The app space is overflowing with math-related apps for preschoolers and early elementary. Shapes, counting, very simple addition. There… are… so… many… Sigh. But what about older kids? They love to play with technology, too. And making learning more fun for them is just as important, if not more so, then for the youngers.

I recently found a set of 16 very straightforward but effective iPhone / iPod Touch math apps for older kids. From regular column addition to dividing fractions, these apps are great for teaching math to the middle years and for giving them plenty of practice with their basic operations.

While each app has a different purpose, they all operate in the same way, with similar options to change and the same kind of number animation. The animation is simple but useful, moving numbers around and using other indicators. Some of the changeable options include changing the screen colors, highlighting (or not) the current problem portion, changing how many numbers to add, changing the number of digits and animation speed. Most of these math problems are reward-free, with a correct answer its own reward. Two of them, though, have puzzle pieces as a reward for each correct answer, but you can turn that off in the settings. Also, several of the apps allow you to set the digits for the math problems to be solved, which can be really useful to help with homework problems. Those apps are marked with “Set.”

A very useful part of these apps is that they highlight where you are in the problem, breaking them down to each little step. It pulls sub-problems out of the larger problem, allowing you to focus just on one part at a time. This can make it much less overwhelming to those who are intimidated by math. You can turn this highlighting off and on, so the apps can grow with your learning children.

Also, if you get the wrong answer for any step in the problems, the app just sits there waiting for you to give the correct answer. There isn’t any negative reinforcement.

**Addition**

**Column Addition (Set)** – This app helps you add numbers with carrying/regrouping. These are the addition problems and method we all learned in school. For each right answer, you get a puzzle piece. Once you’ve gotten six answers correct, you complete a small animal puzzle.

**Everyday Column Addition** – It has you add each column’s numbers without carrying/regrouping, and then you regroup in the end, adding everything up.

**Partial Sums** – This app has you adding from left to right instead of starting in the ones place, which goes against everything I learned. But you get the right answer through this method, so it’s just another way of breaking down the problem steps.

**Opposite-Change Addition** – When you’re adding numbers that require carrying/regrouping, sometimes it is easier to just change the problem. This app allows you to increase one addend and decrease the other until you get a problem that is easier for you to do in your head.

**Subtraction**

**Column Subtraction (Set)** – This app teaches subtraction exactly the way I was taught in school with the same notations and the same kind of borrowing/regrouping. With each right answer, you get a puzzle piece. After 6 correct, your puzzle is completed of a picture of an animal.

**Left to Right Subtraction** – This one is unusual, dividing up some of the numbers into their parts (whole ones, whole tens, etc.), and subtracting the parts. This works if you know what is going on, so it’s good to play with this one for a while before giving it to your child.

**Trade-First Subtraction** – This is basically regular column subtraction, except you do all the borrowing you need to do before starting the subtracting. Then you subtract each column. For people who forget to borrow sometimes (like my daughter), it’s a new way to look at the problem.

**Same-Change Subtraction** – This app works just like Opposite-Change Addition. Increasing or decreasing both numbers that you need to subtract will leave you with the same answer, but a potentially easier problem to solve.

* Partial Differences Subtraction – *Of all the apps, this was the only one that confused me at all. It’s filled with problems that require borrowing/regrouping, and then it teaches you to subtract the tens place first, and then subtract the ones place. But in the ones place you end up with a negative number. Where I’m from, we learned column subtraction before we learned negative numbers, but Esa Helttula, the app author, is from Finland, so perhaps they do things differently there. It’s still solid math, but to me it was more confusing than helpful.

**Multiplication**

**Long Multiplication (Set)** – This app lets you practice the usual way of multiplying numbers. The default setting, though, is to have the carrying/regrouping digits written below the problem, but you can change this to have them above if that’s what you are familiar with (as I am).

**Lattice Multiplication** – This was one form of multiplication that I’d never done before, but the app taught me very clearly. It makes multiplying large numbers easier, and allows you to see it all visually. It’s a great option if you ever find yourself losing your place in a multiplication problem. It makes multiplying large numbers less daunting to people daunted by such things.

**Partial Products Multiplication** – This app allows you to multiply one number pair, then another, then add them. It’s similar to Long Multiplication, but it breaks the problem down into the smallest steps possible.

**Division**

**Long Division (Set)** – This is your usual long division. The app breaks it down, step by step, and lets you practice. It’s very clear, and very useful.

**Column Division** – Done slightly differently from how I was taught, this one is pretty similar to Long Division. It gives a bit more visual explanation of what is going on, crossing out numbers that have already been dealt with.

**Partial Quotients (Set)** – I could have really used this app when I was doing a lot of long division in school. It teaches you to estimate how many times a number goes into another number. It then helps you complete the long division problem. This is excellent for dividing by larger numbers that you usually just have to guess at. The app has you whittling away at the answer until you get all the parts, which you then add up. Practicing with this app will get you much better at multi-digit long division.

**Fractions**

**Fraction Math** – This app is the only one with a slightly different look. It’s more playful and colorful. If you prefer the usual look, though, you have the option to change the settings among Black, White or Happy. Compared with all the other apps, there is less guidance on this one, requiring more decision making on the part of the user. It does step you through each part, but you have to think about it as you go. Here’s an example of how it works to add fractions: You choose between adding the numerators or finding the lowest common denominator (LCD). You then have to multiply each fraction by the proper numbers to create the LCD. When you’ve got it, the app says OK and you can tap the OK to move on. Add the numerators next. Then it asks if you want to try to reduce the fraction, or leave it as is. It also gives you the option to see what the computation is in decimal form. Tap “Tip” whenever you need assistance in any part of the problem. This is a very versatile app with options to change which operators you use (+, -, x, ÷), whether to use only the same denominators, whole numbers, mixed numbers, negative numbers or big numbers (more than 12). It guides you through all the steps. Quite a useful app for learning many fraction computations.

Depending on your needs, you may not need all of these apps, but each one serves to teach and allow practice in a targeted area. The more ways you play with numbers and manipulate the methods to get to the correct answer, the more you understand how it all works. For anyone having trouble with arithmetic, these apps are an excellent choice for practicing and learning new methods. All also have small file sizes, so you should have plenty of room for them on your iDevice.

One improvement to the apps would be to have the app title somewhere on the screen. Several of them are so similar that it is easy to confuse them.

This collection of 16 math apps is done by idevbooks.com and cost $3.99 per app. To get more information, and to see the apps in action, visit the idevbooks.com website

*I’m just waiting now for some serious algebra, geometry, trigonometry and calculus apps.*

*Note: I received copies of most of these apps for review purposes.*