with Letters, Numbers, Shapes, and Colors: There two different types of activities in this app. In the “Patterns” section, children see a line of letters and numbers and they have to figure out what is next in the pattern. The types of patterns included can be customized. In the “Sorting” section, children arrange shapes, numbers, or letters in ascending or descending order or size. Which of those is included can be customized. This is a good app for helping children learn to make patterns. The sorting game is less impressive, but it provides some good practice, too. I like the way the app reads patterns aloud, so that children can hear what would come next. Hearing a pattern is one of the easiest ways a young child can figure it out. This feature can be turned off if a child no longer needs that support. The inclusion of letters and numbers in patterns is another nice feature of this app. While children are learning how to make patterns, they are also learning numbers, letter names, and letter sounds (a “Phonics” option can be turned on so that children hear the letter sounds instead of the letter names). I also like the way this app discourages random guessing. If a child guessing incorrectly, it gives the answer and then moves on. I have two criticisms, however. First, in the “Sorting” section, it is a little hard to move things around. Sometimes the objects or numbers do not move the way you want them to. Second, the app requires you to make a number of in-app purchases in order to offer different types of patterns (e.g., AABAAB patterns, AABBAABB patterns, letter patterns, number patterns). The fact that each type of pattern requires an additional purchase is frustrating as a consumer.

Kids Numbers and Math: This game includes the following activities. (1) In the “Learning Numbers” section, children simply see numbers and hear what they are. (2) In the “Count” section, children see a number of flowers. As they touch them, a voice counts with them. Then they choose the correct number from four options. (3) Children find the largest number out of two, three, or four options (as adjusted in the preferences). (4) Children find the smallest number out of two, three, or four options (as adjusted in the preferences). (5) In the “Addition” game, children see addition problems and count the apples on two trees, representing the two numbers in the problem. (6) In the “Subtraction” game, children see a subtraction problem. There is a number of apples for the starting number, and then some area eaten, leaving just the core, to represent the number being subtracted. (7) In the “Advanced Exercises” section, children solve combined addition and subtraction problems with three numbers and with no pictures for support. (8) The “Find A Match” game is a memory game with numbers. This app has some pretty good activities, and many can be made more difficult as children gain skills. I have two main criticisms. First, children tend to guess a lot with this app. They are rewarded with encouragement such as, “Perfect!” even if they guess the correct answer last. Second, the “Count” section is not a great tool. Each flower has a number associated with it, going from left to right. So if a child starts counting on the right side, it will count backwards. The voice that counts also has a slight delay. It doesn’t say the number right when touched, and for that reason, it is not very supportive for students who are struggling with one-to-one correspondence.

Wild Kratts Creature Math: Children build homes for animals and make food for them by solving math problems, which follow these two formats: “4 + ? = 6” or “5 – ? = 1.” Below each problem are items and children can add more (in addition problems) or take some away (in subtraction problems) to help them figure out the answers. This is a fun and engaging app. It has the potential to enhance a child’s math skills. But there is not a lot of variety in terms of its math content. I am also critical of one specific design aspect: the way children add items and take items away to help solve their problems. When children touch the objects, it takes one away. Young children usually count by touching objects, but when they try to do so on this app, the number of items changes. Also, the items are shown on a very small portion of the screen. I would suggest using less screen space for the Wild Kratts drawings and animations, and more screen space for the items that help children better understand math concepts.

Math With Mouse: There is an Addition section and a Subtraction section. In each, children see and hear a problem and then drag the answers up from the bottom of the screen. If children need support, they can touch the helipad in the middle of the screen and helicopters will appear. (Sometimes the game does this automatically.) In the “Addition” section, the helicopters appear from the two sides of the screen representing the two numbers in the problem. In the “Subtraction” section, helicopters appear and then some leave, representing the number being taken away. They leave behind ghost-like helicopters so that children can see how many helicopters they started with. The app also gives a few verbal instructions if a child answers wrong once or twice. As children complete rounds, they open up new levels on the map. The early levels only contain problems with very small numbers—five and smaller. This is a good app for practicing addition and subtraction. There are not a lot of bells and whistles, but I like the way it presents the concepts of addition and subtraction. It also does some good things to discourage guessing. If children choose an incorrect answer, it provides more support. However, I have a few criticisms. First, the verbal hints are phrased in a strange way. Instead of counting all of the helicopters with the child, it starts with the first number and then counts up from there. While this is a good approach for some children, many children (especially younger children) would benefit from counting the whole group. Second, this app would benefit from a bit more customizability. In order to get to the harder levels with higher numbers, children first have to complete the simpler levels, which can take quite a while. If a child is already prepared for more challenging numbers, there is no way to skip ahead. Third, when children answer correctly, they hear a little trumpet noise. At first, it is fun, but it’s loud (louder than the other game noise) and it wears on you after a little while. I wish there was an option to turn it off.

Adventures Undersea Addition: Children see a five-by-five grid. An addition problem pops up in one of the squares. Children have to find the correct answer from five choices on the right and drag it to that square. When they do, a part of a picture shows up. In other words, it is a puzzle and children have to solve math problems to get pieces. A timer can be turned on or off, and the “Advanced” option can be turned on to make larger number addition problems. This is a well designed app. Children like to play it, and it provides some pretty good practice with addition problems. But it does not provide any practice with the process of addition, just the math facts. If you use this app with younger children, I recommend giving them some small toys to count or a number line to use, so that they have something to help them learn the process of addition. My biggest criticism of this app is that children tend to guess a lot when they use it. It is easier for them to try all five options than it is to solve the addition problems. I wish the game would move on to a different problem after an incorrect answer, or perhaps provide some reward for completing the puzzle with few mistakes.

Counting Caterpillar: Children feed numbered aphids to a caterpillar in order. At any given time, there are two or sometimes three three aphids to choose from. There are different types of counting. Children can count sets of ten numbers (e.g., from 1-10, from 31-40, from 81-90). Or they can count by 2s, 5s, and 10s. This app offers some good practice with number recognition and counting, but I do not think it does a lot to develop early math skills. Because there are only two numbers to choose from, children are not challenged much and they are inclined to guess. Also, the numbered aphids fly in circles and upside down, making it more difficult for children to recognize the numbers.

Free Kindergarten Math Worksheets: There are seven games in this app. (1) In the “Add Pictures” section and the (2) “Subtract Pictures” section, children are given problems with pictures but no numbers. They select the answer from the numbers below. (3) In the “Counting” game, children see objects on the screen and find the correct number out of four options on one side. As they touch the objects, the game counts with them and marks the objects already counted with the number. In the (4) “Add Numbers” section and the (5) “Subtract Numbers” section, children are given problems with no pictures for support. They select the answers from below. (6) In the “Patterns” game, children have to select the right object to fill in the blank in the pattern. The “Skip Counting” section is just like the “Counting” section, but the items are grouped into groups of 2, 3, 4, or 5. When the children touch the groups, it counts them as groups. For example, if the groups are in threes, then it would count, “3, 6, 9, 12…” This is not an all-around great app, but it does provide some good practice. As a free app, it is worth having, at least for a couple of the activities. The “Counting” section, for example, is a good one to use with children who are still learning how to count. It is well structured to teach one-to-one correspondence and number recognition (although the counting voice sounds a little weird). However, I do not like the “Patterns” game. It has very simple patterns and very difficult patterns mixed together. There is no way to select a level of difficulty. In the “Add Pictures” section, there are no numbers to accompany the pictures, just the objects. When children count the objects to solve those problems, it starts over for each group. So counting them all together is confusing. Generally, this app would be much more useful if it were customizable. For example, I would like to be able to make the “Skip Counting” section count only by twos. Children do not typically learn how to do that at the same time that they learn how to count by fours and fives.

Numberline Frog: Children see an addition or subtraction problem at the top of the screen. A number line below with numbers 1-10 shows a frog resting on the first number in the problem above. When the correct answer to the problem is touched, the frog hops on the numbers, demonstrating how many steps had to be taken to get to the answer. This app has the potential to be a useful tool for teaching how to solve addition and subtraction problems with a number line. However, it is not the most exciting app for children, and there are some elements of the design that are less than ideal. First, nothing is narrated. Children would benefit from hearing the problems read aloud. As it is, they sometimes fail to even notice that there is a problem at the top of the screen. Second, children are inclined to guess with this app. It is much quicker and easier to guess all of the numbers than it is to figure out the answer. Third, there are words of encouragement written at the bottom of the screen, but of course very few young children are able to read those words. Consequently, I suggest that this app is best used with adult interaction. Without adult support, I do not think this app is very useful.

Math Kid: Children are given a math problem. They type the answer into a number pad and then press the ‘OK’ button. After an (adjustable) period of time some hands with appear for support. The hands will either show more fingers appearing or fingers disappearing, depending on the type of problem. The minimum and maximum numbers included can be adjusted. This is a solid, simple app. It is not terribly exciting, but it provides good practice with addition and subtraction. Other games beyond addition and subtraction have to be purchased, but the addition and subtraction functions are free, which is all that you would likely want to use with young children.

**Not Recommended**

Bugs and Numbers: This app has a number of different games in it. (1) The “Identification” game has children touch different numbers as they pass by. (2) The “Left & Right” game has children move a bug left or right to avoid obstacles. (3) “Seek and Find Counting” has children find ladybugs from underneath other objects and it counts them as they are touched. (4) The “Tap & Count” game shows children a number of bugs. When they touch them it counts the bugs aloud. Then they select the correct number out of four choices. (5) The “Color By Numbers” has children color pictures by selecting the correct color of paint, based on the numbers. (6) The “Matching Shapes” game shows different numbers or shapes on a screen. Children find the matches. (7) “Counting to 100” gives children a steady stream of numbers. They find the numbers in order, starting with 1 and going all the way up to 100. (8) In the “Tracing Numbers & Shapes” game, children follow a bug that shows them how to form letters. (9) The “Sequencing” game has children put sizes and numbers in order, smallest to largest, or biggest to smallest. (10) The “Comparisons” game has children tell whether objects are lower/higher, smaller/bigger, shorter/taller heavier/lighter hotter/colder, and more/less. (11) The “Sorting, Tallying, & Counting” game has children sort different candies into different cups. Then it shows children how to make tally marks to mark how many there are of each. (12) The “Math With 10” game shows children an addition problem. It then demonstrates the problem by having ants climbing onto a boat. (13) The “Patterns” game has children use the shape pattern at the top of the screen to guide them through a maze with shapes in it. (14) The “Addition & Subtraction” game gives children problems without any pictures for support. They choose the correct answer out of three choices. There are additional games in this app that offer practice with fractions, money, time, and measurement. This app provides practice with a variety of different skills, but I do not recommend it. I have a number of criticisms. First, there are no ways to customize this app. It would be more useful if you could tailor its content to the level of the child using it. It starts with very simple numbers and concepts and quickly moves to some pretty challenging ones. Many children are bored at first and then frustrated soon after. Second, there are very few verbal instructions offered for when children do not understand what to do. With many of the games included, it is not very clear what is expected. Third, the “Math With 10” game does not read the addition problems, and the problems are presented at the top of the screen, where they might not even be noticed. Lastly, the pattern game does not present a very natural way to learn patterns. A shape pattern is presented at the top of the screen. Children have to guide an ant through a maze with shapes in it by following the shape pattern at the top. However, children do not actually need to look at the shapes to figure out the way through the maze. They may not even notice that there is a pattern.

Wonder Bunny Math Race – Kindergarten: This simple app requires children to memorize solutions to math problems. As bunnies race down a track, a problem appears on the bottom of the screen. Children touch the approaching hurdle with the correct solution. Beyond some engaging graphics, this app does little more than a set of flash cards.

Math in Action: There four different types of activities in this app. (1) A “Sorting” activity has children sort shapes based on different characteristics such as color and shape. A guide at the top of the screen shows how the objects were sorted. Children drag the objects into squares below to sort them in the same way. (2) The “Addition” section gives children a set of directions. First they are told to pull out a number of shapes to match the group in the guide box to the right. Next they count the shapes and drag the appropriate number up. After that, they are told to add another shape or color that is some number longer than the first set. For example: “Arrange a set of green circles, 3 circles longer.” And finally, they are asked to count the second set of shapes. Later levels vary the instructions a little bit. (3) The “Subtraction” activities work much like the “Addition” activities described above, but children are told to make a second group of shapes or colors that is some number less than the first group. For example, “Arrange a set of red squares, 1 square shorter.” (4) A “Transformation” activity, children are first told to build towers of blocks that are identical to the towers on the left side. Then they are asked to do various things, such as counting all of the different colors and changing all of one color to another color. This app is attractive and engaging. But I have a number of criticisms. First, there is not very much content. None of the activities are shuffled. Each time a child clicks on a level, they are given the exact same problem, so the developer’s claims that there are 80 exercises should be taken literally. Second, the app is frustrating stubborn about arrangements being very neat. If children make a stack or row that is a little messy, they are told to “check the arrangement.” I think it is unreasonable to expect young children to be so neat, and it does not reflect whether they understand the concepts. Third, addition and subtraction are presented in a way that likely confuses children. I’ll give an example. One exercise asks children to get out 6 red circles. Then it asks them to get out a set of green circles “three circles longer.” This forces children to solve the problem 6+3. But then they have to get out 9 circles. They end up with 15 circles on the screen. Are they adding 3, or are they adding 9? Young children would benefit more from much simpler instructions such as, “add 3 more circles.” The same issue exists with the subtraction exercises.

Love to Count By Pirate Trio: There are many different games in this app. Children are led from game to game at random. Games focus on various skills, ranging from counting small groups and putting small numbers in order, to basic fractions and algebra-like problems (e.g., “How many more beads does the pirate need to make 10?”). This app provides some good practice with math. But the range of activities covers a skill set that is much too broad. If it were possible to adjust which activities to include, this app would be much more useful. As it stands, most children who use this app will encounter a large number of activities that are too simple or too difficult, and only a handful that are appropriate for their skill levels. This app also encourages guessing. The rewards are given whether the correct answer is selected first or last, and it is easier to guess each option than it is to figure out the answers.

iGet Math: Addition: Children are told to create an equation, such as “two plus three equals five,” by moving animals to the two sides of the screen. The equation at the top of the screen represents how many animals there are on the left and right sides at any time. This app is not well designed. Children must wait for long periods of time before being given problems to solve, and it’s very difficult to move the fish. Moreover, the way that it presents addition isn’t how I would choose to introduce the concept to young children.

Thinking of a Number: Children see a grid with numbers in order. They have to guess the secret number by touching it. After each guess, rectangles on the sides of the screen that are labeled “Too Low” and “Too High” are adjusted, showing the range the secret numbers falls within. The numbers outside the range also disappear from the grid. You can let the app choose the secret numbers, or you can have a friend set the secret number for each turn. This app is well conceived, but not well implemented. It has the potential to provide good practice with number comparisons, but it is confusing and difficult to use. Children tend to touch random numbers. They tend not to actually compare numbers to a beneficial degree. It would help if there were verbal cues such as, “The secret number is higher/more/lower/less than 25.” Also, setting the secret number in the “Play a Friend” mode is unnecessarily difficult and time consuming.

Counting and Matching: Children count pictures of objects on the left side of the screen. As they count the objects, a voice counts with them and numbers appear on the objects as they’re counted. Then children make lines in a key on the side of the screen to match either the number of each shape or the number of each color. There are three difficulty levels to choose from. This app provides some good practice, but it is not well-designed. Sometimes, it is difficult to get the line to match up with the numbers. You have to be very precise with your finger. There is also a constant add showing at the top of the screen. And they are random adds, not child-focused. If you do use this app, I recommend that you turn on restrictions in the iPad settings menu so that children don’t see the adds.

Addition & Subtraction for Kids: An addition or subtraction problem is shown at the top of the screen and heard aloud. Pictures of fish are shown below the problem for support. When an addition problem is presented, there are two groups of fish to count together. When a subtraction problem comes up, some of the fish are crossed off. Children choose the correct answer to the problem from three choices below. This app provides a little bit of practice with the concepts of addition and subtraction. But it has very little content, and the format is not very engaging.

Dominoes Easy Match: Children see a screen with three dominoes and three numbers. They count the dots on the dominoes and drag them up to the matching number. This app is very simple and can be useful, but it does not provide much good practice. There are always only three options to choose from, and children often just guess. The dots on the dominoes are also very small, which makes them hard to count with a finger. The children who would benefit most from this sort of basic counting skills game need plenty of room between objects they are counting, so that they can develop strong one-to-one correspondence.